The Monist

THE MONIST

A QUARTERLY MAGAZINE

DEVOTED TO THE PHILOSOPHY OF SCIENCE

VOLUME XXII.

CHICAGO

THE OPEN COURT PUBLISHING COMPANY
1912

NT

l <A </V

COPYRIGHT BY

THE OPEN COURT PUBLISHING Co.
1911-1912

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CONTENTS OF VOLUME XXII.

ARTICLES AND AUTHORS.

PACK

Alexander, Hartley Burr. The Mystery of Life (Poem) 361

Andrews, W. S. and L. S. Frierson. Notes on the Construction of Magic

Squares 304

Anti-Intellectual Movement of To-day, The. By Paul Carus 397

Arreat, Lucien. Alfred Binet (Obituary) 158

Atomic Theories of Energy. By Arthur E. Bostwick 580

Attention. By Eugenio Rignano I

Automatism. By Stewart P. Foltz 91

Bergson and Religion. By James G. Townsend 392

Bergson, Kant and. By Dr. Bruno Jordan 404

Bergson, Pragmatism and Schopenhauer. By Giinther Jacoby 593

Bergson, The Philosophy of. By Bertrand Russell 321

Binet, Alfred (Obituary) . By Lucien Arreat 158

Bostwick, Arthur E. Atomic Theories of Energy 580

Bradley, The Rev. James, on the Motion of the Fixed Stars 268

Buddhism and Christianity, Postscript on. By Richard Garbe 478

Buddhism, Contributions of Christianity to. By Richard Garbe 161

Buddhist Loans to Christianity. By Albert J. Edmunds 129, 636

Buddhist Research, The Progress of. By Albert J. Edmunds 633

Capture Hypothesis of T. J. J. See. By H. Poincare 460

Capture Theory of Cosmical Evolution. By T. J. J. See 618

Carus, Paul.

The Anti-Intellectual Movement of To-day 397

Gellert's Philosophical Poetry 124

Magic Squares by Reversion 159

A New Theory of Invention 314

The Philosophy of Relativity 540

Poincare' s Cosmogonic Hypotheses 480

The Principle of Relativity 188

Chance. By Henri Poincare 31

Chatley, Herbert. Two Studies in Suggestion 82

Christian Science; Mind Cure; New Thought. By James H. Leuba 348

Christianity, Buddhist Loans to. By Albert J. Edmunds 129

Christianity, Postscript on Buddhism and. By R. Garbe 478

Christianity to Buddhism, Contributions of. By Richard Garbe 161

IV THE MONIST.

FACE

Couturat, Louis. For Logistics 481

Edmunds, Albert J. Buddhist Loans to Christianity, 129, 636 ; The Prog-
ress of Buddhist Research, 633.
Edmunds vs. Garbe: ist Century Intercourse between India and Rome.

By Wilfred H. Schoff 138

First Century Intercourse between India and Rome. By Wilfred H

Schoff 138

Fixed Stars, On the Motion of. By the Rev. James Bradley 268

Foltz, Stewart P. Automatism 91

Frierson, L. S. and W. S. Andrews. Notes on the Construction of Magic

Squares 304

Garbe, Richard. Contributions of Christianity to Buddhism, 161 ; Post-
script on Buddhism and Christianity, 478.
Garbe, Edmunds vs. : ist Century Intercourse between India and Rome.

By Wilfred H. Schoff 138

Gellert's Philosophical Poetry. By Paul Carus 124

Gilchrist, Edward. The Weird of Love and Death (Poem with Introduc-
tion) 257

India and Rome, First Century Intercourse between. By Wilfred H.

Schoff 138

Indo-Roman Relations in the First Century, A Postscript to. By Wilfred

H. Schoff 637

Invention, A New Theory of 314

Inventors I Have Met. By Ernst Mach 230

Jacoby, Gunther. Henri Bergson, Pragmatism and Schopenhauer 593

Jordan, Dr. Bruno. Kant and Bergson 404

Jourdain, Philip E. B. Henri Poincare: Obituary, 611; Maupertuis and
the Principle of Least Action, 414; Mr. Bertrand Russell's First
Work on the Principles of Mathematics, 149 ; The Principle of Least
Action (Remarks on Mach's Mechanics), 285.

Kant and Bergson. By Dr. Bruno Jordan 404

Least Action, Maupertuis and the Principle of. By Philip E. B. Jourdain. 414
Least Action, The Principle of (Mach's Mechanics). By Philip E. B.

Jourdain 285

Leuba, James H. Psychotherapic Cults: Christian Science; Mind Cure;

New Thought 348

Logics, The New. By Henri Poincare ' 243

Logisticians, The Latest Efforts of the. By Henri Poincare 524

Logistics, For. By Louis Couturat 481

Mach, Ernst. Inventors I Have Met 230

Mach's Mechanics, Remarks on. By Philip E. B. Jourdain 285

Magic Squares by Reversion. By Paul Carus 159

Magic Squares, Notes on the Construction of. By Harry Sayles 472

Magic Squares, Notes on the Construction of. By W. S. Andrews and

L. S. Frierson 304

Mathematics, Mr. Bertrand Russell's First Work on the Principles of.

By Philip E. B. Jourdain 149

Maupertuis and the Principle of Least Action. By Philip E. B. Jourdain. 414
Mystery of Life, The (Poem). By Hartley Burr Alexander 361

CONTENTS OF VOLUME XXII. V

PAGE

Planck, C. The Theory of Reversions 53

Poincare, Henri. Chance, 31; The Capture Hypothesis of T. J. J. See,
460; The Latest Efforts of the Logisticians, 524; The New Logics,

243.

Poincare, Henri : An Appreciation. By William Benjamin Smith 615

Poincare, Henri : Obituary. By Philip E. B. Jourdain 6n

Poincare's Cosmogonic Hypotheses 480

Pragmatism and Schopenhauer, Henri Bergson. By Giinther Jacoby 593

Psychotherapic Cults : Christian Science ; Mind Cure ; New Thought. By

James H. Leuba 348

Relativity, The Philosophy of. By Paul Carus 540

Relativity, The Principle of. By Paul Carus 188

Reversion, Magic Squares by. By Paul Carus 159

Reversions, The Theory of. By C. Planck 53

Rignano, Eugenic. Attention i

Rome and India, First Century Intercourse between. By Wilfred H.

Schoff 138

Russell, Bertrand. The Philosophy of Bergson 321

Russell's, Mr. Bertrand, First Work on the Principles of Mathematics. By

Philip E. B. Jourdain 149

Sayles, Harry. Notes on the Construction of Magic Squares 472

Schoff, Wilfred H. First Century Intercourse Between India and Rome

(Edmunds vs. Garbe), 138; A Postscript to Indo-Roman Relations

in the First Century, 637.

Schopenhauer, Bergson, and Pragmatism. By Giinther Jacoby 593

See, T. J. J. The Capture Theory of Cosmical Evolution 618

See, T. J. J., The Capture Hypothesis of. By H. Poincare 460

Smith, William Benjamin. Henri Poincare: An Appreciation 615

Suggestion, Two Studies in. By Herbert Chatley 82

Townsend, James G. Bergson and Religion 392

Weird of Love and Death (Poem). By Edward Gilchrist 257

BOOK REVIEWS AND NOTES.

Apelt, Dr. Otto (Tr.). Platons Dialog Theatet 320

Baensch, Otto (Tr.). Baruch de Spinoza, Ethik 320

Baumann, Julius (Ed.). Wolffsche Begriffsbestimmungen 320

De Vries, Hugo 640

Engelmeyer, P. K. von. Der Dreiakt 314

Fawcett, Edward Douglas. The Individual and Reality 317

Hegel, G. W. F. The Phenomenology of Mind 318

Heymans, G. Das kiinftige Jahrhundert der Psychologic 319

M'Giffert, Arthur Cushman. Protestant Thought Before Kant 318

Molee, Elias. Altutonish 640

Monists, A New Society of 320

Nernst, Prof. W. Traite de chimie generate 320

Pieron, Henri. L'evolution de la memoire , 319

Poincare, H. Lemons sur les hypotheses cosmogoniques 480

Rupp, Julius. Ueber Klassiker und Philosophen der Neuzeit 318

Schoff, Wilfred H. The Periplus of the Erythraean Sea 317

VI THE MONIST.

PAGE

Schubert, Johannes (Ed.). Wilhelm von Humboldts ausgewahlte philo-

sophische Schriften . 320

Spranger, Edouard (Ed.). Fichte, Schleiermacher, Steffens iiber das

Wesen der Universitat 320

Thomsen, Anton . David Hume, hans liv og hans filosofi 319

Tiele, C. P. The Religion of the Iranian Peoples 639

1

VOL. XXII. JANUARY, 1912. NO. i

THE MONIST

ATTENTION.1

AFFECTIVE CONFLICT AND UNITY OF CONSCIOUSNESS.

A LTHOUGH attention may boast of possessing more
JL~\ abundant literature than any other psychical phe-
nomenon, yet it is still far from being fully explained ; that
is to say, it has not been brought to any extent into rela-
tion and association with other psychic phenomena, espe-
cially with those to which it is most closely related. And
although attention, as Titchener rightly emphasizes, forms
the very pivot upon which all psychology hinges, yet to-day
the question as to its inmost nature is still very far from
solution. What a great loss this branch of science suffers
thereby it is easy to conceive.

The cause of this delinquency in the scientific explana-
tion of attention holds true also for all other psychic activi-
ties, namely, that the investigation of all these phenomena
has been begun at just the point where they are the most
complex and intricate instead of beginning with the sim-
plest forms. The question of attention has usually been
taken up by means of self-contemplation and at the moment
of philosophical reflection, instead of by observing, for
instance, the beast of prey, impatient to fall upon the
quarry he has espied and for which he has long lain in wait,
or the child who would fain put a white pellet in his mouth
but is in doubt whether it is a piece of candy as usual, or
may turn out to be a bitter pill as was yesterday the case.

1 Translated from the German which is to appear in the Archiv fur Psy-
cho logie.

2 THE MONIST.

The expediency of beginning the investigation with
the simplest forms involves the expediency of pursuing the
phylogenetic method and following the course of evolu-
tion back as far as possible in order to reveal the phe-
nomenon in the very moment of its first appearance. This
is the course we pursued when investigating the inmost
nature of another psychic phenomenon no less important
and fundamental, namely that of affective tendencies, and
the phylogenetic research which showed us their mnemonic
origin and nature at once threw light upon that class of
phenomena previously so obscure.2

We believe that this procedure will attain the same
success in our study of attention, which however as we
shall see is only a secondary phenomenon directly derived
from affective tendencies.

In the treatise just mentioned, "On the Mnemonic Ori-
gin and Nature of Affective Tendencies/' we have seen
that these tendencies are originally only expressions of one
and the same intrinsic tendency of the organism to pre-
serve or restore the state of its physiological equilibrium,
or to reestablish a previous physiological state which had
been determined in the past by certain environmental re-
lations. As soon as these relations are even partially re-
peated they bring about the "discharge" of the mnemonic
accumulation which this former physiological system had
left behind.

Then from these affective tendencies of direct mne-
monic origin which strive to reestablish certain environ-
mental relations as a whole, arise, according to the
known law of affective transference of the whole to the

2 E. Rignano, "Dell' origine e natura mnemonica delle tendenze affettive,"
Scientia, No. XVII, i, 1911; "Ueber die mnemonische Entstehung und die
mnemonische Natur affektiver Neigungen," Archiv^ fur die gesamte Psycho-
logic, Vol. XX, No. i, 191 1 ; "On the Mnemonic Origin and Nature of Affec-
tive Tendencies," Monist, July, 1911. This treatise later appeared also as
Appendix to the English edition of the author's work, On the Inheritance of
Acquired Characters; An Hypothesis of Heredity, Development and Assimi-
lation. Chicago, The Open Court Publishing Company, 1911.

ATTENTION. 3

part, all the other affective tendencies of indirect mne-
monic origin which strive to reestablish only very definite
parts or details of these environmental relations. Besides
the most important environmental relations usually striven
for eagerly in their original totality, the higher animals,
and especially mankind, always possess a large number of
secondary and even quite specific, environmental relations
which in this way are capable of becoming in their turn
objects of desire.

At this point we must emphasize the fact that when a
physiological system has been disturbed by altered environ-
mental conditions and reduced to a potential state in the
form of a mnemonic accumulation, it can become fully re-
activated and continue active in a stable physiological state
only when its internal and external relations are en-
tirely and exactly the same as when they induced this
physiological state. Thus the physiological system of an
infusorian which has previously lived in a certain tempera-
ture or in a salt solution of a certain proportion will gen-
erate an affective tendency toward return to its former
habitat as soon as it is removed to other environmental
relations ; and this tendency will be expressed by negative
reactions to every other change of its environmental rela-
tions which tends to remove it still further from its original
habitat, and by positive reactions to every change which
brings it nearer to its former habitat (Jennings). But the
original physiological state can not be perfectly reestab-
lished and made to persist in regular activity until the
little animal by its own movements has succeeded in getting
again into an environment identical with the former one.

Likewise the diminution of histogenetic substance in
the blood which prevents the continuance of the metabolic
state hitherto active and stable, will provoke the affective
tendency of hunger and all the acts of seeking and absorb-
ing nourishment proceeding therefrom; but the normal

4 THE MONIST.

metabolic state can not be completely reestablished until
hunger is allayed ; that is to say, until the acts carried on
for the purpose of seeking and absorbing nourishment and
the processes of digestion have endowed the blood with
the same intrinsic quality, hence the same proportion of
histologic substance, as formerly.

As with all mnemonic evocations in general, a small
part of a certain former complex environmental state is
sufficient, if not to "satisfy" the associated affective tend-
ency, at least to "discharge" it. That is why the sen-
sations in so far as they represent parts of environmental
conditions, become in a very special manner the "dis-
chargers" of affective tendencies. But in this respect there
is an essential difference between the "non-distance recep-
tors" and the "distance-receptors" which Sherrington
rightly emphasizes, so that a very significant phylogenetic
advance was made when the latter gradually developed
from the former. For the non-distance receptors (senses
with direct contact) usually permit the immediate or al-
most immediate satisfaction of the affective tendencies
which they "discharge." Frequently the sensation dis-
charging a certain affective tendency is identical with its
satisfaction. On the other hand the "distance-receptors"
usually produce that particular state in which an affective
tendency is discharged and held in suspense, and which
we are now ready to investigate.

"Between touch and assimilation," says Spencer, "there
exists in the lowest creature an intimate connection. In
many Rhizopods the tactual surface and the absorbing sur-
face are coextensive. The ameba, a speck of jelly having
no constant form, sends out in this or that direction pro-
longations of its substance. One of these meeting with
and attaching itself to some relatively fixed object, becomes
a temporary limb by which the body of the creature is
drawn forward; but if this prolongation meets with some

ATTENTION. 5

relatively small portion of organic matter it slowly ex-
pands its extremity around this, slowly contracts, and
slowly draws the nutritive morsel into the mass of the
body, which collapses around it and presently dissolves it.
That is to say, the same portion of tissue is at once arm,
hand, mouth, and intestine — shows us the tactual and ab-
sorbent function united in one/'3

Sherrington in his turn says : "Animal behavior shows
clearly that in regard to these two groups of receptors the
one subserves differention of reaction, i. e., swallowing
or rejection, of material already found and acquired, e. g.,
within the mouth. The other, the distance-receptor, smell,
initiates and subserves far-reaching complex reactions of
the animal anticipatory to swallowing, namely, all that
train of reaction which may be comprehensively termed
the quest for food. The latter foreruns and leads up to
the former. This precurrent relation of the reaction of
the distance-receptor to the non-distance receptor " (as
well as the 'conative feeling' which the distance-receptor
induces) "are typical."4

Accordingly non-distance-receptors occasion no "sus-
pended" affective tendencies, no "conative feeling," but
instead they bring about the immediate satisfaction of
affective tendencies at the moment they are discharged, or
the immediate accomplishment of the acts contributing to
their satisfaction ("final or consummatory reactions," as
Sherrington expresses it). Distance - receptors, on the
other hand, discharge the affective tendency involved and
keep it active during the entire time of expectation and
during the whole series of acts required of the animal be-
fore it can carry out the last consummatory act which is
to satisfy this affective tendency. Therefore in general

"Herbert Spencer, The Principles of Psychology, 4th ed., Vol. I, p.307.
London, Williams and Norgate.

* C. S. Sherrington, The Integratvue Action of the Nervous System, page
326 f. London, Constable, 1906.

6 THE MONIST.

only the distance-receptors but not the non-distance-recep-
tors can bring about a more or less lasting condition of un-
fulfilled desire: "If all motive impulses could be at once
followed up desire would have no place/'3

Now the question arises how can we explain the fact
that the affective tendencies discharged or evoked by the
distance-receptors, nevertheless remain "suspended' '; in
other words, how is it that although they have been evoked
and persist in this state, yet for a long time they occasion
no actual performance of any of those consummatory acts
which to be sure would not now have any result but to
which they nevertheless impel, as is shown by the incipient
performance of these acts? The beast of prey, for in-
stance, whose appetite is aroused from afar by the scent
and sight of his victim coming towards him without pre-
sentiment of danger and is whetted constantly more and
more, nevertheless does not bound at once toward the
longed-for victim, but waits motionless and trembling with
all the muscles tense, until the poor victim has come within
springing distance. What then prevents the affective tend-
ency so evoked from being at once completely discharged
in the consummatory act of springing upon the prey and
tearing it to pieces?

This can only be the counteraction of a conflicting
tendency by which the first tendency is prevented from
accomplishing its consummatory act. And the conflicting
tendency in this case can be only the combined result of all
consummatory acts which were actually performed in the
past at the first awakening of the affective tendency, but
every time without result. Accordingly we may make the
assertion that it was the "deception'' at each premature
activation of the affective tendency called forth by the dis-

8 A. Bain, The Emotions and the Will, 4th ed, p. 423. London, Long-
mans Green, 1899.

ATTENTION. 7

tance-receptor, which called into being the opposite tend-
ency by which the other is now held in suspense.

A familiar instance is Mobius's experiment with the
pike. By means of a pane of glass he divided a large glass
bowl full of water into two parts. In one side he placed
the pike and in the other he put tiny whitings which pro-
vide the pike's customary food. It now happened that
whenever the pike dived after one of the small fishes he
fell against the obstructing pane of glass. For a week he
continued to make these vain attempts. Then he gave
up entirely the pursuit of his unattainable prey and did
not change his behavior even when the obstructing pane
of glass had been taken away.

Now the constantly repeated deceptions which resulted
when the affective tendency released by a distance-receptor
produced immediately the performance of a consummatory
act which was necessarily unsuccessful, must have a very
similar effect on all animals provided with these senses.
And so it has come to pass that the very discharge effected
by the distance-receptors of any affective tendency and the
premature beginning of the movement connected with it,
now, thanks to the memory of former unsuccessful at-
tempts, provoke the antagonistic tendency, like that which
prevented the pike from falling upon its prey. And this
conflict produces that state of an affective tendency "held
in suspense" which constitutes the state of attention.

Accordingly we may say that phylogenetically atten-
tion originated with the distance-receptors, and that it con-
sists in the conflict of two affective tendencies, the second of
which is "discharged" by the first, prevents it for a time
from complete activation and hence keeps it "in suspense."

The state of attention therefore does not consist of a
single affective state but of the conflict of tendencies aris-
ing from the coexistence of two affective states. It is be-
cause this fact has been overlooked that it has not been pos-

8 THE MONIST.

sible heretofore to understand in what the specific nature
of this state of attention really consists, and so to under-
stand the real significance of the holding of an affective
tendency "in suspense" which is characteristic of attention,
nor to understand why all those movements which the first
of the two affective tendencies would itself have provoked
at once, are arrested "in the nascent state," whereas had
this affectivity alone been active they would have proceeded
directly to completion.

But aside from the case just considered of a pre-
mature performance of the consummatory act involved,
the distance-receptors under many other circumstances
arouse a second affectivity in conflict with the first which
for some time prevents the complete activation of the
former, as a consequence of the unexpected, unpleasant
results which had some time previously been associated
with it. However and whenever such an affective conflict
occurs there at once arises also a corresponding state of
attention; and vice versa, there is no state of attention
without such a conflict of tendencies. For we need only
consider carefully a few of the most significant cases, se-
lected so as to be as different as possible from one an-
other, in order at once to see in operation this conflict of
tendencies in every state of attention.

"A young chick two days old, for example," says Lloyd
Morgan, "had learned to pick out pieces of yolk from
others of white of egg. I cut little bits of orange-peel of the
same sizes as the pieces of yolk and one of these was soon
seized but at once relinquished, the chick shaking its head.
Seizing another he held it for a moment in the bill but then
dropped it and scratched at the base of his beak. That was
enough. He could not again be induced to seize a piece
of orange-peel. The obnoxious material was now removed
and pieces of yolk of egg substituted but they were left
untouched, being probably taken for orange-peel. Sub-

ATTENTION. 9

sequently he looked at the yolk with hesitation, but pres-
ently pecked doubtfully, not seizing but merely touching.
Then he pecked again, seized, and swallowed it."6

Accordingly we see here how the first act of attention of
the newly hatched chicken arose from the conflict between its
first tendency to seize the yolk of the egg and the conflicting
tendency aroused by the memory of the unpleasant expe-
rience produced by picking up the orange-peel. The "effec-
tive guidance and control of consciousness," of which Lloyd
Morgan speaks as one factor which influenced the instinc-
tive pecking of the chicken, was thus only the arousing of
a new affectivity, repugnance, that inhibited the first affec-
tivity, hunger, which of itself impelled toward the comple-
tion of the instinctive act.7

A little girl is taken out walking by a servant. The
child unexpectedly catches a glimpse of her mother on
the other side of the street and wishes to run over to her
at once. But the maid warns her with a cry, "Look out
for the carriage!" and the little one stops. The carriage
has hardly passed and she has almost taken a step ahead
when another approaching vehicle forces her to give way
again. The conflict of the two tendencies of hope and fear,
kept alive in the child by the sight of her mother and the
repeated passing of vehicles, is shown very clearly by the
direction of her steps first forward and then backward.
It is faithfully reflected in the expression of the small
bright eyes which shine with anticipation and joy as soon
as they are turned upon her mother and the child takes a
step nearer to her, but at once look anxious and confused
when they observe one of the heavy wagons of which
there seems to be no end. Finally, however, the street-
crossing is unobstructed. The state of fear and also the
"state of attention," has entirely disappeared so that the

' Lloyd Morgan, Habit and Instinct, p. 40 f. New York, Arnold, 1896.
7 Lloyd Morgan, op. cit., pp. 129-131, 135, 139 f.

IO THE MONIST.

little girl may at last satisfy her wish and throw herself
into her mother's arms.

The conflict of tendencies is likewise exhibited with
great distinctness in certain typical states of attention
where it is expressed in the exceedingly subtle choices be-
tween almost imperceptible modalities of a certain act.

A billiard player, for instance, who has already directed
his cue at the ball, wishes first of all to make a successful
stroke. He is ready to make the stroke but the extreme
tension of the muscles in his arm causes him to fear that
the stroke may turn out to be too strong, as it did shortly
before. In consequence of this conflicting affectivity his
muscles become somewhat lax. Nevertheless the weaker
tension he now feels reawakens in him the memory of an
earlier unsuccessful stroke when the movement of the ball
had not been swift enough, and now he finds himself per-
plexed by the opposite fear lest the stroke may be too weak.
By the swings of his arm, now longer and now shorter,
which precede the stroke and bring the point of the cue
nearer to the ball or farther from it, a spectator can discern
the rapid alternation of conflicting affectivities which dis-
charge each other and exaggerate or moderate each other
in order finally to bring about the result of giving to the
ball exactly the necessary force.

The same is true when a person who is writing attempts
to remove with his finger a tiny hair from his steel pen.
This rarely succeeds at the first attempt because the fear
of soiling his finger-tips causes him to press them together
before they are near enough to the point of the pen and
the hair. The first failure gives rise to care lest the second
attempt may also fail, and this opposite fear partly sup-
presses and moderates the fear of soiling the fingers, so
that the wish to remove the hair by this time lends to the
arm and fingers exactly the degree of muscular contraction

ATTENTION. II

necessary to get hold of the extending end of the hair with-
out touching the inky pen.

From this conflict of tendencies, inevitably occurring
as soon as we attempt to perform an act "carefully,"
arises the well-known fact that attention, when directed
to actions which by long practice have become mechanical,
makes their execution less rapid and perfect than if they
had taken place quite automatically.

"An automatic connection of contents or movements
has nothing to gain from the intervention of attention, —
nay suffers a very positive loss in accuracy and rapidity
of realization, if the attention be directed upon it."8

Thus the recitation of a poem which has been learned so
well by heart that it can be repeated mechanically becomes
uncertain and hesitating when the speaker gives it his
whole attention. And a person who writes his name with
the greatest facility when he gives no thought to it is pretty
sure to do it disconnectedly and without ease as soon as
some one asks him for his autograph. For in this case
every stroke of the pen needs a short preparation and re-
quires a certain application of the will to begin and com-
plete it, whereas the transference from one stroke to an-
other becomes studied and awkward instead of easy and
running as usual.9

Nevertheless there are individual cases, even where
the attention is greatly aroused, in which the conflict of
tendencies appears less distinct. For instance in Sardou's
drama, "Tosca," we have the scene where Tosca's lover
is tortured. It arouses the keenest sympathy and attention
of all the spectators. Where is there any conflict of ten-
dencies in this case? And yet we shall find it if we reflect
a little. On the one hand there is the tendency, according

•O. Kiilpe, "The Problem of Attention," Monist, XIII, p. 61. Chicago,
Oct. 1902.

"H. Maudsley, The Physiology of Mind, p. 520 f. London, Macmillan,
1876.— The Pathology of Mind, p. 143. London, Macmillan, 1895.

12 THE MONIST.

to the character of the spectator, either to fall upon the
crafty Scarpia and slay him, or to throw oneself at his
feet and with Tosca beg his mercy for her lover; or one
might hasten to the aid of the unfortunate man and lib-
erate him after driving away or killing the agents of the
torturer. On the other hand the cultured man has ac-
quired a tendency by education or custom to do nothing
which conventionality does not permit, and not to make
himself ridiculous by acts which would be the more ridic-
ulous since every one knows that he is not beholding a real-
ity but a mere invention. And that this is really the case is
proved by the village theaters where the actor who plays
the part of the tyrant is often hissed by the public, and some-
times even becomes the target of more or less harmless mis-
siles thrown by the more unsophisticated spectators. The
author once attended such a spectacle. Some conspirators
were in hiding behind a curtain, waiting to kill the king,
who by this time had won the favor of the public by his
generosity and fearlessness. He had hardly appeared when
a voice was heard to call out at the first movement of the
curtain, "Look out, they are going to kill you !" The entire
audience laughed uproariously, and the simple spectator
was overcome with confusion. He will doubtless succeed
another time in repressing his magnanimous outburst,
thanks to the conflicting tendency not to make himself
again the object of derision.

Attention which is aroused by novelty is likewise the
result of a conflict of tendencies arising from the fact that
just because the object is new, it has not yet been "affec-
tively classified," and therefore arouses both hope and
fear at the same time.

If the space at our disposal permitted, we could easily
show that any "classification" whatever is based either di-
rectly or indirectly upon ah affective tendency. The prin-
ciple upon which it rests consists originally in the fact that

ATTENTION. 13

no sensation or perception of the distance-receptor has any
value for the organism except as a symbol of a possible
environmental state, near or remote, to be striven after or
avoided. As long as this symbol has not been placed in
either category, the conflicting affectivities of hope and
fear oppose each other and hold each other in suspense.
This opposition is seen distinctly, for instance, in a child
who is undecided whether or not he should drink the tea
offered him by his mother and which this time has an un-
usual color, because he is not sure whether it is a sweet or
bitter draught; or in a beast of prey that sees a strange
looking animal and is in doubt whether it is a dangerous
enemy or perhaps a suitable quarry and therefore makes
its muscles tense, ready at the same time for either attack
or flight.

Curiosity is only one of the least forms of this conflict
of tendencies or of this particular state of attention pro-
duced by novelty. "The craving for knowledge in its in-
stinctive form is called curiosity. It exists in all degrees,
from that of the animal which touches or smells an un-
known object, to the all-examining, all-embracing scrutiny
of a Goethe." "Curiosity consists of two questions ex-
pressed or implied: What is it? What use is it?. . . .The
dog brought face to face with an unknown object, looks
at it, smells it, approaches, withdraws, ventures to touch
it, returns, and begins again ; he is pursuing this investiga-
tion after his own fashion ; he is solving a double problem
of nature and utility."10

On the other hand the "not new" — and this also may be
any specific object when we see it for the first time — com-
prises everything we know how to classify in one of our
various affective categories. It either brings about imme-
diately the evocation and satisfaction of the affectivity con-

10 Th. Ribot, Psychologie des sentiments, pp. 369, 371. Paris : Alcan, 1906.
Second English edition, pp. 368, 370. London, Walter Scott, 1911.

14 THE MONIST.

cerned, like the little waterfall in the mountain which awak-
ens the desire to drink from it; or it evokes the affective
tendency but holds it in suspense for fear lest its immediate
complete satisfaction might involve some evil consequences
as we have previously seen ; or finally it may at that moment
be altogether unable to evoke any tendency, like the sight
or odor of a familiar dish when we have had enough. In
this case the affective activity is reduced to a minimum,
the state of attention entirely ceases, and we experience
monotony or tedium. If this state of minimum affective
activity is reduced to zero, we have the condition of sleep.
"Sleep," as Bergson very truly says, "means to disinterest
oneself (se desinteresser) . We sleep in direct proportion
to our disinterestedness."3

Finally there is only a very slight distinction between
"curiosity" and the state of attention of the investigator.
The investigator observes a certain object or a certain
phenomenon in order to convince himself whether this ob-
ject or this phenomenon really proves to possess certain
properties whose presence has been asserted by others, or
which he himself thought he noticed at the first glance, or
which in his opinion should exist. The presence or absence
of these properties is of exceedingly great value to the
observer as is apparent from the fact that he applies him-
self with such great care to observe them, for they may
for instance confirm certain preconceived theories or rep-
resent a highly important scientific discovery. Hence on
the one hand he cherishes the ardent hope that the sup-
posed properties would really be found to exist. On the
other hand he is restrained from prematurely making
known a discovery whose accuracy might later be con-
tested by other inquirers to the great injury of his own
scientific prestige. Just think for instance with what great

u H. Bergson, "Le reve," Bulletin de I'Institut Psychologique International,
p. 118. Paris, Alcan, May 1900.

ATTENTION. 15

attention — that is to say, with what great care lest he
may have been a victim of an optical illusion — Schiapa-
relli must have carried on his ovservations before he de-
cided to make known his discovery of the canals of Mars.
Here too this hope and this care furnish the conflict of two
affectivities without which here as elsewhere no actual
state of attention would or could be present.

As we have by this time come to recognize the inmost
nature of the affective conflict which, as appears from the
few examples here adduced, is characteristic of every state
of attention, so all other properties which always accom-
pany this state prove at the same time to be so many simple
and direct consequences of its nature.

Especially are we able to perceive at once the uncon-
vincing character of Ribot's definition of attention as the
state of "relative monoideism." We might if necessary call
it a state of "monoaffectivity held in suspense," but as we
have seen, it is still better to define it as a state of "double
conflicting affectivity."12

Ribot's motor or peripheral theory proves to be equally
erroneous : "Are the movements of the face, the body and
the limbs, and the respiratory modifications that accompany
attention, simply effects, outward marks as is usually sup-
posed? Or are they, on the contrary, the necessary con-
ditions, the consistent elements, the indispensable factors
of attention? Without hesitation we accept the second
thesis."13

On the other hand the so-called theories of "central
origin" seem to be perfectly correct.14 Attention is indeed
a "central," psychological phenomenon ; for the awakening
of the primary or active affectivity and the counter-awak-

12 See Th. Ribpt, Psychologie de I'attention, pp. 6-8, 6th edition. Paris
Alcan, 1902. English edition, p. 10.

13 Ribot, op. cit., p. 32. English edition, p. 25.

14 See, e. g., J. Sully, "The Psycho- Physical Process in Attention," Brain,
July 1890, especially pp. 155-157. London, Macmillan.— Vaschide and Meu-
nier, La Psychologie de I'attention, pp. 196 f. Paris, Blond ,1910.

l6 THE MONIST.

ening of the secondary affectivity which holds the other
in suspense, are phenomena of this nature. Attention
therefore is first of all an essentially affective phenomenon
and only indirectly and in a subordinate manner does it
become a motor phenomenon by the fact that the awakening
of any affectivity whatever always produces motor and
peripheral phenomena which are therefore only accom-
panying or derived phenomena.

Ribot's error comes from the fact that he has not suc-
ceeded in correctly comprehending the nature of affective
tendencies, for he sees very well that "attention always
depends upon affective states," but he adds soon after:
"How are we to represent to ourselves these tendencies?
The only positive idea that we can get of them is to con-
sider them as movements (or as inhibitions of movements),
be they real or nascent/'13

Accordingly for this inquirer the motor elements would
by themselves constitute the entire essence of affective
tendencies. But it is the affective tendencies which are the
foundation of the motor elements, and the reverse is false.

As we have seen in our frequently cited treatise "On
the Mnemonic Origin and Nature of Affective Tenden-
cies," an affective tendency is only a gravitation, so to
speak, toward that environment or those environmental
relations which permit the reactivation of the mnemonic
accumulation constituting this affective tendency. But of
itself, it does not produce any preferential impulse toward
one rather than toward another series of movements. For
even if these movements were such as could eventually
bring the organism back into the desired environmental
conditions, yet in themselves they have nothing to do with
the ultimate satisfaction of this affective tendency. It is
only when one series of movements succeeds in bringing
the organism back to the requisite environmental condi-

15 Ribot, Psychology of Attention, pp. 166, 172. English edition, pp. 112, 116.

ATTENTION. 17

tions sooner or better than the others and only from this
moment, that it becomes preferred to the others. Only
from this moment will the awakening of the affective ten-
dency give rise to definite motor elements.

But before this occurs, that is to say before the affective
tendency has found preferable any one of the movements
capable of leading to the desired end, the affective tendency
towards that end will already exist. The very fact of this
affective choice proves that in point of time the choosing
factor precedes the element chosen, whence it follows that
there can be an affective tendency even in the absence of
any motor element. For instance a new and unusual in-
disposition which may attack us arouses the affective tend-
ency to be freed from it, but this does not and cannot
initiate any motion whatever.

Hence if affective tendencies and motor elements are
two different things, and if the latter are based upon the
former but not the reverse, then this is also true with
regard to attention for which the motor elements are not
an indispensable condition but merely quite secondary phe-
nomena.

Since every conflict of affective tendencies is expressed
in a conflict of the motor elements induced by them, so a
clear explanation is afforded even with the "central origin"
for the fact that "muscular tension/' "motor innervation,"
"tonic contraction," and the "elevation of the entire psychic
life," characterize every state of attention, as all have ob-
served.16

Affective choice determines not only the particular
movements of locomotion, of seizing, etc., which make for
the desired object, but also the adjustment of the sense-
organs, itself a musculo-motor phenomenon on which de-
pends the more or less successful result of the movements,

16 Maudsley, The Physiology of Mind, p. 313.— Ch. Fere, "Physiologic de
1'attention," Revue philosophique, Oct. 1800, pp. 401, 404. — K. B. R. Aars, 'Ttfotes
sur I'attention," Annee psychologique, VIII, p. 216. Paris, Schleicher, 1902.

l8 THE MONIST.

of whatever kind they are, and in which therefore both of
the two conflicting affectivities cooperate. Now for in-
stance when we are surprised by a sudden noise and direct
our glance at once to the distant object from which it seems
to come, the state of attention is alert during the whole
interval preceding the moment in which the eyes have be-
come adjusted to the new distance, which requires a certain
length of time when the object- is far away. Thus atten-
tion is awakened (here too in conformity with the theory
of central origin) before and not after the adjustment of
the organ concerned.17

Since on the other hand the peripheral sensory re-
lations remain the same, the attention may be directed
now to some and now to other sense-perceptions, just as
when, confined within our room, we give more heed to
certain noises in the street than to others which come from
the same direction; for instance, to the hoof -beat of the
horses belonging to an equipage that stops before our
door, in order to determine by the sound which of our
friends has come to call; or to the roll of the wheels in
order to find out whether the friend who has come to take
us out driving is riding in a closed or open carriage. Atten-
tion may even be directed to certain properties of a sense-
impression, for instance to the strength or pitch of a note
of music, or to certain other characteristics such as its
timbre. No other examples could demonstrate better than
these how entirely attention is independent of the ad-
justment of the sense, as well as in general of every
other "peripheral factor."18

From this "central origin" of attention which has been
so fully established, and from the inmost nature of the
opposition between two mutually conflicting affectivities
as above discussed, a conclusion of the utmost importance

"See W. B. Pillsbury, Attention, p. 13. London, Swan Sonnenschein,
1908.

18 O. Kiilpe, loc. cit., p. 50.

ATTENTION. IQ

may be drawn, namely that the object of attention is ob-
served simultaneously from two quite distinct points of
view. Thus a large number of properties and character-
istics, of advantages and disadvantages are perceived, ob-
served, recalled and emphasized, which would by no means
be the case if only a single affectivity were operative.

Wundt's well-known metaphorical definition of the "ap-
perception" produced by attention as consisting in the tran-
sition of the image "from the internal visual field to the
internal visual point of consciousness," accordingly, might
better be replaced by that of an internal double reflector
illuminating the object or the image from several sides at
the same time.19

That is why attention prevents the mnemonic addition
of sensation-evocations, which the affectivity adds to the
rough elementary sensation at the moment it is aroused,
from distorting the perception produced by this mnemonic
contribution into an illusion or hallucination, which on the
contrary is always the case when the affectivity thus
aroused remains alone.

Sudden and intense fear, for instance, makes any state
of attention quite impossible and may give rise — as in the
classical case of the wanderer walking at night through
a dense forest — to those characteristic hallucinations cited
and described in all text-books of psychology and psycho-
pathology. On the other hand that man is "cold-blooded"
who does not flee at the sudden rustling of leaves which
arouses in him at the first moment the vision of some hid-
den robber or dangerous beast behind the trees, but who,
restrained by his repugnance to so cowardly an action,
looks around "with attention" to see whether there really
is a living creature there, and what sort of a one it is, or
whether indeed it was not the wind that made the noise.

19 W. Wundt, Grundziige der physiologischen Psychologic, 5th ed., VoL
HI, p. 333. Leipsic, Engelmann, 1903.— Ostwald, Vorlesungen iiber Natur-
philosophic, 3d ed., pp. 400, 403. Leipsic, Veit, 1905.

2O THE MONIST.

Likewise in a state of passion any attention to all
that is connected with this passion becomes impossible and
the passionate man is therefore exposed to all the auto-
suggestions and hallucinations of an Othello because of the
very singleness of the control by the hypertrophic affective
tendency characteristic of this state. In monomaniacs also
as well as in those suffering from a chronic persecution-
mania and similar psychical diseases, the thing lacking is
the counter-affectivity which would tend to make them
fear that they were making a mistake. They are mono-
affective in the proper sense of the word, therefore in-
capable likewise of a real and proper state of attention.

The absence of any counter-affectivity produces in all
these cases a total absence of "opposing inhibitors," as
Taine would say, which could inhibit the auto-suggestions
and hallucinations produced by the one existing affectivity,
and permit the latter to reign unhindered and exclusively.
On the other hand, great attention always protects from
suggestion practised by others just because the opposite
affectivity, the fear of being deceived, becomes very strong,
as is proved for instance by Binet's experiments on the
susceptibility of school children to suggestion.20

* * *

Now as we pass to the relations existing between atten-
tion and consciousness we must first briefly mention our
theory with regard to the conditions which determine the
consciousness and those which determine the unconscious-
ness of the different psychic states.21

In the above mentioned treatise we have come to the
conclusion that a given psychic state is neither conscious
nor unconscious in itself, but that it seems to possess either

80 H. Taine, De Intelligence, 8th ed., Vol. I, pp. 95 ff. Paris, Hachette,
1897.— A. Binet, La suggestibilite, pp. 166, 177 f., 186, 191, 196, 200 etc. Paris,
Schleicher, 1900.

81 E. Rignano, "Qu'est-ce que la conscience?" Scientictj 1907, Vol. II, No.
IV, 4.

ATTENTION. 21

one or the other of these properties only when, having been
previously present, it is now referred to another psychic
state at present existing. And the necessary and sufficient
condition permitting a complex past psychic state to pre-
sent itself again as "conscious" in relation to a complex
present psychic state is that the affective portion of the mne-
monic evocation of the former correspond at least in part
with the coexisting affective portion of the latter and there-
fore coalesce with it.

Since, as we have seen in our frequently cited treatise,
the possession of a "diffuse seat" is characteristic of affec-
tive tendencies — which in this respect are so different from
sensations and their images whose seat is localized at a
single point or center and which therefore may exist and
be active simultaneously in great numbers in one and the
same brain — it is difficult even for only two affective tend-
encies to have their seats in localities which shall not coin-
cide more or less, so that when these tendencies strive to
be operative at the same time, they either conflict with
each other, or hold each other in suspense, or partially
coalesce.

If the discharge of one does not depend on the dis-
charge of the other, and if the respective nervous activities
in the part of their seats common to both differ specifically
from each other, then the activation of one tendency will
of itself imply the exclusion of the other and vice versa. If
the discharge of the one is caused by the discharge of the
other and the two tendencies are antagonistic, we will then
have the state in which the primary affective tendency is
held in suspense by the secondary; which condition, as we
have seen above, is characteristic of the state of attention.
If on the other hand the respective nervous activities in
that portion of their seats common to both are specifically
similar, then their blending together will make the complex
psychic state to which one of the tendencies belongs "con-

22 THE MONIST.

scious" with reference to the psychic state to which the
other belongs.

Finally a fourth case will occur but much more rarely
for reasons given above, in which the two affective tend-
encies have no part of their seats in common, and accord-
ingly both can be present and operative at the same time
without hindering each other or bearing any relation what-
ever to one another. This case comprises all the phenom-
ena of the so-called double personality. These phenomena
nevertheless are by no means always of a pathological
character, like the typical ones studied especially by Janet,
but they may appear also in normal persons in so-called
instances of absent-mindedness. Such was the case, for
instance, when we were climbing down into the valley
from Ca' di Janzo by a very steep mule path. Leaping from
one stone to another constantly demanded our whole at-
tention in order to measure exactly the distance of the
leap and lest a foot should slip or dislodge a stone. Yet
nevertheless the descent sometimes proceeded "uncon-
sciously" with reference to some other very different affec-
tivity which produced at the same time quite another train
of thought.22

In the first case the exclusion of all other tendencies
with independent discharge as soon as one of them becomes
active — an exclusion which persists throughout the whole
time during which the first of the two affective tendencies
of the state of attention remains "held in suspense" — forms
the so-called "unity of consciousness."

In other words, the impossibility for more than one pri-
mary affective tendency to be active at any one time re-
sults in the impossibility of giving heed to more than one
object at one time: "A plurality of stimulations of the
nerves may co-exist, but they affect the consciousness only

28 P. Janet, L'automatisme psychologique, pp. 263 ft. Paris, Alcan, 1907...
Taine, De I' intelligence, pp. 16 ff.— Rignano, Qu'est-ce que la conscience? pp.
11-13-

ATTENTION. 23

by turns, or one at a time. The reason is that the bodily
organs are collectively engaged with each distinct con-
scious state, and they cannot be doing two things at the
same instant/'23

Consequently attention ordinarily is never divided or
dispersed. If it is greatly roused it will continue to be di-
rected toward any given objects for a while and hence can
not be directed to any others during this entire period.
If it is less aroused it passes from one object to another
in quick succession and accordingly seems to be divided
among many objects at the same time; but in reality even
in this case it is directed at each moment to one object
only, that is, to the one which corresponds to the momen-
tary affective tendency. Accordingly the slpeaker who
passes judgment upon his own speech, the actor who has
command over himself, the chess player who plays several
games at one time, Julius Csesar who dictated several let-
ters at once, do not prove the simultaneous presence of
several states of attention, but rather their rapid succession
and the alternating predominance of first one and then an-
other.24

For this reason the attention directed by self-contempla-
tion upon any affective state brings about the end and
disappearance of that state. It is impossible to direct
one's attention upon an affectivity. If .the attempt is made
that particular mood ceases at once, and we are turned
aside by a compelling sensation or idea which we have not
the slightest desire to observe.25 For the attention which
is directed upon an affectivity within ourselves is a newly
originated affectivity, namely the one that impels us to

23 Bain, The Emotions and the Will, p. 5.

84 E. Meumann, Intelligens und Wille, pp. 22 ff. Leipsic, Quelle & Meyer,
1908.

88 E. B. Titchener, The Psychology of Feeling and Attention, p. 69. New
York, Macmillan, 1908.

24 THE MONIST.

this observation and investigation, and therefore it dis-
places the other we wished to observe.

Since the primary affective tendency of the state of
attention excludes every other affectivity independently
evoked and in this way protects the unity of our conscious-
ness, it makes it possible at the same time for every past
state of attention involved to appear conscious to us if we
now think back to it and to the object which at that time
constituted the end desired. For this memory will now be
recalled to the same object by a more or less similar affec-
tive tendency which therefore will partially blend with the
recollection of the former.

Every state of attention accordingly contains all ele-
ments within itself in order later to seem to us to be con-
scious; but not all past psychic states which now appear
conscious were states of attention, as Kohn maintains to
whom the state of attention and the conscious state are
the same thing. For an affectivity which becomes at
once completely active and therefore does not give rise
to any state of attention — like a hurried flight caused
by sudden terror — is nevertheless able to make the com-
plex psychic state involved appear a conscious one.26 In
other words, the state of attention is a sufficient but not
a necessary condition of consciousness. The only condi-
tion which is at the same time necessary and sufficient is
the presence of some affective tendency, no matter whether
it be in the state of suspense or of full activation.

The acts which have become automatic, for instance
those which originated through affective choice as con-
scious movements, and which later by means of attention
were perfected under the affective conflict of the tendencies
to perform the act but at the same time to avoid one by
one its many imperfections, are finally consummated after

26 See H. E. Kohn, Zur Theorie der Aufmerksamkeit, pp. 19, 27. Halle,
Niemeyer, 1895.

ATTENTION. 25

frequent repetition — according to the mnemonic law that
the part gradually becomes independent of the whole —
without requiring any "impulsion" or any kind of affec-
tive aid whatever, either primarily in the execution or
secondarily by way of improvement. For this reason we
are accustomed to say that rendering acts automatic lib-
erates the attention so that it may be directed to other
objects.27

And just because acts which have become automatic
do not require attention on our part and take place without
the assistance of any affective element, they always seem
to us to be unconscious. Consciousness, as Maudsley
says, directs the process of adaptation, the efforts to be-
come expert in adjusting the various means to their proper
ends and the successive stages of organization; it disap-
pears as soon as the skill has been thoroughly attained.28

"Habit," says James, "diminishes the conscious atten-
tion with which our acts are performed. One may state
this abstractly thus: If an act require for its execution a
chain of successive nervous events, then in the first per-
formances of the action the conscious will must choose
each of these events from a number of wrong alternatives
that tend to present themselves ; for consciousness is always
and chiefly a selective agency. But habit soon brings it
about that each event calls up its own appropriate successor
without any alternative offering itself and without any
reference to the conscious will, until at last the whole chain
rattles itself off as soon as the first event occurs, just as
if this and the rest of the chain were fused into a con-
tinuous stream."29

Just as an act that has become automatic represents a
nervous activity which in the absence of any accompanying

"Meumann, Intelligens und Wille, p. 23.
88 Maudsley, The Pathology of Mind, p. 9.

29 Win. James, The Principles of Psychology, Vol. I, pp. 114, 139. London,
Macmillan, 1901. The same, briefer course, p. 139. New York, Holt, 1893.

26 THE MONIST.

affective tendency remains unconscious, so will every stim-
ulation of our senses remain unconscious when it reaches
its sensory seat if it can not arouse any affectivity in
us. On the other hand every stimulation of our senses
which succeeds in discharging any one of the many affec-
tive tendencies potentially present in the brain, will after-
wards appear conscious to us; and this may also be ex-
pressed by saying that the "stimulation has succeeded in
taking possession of the sensor him."30 Whence it follows
that if all objective and sensitive peripheral relations re-
main the same, it will depend on whether our attention is
or is not directed upon something else and on the degree
of strength and of opposition of the primary affectivity
involved — for thence is derived the power to exclude every
other affective tendency which differs from it — whether
certain stimuli remain quite unobserved or whether they
will appear to us as conscious sensations.31

Says James: "A million things in the outside world
are present to my senses but do not enter my conscious-
ness. Why? Because they do not interest me. Only that
which arouses my attention makes up my experience. Only
the objects to which I give heed constitute my understand-
ing. Without selective interest experience is a veritable
chaos. Interest first gives color and tone to the image,
light and shadow, background and foreground, in a word
a distinct perspective."32

The primary affectivity of a state of averted attention
may be so strong that it can prevent even the most intense
irritations, which at other times would seem altogether
painful and arouse within us the most strenuous effort to
remove them, from reaching our consciousness. Classical,

80 G. E. Miiller, Zur Theorie dcr sinnlichen Aufmerksamkeit, pp. 77. Leip-
sic, Edelmann.

8X Miiller, op. cit.} p. I. — Kiilpe, op. cit., p. 40 f. — Ostwald, Vorlesungen
ilber Natur philosophic, pp. 400 ff.

83 James, op. cit., Vol. I, p. 402.

ATTENTION. 27

for instance, is the case of the Christian martyr whose en-
tranced attention was to such a degree absorbed by the
beatific visions presented to his eyes, that it prevented him
from feeling the pain of the horrible tortures to which his
body was subjected. No less significant is the case of
Robert Hall, some of whose "most eloquent discourses
were poured forth whilst he was suffering under a bodily
disorder which caused him to roll in agony on the floor
when he descended from the pulpit; yet he was entirely
unconscious of the irritation of his nerves by the calculus
which shot forth its jagged points through the whole sub-
stance of his kidney, so long as his soul continued to be
'possessed' by the great subjects upon which a powerful
effort of his will originally fixed it."33

However, a large number of facts go to prove that those
very irritations which do not discharge any affectivity or
are not capable of arousing our attention and therefore
remain unconscious, nevertheless likewise succeed in reach-
ing their sensory seats. "The fact that we sometimes be-
come conscious of many sensuous impressions, such as
for instance the stroke of a bell, after the stimulus has
made itself felt in our sense-organ, tends to show that the
excitation reaches its destination rightly enough, but that
the sensory center happens at the moment to be in a state
not suited for the reception of the afferent stimulus."34

The conflict also between the different states of atten-
tion which the varied stimuli from the outside world would
strive to arouse — owing to the fact that only one single
primary affective tendency can ever be operative at any
one moment — indicates that, whatever the relation of the
stimulations to consciousness may be, they always reach
their habitual psychical center; for otherwise they could
not all tend to discharge their respective affectivities.

88 W. P. Carpenter, Principles of Mental Physiology, 7th ed., p. 138. London,
Kegan Paul, 1896.

84 Miiller, Zur Theorie der sinnl. Aufm., p. 105.

28 THE MONIST.

"When one of the various stimuli succeeds in the struggle to
obtain possession of consciousness we say that we are atten-
tive to it according to the intensity of the corresponding
process of consciousness." "But we can not maintain that
excitations which do not enter our consciousness because
of averted attention do not enter at all into the organ of
consciousness, the cortex of the brain."35

It often happens in my own case, for instance, that I
am reading a newspaper while the other members of the
family are chatting together in the same room or perhaps
while one of them reads aloud from a book or a different
paper. Sometimes I do not succeed in limiting my atten-
tion to what I myself am reading because my interest is
aroused by what I hear read aloud. In other cases, how-
ever, I succeed very well, and then I no longer hear the
words of those in the room. Nevertheless one word pro-
nounced by the reader in exactly the same tone as all the
other words — for he is reading right along in the same
monotonous voice — suddenly draws me completely away
from what I am reading and turns my attention to what
he is reading aloud. Thus my attention vibrates con-
stantly back and forth between what I am reading and
what I am hearing read. The fact of this conflict between
the two states of attention accordingly proves most posi-
tively, I repeat, that the irritations produced by the spoken
words of another reach their sensory center, their sensory
basis, in me even in moments when I am not aware of them ;
otherwise none of them would be able to rivet my interest
or attention.

The same is obviously true for all so-called states of
absentmindedness which at bottom, as we have already
seen, are only the first physiological indications of that
double state of one's own personality which hitherto has

MKohn, Zur Theorie der Aufm., p. 19; and Sigmund Exner, Entwurf su
einer physiologischen Erkldrung der psychischen Erscheinungen. Part I, p.
72. Vienna and Leipsic, Deuticke, 1894.

ATTENTION. 29

been investigated almost exclusively in its pathological
forms. As an example of this we mentioned in our essay
on consciousness the locking of a drawer while attention
was directed elsewhere. This showed that all stimulations
of sight proceeding from the key-hole and the key placed
in it reached their goal although they remained entirely
unconscious. Every one has the experience of walking
absentmindedly through the streets and yet without run-
ning into people, vehicles, or any other obstructing objects
on the way. Our previously mentioned "unconscious"
descent from the Ca' di Janzo proves how perfectly in
every respect the perception of all the difficulties of the way
must have been — the stones, their form, their position, their
state of equilibrium — if I were to succeed in leaping from
one stone to another without falling or knocking down a
stone.

The primary affective tendency which constitutes that
state of attention which is directed on a definite object, by
no means excludes the intrusion of sensations which at the
time have no interest ; or, in other words, it does not pre-
vent excitations of a sensory character from reaching their
goal, their normal destination, even when we are uncon-
scious of them ; but they only oppose the affective tendency
which would endeavor to arouse these sensations.

"The entrance of a stimulus into consciousness" — as
it is expressed by Kohn and others — does not rest upon the
possible intrusion of the stimulus at any particular part
of the brain or sensorium whose specific function would
be that of consciousness. No more does it depend upon a
single "center of perception" as Wundt assumes. But it
consists only in the fact that this stimulus evokes some affec-
tive tendency relating to the object which it represents.
When this evocation takes place the stimulus reaches con-
sciousness; if it does not take place, perhaps because at
this moment another affective tendency referring to other

3O THE MONIST.

sensations is operative, then, although the stimulus may
penetrate physiologically to the same point as usual, it can-
not reach consciousness and hence remains unobserved and
unconscious. The persistence of the mnemonic accumula-
tions of those sensations which remain outside of con-
sciousness and the possibility of evoking them again in
the future are at a great disadvantage from the cir-
cumstance that they are not able to excite any affective
state peculiar to themselves with which they could be con-
nected or associated.

Having thus elucidated the inmost nature of the affec-
tive conflict peculiar to attention in its main points, and
having seen wherein consists that unity of consciousness
which so many inquirers declare to be one of its most es-
sential fundamental properties, space does not now permit
us to pass on to the study of the effects arising from this
inmost nature and fundamental property of attention upon
sensations and ideas, as in general for the whole process
of intelligence.

E. RlGNANO.

MILAN, ITALY.

CHANCE.1

T T OW dare we speak of the laws of chance? Is not
JTl chance the antithesis of all law?" So says Ber-
trand at the beginning of his Calcul des probability. Prob-
ability is opposed to certitude ; so it is what we do not know
and consequently it seems what we could not calculate.
Here is at least apparently a contradiction, and about it
much has already been written.

And first, what is chance ? The ancients distinguished
between phenomena seemingly obeying harmonious laws,
established once for all, and those which they attributed
to chance; these were the ones unpredictable because re-
bellious to all law. In each domain the precise laws did not
decide everything, they only drew limits between which
chance might act. In this conception the word chance had
a precise and objective meaning : what was chance for one
was also chance for another and even for the gods.

But this conception is not ours to-day. We have be-
come absolute determinists, and even those who want to
reserve the rights of human free will let determinism reign
undividedly in the inorganic world at least. Every phe-
nomenon, however minute, has a cause; and a mind in-
finitely powerful, infinitely well-informed about the laws
of nature, could have foreseen it from the beginning of the
centuries. If such a mind existed, we could not play with
it at any game of chance, we should always lose.

In fact for it the word chance would not have any mean-

1 Translated by G. B. Halsted.

32 THE MONIST.

ing, or rather there would be no chance. It is because of
our weakness and our ignorance that the word has a mean-
ing for us. And, even without going beyond our feeble
humanity, what is chance for the ignorant, is not chance
for the scientist. Chance is only the measure of our ig-
norance. Fortuitous phenomena are, by definition, those
whose laws we do not know.

But is this definition altogether satisfactory? When
the first Chaldean shepherds followed with their eyes the
movements of the stars, they knew not as yet the laws of
astronomy; would they have dreamed of saying that the
stars move at random? If a modern physicist studies a
new phenomenon, and if he discovers its law Tuesday,
would he have said Monday that this phenomenon was
fortuitous ? Moreover, do we not often invoke what Ber-
trand calls the laws of chance, to predict a phenomenon?
For example in the kinetic theory of gases we obtain the
known laws of Mariotte and of Gay-Lussac by means of
the hypothesis that the velocities of the molecules of gas
vary irregularly, that is to say at random. All physicists
will agree that the observable laws would be much less
simple if the velocities were ruled by any simple elemen-
tary law whatsoever, if the molecules were, as we say,
organised, if they were subject to some discipline. It is
due to chance, that is to say to our ignorance, that we can
draw our conclusions; and then if the word chance is
simply synonymous with ignorance what does that mean?
Must we therefore translate it as follows?

"You ask me to predict for you the phenomena about to
happen. If, unluckily, I knew the laws of these phe-
nomena I could make the prediction only by inextricable
calculations and would have to. renounce attempting to
answer you ; but as I may chance not to know, I will answer
you at once. And what is most surprising, my answer
will be right."

CHANCE. 33

So it must well be that chance is something other than
the name we give our ignorance, that among phenomena
whose causes are unknown to us we must distinguish for-
tuitous phenomena about which the calculus of probabil-
ities will provisionally give information, from those which
are not fortuitous and of which we can say nothing so long
as we shall not have determined the laws governing them.
For the fortuitous phenomena themselves, it is clear that
the information given us by the calculus of probabilities
will not cease to be true upon the day when these phenom-
ena shall be better known.

The director of a life insurance company does not know
when each of the insured will die, but he relies upon the
calculus of probabilities and on the law of great numbers
and he is not deceived since he distributes dividends to his
stockholders. These dividends would not vanish if a very
penetrating and very indiscrete physician should, after the
policies were signed, reveal to the director the life chances
of the insured. This doctor would dissipate the ignorance
of the director, but he would have no influence on the divi-
dends which evidently are not an outcome of this ignorance.

* # *

To find a better definition of chance we must examine
some of the facts which we agree to regard as fortuitous,
and to which the calculus of probabilities seems to apply;
we then shall investigate what are their common char-
acteristics.

The first example we select is that of unstable equi-
librium; if a cone rests upon its apex, we know well that
it will fall, but we do not know toward what side; it seems
to us chance alone will decide. If the cone were perfectly
symmetric, if its axis were perfectly vertical, if it were
acted upon by no force other than gravity, it would not
fall at all. But the least defect in symmetry will make it
lean slightly toward one side or the other, and if it leans,

34 THE MONIST.

however little, it will fall altogether toward that side. Even
if the symmetry were perfect, a very slight tremor, a breath
of air could make it incline some seconds of arc; this will
be enough to determine its fall and even the sense of its
fall which will be that of the initial inclination.

A very slight cause, which escapes us, determines a
considerable effect which we cannot help seeing, and then
we say this effect is due to chance. If we could know
exactly the laws of nature and the situation of the universe
at the initial instant, we should be able to predict exactly
the situation of this same universe at a subsequent instant.
But even then when the natural laws should have no fur-
ther secret for us, we could know the initial situation only
approximately. If that permits us to foresee the subse-
quent situation with the same degree of approximation,
this is all we require, we say the phenomenon has been pre-
dicted, that it is ruled by laws ; but it is not always so. It
may happen that slight differences in the initial conditions
produce very great differences in the final phenomena; a
slight error in the former would make an enormous error
in the latter. Prediction becomes impossible and we have
the fortuitous phenomenon.

Our second example will be very analogous to the first
and we shall take it from meteorology. Why have the
meteorologists such difficulty in predicting the weather
with any certainty ? Why do the rains, the tempests them-
selves seem to us to come by chance, so that many persons
find it quite natural to pray for rain or shine, when they
would think it ridiculous to pray for an eclipse? We see
that great perturbations generally happen in regions where
the atmosphere is in unstable equilibrium. The meteorol-
ogists are aware that this equilibrium is unstable, that a
cyclone is arising somewhere; but where they cannot tell;
one-tenth of a degree more or less at any point, and the
cyclone bursts here and not there, and spreads its ravages

CHANCE. 35

over countries it would have spared. This we could have
foreseen if we had known that tenth of a degree, but the
observations were neither sufficiently close nor sufficiently
precise, and for this reason all seems due to the agency of
chance. Here again we find the same contrast between a
very slight cause, unappreciable to the observer, and im-
portant effects, which are sometimes tremendous disasters.

Let us pass to another example, the distribution of the
minor planets on the zodiac. Their initial longitudes can
have been any longitudes whatever; but their mean mo-
tions were different and they have revolved for so long
a time that we may say they are now distributed at random
along the zodiac. Very slight initial differences between
their distances from the sun, or, what comes to the same
thing, between their mean motions, have ended by giving
enormous differences between their present longitudes. An
excess of the thousandth of a second in the daily mean
motion will give in fact a second in three years, a degree in
ten thousand years, an entire circumference in three or
four million years, and what is that to the time which has
passed since the minor planets have detached themselves
from the nebula of Laplace? Again therefore we see a
slight cause and a great effect ; or better, slight differences
in the cause and great differences in the effect.

The game of roulette does not take us as far as might
seem from the preceding example. Assume a needle to
be turned on a pivot over a dial divided into a hundred
sectors alternately red and black. If it stops on a red sector
I win, if not, I lose. Evidently all depends upon the initial
impulse I give the needle. The needle will make, suppose,
ten or twenty turns, but it will stop sooner or not so soon
according as I shall have pushed it more or less strongly.
It suffices that the impulse vary only by a thousandth or
a two thousandth to make the needle stop over a black
sector or over the following red one. These are differences

36 THE MONIST.

the muscular sense cannot distinguish and which elude
even the most delicate instruments. So it is impossible for
me to foresee what the needle I have started will do, and
this is why my heart throbs and I hope everything from
luck. The difference in the cause is imperceptible, and the
difference in the effect is for me of the highest importance,

since it means my whole stake.

# * *

Permit me, in this connection, a thought somewhat
foreign to my subject. Some years ago a philosopher said
that the future is determined by the past, but not the past
by the future; or, in other words, from knowledge of
the present we could deduce the future, but not the past;
because, said he, a cause can have only one effect, while the
same effect might be produced by several different causes.
It is clear no scientist can subscribe to this conclusion.
The laws of nature bind the antecedent to the consequent
in such a way that the antecedent is as well determined
by the consequent as the consequent by the antecedent.
But whence came the error of this philosopher ? We know
that in virtue of Carnot's principle physical phenomena are
irreversible and the world tends toward uniformity. When
two bodies of different temperature come in contact, the
warmer gives up heat to the colder ; so we may foresee that
the temperature will equalize. But once equal, if asked
about the anterior state, what can we answer? We might
say that one was warm and the other cold, but not be
able to divine which formerly was the warmer.

And yet in reality the temperatures will never reach
perfect equality. The differences of temperature only tend
asymptotically toward zero. There comes a moment when
our thermometers are powerless to make it known. But
if we had thermometers a thousand times, a hundred thou-
sand times as sensitive, we should recognize that there still
is a slight difference, and that one of the bodies remains

CHANCE. 37

a little warmer than the other, and so we could say this
it is which formerly was much the warmer.

So then there are, contrary to what we found in the
former examples, great differences in cause and slight
differences in effect. Flammarion once imagined an ob-
server going away from the earth with a velocity greater
than that of light ; for him time would have changed sign.
History would be turned about, and Waterloo would pre-
cede Austerlitz. Well, for this observer, effects and causes
would be inverted; unstable equilibrium would no longer
be the exception. Because of the universal irreversibility
all would seem to him to come out of a sort of chaos in
unstable equilibrium. All nature would appear to him de-
livered over to chance.

* * *

Now for other examples where we shall see somewhat
different characteristics. Take first the kinetic theory of
gases. How should we picture a receptacle filled with gas ?
Innumerable molecules, moving at high speeds, flash
through this receptacle in every direction. At every in-
stant they strike against its walls or each other, and these
collisions happen under the most diverse conditions. What
above all impresses us here, is not the littleness of the
causes, but their complexity, and yet the former element
is still found here and plays an important role. If a mol-
ecule deviated right or left from its trajectory, by a very
small quantity, comparable to the radius of action of the
gaseous molecules, it would avoid a collision or sustain it
under different conditions, and that would vary the direc-
tion of its velocity after the impact, perhaps by ninety de-
grees or by a hundred and eighty degrees.

And this is not all ; we have just seen that it is necessary
to deflect the molecule before the clash by only an infini-
tesimal, to produce its deviation after the collision by a
finite quantity. If then the molecule undergoes two sue-

38 THE MONIST.

cessive shocks, it will suffice to deflect it before the first by
an infinitesimal of the second order, for it to deviate after
the first encounter by an infinitesimal of the first order,
and after the second hit, by a finite quantity. And the
molecule will not undergo merely two shocks; it will
undergo a very great number per second. So that if the
first shock has multiplied the deviation by a very large
number A, after n shocks it will be multiplied by An. It
will therefore become very great not merely because A is
large, that is to say because little causes produce big effects,
but because the exponent n is large, that is to say because
the shocks are very numerous and the causes very complex.

Take a second example. Why do the drops of rain in
a shower seem to be distributed at random ? This is again
because of the complexity of the causes which determine
their formation. Ions are distributed in the atmosphere.
For a long while they have been subjected to air-currents
constantly changing, they have been caught in very small
whirlwinds, so that thetr final distribution has no longer
any relation to their initial distribution. Suddenly the
temperature falls, vapor condenses, and each of these ions
becomes the center of a drop of rain. To know what will
be the distribution of these drops and how many will fall
on each paving-stone, it would not be sufficient to know the
initial situation of the ions, it would be necessary to com-
pute the effect of a thousand little capricious air-currents.

And again it is the same if we put grains of powder in
suspension in water. The vase is ploughed by the currents
whose law we know not, we only know it is very compli-
cated. At the end of a certain time the grains will be dis-
tributed at random, that is to say uniformly, in the vase;
and this is due precisely to the complexity of these currents.
If they obeyed some simple law, if for example the vase re-
volved and the currents circulated around the axis of the
vase, describing circles, it would no longer be the same,

CHANCE. 39

since each grain would retain its initial altitude and its
initial distance from the axis.

We should reach the same result in considering the
mixing of two liquids or of two fine-grained powders. And
to take a grosser example, this is also what happens when
we shuffle playing-cards. At each stroke, the cards un-
dergo a permutation (analogous to that studied in the
theory of substitutions). What will happen? The prob-
ability of a particular permutation (for example that bring-
ing to the nth place the card occupying the 4>OHh place
before the permutation) depends upon the player's habits.
But if this player shuffles the cards long enough, there will
be a great number of successive permutations, and the
resulting final order will no longer be governed by aught
but chance; I mean to say that all possible orders will be
equally probable. It is to the great number of successive
permutations, that is to say to the complexity of the phe-
nomenon, that this result is due.

A final word about the theory of errors. Here it is
that the causes are complex and multiple. To how many
snares is not the observer exposed, even with the best in-
strument! He should apply himself to finding out the
largest and avoiding them. These are the ones giving
birth to systematic errors. But when he has eliminated
those, admitting that he succeeds, there remain many small
ones which, their effects accumulating, may become dan-
gerous. Thence come the accidental errors; and we at-
tribute them to chance because their causes are too com-
plicated and too numerous. Here again we have only little
causes each of which might produce only a slight effect;
it is by their union and their number that their effects be-
came formidable.

* * *

We may take still a third point of view, less important
than the first two and upon which I shall lay less stress.

4<D THE MONIST.

When we seek to foresee an event and examine its antece-
dents, we strive to search into the anterior situation. This
could not be done for all parts of the universe and we are
content to know what is passing in the neighborhood of
the point where the event should occur, or what would
appear to have some relation to it. An examination can-
not be complete and we must know how to choose. But it
may happen that we have passed by circumstances which
at first sight seemed completely foreign to the foreseen hap-
pening, to which one would never have dreamed of attrib-
uting any influence and which nevertheless, contrary to
all anticipation, come to play an important role.

A man passes in the street going to his business ; some
one knowing the business could have told why he started
at such a time and went by such a street. On the roof
works a tiler. The contractor employing him could in a
certain measure foresee what he would do. But the
passer-by scarcely thinks of the tiler, nor the tiler of him ;
they seem to belong to two worlds completely foreign to
one another. And yet the tiler drops a tile which kills the
man, and we do not hesitate to say this is chance.

Our weakness forbids our considering the entire uni-
verse and makes us cut it up into slices. We try to do
this as little artificially as possible. And yet it happens
from time to time that two of these slices react upon one
another. The effects of this mutual action then seem to us
to be due to chance.

Is this a third way of conceiving chance? Not always;
in fact most often we are carried back to the first or the
second. Whenever two worlds usually foreign to one an-
other, come thus to react upon each other, the laws of this
reaction must be very complex. On the other hand a very
slight change in the initial conditions of these two worlds
would have been sufficient for the reaction not to have

CHANCE. 41

happened. How little was needed for the man to pass a

second later or the tiler to drop his tile a second sooner.

* * *

All we have said still does not explain why chance obeys
laws. Does the fact that the causes are slight or complex
suffice for our foreseeing, if not their effects in each case,
at least what their effects will be, on the average? To an-
swer this question we had better take up again some of
the examples already cited.

I shall begin with that of the roulette. I have said that
the point where the needle will stop depends upon the initial
push given it. What is the probability of this push having
this or that value ? I know nothing about it, but it is diffi-
cult for me not to suppose that this probability is repre-
sented by a continuous analytic function. The probability
that the push is comprised between « and a+c will then be
sensibly equal to the probability of its being comprised
between <*+* and «+2e, provided « be very small. This is
a property common to all analytic functions. Minute vari-
ations of the function are proportional to minute variations
of the variable.

But we have assumed that an exceedingly slight variation
of the push suffices to change the color of the sector over
which the needle finally stops. From <* to a+c it is red,
from a+e to a+2« it is black; the probability of each red
sector is therefore the same as of the following black, and
consequently the total probability of red equals the total
probability of black.

The datum of the question is the analytic function rep-
resenting the probability of a particular initial push. But
the theorem remains true whatever be this datum, since it
depends upon a property common to all analytic functions.
From this it follows finally that we no longer need the
datum.

What we have just said for the case of the roulette

42 THE MONIST.

applies also to the example of the minor planets. The zo-
diac may be regarded as an immense roulette on which have
been tossed many little balls with different initial impulses
varying according to some law. Their present distribution
is uniform and independent of this law, for the same rea-
son as in the preceding case. Thus we see why phenomena
obey the laws of chance when slight differences in the
causes suffice to bring on great differences in the effects.
The probabilities of these slight differences may then be
regarded as proportional to these differences themselves,
just because these differences are minute, and the infini-
tesimal increments of a continuous function are propor-
tional to those of the variable.

Take an entirely different example, where intervenes
especially the complexity of the causes. Suppose a player
shuffles a pack of cards. At each shuffle he changes the
order of the cards, and he may change them in many ways.
To simplify the exposition, consider only three cards. The
cards which before the shuffle occupied respectively the
places 123, may after the shuffle occupy the places

123, 231, 312, 321, 132, 213.

Each of these six hypotheses is possible and they have re-
spectively for probabilities:

pi, fa, ps, p±, p*> PQ.

The sum of these six numbers equals I ; but this is all
we know of them ; these six probabilities depend naturally
upon the habits of the player which we do not know.

At the second shuffle and the following, this will recom-
mence, and under the same conditions ; I mean that p± for
example represents always the probability that the three
cards which occupied after the nth shufflle and before the
n-(-ith the places 123, occupy the places 321 after the
n+ith shuffle. And this remains true whatever be the
number n, since the habits of the player and his way of
shuffling remain the same.

CHANCE. 43

But if the number of shuffles is very great, the cards
which before the first shuffle occupied the places 123 may,
after the last shuffle, occupy the places

123, 231, 312, 321, 132, 213

and the probability of these six hypotheses will be sensibly
the same and equal to 1/6; and this will be true whatever
be the numbers pi . . . . pQ which we do not know. The great
number of shuffles, that is to say the complexity of the
causes, has produced uniformity.

This wrould apply without change if there were more
than three cards, but even with three cards the demon-
stration would be complicated; let it suffice to give it for
only two cards. Then we have only two possibilities 12,
21 with the probabilities pi and p2 = i — pi.

Suppose n shuffles and suppose I win one franc if the
cards are finally in the initial order and lose one if they
are finally inverted. Then, my mathematical expectation
will be (pi—p2)n.

The difference pi — p2 is certainly less than i ; so that
if n is very great my expectation will be zero ; we need not
learn pi and p2 to be aware that the game is equitable.

There would always be an exception if one of the num-
bers pi and p2 was equal to i and the other naught. Then
it would not apply because our initial hypotheses would be
too simple.

What we have just seen applies not only to the mixing
of cards but to all mixings, to those of powders and of
liquids ; and even to those of the molecules of gases in the
kinetic theory of gases.

To return to this theory, suppose for a moment a gas
whose molecules cannot mutually clash, but may be devi-
ated by hitting the insides of the vase wherein the gas is
confined. If the form of the vase is sufficiently complex
the distribution of the molecules and that of the velocities
will not be long in becoming uniform. But this will not

44 THE MONIST.

be so if the vase is spherical or if it has the shape of a
cuboid. Why ? Because in the first case the distance from
the center to any trajectory will remain constant; in the
second case this will be the absolute value of the angle of
each trajectory with the faces of the cuboid.

So we see what should be understood by conditions too
simple] they are such as conserve something, which leave
an invariant remaining. Are the differential equations of
the problem too simple for us to apply the laws of chance?
This question would seem at first view to lack precise
meaning; now we know what it means. They are too
simple if they conserve something, if they admit a uniform
integral. If something in the initial conditions remains
unchanged, it is clear the final situation can no longer be
independent of the initial situation.

We come finally to the theory of errors. We know
not to what are due the accidental errors, and precisely
because we do not know we are aware they obey the
law of Gauss. Such is the paradox. The explanation
is nearly the same as in the preceding cases. We need
know only one thing: that the errors are very numer-
ous, that they are very slight, that each may be as well
negative as positive. What is the curve of probability of
each of them? We do not know; we only suppose it is
symmetric. We prove then that the resultant error will
follow Gauss's law, and this resulting law is independent
of the particular laws which we do not know. Here again
the simplicity of the result is born of the very complexity

of the data.

* * *

But we are not through with paradoxes. I have just
recalled the figment of Flammarion, that of the man going
quicker than light, for whom time changes sign. I said
that for him all phenomena would seem due to chance.
That is true from a certain point of view, and yet all these

CHANCE. 45

phenomena at a given moment would not be distributed in
conformity with the laws of chance since the distribution
would be the same as for us, who seeing them unfold har-
moniously and without coming out of a primal chaos, do
not regard them as ruled by chance.

What does that mean ? For Lumen, Flammarion's man,
slight causes seem to produce great effects; why do not
things go on as for us when we think we see grand effects
due to little causes? Would not the same reasoning be
applicable in his case?

Let us return to the argument. When slight differences
in the causes produce vast differences in the effects, why
are these effects distributed according to the laws of
chance? Suppose a difference of a millimeter in the cause
produces a difference of a kilometer in the effect. If I
win in case the effect corresponds to a kilometer bearing
an even number, my probability of winning will be 1/2.
Why? Because to make that, the cause must correspond
to a millimeter with an even number. Now, according to
all appearance, the probability of the cause varying be-
tween certain limits will be proportional to the distance
apart of these limits, provided this distance be very small.
If this hypothesis were not admitted there would no longer
be any way of representing the probability by a continuous
function.

What now will happen when great causes produce
small effects? This is the case where we should not at-
tribute the phenomenon to chance and where on the con-
trary Lumen would attribute it to chance. To a difference
of a kilometer in the cause would correspond a difference
of a millimeter in the effect. Would the probability of the
cause being comprised between two limits n kilometers
apart still be proportional to n? We have no reason to
suppose so, since this distance, n kilometers, is great. But
the probability that the effect lies between two limits n

46 THE MONIST.

millimeters apart will be precisely the same, so it will not
be proportional to n, even though this distance, n milli-
meters, be small. There is no way therefore of represent-
ing the law of probability of effects by a continuous curve.
This curve, understand, may remain continuous in the
analytic sense of the word; to infinitesimal variations of
the abscissa will correspond infinitesimal variations of the
ordinate. But practically it will not be continuous, since
very small variations of the ordinate would not correspond
to very small variations of the abscissa. It would become
impossible to trace the curve with an ordinary pencil ; that
is what I mean.

So what must we conclude? Lumen has no right to
say that the probability of the cause (his cause, our effect)
should be represented necessarily by a continuous func-
tion. But then why have we this right ? It is because this
state of unstable equilibrium which we have been calling
initial is itself only the final outcome of a long previous
history. In the course of this history complex causes have
worked a great while: they have contributed to produce
the mixture of elements and they have tended to make
everything uniform at least within a small region; they
have rounded off the corners, smoothed down the hills and
filled up the valleys. However capricious and irregular
may have been the primitive curve given over to them,
they have worked so much toward making it regular that
finally they deliver over to us a continuous curve. And
this is why we may in all confidence assume its continuity.

Lumen would not have the same reasons for such a
conclusion. For him complex causes would not seem
agents of equalization and regularity, but on the con-
trary would create only inequality and differentiation. He
would see a world more and more varied come forth from
a sort of primitive chaos. The changes he could observe
would be for him unforeseen and impossible to foresee.

CHANCE. 47

They would seem to him due to some caprice or another ;
but this caprice would be quite different from our chance,
since it would be opposed to all law, while our chance still
has its laws. All these points call for lengthy explications
which perhaps would aid in the better comprehension of

the irreversibility of the universe.

# * *

We have sought to define chance, and now it is proper
to put a question. Has chance thus defined, in so far as
this is possible, objectivity?

It may be questioned. I have spoken of very slight or
very complex causes. But what is very little for one may
be very big for another, and what seems very complex to
one may seem simple to another. In part I have already
answered by saying precisely in what cases differential
equations become too simple for the laws of chance to re-
main applicable. But it is fitting to examine the matter a
little more closely, because we may take still other points
of view.

What means the phrase "very slight" ? To understand
it we need only go back to what has already been said. A
difference is very slight, an interval is very small, when
within the limits of this interval the probability remains
sensibly constant. And why may this probability be re-
garded as constant within a small interval ? It is because
we assume that the law of probability is represented by a
continuous curve, continuous not only in the analytic sense
but practically continuous, as already explained. This
means that it not only presents no absolute hiatus but that
it has neither salients nor reentrants too acute or too ac-
centuated.

And what gives us the right to make this hypothesis?
We have already said it is because, since the beginning of
the ages, there have always been complex causes cease-
lessly acting in the same way and making the world tend

48 THE MONIST.

toward uniformity without ever being able to turn back.
These are the causes which little by little have flattened
the salients and filled up the reentrants and this is why
our probability curves now show only gentle undulations.
In milliards of milliards of ages another step will have
been made toward uniformity, and these undulations will
be ten times as gentle; the radius of mean curvature of
our curve will have become ten times as great. And then
such a length as seems to us to-day not very small, since
on our curve an arc of this length cannot be regarded as
rectilineal, should on the contrary at that epoch be called
very little, since the curvature will have become ten times
less and an arc of this length may be sensibly identified
with a sect.

Thus the phrase "very slight" remains relative; but
it is not relative to such or such a man, it is relative to the
actual state of the world. It will change its meaning when
the world shall have become more uniform, when all things
shall have blended still more. But then doubtless men
can no longer live and must give place to other beings-
should I say far smaller or far larger ? So that our crite-
rion, remaining true for all men, retains an objective sense.

And on the other hand what means the phrase "very
complex"? I have already given one solution, but there
are others. Complex causes we have said produce a blend
more and more intimate, but after how long a time will
this blend satisfy us? When will it have accumulated
sufficient complexity? When shall we have sufficiently
shuffled the cards? If we mix two powders, one blue the
other white, there comes a moment when the tint of the
mixture seems to us uniform because of the feebleness of
our senses; it will be uniform for the presbyte, forced to
gaze from afar, before it will be so for the myope. And
when it has become uniform for all eyes, we still could
push back the limit by the use of instruments. There is

CHANCE. 49

no chance for any man ever to discern the infinite variety
which, if the kinetic theory is true, hides under the uniform
appearance of a gas. And yet if we accept Gouy's ideas
on the Brownian movement, does not the microscope seem
on the point of showing us something analogous?

This new criterion is therefore relative like the first;
and if it retains an objective character, it is because all
men have approximately the same senses, the power of
their instruments is limited, and besides they use it only

exceptionally.

* * *

It is just the same in the moral sciences and particu-
larly in history. The historian is obliged to make a choice
among the events of the epoch he studies ; he recounts only
those which seem to him the most important. He therefore
contents himself with relating the most momentous events
of the sixteenth century for example, as likewise the most
remarkable facts of the seventeenth century. If the first
suffice to explain the second, we say these conform to the
laws of history. But if a great event of the seventeenth
century should have for cause a small fact of the sixteenth
century which no history reports, which all the world has
neglected, then we say this event is due to chance. This
word has therefore the same sense as in the physical sci-
ences; it means that slight causes have produced great
effects.

The greatest bit of chance is the birth of a great man.
It is only by chance that meeting of two germinal cells,
of different sex, containing precisely, each on its side, the
mysterious elements whose mutual reaction must produce
the genius. One will agree that these elements must be
rare and that their meeting is still more rare. How slight
a thing it would have required to deflect from its route the
carrying spermatozoon. It would have sufficed to deflect
it a tenth of a millimeter and Napoleon would not have

50 THE MONIST.

been born and the destinies of a continent would have been
changed. No example can better make us understand the
veritable characteristics of chance.

One more word about the paradoxes brought out by the
application of the calculus of probabilities to the moral
sciences. It has been proved that no Chamber of Deputies
will ever fail to contain a member of the opposition, or at
least such an event would be so improbable that we might
without fear wager the contrary, and bet a million against
a sou.

Condorcet has striven to calculate how many jurors it
would require to make a judicial error practically impos-
sible. If we had used the results of this calculation, we
should certainly have been exposed to the same disappoint-
ments as in betting, on the faith of the calculus, that the
opposition would never be without a representative.

The laws of chance do not apply to these questions. If
justice be not always meted out to accord with the best
reasons, it uses less than we think the method of Bridoye.
This is perhaps to be regretted, for then the system of Con-
dorcet would shield us from judicial errors.

What is the meaning of this? We are tempted to at-
tribute facts of this nature to chance because their causes
are obscure; but this is not true chance. The causes are
unknown to us it is true, and they are even complex; but
they are not sufficiently so, since they conserve something.
We have seen that this it is which distinguishes causes
"too simple." When men are brought together they no
longer decide at random and independently one of another ;
they influence one another. Multiplex causes come into
action. They worry men, dragging them to right or left,
but one thing there is they cannot destroy, this is their

Panurge flock-of-sheep habits. And this is an invariant.

* # #

Difficulties are indeed involved in the application of the

CHANCE. SI

calculus of probabilities to the exact sciences. Why are
the decimals of a table of logarithms, why are those of the
number w distributed in accordance with the laws of chance ?
Elsewhere I have already studied the question in so far as
it concerns logarithms, and there it is easy. It is clear
that a slight difference of argument will give a slight
difference of logarithm, but a great difference in the sixth
decimal of the logarithm. Always we find again the same
criterion.

But as for the number T, that presents more difficulties,
and I have at the moment nothing worth while to say.

There would be many other questions to resolve, had I
wished to attack them before solving that which I more
specially set myself. When we reach a simple result, when
we find for example a round number, we say that such a
result cannot be due to chance, and we seek, for its explana-
tion, a non-fortuitous cause. And in fact there is only a
very slight probability that among 10,000 numbers chance
will give a round number, for example the number 10,000.
This has only one chance in 10,000. But there is only one
chance in 10,000 for the occurrence of any other one num-
ber ; and yet this result will not astonish us, nor will it be
hard for us to attribute it to chance ; and that simply be-
cause it will be less striking.

Is this a simple illusion of ours, or are there cases
where this way of thinking is legitimate? We must hope
so, else were all science impossible. When we wish to
check a hypothesis, what do we do? We cannot verify
all its consequences, since they would be infinite in num-
ber ; we content ourselves with verifying certain ones and
if we succeed we declare the hypothesis confirmed, because
so much success could not be due to chance. And this is
always at bottom the same reasoning.

I cannot completely justify it here, since it would take
too much time; but I may at least say that we find our-

52 THE MONIST.

selves confronted by two hypotheses, either a simple cause
or that aggregate of complex causes we call chance. We
find it natural to suppose that the first should produce a
simple result, and then, if we find that simple result, the
round number for example, it seems more likely to us to be
attributable to the simple cause which must give it almost
certainly, than to chance which could only give it once in
10,000 times. It will not be the same if we find a result
which is not simple; chance, it is true, will not give this
more than once in 10,000 times; but neither has the simple
cause any more chance of producing it.

HENRI POINCARE.
PARIS, FRANCE.

THE THEORY OF REVERSIONS.*

QUARES like those shown in Figs, i and 2, in which
the numbers occur in their natural order, are known
as natural squares. In such squares, it will be noticed that
the numbers in associated1 cells are complementary, i. e.,
their sum is twice the mean number. It follows that any
two columns equally distant from the central bar of the
lattice are complementary columns, that is, the magic sum

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

1

2

3

4

5

6

7

8

9

10

11

12

13

14

IS

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

Fig. i.

Fig. 2.

will be the mean of their sums. Further any two numbers
in these complementary columns which lie in the same
row have a constant difference, and therefore the sums of
the two columns differ by n times this difference. If then
we raise the lighter column and depress the heavier col-
umn by 11/2 times this difference we shall bring both to the

*This paper was extracted about 18 months ago from three different
parts of an unpublished treatise written in 1894. With regard to footnote
6, p. 63, since this was written Sayles and Worthington have independently
solved the problem of construction for 63.

*Two cells are said to be associated when the straight line joining their
centers intersects the center of the lattice, and they are equally distant from
that center.

54 THE MONIST.

mean value. Now we can effect this change by interchang-
ing half the numbers in the one column with the numbers
in the other column lying in their respective rows. The
same is true with regard to rows, so that if we can make
n/2 horizontal interchanges between every pair of comple-
mentary columns and the same number of vertical inter-
changes between every pair of complementary rows, we
shall have the magic sum in all rows and columns. It is
easy to see that we can do this by reversing half the rows
and half the columns, provided the two operations are so
arranged as not to interfere with one another. This last
condition can be assured by always turning over columns
and rows in associated pairs, for then we shall have made
horizontal interchanges only between pairs of numbers
previously untouched or between pairs, each of whose con-
stituents has already received an equal vertical displace-
ment; and similarly with the vertical interchanges. By
this method, it will be noticed, we always secure magic
central diagonals, for however we choose our rows and
columns we only alter the central diagonals of the natural
square (which are already magic) by interchanging pairs
of complementaries with other pairs of complementaries.

Since the n/2 columns have to be arranged in pairs on
either side of the central vertical bar of the lattice, n/2 must
be even, and so the method, in its simplest form, applies only
to orders EEEO (mod 4). We may formulate the rule thus:
For orders of form 4m, reverse m pairs of complementary
columns and m pairs of complementary rows, and the crude
magic is completed.

In the following example the curved lines indicate the
rows and columns which have been reversed (Fig. 3).

We have said that this method applies only when n/2
is even, but we shall now show that by a slight modification
it can be applied to all even orders. For suppose n is
double-of-odd ; we cannot then arrange half the columns

THE THEORY OF REVERSIONS.

55

in pairs about the center since their number is odd, but
we can so arrange n/2 — i rows and n/2 — i columns, and
if we reverse all these rows and columns we shall have
made n/2 — i interchanges between every pair of comple-
mentary rows and columns. We now require only to make
the one further interchange between every pair of rows
and columns, without interfering with the previous changes
or with the central diagonals. To effect this is always

1

58

59

4

5

62

63

8

(

16

55

54

Id

12

51

50

9

c

17

42

43

20

21

46

47

24

32

39

38

29

28

35

34

25

40

31

30

37

36

27

26

33

41

18

19

44

45

22

23

48

c

56

15

14

53

52

11

10

49

57

2

3

60

61

6

7

64

Fig. 3-

easy with any orders ^2 (mod 4), (6, 10, 14 etc.), ex-
cepting the first. In the case of 62 an artifice is necessary.
If we reverse the two central diagonals of a square it will
be found, on examination, that this is equivalent to re-
versing two rows and two columns; in fact, this gives us
a method of forming the magic 42 from the natural square
with the least number of displacements, thus :

16

2

3

13

5

11

10

8

9

7

6

12

4

14

15

1

Fig. 4.

Applying this idea, we can complete the crude magic

THE MONIST.

62 from the scheme shown in Fig. 5, where horizontal lines
indicate horizontal interchanges, and vertical lines vertical
interchanges; the lines through the diagonals implying
that the diagonals are to be reversed. The resulting magic
is shown in Fig. 6.

The general method here described is known as the
method of reversions, and the artifice used in the double-
of-odd orders is called the broken reversion. The method
of reversions, as applied to all even orders, both in squares
and cubes, was first ( ?) investigated by the late W. Firth,
Scholar of Emmanuel, Cambridge.2

The broken reversion for & may, of course, be made in
various ways, but the above scheme is one of the most sym-

36

32

3

4

5

31

12

29

9

28

26

7

13

14

22

21

17

24

19

23

16

15

20

18

25

11

27

10

8

30

6

2

34

33

35

1

Fig. 6.

metrical, and may be memorialized thus: For horizontal
changes commence at the two middle cells of the bottom
row, and progress upwards and divergently along two
knight's paths. For vertical changes turn the square on
one of its sides and proceed as before.

In dealing with larger double-of-odd orders we may
leave the central diagonals "intact" and invert n/2 — I rows
and n/2 — I columns. The broken reversion can then al-
ways be effected in a multitude of ways. It must be kept
in mind, however, that in making horizontal changes we
must not touch numbers which have been already moved
horizontally, and if we use a number which has received

8 Died 1889. For historical notice vide section on cubes.

THE THEORY OF REVERSIONS.

57

a vertical displacement we can only change it with a num-
ber which has received an equal vertical displacement, and
similarly with vertical interchanges. Lastly we must not
touch the central diagonals.

Fig. 7 is such a scheme for io2, with the four central
rows and columns reversed, and Fig. 8 shows the com-
pleted magic.

It is unnecessary to formulate a rule for making the
reversions in these cases, because we are about to consider
the method from a broader standpoint which will lead up
to a general rule.

1

92

8

94

95

96

97

3

9

10

20

12

13

84

85

86

87

88

19

11

71

29

23

74

75

76

77

28

22

30

40

39

38

67

66

65

64

33

62

31

50

49

48

57

56

55

54

43

42

51

60

59

58

47

46

45

44

53

52

41

70

69

68

37

36

35

34

63

32

61

21

72

73

24

25

26

27

78

79

80

81

82

83

17

15

16

14

18

89

90

91

2

93

4

6

5

7

98

99

100

Fig. 7-

Fig. 8.

If the reader will consider the method used in forming
the magic & by reversing the central diagonals, he will
find that this artifice amounts to taking in every column
two numbers equally distant from the central horizontal
bar and interchanging each of them with its complemen-
tary in the associated cell, the operation being so arranged
that two and only two numbers are moved in each row.
This, as we have already pointed out, is equivalent to re-
versing two rows and two columns. Now these skew inter-
changes need not be made on the central diagonals — they
can be made in any part of the lattice, provided the con-

THE MONIST.

ditions just laid down are attended to. If then we make a
second series of skew changes of like kind, we shall have,
in effect, reversed 4 rows and 4 columns, and so on, each
complete skew reversion representing two rows and col-
umns. Now if n = 2 (mod 4) we have to reverse n/2 — i
rows and colunms before making the broken reversion,
therefore the same result is attained by making (n — 2)/4
complete sets of skew reversions and one broken reversion.

abed

Fig. 9-

In like manner, if n = o (mod 4), instead of reversing n/2
rows and columns we need only to make n/4 sets of skew
reversions.

We shall define the symbol IX] as implying that skew
interchanges are to be made between opposed pairs of the
four numbers symmetrically situated with regard to the
central horizontal and vertical bars, one of which numbers

36

5

33

4

2

31

25

29

10

9

26

12

18

20

22

21

17

13

19

14

16

15

23

24

7

11

27

28

8

30

6

32

3

34

35

1

Fig. 10.

Fig. ii.

Fig. 12.

occupies the cell in which the symbol is placed. In other
words we shall assume that Fig. ga indicates what we have
hitherto represented as in Fig. gb. Further, it is quite
unnecessary to use two symbols for a vertical or horizontal
change, for Fig. Qc sufficiently indicates the same as Fig.
gd. If these abbreviations are granted, a scheme like Fig.

THE THEORY OF REVERSIONS. 59

5 may be replaced by a small square like Fig. 10, which is
to be applied to the top left-hand corner of the natural 62.

Fig. ii is the extended scheme from Fig. 10, and Fig.
12 is the resulting magic. The small squares of symbols
like Fig. 10 may be called "index squares"

The law of formation for index squares is sufficiently
obvious. To secure magic rows and columns in the re-
sulting square, the symbols — and must occur once on
each row and column of the index, and the symbol X an
equal number of times on each row and column; that is,
if there are two series X X .... X the symbol X must ap-
pear twice in every row and twice in every column, and
so on. But we already know by the theory of paths that
these conditions can be assured by laying the successive
symbolic periods along parallel paths of the index, whose
coordinates are prime to the order of the index. If we
decide always to use parallel diagonal paths and always
to apply the index to the top left-hand corner of the nat-
ural square, the index square will be completely represented
by its top row. In Fig. 10 this is |X|~~1 1 1 , which we may call
the index-rod of the square, or we may simply call Fig. 12
the magic |x|-| H. Remembering that we require (n — 2)/4
sets of skew reversions when n = 2 (mod 4) and n/4 when
n = o, it is obvious that the following rule will give crude
magic squares of any even order n :

Take a rod of n/2 cells, n/4 symbols of the form X,
(using the integral part of n/4 only), and if there is a re-
mainder when n is divided by 4, add the symbols | and — .
Place one of the symbols X in the left-hand cell of the rod,
and the other symbols in any cell, but not more than one
in each cell. The result is an index-rod for the magic n2.

Take a square lattice of order n/2, and lay the rod along
the top row of the lattice. Fill up every diagonal slant-
ing downward and to the right which has a symbol in
its highest cell with repetitions of that symbol. The re-

6o

THE MONIST.

suiting index-square if applied to the lop left-hand corner
of the natural n2, with the symbols allowed the operative
powers already defined, will produce the magic n2.

The following are index-rods for squares of even or-
ders:

I02 |x| jilxH
122 |x| I ixlxl I

14^ IxHxl I ixjil

When the number of cells in the rod exceeds the num-
ber of symbols, as it always does excepting with &, the first
cell may be left blank. Also, if there are sufficient blank
cells, a X may be replaced by two vertical and two hori-
zontal symbols. Thus I22 might be given so |x| 1 1 1 |-|xH

144

134

135

9

140

7

6

137

4

10

11

133

24

131

123

124

20

127

126

17

21

22

122

13

120

35

118

112

113

31

30

32

33

111

26

109

48

107

46

105

101

102

43

44

100

39

98

37

85

59

94

57

92

90

55

89

52

87

50

60

73

74

70

81

68

79

78

65

76

63

71

72

61

62

75

69

77

67

66

80

64

82

83

84

49

86

58

88

56

54

91

53

93

51

95

96

97

47

99

45

41

42

103

104

40

106

38

108

36

110

34

28

29

114

115

116

117

27

119

25

121

23

15

16

125

19

18

128

129

130

14

132

12

2

3

136

8

138

139

5

141

142

143

1

Fig. 13.

Fig. 14.

This presentation of I22 is shown in Figs. 13, 14, and I42
from the index-rod given above, in Figs. 15, 16.

Of course the employment of diagonal paths in the con-
struction of the index is purely a matter of convenience.
In the following index for IO2, (Fig. 17) the skew-symbols

THE THEORY OF REVERSIONS.

61

are placed along two parallel paths (2, i) and the symbols
— and | are then added so that each shall appear once in
each row and once in each column, but neither of them on
the diagonal of the index slanting upward and to the left.

196

13

194

4

5

191

189

8

188

10

11

185

2

183

169

181

26

179

19

20

176

175

23

24

172

17

170

28

168

156

166

39

164

34

35

36

37

159

32

157

41

155

43

153

143

151

52

149

49

50

146

47

144

54

142

56

57

58

138

130

136

65

134

133

62

131

67

129

69

70

126

72

73

123

117

121

78

77

118

80

116

82

83

113

98

111

87

88

108

104

106

105

93

103

95

96

100

85

99

97

101

102

94

90

92

91

107

89

109

110

86

112

84

114

115

81

75

79

119

120

76

122

74

124

125

71

127

128

68

60

66

132

64

63

135

61

137

59

139

140

141

55

45

53

145

51

147

148

48

150

46

152

44

154

42

30

40

158

38

160

161

162

163

33

165

31

167

29

15

27

171

25

173

174

22

21

177

178

18

180

16

182

14

184

12

186

187

9

7

190

6

192

193

3

195

1

Fig. 15-

Fig. 16.

Crude cubes of even orders we shall treat by the index-
rod as in the section on squares. The reader will remember
that we constructed squares of orders = o (mod 4) by re-

Fig. 17.

versing half the rows and half the columns, and it is easy
to obtain an analogous method for the cubes of the same
family. Suppose we reverse half the V-planes3 in asso-

8 P-plane = Presentation-, or Paper-plane ; H-plane = Horizontal plane ;
V-plane = Vertical plane.

62

THE MONIST.

ciated pairs; that is, turn each through an angle of 180°
round a horizontal axis parallel to the paper-plane so that
the associated columns in each plane are interchanged and
reversed. We evidently give to every row of the cube the
magic sum, for half the numbers in each row will be ex-

1

62

63

4

5

58

59

8

9

54

55

12

13

50

51

16

33

30

31

36

37

26

27

40

41

22

23

44

45

18

19

48

1

62

63

4

56

11

10

53

60

7

6

57

13

50

51

16

33

30

31

36

24

43

42

21

28

39

38

25

45

18

19

48

Magic in rows and columns.
Fig. 19. Being Fig. 18 with H-planes reversed.

1

62

63

4

56

11

10

53

60

7

6

57

13

50

51

16

32

35

34

29

41

22

23

44

37

26

27

40

20

47

46

17

48

19

18

45

25

38

39

28

21

42

43

24

36

31

30

33

Magic in rows, columns and lines.
Fig. 20. Being Fig. 19, with P-planes reversed.

CRUDE MAGIC 43.

changed for their complementaries. If we do likewise
with H-planes and P-planes the rows and lines4 will become
magic. But as with the square, and for like reasons, these
three operations can be performed without mutual inter-
ference. Hence the simple general rule for all cubes of the
double-of-even orders :

*"Lme" = a contiguous series of cells measured at right angles to the
paper-plane.

THE THEORY OF REVERSIONS.

Reverse, in associated pairs, half the V -planes, half the
H-planes, and half the P-planes.

With this method the central great diagonals, of course,
maintain their magic properties, as they must do for the
cube to be considered even a crude magic.5 To make the
operation clear to the reader we append views of 43 at each

ABC

6'74

7'

46

6'47

2e35

47'6

45'8

'7

46

'7

64

2538

53

82

47

"

28

83S2

.X

"

58

2538

V

3

s35a

Fig. 21.

separate stage, the central pair of planes being used at
each reversion.

By this method the reader can make any crude magic
cube of order qm. With orders of form 4^+2 we find
the same difficulties as with squares of like orders. So
far as we are aware no magic cube of this family had been

15

19

8

7

14

21

20

9

13

26

6

10

12

25

5

4

11

27

Fig. 22.

constructed until Firth succeeded with 63 in 1889, and we
believe those we shall presently construct are the first
which have been published.6 Firth's original cube was
built up by the method of "pseudo-cubes," being an exten-
sion to solid magics of Thompson's method. The cube of
216 cells was divided into 27 subsidiary cubes each con-

5 A cube which is faulty on one of its central great diagonals is no more a
magic than is a square which is faulty on one of its central diagonals.

6 The recent examples published by Willis and Kingery fail in their central
great diagonals, a fatal defect.

64

THE MONIST.

taining 2 cells in an edge. The 8 cells of each subsidiary
were filled with the numbers I to 8 in such a way that each
row, column, line, and central great diagonal of the large
cube summed 27. The cube was then completed by using
the magic 33 in the same way that 62 is constructed from
32. Firth formulated no rule for arrangement of the num-
bers in the pseudo-cubes, and great difficulty was encoun-
tered in balancing the central great diagonals. His pseudo-

II

ill

2

8

134

129

186

192

6

4

130

133

190

188

182

178

21

24

121

125

177

181

22

23

126

122

144

138

174

169

16

10

140

142

170

173

12

14

5

3

132

135

189

187

1

7

136

131

185

191

180

184

18

19

127

123

183

179

17

20

124

128

139

141

172

175

11

13

143

137

176

171

15

9

117

114

146

152

62

60

118

113

150

148

64

58

54

50

109

106

168

164

52

56

110

105

162

166

154

160

70

68

97

102

156

158

66

72

98

101

120

115

149

147

63

59

119

116

145

151

61

59

51

55

112

107

161

165

53

49

111

108

167

163

155

157

65

71

100

103

153

159

69

67

99

104

206

204

42

45

78

76

202

208

46

41

74

80

89

93

198

199

38

34

94

90

197

200

33

37

28

30

82

85

212

214

32

26

86

81

216

210

201

207

48

43

73

79

205

203

44

47

77

75

95

91

193

196

36

40

92

96

194

195

39

35

31

25

88

83

215

209

27

29

84

87

211

213

IV

V
Fig. 23.

VI

skeleton is shown in Fig. 21, where each plate represents
two P-planes of 63, each plate containing 9 pseudo-cubes.
The numbers in the subsidiaries are shown in diagram-
matic perspective, the four "larger" numbers lying in the
anterior layer, and the four "smaller" numbers, grouped
in the center, in the posterior layer.

If we use this with the magic of Fig. 22 we obtain the
magic 63 shown in Fig. 23.

THE THEORY OF REVERSIONS. 65

This cube is non-La Hireian, as is frequently the case
with magics constructed by this method.

The scheme of pseudo-cubes for 63 once found, we can
easily extend the method to any double-of-odd order in the
following manner. Take the pseudo-scheme of next lower
order [e. g., 63 to make io3, io3 to make 143 etc.] . To each
of three outside plates of cubes, which meet at any corner
of the skeleton, apply a replica-plate, and to each of the
other three faces a complementary to the plate opposed to
it, that is a plate in which each number replaces its com-
plementary number ( i for 8, 2 for 7, etc. ) . We now have
a properly balanced skeleton for the next double-of-odd
order, wanting only its 12 edges. Consider any three
edges that meet at a corner of the cube; they can be com-
pleted (wanting their corner-cubes) by placing in each
of them any row of cubes from the original skeleton. Each
of these three edges has three other edges parallel to it,
two lying in the same square planes with it and the third
diagonally opposed to it. In the former we may place
edges complementary to the edge to which they are par-
allel, and in the latter a replica of the same. The skeleton
wants now only its 8 corner pseudo-cubes. Take any cube
and place it in four corners, no two of which are in the
same row, line, column, or great diagonal (e. g. B, C. E, H
in Fig. 38), and in the four remaining corners place its
complementary cube. The skeleton is now complete, and
the cube may be formed from the odd magic of half its
order.

This method we shall not follow further, but shall now
turn to the consideration of index-cubes, an artifice far
preferable.

Before proceeding the reader should carefully study
the method of the index-rod as used for magic squares
(pp. 57-61).

The reversion of a pair of planes in each of the three

66

THE MONIST.

aspects, as previously employed for 43, is evidently equiva-
lent to interchanging two numbers with their complemen-
taries in every row, line, and column of the natural cube.
If therefore we define the symbol X as implying that such
an interchange is to be made not only from the cell in
which it is placed, but also from the three other cells with
which it is symmetrically situated in regard to the central
horizontal and vertical bars of its P-plane, and can make

Fig. 24.

one such symbol operate in every row, line and column of
an index-cube whose edge is half that of the great cube,
we shall have secured the equivalent of the above-men-
tioned reversion. For example, a X placed in the second
cell of the top row of any P-plane of 43, will denote that the
four numbers marked a in Fig. 24 are each to be inter-
changed with its complement, which lies in the associated
cell in the associated P-plane.

FIG. 25.

From this it follows that we shall have a complete
reversion scheme for any order 4m, by placing in every
row, line and column of the index (2m) 3, m of the symbols
X. In the case of orders 47/1+2, after placing m such sym-
bols in the cube (2m-(-i)3, we have still to make the equiva-
lent of one reversed plane in each of the three aspects.
This amounts to making one symmetrical vertical inter-
change, one symmetrical horizontal interchange, and one

THE THEORY OF REVERSIONS. 67

symmetrical interchange at right angles to the paper-plane
in every row, line and column. If we use the symbol | to
denote such a vertical interchange, not only for the cell
in which it stands, but also for the associated cell, and give
like meanings to — and ', for horizontal changes and
changes along lines, we shall have made the broken re-
version when we allow each of these symbols to operate
once in every row, column and line of the index. For
example, a in Fig. 25 means b in its own P-plane, and c in
the associated P-plane ; while d indicates that the numbers
lying in its own P-plane as in e are to be interchanged, A
with A and B with B, with the numbers lying in the asso-
ciated plane f. We can always prepare the index, provided
the rod does not contain a less number of cells than the
number of symbols, by the following rule, n being the
order.

Take an index-rod of n/2 cells, n/4 symbols of the form
X, (using the integral part of 11/4. only), and if there is
any remainder when n is divided by 4 add the three sym-
bols |, — , •. Now prepare an index square in the way
described on p. 59, but using the diagonals upward and
to the right instead of upward to the left,7 and take this
square as the first P-plane of an index-cube. Fill every
great diagonal of the cube, running to the right, down and
away, which has a symbol in this P-plane cell, with repeti-
tions of that symbol.8 This index-cube applied to the near,
left-hand, top corner of the natural n$, with the symbols
allowed the operative powers already defined, will make
the magic n$.

This method for even orders applies universally with
the single exception of 63, and in the case of 63 we shall
presently show that the broken reversion can still be made

1 Either way will do, but it happens that the former has been used in the
examples which follow.

8 More briefly, in the language of Paths, the symbols are laid, in the square,
on (1,1) ; their repetitions in the cube, on (i, — I, i).

68

THE MONIST.

by scattering the symbols over the whole cube. The fol-
lowing are index-rods for various cubes.

43
83

123 I I JXjXl |X|

I43 I IxHxHxl

103 |x|l|-|x|.|

As in the case of index-rods for squares, the first cell
may be left blank, otherwise it must contain a X.

II

in

64

2

3

61

5

59

58

8

9

55

54

12

52

14

15

49

48

18

19

45

21

43

42

24

25

39

38

28

36

30

31

33

Fig. 26.

Fig. 26 is a 43, made with the index-rod given above.
It has only half the numbers removed from their natural
places. Figs. 27 and 28 are the index-rod, index-square
and index-cube for io3, and Fig. 29 is the extended rever-
sion scheme obtained from these, in which \ and / denote
single changes between associated cells, and the symbols
|, — , and •, single changes parallel to columns, rows, and
lines. Figs. 30 and 31 show the resulting cube.

I*!*!* I i M

Index Rod.

Index Square.

Fig. 27.

Fig. 28. Index Cube.

THE THEORY OF REVERSIONS.

\

\

•

\

-

-

/

/

1

—

X

X

•

/

/

-

X

•

1

—

X

/

-

/

s

•

1

-

X

/

—

/

-

X

X

•

1

/

/

—

•

1

—

X

X

/

/

—

•

1

—

X

X

/

/

—

X

X

•

—

-

/

/

1

—

X

X

•

/

/

—

1

-

X

X

•

/

/

—

X

•

1

—

X

/

—

/

—

X

X

•

1

/

/

—

-

\

X

•

1

/

/

—

•

1

—

X

X

/

/

-

X

X

•

1

—

—

/

s

/

/

1

•

X

\

1

/

/

\

X

•

/

/

1

•

X

X

1

/

/

•

X

X

/

1

/

X

•

X

/

/

1

•

X

X

\

/

/

X

X

•

/

/

1

•

X

X

1

/

/

•

X

X

/

\

/

X

.

X (

/

/

1

•

X

X

1

/

/

X

X

•

/

/

1

•

X

X (

1

/

/

•

X

\

/

1

/

X

•

X

—

X

X

•

1

/

/

—

•

1

—

X

X

/

/

—

•

X

X

/

/

1

\

\

•

1

—

—

/

/

1

—

X

X

•

/

/

—

X

X

•

/

/

1

s

•

1

—

\

/

—

/

—

\

X

•

1

s

/

—

X

X

•

1

/

/

•

1

—

X

X

/

/

—

X

X

•

1

—

—

/

/

X

X

•

1

/

/

1

—

X

X

•

/

/

—

X

•

1

—

X

/

—

/

X

•

X

/

\

/

1

/

/

•

X

X

/

1

/

X

•

\

/

—

/

X

—

\

•

X

1

/

/

X

X

•

/

/

1

•

X

X

/

/

—

—

1

•

X

X

/

1

/

X

•

X

/

/

\

•

X

X

-

/

/

1

•

X

X

—

/

/

1

*

\

X

\

/

/

•

X

X

—

/

/

•

X

X

—

1

/

/

1

•

X

X

1

/

/

X

X

•

—

/

/

X

X

—

1

•

X

X

•

1

/

/

X

•

X

/

1

/

X

X

•

/

/

1

\

X

•

1

/

/

•

X

X

/

/

I

X

X

•

1

/

/

\

•

X

/

\

/

X

X

•

/

/

\

X

X

•

1

/

/

•

X

X

/

/

\

X

X

•

\

/

/

X

•

X

/

\

/

X

\

•

/

/

\

X

X

•

\

/

/

•

X

X

/

/

\

—

/

/

•

X

X

—

\

/

/

—

-

\

•

X

X

—

/

/

X

X

—

\

•

—

/

/

\

X

—

1

•

~

/

/

1

•

X

X

—

/

—

/

X

—

1

•

X

/

—

/

X

—

1

•

X

—

/

/

•

X

X

—

1

/

/

—

—

1

•

X

X

/

/

—

—

I

•

X

X

~

/

/

X

X

—

i

•

—

/

/

1

•

X

X

—

—

/

/

!

•

Ni

X

—

/

—

/

X

~

!

.

X

—

/

/

•

X

\

—

1

X

X

•

1

/

/

X

•

X

/

1

/

•

X

X

/

/

1

X

X

•

/

/

1

X

X

•

\

/

/

—

/

/

1

•

X

X

—

—

/

/

•

X

X

—

1

—

/

/

X

X

—

1

•

' /

—

/

X

—

1

•

X

/

/

-

-

1

•

X

X

Fig. 29. Extended Reversion Scheme for io8.

THE MONIST.

100C

999

903

94

6

5

7

8

992

991

990

912

83

17

986

985

14

18

19

981

921

72

28

977

976

975

974

23

29

30

61

39

968

967

935

36

964

963

32

40

SO

959

958

944

55

46

47

953

952

41

51

949

948

54

45

56

957

943

942

60

31

62

938

937

65

966

934

933

69

70

71

22

73

927

926

925

924

78

79

980

920

82

13

84

916

915

87

88

989

911

910

909

93

4

95

96

97

998

902

901

800

702

293

207

796

795

204

208

209

791

711

282

218

787

786

785

784

213

219

220

271

229

778

777

725

226

774

773

222

230

240

769

768

734

265

236

237

763

762

231

760

759

743

254

246

245

247

248

752

751

750

749

253

244

255

256

257

758

742

741

261

739

738

264

235

266

767

733

732

270

221

272

728

727

275

776

724

723

279

280

281

212

283

717

716

715

714

288

289

790

710

292

203

294

706

705

297

298

799

701

501

492

408

597

596

595

594

403

409

410

481

419

588

587

515

416

584

583

412

420

430

579

578

524

475

426

427

573

572

421

570

569

533

464

436

435

437

438

562

561

560

542

453

447

556

555

444

448

449

551

550

452

443

454

546

545

457

458

559

541

540

539

463

434

465

466

467

568

532

531

471

529

528

474

425

476

577

523

522

480

411

482

518

517

485

586

514

513

489

490

491

402

493

507

506

505

504

498

499

600

191

109

898

897

805

106

894

893

102

110

120

889

888

814

185

116

117

883

882

111

880

879

823

174

126

125

127

128

872

871

870

832

163

137

866

865

134

138

139

861

841

152

148

857

856

855

854

143

149

150

151

142

153

847

846

845

844

158

159

860

840

162

133

164

836

835

167

168

869

831

830

829

173

124

175

176

177

878

822

821

181

819

818

184

115

186

887

813

812

190

101

192

808

807

195

896

804

803

199

200

310

699

698

604

395

306

307

693

692

301

690

689

613

384

316

315

317

318

682

681

680

622

373

327

676

675

324

328

329

671

631

362

338

667

666

665

664

333

339

340

351

349

658

657

645

346

654

653

342

350

341

352

648

647

355

656

644

643

359

360

361

332

363

637

636

635

634

368

369

670

630

372

323

374

626

625

377

378

67,9

621

620

619

383

314

385

386

387

688

612

611

391

609

608

394

305

396

697

603

602

400

401

502

503

497

496

495

494

508

599

510

511

512

488

487

415

516

484

483

519

590

521

479

478

424

525

576

527

473

472

530

470

469

433

534

535

536

567

538

462

461

460

442

543

544

456

455

547

558

549

451

450

552

553

557

446

445

554

548

459

441

440

439

563

564

566

565

537

468

432

431

580

429

428

574

575

526

477

423

422

571

581

589

418

417

585

486

414

413

582

520

591

592

598

407

406

405

404

593

509

500

Fig. 30. First 6 plates of io8, made from Fig. 29. (Sum = 5005.)

THE THEORY OF REVERSIONS.

601

399

398

304

605

696

607

393

392

610

390

389

313

614

615

616

687

618

382

381

380

322

623

624

376

375

627

678

629

371

331

632

633

367

366

365

364

638

669

640

641

642

358

357

345

646

354

353

649

660

651

659

348

347

655

356

344

343

652

650

661

662

668

337

336

335

334

663

639

370

330

672

673

677

326

325

674

628

379

321

320

319

683

684

686

685

617

388

312

311

700

309

308

694

695

606

395

303

302

691

300

202

703

704

296

295

707

798

709

291

211

712

713

287

286

285

284

718

789

720

721

722

278

277

225

726

274

273

729

780

731

269

268

234

735

766

737

263

262

740

260

259

243

744

745

746

757

748

252

251

250

249

753

754

756

755

747

258

242

241

770

239

238

764

765

736

267

233

232

761

771

779

228

227

775

276

224

223

772

730

781

782

788

217

216

215

214

783

719

290

210

792

793

797

206

205

794

708

299

201

801

802

198

197

105

806

194

193

809

900

811

189

188

114

815

886

817

18.1

182

820

180

179

123

824

825

826

877

828

172

171

170

132

833

834

166

165

837

868

839

161

141

842

843

157

156

155

154

848

859

850

851

852

858

147

146

145

144

853

849

160

140

862

863

867

136

135

864

838

169

131

130

129

873

874

876

875

827

178

122

121

890

119

118

884

885

816

187

113

112

881

891

899

108

107

893

196

104

103

892

810

100

99

3

904

905

906

997

908

92

91

90

12

913

914

86

85

917

988

919

81

21

922

923

77

76

75

74

928

979

930

931

932

68

67

35

936

64

63

939

970

941

59

58

44

945

956

947

53

52

950

960

49

48

954

955

946

57

43

42

951

961

969

38

37

965

66

34

33

962

940

971

972

978

27

26

25

24

973

929

80

20

982

983

987

16

15

984

918

89

11

10

9

993

994

996

995

907

98

2

1

Fig. 31. Last 4 plates of 10', made from Fig. 29. (Sum = 5005.)

If we attack 63 by the general rule, we find 4 symbols,
X, — , |, *, and only 3 cells in the rod; the construction is
therefore impossible. Suppose we construct an index-cube
from the rod |x|i|-|, we shall find it impossible to distribute
the remaining symbol H in the extended reversion-scheme
obtained from this index. The feat, however, is possible
if we make (for this case only) a slight change in the
meanings of | and — . By the general rule X operates on
4 cells in its own P-plane, where, by the rule of association,

i with 6

the planes are paired thus:

In interpreting

THE MONIST.

Thus for

1 with 5

2 " 4

3 " 6

This

the meanings of | and — , in this special case, we must make
a cyclic change in the right-hand column of this little table.

i with 4

and for "— " 2 " 6
3 5

means that a M, for example, in the second P-plane has its
usual meaning in that plane, and also acts on the two cells
which would be the associated cells if the 4th plane were
to become the 5th, etc. If we extend this scheme, there
will be just room to properly distribute the M's in the two
parallelepipeds which form the right-hand upper and left-
hand lower quarters of the cube, as shown in Fig. 32.

ii

IV V VI

Fig. 32. Extended Reversion-Scheme for 6*.

This scheme produces the cube shown below, which is
magic on its 36 rows, 36 columns, 36 lines, and on its 4
central great diagonals.

Fig. 32 is the identical scheme discovered by Firth in
1889, and was obtained a few months later than the pseudo-
skeleton shown in Fig. 21. A year or two earlier he had
discovered the broken reversion for squares of even order,
but he never generalized the method, or conceived the idea
of an index-cube. The development of the method as here
described was worked out by the present writer in 1894.

THE THEORY OF REVERSIONS.

73

About the same time Rouse Ball, of Trinity College, Cam-
bridge, independently arrived at the method of reversions
for squares (compare the earlier editions of his Mathemat-
ical Recreations, Macmillan), and in the last edition, 1905,
he adopts the idea of an index-square ; but he makes no ap-
plication to cubes or higher dimensions. There is reason
to believe, however, that the idea of reversions by means
of an index-square was known to Fermat. In his letter to

ii

in

216

32

4

3

185

211

25

11

208

207

8

192

18

203

21

196

200

13

199

197

15

22

194

24

7

206

190

189

29

30

186

2

213

34

35

181

67

41

178

177

38

150

48

173

63

154

170

43

168

56

52

51

161

163

162

50

165

58

59

157

169

155

45

64

152

66

37

176

148

147

71

72

78

143

105

112

140

73

138

98

82

81

119

133

91

89

130

129

86

126

85

128

124

123

95

96

120

80

135

100

101

115

139

113

75

106

110

108

109

107

111

76

104

144

102

116

117

136

83

97

121

122

94

93

131

90

132

92

88

87

125

127

84

137

99

118

134

79

103

77

142

141

74

114

145

146

70

69

179

42

151

65

153

46

62

174

60

158

159

166

53

55

54

167

57

160

164

49

61

47

172

171

44

156

180

68

40

39

149

175

36

182

183

214

5

31

187

188

28

27

209

12

193

23

195

16

20

204

19

17

202

201

14

198

210

26

10

9

191

205

6

215

33

184

212

A

IV

VI

Fig. 33, made from Fig. 32. Sum = 651.

Mersenne of April i, 1640, (CEuvres de Fermat, Vol. II,
p. 193), he gives the square of order 6 shown in Fig. 34.
This is obtained by applying the index (Fig. 35) to the
bottom left-hand corner of the natural square written from
below upwards, i. e., with the numbers i to 6 in the bottom
row, 7 to 12 in the row above this, etc. There is nothing
surprising in this method of writing the natural square,
in fact it is suggested by the conventions of Cartesian
geometry, with which Fermat was familiar. There is a

74

THE MONIST.

much later similar instance: Cayley, in 1890, dealing with
"Latin squares," writes from below upwards, although
Euler, in his original Memoire (1782), wrote from above
downwards. Another square of order 6, given by Fermat,
in the same place, is made from the same index, but is dis-
guised because he uses a "deformed" natural square.

6

32

3

34

35

1

7

11

27

28

8

30

19

14

16

15

23

24

18

20

22

21

17

13

25

29

10

9

26

12

36

5

33

4

2

31

Fig. 34-

Fig. 35-

It is interesting to note that all these reversion magics
(unlike those made by Thompson's method), are La Hire-
ian, and also that the La Hireian scheme can be obtained
by turning a single outline on itself. To explain this state-
ment we will translate the square in Fig. 12 into the scale

A

55

04

52

03

01

50

40

44

13

12

41

15

25

31

33

32

24

20

30

21

23

22

34

35

10

14

42

43

11

45

05

51

02

53

54

00

Fig. 36.

whose radix is 6, first decreasing every number by unity.
This last artifice is merely equivalent to using the n2 con-
secutive numbers from o to n2 — I, instead of from i to n2,
and is convenient because it brings the scheme of units
and the scheme of 6's digits into uniformity.

If we examine this result as shown in Fig. 36 we

THE THEORY OF REVERSIONS.

75

find that the scheme for units can be converted into that
for the 6's, by turning the skeleton through 180° about
the axis AB; that is to say, a single outline turned upon
itself will produce the magic.

ii

in

555

051

003

002

504

550

040

014

543

542

Oil

515

025

534

032

523

531

020

530

524

022

033

521

035

010

541

513

512

044

045

505

001

552

053

054

500

150

104

453

452

101

405

115

444

142

413

441

110

435

131

123

122

424

430

425

121

432

133

134

420

440

414

112

143

411

145

100

451

403

402

154

155

205

354

252

303

351

200

345

241

213

212

314

340

230

224

333

332

221

325

220

331

323

322

234

235

315

211

342

243

244

310

350

304

202

253

301

255

300

254

302

203

251

355

245

311

312

343

214

240

320

321

233

232

334

225

335

231

223

222

324

330

215

344

242

313

341

210

250

204

353

352

201

305

400

401

153

152

454

105

410

144

412

113

141

445

135

421

422

433

124

130

125

434

132

423

431

120

140

114

443

442

111

415

455

151

103

102

404

450

055

501

502

553

004

050

510

511

043

042

544

015

520

034

522

023

031

535

030

024

533

532

021

525

545

041

013

012

514

#0

005

554

052

503

551

000

Fig. 37-

The same is true of the cube; that is, just as we can
obtain a La Hireian scheme for a square by turning a
single square outline once upon itself, so a similar scheme
for a cube can be obtained by turning a cubic outline

Fig. 38. Fig. 39. Fig. 40.

twice upon itself. If we reduce all the numbers in Fig.
33 by unity and then "unroll" the cube, we get the La Hire-
ian scheme of Fig. 37 in the scale radix 6.

If now we represent the skeleton of the62>s : (left-hand)
digits by Fig. 38, and give this cube the "twist" indicated

THE MONIST.

by Fig. 39, we shall get the skeleton of the 6's (middle)
digits, and the turn suggested by Fig. 40 gives that of the
units (right-hand) digits. Thus a single outline turned
twice upon itself gives the scheme.

We can construct any crude magic octahedroid9 of

Fig. 41, ist reversion. Fig. 42, 2d reversion. Fig. 43, 3d reversion.

as

double-of-Jeven order, by the method of reversions,
shown with 44 in Figs. 41 to 44.

The first three reversions will be easily understood
from the figures, but the fourth requires some explanation
It actually amounts to an interchange between every pair

A B C D

Fig. 44, 4th reversion.

of numbers in associated cells of the parallelepiped formed
by the two central cubical sections. If the reader will use
a box or some other "rectangular" solid as a model, and
number the 8 corners, he will find that such a change can-
not be effected in three-dimensional space by turning the

DIMENSIONS

REGULAR FIGURE

BOUNDARIES

2

3
4
etc.

Tetragon (or square)
Hexahedron (cube)
Octahedroid
etc.

4 one-dimensional straight lines
6 two-dimensional squares
8 three-dimensional cubes
etc.

THE THEORY OF REVERSIONS.

77

parallelepiped as a whole, on the same principle that a right
hand cannot, by any turn, be converted into a left hand.
But such a change can be produced by a single turn in
4-dimensional space; in fact this last reversion is made
with regard to an axis in the 4th, or imaginary direction.

1

2

3

4

248

247

246

245

252

251

250

249

13

14

15

16

129

130

131

132

120

119

118

117

124

123

122

121

141

142

143

144

Fig- 45-

The following four figures (45-48) show each stage of the
process, and if the reader will compare them with the re-
sults of a like series of reversions made from a different
aspect of the natural octahedroid, he will find that the
"imaginary'' reversion then becomes a real reversion, while

THE MONIST.

one of the reversions which was real becomes imaginary.
Fig. 45 is the natural 44 after the first reversion, magic in
columns only; Fig. 46 is Fig. 45 after the second reversion,
magic in rows and columns; Fig. 47 is Fig. 46 after the
third reversion, magic in rows, columns and lines; and

33

222

223

36

216

43

42

213

220

39

38

217

45

210

211

48

49

206

207

52

200

59

58

197

204

55

54

201

61

194

195

64

65

190

191

68

184

75

74

181

188

71

70

185

77

178

179

80

81

174

175

84

168

91

90

165

172

87

86

169

93

162

163

96

97

158

159

100

152

107

106

149

156

103

102

153

109

146

147

112

113

142

143

116

136

123

122

133

140

119

118

137

125

130

131

128

129

126

127

132

120

139

138

117

124

135

134

121

141

114

115

144

145

110

111

148

104

155

154

101

108

151

150

105

157

98

99

160

161

94

95

164

88

171

170

85

92

167

166

89

173

82

83

176

177

78

79

180

72

187

186

69

76

183

182

73

189

66

67

192

193

62

63

196

56

203

202

53

60

199

198

57

205

50

51

208

209

46

47

212

40

219

218

37

44

215

214

41

221

34

35

224

225

30

31

228

24

235

234

21

28

231

230

25

237

18

19

240

Fig. 46.

Fig. 48 is Fig. 47 after the fourth reversion, magic in rows,
columns, lines and i's, = crude magic 44. The symbol i
denotes series of cells parallel to the imaginary edge.

Fig. 48 is magic on its 64 rows, 64 columns, 64 lines,
and 64 i's, and on its 8 central hyperdiagonals. Through-

THE THEORY OF REVERSIONS.

79

out the above operations the columns of squares have been
taken as forming the four cells of the Pi-aspect ;10 the rows
of squares taken to form cubes, of course, show the P2-
aspect.

1

254

255

4

248

11

10

245

252

7

6

249

13

242

243

16

65

190

191

68

184

75

74

181

188

71

70

185

77

178

179

80

224

35

34

221

41

214

215

44

37

218

219

40

212

47

46

209

48

211

210

45

217

38

39

220

213

42

43

216

36

223

222

33

177

78

79

180

72

187

186

69

76

183

182

73

189

66

67

192

241

14

15

244

8

251

250

5

12

247

246

9

253

2

3

256

Fig. 47-

This construction has been introduced merely to ac-
centuate the analogy between magics of various dimen-
sions; we might have obtained the magic 44 much more

10 Since the 4th dimension is the square of the second, two aspects of the
pctahedroid are shown in the presentation plane. The 3d and 4th aspects are
in H-planes and V-planes. Since there are two P-plane aspects it might appear
that each would produce a different H-plane and V-plane aspect; but this is
a delusion.

8o

THE MONIST.

rapidly by a method analogous to that used for 43 (Fig.
26). We have simply to interchange each number in the
natural octahedroid occupying a cell marked tx] in Fig. 49,
with its complementary number lying in the associated cell

1 >

254

255

4

248

11

10

245

252

7

6

249

13

242

243

16

128

131

130

125

137

118

119

140

133

122

123

136

116

143

142

113

161

94

95

164

88

171

170

85

92

167

166

89

173

82

83

176

145

HO

111

148

104

155

154

101

108

151

150

105

157

98

99

160

48

211

210

45

217

38

39

220

213

42

43

216

36

223

222

33

241

14

15

244

8

251

250

5

12

247

246

9

253

2

3

256

Fig. 48.

of the associated cube. Fig. 49 is the extended skew-
reversion scheme from the index-rod I |x|.

All magic octahedroids of double-of-odd order >io4
can be constructed by the index-rod, for just as we con-
struct an index-square from the rod, and an index-cube
from the square, so we can construct an index-octrahedroid

THE THEORY OF REVERSIONS.

8l

from the cube. The magics 64 and io4 have not the capac-
ity for construction by the general rule, but they may be

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Fig. 49. Skew Reversion for 4*.

obtained by scattering the symbols over the whole figure
as we did with 63.

C. PLANCK.
HAYWARD'S HEATH, ENGLAND.

TWO STUDIES IN SUGGESTION.

THE BOXERS.

A^L the world knows how the North of China was con-
vulsed in the year 1900 by a wave of patriotic feeling
stimulated by certain enthusiasts named by foreigners
"Boxers." It is not quite so well known that this enthu-
siasm was propagated by recognized methods of psychical
excitement.

This society, known as the / ho ch'uan or "Public Har-
mony Fists," arose in Shantung province, and, by the con-
nivance of certain local officials whose national feelings
outran their prudence, expanded and spread throughout
that province and into the adjoining one of Chin-Li. In
the course of the summer of 1900 all the provinces north
of the Yellow River were permeated, the matter coming
to a climax in the famous siege of the Peking legations.

All narrators agree that certain rites were performed
by the propagators of the movement, which came to receive
the vague title of "Boxer drill."

The following quotations will indicate the general na-
ture of this process :

A. "They were not successful in getting the people to
take it up at first, so they began with boys ten to twelve
years of age. . . . After a few days it grew very rapidly.
The drill, if it may be called so, consists in the boy repeating
four short lines of some mystic words, and bowing to the
south and falling backwards, when he goes into a trance,

TWO STUDIES IN SUGGESTION. 83

remaining lying on his back for an indefinite time, when
he rises and is endowed with wonderful strength, boys
of twelve being as strong as men. They brandish swords
and spears, not seeming to try to be skilful in handling
them, but merely to show strength and place themselves
under the protection of their symbols. They claim to be
invulnerable." — Rev. C. W. Price of Fen-Chou-Fu, Shansi,
in With Fire and Sword in Shan-si (Diary, June i, 1900).

B. "Drill consisted in incense before a tablet. . . .and
then working themselves by gymnastics, etc., into a state
when they were no longer masters of themselves, but be-
came unconscious. After remaining in this state for some
time they would rise, declaring themselves possessed by
the spirit of one of the heroes of antiquity. In this state
they could perform great feats, but the chief mark was
that they were invulnerable. Swords did not hurt, and
they knocked their heads till great bumps appeared, but
never felt it." — Slightly abridged from Mrs. A. H. Mateer,
Siege Days, New York, Redell.

According to the Rev. G. T. Candlin (author of Chi-
nese Fiction, Chicago, Open Court Pub. Co.) who was in
Tung Shan during the outbreak, the "four mystic lines"
were as follows, and were accompanied by certain postures
(bowing in the Chinese ceremonial style of prostrating
and beating the head on the ground) :

T'ien ta, T'ien chiu k'ai
Ti ta, Ti chiu k'ai
Yao hstieh I ho ch'uan
Huan te Shih Fu lai.

"Beat the heaven, the heaven will open;
Beat earth, and earth will open;
Desire to learn the public-harmony-force1
Also get the masters to come."

He has also expressed an opinion that Buddhist and
Taoist priests were connected in some way with the move-

1 Ch'uan is "fist" but has in this case the sense of the power of the fist.

84 THE MONIST.

ment and employed hypnotic methods. In this connection
it is interesting to note that Putnam Weale in his famous
book Indiscreet Letters from Peking speaks of a temple
which had been specially frequented by Boxers, and that
native Christians had been murdered there, presumably in
some sense as sacrifices. He also mentions the large part
played by boys in the movement.

If we survey the whole of the information available
(of which the above is but a representative selection) it is
evident that

1. Ceremonial rites including prostrations and chants
formed the initial feature of the process and were pro-
longed until the cerebral consciousness became dormant;

2. A period of trance supervened;

3. The trance was followed by a period of great excite-
ment in which excessive muscular energy and anesthesia
were shown;

4. Boys were more subject to the influence than men,
but once started it was very contagious ;

5. The dominant idea was to expel the foreigner, and
this was readily acceptable to the people at the time on
account of public events. This was shown in the motto

Pao ch'ing, mieh yang,
"Guard the Ch'ing Dynasty, destroy the foreigner."

The Chinese are peculiarly subject to the suggestive
value of epigrammatic sentences like this, and in this case
we have not far to look for the master-thought.

The belief in possession by spirits is of course not pe-
culiar to them, but an example of it in China is given in
the Rev. MacGowan's book on Side Lights on Chinese
Life, quoted in my article on "Chinese Philosophy and
Magic" in the Journal of the Royal Society of Arts, April
21, 1911. The Confucian philosophy as expounded by
Chu Hsi implies that the vital spirit in men is one and

TWO STUDIES IN SUGGESTION. 85

the same with that of their ancestors, so that it is not
difficult for them to conceive that the peculiar individuality
of an heroic ancestor may well up in the soul of his descen-
dant. Such an idea forms a simple (and to them, rational)
explanation of the enthusiasm and modification of personal-
ity which immediately succeeded the trance.

The words Shih-Fu, "master," may be taken as singu-
lar, plural or general, just as one thinks fit. Probably the
intellects of the I Ho Ch'iian would instruct their followers
specially as to the particular incarnation with which they
happened to be favored.

The word ta, "to beat," is of very great idiomatic power
in Mandarin speech, and must not necessarily be taken in
its literal sense. It can mean "to appeal to," or "to serve,"
and undoubtedly is to be so taken.

Heaven and earth are of course the great Chinese
polarities, the reservoirs of positive and negative energy.

The general sense of the chants is then that heavenly
and earthly powers will respond if called upon, so that one
should desire the patriotic vigor and call upon the dead to
enthuse one.

The phenomenon of anesthesia (incorrectly regarded as
invulnerability) is of course a usual concomitant of hystero-
epilepsy. The dauntless frenzy of the Mahdi's followers
undoubtedly sprang from the same conviction of personal
safety, their master having assured them that neither
sword nor bullet could harm them.

The success of the influence with boys indicates the
hindrances which the auto-suggestions of reason placed in
the way of the submission of adults. Boys have universally
been employed as "mediums" in the East.2

An interesting point in the whole question is whether
it was incepted by intellects who understand more or less
well the laws of psychology, or merely arose from the nat-

* See Lane's Modern Egyptians.

86 THE MONIST.

ural aggregation of anti-foreign influences. It will per-
haps be useful to consider what are the Chinese notions as
to psychology.

Primitive Psychology in China.

The only character in the ancient Chinese hieroglyph-
ics which takes a permanent place in psychological ideas is
hsin, "the heart." Egyptian and Semitic literature show
the same feature. In all three languages other symbols
are used for external quasi-psychical phenomena, but the
individual's own feelings and thoughts are almost all ex-
pressed in terms of the "heart." In other words, the heart
was regarded as the seat of the intellect and emotions,
presumably because the emotions when of a violent char-
acter affect t|ie "sympathetic" or ganglionic nervous sys-
tem and the heart shows the disturbance most strongly.
As example we cite the following compound characters:
The term "virtue" consists of a radical meaning "to walk"
combined with "straight" and "heart."
The character "like" above "heart" means "reciprocity."
The character "slave" above "heart" means "anger."
The character "receive" above "heart" means "love."
The character "inferior" above "heart" means "hate."
The character "scholar" above "heart" means "will."
The character "mutual" above "heart" means "think."
The character "middle" above "heart" means "sincerity/1

Dual Consciousness in Chinese Psychology.

The distinction between the central energies of the
cerebro-spinal nervous system and those of the ganglionic
(sympathetic) system has only recently been made out
(See Hudson's Law of Psychic Phenomena) and is clearly
adumbrated in the scholastic animus and anima and the Chi-
nese hun and p'o. These are the personalized forms of the
psychic quantities shen and kuei. The energies are re-

TWO STUDIES IN SUGGESTION. 87

spectively termed ch'i and ching, and are regarded as
special forms of the positive (yang} and negative (yin)
polarities of energy. The hun is supposed to wander at
times during life and after death, while the pfo controls the
animal functions and only persists in a shadowy form after
death. Stimulated, the hun manifests as chih the will,
while the p'o is the seat of emotion, Ming.

The ideas outlined above are almost all that can be
gleaned from the ordinarily accessible native works. The
practice of meditation in Buddhist and Taoist monasteries
is undoubtedly based on careful observations of the re-
sults of "religious exercises." The Rev. Timothy Richard
of Shanghai has translated a book which he calls the
"Guide to Buddhahood," Hsiian Fo pfu (literally "The
Record of the Selection of the Buddha").

This is a graduated statement of the development of
the soul on ecstatic lines and reminds one of St. Teresa's
Castillo Interior. Commencing with introspection of mor-
als, it passes to contemplation of virtue and then through
a whole series of meditations on mythological concepts,
which will culminate in Nirvana. The analogy with the
stages of apotheosis described by Plotinus and the Sufis
is obvious.

An acquaintance with such mental conditions (prob-
ably accompanied by strange phenomena in various cases
due to the nervous idiosyncrasies of the individual) would
be quite sufficient to provide a working hypothesis for such
a movement as that of the I-ho-ch'uan. By those who care
for the terminology it may be legitimately called "black
magic," although it amounts to very little more than the
control exerted by religious fanatics generally on those
of their disciples who have been "worked up" to the point
of hysteria. There is this difference, however, that in the
East the moving spirits generally know to some extent
what they are doing, whereas in the West this knowledge

85 THE MONIST.

is only possessed by those who have little or no occasion
to employ it.

In conclusion the writer would point out that the normal
Chinese mind is very acute, but conservative and lacking
initiative. When excited however beyond a certain point,
it exhibits a wild frenzy which is utterly reckless of con-
sequences. These characteristics of course are not peculiar
to the people but seem, at least to the writer, to be more
marked than in the European. Speaking broadly, the
European in China behaves as if he had little or no self-
control in small matters, whereas in important things he
generally becomes cool. With the Chinese it is the re-
verse, perfect nonchalance in ordinary affairs but imper-
fect balance in large ones. The writer does not of course
suggest this is universally true of individuals.

THE MAGICAL USE OF BLOOD.

In the highest and lowest of ceremonial religions, and
almost universally in connection with magic, we find ref-
erences to the potency of blood.

The standard methods of ancestor-worship3 include a
bloody sacrifice to the manes, and an anointing with blood
of the eidolon which represents the spirit. Primitively the
blood is placed in the mouth of the figure. Almost in all
cases it is conceived as providing vitality to the ghost. The
invocation of the ghosts in the Odyssey is a typical case.
The Pentateuch says "the blood is the life," and to this
day the Jews abstain from meat which is not kosher, i. e.,
deprived of blood.

In China there are similar notions. Thus under the
character hsueh, "blood," in Giles's Dictionary the follow-
ing phrase occurs :

Jen hsueh chih wei yeh huo yeh, "Man's blood causes
strange fire."

' See Grant Allen's Evolution of the Idea of God.

TWO STUDIES IN SUGGESTION. 89

This emanation from blood is also termed kuei huo,
"ghostly fire."

Again in the medieval books on magic we find that

1. Numerous prescriptions and charms require blood,
and even bloody sacrifices are necessary in some cases ;

2. Books professing to teach only pure theurgy recom-
mend the practitioner to avoid the use of blood.

The aversion for blood also appears in the practices
of bloodless execution employed by the Turks and the In-
quisition.

The atoning power of blood is referred to in the seven-
teenth chapter of Leviticus, and developed in Christianity
into the eucharistic sacrifice. It is also fairly clearly rec-
ognized in all bloody rites performed in the service of
spirits.

Other references can be drawn from numerous sources.
The marvelous blood-stains which remain on hero's sword
and in haunted house; the practice of signing important
acts (such as pacts with the devil!) in blood; the impurity
of blood when on the person ; all illustrate the general con-
ception of its extraordinary properties.

The persistence and generality of such ideas point to
some underlying psychical fact. At first sight the com-
mon experience of nausea or fainting at the sight of blood
might be regarded as the fundamental cause, but a little
consideration will show that this is either one of the effects
of the cause we seek or a vestigial retro-reminiscence of
the beliefs on the subject which dominated our forefathers.

To the writer it appears that the mere continuous juxta-
position of blood with pain and death in common experi-
ence, extending through untold generations, is quite suffi-
cient to account for the effects and beliefs which have been
referred to, acting in accordance with the laws of psychic
change. In minds which have not been trained to oppose
the quasi-mechanical suggestions of revived memories by

9O THE MONIST.

specially developed associations (religious or scientific),
the percept of blood will . immediately call up memories of
pain and death. These again will be followed by memories
of incipient insensibility and fear, which will tend to be
realized again in the organism by a partial paralysis of the
motor centers etc., i. e., the organism will reproduce as far
as possible the state remembered.

These changes, proceeding from a cause not imme-
diately apparent to sense, are naturally ascribed to an ex-
ternal source, more particularly in view of the fact that
another person (such as a wizard) can by insistent sug-
gestion (with or without hypnosis) set the train of trans-
formation in motion.

Blood has a quite perceptible smell (the extraordinary
sensitiveness of carnivorous animals and insects needs only
to be mentioned in support of this fact) and a perception
of this is sufficient to provide a basis for the belief in pecu-
liar sanguinary emanations. Add to this the obvious con-
nection between blood and vitality, and we have a complete
nexus of percepts which will suggest all the magical ideas
mentioned, and by the encouragement of such suggestions
will tend to realize the psychical counterparts of such mag-
ical causes.

Some modifications in this statement may be conceded
to those who under the vague name of occultists contend
that a whole series of supernormal laws continuously ope-
rates on human affairs. Such will say that all the prop-
erties attributed to blood in universal spiritualistic belief
are real, that spirits (shells) can absorb sanguinary ema-
nations and thereby vitalize themselves, etc. To them it
may be said that using the word "spirit" as equivalent to
"idea" the difference is merely a matter of terminology.

HERBERT CHATLEY.

T'ANG SHAN, NORTH CHINA, Oct. 1911.

AUTOMATISM.

IN approaching a subject of such an uncertain nature, of
such wide bearing and interest to humanity, and resting
on the much disputed border of the unknown, it is only
with the greatest regard for fact and approved hypotheses,
and the utmost caution in reasoning that I have felt myself
at all capable of developing it to any conclusion. The na-
ture of the subject forbids any actual proof by our present
facilities and in no place would I wish to assume my own
infallibility. While the metaphysics of the question is, at
present, of no practical use or bearing, yet a knowledge of
the government of our actions and a conception of what
this government and its rules should be, I may state to be
the thing of highest utility and interest to us. According
to Mill, "no belief which is contrary to the truth can be
really useful," and so, at least, there is some excuse, aside
from complete treatment of the subject, for developing its
metaphysical side before proceeding to that of more im-
mediate utility — the educational and moral phases. Many
treatises and good have been written upon this subject,
and many strong arguments pro and con adduced, but there
is always a last word to be said, and the best inferences
and reasons have been put to shame as the truth has slowly
come to light.

No man is so presumptuous as to assert that he recog-
nizes all causes which tend toward the production of any
phenomenon, but a faith that they exist and are discover-
able, is what has led to the present glory and brilliance of

92 THE MONIST.

science. Man wonders and is curious now even as he was
in the dim ages, but he has learned one lesson, — to investi-
gate for natural causes instead of "explaining away" his
ignorance by the creation of supernatural powers ; and the
answers which he gives to the questions of the universe
to-day are not mere placebos to console his passion for an
answer and to feed his emotions, but passion has been sup-
planted by a higher and more lasting emotion; namely,
the desire for the satisfaction of reason with positive and
logically deduced knowledge; and nothing more and noth-
ing less will suffice.

In order to conform to this inner desire and all that is
implied with it, it is not necessary to exclude all belief and
remain purely agnostic, but to have that belief bounded and
governed by the known facts of science and its articles
determined by the most plausible inferences adducible
therefrom. All men, no matter in what age or circum-
stances, have with the greatest legitimacy constructed a
cosmos and not a chaos as their picture of the nature of
things. For do they not see around them at all times direct
evidence of law and order in the workings of all material
forces ? And the least of confirmation is a pillar to belief.

To develop here whatever system of belief might be
entertained with the sanction of facts would hardly be
within the confines of my subject, but suffice it to say that
I agree with Spinoza who says that "an appeal to the inter-
ference of a soul (or unknown spiritual force) in order to
explain a corporeal state, is an admission that we do not
know its cause." I can in no way sympathize with the
inert mind of the Orient which, too drunk with sun and
plenty, must depend upon the spirit to fill the vacancy in
its knowledge, — a spirit about which it has even less of an
idea than of the material phenomenon itself. In the ab-
sence of knowledge we are only justified by an inference
which we believe to be in the direction pointed out by facts.

AUTOMATISM. 93

Now the material and its actions are the only facts with
which we are acquainted. Science has classified these facts
of experience and induced laws therefrom and in every
case the fact has been of a material and causative nature.
It therefore becomes our first duty to attempt the reduc-
tion of all phenomena to a physical, substantive basis and
not, when we have no conception of the cause, to say that
its nature is "spiritual," but courageously to assert our
ignorance concerning it and work with the faith that it
may be reduced to a natural, materially caused phenom-
enon. Never ignorabimus ! I shall preserve this rule, and
work with this end in view in all that follows.

It may satisfy some to ease their desire for rationality
with the following statement of Haeckel, but, however true,
it does not make a direct argument against the reason of
the indeterminist, which first of all must be shown falla-
cious before our own can trust the evidence. Professor
Haeckel says, "As to the question of free-will which has
kept the world busy for two thousand years, and which
has produced so many books that encumber our libraries
and accumulate dust therein, — this question also is no more
than a memory. Of what value are vague suggestions
based upon sentiment, in comparison with scientific deduc-
tions ? The will indeed is not an inert force. It is a power
of automatic and conscious reaction which is regulative
and actively influential. But the inclinations that are in-
separable from life itself explain this attribute, and as to
the mode of action inherent in the will we only consider
it free because, following the abstract and dualistic method
of metaphysicians, we isolate this faculty from the condi-
tions which determine it. We have not, first of all, to con-
sider the will separately, and then examine the circum-
stances wherein it acts. The will as given is burdened
with a thousand determinations which heredity has settled
upon it. And each of its resolutions is an adaptation of its

94 THE MONIST.

pre-existing inclination to actual circumstances. The
strongest motive prevails mechanically by virtue of the
laws which govern the statics of emotion. If then the
merely abstract and verbal will appears free, the concrete
will is determined like everything else in the universe."

To say this in the face of the overwhelming number of
scientific and unscientific indeterminists is not enough,
and it is the object of this essay to adduce such reasons as
will lead to the establishment of these statements as facts.
In doing so, let me say that I do not consider it inconsistent
to accept and reason from the tried theories of science
which have stood the test of time and criticism.

We know that during that comparatively simple condi-
tion of the earth, before the Laurentian age and the pri-
mordial deposits, a simple organic unit was produced.
Bernard, who has made the cell his life-study, has reduced
the cell, which had been formerly considered the unit of
structure, to what he terms the "chromidial unit," a more
elementary organic structure, having as definite a mor-
phological significance in its own way as the cell. It can
be claimed therefore that some such unit produced all the
pre-cellular organisms which built up, among other less
successful organisms, the famous cell with which biol-
ogists usually start their record of life. Not only was the
cell a highly efficient organism in itself, as is shown by the
fact that so many unicellular organisms exist to-day, but
it had the power of multiplying indefinitely and forming
colonies, which colonies have become organisms specialized
to numberless more and ever more complicated environ-
ments. For the specialization of a large colony of cells
as a whole must necessarily be able to reach a level of com-
plexity higher than that to which any single cell could
possibly attain. So thus life was raised from one level of
complexity to a higher one, and it is by comparatively little
reasoning that we reach the age of man.

AUTOMATISM. 95

Now in the simple stage of the earth's history and even
later in the postcellular age, it is acknowledged that all
phenomena obeyed explicitly the omnipotent, omnipresent
law of cause-effect. The actions of the ameba are nothing
but the simplest of reflexes from external stimuli and
this same action is admitted to continue up to the lower
vertebrates. All those who have expounded the doctrine
of free will have, therefore, consciously or unconsciously,
stated that at some unknown instant of time in the slow,
gradual evolution of organic life, and also in the growth of
the embryo or early life of the infant, the animal has
ceased to act according to the natural laws of its previous
action and a force has crept into a universe which em-
braces all space, which is able to produce material phe-
nomena on its own account and aside from the law that
all motion possesses a cause of which it is the direct effect.
Is it not absurd to hold that the action of a few of the
higher animals are not caused and so proceed by "their
own virtue?" Is this not exactly how primitive man "ex-
plained away" any phenomenon of the cause of which he
was ignorant? How unreasonable it is when we realize
the complex nature of the subject of our study and the
complex environment upon which he must react, to infer
that his action is not a more complex one working by the
same rules as his simpler action did in past ages at the
time of his humble origin. It is a case of realizing that a
million phenomena whose cause is known to reside in a
certain law, surround one phenomenon, — that of the ac-
tion of the higher animals, the complexity of which has
baffled our investigation, and therefore that we do not
assign this one to law, but label it a causeless phenomenon
the action of which is based upon the "virtue of the will."
It is the insignia and confession of the lack of knowledge
and the lack of inductive reasoning power of a great num-
ber of our professed scientific thinkers. They should ob-

96 THE MONIST.

serve their rule, namely, that if the law applies in a thousand
cases the probability is a thousand to one that it will apply
in the thousand and first case.

There is also another serious difficulty which presents
itself to the exponents of free will, and as yet none have
replied successfully to Professor Clifford who I believe
was the first to discover it. In extract it is this : the will,
in being pure and uninfluenced in its choice or production
of a material phenomenon, and therefore free, as they say,
must, in not being governed according to cause-effect, in-
fluence matter through the immaterial ; and aside from the
fact that the existence of the immaterial is inconceivable,
otherwise than that matter should be governed by any-
thing but surrounding matter is also inconceivable, and
both are therefore highly improbable. The conclusion
therefore is inevitable that the will is a physical manifesta-
tion and governed by the laws of physics.

No real boundary exists between the unconscious in-
voluntary actions of instinct born in us or of habits formed,
and the subconscious "quasi-voluntary" action of brushing
the dust off one's sleeve during a conversation, or between
the subconscious and more complex reactions in full con-
sciousness. It is a known fact that when the higher forms
of memory appear in animal life, a fuller and more com-
plete consciousness exists. And this is necessarily the case,
for in order to obtain the more complex reactions of the
higher animals, it is necessary that a greater memory of
the results of actions be had and so a fuller consciousness
for the revolving of the many memories to obtain the most
favorable idea of the would-be consequence and so its en-
actment. For the most favorable memory or idea of the
consequences of actions determines our choice, on account
of the self-instinct necessitated by the law of natural selec-
tion and whatever social education we have had.

Most indeterminists, believing that ab extra the mental

AUTOMATISM. 97

and physical processes go along on two parallel platforms
—the mental activity opposite the corresponding physical
activity — are confronted by this argument: Since we are
reasoning beings, there is a chain of mental facts be-
tween the incoming and a motor action, and so there is a
complete chain of physical facts sufficient to produce the
action ; for before and along with the mental act of willing
there is a parallel brain action which is caused and which
causes the motor action. There is then no need for the
parallel mental process theory, for by its parallelistic nature
it destroys our incapacity for accounting for all phenomena
physically, which incapacity caused its creation to "explain
away" certain of the higher animal actions. The word
mental should signify only in consciousness.

Again, how can pure abstract "will" influence material
action ? Allowing that not only to us but in abstract that
"mental" processes intervene between the sensation and
motor action, how is one to get across from the physical
to the mental platform and then back onto the physical
again? This detour, made by metaphysicians on account
of ignorance, leads me to doubt the existence of the "men-
tal," immaterial platform. I fail to see the relation between
will and motion by which one can cause the other, unless
"will" and "mind" are inherent in it, i. e., a manifestation
of molecular or molar motion and therefore governed ac-
cording to cause-effect and not free. The following dia-
gram will illustrate the point:

If it be asserted that the psychical is inherent in in-
organic nature, I have nothing to say, for molecular,
atomic, and ionic structure is too little known ; but I believe

98 THE MONIST.

that it is inherent only in the sense that material compo-
sition is such that it could produce (by combinations and
processes unknown) conscious life. It has been said that
consciousness as a form of motion is inconceivable, but ad-
mitting its truth I do not consider it a valid argument
against materialism, for what kind of an idea of conscious-
ness can we have when consciousness can only be the sub-
ject and never the object, as we are contained in it?

So in conclusion on the physical facts of the case, the
argument may be summed up in these words : In our devel-
opment from the first transitional organic form to the cell
and on through the gastraedic and invertebrate age our
condition has resembled that of the monera, amoeba, pla-
tode, and up to the lower vertebrates, whose action is so
simple that it is readily admitted to be mechanical. But
when we come to higher vertebrates and promammals,
which we resembled at a more recent period, their constitu-
tion and action has become so complex that we must aban-
don consistency and say : because we see no cause of their
actions is there none? No, reason forbids. Upon the
fertilization of the ovum and the formation of the stem-
cell the life of a human individual begins. This is a me-
chanical process as is the development of the embryo; the
early life of the infant is a combination of instinct and
reflex action — purely mechanical. But after the plastic
brain substance of the infant has received and held many
impressions from the outside world he is equipped for a
more complex reaction against it, and since many pro-
fessed scientists neither realize what his memories are nor
see how the most favorable one coupled with the self-pres-
ervation instinct sets forth his action, so they assign the ac-
tion to his pure will to do it and nothing else. Let us use
reason in this case. If the action were considered dynam-
ically and an investigation made of its exact molecular
cause and its force it would be an operation among those

AUTOMATISM. 99

physiological infinitesimals which present calculation must
neglect but to which faith must grant an existence. The
removal of the cerebral hemisphere reduces all action to
a pure and simple automatic nature and no one has had
the opportunity, knowledge or facilities to watch and trace
the origin of the so-called voluntary actions in the myste-
rious mazes of the frontal brain. It remains for us but to
wait until methods are so perfected and until men, realizing
that knowledge is power, educate themselves unhesitatingly
to investigate with a view towards their high aim, upon
the highest form of living subject obtainable, for a con-
firmation of those inferences we have deemed reasonable.
"The higher we ascend in the vertebrate series toward
man," says Dr. Carpenter, "the more evident does it become
that the ordinary course of action is determined rather by
the direction given through the cerebrum to the workings
of the automatic mechanism than by its (the cerebrum's)
ow-n unconscious action." In other words, by reason rather
than by instinct. And in man we find that everything is
to be learned by experience, save what is imperatively re-
quired for the maintenance of life — such as the rhythmical
contractions of the heart, the peristaltic movements of the
alimentary canal, the acts of swallowing and respiration
and the like. It has already been mentioned that memory
is the great prerequisite for all "voluntary" action, and it
it is also known that the actions of the human embryo are
not of that sort until

"Nature whose heedless might
Casts like some shipwrecked sailor, the poor babe,
Naked and bleating on the shores of light."

From that instant the memory is in process of formation,
the conscious personality begins, habit adds to the role
of the involuntary centers, which previously possessed only
instinct, and the infant can thus react more perfectly upon
complex conditions and exert less effort in the performance

IOO THE MONIST.

of simple and necessarily repeated actions, for their per-
formance has become habitual and subconscious. Thus he
is able to direct his higher activities to the more difficult
phases of his being — to this end has the law of natural
selection, joined with variation, ever worked in the mental
field. This is the pregnant fact upon which I shall build
my argument from the mental side of the question.

As shown under hypnosis, an impression of every ex-
perience, of the sight of every performance of others, of
the result of every action, is indelibly recorded in the
brain, whether it ever be brought into consciousness or
not. We therefore have for our use the knowledge of the
result of a thousand actions, whether it be of the tongue
or of the hand. Now we also possess from heredity the
overwhelming instinct of self-preservation and its brother,
the desire for what is productive of the greatest happiness
to us. The following mental process is easily discernible
by introspection: a condition arises in the environment
necessitating a reaction; the memory arises of certain re-
sults upon the individual of an action of his own or of
some one else ; if it be a favorable result his interest in the
possible action is aroused and his attention is then directed
toward it; the same occurs (from association of ideas in
the memory) to four or five (taking an extreme case of
indecision) ideas of possible action; the attention is di-
rected then from one to the other and a comparison of
them is made according to the individual's belief m the
probable nature of their results; one appears more favor-
able to his happiness and welfare than the others, where-
upon it is acted out. Thus truly considering the necessity
of memory, Plato has reason to name it a great and mighty
goddess. If it were not for this cause-effect mental process,
I would fear greatly for the happiness and interests of the
individual, if there could be individual life without it. One
of the potent factors in causing such a strenuous advocacy

AUTOMATISM. IOI

of free-will is the pride and vanity of man in himself and
his powers. But how often has that pride been humbled
and how often must it be in the future when such facts
as his low origin or his unlikeness to the image of God
are forced upon his realization!

The power of suggestion and association of idea with
idea, such as I experience as I sit here writing, must also
be thoroughly recognized and considered before any valid-
ity, let alone prestige, can be given to the statements of an
indeterminist. The previous paragraph has shown the
method of the objective or higher faculties in arriving at
a conclusion for action, but the memory, or what has been
termed the unconscious, subjective mind is always amen-
able to suggestion and will catch the objective faculties
off their guard if possible. A friend related an excellent
example of this some days ago: A young man who had
determined to stop drinking was invited to step into a
saloon and have a glass. He was prepared for this and
the suggestion brought up the reply no. A few days later
an old school friend met him and said, "Let's go in and
sit down and talk over old times." He went in and it is
unnecessary to say, succumbed. Taking up the association
of memories or ideas, let me ask the free-will exponents
if the "chance" were at all probable, of my turning ten
minutes ago to the beginning of this paragraph and writ-
ing the word the with which to start this paragraph, the
idea of what I have just written springing spontaneously
from my brain ? I also ask them to exercise their powers
of introspection until they have gained proficiency enough
to trace back why they did this or thought that the moment
before, winding the string (of cause-effect) as they go
along and reach, say, their experience an hour ago. My
opponents paradoxically admit that they are not reasoning
men, for they say they do just as their "free will" pleases
and, although moral men, are not governed by duty, re-

IO2 THE MONIST.

sponsibility, or fear of consequences. Freedom consists
of a recognition of facts and a self-government according
to them; bondage, of a struggle against them. I have al-
ready determined what pleases us, — namely that of which
the consequences are productive of our happiness and well-
being. And the proud "free-willers," I believe, have some
hedonists in their ranks who will acknowledge what pleases
them, so their acts being governed by that, they prove
themselves traitors to the cause. Many people may become
indeterminists and reach that abnormal state of mind in
which they can trust themselves to a universe where law
and lawlessness interchange indiscriminately, but I con-
fess myself unable to reach that Nirvana.

Our own immediate mental experience, therefore, has
shown that we are no exception to the rule (in that
we realize the mental antecedent — the why of our pur-
pose) and they are as worthy of confidence, according to
Dr. Carpenter, as are "deductions drawn from phenomena
outside ourselves, which we can only rightfully interpret
on the basis afforded by those very experiences, the test
of the validity of such interpretation being furnished by
their conformity to our other immediate experiences. " It
is well known that the hemisphereless frog or pigeon acts
automatically when any thing directly stimulating is ad-
ministered, but remains perfectly passive until then. The
hemispheres, therefore, are the seats of higher conscious-
ness wherein a more complex reaction is aroused from
more distant and delicate stimuli from without — after the
formation of the memory within — but not less automatic
action. Our consciousness of effort arises from the many
and intricate processes of conscious reasoning, judgment,
etc., before arriving at a decision or choice, and is accom-
panied by the feeling of effort arising from muscular move-
ment. It has been often urged that, since neurosis can
give rise to psychosis, it is surely quite accordant with the

AUTOMATISM. 103

fundamental principle of interaction to affirm that con-
versely, psychosis can give rise to neurosis, just as the
electricity generated in a voltaic battery by chemical change
can itself produce chemical change. I quite agree — the
psychosis being neurosis consciously felt. The neurosis
afferently causes psychosis, i. e., causes will; the psy-
chosis efferently (in regard to the ego) causes neurosis
and bodily motion. He simply affirms the chain of cause-
effect and the law of the conservation of energy.

In fact, unless combination of memories were used to
determine our actions and memory be but a rudiment, or
else that memory is used for that purpose now, I can see
no object past or present toward which it would be of
utility. Darwin and his followers have shown that an
animal possesses a function because it was either of use
to its ancestors or to itself. Therefore since memory
would be useless unless it helped and guided our actions
we must concede that it does ; and we can also conclude that
where animals acted in accordance with a more perfect
memory (arising from variation) their actions were more
in accordance with the requirements of nature and they
more fit to live. Thus natural selection has produced this,
as well as all other necessary functions. Who would at-
tempt an explanation of the molecular causes of those
imaginary actions in dreams? Memory is involved here
but the channels through which we come to those imagina-
tions are so subconscious as to baffle all introspection; yet
there is no manifestation of will in them and it is compara-
tively easy to see the by-cause of conscious volitions.

Under hypnotism the will or judgment is unconscious.
The man is under the complete control of the present sug-
gestion. Now we see that it is not a very beneficial reac-
tion when no distinction can be made between the false and
true, right and wrong, etc. And thus natural selection
gave rise to the will — judgment (comparison of memories)

IO4 THE MONIST.

coupled with action. The comparison was and is necessary
for existence by a high reaction even as the hemispheres
were and are necessary to a reaction from more distant
and delicate stimuli. The hemisphereless frog and the
hypnotized man are admitted automatons but when there
were neither of these conditions and the reaction was com-
plex— from revolving of memories and comparison of them,
and from distant stimuli they were thought uncaused as we
had no knowledge or perception of them. Now that we
see the why, we realize that automatic nature in the ab-
sence of hypnoses or presence of the hemispheres as well as
in the opposite conditions.

On the freedom of choice this is the sole reply which
I find from the indeterministic pen. "And yet on the
deterministic doctrine, if I am attracted by the temptation
of an immediate but immoral pleasure, and am deterred
from it either by a sense of duty or by the fear of the
remote consequences of the sin, I have no more 'choice*
as to the course I shall take than has the piece of iron that
is attracted in opposite directions by two unequal equi-
distant magnets. Now my contention is not merely that
I have a choice, but that the very existence of an idea that
can be derived from no other source than human experi-
ence, confirms that effect." I believe Dr. Carpenter per-
fectly justified in making this statement. As to the person
it is a choice (at the moment he does not figure out all
reasons or causes, they being subconscious), but the
"choice," not to us but abstractly, is determined and non-
existent. The fact that all experience shows that motives
which may exert a preponderating influence at one mo-
ment, are comparatively powerless at another, and that,
on the other hand, motives whose influence at one moment
is scarcely felt, may come to acquire a force that makes
them far outweigh those which at first overbalanced them,
shows that, although we do not know what is really the

AUTOMATISM. 10$

best decision, if we can be made to believe that a certain
one is (by any means whatever) better, that is the one
which the self-instinct, or whatever social education we
have had, embodies with the proper action. Indeterminism
confesses its inability to trace anything behind the will or
existing before it which is in any way connected with it;
determinism confesses that it sees and also consciously ex-
periences (and what our consciousness tells us is the surest
reality to us) a phenomenon existing before it in time and
determinedly related to it. In other words, the will is not
a spontaneous and independent thing leaning only against
itself.

Santayana says, "Mankind and all its works are un-
deniably subject to gravity and to the law of projectiles;
yet what is true of these phenomena in bulk seems to a
superficial observation not to be true of them in detail,
and a person may imagine that he subverts all the laws
of physics whenever he wags his tongue, only in inorganic
matter is the ruling of mechanism open to human inspec-
tion ; here changes may be seen to be proportionate to the
elements and situation in which they occur. . . . Physics
cannot account for that minute motion and pullulation of
the earth's crust of which human affairs are a portion.
Human affairs have to be surveyed under the categories
lying closer to those employed in memory and legend. . . .
That this gulf is apparent only, being due to inadequacy
and confusion in human perception rather than to inco-
herence in things, is a speculative conviction altogether
trustworthy .... Now the human senses are not at all fitted
to represent an organism on the scale of the human body.
They catch its idle gestures but not the inner processes
which control its action. The senses are immeasurably too
gross. What to them is a minimum visibile, a just per-
ceptible atom, is in the body's structure, very likely, a
system of worlds, the inner catclysms of which count in

106 THE MONIST.

producing that so-called atom's behaviour and endowing
it with affinities apparently miraculous. What must the
seed of animals contain, for instance, to be the ground,
as it notoriously is, for every physical and moral property
of the offspring?. . . . Any one who can at all catch the
drift of experience — moral no less than spiritual — must
feel that mechanism rules the whole world."

According to Spinoza, that masterful combination of
reason and intuitional insight, "A thing is said to be free
(liber a) which exists by the mere necessity of its own
nature, and is determined in its actions by itself alone."
If, then, men can attribute no reason for the willing of
anything beyond the immediate cause, then the will is in-
finite beyond that cause ; then the will is equal in power to
God, in that He would have no control thereover and all
the burden and responsibility of a choice, which may affect
the lives of many men, is placed upon this will, infinite
in its nature yet limited in its knowledge. It is not just nor
right that God should place such responsibility in the un-
governed hands of ignorance. As God is just and right-
eous it follows "from these premises then, that men think
themselves free inasmuch as they are conscious of their
volitions and desires, and, as they are ignorant of the
causes by which they are led to wish and desire, they do
not even dream of their existence." It is then concluded
(Prop. 48, Part II) "There is in no mind absolute or free
will, but the mind is determined for this or that by a cause
which is determined in its turn by another cause, and this
one again by another, and so on to infinity. Proof. — The
mind is a fixed and determined mode of thinking and
therefore cannot be the free cause of its actions. It cannot
have the absolute faculty of willing or unwilling, but in
willing this or that, it must be determined from an infinite
line of causation."

Dr. James says in one of his essays, "The sting of the

AUTOMATISM. IO7

word 'chance' seems to lie in the assumption that it means
something positive, and that if anything happens by chance
it must needs be something of an intrinsically irrational
and preposterous sort." But I confess I can not see that
unless chance is governed (or as he says, "needs be,") by
reason or law (a contradiction in itself) how the result of
the comparatively few higher animal actions of the future
could be anything but "irrational or preposterous." It is
a case of to be or not to be. If "chance" is to be governed
by reason and by law we may expect the world to continue
a part of a universe in the future and if it is not, that it will
become participant in a nulliverse. Regret for our past
actions and therefore the wish that something might be
otherwise takes place in every passing hour and is but a
confession that had we been wise enough our act would not
have occasioned regret as it would have been governed by
that wisdom.

The distinct purposive intervention of the self-conscious
ego is what should be designated as will, though the pur-
pose and intervention be caused; it is purely voluntary to
us and gives no feeling of oppression although in the true
sense not "will." Therefore to say that you cannot per-
form will as I have re-defined it is untrue, for the memories
and instincts — caused causes of the will, are a part and
contained in yourself, i. e., to you the act is will. From a
point of view outside of the self the ego is not responsible,
but you are to yourself since the will is responsible for its
conduct to the memories and instincts — the basis of the
personality. Yes, and the responsibility is exactly fulfilled.

I can do no better than conclude my argument from
the mental point of view with an illustration from the
thoughtful pen of Thomas Huxley : "Suppose that an adult
man, in the full rigor of his faculties, could be suddenly
placed in the world, as Adam is said to have been, and
then left to do as he best might. How long would he be

IO8 THE MONIST.

left uneducated? Not five minutes. Nature would begin
to teach him, through the eye, the ear, the touch, the
properties of objects. Pain and pleasure would be at his
elbow telling him to do this and avoid that; and by slow
degrees the man would receive an education which, if nar-
row, would be thorough, real, and adequate to his circum-
stances, though there would be no extras and very few
accomplishments. And if to this solitary man entered a
second Adam, or, better still, an Eve, a new and greater
world, that of social and moral phenomena, would be re-
vealed. Joys and woes, compared with which all others
might seem but faint shadows, would spring from the
new relations. Happiness and sorrow would take the
place of the coarser monitors, pleasure and pain; but con-
duct would still be shaped by the observation of the nat-
ural consequences of actions; or, in other words, by the
laws of the nature of man. Nor should I speak of this
process of education as past, for any one, be he old as he
may. For every man the world is as fresh as it was the
first day, and as full of untold novelties for him who has
eyes to see them. And nature is still continuing her patient
education of us in that great university, the universe, of
which we are all members, nature having no Test-Acts.
Those who take honors in nature's university, who learn
the laws which govern men and things and obey them, are
the really great and successful men in this world. The
great mass of mankind are the Toll/ who pick up just
enough to get through without much discredit."

I have quoted this at length because it so admirably
conveys the meaning which I have tried to express in
other words, and because it contains the foundation of my
argument from the moral side of the question which is
about to follow. In this domain the exponents of free will
have considered themselves least needful of defence, but,
as yet, I have not come upon any elucidation of this side

AUTOMATISM. ICX)

of the question which was exactly satisfactory to my de-
mands. Either we are wrong when we blame, or God is
immoral, and I greatly suspect that the fault is to be found
in our lack of true moral comprehension, rather than in
God. It then becomes my duty to whitewash the Devil,
although to compel him to keep indoors is the work of the
centuries.

Going to the foundations of morality must necessarily
give us a truer conception of the import of things, and must
also lead, by way of our determinism, to a rational, opti-
mistic, trusting conception of the universe if that doctrine
is to be entertained by us for one moment. Before the
advent of man, it is easily seen that nothing was moral or
immoral, for those terms are merely relative to our mode
of thinking and arose with it. Nothing therefore is within
itself bad or good and the words signify only the fulfillment
of the demands of our nature upon phenomena or the lack of
it. That which does not acquiesce to our demands is called
bad or evil and if it is shown that our demands are the
result of comprehensive reasoning, i. e., that we can see
to \vhat end the action or being is directed, and that it is
evil (detrimental to happiness and well-being of men) then
we have a right to a pessimism toward that universe which
would produce good and evil in motley alternation. It
therefore devolves upon us here to prove that the tendency
of all phenomena is that which would secure the approba-
tion of our moral nature if we could realize their end. Of
course we can conceive what would be to us a perfect uni-
verse where all pain and evil had a good in its place, but I
think we can not censure the scheme or entertain a pes-
simism if we find that all that is not good is productive of
good, regardless of the conscious experience of the indi-
vidual through whose sufTering good is to be realized.
Darwin truly states that no species or individual is perfect
for its reaction upon its environment (whether of the com-

IIO THE MONIST.

plex nature or of the continual change of the latter) and
Hoffding perceives in his "critical" realism the never end-
ing progress of life toward that perfection. Man's becom-
ing a social animal has raised the complexity of his en-
vironment a thousandfold, both in relation to the acts and
thoughts of other men, and in the increased menace of dis-
ease. Now although not so potent a factor as it was thought
at first, the law of the natural selection of variant forms,
cruel in itself, has been the sole means toward that good
end, our mind. She selected those who gained and re-
tained from dear experience (a seeming evil) the requisite
knowledge. Although the weaklings and the deficients
may have been fostered by an unexacting environment
and the more fit cut off by accident, yet, in the first case,
if the environment remained and nothing stepped in to
improve the unfortunates and they generated degenerates
which were still fostered by easy surroundings, the time
came when the environment changed and their extermina-
tion proceeded. If the fit were plucked by accident, and it
was exceptional, yet the weeding still went on until ones of
just as high a level of fitness were produced. Nature
works slowly now through painful education (each age
building upon the knowledge gained by the preceding ages
from their diligence and to a less extent their lack of it
and mistakes) and reaching a higher social scale, after
having gone as far as possible with painful extermination,
(natural selection has caused reason which has supplanted
instinct and selection as factors in our development) toward
that consummation, the craving for which has produced
the greatest hope of the human breast — knowledge and
happiness (perfect adaptation to environment). Thus
science confirms with positive knowledge that these beliefs
which originated in the heart of primitive man, are not
empty and groundless, but even confirms them along with
that other — of an omnipresent, omnipotent God, which it

AUTOMATISM. Ill

explains as a realization of the presence of The Law (of
cause-effect).

The morphine fiend could not help himself because he
was fated from eternity to pain; he had better not been
born ; but the law of life and of death cares not if a spark
of consciousness suffer nor whether the spark know the
consequences of its action or not. "Ignorance of the law
is no excuse, and the wages of sin is death." Whether the
victim is able to help his action or not the evil to him
exists and although the act is an "evil" which, according
to free-will, might not have been, it happened and the
universe, be it a monism or dualism, possess we one element
(causality) or two elements (causality and free-will), is
responsible for its existence and the victim a right to
pessimism as long as he regards himself. In either doc-
trine the only way out of the difficulty that I can see is to
take the more comprehensive view, whether you be the
victim or not. The invisibility and slow working of the
evolutionary law (physical, mental, or social) may make
this seem to be closet philosophy, but it is only when we
make a retrospection of the ages that the great underlying
influences come into broad daylight.

Let us take, by way of illustration, an event told by Dr.
James. He says: "At Brockton, the other day, a man,
to get rid of the wife whose existence bored him, inveigled
her into a desert spot, shot her four times and then as she
lay on the ground and said to him, 'You didn't do it on
purpose, did you dear ?' replied, 'No, I didn't do it on pur-
pose/ as he raised a rock and smashed her skull." The
Doctor remarks, "We feel that although a perfect mechan-
ical fit to the rest of the universe, it is a bad moral fit and
that something else would really have been better in its
place." I do not say that something else would not have
been better in its place, but his universe, as well as mine,
must account for it and palliate the crime to us with a

112 THE MONIST.

reason which gains our moral approbation for its existence.
I say that our moral view is not the true view, else it would
allow the existence of these "evils/' No evil is necessary,
but as long as we are ignorant or governed by blind pas-
sion, we are not perfect in our environment, and the "evils"
are bound to exist. The causes of such actions as these
are unhealthy bodies, or minds which have not learned
from their own or others experience (i. e., educated to
a wrong environment), or who do not recognize the
stronger demands of society or are guided by passion in
lieu of the only legitimate monitor reason. Now, seeing
these causes, could we blame the action of this Brockton
man ? Or could we blame the universe as immoral when it
is necessary to evolve slowly into the social state and
therefore actions such as this, reversions, come to pass in
a state of society where they are immoral — individual
strife was not immoral where individualism and natural
selection were working as it led to a great good, — the
physical and brain development of the race. But reason,
experience, and social or moral education are taking place
and the future we believe to promise a better condition.
There is no more immorality in this mental reversion than
in a physical reversion such as the famous Miss Julia Pas-
trana or a tailed boy. In fact, unless the experience of
the past and our possession of reason counted for some-
thing in our life, I do not see how any social evolution,
an optimistic view of the future, or any reason for our
progress thus far can be had, since natural selection has
become nil to us. The conscious experience of healthy men
affirms the potency of reason and experience and as this
is the surest of reality to us, I believe no doubt can be had.
Even if there were no other palliation to our just desire
for a rational and moral universe, the fact of the educa-
tional value of this Brockton example as an admonition to
posterity would be sufficient.

AUTOMATISM. 113

But this action which I have just explained is rudi-
mentary— the remains of a lower stage of mental evolu-
tion. The self-instinct was necessarily the first produced
by natural selection and still remains with us although not
playing such an important part. The preservation of the
young or the family next arose and all actions were sacri-
ficed to it ; outside of the family the self-instinct was then
guide. So lived our remote ancestors. But the develop-
ment of the brain meant the birth of memory, comparison,
and reason, for those individuals who possessed a little
better memory of the consequences of actions were able to
determine what would be the most probable result of one
not yet performed and so could better serve their self or
family instincts. Thus with the birth of reason, instinct
became but a secondary factor, and our primitive ancestors,
reasoning that a greater surety of food and protection was
given by that social institution, the tribe, formed in those
more efficient bodies, which had a greater scope of action
than was possible for an individual. Natural selection
still kept up a certain low standard within the tribe (by
rivalry for females and by disease) and also outside of the
tribe by selecting those tribes of the greatest population
or best organization, thus spreading tribal formation over
the continents. But to-day with the decrease of rivalry
inside and outside of our social institutions, i. e., decrease
of war, disease and personal conflict, natural selection has
become almost inert. Our evolution — the evolution of our
organization — is proceeding by means of the reasoning
powers of man and by the necessity for social action forced
upon him by his fellows. In early life he imitates and then
sees the reason and expediency of social action. The self-
instinct, the love instinct, the family instinct are here to
stay, but as social evolution advances all actions are not
caused by the first or as later by the first and second or as
later when the field of action was divided among the first,

114 THE MONIST.

second and third, but the field of each of these instincts
approaches its limits as the broader fields of service to the
nation, and later to society, develop.

Thus we see that natural selection produced a high
type of individual, produced the self-instinct, the family-
instinct, and had a small part in producing the tribe semi-
instinct. Then as reason also developed and partly by it,
by instinct, or by imitation, men banded into nations, nat-
ural selection slowly subsided and organization and edu-
cation appeared. The self-instinct of the leaders was lim-
ited by the strength of the demands of the others even as
it is to-day, the difference being in the strength of the
demands. People seldom obtain any more than they de-
mand as self-instinct has the field (produces actions) until
it is encroached upon by the stronger demands of our fel-
lows. Thus the only moral law, and the only expedient
mode of action for ourselves is to comply with the stronger
social demands as far as they extend — not so far that we
are overcome by the self-action of others. Thus we must
fight individually to the extent that individualism is prac-
ticed by others and must conform to the growing demand
for social action — but not as far as the new twigs which
must find nourishment and grow before they will bear our
weight. The cause of great suffering has been and will
be, (until the limit — utilitarianism — is reached through
education) in social evolution, in determining how far, in
regard to one's self, social action encroaches our field of
expedient self-action. In the most successful lives this di-
viding line is more approximately determined, and those
are unfortunates, who from lack of observation or fore-
sight act either as the criminal, robber, small tyrant, etc.,
(too much individualism) or such few and unnatural men
as Timon of Athens of whom it could be said:

"Poor honest lord, brought low by his own heart,
Undone by goodness ! Strange unusual blood,
When man's worst sin is, he does too much good !"

AUTOMATISM. IIS

They are to be pitied, but that which caused their action
cannot be censured as immoral because it is a necessary
accompaniment of the individual-social metamorphosis, and
all admit that the end of social evolution is one of the great-
est goods attainable by man.

At the present day an excellent example of this is af-
forded by the action of Germany in European affairs, and
is applicable individually as well as nationally. Germany
has asserted her self-rights as far as possible. She has
exacted Alsace-Lorraine from France and is now endeav-
oring to shut her out of Morocco. It is a case of get as
much as you can without burning your fingers. Now were
England, France, and Russia to form a coalition, a strong
demand would be created and, being expedient, Germany
would have to comply with it. This is of course explaining
the extreme expedient selfish case as it exists to-day. But
there are others against whom there is not so strong an
individual competition and who then can comply also with
the lesser demands of society. As social evolution pro-
gresses these necessarily become greater in numbers and
the evolution gains increasing force as it advances. As
the child's first social acts are imitative and educationally
induced and as later he sees the expediency of social insti-
tutions and demands, so progresses his moral education.
And if he has the self-instinct strongly developed, its field
of action in him will be limited only by the strongest and
most immediate demands of society — demands which re-
quire the minimum amount of social action only, and he
will not contribute to social progress. But those in whom
the instinct is not of such force or who have been educated
in highly organized communities, do not stop social action
and revert to self-action only at the strongest demands
of society, but comply with the lesser demands ; themselves
create lesser demands and strengthen the pre-existing
ones, so that the social evolution of any community or

Il6 THE MONIST.

people depends on the number of this type of individual
that it contains — if the self-actors predominate evolution
would necessarily tend to revert to the remote unsocial
period and vice versa. The great factor in producing the
less selfish actors in the majority is, that once headed in
the direction (usually by education) like habit, the tend-
ency is to let the field of self-instinct be encroached upon
gradually more and more (of course retaining as much
of the instinct as is required by expediency to combat with
the amount of self-action of others at the stage of evolu-
tion of the time of the individual). Thus the field of
social action widens and limits that of self-action. New
demands are created, by a majority; the former weak ones
strengthened, and the strong ones are become a matter of
course and habit.

It is apparent from this how any set rule for moral
action has only been valid for the state of society at its
birth, and how in order to lead the most satisfactory life
we must comprehend (approximately) the existing state
of social evolution — must observe and follow the amount
of social action that can be indulged in without neglecting
the individual action necessary to maintain one's self. Thus
utilitarianism in being the consummation of moral or so-
cial evolution — all actions for the good of society and the
maximum individual welfare possible for all (the welfare
of society's individuals being its own) is not a fit "working
hypothesis" to-day as a certain amount of self-action must
be mixed with the social. It is, I believe, the goal of social
evolution — distant, undiscernible, on the other brow of the
earth — and we know the earth is round. Utilitarianism,
service substituted for gain, thus seems the far off end
of moral action.

I can in no way agree with M. Elie Metchnikoff, who,
after showing the insufficiencies of the moral doctrines
of Kant and Spencer says, 'The ideal will rather be that

AUTOMATISM. 117

of men who will be self-sufficient and who will no longer
permit others to do them good" — in other words the
super-man of Nietzsche. He, a biologist and scientist,
fails to scan the field of organic development and does
not see that organization is the keyword to all progress
in that field. The organization of "chromideals" into
cells; the organization of cells into communities or organ-
isms and lastly the organization of organisms into what
we call nations and states. The key-word to organization
is not self-sufficiency but specialization, cooperation, recip-
rocal action. The cells perform different functions and
loyally work with the welfare of all the other cells (the
community) in view, and the organism or community can
function where the single cell could not. The analogy is
complete. He fails to see that in order for the family to
exist, one member must procure food and protection, one
must raise the offspring, and the offspring when indepen-
dent can then become the head of another family (it being
necessary for the higher action of the animal that its in-
fantile development be longer). In the tribe some must
procure food, others make implements, others protect, etc.,
in order that individually the tribe may better live and
function in accordance with a more complex environment.
Would this not be a low social state if each individual had
to grow or hunt his own food, manufacture his clothes,
his house, his vehicles, etc. ? He would be self-sufficient
and no one would be doing him good !

The relations of the part to the whole in any highly
specialized society are analogous to those of the vital or-
gans to the human body. There is paralysis throughout
the system when its functions are interrupted. The lower
forms of life are so simple that you cut and subdivide them
at will without any impairment of vitality, but as organi-
zation develops, with a circulatory system and coordinate
functions for the several parts, their independence is lost.

Il8 THE MONIST.

And so in a primitive society the individual is compara-
tively independent, but as organization takes place and
specialization proceeds and the exchanges of civilized life
develop, the well-being of the individual becomes more
and more dependent upon his cooperation with the other
individuals. "Our civilization is based upon the division
of labor. Its industrial efficiency, its wealth of production,
its comfort and luxuries and variety of opportunity, are
the results of cooperative effort. If each member of the
community, instead of supplying his own wants, devotes
himself to one thing and all exchange the surplus products
with each other, the sum-total of their production and pos-
sessions is increased." Specialization and not self-suffi-
ciency is the first word in organization, civilization, and
social evolution.

Society is automatically regulated, for each man will
select as his vocation that mode of action for which society
pays most and which he believes himself capable of ful-
filling, i. e., to him the strongest demanded (highest paid)
mode of action. And according to his ability will he suc-
ceed in supplying the demand or descending to a position
where he can. To trace the demands of society upon the
individual, is to trace the social and moral evolution of the
race.

I can see nothing but benefit and increase of happiness
from the struggle of the old with the increasing new idea
of social duty and in the unhappiness, pain, and sorrow
caused by the non-conformity of those unlucky individuals
who lacked the wisdom to obey the demands of society as
far as these went, or who disregarded the necessary, indi-
vidual self-action for their happiness in that state of social
evolution. The battle has brought and is bringing our
more complete organization and individual specialization,
and hence greater individual safety from disease, from im-
proper education and from all such mistakes and imper-

AUTOMATISM. IIQ

factions as now exist in our governmental and labor or-
ganization. The mistakes are a benefit to posterity as it
learns from them what should be built upon the present
inherited foundation to further the completion of the struc-
ture.

So I have shown the reasons, the why, the by-cause of
our social actions — which form a great percent of all our
actions, and have also shown therefore that they are no
less automatic than the others. And not only that but I
have palliated to our demands for a completely good, un-
sullied universe, the number of so-called evils, — the sor-
rows and pains, which have arisen along with the social
evolution as well as those which have arisen from the
physical evolution.

It is asked, what is the meaning, the import, the pur-
pose of it all, why the necessity of this development ? I can
only answer, the universe is infinite. What could be the
purpose of the purpose, or the import of the import ? Were
matter absolutely dense — without motion, we would have
no problem; but change is the second most apparent phe-
nomenon. There can be but one kind of change and that
is of the position of matter. This may be resolved into
molecular and molar motion. If a change in the kind of
motion is made it is in the cycle of molecular to molar and
by contact of bodies back into molecular motion. There
is no purpose, that is too human a mode of thinking. There
is but one possible process and that is change. In the
universe existence and necessity are the factors; they are
not finite as the mind, but free — on account of themselves
alone. I sit and watch the development of a crystal — of
which we are the molecules, our cells atoms, and our
"chromidials" ions. The change of this crystal is molec-
ular into the more substantial molar state accompanying
and a part of the earth's change from nebulous to a more
solid condition. There is as much import in our develop-

I2O THE MONIST.

ment as the development of a grain of salt from solution,
and the performance of the experiment is a show con-
tinuous. So much for the metaphysics of the question.

I have now, I believe, covered the entire scope of phe-
nomena, have shown the reasons, — the causes of all actions,
individual and social, and have shown how each leads life
on to "a consummation devoutly to be wished." Thus the
dread figure of "evil" has been exposed as a negative quan-
tity while we admit and try to exterminate the to us evil.
I have shown that we can blame nothing and that an op-
timism concerning the universe and its automatism is enter-
tainable. Viscount Amberly has written, "Not in so slov-
enly a manner has the work of nature been performed.
We are no more free to disturb the harmony and beauty
of the universe than are the stars in their courses or the
planets in their orbits . Our courses and orbits are no less
fixed than theirs, and it is but the imperfection of our
knowledge, if they have not been and cannot yet be dis-
covered. But it would be a lamentable blot upon a uni-
verse, where all things are fixed by a law 'in whom there
is no variableness nor shadow of turning' were there per-
mitted to exist a race of creatures who were a law unto
themselves." It is already recognized that knowledge re-
pays a hundredfold the sweat that it cost us in this martyr-
dom of man, for we are thereby enabled to govern our
future actions with greater wisdom and with more perfect
reasoning, so I need not lay so great stress upon the almost
omnipotence of the environment, the education of us all.

Thus, in the belief that "Alles verstehen ist Alles dul-
den" I widen my moral horizon from that of Dr. James,
and find no phenomenon caused by that law-perfect-in-
itself : cause-effect, which is not perfect mechanically and
morally. I make suffering a good and destroy the word
evil. Concerning the necessity for "evil"; there is no ne-
cessity and its existence is only caused by our imperfec-

AUTOMATISM. 121

tion, our ignorance. I no more regret the above incidents
than I commend one of the opposite character (except for
purpose of encouragement) or blame hydrochloric acid for
acting upon zinc. If they say, well then there is no use
in our trying, things will happen as set from eternity, I say,
unless you do act according to that necessary instinct and
competent memory you will justly become a victim and
you or your life, if nothing of an opposite influence affect
you or it, will justly become martyrs and perish in the
cause of good. Nature cares nothing for individuals and
it is the individual's self-instinct which has brought the
free-will and immortality doctrines into being. "The op-
timism of scientific minds rests in the belief that upon the
physical plane — the development of bodily vigor, or upon
the intellectual plane — making him capable of reasoning
and thinking for himself, or upon the ethical plane — mak-
ing him a useful, trustworthy human being, all dependent
upon beneficial heredity and educational environment, that
mankind must be strong, able and free, and that we shall
not dwindle into physical weaklings, intellectual nonenti-
ties, or spiritual slaves or fanatics." Munro continues,
"Life consists in the free exercise of our faculties and
happiness in the successful performance of duty and
achievement." Indeed I am sure we can rely upon that
factor which exterminates human inertness, and without
which I can see no advancement, no cause for the struggle
and no justification of evil to our moral natures.

Some say that the effect of this belief on them would
be a feeling of a weight and pressure of the rule of mech-
anism, that they must feel free in order to remain happy
and that there is something uncanny in regarding living
creatures as mere complicated machines. These are cer-
tain preconceived ideas, arising, not from a change of belief
induced by reason or by considering, as I have shown, that
the will to us exists, but from a certain fear of the un-

122 THE MONIST.

accustomed caused by the absence or removal of a belief
which had become a habit. Many peoples have lived happy
with no feeling of oppression and been fatalists, — such as
the old Anglo-Saxons and their wierd or fate, the Arabians
and Persians who saw in all that took place the inevitable
will of Allah, or, in more recent times, the Calvinists and
others who betook themselves to this belief as the great and
only consolation against the wrongs and injustices of the
world. They were taught the belief ; it was a part of them
the same as the idea of free willing is a part of the majority
of people to-day and so the opposite doctrine repulsive. We
are thus human. It is a simple matter of attaining the cor-
rect attitude of mind and accustoming oneself to the idea,
which is facilitated by the fact that will to us exists and that
mechanism is more rational, more truthful, and more easily
conceived.

A few more remarks will conclude all that I have to say.
The belief that events are determinedly related to the con-
dition of things immediately preceding them, is now held
by all important thinkers in respect to all kinds of phe-
nomena except higher animal volitions. In each successive
department of fact, conflicting modes of thought have re-
ceded and faded until at last they have vanished every-
where except from this "mysterious citadel of the will."
Then if we have any regard for consistency, and any re-
gard for what facts, so far as we can see, tend to state, it
is without the least disturbance of our scientific conscience
that we can hold, until otherwise proven, that man is only
a more complicated and variously endowed automaton,
physical causes solely determining his bodily actions; the
molecular activities of his cerebrum producing the succes-
sion of his mental states ; and brain changes the real origin
of those movements he is accustomed to regard as express-
ing his feelings, or as executing his intentions, those feel-
ings and intentions being the mere "concomitant symbols

AUTOMATISM. 123

in consciousness." That the universe ought to be rational
is what these conscious feelings tell us, and I think I have
ascertained that most rational conception, monism. Reason
should be satisfied and I have shown that all things are gov-
erned according to that reason which actuates them. Know-
ing that we cannot help doing what our heredity and en-
vironment necessitates, I have inferred the direction that
may be given to the whole course of a life by a little effort
on the part of another to fit the man better to his surround-
ings and to insure his well-being. And lastly, the most
important, I have shown that we may entertain an opti-
mism concerning the universe, a view at once so necessary
to our peace of mind and to our obtaining the best out of an
existence where life must be thought worth the living and
the struggle to repay its cost. In fact I see no reason why
we should not welcome with open arms a conception so
beneficial to the body, to the understanding and to the
craving of the heart.

STEWART P. FOLTZ.
ASHEVILLE, N. C.

GELLERT'S PHILOSOPHICAL POETRY.

ADOPTED BY BEETHOVEN AS THE CONFESSION OF HIS RE-
LIGIOUS FAITH.

BEETHOVEN was born a Roman Catholic and in his
early childhood he received impressions exclusively
of Catholic traditions, Catholic worship, and Catholic art.
It must always have appeared to the boy that the Catholic
church was the only religious institution. When he left the
city of his childhood and youth whose government was in the
hands of a prince-archbishop, one of the electors of the Holy
Roman empire, he came to Vienna which is now and was
especially in his days a typically Roman Catholic city. It
is remarkable that under these circumstances he was not
more limited in his religious conviction and art by the
ecclesiastical influence which had a strong hold, for in-
stance, on Liszt. Beethoven's religion had broadened
under the influence of his acquaintance with other world-
conceptions, and it appears that Gellert contributed most
to the formation of his views.

Beethoven was a great reader, and we can trace the
growth of his conceptions not only by the books he read but
also by the very sentences which impressed him, for he
had a habit of underlining what struck him forcibly, and
thus we can trace his philosophical and religious develop-
ment. Though he never broke away from the church, he
broadened, and his general attitude was not greatly dif-
ferent from that of any other great man of his age. He

GELLERT'S PHILOSOPHICAL POETRY. 125

admired Goethe though the two men were too different in
character and disposition to become friends.

Beethoven's religion was strongly tinted by the ra-
tionalism of the Kantian school. His God was not the
miracle worker, not the God who had revealed himself
exclusively to Jews and Christians, and yet Beethoven did
not hesitate to lend his art to the composition of a great
mass. He was too broad to reject the artistic conception
of a religion the dogmas of which he had outgrown.

As a rule when people broaden they become narrow in
the very field of their mental growth. They love to parade
their breadth of mind by objecting to those forms which
characterize the narrower views. Not so Beethoven. He
did not frequent the church or attend service, but he did
not hesitate, when the opportunity offered, to write a
mass for his friend the archduke Rudolf at his installation
as archbishop of Olmutz, utilizing the traditional form
of service that was customary in the Roman Catholic
church. But his composition outgrew the limits of its
earlier form. It became a cosmic epic, a doxology of the
Creator, a triumphal song of God's glory and a proclama-
tion of his divine dispensation.

The composition of this Missa Solemnis is no longer
ecclesiastical in style. It has become poetry, and as such
the Roman Catholic mode of worship serves as the basis
for the presentation of a broader theme. It is like a
philosophical drama in music; it is the denouement of
the entire world process, an anthem to the infinitude of
existence and the victorious advance of evolution, a hymn
to the world-order.

In this same sense we have to interpret also Bee-
thoven's compositions of the six religious songs of Gel-
lert. They are Protestant in tone and Protestant in the
austerity of their devotion. Beethoven accepts them not
in the letter of the word but more as an artistic attitude

126 THE MONIST.

to express his own sentiments. We cannot doubt that
upon the whole he made the thoughts his own, and
here in Gellert's songs, if anywhere, is expressed his
own religious conviction. From the sentiment of the sixth
of these songs, called "Penitential Hymn," the present
generation has become estranged, and it will be difficult
for us to understand Beethoven's attitude ; but it will ex-
plain itself if we consider that Beethoven in his constant
fear of appearing insincere frequently gave offense to his
best friends, and then showed his regret by profuse ac-
knowledgement of his mistake. These outbursts of temper
and an ostensible show of discourtesy toward his very best
friends, most of whom belonged to the highest circles of the
Austrian aristocracy, are mainly due to his democratic
pride and to the fear lest he depart from his ideal of inde-
pendence. It was for the sake of the God within him that
he was carried away to brusqueness and rude behavior, and
he felt the adjustment had to be made with himself before
God alone.

We here insert a translation of the six hymns of Gel-
lert, following mainly the translation of H. Stevens. They
read as follows :

PRAYER.

O Lord, thy goodness reaches far,

As far the clouds are guided ;

By mercy crown'd, thy creatures are

With needful help provided.

Lord! my defense, my tower and shield,

To me a gracious audience yield,

Approve my supplication.

LOVE THY NEIGHBOR.

If one shall say, "I love the Lord,"
While yet his brother hating,

GELLERT'S PHILOSOPHICAL POETRY. 127

With mockers he shall reap reward,
God's truth abominating;
For God is love, and wishes me
With all on loving terms to be.

DEATH.

Life is ebbing fast away,
Hourly towards the grave I hasten ;
Death may come without delay,
Let this thought my spirit chasten.
Man bethink thee Death is rife,
One thing needful is in life.

NATURE PRAISES GOD.

The Heavens declare the Lord's infinite glory,

The sea and earth sound forth his name,

And tell their origin's wonderful story,

Mark well, O Man, what they proclaim.

Who gave the numberless stars their existence,

Who calls the Sun from his abode,

He cames in brightness and smiles from the distance,

And like a hero keeps his road.

POWER OF GOD.

God is my song!

In strength he reigns victorious,

High is his name,

And all his works are glorious;

Earth, Sea and Heaven to him belong.

PENITENTIAL HYMN,
i.

'Gainst thee alone, God, have I sin committed,
And evil done in thy dread sight,
Thou seest my guilt for which thy wrath is fitted,
See, Lord, my woe and sore affright.

128 THE MONIST.

My piteous wail, my sighs are all before thee,
My tears of deep and bitter grief.

0 God, my God, shall I in vain implore Thee ?
How long wilt thou deny relief?

Lord, do not after my deserts reward me.
Chastise me not! Show me thy face;

1 crave for thee ! thy pardon, Lord, accord me,
O God of patience and of grace.

ii.

0 grant me early, God, thy consolation,
Oh Father of mercy, God of love,

For thine own name's sake grant my supplication,
Thou lov'st to bless from Heav'n above.

Let me thy pathway tread; let me be steady

In my obedience to thy word.

To do thy will I shall be always ready,

1 am thy servant, thou my Lord.

Lord, hasten thou to shelter and defend me ;

Thy light shall lead, point out the goal.

Thy helping hand, O Lord, thy helping hand extend me

And with thy comfort fill my soul.

PAUL CARUS.

CRITICISMS AND DISCUSSIONS.
BUDDHIST LOANS TO CHRISTIANITY.

WITH SPECIAL REFERENCE TO RICHARD GARBE.

In the October Monist Professor Garbe, of Tubingen, admits
a Buddhist basis for the Christian legends of Saints Christopher
and Eustace. In the early part of the same article he also admits
Buddhist influence in the Christian Apocryphal Gospels, but denies
it in the Canonical ones. I herewith submit two passages from the
Gospel of Luke which appear to me to agree as closely with the
earliest Buddhist texts as do the saint-legends admitted by Garbe.

The first parallel is taken from my now forgotten pamphlet of
1905, Can the Pali Pitakas aid us in fixing the Text of the Gospels?
The second is from my Buddhist and Christian Gospels, as indicated
in the first edition (1902) and partially printed in the third and
fourth (Tokyo, 1905, and Philadelphia, 1908).

THE ANGELIC HERALDS AND THEIR HYMN.

Sutta Nipato, Mahavaggo, Nalaka-

Luke ii. 8-14. sutta (known only in Pali, but with

analogues in later Buddhist books).

And there were shepherds in the The heavenly hosts rejoicing, de-
same country abiding in the field, and lighted,

keeping watch by night over their And Sakko the leader and angels

flock. And an angel of the Lord white-stoled

stood by them, and the glory of the Seizing their robes, and praising ex-
Lord shone round about them: and ceedingly,

they were sore afraid. And the angel Did Asito the hermit see in noonday

said unto them, Be not afraid ; for be- . rest,
hold, I bring you good tidings of great

joy which shall be to all the people : for [He asks the angels why they re-

thereis born to you this day in the city joice, and they answer:]
of David a Saviour, which is Christ the

Lord. And this is the sign unto you ; The Buddha-to-be, the best and

Ye shall find a babe wrapped in matchless Jewel,

I3O THE MONIST.

swaddling clothes, and lying in a Is born for weal and welfare in the

manger. And suddenly there was world of men,

with the angel a multitude of the In the town of the Sakyas, in the re-

heavenly host praising God, and say- gion of Lumbini i1

ing, Therefore are we joyful and exceed-

Glory to God in the highest, ing glad.

And on earth peace, divine favor
among men.

The parallel is further carried out in the narrative. The her-
mit, like the shepherds, goes to pay his reverence to the newborn
Saviour.

Considering that between the Greek of Luke and the Pali of
the Sutta Nipato there may lie some lost book, the words in italics
are practically identical. The Pali words hita-sukhataya ("for bles-
sing and happiness") are a convenient phrase, often recurring in
the texts. We here translate them "weal and welfare" for the sake
of poetic effect, but they mean much the same as the English phrase,
"peace and prosperity." Now if Luke, or rather his Oriental inter-
mediary, did actually use the Pali poem, it is evident that omitting
jato ("born"), we find a very good equivalent of the line:

Manussaloke hitasukhatdya jato,
in the line:

«ri TT/S yys cipYjvr) iv dv0pa>7rois euSo/aa.

It is thrown into the form of a Hebrew parallelism, in which
peace on earth and divine favor among men are interchangeable
terms. It is well known that the oldest manuscripts of the New
Testament are at variance here over the word evSo/cia. Some read
cvSoKias (genitive) and then we must render: "among men of good
will" (or the divine favor, i. e., the elect, as Alford says).

This is the reading of the Vulgate and of the English and
American Revised Versions. It is because evSoKia in the Septuagint
means so often the divine good pleasure that the Revised Version
has "men in whom he is well pleased." But the old King James
reading (following the textus receptus afterwards fixed by the
Dutch printers Elzevir) is borne out by the analogy of all Hebrew
parallelisms. This is therefore a passage wherein the Pali Pitakas
can probably aid us in fixing the text of the New Testament.

This parallel is ignored by Garbe, though he mentions that of
Asito and Simeon, which is connected with it in the Pali. But the

*A pre-Christian inscription was lately discovered, marking the site of
Lumbini.

CRITICISMS AND DISCUSSIONS.

Lalita Vistara and other late books relied on by Garbe, and by San-
skrit scholars generally, do not contain the Angelic Hymn. I admit
the weakness of the Asito-Simeon parallel, when taken by itself;
but its strength consists in its organic connection with the Angelic
Hymn, both in Luke and the Sutta Nipato.

In Buddhist and Christian Gospels (4th ed. only) I have shown
that Luke's alteration of the Buddhist legends is no more than his
alteration of the Synoptic tradition (Mark xvi. 7, compared with
Luke xxiv. 6).

When all this has been studied as carefully as older points of
Gospel criticism, the day will come when school-children will know
that "Peace on earth, good will to men" is a Buddhist text.

THE LORD'S THREE TEMPTATIONS.

Classified Collection, Book of Temp-
tations (Pali and Chinese).

In the Wilderness.

And Jesus, full of the Holy Spirit, At one season the Lord was stay-
returned from the Jordan, and was ing in the land of the Kosala, among
led by the Spirit in the wilderness the Himalayas, in a log-hut. While
during forty days, being tempted of thus living in hermitage retired, the
the devil. And he did eat nothing reflection arose within him: "It is
in those days; and when they were really possible to exercise dominion
completed, he hungered. by righteousness, without slaying, or

causing slaughter ; without oppression
or the making thereof; without sor-
row or the infliction thereof."

Temptations to Assume Empire and Transmute Matter.
(In different order in Luke and the Pali.)

And the devil said unto him, If Then Maro, the Evil One, perceived

thou art the Son of God, command in his heart the thought which had

this stone that it become bread. And arisen in the heart of the Lord and

Jesus answered unto him, It is writ- he approached the Lord and spake

ten, Man shall not live by bread alone. thus : "Lord, may the Lord exercise

And he led him up? and shewed him dominion; may the Auspicious One

all the kingdoms of the world in a exercise dominion by righteousness,

moment of time. And the devil said without slaying or causing slaughter;

unto him, To thee will I give all this without oppression or the making

authority, and the glory of them : for thereof ; without sorrow or the in-

it hath been delivered unto me; and fliction thereof."

to whomsoever I will I give it. If "What seest thou in me, O Evil

thou therefore wilt worship before One, that thou speakest thus to me?"

a Matthew has : unto an exceeding high mountain (thus agreeing with the
Pali idea of the Himalayas).

132

THE MONIST.

me, it shall all be thine. And Jesus
answered and said unto him, It is writ-
ten, Thou shalt worship the Lord thy
God, and him only shalt thou serve.

(Continuous in Luke).

"Lord, the Lord hath practised the
four principles of psychical power,
hath developed them, made them ac-
tive and practical, pursued them, ac-
cumulated, and striven to the height
thereof. So, Lord, if the Lord de-
sired, he could turn the Himalaya,
the monarch of mountains, into very
gold, and gold would the mountain
be."

[Buddha replies:]
"The whole of a mountain of gold, of

fine gold,

Twofold, were not enough for one;
Let him who knoweth this govern his

life.
He who hath seen Pain and whence

its rise,

How could such a one bow to lusts?
He who knoweth that the substratum

of existence is what is called in the

world 'Attachment/
Let that man train himself in the

subdual thereof."

Then Maro, The Evil One, said,
"The Lord knows me; the Auspicious
One knows me" And he vanished
thence, unhappy and disconsolate.

Temptation to Commit Suicide.

Book of the Great Decease: Long
Collection, Dialogue 16; Chinese,
No. 2. (Three months before Bud-
dha's death).

And he led him to Jerusalem, and
set him on the pinnacle of the temple,
and said unto him, If thou art the
Son of God, cast thyself down from
hence: for it is written,
He shall give his angels charge con-
cerning thee, to guard thee:
and,
On their hands they shall bear thee

up,

Lest haply thou dash thy foot against
a stone.

Now not long after St. Anando
had gone, Maro, the Evil One, ap-
proached the Lord, and standing be-
side him, addressed him thus:

"O Master, let the Lord now die
the death of an Arahat,8 let the Auspi-
cious One die the death of an Ara-
hat: now, O Master, is the time for
the Lord to die this death ; and more-
over this word was spoken by the
Lord: 'O Evil One, I shall not die
the death of an Arahat until my

8 Parinibbatu, literally "become extinct," conveying the double idea of
physical and passional death. See note in Buddhist and Christian Gospels,
fourth ed., Vol. II, p. 99.

CRITICISMS AND DISCUSSIONS. 133

And Jesus answering said unto him, monks and nuns, my laymen and
It is said, Thou shalt not tempt the lay-women become wise and trained
Lord thy God. disciples, reciters of the Doctrine,

walking in the doctrine and the pre-
cepts, walking consistently, living out

the precepts

"And now, Master, [is this the
case]. O Master, let the Lord now
die the death of an Arahat, let the
Auspicious One die the death of an
Arahat; now, O Master, is the time
for the Lord to die this death !"

When he had thus spoken, the Lord
said unto Maro, the Evil One: "O
Evil One, be content ; the Tathagato's
Arahat-death will not be long: at the
end of three months is the time for
the Lord to die the death of an Ara-
hat."

The Demi Disappears.

And when the devil had completed

every temptation, he departed from Claf lfie* Collectlon <« Se1uence
him for a season. above)'

Here we have, in the Pali and the Chinese of the Classified
and Long Collections, representing two Buddhist sects of great an-
tiquity, the following root-ideas:

1. Appearance of the Tempter to the Saviour in a wilderness.

2. Temptation to assume empire.

3. To use mystical power to transmute matter.

4. To commit suicide.

5. Disappearance of the Tempter when foiled.

Now Luke has these same root-ideas, though expressed differ-
ently in the third case (or, in his text, the first) : viz., the trans-
mutation of stones into bread instead of into gold. Matthew also has
them, but he interpolates Luke's third temptation (that of suicide)
between them. I therefore give the text of Luke, because it agrees
with the Buddhist association, as Luke so often does.4

It is imperatively necessary to study these parallels by means
of their earliest sources ; viz., the Pali and Chinese Hinayana texts

4 See the article Luke and Buddhism, in the General Index to the fourth
edition of Buddhist and Christian Gospels. Of course there is the possibility
that the Temptation scenes of Luke and Matthew (they are not in Mark,
though he mentions the Temptation) belong to a lost book whereto both are
indebted. I believe scholars generally consider that these scenes were not in
the Logia source. My own belief is that Luke was the first to introduce them,
and the editor of Matthew adopted them from his text.

134 THE MONIST.

on the one hand and the Greek Gospels on the other. Seydel made
the great mistake of dealing with late books like the Lalita Vistara,
without distinguishing its lesser value for the comparison. Even so
learned a scholar as Garbe still holds to the Seydel tradition, and
consequently makes short work of the Temptation parallel by quot-
ing these later legends (Monist, October, 1911, pp. 517, 518).

I maintain that there is as much striking agreement between
Luke and the Hinayana texts as there is between the Jatakas and
the legends of Saints Christopher and Eustace, except that the latter
are much longer and furnish more details for comparison.

In the temptation story there is the same Christian coloring as
in the saint-legends, and yet the root-ideas agree. The Christian
coloring consists in making the Master quote scripture, whereas
the Buddhist idea requires him to state some truth. Again and again
in the Jatakas do we find the same magical efficacy ascribed to the
calm enunciation of a truth which the Brahmins ascribe to the
words of the Veda and the Jews to those of the Torah. In the
Zend-Avesta the Tempter uses a similar sacred word, but, as hinted
elsewhere (Buddhist and Christian Gospels, 4th ed., Vol. I, p. 106),
the Mazdean temptation story is only like the Christian one in its
theism and its quotation of scripture. The earliest account of the
temptation of Zoroaster is in the Vendidad, and it consists of only
one, viz., that of empire. Before the temptation the fiend makes a
vain attack on the prophet's life, and after it the prophet declares
that he will defeat the forces of evil by two things:

1. The eucharistic utensils and sacred drink;

2. A magical word taught him by the Godhead in a past eternity.
While all this is of fascinating interest to the student of religion

and of the New Testament in particular, yet it is by no means so
close to the Christian stories as are the earliest Buddhist ones.

The Classified Collection and the Decease Book represent home-
grown primitive Buddhism. And with these does Luke agree rather
than with the geographically and theologically nearer Zoroastrian
account.

In two other cases does Garbe neglect important parallels from
the Pali Nikayas. On page 521 he gives us interesting evidence,
from his Sanskrit reading, of the Hindu character of the idea of
walking upon the water, and says (as since amended) that it "be-
longs not only to the India of Budhism, but to that of Brahminism
also." He ought to have added that the power to walk on the water
is among the gifts of a pious Buddhist, ascribed to him by Buddha

CRITICISMS AND DISCUSSIONS. 135

himself, in the sixth sutra of the Middling Collection in the Pali
(No. 105 in the Chinese version of A. D. 397) — a Hindu book far
older than the Brahmin Mahabharata (though not of course than
its ancient nucleus).

Again on page 517 Professor Garbe says: "Christ fasts forty
days before the Temptation, Buddha twenty-eight days after the
Temptation." But in the thirty-sixth sutra of the Middling Col-
lection we read that Buddha fasted nearly to death before his
illumination, and therefore before his Temptation, which latter oc-
curred after he was Bhagava (the Lord).5

No one who studies the Periplus of the Erythrcean Sea, a cap-
tain's log book of the first century (now newly translated by Wilfred
H. Schoff of Philadelphia) will be able to agree with Professor
Garbe (p. 524) in his limitation of the probability of Indian in-
fluence on Palestine to later times. The Periplus agrees, for the
sixties, with Strabo, who saw 120 ships ready to sail from a Red
Sea port to India in the twenties of the first century. And, as Wil-
fred Schoff has shown in his article on another page of this issue,
the Roman Empire had a sort of Indian craze at that very time.

In Buddhist and Christian Gospels, the Lalita Vistara and other
later books are treated in the Appendix as "Uncanonical Parallels,"
while the body of the book deals with canonical parallels, translated
from the Pali texts by myself and compared with the Chinese ver-
sion of another ancient recension of the Buddhist scriptures (the
Hindu original of which is lost) by Professor Anesaki of Tokyo.

When Rhys Davids's Buddhist Suttas (Sacred Books of the
East, Vol. XI) were sent me by my bookseller in 1881, I found
therein a vigorous protest against any attempt to trace Buddhist
loans in the New Testament. This made a great impression upon
my youthful mind, and acted as a deterrent in that direction until
nearly the end of the century. Then, in 1899, Rendel Harris
astonished me by postulating a Buddhist influence in the Acts of
Thomas and (save the mark!) in the Gospel of Luke! I was
stunned at first, then rallied myself and returned to my old ob-
jections. During the next seven years, however, deeper research
caused me to change ; and when in 1906 I observed the double quo-
tation in John,6 I admitted that here at least was tangible influence.
It was anent the essay which I then wrote that Rhys Davids said

6 Samyutta Nikayo, already quoted. Had the Temptation occurred before
the Illumination we should have read Bodhisatto.

'See "Buddhist Texts in the Fourth Gospel," Open Court, May, 1911.

136 THE MONIST.

to me : "The evidences in favor of intercommunication are growing
every day." (I asked his permission to quote this, and he granted
it). Paul Carus, in The Open Court, October, 1911, has adduced
a remarkable picture from a Greek vase, portraying a goddess with
water for her lower body, and he thinks that both the Buddhist
and Johannine texts may be dependent upon some such ancient
idea. So they may, but the strength of my case lies in the fact that
the Fourth Gospel's express quotations from sacred literature (Law
and Scripture). Instead of admitting that the quotations are from
the Buddhist writings, where I have found them, several of my
critics prefer to ascribe them to some lost apocryphal Jewish book.
But the time is rapidly passing when scholars will feel compelled to
adopt any hypothesis rather than admit the greatness of ancient
India and the supremacy of Buddhism which, at the time of Christ,
was the most powerful religion on the planet and the dominant
spiritual force upon the continent of Asia.

In Buddhist and Christian Gospels (4th ed., Vol. II, p. 237)
we read:

"A collection of [uncanonical] parallels would probably sug-
gest a Christian influence upon later Buddhism; and indeed we
know that, in the eighth century, a Chinese emperor had to forbid
the two religions to be mixed. (See Takakusu's note in his I-Tsing,
Oxford, 1896, p. 224.) This whole field needs very careful work-
ing, more than I am able to give."

Two Anglican clergymen, the late Samuel Beal and Arthur
Lloyd recently deceased, have maintained this position. The fact
is that after Kanishka's Council a new type of Buddhism, pre-
dominantly Mahayana, gradually supplanted the earlier. This new
type was largely foreign, as the primitive type had been native
Hindu. Before the Scythian invasions at the end of the first cen-
tury, the Buddhism of Asoka, with its Pali texts, had been in the
ascendant ; and as, in the first century, Christianity was in a forma-
tive stage, while Buddhism was settled and aggressive, the loans
went from east to west. But afterwards there was a change. In
the first place, a different race of sailors appeared in the Red Sea
ports,7 bearing with them the newer Buddhism which they them-
selves were helping to modify ; and, secondly, Christianity itself was
becoming a rival to Buddhism, and was beginning to assert itself.

It may be that Buddhism influenced the Roman Empire by

7 1 owe this information to Wilfred H. Schoff, translator of the new edi-
tion of the Periplus.

CRITICISMS AND DISCUSSIONS. 137

means of intermediary books, such as that of Elkesai which had a
confessedly Buddhist origin ("Seres of Parthia") ; but I maintain
that the Nikayas of primitive Buddhism were strong enough to
make themselves felt more directly. In A. D. 149 a Parthian prince
headed a long series of scholars who translated them into Chinese;
but Buddhism had been established in the Greek empire (Yona-
loko) since the third century B. C, and was quoted, chapter and
verse,8 by a Greek king, Menander, in the second. Now, the
Chinese began to translate Buddhist books immediately upon that
religion's introduction into their country in the sixties of the first
century ; and after a generation or two of translating manuals, lives
of Buddha etc., they spent three centuries (circa 1 50-450 )9 in trans-
lating the Nikayas (or Agamas). Were the Greeks less curious
than the Chinese? Had not they also begun to translate the books
they admired long before the time of Christ ? My thesis is this :10

While a religion is in its formative stage, its founders take ideas
from their environment, and especially from any system of thought
that is paramount, whether in their own country or in those where-
with they have intercourse. But, once knit together, and moving
by its own momentum, a religion can no longer add to its primitive
documents, though it may give way to new influences in later sec-
tarian developments.

The thesis applied is this :

During the first century Christianity was in its formative stage,
and was influenced by the Old Testament, the Greek mysteries, the
Philonic philosophy and by Hinayana Buddhism. After the first
century Christianity was strong enough to influence another religion
in its formative stage. And such was Mahayana Buddhism, which
was, in fact, a new religion, with new doctrines and new sacred
books. At the same time, Hinayana Buddhism still existed, and indeed
its votaries often cultivated the Mahayana too. Consequently there
could be and there was a complex interchange between Christianity
and Buddhism, both of them giving and taking. But the earliest
interchange was when the Hellenizing Evangelists Luke and John
borrowed some minor features from the Hinayana Nikayas, then
in the ascendant.

Before closing, let me add a note on the Wandering Jew legend

8 So in the Pali, though Chinese versions do not bear it out.

9 Anesaki in Transactions of the Asiatic Society of Japan, 1908, p. 15.

18 See my remarks on the Imperfection of the Record (following Darwin)
in Buddhist Texts in John (2d ed., 1911, p. 27).

138 THE MONIST.

among the "Uncanonical Parallels" in my Buddhist and Christian
Gospels. I lately learned that Sabine Baring-Gould in 1866 pointed
out that the germ of the legend is actually found in the canonical
Gospels :

Mark ix. 1 : "Verily I say unto you, There be some here of them
that stand by, who shall in no wise taste of death, till they see the
Kingdom of God come with power."

Let me repeat what I said last May in The Open Court, and
which Professor Garbe does me the honor to quote: Each religion
is independent in the main, but the younger one arose in such a
hotbed of eclecticism that it probably borrowed a few legends and
ideas from the older, which was quite accessible to it. The loans
are not an integral part of primitive Christian doctrine, as I said
in my Tokyo preface (1905), but lie outside of the Synoptical narra-
tive, and occur in the two later Gospels of Luke and John, both open
to Gentile influences.

Even now I only put forth these parallels upon the same footing
as Gaster, Speyer and Garbe's Christopher and Eustace; and if the
scholars of Europe and Asia finally decide that they are wrong, I
shall withdraw my venture with a good grace. But if this great
admission of Buddhist influence upon the Christian Apocryphal
Gospels and the Eustace and Christopher legends receives its "brevet
of orthodoxy/' the next step will lead a new generation of scholars
back to the canonical Gospels and the canonical Nikayas.

ALBERT J. EDMUNDS.

PHILADELPHIA, PA.

FIRST CENTURY INTERCOURSE BETWEEN INDIA AND

ROME.

EDMUNDS VS. GARBE.

In The Monist for October, 1911, appears a paper by Prof.
Richard Garbe of Tubingen entitled "Contributions of Buddhism to
Christianity," the essence of which is that common material is found
in the Apocryphal writings of both religions, but that no connection
can be proved between the Canonical texts, and that this is due to
the fact that active intercommunication between India and the Medi-
terranean did not exist until the second century, or, as Professor
Garbe puts it, "Buddhist influence might have penetrated to Pales-
tine by way of Alexandria, but still more probably by way of
Antioch in Syria, but they" (that is, writers pointing out similari-

CRITICISMS AND DISCUSSIONS. 139

ties) "are not apt to raise this possibility to a serviceable degree
of probability for as early a period as the first post-Christian cen-
tury."

In thus denying the existence of a rapidly growing and very
important stream of commerce between India and Rome, it seems
evident that Professor Garbe has overlooked historical facts which,
if duly recognized, may compel him to revise his opinion in this
matter as he changed his mind in regard to the migration of the
fish-symbol from India to Rome.

The incontestable facts of history are that a large Indian in-
fluence and an active commerce existed as far as the Mediterranean
coast of Syria soon after the conquests of Alexander, and that the
conquest of these territories by Roman armies ending in the public
triumphs of Pompey the Great, created in the Roman capital a craze
for Indian products and luxuries of all kinds which during the
actual lifetime of Christ had become a serious problem to the Roman
government, leading to numerous efforts at discouragement of the
taste for Eastern luxuries which was draining the Empire of its
resources. This craze met with a temporary check at the death of
Nero. It regained full intensity under Trajan and Hadrian, and
was again in a decline during a considerable part of the second
Christian century, reviving during the reign of Commodus, and
again more seriously declining with the failing powers of the Em-
pire. The existence of this craze for Indian imports and of the
substantial remittances of gold coin required to balance the trade,
may be surely proved by the hoards of Roman coin unearthed in
Southern India and catalogued by the Government Museum at
Madras ; in which these fluctuating eras of trade prosperity and
depression clearly appear. Instead, therefore, of the creation of a
new import trade from India in the second century, as Professor
Garbe asserts, the most active trade was in the first half of the first
century, with two revivals at the beginning and the end respectively
of the second ; and the drain of specie from Rome to the East had
set in even before the birth of Christ.

Space forbids a statement in detail of the almost innumerable
facts existing to support the foregoing statement. The following
may at least serve as suggestions.

Alexander married a Persian princess, but numbers of his
officers took Bactrian and Indian wives.

Greek colonies were established by him along the entire Indian
frontier, and colonies of his newly established Indian subjects were

I4O THE MONIST.

similarly established nearer Greece. A Greek dynasty ruled in
Bactria after the Parthian revolt disrupted the Seleucid empire, and
one of its rulers, Menander, powerfully influenced the spread of
Buddhist thought through the Greek-speaking world.

A Greek ambassador at the Maurya court, Megasthenes, wrote
a detailed account of its customs, its Brahmin religion, and its cap-
ital Pataliputra; which was widely read and commented upon for
centuries.

The conquest of Judea by the Persians and the destruction of
the Persian empire by Alexander, reduced the force of Judaism and
Mazdaism as world-religions, while the exodus of the Greeks into
the East broke down what was left of the distinctive Greek religion.
There existed then no faith strongly upheld in the Eastern Medi-
terranean basin from the third to the first centuries B. C.

Two generations after Alexander's conquests, the Emperor
Asoka established Buddhism as the state religion of India, and in
his second edict, preserved to us in a rock inscription, he mentions
the sending of envoys to all countries with which he entertained
relations ; particularly mentioning "the dominions of the Greek king
Antiochus, and those of the other kings subordinate to that An-
tiochus." This ruler is identified with Antiochus Theos (B. C. 261-
246) in whose capital of Antioch these Indian envoys, physicians
and missionaries, for they seem to have held that triple character,
were received. In the capital of that ruler who profaned the Jewish
Holy of Holies in order to set up the worship of himself, the Bud-
dhist faith was preached by men sent from the head of the Buddhist
organization, the ruler of the richest, most powerful and most popu-
lous empire in the world at that time.

During the better days of the Seleucidae, overland communica-
tion between India and Syria was unhampered, and there is every
indication that it carried an active commerce. The fall of the Se-
leucid power and the rise of the Parthian monarchy interposed a
fiscal obstruction which the Greek rulers in Egypt, the Ptolemies,
quickly turned to their advantage. By the establishment of ports
on the Red Sea, Egyptian shipping was enabled to trade in the Gulf
of Aden and obtain Indian merchandise with less transshipment
than had formerly been made, and the opulence of this trade is
vividly described by Agatharchides, writing in the closing years
of the second century B. C.

For two centuries following Alexander's death we may assume
that the Indian trade went no further than the Eastern Mediter-

CRITICISMS AND DISCUSSIONS. 141

ranean ; but the rise of Rome as a world-power, dating finally from
the sack of Carthage and Corinth in 146 B. C, brought the Romans
into active trade with the Levantine ports, as evidenced by the growth
of piracy in that region, preying on the Roman ships. Pompey's
contributions to the Roman state were the suppression of the pirates
and the conquest of the Levant ; and in his triumphal processions,
which are repeatedly mentioned by Pliny in his "Natural History,"
all the more precious varieties of Indian merchandise were exhibited
and brought into popular demand. This point is of importance.
Two generations before the birth of Christ the spoils of a conquered
land resulted in a fashion for the imports of that land rather than
for its own products: for the Indian goods transshipped at the
Syrian ports, rather than for the products of Syria itself. The Indian
trade had become Syria's richest asset.

The same facts are in evidence upon the conquest of Egypt and
the incorporation of the Alexandrian trade into the Roman fiscal
system. Primarily grain was the staple export from Egypt to Rome,
but the more profitable trade consisted in the incense of Arabia and
the gems and spices and textiles of India.

In 22 A. D., in a letter from the Emperor Tiberius to the
Roman Senate set forth by Tacitus in his "Annals," the growing
drain of specie is pointed out and a remedy demanded. "How,"
said the Emperor, "are we to deal with the peculiar articles of fem-
inine vanity, and in particular with that rage for jewels and precious
trinkets, which drains the Empire of its wealth and sends, in ex-
change for baubles, the money of the Commonwealth to foreign
nations; even the enemies of Rome?"

The geographer Strabo, writing in almost the same year, records
having seen a single fleet of 120 ships about to start by the favorable
monsoon from an Egyptian Red Sea port to India. Two genera-
tions later, according to Pliny, the unfavorable trade-balance had
grown more serious still ; as he says "in no year does India drain
us of less than 550,000,000 sesterces, giving back her own wares,
which are sold among us at fully 100 times their first cost."

550,000,000 sesterces in those days was a very considerable
sum. In modern valuation it would approach $25,000,000, and this
was the state of affairs existing at the end of the reign of Nero.
Can one imagine a modern trade requiring so enormous an export
of specie without a corresponding influx of merchants, bearing
ideas no less than goods, from the producing to the purchasing
market? This condition is indeed set forth with sufficient exactness

142 THE MONIST.

by the writer of the Apocalypse, where he describes, under a veil
of fiction, the burning of Rome and the ruin that thereby came upon
"every ship-master and all the company in ships, and sailors, and
as many as trade by sea," while of the merchandise they handled are
specified numerous Indian products, precious stones, pearls, silk,
ivory, fragrant wood, iron (Indian steel was known even to the
Greeks), cinnamon, odors, ointments. This was in 64 A. D. A
year or two before, according to Pliny, at the funeral of Nero's con-
sort Poppsea, there was burned a store of Eastern spices representing
a year's imports and valued at millions.

The unknown merchant of this same period who has left us
that interesting log of his trading voyages from Roman Egypt to
India which we know as the "Periplus of the Erythrsean Sea/'1
enters more specifically into the various articles dealt in and the
marked growth in the trade. Briefly following him along his
voyage, at the lower western shore of the Red Sea were imported
Indian iron and steel, Indian cloth, muslin and lac. On the oppo-
site shore, at the Arabian side of the straits, was a special port
established for incoming Indian ships, which were apparently for-
bidden to trade by the Arabs' port of Muza. On the outer coast,
which we know as Somaliland, Indian cinnamon was found and
ships of larger size were now required to handle it. Other Indian
gums are specified, among them gum dammar, and an Indian rem-
edy for tropical disorders, macir, which does not again appear in
western commercial annals until the days of the Portuguese. At
Cape Guardafui was a regular trading rendezvous to which came
numerous ships from the Gulf of Cambay bringing cereals, clari-
fied butter, sesame oil, cotton goods, and honey from the reed called
"sacchari" ; the first known record of sugar as an article of com-
merce.

On the southern coast of Arabia were two ports at which In-
dian shipping regularly called. At the one Roman coral, tin, cop-
per and storax were transshipped for the Indian trade, and at the
other, more to the east, Indian shipping often wintered. Proceed-
ing with our merchant to the mouth of the Indus, we find these
same Roman products recorded among the imports of Northwestern
India including, strange to say, Italian wines, preferred to the Syr-
ian, or Arabian; all of which were imported. At the port of Bary-
gaza in the Gulf of Cambay, the newly established Saka government

*A new translation, with learned notes, of this document is listed by
Longmans for 1912. The translator is the writer of this article. — ED.

CRITICISMS AND DISCUSSIONS. 143

maintained a regular system of pilotage which was necessary to
avoid destruction of foreign vessels by the tremendous tides of that
estuary. These pilot-boats coasted the shores of the Gulf for 100
miles outside the port, and our merchant records that both Greek
and Arabian shipping was guided by them. Here he found among
other things, spikenard, highly treasured in the ointments of the
time as appears in the Gospel of Mark, chap. xiv. 3-5 ; and more
important still, murrhine, that Indian carnelian, its colors heightened
by slow heat and shaped into drinking vessels for which, according
to Pliny, fabulous sums were paid in Rome. Petronius broke one
of Nero's basins valued at 300,000 sesterces, while Nero himself
paid one million sesterces for a single cup. Here at Barygaza were
also imported for the Indian markets Italian wine, copper, tin and
lead for the coinage of the country, coral and topaz, storax for the
Chinese trade, glass, gold and silver coin on which there was a
profit when exchanged for the money of the kingdom, — the Roman
coinage being superior to the Hindu, which was of base metals
only, while the Roman gold coin formed the standard of exchange
for all the nations of India. Further down the coast in the back
waters of Cochin and Travancore he found especially pepper and
malabathrum (cinnamon leaves), on account of the great quantity
and bulk of which our merchant tells us, large ships were sent to
those ports, Greek and Arabian as well as Hindu. Here were found
also great quantities of fine pearls, ivory and precious stones, beryls,
diamonds and sapphires, and tortoise-shell, coming from as far dis-
tant as the Straits of Malacca in ships specially recorded as "of great
size" in comparison with those Roman ships with which our author
was familiar. In the adjoining nation, easily recognizable as the
Chola Kingdom, whose capital Uraiyur (Trichinopoly) is recog-
nizable under the author's corruption of Argaru, were found in
profusion all the merchandise sent from Egypt ; while its ports were
a center of shipping not only from Egypt but from the Ganges and
Malacca. Here our author digresses to mention Chinese silk brought
overland through Bactria to Western India for reshipment to the
Roman empire, and among the exports from Rome to balance this
trade is again mentioned "a great quantity of coin," fully support-
ing the testimony of the hoards unearthed in Southern India and
recorded at Madras. The coins of Claudius and Nero are among
the most numerous of all discovered.

The word which the author of the Periplus uses for the palm
oil found by him at Zanzibar, was a word brought from India, the

144 THE MONIST.

Prakrit nargil, coconut. The most authentic information at the
disposal of Lieutenant Speke in preparing for his expedition for the
discovery of the sources of the Nile, was a map based on the Hindu
Puranas, and setting forth information brought by these same In-
dian vessels found by the merchant of the Periplus on the African
coast. These traders had penetrated the interior and knew of the
Nyanza lakes, as the Egyptians did not. The facts already cited
are surely sufficient to show a volume of trade not only inter-
nationally important, but so great and so one-sided as to be recog-
nized as a serious menace to the prosperity of the newer, poorer,
and less populous empire of the West.

Petronius, Nero's crony whom Pliny connects with the mad
auction of murrhine cups, has left us Trimalchio's Dinner, that in-
imitable sketch of parvenu society in Rome at the middle of the
first Christian century, in which it is mentioned as a matter of course
that a rich man sent to India for so slight a thing as mushroom
spawn. Pliny tells how Lollia Paulina, wife of the Emperor Ca-
ligula, wore at an ordinary betrothal entertainment emeralds and
pearls to the value of 40,000,000 sesterces; "indeed, she was pre-
pared to prove the fact by showing the receipts and acquittances."
And he goes on to bemoan the prodigality in the use of Indian
pearls by Roman women ; "now, at the present day" (about 70
A. D.) "the poorer classes are even affecting them.... they put
them on their feet, not only on the laces but all over the shoes; it
is not enough to wear pearls but they must tread upon them."

The author of the Periplus tells how the Indian trade, as far
as western shipping at least was concerned, used to be done in small
vessels close to shore; and how Hippalus "by observing the loca-
tion of the ports and the conditions of the sea, discovered how to
lay his course straight across the ocean" — the monsoon being called
the "wind of Hippalus" — so that from that time ships steered
direct from the Gulf of Aden and Cape Guardafui to the ports of
India, "holding their course straight out to sea with a favorable
wind, quite away from the land." This discovery of Hippalus oc-
curred in the time of Claudius, and the resulting increase of trade
culminated under Nero. Pliny recounts the same story.

The distinction made by Professor Garbe between the paral-
lelisms in the Canonical texts and those in the Apocrypha points
to a period of change in the national and religious politics of India
which is apparently not realized, and is yet of importance in the
study of the interrelations between East and West. At the be-

CRITICISMS AND DISCUSSIONS. 145

ginning of the second century came the Council of Kanishka, the
Scythian conqueror of the northwest, the second great Buddhist
Council. The Scythians were looked upon askance by the native
Hindus. It is recorded in the annals of the Andhra dynasty that
after a victory over the Scythian or Kushan dominion, a memorial
was set up at Karli telling how the orthodox Andhra king had
"destroyed the Sakas, Yavanas and Pahlavas, properly expended
the taxes levied in accordance with the sacred law, and prevented
the mixing of the four castes." A schism was thus set up in India,
racial rather than religious at its root, which later expanded into
the great division between the early Buddhist canon and its Maha-
yana corruptions. It was the earlier Buddhism which was carried
to the Syrian coast by the messengers of Asoka. It was still a
conservative Buddhism, but mingled with various central Asian
religions, which was carried to the same region by the subjects of
Kanishka; while the great changes of the succeeding centuries
brought into Buddhism, no less than into Christianity, a mass of
childish apocryphal legends which passed from one faith to the other
in much the same way as the earlier ideas, which to some extent at
least are found paralleled in the Canonical texts. The distinction is
important ; but it is a distinction based on changed national politics,
rather than newly created trade, as Professor Garbe would infer.
This change at the coming of the Scythian shipping into the Indian
Ocean is vaguely indicated by Pausanias in a passage not usually
understood, where he speaks of the Island of Seria (which was
really Masira off the Southern coast of Oman) but which he con-
fuses with the Seres of China. He tells us that "both the Seres and
the inhabitants of the neighboring islands of Abasa and Sacsea [the
modern Kuria Muria] are of the Ethiopian race. Some say, how-
ever, that they are not Ethiopians but a mixture of Scythians and
Indians."

At that ancient meeting-point between the Nile trade and that
of the Indian Ocean, the Abyssinian highlands, the author of the
Periplus gives us the first mention of the Kingdom of Abyssinia,
then newly established, and of its capital, "the city of the people called
Axumites." The great series of monoliths at Axum dates probably
from the first century rather than the second and shows orthodox
early Buddhist influence rather than the Buddhism of later ages.
James Fergusson's description of the great monolith has not been
bettered, "the idea Egyptian but the details Indian, an Indian nine-
storied pagoda translated in Egyptian in the first century of the

146 THE MONIST.

Christian era." He notes its likeness to such temples as the Bodh
Gaya, and says it "represents that curious marriage of Indian with
Egyptian art which we should expect to find in the spot where the
two peoples came in contact and enlisted architecture to symbolize
their commercial union." And so obviously Hindu a ceremony as the
Brahman's investiture with the sacred cord is 'still preserved as the
sign of baptism in Abyssinian Christianity.

Now the very existence of the Abyssinian state in the beginning
was dependent upon the alliance of the Romans in Egypt, who en-
couraged its growth in order to counteract the Arabian domination
of the Red Sea trade; and this was originally a matter of first-
century diplomacy, culminating with the decay of the ancient Sa-
baean capital Marib, and the conquest of the Nabatsean kingdom
under Trajan.

While these relations between India and the West were being
developed, a similar connection was formed with the East. The
silk-market of the world was in a fertile valley of the Pamirs, whither
Chinese merchants brought their goods by the great Pei-lu or
"Southern way" along the desert of Turkestan. Nomadic marauders
hampered the trade, so that the author of the Periplus remarked of
China that "few men come from there and seldom"; but the armies
of Pan-Chao forged the last link of the great chain, and before the
end of the first century communication was unbroken from the
English Channel to the Yellow Sea, and the tin of Cornwall ex-
changed for the silk of Ts'in.

We are therefore forced to the conclusion that the middle of the
first century of the Christian era was a time of unexampled com-
mercial activity between East and West, that political turmoil
both in Rome and India then caused a lull in this traffic, which did
not fully revive until the later years of the second century, and that
Professor Garbe's argument, in so far as it affects the general inter-
relation between Buddhism and Christianity, is to that extent in
need of revision.

A Freeman could write "our business is with Europe, and with
other parts of the world only so far as they concern Europe." And
the Christian Gospels have been read with Western eyes. The Holy
Land out of which they came has been conceived as a sort of Ultima
Thule, beyond which lay a great void; the country beyond Jordan
being remembered as a wilderness, wherein One was tempted of
the devil. A barrier is thus set up and maintained, artificial and

CRITICISMS AND DISCUSSIONS. 147

without foundation, the defence of which some would assert to be a
condition of right belief.

For some reason this type of critic would deny that an influx
of new commodities carried with it a renascence of ideas, and would
draw the old line about Christianity, limiting its environments to the
country this side Jordan ; inevitably admitting the larger expression
which it received from the Gentile peoples of the northern coast
of the Mediterranean, but ignoring that which came from the Gen-
tile peoples beyond the Euphrates and the "Erythraean Sea." It is
difficult to understand what is gained by so obviously tearing Chris-
tianity half out by the roots. The new faith reached out toward
the East no less than toward the North and the West, and was so
formulated as to be understood by all, — to be part and parcel of the
intellectual environment of all. It would therefore be almost a
matter of course that Christianity, making its appeal in the centers
of trade, at the terminus of the great commercial highways from the
East, should express its message in terms likely to be understood
by those acknowledging Buddhism, the faith of the countries at the
eastern terminus of those highways, and of all the world's faiths
at that time, unquestionably the most influential.

Of lasting value, therefore, are all works which help to break
down and destroy the ancient but artificial barriers between East
and West; and of such works a very notable one is by Mr. Albert
J. Edmunds, Buddhist and Christian Gospels Now First Compared
from the Originals (Philadelphia, 4th edition, 1908-09).

Mr. Edmunds's work goes back to the age in which the Gos-
pels were formulated, and reconstructs the background of world-
thought and politics of which they have been so generally deprived.

It is necessary to a clear understanding of the Christian religion
that a painstaking study be made of its points of contact with the
Buddhist, and of the many thoughts which are their common prop-
erty. Such a study can detract from neither faith, but must rather
serve both, by showing more fully the human ideas and aspirations
out of which they arose; by showing them to be living realities in
the upward path of mankind, rather than abstractions limited each
to its own area. It remains for the individual to make his choice
between the two, but he must no longer be hedged in by an arti-
ficial barrier, which for centuries has separated peoples closely re-
lated at the Christian era, and now by the march of events, once
more brought into contact. It is no longer possible for the Teuton
to hold aloof from the Tartar, the Anglo-Saxon from the Japanese;

148 THE MONIST.

mutual interest requires a closer understanding, a readier sym-
pathy, and a fuller acknowledgment of common aspirations. Pres-
ent-day commerce has its influence in this direction, and history
likewise; but sympathetic comparison of the religions of the two
races is among the most important of all such influences.

This work by Mr. Edmunds is therefore especially timely, and
the ripe learning which he brings to this great subject assures its
permanence.

Previous comparisons, such as those of Hardy and Seydel, had
depended on translations and secondary authorities and had neces-
sarily confused primitive writings with commentary and patristics,
sometimes of late date ; while Mr. Edmunds works with the advan-
tage of an intimate knowledge of both the Pali and Greek originals.
He has limited himself to parallels occurring only in the primitive
writings of either religion, and his presentment is most convincing.
The facts of history would naturally lead the open-minded investi-
gator to look for a certain parallelism growing out of this ancient
culture-field, but hardly to expect so formidable a list as 102 paral-
lels of word or thought in the Canonical writings and 13 more in
the books relegated to the Apocrypha, but of early date, in both
religions. Furthermore, as Mr. Edmunds has shown in another
place (Buddhist Texts in John, see also Open Court, May, 1911)
Buddhist writings are actually twice quoted as scripture in the
Christian Gospel of John. The proof of intercommunication is
abundant.

Mr. Edmunds's comparisons provide a rich field of information
for the student of comparative religion, and his conclusion is con-
servative enough to satisfy scholars of every kind. "No borrowing
is alleged on either side — Christian or Buddhist. In these parallels
we offer no theory but present them as facts. They at least belong
to a world of thought which the whole East had in common."

Were it necessary, many other facts in the history of Syria and
Palestine might be cited in support of Mr. Edmunds's argument.
The Persianizing tendencies in the later Jewish church, due to the
captivity in the Empire of Cyrus, are well known, while recent
works by such British investigators as General Sir Thomas Holdich
in upper India and Afghanistan, marshal abundant evidence of the
eastern extension of the Assyrian Empire and actually of the settle-
ment of Jewish captives in considerable numbers at the very gates
of India. Here then was a central administration dominant from
the Nile to the Indus seven centuries earlier than the period when

CRITICISMS AND DISCUSSIONS. 149

Mr. Edmunds seeks to prove active intercommunication. Six cen-
turies before the same period, one of the last of the Pharaohs opened
a canal from the Nile to the Red Sea to bring his country into com-
munication with the Eastern trade in defiance of her Mesopotamia!!
oppressors. Six centuries after the Christian era Buddhist and
Christian legends were so mingled in Western Asia, that the Koran
absolutely confused the two; while a little later in Eastern Asia a
Chinese emperor issued an edict forbidding the same confusion then
prevalent in his dominions.

It should hardly be necessary to recall that Palestine was the
West-land of the Mesopotamian civilization just as India was the
East-land ; and that it was at the western rim of that ancient culture-
field, and not from the Greek or Roman environment, that the Chris-
tian Gospels arose, just as it was at the eastern rim that the Buddhist
writings were formulated. Without in any way assuming identity
of origin or purpose, it would be strange indeed if there were not
identity of expression and parallelism of thought between these two
great Canons ; and Mr. Edmunds's proof of that identity is a distinct
contribution to human knowledge.

WILFRED H. SCHOFF.

PHILADELPHIA, November, 1911.

MR. BERTRAND RUSSELL'S FIRST WORK ON THE
PRINCIPLES OF MATHEMATICS.

In The Monist for January, 19 10,1 Dr. Carus has criticized an
article of Mr. Bertrand Russell's on "Recent Work on the Principles
of Mathematics," published in the International Monthly for 1901.
A copy of the article lately came into my hands, corrected in Mr.
Russell's handwriting back again to what he originally wrote.2 The
editor or type-setter occasionally changed Mr. Russell's words to
words which he considered more dignified, perhaps. Thus, the
International Monthly makes Mr. Russell says that in pure mathe-
matics we "take any hypothesis that seems assuring, and deduce its
consequences." Mr. Russell had written "amusing," and the sub-
stitution of "assuring" rather took away from the force of Mr.
Russell's contention that in mathematics we are not in the least con-

1 Vol. XX, pp. 46-63.

8 Mr. Russell has since kindly told me that this statement is correct.

8 Quoted in The Monist, Vol. XX, p. 50.

I5O THE MONIST.

cerned with the truth or otherwise of our hypotheses or consequents,
but merely with the truth of the deductions.

The import of another alteration I quite fail to grasp. Mr.
Russell wrote that "pure mathematics consists entirely of assertions
to the effect that, if such and such a proposition is true of anything,
then such and such another proposition is true of that thing." The
International Monthly* put "asseverations" for "assertions" ; and so
Dr. Caruss remarked : "I wish Professor Russell would not describe
mathematics as consisting of 'asseverations' ; the very idea is jarring
on my conception of the nature of mathematics."

When Dr. Carus6 uses here, as he often has before, the word
"anyness" to describe what is the fundamental characteristic of
mathematics in his conception, he seems to be in agreement with
one of the main tenets of Mr. Russell:7 the propositions of logic
"can be put into a form in which they apply to anything whatever" ;
"we never know what [which thing] we are talking about" in
mathematics ; the assertions are that, "if such and such a proposition
is true of anything, then such and such another proposition is true
of that thing."

I am going to try shortly to explain Mr. Russell to my readers.
Mr. Russell's work on the principles of mathematics and the rela-
tion of mathematics to logic "is by no means," as Couturat said,8
"like certain philosophical systems in fashion, a brilliant paradox,
an individual and ephemeral fantasy, without roots in the past and
without fruits in the future, but the necessary culmination and
crowning of all the critical researches to which some mathematicians
have given themselves up for the last half-century. It is a well-
known fact that modern mathematics have constantly tended to
deductive rigor of the reasonings and logical purity of the concepts.
To these new needs of the scientific spirit a logic more and more
exact and refined had to respond ; the indispensable instrument of
this new logic is the 'symbolic9 logic' invented by Peano, practised
by a whole school of mathematicians, and perfected by Russell.

4 Quoted in The Monist, Vol. XX, p. 50.

° Ibid., p. 53.
9 Ibid., p. 50.
''Ibid., pp. 47, 49, 50.

8 Les Principes des mathematiques, Paris, 1905, pp. v-vi. A translation of
Couturat's work by the author of this article is in preparation.

"As a matter of fact, Peano has always called his system "mathematical
logic." The name of Frege ought to be mentioned with Peano's in this con-
nection.

CRITICISMS AND DISCUSSIONS.

It is owing to this logistics (as we will call, it) that all mathe-
matical theories have become susceptible of being subjected to
a precise and subtle analysis, and of being reconstructed logically
with a small number of fundamental data (primitive principles and
notions). It is owing to this that Russell has been able, while com-
pleting on certain points this work of logical reduction, to system-
atize all the results acquired in a vast and profound synthesis, which
is the quintessence of preceding works, and which manifests the
spirit of modern mathematics."

Consider, for a moment, what this logical analysis means. Take
the science of arithmetic. All its material and principles have to
be reduced to logical terms and expressed unambiguously. This
enormously important work is extraordinarily long and often tedious.
Processes of thought that most mathematicians perform more or less
accurately by "intuition" often take up, in expression, pages of
symbols of logical deduction — if such deduction is possible ; but then
we get complete, and not only "moral," certainty, and an insight into
the structure of certain truths. In Dr. Whitehead and Mr. Russell's
latest book10 there are 666 pages, most of them written in symbols,
often with abbreviated proofs, and yet the definition of numbers is
not yet reached! Things called "1" and "2" are defined, but not
till the second volume will it appear that they are numbers!

There is a story current in Cambridge that, after a term's lec-
turing on the principles of mathematics, Mr. Russell informed his
hearers that if they were good they should do simple addition next
term. . . .And so recently as 1888 Dedekind's tract of 58 pages, Was
sind und was sollen die Zahlenf11 was derided by some mathema-
ticians because it devoted so much space to the foundations of arith-
metic !

Few people can see the immense importance of Mr. Russell's
work ; fewer know how laborious it has been and by what splendid
qualities of mind and character it has been inspired. That is all
I can say on this head, as I do not wish to gush and am not writing
an obituary notice. Not quite so few people know how brilliant
Mr. Russell's work is. Mr. Russell's investigations have revealed
some very striking things, and Mr. Russell has said them strikingly
— said them, too, in books and articles which are read with delight,
and sometimes with profit, by those who are untrained to follow

10 Principia Mathematica, Vol. I, Cambridge, 1910.

"English translation by W. W. Beman, in Dedekind's Essays on the
Theory of Numbers, Chicago, 1901.

152 THE MONIST.

Mr. Russell's work. I suppose Mr. Russell has a natural love of
paradox, but his paradox is always used to give point to the state-
ment of some truth. In his talk and writings, Mr. Russell is con-
scientious, truth-loving, keen and witty.

I now propose to analyze the International Monthly article and
to try to show how the fundamental doctrines of the Principles of
Mathematics are shortly stated in it. This will continue my article
in The Monist for January, 1910 ;12 and in future I hope to trace
Mr. Russell's work beyond 1903.

The first published indication of the effect of Peano's work
on Russell appeared in an article by Russell on "Recent Work on
the Principles of Mathematics" in the International Monthly for
1901. 13 Boole, he said,1* was "mistaken in supposing that he was
dealing with the laws of thought: the question how people actually
think was quite irrelevant to him, .... His book was in fact con-
cerned with formal logic, and this is the same thing as mathematics."
Then came1* a definition of pure mathematics: "Pure mathematics
consists entirely of assertions to the effect that if such and such a
proposition is true of anything, then such and such a proposition
is true of that thing. It is essential not to discuss whether the first
proposition is really true, and not to mention what the anything is of
which it is supposed to be true. Both these points would belong
to applied mathematics. We start, in pure mathematics, from
certain rules of inference, by which we can infer that */ one propo-
sition is true, then so is some other proposition. These rules of in-
ference constitute the principles of formal logic. We then take any
hypothesis that seems amusing, and deduce its consequences. //
our hypothesis is about anything, and not about some one or more
particular things, then our deductions constitute mathematics. Thus
mathematics may be defined as the subject in which we never know
what we are talking about, nor whether what we are saying is true."

The reduction of mathematics to logic was spoken of:16 "Now
the fact is that, though there are indefinables and indemonstrables
in every branch of applied mathematics, there are none in pure

12 Vol. XX, pp. 93-"8.
"Vol. IV, pp. 83-101.
ulbid.f p. 83.

15 Ibid., pp. 83-84. For "assertions" was misprinted "asseverations," and
for "amusing" was misprinted "assuring."
19 Ibid., p. 84.

CRITICISMS AND DISCUSSIONS. 153

mathematics except such as belong to general logic. Logic, broadly
speaking, is distinguished by the fact that its propositions can be
put into a form in which they apply to anything whatever. All pure
mathematics — arithmetic, analysis, and geometry — is built up by
combinations of the primitive ideas of logic, and its propositions are
deduced from the general axioms of logic, such as the syllogism
and the other rules of inference."

When dealing with questions of the principles of mathematics,
the function of symbolism is exactly the opposite to that of sym-
bolism in the other parts of mathematics. Russell said:1? "The fact
is that symbolism is useful because it makes things difficult. (This
is not true of the advanced parts of mathematics, but only of the
beginnings.) What we wish to know is, what can be deduced from
what. Now, in the beginnings, everything is self-evident; and it
is very hard to see whether one self-evident proposition follows
from another or not. Obviousness is always the enemy of correct-
ness. Hence we invent some new and difficult symbolism, in which
nothing seems obvious. Then we set up certain rules for operating
on the symbols, and the whole thing becomes mechanical. In this
way we find out what must be taken as premise and what can be
demonstrated or defined."

ii.

Referring to Peano's three indefinables in arithmetic, Russell
remarked:18 "Even these three can be explained by means of the
notions of relation and class ; but this requires the logic of relations
which Professor Peano has never taken up."

Russell19 then indicated his contradiction:

"There is a greatest of all infinite [cardinal] numbers, which
is the number of all things altogether, of every sort and kind. It
is obvious that there cannot be a greater number than this, because,
if everything has been taken, there is nothing left to add. Cantor
has a proof that there is no greater number, and if this proof were
valid, the contradictions of infinity would re-appear in a sublimated
form. But on this one point, the master has been guilty of a very

subtle fallacy, which I hope to explain in some future work."

* * *

Russell's statement of Zeno's puzzle about Achilles and the
tortoise was:20

17 Ibid., pp. 85-86. 18 Ibid., p. 87. 10 Ibid., p. 95-

30 Ibid., pp. 95-96.

154 THE MONIST.

"The argument is this: Let Achilles and the tortoise start
along a road at the same time, the tortoise (as is only fair) being
allowed a handicap. Let Achilles go twice as fast as the tortoise,
or ten times or a hundred times as fast. Then he will never reach
the tortoise. For at every moment the tortoise is somewhere, and
Achilles is somewhere; and neither is ever twice in the same place
while the race is going on. Thus the tortoise goes to just as many
places as Achilles does, because each is in one place at one moment,
and in another at any other moment. But if Achilles were to catch
up with the tortoise the places where the tortoise would have been
would be only part of the places where Achilles would have been.
Here, we must suppose, Zeno appealed to the maxim that the whole
has more terms than the part. Thus, if Achilles were to overtake the
tortoise, he would have been in more places than the tortoise; but
we saw that he must, in any period, be in exactly as many places
as the tortoise. Hence we infer that he can never catch the tortoise.
This argument is strictly correct if we allow the axiom that the
whole has more terms than the part. As the conclusion is absurd,
the axiom must be rejected, and then all goes well. But there is
no good word to be said for the philosophers of the past two thou-
sand years and more, who have all allowed the axiom and denied

the conclusion."

* * *

The converse of the Achilles, which Russell called "the paradox
of Tristram Shandy," was then described ;21 and the remark was
made22that the notion of continuity depends upon that of order, and
that "nowadays, quantity is banished altogether [from mathematics]
except from one little corner of geometry, while order more and
more reigns supreme." Nowadays, too, a limit is defined ordinally.23

Then :2« "Geometry, like arithmetic, has been subsumed in recent
times under the general study of order. It was formerly supposed
that geometry was the study of the nature of the space in which we
live, and accordingly it was urged by those who held that what exists
can only be known empirically, that geometry should really be
regarded as belonging to applied mathematics. But it has grad-
ually appeared, by the increase of non-Euclidean systems, that ge-
ometry throws no more light upon the nature of space than arithmetic

n Ibid., pp. 96-97-
"Ibid., p. 97.
*Ibid., pp. 97-98.
"Ibid., p. 98.

CRITICISMS AND DISCUSSIONS. 155

throws upon the population of the United States. Geometry is a
whole collection of deductive sciences based on a corresponding col-
lection of sets of axioms. One set of axioms is Euclid's; other
equally good sets of axioms lead to other results. Whether Euclid's
axioms are true, is a question as to which the pure mathematician
is indifferent ; and what is more, it is a question which it is theoret-
ically impossible to answer with certainty in the affirmative. It
might possibly be shown, by very careful measurements, that Euclid's
axioms are false ; but no measurements could ever assure us (owing
to the errors of observation) that they are exactly true. Thus the
geometer leaves to the man of science to decide, as best he may,
what axioms are most nearly true in the actual world. The geometer
takes any set of axioms that seem interesting, and deduces their con-
sequences. What defines geometry, in this sense, is that the axioms
must give rise to a series of more than one dimension. And it is thus
that geometry becomes a department in the study of order."

Russell25 then shortly dealt with the methods used by Peano
and Fano in geometry, and finally26 remarked that "the proof that
all pure mathematics, including geometry, is nothing but formal
logic, is a fatal blow to the Kantian philosophy."

in.

Let us now point out how this popular article gives indications
of his logical work up to 1903.

To begin with, the two great influences on Russell's mathemat-
ical and logical work were Georg Cantor and Peano. Cantor had,
in 1895 and 1897,27 brought his researches on transfinite numbers
and ordinal types to a close by two articles in which the principles of
the subject were stated in an almost perfect logical form. Obviously,
the whole question threw a great and welcome light on the prin-
ciples of arithmetic.28 Peano invented a symbolic logic which was
especially adapted to the analysis and expression of mathematical
theories. But Peano's logic was incomplete. It neglected the logic
of relations, which was founded and developed by De Morgan,
C. S. Peirce, and Schroder; and only contained a symbolical ex-
pression of the theory — unused, by the way, in Peano's symbolic

xlbid.f pp. 99-100.

M Ibid., p. 101.

* Mathematische Annalen, Vols. XLVT and XLIX. An annotated trans-
lation of these articles by the author is in preparation.

88 Cf. my article on "Transfinite Numbers and the Principles of Mathe-
matics" in The Monist for January, 1910.

156 THE MONIST.

exposition of arithmetic — of the "representations" of Richard Dede-
kind.29 The logic of relations was, as Schroder had observed, neces-
sary for the translation of Cantor's conceptions and proofs into a
symbolic (speaking technically) form; and it was necessary in order
to complete Peano's theory of arithmetic by denning in logical
terms the three indefinables referred to above. Russell completed
Peano's logic by a logic of relations in which the Peirce- Schroder
ideas were modified so as to fit in with a logic which comprised
more subtle distinctions than that of Schroder, in two papers, "Sur
la logique des relations, avec des applications a la theorie des series,"
and "Theorie des series bien-ordonnees," which were published in
Peano's Revue de Mathematiques for 1902,3° and of the first of
which an account was given in Russell's Principles of Mathematics
of 1903.3 l The logic of relations gave to Russell the means of
defining Peano's indefinables of arithmetic, and of proving his primi-
tive propositions of arithmetic.32

Peano had emphasized that it was the notion of implication
between propositions containing variables — or, as Russell expressed
it, of formal implications33 between prepositional functions?* and
not implication between (constant) propositions, that is used in
mathematics. Further, the development of non-Euclidean geom-
etry had shown in the most striking manner that, in pure mathe-
matics, as in formal logic, we are not concerned with the truth or
otherwise of the hypotheses. "Until the nineteenth century," said
Russell,35 "geometry meant Euclidean geometry, i. e., a certain
system of propositions deduced from premises supposed to describe
the space in which we live. . . .," but now, owing to investigations
with premises other than Euclid's, "geometry has become. . . .a sub-
ject in which the assertions are that such and such consequences
follow from such and such premises, not that entities such as the
premises describe actually exist." And all this goes some way

29 Cf. the English translation of Dedekind's pamphlet in Dedekind's Essays
on the Theory of Numbers, Chicago, 1901.

80 An account of Peano's and Russell's logic was given by A. N. White-
head in his paper "On Cardinal Numbers" in the Amer. Journal of Math.,
Vol. XXIV, 1902, pp. 367-394-

31 The Principles of Mathematics, Vol. I [the Principia Mathematica of
Whitehead and Russell, of which the first volume was published in 1910, takes
the place of the second volume], pp. 23-26; cf. Couturat, op. cit., pp. 27-34.

38 Principles, pp. 124-128.

83 Ibid., pp. 5, n, 14, 36-41; Couturat, op. cit., pp. 4, 21.
** Principles, pp. 13, 19; Couturat, op. cit., p. 17.
88 Principles, pp. 372-373-

CRITICISMS AND DISCUSSIONS. 157

towards explaining the definition of pure mathematics with which
Russell's book begins:

"Pure mathematics is the class of all propositions of the form
(p implies q,' where p and q are propositions containing one or more
variables, the same in the two propositions, and neither p nor q
contains any constants except logical constants. And logical con-
stants are all notions definable in terms of the following: Implica-
tion, the relation of a term to a class of which it is a member, the
notion of such that, the notion of relation, and such further notions
as may be involved in the general notion of propositions of the
above form. In addition to these, mathematics uses a notion which
is not a constituent of the propositions which it considers, namely
the notion of truth."

In this definition culminates the discovery contributed to by
Leibniz, Frege, Dedekind, Schroder, and a host of others, that pure
mathematics is logic and logic alone. Hence Russell's36 anti-Kant-
ianism.

* * *

In the question of infinity, we have a discussion of Zeno's
puzzles,37and meet again the paradox of Tristram Shandy.38 When
discussing continuity, Russell39made more explicit Cantor's dis-
covery (1895) that it is a purely ordinal notion; and then, too,
Russell succeeded in maintaining his theses that the theory of limits
is purely ordinal,*0 that geometry is the study of order,*1 and that
the notion of quantity is superfluous in mathematics.*2

* * *

Finally we come to Russell's*3 contradiction. Starting from a
study of Cantor's proof of 1892 that there is no greatest cardinal
number, Russell discovered a very simple argument: If w denotes
the class of all those entities x such that x is not a member of x ;
then, obviously, if w is a member of w, w is not a member of w,
while if w is not a member of w, w is a member of w. This contra-

86 Principles, pp. 4, 158, 259, 373, 442, 456-461; Couturat, op. cit., pp. 235-
308.

87 Principles, pp. 347-353, 358-360.
"Ibid., pp. 358-360.

89 Ibid., pp. 296-303 ; Couturat, op. cit., pp. 91-97.

40 Principles, pp. 276-277.

41 Ibid., p. 372 ; Couturat, op. cit., p. 134.

a Principles, p. 158; Couturat, op. cit., p. 98.
48 Principles, pp. 364-368, 101-107.

158 THE MONIST.

diction, which threw doubt upon the legitimacy of the concept of class,
and hence upon that of the science of arithmetic, showed itself as
allied in principle to the paradoxes in the theory of aggregates dis-
covered by Burali-Forti, Konig, Richard, and others, and to the
old logical difficulty about the Cretan who said that Cretans were
liars, and was only satisfactorily solved by Russell in 1905. Of
this more elsewhere.

It only remains at present to refer to the work of Frege. He
did his magnificent work on the principles of logic and mathematics
alone and almost too independently, and his subtle distinctions and
acute analysis have had great influence on modern work. But at
first Russell had hardly heard of him, and re-discovered for himself
many of his distinctions and views. In his Principles,44 Russell de-
voted many pages to a careful critical estimate of Frege's work.
I hope to give an account of Frege's work later.

PHILIP E. B. JOURDAIN.

THE LODGE, GIRTON, CAMBRIDGE, ENGLAND.

ALFRED BINET.*

OBITUARY.

Readers of The Monist are well acquainted with the name of
Alfred Binet. That eminent psychologist died at Paris October 18,
1911, at the age of 54, from an attack of cerebral apoplexy. He was
born at Nice, July 11, 1857. He first took up the study of law,
but later turned his attention to natural sciences, and finally directed
all his efforts to psychology. In 1894 in collaboration with Beaunis
at the laboratory of physiological psychology of the Sorbonne,
he founded the Annee psychologiqne, an important publication of
permanent value.

His principle works are Vie psychique des micro-organismes
(English edition, The Psychic Life of Micro-Organisms, Open
Court Publishing Co., 1894) ; Psychologic du raisonnement (English
edition, The Psychology of Reasoning, Open Court Publishing Co.,
1899) ; Le magnetisme animal, Les alterations de la personnalite,
Psychologic des grands calculateurs et joueurs d'echechs, Etude ex-
perimentale de ^intelligence, L'ame et le corps. To these we should
also add a number of articles on an equal variety of subjects, capil-

44 Pp. 501-522.

* Translated for The Monist.

CRITICISMS AND DISCUSSIONS.

lary circulation, the pulse, emotions, character, graphology, the
mystery of painting, etc.

In his last years he was particularly interested in the "psycho-
logical study of the child" and for this purpose founded a society
which bore this title. In collaboration with Dr. Simon he published
a number of studies on abnormal children. Very recently he sug-
gested a system of "measurement of the development of intelligence
in children" which seemed very simple and practical and has been
tested by educators in many countries.

Simply to read the list of books and articles published by Binet
might give the impression of too great a dispersion of forces. It
is further true that the work of Binet does not, like that of other
psychologists, present the development of one dominant thought pur-
sued through all the problems of psychology. Nevertheless his work
shows a unity of quite another kind, a unity of method. Binet
always endeavored to apply the processes of experimentation or di-
rect observation to the most diverse questions, and consequently we
may say that inasmuch as his works tended towards the control or
invention of facts, they form an important whole and bear constant
witness to a truly scientific spirit. Although he did not conceive
any broad hypotheses and did not aim at extended or conclusive
solutions he was a prudent investigator of broad culture, rich and
versatile intelligence and an excellent worker.

LUCIEN ARREAT.

PARIS, FRANCE.

MAGIC SQUARES BY REVERSION.

The present number of The Monist contains an article on magic
squares by Dr. C. Planck entitled "The Method of Reversion." This
reminds the Editor of his own contributions to the problem of the
construction of magic squares which appeared in Mr. W. S. An-
drews's book on Magic Squares and Cubes under the title, "Reflec-
tions on Magic Squares."

Since these reflections were written I have come to the conclu-
sion that a popular name for the several arrangements of the num-
bers in their cells would help greatly to make the idea clearer. On
page 115 I have called the ordinary order o, the reversed ordinary
ro, the inverse of the ordinary arrangement if and by ri is understood
the reversed inverted order. Considering the fact that all these

l6O THE MONIST.

arrangements are brought about by a system of inversion which
corresponds closely to reading the figures off in mirror writing, we
may consider them as originated by placing a mirror on two sides
of the original square. If o is flanked by a mirror from the top
to the bottom it produces the order i. If the mirror is placed at the
bottom it produces the order n which mirrors the picture as if re-
flected in the surface of a lake, while the order ro lies in the corner
between the two mirrors, being the reflection of either mirror in
the other and this double inversion which we have called ro cor-
responds directly with the picture which appears on the ground
glass of a photographer's camera. Accordingly the several orders
on a plane surface might popularly be called the "original," the
"mirror" reflection, the "lake" reflection and the "ground glass" pic-
ture.

original mirror

jd LL

771 F

lake ground glass
FOUR WAYS OF INVERSION IN A PLANE.

Of course the conditions of such reflections grow more com-
plicated if we venture from the plane into tridimensional space, and
it can be extended into 4- and w-dimensional spaces. It appears to
me that this idea of inversion rests ultimately on the same basis as
Dr. Planck's method of reversions. p. c.

IM
VOL. XXII. APRIL, 1912. NO. 2

THE MONIST

CONTRIBUTIONS OF CHRISTIANITY TO BUD-
DHISM.1

THE Buddhist religion had penetrated to the most ex-
treme northwestern part of India about the middle of
the third century B. C. There it developed in the direction
which expressed itself most distinctively in the deification
of the person of Buddha and in the transformation of the
Nirvana-concept into the idea of a beatified continuous
existence ; there too arose the most essential points which
distinguish northern Buddhism from southern in doctrine
and forms of worship. This development found a positive
conclusion in the establishment of a new school which
assumed the name Mahayana, "The Great Vehicle/' and
which flourished in that region until about the eighth cen-
tury A. D. After the founding of that school the older
original Buddhism in contrast to it was called Hinayana,
"The Small Vehicle."

Expositions of Buddhism usually treat the Mahayana
disparagingly, first because it places value upon the ex-
ternalities of worship, and in the second place because in
its philosophical speculation it evinces the strongest skepti-
cism in teaching that Nothing is the true essence of things.
But more important than these aspects of the varied con-
tents of the Mahayana is the new ideal of life with which
it has replaced the benevolent but fundamentally egoistic
indifference — freedom not only from passions but even
from all human emotions. This new ideal, which the early

1 Authorized translation from the German by Lydia G. Robinson.

l62 THE MONIST.

Buddhist type of saint no longer satisfied, was that of
loving devotion and active compassion. H. Kern2 says
truly : "It is by that feeling of fervent devotion, combined
with the preaching of active compassion, that the creed
has enlisted the sympathy of numerous millions of people
and has become a factor in the history of mankind of much
greater importance than orthodox Buddhism." Southern
Buddhism, which remained true to the ancient ideal, pos-
sessed no such winning power.

Moreover, the Mahayana exhibits ideas pleasing to the
heart and imagination which run directly counter to the
doctrines of the Hinayana. The old Buddhism acknowledges
no soul persisting throughout the course of life and knows
no God, for the national gods which it recognizes are
transient beings held captive in Samsara. In the Maha-
yana we find a belief both in a personal soul and in God,
at least in a kind of God. In a paradise called Sukhavati
where a reflection of the earthly Buddha, Amitabha, "the
one surrounded by immeasurable light," sits enthroned
in godlike fashion, the souls of the pious are born again
after death in the buds of lotus flowers gradually to grow
in the blossoms according to their deserts ; and resting upon
the lotus leaves they hear the good law preached to them
by Amitabha or sung by birds in the leafy trees.3

According to the traditional statement, repeated even
by Pischel and Edv. Lehmann,4 the Mahayana was founded
by Nagarjuna, whose activity we would place rather in the
middle than in the second half of the second century after
Christ. But this statement is not correct. Nagarjuna, who
as originator of the Madhyamika sect introduced into Bud-

2Manual of Indian Buddhism (Grundriss der Indo-arischen Philologie und
Altertumskunde, III, 8, Strassburg, 1896), p. 124.

3Teitaro Suzuki, Outlines of Mahayana Buddhism, London, 1907; H.
Hackmann, Buddhism as a Religion, London, 1910, pp. 50 ff. ; Max Miiller,
Last Essays, II, pp. 304, 305.

* Pischel, Leben und Lehre des Buddha. Leipsic, 1906, p. 108; 2d ed. by
Liiders, p. 104. Lehmann, Der Buddhismus, p. 227.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 163

dhism the doctrine of Nothing as the only reality, was in-
deed one of the most significant and influential exponents of
the Mahayana5 and presumably the organizer of that
school; but its foundation, that is to say the first literary
exposition of its doctrines, must be placed about sixty to
seventy years earlier. This was the work of a man who
has latterly engaged the attention of the most distinguished
Indologues, namely the famous and versatile monk Ashva-
ghosha, an elder contemporary of King Kanishka, hence
in all probability living in the second half of the first cen-
tury after Christ.6 Ashvaghosha was an old man at the
time of the birth of Nagarjuna, that is to say, when the
last Buddhist council was held at Jalandhara under King
Kanishka about 100 A. D., if we may take as a basis of
calculation the most probable but not quite assured dating
of King Kanishka (last quarter of the first and the be-
ginning of the second century). Cunningham, Pischel,
the sinologue O. Franke, Fleet, and Liiders place Kanishka
in the first century before Christ.

Therefore the appearance and the first propagation of
the ideas of the Mahayana fall in the last decades before
the council at Jalandhara.

It has occurred to many that Christian influences may
have had some effect in the transformation of the Buddhist
religion into the Mahayana form. Thus the sinologue
Samuel Beal7 found "in Ashvaghosha's writings many

5H. Kern, Manual, 6, pp. 122, 127. Teitaro Suzuki, Agvaghosha's Dis-
course on the Awakening of Faith in the Mahayana', translated for the first
time from the Chinese version. Chicago, 1900, p. 43.

6 Besides his best known work, the Buddhacharita which is a poetical
biography of Buddha, Ashvaghosha wrote a collection of didactic tales
(Sutralarnkara) and theological works and was also a successful composer
and musician. Lately too by a happy discovery of Heinrich Luders he has
been shown to be a dramatist (Sitzungsberichte der K. Preussischen Akademie
der Wissenschaften, phil. hist Klasse, 1911, pp. 388 ff., especially 399; cf. also
M. Anesaki, Encyclopaedia of Religion and Ethics, II, pp. 159, 160; S. Levi,
"Agvaghosha, le Sutralarnkara et ses sources," Journ. As. S., Series X, Vol.
XII, pp. 57 ff-

7 Abstract of Four Lectures on Buddhist Literature in China. London, 1882,
P- 95-

164 THE MONIST.

allusions and illustrations derived apparently from foreign,
and perhaps Christian, sources/' and arrived at the view
"that much in the Buddhist development coming under
the name of the Greater Vehicle may be explained on this
ground." In another passage8 he speaks in a more de-
cided tone of the intercommunication in those days between
East and West that "shaped the later school of Buddhism
into a pseudo-Christian form."

A similar judgment has latterly been the fate of the
oldest text-book of the Mahayana, Ashvaghosha's Dis-
course on the Awakening of Faith in the Mahayana, which
is not preserved in the Sanskrit original but only in two
Chinese translations.9 The missionary Dr. Timothy Rich-
ard, who has translated this work into English ( Shanghai,
1907), finds in it Christian ideas and influences and there-
fore reproduces the Buddhist terminology very freely in
an entirely Christian mode of expression,10 whereas on the
other hand an earlier and more exact translator, the Japa-
nese Teitaro Suzuki, a Buddhist (see above Note 4) has
discovered no Christian traces of any kind in the book.

Lately, too, Christian influence in the Mahayana has
been maintained by the Jesuit Joseph Dahlmann11 with
great determination and with an attempt at detailed scien-
tific proofs. In what follows I shall first have to take his
expositions into critical account.

In chapters 25-27 relating to the art of Gandhara, that
is of the Kabul valley and the surrounding country, Dahl-
mann has undertaken to show that these monuments of
Buddhist art which reflect the Mahayana thought-cycle
betray not only the generally recognized Greco-Roman

8 Op. dt. Introduction, p. xiv.

"Bunyiu Nanjio, Catalogue of the Chinese Translation of the Buddhist
Tripitaka. Oxford, 1883, No. 1249, 1250. There the title of the Sanskrit
original is given as Mahayana-shraddhotpada[na]-shastra.

10 The Open Court, XXV, 1911, pp. 251 ff

11 Indische Fahrten (2 vols., Freiburg, 1908) II, pp. 100 ff.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 165

influence but also a profound Christian influence. From
the middle of the first century of the Christian era "that
change in worship and art began to be consummated in
Gandhara. The same Buddha whose figure had been pains-
takingly avoided appears all at once in the monuments of
Buddhist art, and not indeed as the simple herald of salva-
tion as in ancient Buddhistic legend, but as in the message
of salvation of the Gospels, as God and as Saviour of the
world. He appears as God and Saviour not in Indian gar-
ments but in a garb such as was worn by the higher classes
in Antioch and Alexandria, in Jerusalem and Rome during
the first centuries of the Roman empire."12

True and noteworthy, to be sure, is the circumstance
that the likeness of Buddha appears first of all in the art
of Gandhara. Most investigators in Indian archeology
have sought the reason for this strange fact and have
found it in part (as in the case of Fergusson and Cunning-
ham) in the assumption that the Buddhists had learned
idolatry from the Greeks, whereas Griinwedel would fain
explain the rise of the Buddha image from the natural
development of Buddhism. In early Buddhist art as rep-
resented in the monuments of Sanchi, Bharhut and Bud-
dhagaya in Central India, the original home of Buddhism,
since the middle of the third century B. C., any likeness
of Buddha is entirely absent. Where a likeness of Bud-
dha would naturally be expected in the representations
of his life and works we regularly find instead, in strange
contrast to the lifelike pictures of all other participants in
the scene, a symbol such as the tree of knowledge, a reli-
quary, or the wheel of the law. In the art of Gandhara,
on the other hand, the likeness of Buddha is the central
figure. Here it appears everywhere in a commanding
form even in the very same scene in which in ancient art
it was replaced by a symbol. This likeness of Buddha

aOp. cit.,11, p.is;.

1 66 THE MONIST.

passed with Buddhism from Gandhara into all foreign
countries which Buddhism conquered — into central Asia,
China, Japan and the peninsula of Farther India.

That this surprising change which marks an epoch in
Buddhist art can not be explained by external influences
alone is obvious, although it must seem very natural that
the artists of Gandhara should rely upon the Greek types
already known to them when they felt the need for the
production of religious images. But these models would
never have been able to accomplish this revolution alone.
Such a change presupposes a transformation of Buddhist
doctrine. In the original Buddhism Buddha was only a
man who by his own power had found salvation from the
sorrows of continuous existence and had shown the way
by which it might be attained by everyone. Here there
could be no worship ; here the teaching was more important
than the personality of the teacher, just as Buddha him-
self had said before his death in his last sermon: "The
Doctrine and the Order which I have taught and pro-
claimed unto you — they are your master when I am
gone."13 The art of Gandhara shows that the personality
of Buddha had taken the place of the Doctrine and had
become the object of worship. It is the visible witness
of a transformation of fundamental views as it had ad-
vanced on the road towards the Mahayana.

Dahlmann's line of argument, however, places the
greatest value on the role played in the Mahayana by the
future Buddha, Maitreya. As we are later to criticise
Dahlmann specially it will be better to give his standpoint
in his own words. For this reason I have extracted a con-
siderable passage from his work (II, pp. 127, 128) :

"Many other Buddhas at long intervals had preceded
Gotama Buddha in his calling as teacher of mankind. Go-
tama himself as the twenty-fifth was claimed to have com-

13 Oldenberg, Buddha, 5th ed., p. 233.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 167

pleted forever the series of the teachers of mankind. There-
fore all hope of salvation was based on the doctrine he
proclaimed. No other Buddha was to be expected in the
future as teacher of salvation. To this idea a newly arisen
school (the Mahayana) took exception, in so far as it
supplied a successor as teacher of salvation to the Buddha
now worshiped .... The Buddha Maitreya constituted the
central point of this school. The earlier tradition knew
nothing of Maitreya. As simple as it would have been
to continue to spin the thread of the Buddhas reappearing
at periodical intervals, yet the myth stood still at Gotama
as the last Buddha. Buddha Maitreya in the form in which
he is transmitted to us is a new creation .... But in the
introduction of the Buddha Maitreya we have not merely
to do with a new Buddha. Maitreya became the center
of a new cult in a character fundamentally different from
the old Buddha, and this character was that of the loving
compassionate Saviour who will one day come to liberate
the world from the bonds of suffering. ' Herewith there
entered into this doctrine of salvation an entirely new ele-
ment in contradiction to the old tradition. It directed the
cult into the very path which the communities of monks
had always resisted hitherto. The teacher becomes a
Saviour] the human being, a divine being to whom man
needs only to turn in trustfulness in order to be saved. In
other words it is the Saviour-idea as incorporated in the
Buddha Maitreya which called the Mahayana into exist-

ence."

That this conception of Dahlmann is in the main in-
correct and easily disproved we shall see later on. At pres-
ent we shall anticipate only one point. It must be granted
that in the Mahayana a different character is assigned to
the future Buddha Maitreya than formerly to the real
Buddha, and that here indeed there exists a new element of
which the old tradition knew nothing.

l68 THE MONIST.

Dahlmann thinks that this new element can be explained
only by foreign influence, and to him the only foreign in-
fluence worthy of consideration is that of Christianity.

The ardent joy with which Dahlmann proclaims this
presumed discovery is easily understood, for in earlier
works14 he had tried to explain the fall of Buddhism in its
own country by its intrinsic corruption. How well did
this standpoint seem to agree with the knowledge, which
Dahlmann thinks he has gained, that Buddhism does not
owe its triumphal procession through central and eastern
Asia and its dispersion over a third of all mankind to its
own power but to Christian ideas by which it was enriched
in northwestern India and attained its peculiar world-
conquering vitality ! Thus it would not be Buddhism which
had subjected the peoples of eastern Asia but an offshoot of
Christianity in Buddhist garb.

As comprehensible as Dahlmann's joy in his discovery
is the enthusiastic applause which his thesis has received
from some quarters of the Catholic press. Indeed, the
positiveness of the assertion and the brilliant exposition in
which Dahlmann has disposed of it seemed once for all "to
have made an end of the Buddhism humbug." When we
approach Dahlmann's spirited demonstration with a dis-
passionate critique it vanishes into nothing.

In the first place, what is the chronological possibility
for the assumption that the appearance of the likeness of
Buddha in the art of Gandhara, the divinity of Buddha
as attested by this art, and the conception of Maitreya
as a divine Saviour can be explained by Christian in-
fluence ? It is pretty well established that the art of Gan-
dhara reached its height at the end of the first and be-
ginning of the second century A. D., but no time can as yet
be definitely fixed upon for its beginning. The probability is

** Nirvana, eine Studie zur Vorgeschichte des Buddhismus, Berlin, 1896;
Buddha, ein Kulturbild des Ostens, Berlin, 1898.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 169

in favor of the pre-Christian period. The best specialists in
this field, Griinwedel and Aurel Stein, have been inclined on
account of the new discoveries in Turfan and Khotan to
place the beginning of the Gandhara art in the first or per-
haps even in the second century before Christ.15 And the
first contemporary expert of Northern Buddhism, Louis
De la Vallee Poussin, has practically settled16 that the
deification of Buddha in mythology and religion had taken
place before the Christian era.

But if in spite of this we take Dahlmann's standpoint
that the religion and art of Gandhara originated in the
Christian era we must further concede to him that Chris-
tianity had penetrated as early as the first century into the
valleys of the Kabul and Indus — an assumption whose
"possibility is not contested to-day in any quarter ( !)"17 Of
course Dahlmann has to base this assumption upon a de-
fense of the historicity of the St. Thomas legend because
he needs the apostleship of St. Thomas in the Indo-Iranian
territory for his demonstration.

Whereas earlier advocates of the historical character
of the legend of St. Thomas, in so far as it relates to the
Indo-Iranian territory, based their thesis upon discoveries
of coins and one inscription by which the king in the Acts
of St. Thomas, Guduphara-Gondaphares, was proved to
belong to the first half of the first century after Christ, as
well as upon reports of the international commercial rela-
tions of that day, Dahlmann brings forward the combina-
tion of apostleship and art in the person of St. Thomas as
new and in his opinion the strongest evidence that the
Christian influence in the art of Gandhara could be ex-
plained through the activity of St. Thomas in India. This
idea must be objected to on two grounds : ( i ) that Christian

"Wecker, Tiibinger Theol. Quartalschrift, 92, note on p. 432.
uBouddhisme, Opinions sur I'histoire de la dogmatique, Paris, 1909.
17 Dahlmann, II, p. 138.

I7O THE MONIST.

influence can not be proved in the art of Gandhara; (2)
that in the legend of St. Thomas, as O. Wecker justly re-
marks,18 "the Christian apostle is not brought into relation
with that kind of artistic activity which most clearly be-
trays the connection between Gandhara and the west, that
is to say with sculpture, but with the work of an architect
and carpenter/' which may probably be accounted for by
the imagery of the construction of church or temple cur-
rent in Christian modes of speech. Since I have given the
reasons in this periodical (October 1911) why there can
be no question of an historical nucleus in the Thomas
legend, but that on the contrary Christianity did not pene-
trate into northwestern India at the earliest before the
beginning of the third century, Dahlmann's theory becomes
for us an historical impossibility.

But even a person who is not convinced of the unhis-
torical character of the legend of St. Thomas and who
accordingly finds no difficulties in the question of chronol-
ogy to prevent him from following Dahlmann's lead, can
not be convinced by the arguments adduced by Dahlmann
for Christian influence on the art and religion of Gan-
dhara, provided he understands how to pursue with the
correct scientific method the beginnings of the development
in early Buddhism which led to the later phenomenon of
the Mahayana in dogma and worship. This has been
shown very clearly by O. Wecker,19 who nevertheless re-
gards the historicity of the fundamental features of the
Thomas legend as possible. To him everything that Dahl-
mann understands only on the assumption of Christian in-
fluence is to be accounted for quite spontaneously from the
natural development of Buddhism. Some of his statements
may follow here in his own words:20 "In strange contrast
to the theoretical universality of the message of salvation,

18 Tiibinger Theol Quartalschrift, 92, note on p. 561.
19Loc. cit., pp. 441 ff.
510 Pages 442-444-

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM.

there stood from the beginning the difficulty with which
the redeeming knowledge is to be gained, a difficulty so
great that in fact the salvation of Buddha could never be
a salvation for all, especially not for the many small and

poor and weak As soon as the consequences were

drawn from the universality of the salvation which Buddha
preached, the exclusiveness of the pure Buddha doctrine
must have been shattered; the postulates and ideas must
necessarily be leveled and accommodated to the needs of
every-day people as soon as the sermon becomes serious
with its 'All ye, come unto me.' Is not this what happened?
We need only point to the transformation of the Nirvana
ideal21 to illustrate by a classical example the process of
conversion which changed the pure teaching of Buddha
into a popular religion....^ similar transformation of
the person of Buddha was the natural consequence of this
evolution."

The transformation of the Nirvana concept, which
moreover can not be explained solely by the change of
the original doctrine of Buddha into a folk-religion, but

21 When speaking in this essay of Nirvana we mean salvation after death.
Many discussions on the concept of Nirvana suffer greatly from lack of clear-
ness for the reason that they do not take into consideration the ambiguity of
the word Nirvana, to which attention has been called first by Rhys Davids
(Buddhismus, n8ff.) and later by Pischel in an exhaustive argument (Leben
und Lehre des Buddha, 2d ed., pp. n ff.). Even in ancient Buddhism the word
Nirvana was used not only in the sense of salvation proper which took place
at the death of the Perfect One, that is in the sense of annihilation of exist-
ence, but also to denote salvation during life, that is the condition of complete
rest and sinlessness which endures until death and is brought about by right-
eous living and redeeming knowledge. In distinction from this "salvation
during life," which has also been a very current idea in the Brahman systems
from pre-Buddhistic times until to-day, the real final salvation in death is for
the sake of clearness often called Parinirvana, "perfect Nirvana" ; but usually
this distinction is not observed by the language in the texts.

I mention here this ambiguity in the Nirvana concept because it continues
also in the Mahayana. What Ashvaghosha says in his Awakening of Faith
(Teitaro Suzuki, p. 87) about Nirvana ("As ignorance is thus annihilated,
the mind is no more disturbed so as to be subject to individuation. As the
mind is no more disturbed the particularization of the surrounding world is
annihilated. When in this wise the principle and the condition of defilement,
their products, and the mental disturbances are all annihilated, it is said that
we attain Nirvana"), and what the translator (page 119 note) gives as the
general conception of the Mahayanists on the four stages of Nirvana does not
refer to the final Nirvana but very distinctly to Nirvana during life.

172 THE MONIST.

also by the progress of the doctrine among more active
peoples filled with different desires and hopes, would ac-
cording to Dahlmann's standpoint have to be referred to
Christian influence, but strange to say Dahlmann has laid
no stress upon the transformation of the Nirvana ideal in
his demonstration.

The deification of the person of Buddha becomes com-
prehensible from the natural evolution of Buddhistic doc-
trine not only by means of such general considerations as
those we have just discussed. We can also22 discover
quite positive starting points for the path pursued in the
alteration of the concept of Buddha. We must remember
the charm exercised by the personality of Buddha upon
his environment, and the reverence which was shown the
master and which of course increased greatly after his
death. Even in the formula of admission, "I take my
refuge in Buddha, etc.," in the earliest period of Bud-
dhism the person of the founder was placed before the
doctrine. Then the worship of sacred places which played
a role of particular importance in Buddha's life, and the
worship of relics, which started up in circles of the laity
immediately after his death must have contributed to the
exaltation of his person, as did also the formation of leg-
ends in which not only the life of the historical Buddha
but also all the former existences ascribed to him were
surrounded by the creations of an unchecked fancy. Even
the monuments of early Buddhist art testify that the
memory of the founder held the central place in religious
thought ; for although the likeness of Buddha was avoided
(in order to give expression, as a matter of principle, to the
thought that the doctrine is more important than the
teacher) yet in reality all those old reliefs are "Buddha-
centric."23

M With Wecker, pp. 445 ff .
"Wecker, p. 451.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 173

Wecker is right however in laying most emphasis upon
the speculative and dogmatic development of the old Bud-
dhism. If the form of the one historical Buddha here be-
comes multiplied, further if beside those Buddhas (called
in Sanskrit pratyeka-, in Pali pacceka-Buddhas} who are
capable of attaining saving knowledge only for themselves
but have not the ability to bring salvation to others, there
appear the samyak- (Pali samma-} sambuddhas, the holy
universal Buddhas who appear at definite times in the var-
ious ages of the world in this and in other worlds with
quite decided powers and signs in order to preach the sav-
ing knowledge, then already "Buddha's form in the belief
of the Order had exceeded the limits of earthly human re-
ality."5 This elevation into the sphere of the supernatural
may also have been favored by such stories as that of the
conversation with the Brahman Dona25 in which Buddha
expressly states that men who have attained Buddhahood
form a special category of beings different from gods,
demigods and men.

With the multiplication of the historical Buddha there
grew up the faith in future Buddhas for which there is
evidence in the canonical Pali literature.26 The dogma of
the Buddha of the future is explained as readily as the
deification of the historical Buddha from the evolution of
the Buddhist religion. At the same time we do not deny
that in the formation of the ideas of the future Buddha
analogous foreign elements have cooperated. If the his-
torical possibility and probability of such an influence must
be admitted, it even becomes very credible. Dahlmann27

**Oldenberg, Buddha, 5th ed., p. 382; English translation by Wm. Hoey,
P- 325.

*H. Kern, Manual of Indian Buddhism (Grundriss der indoarischen
Philologie und Altertumskunde, II, 8) p. 64.

"In the Mahaparinibbanasutta, Dighanikaya, XVI, i, 16, (in the Rhys
Davids-Carpenter edition, II, p. 82) according to a kind communication from
O. Franke.

"II, pp. 131-134-

174 THE MONIST.

takes action with great energy but with quite inadequate
grounds against the theory that the Iranian ideas of the
future Saviour, the Saoshyant (later Sosiosh) could have
influenced the thought-cycle of the Mahayana. And yet
nothing is more obvious than this, since we are dealing
with a time in which Iranian influences upon northwestern
India have been plentifully established, as shown for in-
stance on the coins of the Gandhara period.28

Even in the Mahayana speculations on the five Dhyani-
buddhas, the "Buddhas arisen from meditation," which
are reflexes of the earthly Buddhas in transcendent worlds,
the influence has been recognized of the Iranian doctrine
of the Fravashis, those prototypes of all good creatures
existing from eternity to eternity.

The main point against Dahlmann's theory, which
brings the whole artificial structure to the ground at one
stroke and which, strange to say, has been overlooked by
Wecker, I have saved until the last. The foundation upon
which Dahlmann's demonstration rests consists of the
statement that the older tradition does not know anything
at all of Maitreya, but that he is a new creation of the
Mahayana. This assertion is also found elsewhere. Griin-
wedel29 has the following to say about Maitreya: 'The
northern school is acquainted with him in full detail and
puts revelations in his mouth ; yes, he is everywhere highly
venerated, almost more than Gautama. In the southern
canon, as far as I can see, he does not appear, although
the Singhalese chronicle Mahavansa is acquainted with
him."30 Similarly we read in the supplemental volume of

28 Wecker, loc. cit., pp. 439, 440, 455. Griinwedel, Buddhistische Kunst,
2d. ed., p. 167: "Hence we are perhaps justified in pointing out that here
again contact with Iranian ideas has taken place. The similarity of the idea
of the future Buddha Maitreya with the Saviour of the Parsi religion Sao-
shyant (Sosiosh} is very striking. Although we do not know when the
legend of the Saoshyant as it now exists developed among the Iranians yet
the dominant position of the Maitreya within the northern church has cer-
tainly been influenced by it."

39 Buddhistische Kunst, 2d ed., p. 158.

30 Except the later continuations, it dates from the end of the fifth cen-

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM.

Brockhaus's Konversationslexikon (i4th edition) in the
article "Buddhismus," page 2290, on Maitreya (Pali, Met-
teyya) : "The southern church acknowledges him but the
canonical writings do not mention him. The Mahayana
school which originated in the north betakes itself with
peculiar zeal to the Maitreya cult and other Bodhisatvas."
Of these two sentences only the second one is correct. A
glance into the best known work on Buddhism31 shows that
the idea of the future Buddha Metteyya was not unknown
to ancient Buddhism. T. W. Rhys Davids also says ex-
pressly that this doctrine already forms part of the system
of the Small Vehicle (Hinayana).32

The passage cited by Oldenberg (loc. cit.) is taken from
the Cakkavattisuttanta, a part of the Dighanikaya and
hence belonging to the canonical Pali literature. It reads :
"He will be the leader of a band of disciples containing
hundreds of thousands as I now am the leader of a band of
hundreds."33

Further, Metteyya is called the future Buddha in the
Buddhavamsa (27. 19), 34 a short poetical biography of
the twenty-four former Buddhas which belongs to the ap-
pendices of the Suttapitaka. According to the preceding
verse Kakusandha, Konagamana and Kassapa were enu-
merated as the three Buddhas preceding the historical
Buddha in this "blessed eon" (bhaddaka kappa). Now to
be sure, as the editor observes, the Buddhavamsa orig-

tury after Christ. (See the citations for Metteyya in Childers's Dictionary of
the Pali Language}. Metteyya is moreover mentioned also in the Milinda-
panha, p. 159, which probably belongs to the second century after Christ.

"Oldenberg, Buddha, 5th ed., p. 164, note; 384 note i.

sa Der Buddhismus, translated into German by A. Pf ungst, Leipsic, p. 208.

88 Dighanikaya, Sutta 26. Even a scholar so familiar with canonical Pali
literature as Prof. O. Franke considers this passage above suspicion and de-
clares it to be impossible that it could have been interpolated in post-Christian
times. Compare further C. A. F. Rhys Davids's review of Carpenter's edition
of the Dighanikaya, Vol. Ill, Journal of the Royal Asiatic Society, 1911, p.
557. Professor Oldenberg has kindly called my attention to part of the follow-
ing passages.

84 Page 67 of Morris's edition, Pali Text Society.

176 THE MONIST.

inally ended with verse 18, and hence the two following
verses and the last song (28) would be a later addition;
but verse 19 only contains expressly stated what was al-
ready implied in the eighteenth verse. For according to
the Buddhist doctrine there are not four but five Buddhas
in a bhadda kappa (Sanskrit, bhadra kalpa) ; hence the
mention of such a kappa implies the expectation of the
fifth Buddha.35 The eons are divided into "void" (San-
skrit, shilnya; Pali, sunna) in which no Buddha appears,
and "not-void" (Sanskrit, ashunya; Pali, asunna), that
is, full periods in which there are one or more Buddhas.
The not-void eons bear special names according to the
number of the Buddhas which appear in them (from one
to five).36 A bhadda kappa with five Buddhas like the
present one always comes only after a long interval.

We have no reason to doubt that this entire idea of the
different kinds of eons and the "eons blessed" with five
Buddhas belonged to Buddhism before its development
into the Mahayana. And since the name Maitreya-Met-
teyya, which from what we have said must be old (belong-
ing to about the fourth century before Christ), is derived
from the Sanskrit maitri (Pali, metta) "love," so we can
conclude that even in olden times the idea of loving com-
passion was bound up with that of the future Buddha.

We see that there is hardly a question in the history
of religion which can be decided with greater certainty
than that raised by Dahlmann and decided without any
doubt, according to his opinion, in the opposite sense. The
Mahayana has arisen without any influence on the part of
Christianity and has overcome the eastern Asiatic world
by its own power in a mighty triumphal procession, and

"Oldenberg, Buddha, 5th ed., p. 384, Note i; Koppen, Die Religion des
Buddha, I, p. 315.

86 Spence Hardy, A Manual of Buddhism, p. 8 ; Childers's Dictionary of
the Pali Language, s. v. "Kappo," p. 186; Pischel, Leben und Lehre des
Buddha, 2d ed., p. 94,

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 177

at the same time to be sure without shedding a drop of
blood, solely by the power of conviction and example. How
great an influence, lasting even down to the present day,
the Mahayana has exerted on the higher spiritual develop-
ment of China, we learn from the great sinologist J. J.
M. de Groot who lived in China for years among Buddhist
monks and who declared that the Buddhists were the only
Chinese who possessed refinement of heart, and the only
ones with whom one could discuss spiritual matters.37

If we now turn to the question whether at a later date
the demonstrable contacts with Christianity have left ap-
preciable traces on northern Buddhism, I am inclined to
answer in the affirmative, although it is difficult to give a
positive proof.

Before I enter upon the subject of the Buddhism of
Tibet, which here comes mainly into consideration, I shall
add an incidental remark.

To the best known writings of the Mahayana literature
belong the "Lotus of the Good Law" and the biographies
of Buddha called Lalitavistara and Mahavastu, none of
which can be placed before 200 A. D. Most of the paral-
lels with the Gospel stories which have been met with in
Buddhist literature are found in these three works38 (and
besides in the Pali Nidanakatha, the introduction to the
Jataka book, dating from the fifth century after Christ).

Nothing more can now be said about these parallels
except that it is not impossible that they were borrowed
from Christianity. When in the later Mahayana writings
mention is made of Buddha as a fisherman who catches
men like fishes, and this comparison has passed over into
Chinese art in which Buddha is represented as a fisherman
with rod and hook,39 we cannot fail to recognize here a

87 See Edv. Lehmann, Der Buddhismus, p. 256.

"The Monist, XXI, October 1911, p. 520.

89 Paul Carus, The Open Court, June 1911, p. 357.

IjS THE MONIST.

transference of the Christian symbol into the Buddhist
world, because the catching of fish is an entirely un-Bud-
dhistic act. The same is true of the typical representation
of the mother with the child Buddha. That this goes back
to Christian prototypes one glance at the "Buddhist Ma-
donna" from Chinese Turkestan in the Ethnological Mu-
seum at Berlin, is sufficient to prove.40

For such transmissions the conditions of those days
were particularly favorable. Kennedy mentions,41 al-
though without stating his source, that in the eighth
century a Christian monk and a Bactrian Buddhist to-
gether composed a Christian-Buddhist text-book. The fact
is that in Singan-fu, the ancient capital of China, the Nes-
torian missionary Adam, the "presbyter, chorepiscopus and
papas of China" — called by the Chinese King Tsing, the
"distinguished and pure one" — together with Prajfia, a
Buddhist from Kapisha in Northern India, translated into
Chinese the Buddhist Shatparamitasutra from the Uigu-
rischen.42 Through the famous Chinese-Syriac inscription
of Singan-fu, written in the year 781 by the above men-
tioned Adam with the aid of other Nestorians, we further
learn that at that time in a monastery in that vicinity Bud-
dhist monks and Nestorian Christians were living and
working together side by side in a spirit of comradeship.43
Such friendly intercourse between Buddhists and Chris-
tians probably existed in many places in central Asia in
those times.

Buddhism did not penetrate into the icy highland of

40 See frontispiece in A. Foucher's Beginnings of Buddhist Art and Other
Essays on Indian and Central Asian Archeology, translated by L. A. and W.
F. Thomas. Paris, 1912.

"Journal of the Royal Asiatic Society, 1907, p. 481.

^Takakusu, T'oung Tao VII, 1897, pp. 589-591; Berthold Laufer, The
Open Court, August, 1911, pp. 451-452. According to this the emperor Tai-
Tsung (780-804) distinctly issued a warning against the confusion of Chris-
tian and Buddhist doctrines.

"Max Miiller Last Essays, I, p. 258; II, pp. 310 ff., according to James
Legge, Christianity in China, 1888.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 179

Tibet in the form of the Mahayana but of the Yogachara
system,44 which indeed wishes to be recognized as only a
particular school of the Mahayana and which according to
its own text-books is also called the Tantra school. This
school was founded in the sixth century by the monk Arya-
sanga of Peshawar, who adopted the Brahman — especially
the Shivaitic — gods into Buddhism as defenders of the
church against the world of demons, and furnished the
religion with a confused theory of witchcraft in which
predominated mystical formulas (dharani) for the attain-
ment of supernatural powers and the accomplishment of all
possible desires.

In this degenerate form Buddhism reached Tibet in the
middle of the seventh century,45 and about a century later
the church known under the name Lamaism, which soon
developed into an ecclesiastical state, was founded by the
artful "conjurer"" Padmasambhava whom the Indian mis-
sionaries of Buddhism called to Tibet from his native land
Kafiristan in order to overcome the opposition of the native
Shamans.46 Padmasambhava succeeded in this conquest
by incorporating the teachings and usages of these Sha-
mans, who had great influence among the people, into
Tibetan Buddhism in which since that time they have
formed an important component part.

The possibility of Christian influence upon Buddhism
in Tibet and China has existed since 635, for from this
year we have evidence of a Nestorian mission which set out
for those lands under a leader by the name of Olopan or
Alopen.47 This mission was received in northern India

" Literally, "practice of witchcraft," the chief characteristic of this school.

"Griinwedel, "Der Lamaismus," p. 141, (In Hinneberg's Kultur der
Gegenwart, Part I, Section III, i: "Die Orientalischen Religionen." Berlin
and Leipsic, 1906.)

46 Ibid., p. 143. L. Austine Waddell, The Buddhism of Tibet or Lamaism,
London, 1895, PP- x, 24 ff. ; see index.

" Waddell, op. cit., p. 422.

180 THE MONIST.

by the famous king Shiladitya at his court in Kanoj in the
year 639**

Later there arose in Nepal and Tibet the belief in the
Adibuddha, that is, in an omnipotent and omniscient pri-
meval Buddha, who was supposed to have begotten the
above-mentioned five Dhyanibuddhas by his meditation—
hence a monotheistic transformation of the original atheistic
Buddhism. Rhys Davids,49 following Csoma de Koros,
places the rise of this faith in the tenth century, L. de la
Vallee Poussin50 somewhat earlier. At any rate H. Kern
and Waddell,51 who rests upon his authority, are wrong in
placing the beginnings of the doctrine of the Adibuddha
as early as the first century after Christ.

Poussin regards this entirely theistic (aishvarika) Bud-
dhism, which may be divided into several — at least into
two — different Adibuddha systems, merely as a final stage
in the evolution of the Mahayana. He says :52 "Buddhist in
fact only in name and in so far as it employs Buddhist
terminology, it nevertheless is, as it were, the consumma-
tion of the philosophical, mystical and mythological specu-
lations of the Great Vehicle, and differs from several other
systems widespread in the Buddhist world, only by its
markedly 'theistic' coloring." He mentions relations with
Hinduism but never even alludes to the possibility of Chris-
tian influence. We shall have to concede to him that to
insert a personal God, inactive in principle but in reality
looked upon as creative — and as such we must consider
Adibuddha — into the fantastic system of the later Maha-

"Takakusu, I-Tsing XXVIII, note 8; Athenaeum, July 3, 1880, p. 8 in
the review of Edkins's Chinese Buddhism; Grierson, Encyclopaedia of Re-
ligion and Ethics, II, p. 548 b.

*• Buddhismus, p. 214.

60 In the scholarly and exhaustive article "Adibuddha," Enc. of. Rel and
Eth., i, pp. 93 ff., at the end of which is appended a comprehensive bibliog-
raphy.

51 Buddhism of Tibet, pp. 126, 130.
M Loc. cit., p. 93 b.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. l8l

yana is quite comprehensible without foreign influence. As
at first the imaginary Dhyanibuddhas and Dhyanibodhi-
sattvas had been placed above the earthly Buddha and his
many manifestations in the past and future, which had
been accounted for as their earthly reflections, so later a
basis might be sought from which those imaginary figures
could be deduced, and this basis might be found in a su-
preme God. It is also conceivable that the desire to obtain
adherents for the Buddhist religion among theistically in-
clined circles has contributed to the production of the Adi-
buddha. Poussin might have pointed out an analogous
phenomenon in the history of Brahman philosophy, namely
the introduction of the personal God (ishvara) into the
atheistic Samkhya system, which in a less indirect manner
was adopted in the formation of this system into the Yoga
doctrine. Nevertheless it must be repeated that the con-
ception of the Adibuddha may possibly be reducible to
Christian influence since in Tibetan Buddhism religious
discussions with Nestorians had undoubtedly preceded it
in point of time.

With greater distinctness we can recognize the often
alleged Christian influences on the later development of
the Lamaistic form of worship which has been called a
caricature of the Catholic service. Yet Catholic mission-
aries who had penetrated as far as Tibet have reported
with horror that the devil had created a caricature of the
ritual of the Roman Catholic church there in order to bring
it into derision.

From Grunwedel's excellent exposition of Lamaism53
we learn that the European Christian mission had exerted
itself in behalf of Tibet ever since the first half of the four-
teenth century. In the year 1330 Odoricus of Pordenone,

"In Hinneberg's Kultur der Gegenwart, Part I, Sec. Ill, I: "Die orien-
talischen Religionen," pp. 136 ff. ; X, "Europaische Reisende in Tibet," pp.
156 ff. See also O. Wecker, Lamaismus und Katholizismus, ein Vortrag.
Rottenburg, 1910; and Hackmann, Buddhism as a Religion, pp. 71 ff., 154 ff.

1 82 THE MONIST.

the first European who had succeeded in reaching the place,
found Christian missionaries and some converts already
in the capital of Tibet, — that is, in Lhasa. At any rate we
must understand these missionaries to be Syrian Chris-
tians. In 1624 after a long interval the Portuguese Jesuit
d'Andrada, coming from Delhi to the city of Chaprang in
western Tibet, was received with honor by the ruling king
and with his permission laid the corner-stone for a Chris-
tian church. We learn then of a series of other mission-
aries, Dominicans and Jesuits, from the beginning of the
eighteenth century, of many hardships with which they had
to contend, but also of protection and benevolence on the
part of the king. In 1719 begins the missionary activity
of the Capuchins, who had been successful at Rome in
having the monopoly of the Tibetan mission conferred
upon them. It was at once taken in .charge by the Capu-
chins to a much greater extent. In the same year Horatio
della Penna came to Tibet with twelve Capuchins, again
in 1737 with nine, since most of his first companions had
died or had become incapable of work. But towards the
middle of the eighteenth century, soon after the death of
Horatio, the Capuchins gave up the evangelization of
Tibet.

We have no knowledge of any success their exertions
may have had. If they had made converts to any con-
siderable extent, surely all accounts of them could not
have been so lost as to leave no trace. The missionaries
were apparently wise enough to judge the matter correctly
and to recognize the hopelessness of any considerable ex-
tension of Christianity in Tibet. But from the syncretistic
character of Lamaism, which had adopted not only the
Brahman gods but also the national divinities of the Tib-
etans and finally after the conversion of the Mongols even
some of their ideas, they must also have been justified in

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 183

expecting there would be room within it for Christian ideas
and Christian forms of worship as well.

With a similar view the Jesuits in China who had come
in 1581 under the leadership of Ricci in the garb of Bud-
dhist monks in order to secure a kindly reception, started
out towards the end of the sixteenth century, and while
publicly participating in Confucian worship diffused Chris-
tian ideas so that many Chinese accepted Christianity, but
did not for that reason cease being Confucianists, Taoists
or Buddhists, until finally a peremptory order from Rome
put an end to this adjustment of Christianity to Chinese
requirements.54 So the Christian missionaries in Tibet
would naturally have aimed upon the whole at the peace-
ful infiltration of Christian ideas into Lamaism in the hope
of imperceptibly Christianizing it in time. That they suc-
ceeded better in this with regard to forms of worship than
doctrine may be explained by the fact that Lamaism in
contrast to the original Buddhism was directed essentially
to externalities. In the high value placed upon sanctimoni-
ous observance Lamaism and Catholicism must have met
on the same level.

In the year 1760 Tibet closed its doors to European
visitors, and since that time only isolated Europeans —
usually in the dress of Asiatics — have succeeded in pene-
trating into that country, but without reaching the capital
Lhasa, with the exception of the British expedition under
Colonel Younghusband, whose entry into Lhasa in the year
1904 is still fresh in our memories.

At any rate the seclusion of Tibet was complete when
the two Lazarist fathers Hue and Gabet, in the garb of
Buddhist ecclesiastics, arrived at Lhasa from Mongolia
in January 1846 after a toilsome journey of a year and a
half, and were compelled to leave again in March upon the
demand of the Chinese Resident. The information which

64 Max Muller, Last Essays, II, pp. 315-317.

184 THE MONIST.

Hue has given in his famous book55 on Lamaistic forms of
worship is an important source for all who have written on
Lamaism.

Rhys Davids's Buddhism closes with the following com-
prehensive description : "Lamaism, indeed, with its shaven
priests, its bells, and rosaries, its images, and holy water,
and gorgeous dresses ; its service with double choirs, and
processions and creeds, and mystic rites, and incense, in
which the laity are spectators only; its abbots and monks,
and nuns of many grades; its worship of the double vir-
gin, and of the saints and angels; its fasts, confessions
and purgatory, its images, its idols and its pictures; its
huge monasteries and its gorgeous cathedrals, its powerful
hierarchy, its cardinals, its pope, bears outwardly at least,
a strong resemblance to Romanism, in spite of the essen-
tial difference of its teachings and of its mode of thought."

This description could be further supplemented by ref-
erence to the crozier and the bishop's mitre, exorcism of
demons, the censer with five chains which can be closed
or opened at will, the benediction in which the Lama lays
his right hand upon the head of the believer, the religious
exercises in seclusion, and still* other particulars.56 Further-
more the practice of the higher Lamas to cross themselves
before the beginning of a religious service57 seems to me
to deserve special mention, as does also a ceremony which
bears a remarkable resemblance to the celebration of the
Lord's Supper.58 In this we have the distribution of con-
secrated bread and wine to the devout congregation. In
place of the bread consecrated pellets of puff-paste are also
mentioned, and by wine we must probably understand a

55 Souvenirs d'un voyage dans la Tartarie, le Tibet et la Chine, 2 vols.
Paris, 1850 (second edition, 1853) ; English edition, Chicago, Open Court Pub-
lishing Company.

M Hue in Wecker, loc. cit., p. 37.

67 Waddell, Buddhism of Tibet, p. 423.

68 Ibid., pp. 444 ff.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 185

different sort of alcoholic drink.59 At any rate "bread and
wine" are enjoyed by the participants in this ceremony
"for the attainment of long life." By long life may be
understood a circumlocution for the Christian idea of
eternal life.

One other fundamental idea of Lamaism appeals to us
as strictly Catholic, namely that the priests "hold the keys
of hell and heaven, for they have invented the common
saying: Without a Lama in front (of the votary) there
is no (approach to) God/"60

One might be tempted to account for these correspon-
dences between Catholic and Lamaistic worship as parallel
phenomena by the statement that the human mind when
moved in the same direction of thought arid feeling arrives
externally at the same results. But the correspondences
are too close and too numerous for us to get along without
the assumption of a loan. As at the close of my former
essay in this periodical (October, 1911) on "Contributions
of Buddhism to Christianity" I could not avoid the con-
viction that many fundamental features in the worship of
the early Christian church have been taken over from Bud-
dhism, so on the other hand at a more recent date many
Christian forms of worship of a later stage of development
have found acceptance in the most degenerate form of Bud-
dhism, Lamaism.

I have pointed out above (pp. 182-183) how in my
opinion this has come about. Hue has called attention
to still another possibility.61 In the thirteenth century in
the times of the Mongolian supremacy, ambassadors from
the rulers of the world came to Italy, Spain, France and
England, and took home, so Hue thinks, a deep impression
of the glitter and splendor of the Catholic worship. Per-

68 "Ambrosia brewed from spirit or beer," Waddell, p. 445 ; in the middle
of page 448 he speaks again of the sacred wine.
60 Ibid., pp. 422-423.
81 In Wecker, Lamaismus und Katholizismus, pp. 37-39.

l86 THE MONIST.

haps they did; but the incidental enthusiastic descriptions
of these secular ambassadors would have assumed only
very general outlines and could hardly have exercised any
influence on the later worship of the Mongols. Still less
propable is it that the Mongols would have carried traces
of this influence to Tibet, since indeed they took Lamaism
away from Tibet with them and have remained its true
devotees until the present day. Moreover, at the time of
their greatest power the Mongols, who were then adherents
of Shamanism, were religiously indifferent, and ambassa-
dors of Buddhism, of Islam and even of Christianity waited
upon them in vain. When Kubilai Khan was converted
to Buddhism in the thirteenth century the Mongolian em-
pire had already, fallen to pieces.

For the channels of Christian influence upon Lamaistic
worship search must be made within Tibet itself, and at
any rate the assumption of Hue62 can not be ignored that
the famous reformer of Lamaism Tsong-Kha-Pa (1356-
1418), who introduced clerical vestments and a definitely
prescribed ritual, had been under the influence of Christian
missionaries, even though we possess no record from this
period of a Catholic mission to Tibet. But central Asia
was traversed in those days by numerous Christian mis-
sionaries, and so the "man from the west with the long
nose and eyes gleaming with supernatural fire,"6 with
whom Tsong-Kha-Pa is said to have conversed, may have
been a Christian monk who found his way there not from
India (for then something more definite would be known
of him) but from the north into the interior of Tibet.

At any rate since the Nestorians of the seventh cen-
tury there have never been wanting channels through
which Christian elements of worship might have been in-
troduced into Tibetan Buddhism.

61 See also Waddell, p. 59; Hackmann, Buddhism as a Religion, pp. 74,
75, 180.

68 Hue, Souvenirs, II, 2d ed., p. 106.

CONTRIBUTIONS OF CHRISTIANITY TO BUDDHISM. 187

In conclusion I should like to deny one possibility which
has occasionally been suggested, namely that the Catholic
ritual may not have influenced the Lamaistic, but vice
versa may have been influenced by it.64 Lamaism has
never possessed the requisite strength for this. The side
which is much weaker morally and intellectually can not
urge its forms of life upon the stronger.

As we have seen, Christian influences upon the develop-
ment of Buddhism are limited to secondary products of a
late day; just as inversely Buddhist influences upon Chris-
tianity may be pointed out only in non-essential particu-
lars and from times in which the doctrine of the Christian
faith was established as a firm system. All identities and
similarities in the teachings of these two great world-
religions have, so far as essential matters are concerned,
originated independently of one another, and therefore are
of far greater significance for the science of religion than
if they rested upon a loan.

RICHARD GARBE.

TUBINGEN, GERMANY.

"Waddell, pp. 421-422: "It is still uncertain how much of the Lamaist
symbolism might have been borrowed from Roman Catholicism, or vice versa" ;
Pischel, Leben und Lehre des Buddha, p. 124 : "Without doubt much has trav-
eled from Lamaism into the Catholic church since even Buddha himself as
Josaphat = Bodhisattva has been accepted among its saints in the Roman
martyrology" — but not from Lamaism! We have distinct indications that
Pischel is also the author of the (anonymous) article on Indian religions in
Brockhaus's Konversations-Lexikon, I4th ed., XVII, where we read on page
594 b: "....so that the service of Lamaism closely resembles the Catholic
service from which many would derive it. .. .But the reverse path of the loan
is equally probable."

THE PRINCIPLE OF RELATIVITY.

INTRODUCTORY.

PHYSICAL science seems to have entered into a new
phase, the slogan of the new school being THE PRIN-
CIPLE OF RELATIVITY. In some quarters the current modes
of thought are declared antiquated, and the promise is
made that the old truths will acquire a new meaning.
Physicists speak of the relativity of time and space, and
we will add that they ought as well speak of the relativity
of things, of the whole actual world in all its parts and
interrelations.

Many who have watched the origin and rise of the
new movement are startled at the paradoxical statements
which some prominent physicists have made, and it is re-
markable that the most materialistic sciences, mechanics
and physics, seem to surround us with a mist of mysticism.
The old self-contradictory statements of the Eleatic school
revive in a modernized form, and common sense is baffled
in its attempt to understand how the same thing may be
longer and shorter at the same time, how a clock will
strike the hour later or sooner according to the point of
view from which it is watched; and the answer of this
most recent conception of physics to the question, How is
this all possible? is based on the principle of the relativity
of time and space.

The man who started this movement and was the first
to formulate it in concise language and to base it upon close

THE PRINCIPLE OF RELATIVITY. 189

argument was Professor Einstein,1 who was followed by
Lorentz,2 and so we hear often of the Einstein-Lorentz
theory. The strangest thing about it is that the question
is seriously debated whether or not this theory is true, and
the answer is expected from experiments; while in our
opinion we are here confronted with a method, and the
problem is simply how we can best deal with certain diffi-
culties due to the relativity of all things. These difficulties
have originated through the need of a greater exactness
in measurements, but the underlying truth — the relativity
of all things — is not a question of fact, but a recognition
of certain complications with which we must learn to deal.

On reading recent expositions of the principle of rela-
tivity the man of good education, or the one who has at-
tended universities without being a specialist in either
mathematics or physics, feels the terra firma give way
under his feet, and when he finds that the principle of
identity seems to fail in his comprehension of things, a
dizziness comes over his intellect and he sinks into the
bottomless abyss of the incomprehensibility of existence.
A general earthquake seems to quiver through his mind.
Everything totters around him and he stands in awe at the
significance of the new thought. Nor is there any one
who dares to contradict; for the most learned arguments
are adduced, the mathematical and logical conclusions of
which bristle with formidable formulas, — yea, experiments
are made to prove the truth of the relativity of time and
space.

For the sake of convenience we will speak of the repre-
sentatives of this new conception as the "relativity physi-
cists" in contradistinction to the old-fashioned physicists
of the old school. It has been said that the former repre-
sent more the mathematical aspect of physics while the

1Jahrbuch der Radio aktivit at und Elektronik, 1905-1908.
* H. A. Lorentz, Theory of Electrons (Teubner) 1910.

THE MONIST.

latter are the realistic physicists proper, too realistic to
understand the significance of the new truth.

In order to facilitate a comprehension of the situation
as well as our own conception, we will here at once and
dogmatically state that the relativity physicists are per-
fectly right; what they claim is really and truly a matter
of course, and if they only would present their proposition
without dressing up their theory in paradoxical statements,
nobody would in the least hesitate to accept the new view.
But as soon as this is done people will at the same time
find out that the new view is not novel. Its importance
has been greatly exaggerated, for the principle has been
tacitly understood in the correct way by all preceding phys-
icists who, at the time however, ignored, or better did not
enter into, the problem, because they had other more press-
ing work on hand. Nor is it unlikely that they regarded
this problem of relativity as a philosophical question which
strictly speaking had no place before the forum of physics.

ON THE ABSOLUTE.

Perhaps the easiest way of elucidating the true mean-
ing of the relativity of time and space will be by setting
forth our own position as we held it long before the prin-
ciple of relativity gained prominence or had even been men-
tioned or alluded to.

The writer's book Fundamental Problems contains the
following statement under "Definitions and Explanations"
(first edition, page 254; seecond edition, page 252) :

"Absolute existence (in fact everything absolute) is
impossible. Reality is properly called Wirklichkeit in Ger-
man, derived from wirken, to take effect. Reality is not
immovable and unchangeable absoluteness, but the effec-
tiveness of things in their relations. Reality therefore im-
plies not only existence, but the manifestation of existence

THE PRINCIPLE OF RELATIVITY.

also. Existence and its manifestation are not two different
things; both are one."

Since the days of Heraclitus it has been a trite truism
that all existence is in a flux. There is no rest anywhere,
and actuality consists in the effects which these changes
exercise upon one another by action and reaction. Upon
this lack of stability, resulting from a universal and in-
trinsic relativity, Mr. Spencer bases one of the strongest,
though quite untenable, arguments of his agnosticism. He
seems to expect that time, space, motion, and matter are
or should be things-in-themselves, and forgets that they
represent relations, i. e., certain features of reality. We
will here quote his exposition of the unknowableness of
motion in space. In his First Principles Spencer says :

"Here, for instance, is a ship which, for simplicity's sake, we
will suppose to be anchored at the equator with her head to the
west. When the captain walks from stem to stern, in what direction
does he move? East, is the obvious answer, — an answer which for
the moment may pass without criticism. But now the anchor is
heaved, and the vessel sails to the west with a velocity equal to
that at which the captain walks. In what direction does he now move
when he goes from stem to stern? You cannot say east, for the
vessel is carrying him as fast towards the west as he walks to the
east ; and you cannot say west for the converse reason. In respect to
surrounding space he is stationary ; though to all on board the ship
he seems to be moving. But now are we quite sure of this conclusion ?
Is he really stationary? When we take into account the earth's
motion round its axis, we find that instead of being stationary he is
traveling at the rate of 1000 miles per hour to the east; so that
neither the perception of one who looks at him, nor the inference
of one who allows for the ship's motion, is anything like the truth.
Nor indeed, on further consideration, shall we find this revised con-
clusion to be much better. For we have forgotten to allow for the
earth's motion in its orbit. This being some 68,000 miles per hour
it follows that, assuming the time to be midday, he is moving, not at
the rate of 1000 miles per hour to the east, but at the rate of 67,000
miles per hour to the west. Nay, not even now have we discovered
the true rate and the true direction of his movement. With the

THE MONIST.

earth's progress in its orbit, we have to join that of the whole solar
system towards the constellation of Hercules ; and when we do this,
we perceive that he is moving neither east nor west, but in a line
inclined to the plane of the ecliptic, and at a velocity greater or less
(according to the time of the year) than that above named. To
which let us add, that were the dynamic arrangements of our sidereal
system fully known to us, we should probably discover the direction
and rate of his actual movement to differ considerably even from
these. How illusive are our ideas of motion, is thus made sufficiently
manifest. That which seems moving proves to be stationary; that
which seems stationary proves to be moving; while that which we
conclude to be going rapidly in one direction, turns out to be going
much more rapidly in the opposite direction. And so we are taught
that what we are conscious of is not the real motion of any object,
either in its rate or direction ; but merely its motion as measured
from an assigned position — either the position we ourselves occupy
or some other."

The same argument of the captain walking the deck
of a ship was made before Spencer, though mostly it was
a ball rolling on deck; Bradley refers to it as well known
in his time, 1727, and the same story has been repeated
after Spencer. In fact it is one of the arguments of the
relativity of space among modern relativity physicists.

The principle upon which the representatives of the
new view take their stand is a consideration of actual life.
Things are in a flux, and this is an undeniable fact. We
must bear in mind that the way of making knowledge pos-
sible at all in the flux of being is to ignore what has nothing
to do with the problem under investigation. Our method
is based upon a fiction or, if you please, upon an artificial
trick, viz., to ignore complications and to consider a certain
thing as fixed; but there are cases in which we must re-
member that we ourselves change and that the very posi-
tion we assume is moving.

This trick of assuming that our position is stable is easy
enough because man does not at once notice that there is
any change; but all things are in a flux and he himself

THE PRINCIPLE OF RELATIVITY.

changes unconsciously. A primitive unsophisticated man
does not know that the earth on which he stands is whirling
around itself at the rate of 1037 miles an hour, on the
equator, further that it is also revolving with incredible
speed around the sun, and that with the sun it is proceeding
in a spiral motion towards one of the constellations, prob-
ably the constellation Heracles, around an unknown center
situated somewhere in the Milky Way. God only knows
what else takes place and what kind of whirling dances
the Milky Way performs. The savage has not the slightest
idea of all this, and so it is easy for him to ignore the mo-
tion of which he unconsciously partakes.

If man really were aware of all the events which in-
fluence him, his head would swim, and he would be inca-
pable of thinking any sober thought. Fortunately he is
concerned solely with his own narrow interests. The more
man in the further growth of his mind becomes familiar
with these unnoticeable events, the more he discovers that
for any particular purpose he must ignore what does not
belong to the solution of the special problem under con-
sideration.

This way of ignoring what does not concern us at the
time is an artificial process, a process of abstraction and
elimination, of cutting off all disturbing incidents, and in
doing so the philosophically minded scientist will become
aware of the fiction of arbitrarily laying down a point of
reference which is treated as if it were stable while in fact,
like everything else, it too is caught in the maelstrom of
cosmic existence.

There is nothing wrong or harmful in this fiction; on
the contrary it is an indispensable part of our method of
comprehending things. The universe is too complicated to
be understood or viewed at a glance, and knowledge, sci-
ence, cognition as well as all mental processes become pos-
sible merely by concentration, i. e., by selecting a point of

THE MONIST.

view as being a certain fixed location from which we ob-
serve a change, an event, a transformation, in order to
gain a comprehension of this or that piece of existence in
contrast to others of the same or of a different kind. Such
is the nature of cognition, and this artificial trick is an
essential condition of observation.

Knowledge is relative. It is the relation between sub-
ject and object, the thinker and the thing, and this, far
from being objectionable, is only the universal condition of
all existence ; for all existence is relative. All reality is the
result of action and reaction; it is a forming and being
formed under definite conditions; it is transformation.
There is no existence in and by itself. Relativity is the
principle of all real and actual being.

TRICKS OF COGNITION.

If the standpoint of an observer changes, the thing ob-
served will naturally change too in its relation to him.
Formerly physicists were in the habit of not seriously bear-
ing in mind that the fixedness of their standpoint was an
assumption; they did not follow this principle to its ulti-
mate consequences. For their special problems it was not
necessary to do so, and there is very little use in bearing
it constantly in mind. The difference in time between the
moment when the observer looks at an object and that in
which the rays of light indispensable for observation strike
his eye is too inconsiderable to be taken into account; it is
a negligible quantity. But if the object under considera-
tion is at such an enormous distance that it takes the rays
of light thousands of years to reach the eye of the astron-
omer it does make a difference, and so James Bradley was
astonished to register the fact that the fixed stars in the sky
were not always in the same place but that they pendulated
semi-annually above us with the motion of the earth around
the sun. The direction in which we see them swings from

THE PRINCIPLE OF RELATIVITY.

the aphelion to the perihelion, and a closer consideration
of the facts shows that the rays of very distant stars which
we catch in the aphelion are not caused at the moment when
we see them but started thousands of years prior to the
moment in which they strike the lens of the astronomer's
telescope, and so the transference of rays of light from the
star to the astronomer's eye at this enormous distance rep-
resents a relation which most forcibly drives the truth
home to us that there is nothing absolute.

The same is true of all things. The object before us
seems to stand there in a perfect and quiet completeness,
and yet the changes that work unnoticed by our dull senses
are constant, continuous and rapid. Heraclitus used to say
that he could not come out of the same river into which he
had stepped a moment before, because the water was al-
ways rushing by. Never is a drop of it the same, and this
is true of all things, even of ourselves. The observer has
to exclude from his methods of observation the fact that
he himself, his senses and his mind, are in a constant flux.

In order to elucidate the significance of the nature of
cognition as being a limitation and concentration upon one
point and constructing artificial units, the writer has on
former occasions used the analogy of the kinematoscope,
the machine which produces moving pictures.

In order to make any picture possible we need a lens,
and the lens focuses the rays of light so as to throw rays
from the same spot upon one and the same place on the
plane where the picture appears. The rays of light which
proceed from an object scatter in all directions, and unless
we use a lens to concentrate the rays, the formation of a
picture of the object would remain impossible. Thus the
method of producing a picture is by concentration.

The lens produces a picture by focusing rays of light,
that is by throwing the same rays upon the same spot;
but it would also be possible to produce a picture by cutting

196 THE MONIST.

off the redundant rays of light and singling out one or
very few rays, each one coming from each of the several
points of the object. Accordingly we can photograph ob-
jects through a pinhole; there is only this difference that
the picture is weak and needs long exposure. This proves
that the process of concentration is fundamentally a pro-
cess of abstraction, of leaving out, of omitting the disturb-
ing multiplicity of the innumerable facts of real life as
represented in the totality of objective experience.

The kinematoscope involves not only the static form
of things, their spatial expression, the juxtaposition of
parts, but it also adds the changes that are taking place in
time. The film of the kinematoscope consists of a series of
pictures, one always a little different from another, and
if these are presented in rapid succession the series is fused
into one picture in which the succeeding differences appear
as motion. This is accomplished by the introduction of a
little winged wheel which in rapid succession covers and
uncovers the several pictures. If we would take this little
wheel with its wings out of the kinematoscope, and if other-
wise the pictures on the film would succeed one another
in a rapid continuous motion without this artificial separa-
tion by the wings of the wheel, we would see no picture at
all but simply have a blur on the canvas. In order to
have distinct pictures appear on the canvas, we must cut
the flux of motion into little separate moments which we
may allegorically characterize as atoms of time.

Reality is a continuous flux, but in order to follow it
step by step we must do the same thing that the mathema-
tician does with his differential calculus. In the calculus
the curve is cut up into infinitesimal lines, which in con-
tinuous succession change their directions, and the smaller
we conceive these lines to be, the less is the mistake made
by this fiction, if they are treated like straight lines.

The method of the calculus, based upon the fiction of

THE PRINCIPLE OF RELATIVITY.

substituting for a continuous curve a series of little straight
lines constantly changing their direction, is not so very
different from the method of cognition in general. Nor
is there anything wrong in it, only we must remain con-
scious of the fiction. In a similar way we must know that
existence itself is a continuous system of relations, or in
other words, that relativity is the principle of all existence
in the world of actual life as well as in the domain of
thought. We must cut up the general flux according to the

needs of our investigation and lay down artificial limits.

* * *

If we view the new physics under this aspect, it will
lose its mystic glamor and at the same time appear intelli-
gible. In fact we shall understand that the principle of
relativity is a matter of course, and if we cut up reality
into things, as if they were things-in-themselves, into units
or atoms, we employ a trick of cognition which makes it
possible to focus things and picture them distinctly in our
mind.

There are large numbers of scientists possessed of an
odium philosophicum because philosophy means to them
some abstruse metaphysical system of thought which ig-
nores the natural sciences and, spiderlike, spins a world-
conception out of pure thought derived from the thinker's
subjectivity. The result is that they are soon perplexed in
their own science by philosophical problems; for true phi-
losophy— the philosophy of science — is an indispensable
factor of cognition, and its influence extends into the fabric
of all scientific labors. Thus it happens that problems of
a philosophical character arise unexpectedly, and then the
information given by nature in reply to experiments is apt
to be misunderstood.

If the reference point (R) from which an observer
measures is in motion toward RI, and the object observed
(O) also possesses a motion of its own, we are confronted

198 THE MONIST.

with a complicated phenomenon. If R moves toward O,
the object measured will be shorter than if it stands still,
and it will be longer if R moves with O in the same direc-
tion. We have only to forget, after the fashion of the
pragmatist, that there is an ideal of objective cognition,
and assume that all there is about size or the objective
measure of things consists in the result of our measuring
and we have the clue to the paradoxes of the physics of
relativity. If the point of reference is not stationary and
if we neglect to account for its motion, the result of our
measurement is necessarily vitiated thereby as much as
the pragmatist's philosophy by his personal equation.

O

R >- Ri

Fig. i.

There are further complications of measurement. The
time needed for the transmission of signals must also be
taken into consideration. The rays of light travel at an
enormous velocity but the distances in the starry heavens
are also enormous and the distance between O and R is
less than between O and RI. The rays which were sent
out from O at the moment of measurement have already
passed the track of the observer at R, while this same ob-
server has moved on to RI, and there he catches the rays
sent out from O in its position at O ; in the meantime how-
ever the object O has in its turn also changed its place.
From RI it appears at O, where it stood while the observer
was stationed at R, but in fact it stands no longer at O but
has in the meantime proceeded on its own path whither-
soever that may have led O, backward or forward, in any

THE PRINCIPLE OF RELATIVITY. 199

other direction than R, possibly in the same direction as R.
Such phenomena are necessary results of the relativity of
existence, and we must bear them in mind when confronted
with complicated conditions which present themselves, for
instance in astronomical cases. Here the mistakes rising
from the fiction of assuming our reference point to be stable
are considerable enough to enforce attention, and in that
case we shall have to make allowance for the instability of
our reference point, as well as for the time which the rays
of light need for their travel through space.

That was exactly Bradley's case as set forth in his
essay written in 1727, one hundred and eighty-five years
ago, and thus he became the forerunner of the relativity
physicists. To state it in other terms, Bradley correctly
solved a problem which in our days led to the formulation
of the principle of relativity, and he did so without men-
tioning this theory, yea without feeling the need of formu-
lating it. He simply took it for granted that he had in this
case to consider the motion of the earth that served him
as a reference point — the place of his observations.

COMSTOCK ON RELATIVITY.

The most popular and at the same time the most exact
characterization of the principle of relativity comes from
the pen of Prof. D. F. Comstock, of the Massachusetts
Institute of Technology. It appeared in Science (Vol.
XXXI, 1909, p. 767), and we quote from it the passages
which contain the statement of the problem:

Professor Comstock starts with the following two pos-
tulates :

"The uniform translatory motion of any system can not be de-
tected by an observer traveling with the system and making obser-
vations on it alone.

"The velocity of light is independent of the relative velocity
of the source of light and observer."

20O THE MONIST.

The main passages of his exposition state the problem
thus:

"The whole principle of relativity may be based on an answer
to the question: When are two events which happen at some dis-
tance from each other to be considered simultaneous? The answer,
'When they happen at the same time/ only shifts the problem. The
question is, how can we make two events happen at the same time
when there is a considerable distance between them.

"Most people will, I think, agree that one of the very best
practical and simple ways would be to send a signal to each point
from a point half-way between them. The velocity with which
signals travel through space is of course the characteristic 'space
velocity/ the velocity of light.

"Two clocks, one at A and the other at B, can therefore be set
running in unison by means of a light signal sent to each from a
place midway between them.

2

Fig. 2.

"Now suppose both clock A and clock B are on a kind of
sidewalk or platform moving uniformly past us with velocity v.
In Fig. 2 (2) is the moving platform and (1) is the fixed one,
on which we consider ourselves placed. Since the observer on
platform (2) is moving uniformly he can have no reason to con-
sider himself moving at all, and he will use just the method we
have indicated to set his two clocks A and B in unison. He will
send a light flash from C, the point midway between A and B,
and when this flash reaches the two clocks he will start them with
the same reading.

"To us on the fixed platform, however, it will of course be
evident that the clock B is really a little behind clock A, for, since
the whole system is moving in the direction of the arrow, light will
take longer to go from C to B than from C to A. Thus the clock
on the moving platform which leads the other will be behind in time.

"Now it is very important to see that the two clocks are in uni-
son for the observer moving with them (in the only sense in which
the word 'unison' has any meaning for him), for if we adopt the first

THE PRINCIPLE OF RELATIVITY. 2OI

postulate of relativity, there is no way in which he can know that he
is moving. In other words, he has just as much fundamental right
to consider himself stationary as we have to consider ourselves sta-
tionary, and therefore just as much right to apply the midway signal
method to set his clocks in unison as we have in the setting of our
'stationary clocks.' 'Stationary/ is, therefore, a relative term and
anything which we can say about the moving system dependent on
its motion, can with absolutely equal right be said by the moving
observer about our system.

"We are, therefore, forced to the conclusion that, unless we
discard one of the two relativity postulates, the simultaneity of two
distant events means a different thing to two different observers if
they are moving with respect to each other."

We quote further :

"It must be emphasized that, because of the first fundamental
postulate, there is no universal standard to be applied in settling such
a difference of opinion. Neither the standpoint of the 'moving' ob-
server nor our standpoint is wrong. The two merely represent two
different sides of reality. Any one could ask: What is the 'true'
length of a metal rod? Two observers working at different tem-
peratures come to different conclusions as to the 'true length.' Both
are right. It depends on what is meant by 'true.' Again, asking
a question which might have been asked centuries ago, is a man
walking toward the stern of an eastbound ship really moving west?
We must answer 'That depends' and we must have knowledge of the
questioner's view-point before we can answer yes or no."

The question of the man walking on a ship not only
"might have been asked centuries ago," but it has been
asked centuries ago. Our forebears were more conscious
of the relativity of existence than the relativity physicists
credit them.

Professor Comstock continues:

"It must be remembered that the results of the principle of
relativity are as true and no truer than its postulates. If future
experience bears out these postulates then the length of the body,
even of a geometrical line, in fact the very meaning of 'length,'
depends on the point of view, that is, on the relative motion of the
observer and the object measured."

2O2 THE MONIST.

Professor Comstock's verdict of the case is summarized
in this paragraph:

"The results of the principle for uniform translation are simply
as true as its two postulates. If either of these postulates be proved
false in the future, then the structure erected can not be true in its
present form. The question is, therefore, an experimental one."

Here we demur. We claim that the question is not ex-
perimental but belongs to the department of a priori rea-
soning.

Professor Comstock does not enter into questions of
mass connected with the principle of relativity but is satis-
fied with this comment :

"The apparent transverse mass is, I think, best derived by Lewis
and Tolman,3 in their excellent paper on the principle of relativity,
and the relation between transverse and longitudinal mass is shown
in the most direct and simple way by Bumstead4 making use of the
torsion pendulum. Any one interested in the subject should read
these two papers."

THE A PRIORI.

It is characteristic of modern science to denounce the
principle of the a priori and to extol experiment and expe-
rience. Now it is true that experience and experiment are
indispensable factors in science, and in all the specialties
of science. Jn experience and experiments we deal with
the facts presented to us by nature; but the method of
reasoning is not a thing which is derived from sense ex-
perience.

The method of reasoning is, as Kant truly said, a priori
and, let us add, the a priori is nothing mystical or mysteri-
ous; it is simply the result of pure thought or reflection
from which the data of the senses have been excluded.
Pure thought (or better, purely formal thought) is a men-
tal construction, or, if you prefer, a fiction. We omit every-

9 Phil. Mag., 18, 510-523, 1909.

* Am. Jour, of Science, 26, pp. 493-508, 1909.

THE PRINCIPLE OF RELATIVITY. 2O3

thing concrete and thus we retain a field of abstract possi-
bilities. Elsewhere we have called it a field of anyness.5
Obliterating in our mind all particularity we retain noth-
ing concrete and in this field of nothingness we build up
pure relations. From this domain all real things, com-
prising everything which we subsume under the categories
of matter and energy, has been excluded. But these pure
relations, i. e., pure forms which are non-material con-
structions lacking all concrete qualities such as all real
things possess, serve us as models for the relations of any
possible purely mental or actual existence. Our doings in
this field of abstraction consist in the fiction of pure lines,
pure numbers, pure motion, pure ideas and their inter-
relations such as genera and species, and thus we are ca-
pable of building up a world of purely formal or relational
thought, the totality of which in space is called geometry,
and in the domain of numbers which originate by counting
a series of single units, arithmetic, etc. In the domain of
pure thought, consisting of genera and species, we call the
laws that govern their relations logic, and the law of trans-
formation, of which the positive aspect is properly called
causality, and its negative counterpart the law of conser-
vation of matter and energy, has been called by Kant pure
natural science.

All systems of mental constructions have the advantage
of picturing in our mind any possible configuration of rela-
tivity, and in this sense pure thought (Kant's a priori) is
a field of anyness. It can be applied to any fact or set of
facts of existence, actual or fictitious, and these systems
of mental constructions therefore furnish us with the key
to determine the relations of real nature. They render
possible the systematization of sense impressions and thus

BSee Philosophy of Form, the chapter on "The Foundation of Mathe-
matics and Logic," pp. 7-10. For further details see also the chapter "Form
and Formal Thought" in the author's Fundamental Problems, pp. 26-60.

2O4 THE MONIST.

these systems of pure thought in the field of anyness are
the methods of scientific operation.

Let us not therefore speak contemptuously of the a
priori, or denounce apriorism as something medieval and
elusive, for even here in the attempt at establishing the
principle of relativity in time and space, the arguments of
the physicists are absolutely aprioristic. There is not one
of these so-called experiments, invented to prove the rela-
tivity of time and space, which does not ultimately resolve
itself into a machine that renders visible aprioristic con-
siderations.

The ultimate arguments in all the experiments made
to prove the relativity of time and space move in a domain
of purely formal thought, and the force of them is ulti-
mately of the same kind as the Q. E. D. of Euclidean theo-
rems. We think here mainly of such propositions as locate
an observer on the sun and another on the earth. Their
clocks actually agree, but when compared they are found
to differ. About eight minutes have elapsed when the
observer on earth registers the time as the rays of the sun
reach the earth, and vice versa when the clock on earth
is observed as the rays from the earth strike the sun. The
imitation of the same conditions for the sake of comparing
the registration of two moving systems in an actual ex-
periment amounts to nothing more than the pencil draw-
ings of a Euclidean or logical figure in which the a priori
reasoning is visibly presented as a demonstratio ad oculos.
The argument remains in either case one of pure thought.

The photograph of such an apparatus built for the pur-
pose of making an experiment in the relativity of time and
space to show the difference between a solar clock and a
terrestrial clock may be found in the article of Emil Cohn
of Strassburg, "Physikalisches iiber Raum und Zeit" in
Himmel und Erde, Vol. XXIII. To be sure the instru-
ment does not fulfil the conditions either of distance or of

THE PRINCIPLE OF RELATIVITY. 2O5

the velocity of the transference of the signal, "but," says
Professor Cohn, "that is of secondary importance."

There are two motions both constant and both stand-
ing in a definite proportion. The sun with its clocks has
been made to stand still. The earth with its two clocks
moves, and there is an arrangement by which to represent
the transference of signals. The main thing is that "their
velocities stand in definite proportions and all that concerns
us are these proportions. That we have here replaced the
enormous velocity of light by a velocity of a few centi-
meters per seecond is unessential. It is essential, however,
that the velocity of the earth is three-fourths the velocity
of light, while the real ratio is i : 10,000."

Newton's laws are a priori, and Newton proves that
these laws hold good in, and are serviceable as, interpreta-
tions of the actual world of fact. The empiricist ought to
rebel against Newton's laws, because they never have been
nor ever can be proved by either experience or experiment.
Whoever saw a body moving in a straight line? and has
Newton (from the standpoint of the empiricist) any right
at all to make such sweeping statements of movements
which have never occurred in the experience of anybody?

The most general principle at the bottom of scientific
work is perhaps the so-called law of the conservation of
matter and energy, and even this law is based on purely
a priori arguments.

Incidentally we will say that the law does not hold
good if we restrict the notion of matter to matter in the
sense of the physicist which is mass, i. e., to concrete par-
ticles of existence that are extended and possess weight.
It holds good only if we understand by matter the substance
of being, its objective reality. We had better therefore
speak of the conservation not of matter but of substance,
for gross matter, consisting of the chemical elements, is
constantly being produced before our eyes in the starry

2O6 THE MONIST.

heavens where the astronomers can watch the process
through their telescopes. In the nebulas we see now the
commotion of whirls with which gradually first the lighter
and then the heavier chemical elements are being manu-
factured out of the original world-substance which we
assume to be the same as the luminiferous ether.

Therefore we may surrender the law of conservation
of gross matter, but we still hold to the conception that
there is a conservation of stuff or substance, and the same
is true of energy. There may be energy in the shape of
a stress incorporated in the same wonderful world stuff,
the ether, and this stress may be set free and become actual
motion or kinetic energy, by some cause which creates
those whirls that start the formation of nebulas.

And what proves the law of this conservation of sub-
stance and energy? It is the necessity of a priori thought
which compels us to assume the principle that nothing
originates from nothing and nothing disappears into noth-
ing, which thought rests ultimately on the idea that all
processes of existence are transformations. Everything
that originates is formed by combination from something
that existed before.

It has been maintained that the principle of relativity
must be proved experimentally, but this is a mistake. Real-
ity is everywhere a system of interrelations, yea every
single concrete thing, every phenomenon, every piece of
existence is a bundle of relations. It can be analyzed into
its elements, which are actions and reactions; and that is
all that reality means. Space as well as time are merely
the measures, the former of arrangement or position, the
latter of succession. Space denotes the interrelation of
parts constituting figures or shapes affording a mode of
determining direction and distance. Time measures the
duration of events which is done by counting uniform
cyclical motions or parts thereof. And so we must grant

THE PRINCIPLE OF RELATIVITY. 2O7

that the relativity of time and space, as well as of all real
things is a universal and inalienable condition of all exist-
ence. We can not think of any actuality which would not
be dominated by relativity; which means we must regard
the principle of relativity as an a priori postulate.

The principle of relativity is not established by expe-
rience but is ultimately based upon reflection and pure
ratiocination. It belongs to the category of purely formal
thought as much as all arithmetical and geometrical propo-
sitions.

If any proposition of purely formal thought, such as
2X2 = 4, does not hold good in our experience, we doubt
the correctness of our counting or measuring, but we do
not doubt our a priori proposition. We revise our obser-
vation, not our logic, our arithmetic, our mathematics ; and
suppose our observation proves true, suppose that 2X2
rabbits shut up in a cage are on recounting their number
found to be more than four, say six or ten or any higher
amount, we do not upset our arithmetic or any of our
purely formal propositions, but seek the cause of the ir-
regularity in the objects, in the things or animals counted.
In that case we are positive that some transformation of
the concrete material has set in which adds to the number
to be expected according to arithmetical law.

If the reference point (R) belongs to the same system
of motion as the object observed (O), our measurement
will be correct and indicate the size of the object ade-
quately. But if R moves in a direction and with a velocity
of its own, different from O, the measurement will not be
adequate; it will be warped in an exact proportion to the
motion of R, and this rule holds good in the same way as
all mathematical, logical and generally purely formal theo-
rems.

The reliability of purely formal truths is not merely
theoretical, but finds its application in practical life, in the

2O8 THE MONIST.

objective world of matter and motion, and can be verified
by experience and experiment. And this is true also of
the relativity of time and space.

If for instance a photographer takes the picture of a
rapid express train in motion with a camera provided
with a curtain shutter, the wheels will not be round but
oval in the photograph, and the relativity photographer
who identifies the picture with the thing, in the same way
as the relativity physicist identifies the result of measur-
ing with the objective size of the object measured, will
claim that in proportion to the velocity of the train times
the inverse proportion of the velocity of the slit in the
curtain of the shutter, the wheels will increase their hori-
zontal diameters and become that much more oval. Yea
they will insist that the very same wheel will be at the
same time in one camera, only a little more, in another
one much more oval according to the quickness with which
the slit of the curtain passes over the sensitive plate.

The relativity photographer will claim that the wheels
in motion are oval while common mortals think that they
only appear oval in the photograph.

Photographs do not lie; they show the objects photo-
graphed without any personal equation on the part of the
photographer; their objectivity and impartiality can not
be doubted, and here we see the wheels oval. They are
oval, and their ovality, viz., their deviation from true cir-
cles, depends on the velocity of certain motions. An en-
thusiast for the principle of relativity can justly claim that
every photograph of a rapid train which shows the oval
form of the wheels is a successful experiment in the demon-
stration of the relativity of figure in space.

The truth of the principle of relativity in the domain
of photography can be explained by a priori considerations.
It is a matter of course, and if we argue the subject in our
mind in pure reflection, we find out what we must expect,

THE PRINCIPLE OF RELATIVITY. 2OQ

and if finally we make the experiment, the principle proves
true.

In the same way all the experiments made by machin-
ery so constructed as to represent terrestrial and solar
clocks or yard sticks, and to point out the unavoidable dif-
ference of measurements in both time and size resultant
from their respective motions of the earth and the sun as
well as the time it takes to transmit signals, are not experi-
ments in the physicist's sense but expositions and demon-
strations of purely formal truths which belong to the cat-
egory of mathematics.

If the principle of relativity does not hold good in any
domain of actual life, we must seek the cause in the mate-
rial used and not in the principle of relativity. In other
words we would be confronted with a purely physical prob-
lem which demands a physical solution, and this seems to
be the case of the Fizeau experiment.

Prof. Emil Cohn, of Strassburg,6 says:

"It is strange that the relativity principle of mechanics does not
hold good in radiation — in radiation and therewith in electrodynamics,
for that the spread of radiation is an electrical process we may con-
sider since Heinrich Hertz as an assured matter of experience. The
decisive experiment which has been made by Fizeau is this: In a
liquid, flowing with a uniform velocity, light is to be propagated in
the direction of the current. According to the relativity principle
an observer drifting in the current should find the velocity of propa-
gation to be the same as if the liquid were at rest, and an outside
observer should find the velocity of the light augmented by the full
velocity of the current in the liquid. (Think, e. g., of the ball
rolling on the deck of a ship in motion.) But such is not the case.
There is added only a certain portion, viz., the index of refraction."

The very result of the experiment proves that one of
the determinant factors is the physical property of the
fluid.

When the principle of relativity is applied to positive

6 Loc. cit., p. 7.

2IO THE MONIST.

facts we reach slippery ground, on which we must be on
our guard to avoid mystification, for it would seem as if
the law of the conservation of matter and energy were
upset and all objectivity of scientific truth were lost. Ex-
periments have been made to prove the principle of rela-
tivity with the result that Hupka and Bucherer,7 the former
with cathode rays, the latter with radium rays, demon-
strate that mass increases with velocity as the relativity
principle demands. Kaufmann, however, comes to the
conclusion that there is an increase of mass but not as
ought to be expected according to the principle of relativ-
ity, while Michelson and Morley demonstrate with great
exactness that in spite of the motion of the earth the trans-
mission of light is not changed at all, not within one hun-
dred millionth of its proportion nor even a fraction thereof.
It would lead us too far to discuss the experiments
made to apply the principle of relativity to physics and
electrodynamics; we will only mention that (as a priori
might be expected) they tend to corroborate its applica-
bility in these domains.

ON ABSOLUTE MOTION.

Dr. Philipp Frank in his discussion "Does Absolute
Motion Exist?"8 declares that motion in physics always
means "motion with reference to some definite body," and
he recognizes that "this question is a philosophical one9
but it is certainly not a physical question/' The answer
is the first Newtonian law, viz., "A body not affected by
an exterior force moves in a straight line with a constant

7 A. H. Bucherer, "Die experimentelle Bestatigung des Relativitatsprin-
zips" in Annalen der Physik, XXVIII, p. 513; "Messungen an Becquerel-
strahlen" in Physikalische Zeitschrift, IX, pp. 755-760.

8 "Gibt es eine absolute Bewegung ?" Lecture delivered December 4, 1909,
at the University of Vienna before the Philosophical Society. Wissenschaft-
liche Beilage, 1910.

9 Dr. Frank adds here : "Perhaps the psychologist would call it a psycho-
logical one," but this would be a mistake. Psychology has nothing to do
with the subject.

THE PRINCIPLE OF RELATIVITY. 211

velocity which of course may be zero.10 This is called the
law of inertia."

If another force affects the moving body it is subject to
the second law, the law of the parallelogram of forces, ac-
cording to which the body will move along the diagonal of
the two forces.

The following extracts translated from Dr. Frank's
essay on absolute motion will prove instructive:

"The system of the fixed stars constitutes a fundamental body.
Even in shooting a cannon ball towards the south we see no devia-
tion from the law of inertia if we consider it with reference to the
fixed stars. The ball remains in the same plane ; but this plane does
not retain the same relative position to the meridian of the earth,
wherefore, of course, with reference to the earth the law of inertia
is violated. On the whole it is evident that we really recover all the
observed motor phenomena when we refer Newton's laws of motion
to the fixed stars. Not until they are referred to the fixed stars do
these laws acquire an exact sense which makes it possible to apply
them to concrete conditions.

"We shall call those motions which are referred to a fundamental
body 'true movements' and those related to any other body of ref-
erence 'apparent movements.' For instance the immobility of my
chair is only apparent, for when referred to the fixed stars it is in
motion.

"We now ask whether there are any other fundamental bodies
aside from the system of the fixed stars. Obviously not any body
revolving in an opposite direction to the fixed stars can be such a
fundamental body, for considered with reference to such a body all
rectilinear movements are curved. Therefore the law of inertia
could not hold with reference to the body in question if it is valid
with reference to the fixed stars. Then too a fundamental body can
possess no acceleration with reference to the fixed stars, because
otherwise there would be no uniformity of the motion of inertia with
reference to it. However, these conditions are not only necessary
but they are sufficient to characterize a fundamental body. All bodies
moving uniformly and in a straight line with reference to the fixed
stars will also be fundamental bodies inasmuch as rectilinearity and

10 The original reads thus: "Corpus omne perseverare in statu suo quies-
cendi vel movendi uniformiter in directum nisi quatenus a viribus impressis
cogitur statum ilium mutare."

212 THE MONIST.

uniformity continue to hold for them, as do likewise the supple-
mentary velocities determined by the second law. Accordingly New-
ton's laws do not indicate one single fundamental body, but an in-
finite number moving in opposite directions with a uniform and
rectilinear motion.

"Hence we may well speak of 'true' in contrast to apparent
rotary motion; for all bodies revolving with reference to a funda-
mental body revolve with reference to all other bodies. The same
is true of true acceleration because an acceleration with respect to
a fundamental body is also acceleration (i. e., change of velocity)
with respect to all the rest. On the other hand, there is no sense
in speaking of 'true' uniform rectilinear motion ; for if a body pos-
sesses a uniform velocity with respect to the fixed stars, it is itself a
fundamental body possessing of course with respect to itself a
velocity of zero ; it is at rest.

"Accordingly there is true acceleration, but not true velocity.
From this is easily derived a proposition established by Newton
which is called the principle of relativity of mechanics, namely that
a uniform rectilinear movement of the system as a whole makes no
change in the processes within the system ; that is to say, we can not
tell from the processes within the system what velocity the uniform
rectilinear movement possesses with reference to the fixed stars.
On the other hand, the rotary motion of a system has indeed an in-
fluence on the processes within the system, as for instance in the
phenomena of centrifugal force ; thus the earth has become flattened
at its poles because of its rotation, or if I revolve a dish full of water
the water will rise at the sides."

ABSOLUTE SPACE.

If we make measurements of motions which are lim-
ited to terrestrial conditions, the earth is and must be the
system which, though not absolute, must for the nonce be
so considered, and in that case the earth is called the funda-
mental or inertial body, of our measurements. But in
many purely terrestrial motions we observe in very precise
and exact measurements, deviations which compel us to
seek for another fundamental body.

This happens in the case of the Foucault pendulum ex-
periments and may also be observed in a cannon ball which

THE PRINCIPLE OF RELATIVITY. 213

if shot south along the meridian will at a great distance
show a deviation toward the west. Such experiments
point out that the entire system of the fixed stars ought
to be regarded as the fundamental body which thus would
represent to us absolute space. I say here on purpose
"represent to us/' not "be," because we are most probably
in the same predicament as persons moving in a train to
whom the train and its interrelations, so long as the train
does not move in a curve, represent the fundamental body
or absolute space, viz., the ultimate system of reference.

It stands to reason that bodies in translation (in which
the entire system as a whole moves in the same direction
with the same velocity and without any internal change
even of its smallest particles) behave as if they were at
rest, and so the motion of a straight line cannot be observed
so long as the observer remains limited to his own system.
Every deviation from a straight line, however, implies a
retardation on the inner side of the curve, or, what means
the same, an acceleration on the outside of the curved path
of motion. Accordingly all rotations bear witness to the
character of their motion as appears in the Foucault pen-
dulum experiment and in the flattening of the earth at the
poles. Since further the idea of a rectilinear motion is a
mere a priori postulate which can never be realized in
actual nature, we see that every motion that takes place
anywhere is affected by the totality of the universe. We
must assume that its existence (the existence indeed of
every particular thing or the recurrence of any event) must
be understood to be a part of the whole. It bears traces of
all the influences of all masses, and of all forces of the rest
of the world according to the way it is interrelated with its
surrounding conditions.

The fixed stars have so far proved sufficient for our
terrestrial needs to serve us as a fundamental body for

214 THE MONIST.

calculations of a mechanical nature; but here the problem
of absolute space presents itself.

We know positively that though the fixed stars are
practically a fundamental body to us for mechanical meas-
urements, they are shifting about among themselves and no
more constitute something absolute than does our own
earth ; and yet there has risen a controversy on this subject
in which Ernst Mach applies the principle of relativity
throughout the universe while Prof. Alois Hofler stands up
for what he calls the absolutist theory. We will hear what
Dr. Frank has to say on this point :

"Is it to a certain extent accidental, or is it essential, that the
tatality of the fixed stars coincides with that fundamental body in
relation to which the laws of Newton hold valid? Or to put it
more clearly: If the fixed stars were set violently in motion among
each other and hence could no longer constitute a fixed body of
reference, would the mechanical processes on earth proceed exactly
as they did before? For instance, would the Foucault pendulum
move just as at present, even though it now turns with the fixed
stars, whereas in that case it would not be quite clear which con-
stellation's revolution it should join?

"Were everything to remain as of old the fundamental system
of reference would not be determined by the fixed stars but would
only accidentally coincide with them, and would in reality be
some merely ideal or yet undiscovered body. In the other case all
mechanical occurrences on earth would have to be completely altered
to correspond with the promiscuous movements of the fixed stars.

"It is well known that this is the view held by Ernst Mach. It
alone holds with consistent firmness to physical relativism, and it
alone answers the second main question of physics in the relativistic
sense.

"The opposite view is represented by Alois Hofler in his studies
on the current philosophy of mechanics, and lately by G. Hamel, pro-
fessor of mechanics at the technical high school of Briinn, in an
essay which appeared in the annual report of the German mathemat-
ical society of 1909 on 'Space, Time and Energy as a priori Forms
of Thought/

"Before I enter upon the controversy itself I would like further

THE PRINCIPLE OF RELATIVITY. 215

to elucidate Mach's view by carrying out its results somewhat farther.
In his well-known essay on the History and Root of the Principle
of the Conservation of Energy^ Mach ascribes to the distant masses
in space a direct influence on the motor phenomena of the earth
which supplements the influence afforded by gravitation. Of course
no effect of gravitation from the fixed stars upon the earth can be ob-
served, yet in spite of this they influence, for instance, the plane of
oscillation of the Foucault pendulum because in Mach's opinion it
remains parallel to them.

"The question now arises according to what general law of
nature this influence operates which does not, like gravity, produce
accelerations but velocities instead. Obviously this influence must
be a property belonging to every mass, for according to our present
conception the fixed stars of course are precisely the same sort of
masses as earthly bodies.

"However, experience teaches us that terrestrial masses have
no more influence on the plane of oscillation of the Foucault pendu-
lum than has the changing position of the moon, sun and planets ;
but on the other hand it is exactly the most distant masses, the fixed
stars, which determine its plane of oscillation. Accordingly we must
either assume that the effect is directly proportional to the distance
of the masses (which would be very strange indeed) or simply
assume that this effect is proportional to the effective masses and
independent of the distance, whence the dominant influence of the
more remote, as the far greater and more numerous, bodies would
naturally follow, and Mach inclines to this latter view.

"Mach's view shows most clearly in his position with regard
to Newton's famous bucket experiment. In this Newton intended
to show that the centrifugal force produced by a revolving body is
due not to its relative but to its absolute velocity of rotation. He
suspended a bucket filled with water by a vertical cord, twisted the
cord quite tightly and then let it untwist itself, in this way setting the
bucket to revolve rapidly. At first the water did not rotate with the
bucket and therefore the bucket had a velocity of rotation with
reference to the water while in the meantime the surface of the
water remained undisturbed. In time, however, friction caused the
water to become so affected by the rotary motion that bucket and
water revolved like one homogeneous mass whereby the centrifugal

11 Second edition, Leipsic, 1909 ; English translation by P. E. B. Jourdain,
Chicago, 1911.

2l6 THE MONIST.

force caused the water to rise at the sides of the bucket and the sur-
face became concave.

' 'Hence it is evident that the centrifugal force reached its great-
est strength at the moment when the relative motion of the water
with respect to the bucket became zero ; hence according to New-
ton this force can be produced only by the absolute rotary motion of
the water.

"To this now Mach justly protests that only the relative rotation
of the water with reference to the fixed stars is to be considered, for
this system of the fixed stars and not the bucket is the fundamental
body. And indeed at first the water was at rest with reference to the
fixed stars, but at the close of the experiment it was revolving.
The mass of the bucket compared to the mass of the fixed stars is
an entirely negligible quantity, so that it does not depend in the
least upon the rotation. But we can not know, adds Mach, how
the experiment would turn out if the sides of the bucket were miles
thick ; and by this he apparently means so thick that their mass would
be considerable even when compared with the mass of the system of
fixed stars. Then indeed might the rotation of the bucket disturb
the action of the fixed stars.

"Hofler protests, on the other hand, that a system which is
symmetrical round its axis could not according to all our experience
in mechanics produce by its rotation that sort of an effect on the
water within it.

"This also is quite true. But the effect of the masses assumed
by Mach is such that it can not be expressed in our ordinary ex-
periences with mechanics except by means of the facts of the iner-
tia of all motion with reference to the fixed stars. New conditions
such as the rotation of an enormously thick bucket might give rise
to new phenomena. If we agree with Mach's view that the rotation
of the plane of the Foucault pendulum is directly produced by the
masses of the fixed stars, we must likewise admit, in order to be con-
sistent, that the relative rotation of the very thick bucket might give
rise to similar effects with reference to the water, as the rotation of
the system of the fixed stars with reference to the earth to the plane
of oscillation.

"Hofler expresses his contention against Mach's thesis in the
form of the following question: If in Galileo's time the sky had
been clouded over and had never become clear again so that we
would never have been able to have taken the stars into our calcu-
lation, would it then have been impossible to have established our

THE PRINCIPLE OF RELATIVITY. 217

present mechanics solely by the aid of terrestrial experiments?
By this question Hofler means to say that if the connection with the
fixed stars were a constituent of the concept of uniform motion, we
would never have been able in such an overclouded world to have
established the law of inertia, for instance, whereas in reality it is
clear that this would nevertheless have been possible.

"I will not dwell on the more psychological question as to
whether or how easily this would have been possible, but will only
consider now the logical construction of mechanics in such a dark-
ened world on the hypothesis that easily or with difficulty in one
way or another we would have attained to our present knowledge
of mechanics.

"Let us for a moment imagine ourselves in such a world.
Above our heads extends a uniform vault of uninterrupted gray or
black. Were we to shoot projectiles toward the south we would
see that they describe paths which are curved towards the west; if
we started pendulums to vibrating we would see that they would re-
volve their planes of oscillation in mysterious periods — I say mys-
terious because we might perhaps be able to perceive the change of
day and night as an alternation of light and darkness, but would not
be able to refer it to the movements of celestial bodies. Perhaps
at first we would surmise that the motion of the pendulum could be
ascribed to optical influences. I would like to see placed in such a
world one of the philosophers who regard the law of inertia as an
a priori truth. In the face of these mysterious curvatures and de-
flections he would probably find no adherents and he would not
know himself what to make of his own standpoint.

"Finally, let us assume, there arises a dauntless man, the Coper-
nicus of this starless world, who says that all motions proceed spon-
taneously in a straight line, but that this straight line is not straight
with reference to the earth but with respect to a purely ideal system
of reference which turns in a direction opposite to that of the earth.
The period of this rotation is supplied by the period of the Foucault
pendulum.

"This man would of course deny physical relativism upon the
earth, for in his opinion terrestrial processes would not depend only
on the relative velocities of terrestrial bodies but on something
else besides, viz., their velocities with respect to a purely ideal sys-
tem of reference. Nevertheless, he would not introduce any non-
physical element because for the purpose of the physicist a purely
ideal system of reference whose motion with respect to an em-

2l8 THE MONIST.

pirical system is known serves the same purpose as would the em-
pirical system itself. This bold innovator might finally refer the
words 'true rest' and 'true motion' to his ideal fundamental body
and so ascribe true motion and only apparent rest to the earth, thus
maintaining a mechanics which would coincide literally with that of
ours to-day, except that no small luminous points would be seen
sparkling in connection with the fundamental body.

"Hence we see that physical relativism is not a necessary tool
of the physicist. Apart, perhaps, from the psychological improb-
ability— of which, however, nothing more positive can be said — the
possibility of the development here indicated is logically free from
objections throughout, and therefore the same is also true "of the
possibility of a nonrelativistic physics.

"But I would like to strengthen the argument of Hofler even
somewhat further. That is to say, I would ask whether the world
in which we live is then really so essentially different from that
fictitious one. Imagine the dark roof which conceals the sky placed
somewhat higher so that there is room beneath it for the fixed stars,
perhaps as the dark background which may be seen nightly in the
starry sky. The whole difference then consists in the fact that not
only the Foucault pendulum and similar appliances move with ref-
erence to the earth, but enormously greater masses as well — all the
twinkling lights of the sky by which the thought of a fundamental
body in motion with respect to the earth is psychologically greatly
facilitated, but logically is not much changed. Now imagine the
sky of this earlier dark world suddenly illuminated ; then we would
see that the fictitious system of reference is closely linked to enormous
cosmic masses, and it would be easy enough to accept Mach's hy-
pothesis that these masses condition the fundamental system ....

"If a distinction must be drawn between the respective values
of the conceptions of Mach and Hofler, it is as follows : Mach's view
adds decidedly more to the observed facts ; for that it retains phys-
ical relativism does not involve freedom from hypothesis, because
at best this relativism is theory and not fact. Mach sets up, hypo-
thetically of course, a new formal natural law with regard to the
action of masses existing side by side with gravitation, affecting
the experiment very materially but unable to raise any claim to the
simplest description of actual conditions.

"The other view, which simply introduces the system of ref-
erence procured by observation of the terrestrial and celestial move-
ments without asking whence all this is derived, represents the pres-

THE PRINCIPLE OF RELATIVITY.

ent state of our knowledge most adequately without any arbitrary
addendum but also without giving the spirit of inquiry any incentive
to new experiments.

"It is the old contrast between the most exact and least hypo-
thetical representation possible of the known science, and progressive
inquiry after new things in more or less daring and fantastic hypoth-
eses. But Mach in this case stands in the opposite camp as in most
other cases where his repugnance to all hypothesis has made him a
pioneer in the phenomenological direction ....

"I therefore believe I have proved that we can grant the follow-
ing: Physical phenomena do not depend only on the relative motion
of bodies without at the same time admitting the possibility of the
concept of an absolute motion in the philosophical sense."*

Strange that Mach, with his reluctance to introduce
anything hypothetical except what is absolutely indispen-
sable, should range on the side of the theorists, and after
some reflection I believe that there may be a slight hitch in
Dr. Frank's interpretation of Mach's view.

First I myself, from my own point of view, would refuse
to call the principle of relativity an hypothesis; it is an
a priori proposition, a theorem, or if you prefer, a postu-
late of pure thought which either holds good universally,
or has no validity whatever. So far as I know, Mach has
not discussed this side of the subject but he has instinctively
acted upon this view, and I would say that there is a
greater hypothetical element in the assumption that the
theorem 2 X 2 = 4, or any other proposition of the same
kind, holds good only for our earth but not for Mars and
Venus, than to say that it holds good also for the fixed
stars and in the possible worlds outside of our Milky Way.
Accordingly, whatever Mach's personal opinion may be,
I would regard the universal application of the principle
of relativity as less complicated and more free from hypo-

* This last paragraph is printed in spaced letters which indicates the em-
phasis of the author, and so we print the text of his summary in the original.
Dr. Frank says : "Die physikalischen Erscheinungen hangen nicht nur von der
Relativbewegung der Korper ab, ohne doch damit die Moglichkeit des Be-
griffes einer absoluten Bewegung im philosophischen Sinne zuzugeben."

22O THE MONIST.

<•

thetical elements than its limitation to a portion of the
world.

I can not as yet make up my mind to believe that our
system of the Milky Way which furnishes us the grand
sight of the fixed stars is an ultimate possessing the charac-
teristics of absolute space.

According to Kant the totality of the fixed stars which
are thickest in the Milky Way forms a great system (the
system of the Milky Way) and our sun as well as all the
visible fixed stars belongs to it. Kant believes that this, our
own universe, which in the Milky Way appears to us as an
enormous ring but together with the totality of the fixed
stars must resemble an oblate spheroid, is not the only cosmic
system, but that there are other similar systems outside of it
and that they too whirl on through the infinity of space, in
company with our Milky Way system, around some center
of their own; and this very center of many Milky Ways
may partake of a motion the observation of which lies
hopelessly beyond our ken. Accordingly the space condi-
tions of the Milky Way may serve us as absolute space,
but there is a probability that this space is not more abso-
lute than are the space relations in a quick but quietly mov-
ing train to the passengers.

Another point where we feel justified in doubting Dr.
Frank's exposition is the statement that Mach hypothet-
ically assumes a new law of nature as to the efficacy of
masses, besides the law of gravitation. The passage in
Mach's writings to which Dr. Frank refers does not (in
my opinion) suggest the idea of an additional law of nature
according to which the distant fixed stars should exercise
a mysterious influence on the Foucault pendulum. We will
later on let Mach speak for himself. In our opinion it
seems that it would be sufficient to ascribe the rotation of
the pendulum to its inertia while the earth revolves round
itself, and this takes place in the space in which the earth

THE PRINCIPLE OF RELATIVITY. 221

has its motion, viz., the space of the Milky Way system.
The pendulum remains in the plane of oscillation in which
it started while the earth turns around underneath. If
there are influences at work beyond the expanse of the
space of the fixed stars in our Milky Way system, they
must affect the totality of our system and would therefore
be contained in its space conditions ; acting with an unfail-
ing constancy they could not be separated from the prop-
erties of our space and would scarcely be discoverable.

There seems to me no need of inventing a new force
besides gravitation. The law of inertia seems to explain
the Foucault pendulum experiment satisfactorily.

The fixed stars as a totality remain in their places (at
least as far as concerns the experiment) and the plane in
which the pendulum swings keeps its original direction;
thus the apparent motions of both coincide. Their space
relations (the space relations of the pendulum and of the
fixed stars) are the same, and there is no need to assume
the existence of any unknown force exercised by the fixed
stars upon the pendulum.

ERNST MACH.

We will let Mach state his views in his own words :

"Obviously it does not matter whether we think of the earth as
turning round on its axis, or at rest while the celestial bodies revolve
round it. Geometrically these are exactly the same case of a relative
rotation of the earth and of the celestial bodies with respect to one
another. Only, the first representation is astronomically more con-
venient and simpler.

"But if we think of the earth at rest and the other celestial
bodies revolving round it, there is no flattening of the earth, no
Foucault's experiment, and so on — at least according to our usual
conception of the law of inertia.

"Now, one can solve the difficulty in two ways: Either all mo-
tion is absolute, or our law of inertia is wrongly expressed. Neu-
mann12 preferred the first supposition, I, the second. The law of
12 Ueber die Principien der Galilei-Newt on 'schen Theorie. Leipsic, 1870.

222 THE MONIST.

inertia must be so conceived that exactly the same thing results
from the second supposition as from the first. By this it will be evi-
dent that, in its expression, regard must be paid to the masses of
the universe.

"In ordinary terrestrial cases, it will answer our purposes quite
well to reckon the direction and velocity with respect to the top of a
tower or a corner of a room; in ordinary astronomical cases, one
or other of the stars will suffice. But because we can also choose
other corners 'of rooms, another pinnacle, or other stars, the view
may easily arise that we do not need such a point at all from which
to reckon. But this is a mistake ; such a system of coordinates has
a value only if it can be determined by means of bodies. . . .

"If we wish to apply the law of inertia in an earthquake, the
terrestrial points of reference would leave us in the lurch, and, con-
vinced of their uselessness, we would grope after celestial ones.
But, with these better ones, the same thing would happen as soon
as the stars showed movements which were very noticeable. When
the variations of the positions of the fixed stars with respect to one
another cannot be disregarded, the laying down of a system of co-
ordinates has reached an end. It ceases to be immaterial whether
we take this or that star as point of reference ; and we can no longer
reduce these systems to one another. We ask for the first time
which star we are to choose, and in this case easily see that the stars
cannot be treated indifferently, but that because we can give prefer-
ence to none, the influence of all must be taken into consideration.

"We can, in the application of the law of inertia, disregard any
particular body, provided that we have enough other bodies which
are fixed with respect to one another. If a tower falls, this does not
matter to us ; we have others. If Sirius alone, like a shooting star,
shot through the heavens, it would not disturb us very much ; other
stars would be there. But what would become of the law of inertia
if the whole of the heavens began to move and the stars swarmed
in confusion? How would we apply it then? How would it have
to be expressed then? We need not worry about one body as long
as we have others enough. Only in the case of a shattering of the
universe we learn that all bodies, each with its share, are of im-
portance in the law of inertia. . . .

"Yet another example : A free body, when acted upon by an in-
stantaneous couple, moves so that its central ellipsoid with fixed cen-
ter rolls without slipping on a tangent-plane parallel to the plane of
the couple. This is a motion in consequence of inertia. Here the body

THE PRINCIPLE OF RELATIVITY. 223

makes very strange motions with respect to the celestial bodies.
Now, do we think that these bodies, without which one cannot
describe the motion imagined, are without influence on this motion?
Does not that to which one must appeal explicitly or implicitly when
one wishes to describe a phenomenon belong to the most essential
conditions, to the causal nexus of the phenomenon? The distant
heavenly bodies have, in our example, no influence on the accelera-
tion, but they have on the velocity."

Now follows the passage to which Dr. Frank obviously
refers :

"Now, what share has every mass in the determination of direc-
tion and velocity in the law of inertia? No definite answer can be
given to this by our experiences. We only know that the share of
the nearest masses vanishes in comparison with that of the farthest.
We would, then, be able completely to make out the facts known to
us if, for example, we were to make the simple supposition that all
bodies act in the way of determination proportionately to their
masses and independently of the distance, or proportionately to the
distance, and so on. Another expression would be: In so far as
bodies are so distant from one another that they contribute no notice-
able acceleration to one another, all distances vary proportionately
to one another."

We do not here understand Mach to fall back on the
assumption of a new kind of force, and if we must grant
that the distant masses exercise a dominant influence while
the influence of the nearest ones (of the earth, the moon,
and the sun) vanishes, we would say that this is due to the
constancy of the distant masses which, as it were, is an
inherent and inalienable part of all mass in the entire sys-
tem and may be said to characterize its space conditions.

In speaking of "space conditions" I am conscious of
using a term which Mach would repudiate, for he claims
that for a comprehension of the concatenation of events,
the notions of time and space are redundant. He says
(loc. cit. pp. 60-61) :

"To say the least, it is superfluous in our consideration of causal-
ity to drag in time and space. Since we only recognize what we

224 THE MONIST.

call time and space by certain phenomena, spatial and temporal deter-
minations are only determinations by means of other phenomena.
If, for example, we express the positions of earthly bodies as func-
tions of the time, that is to say, as functions of the earth's angle of
rotation, we have simply determined the dependence of the positions
of the earthly bodies on one another.

"The earth's angle of rotation is very ready to our hand, and
thus we easily substitute it for other phenomena which are connected
with it but less accessible to us ; it is a kind of money which we spend
to avoid the inconvenient trading with phenomena, so that the pro-
verb "Time is money" has also here a meaning. We can elim-
inate time from every law of nature by putting in its place a phenom-
enon dependent on the earth's angle of rotation.

"The same holds of space. We know positions in space by the
affection of our retina, or our optical or other measuring apparatus.
And our x, y, z in the equations of physics are, indeed, nothing else
than convenient names for these affections. Spatial determinations
are, therefore, again determinations of phenomena by means of other
phenomena.

"The present tendency of physics is to represent every phenom-
enon as a function of other phenomena and of certain spatial and
temporal positions. If, now, we imagine the spatial and temporal
positions replaced in the above manner, in the equations in question,
we obtain simply every phenomenon as function of other phenomena.

"Thus the law of causality is sufficiently characterized by saying
that it is the presupposition of the mutual dependence of phenomena.
Certain idle questions, for example, whether the cause precedes or
is simultaneous with the effect, then vanish by themselves."

We understand that Mach endeavors to eliminate the
terms time and space, because he wishes to correct the
common notion which regards space as a big box into
which the world has been packed. Mach says:

"Space and time are not here conceived as independent entities,
but as forms of the dependence of the phenomena on one another.
I subscribe, then, to the principle of relativity, which is also firmly
upheld in my Mechanics and Warmelehre"™

We agree with Mach. There is no time in itself; there

18 Cf. "Zeit und Raum physikalisch betrachtet," in Erkenntnis und Irrtum.
Leipsic, 1905 (ad ed. 1906, pp. 434-448) ; See also Space and Geometry, pp. 94 ff.

THE PRINCIPLE OF RELATIVITY. 225

is no space in itself. Nevertheless, Mach has given much
attention to physical space and appreciates the important
part which it plays not only in the formation of our space-
conception, but also in the actual world, for every spot of
space possesses physical qualities according to the particles
of mass which are there aggregated. Mach says:

"Since the positions in space of the material parts can be recog-
nized only by their states, we can also say that all the states of the
material parts depend upon one another.

"The physical space which I have in mind — and which, at the
same time, contains time in itself — is thus nothing other than de-
pendence of phenomena on one another. A complete physics, which
would know this fundamental dependence, would have no more need
of special considerations of space and time, for these latter consid-
erations would already be included in the former knowledge."

The same idea is expressed by Mach in his Essay
"Ueber den Zeitsinn des Ohres:14

"Physics sets out to represent every phenomenon as a function
of time. The motion of a pendulum serves as the measure of time.
Thus, physics really expresses every phenomenon as a function of
the length of the pendulum. We may remark that this also happens
when forces, say, are represented as functions of the distance ; for
the conception of force (acceleration) already contains that of time.
If one were to succeed in expressing every phenomenon — physical
and psychical — as a function of the phenomenon of pendulum-
motion, this would only prove that all phenomena are so connected
that any one of them can be represented as a function of any other.
Physically, then, time is the representability of any phenomenon as
a function of any other one."

We do not deny the truth of Mach's view. Neverthe-
less time and space are very convenient terms denoting
two categories of certain interrelations (he would call
them interdependencies) in the flux of things. Popular
terms mostly originate because there is a need of them,
and it seems to me it would be wiser to correct the errors
connected with them than to drop them. If we pursue the

"Sitgb. der Wien. Akad., 1865. Compare Conservation of Energy, p. 90.

226 THE MONIST.

latter policy we shall find ourselves obliged to reinvent a
new collective term for certain classes of relations which
belong together and can not be identified with other rela-
tions. The space and time relations are radically different
from those of a purely physical, chemical or psychological
nature.

We need not fear to retain the old terms, space and
time, if we only bear in mind that there is neither absolute
space nor absolute time but that the words denote relations.
It seems to me that when Kant speaks of the ideality of
space and time and insists on their non-existence as ob-
jective beings (We sen or Wesenheiten) he attempts to say
the same as Mach who declares that they are not "inde-
pendent entities."

The conclusion at which we arrive in considering the
nature of time and of space, be it from our standpoint of
philosophy or from Mach's physical point of view, may
be expressed in one word, that their most obvious char-
acteristic is relativity.

CONCLUSION.

Professor Mach says in one of his notes quoted above,
"I subscribe then to the principle of relativity," and so do
I. Indeed I go one step further. I consider relativity as
an inherent quality of existence and so I adopt the prin-
ciple of it not as a result of experience but on a priori
grounds. The principle of relativity, however, is fre-
quently stated by relativity physicists as if the old ideal
of science in its objective significance had to be abandoned,
as if physics had to be remodeled, and as if the proclama-
tion of the principle of relativity indicated a new departure
from our traditional methods. This is not so, and I must
insist that the principle of relativity has always been sub-
consciously in the minds of scientists. Only it has lately

THE PRINCIPLE OF RELATIVITY. 227

been forced upon the attention of physicists by the progress
in astronomical measurements.

How helpful the emphasis recently laid upon the prin-
ciple of relativity will prove remains to be seen. Its ardent
adherents exhibit great zeal which in many directions
seems to be misdirected, and it appears to me that in spite
of the correctness of the underlying idea their hopes are
greatly exaggerated. After a while when the opponents
of the principle of relativity will understand that its truth
is as much a matter of course as the truth of the law of
conservation of matter and energy, the contentions about
it will cease and the evolution of science will no longer
show evidence of excitement but will continue in its old
quiet way.

There is more philosophy in our science than the school
of empiricists are inclined to believe. It is very desirable
that in familiarizing themselves with philosophy, these
scientists should not fall back on the old systems of a vision-
ary absolute, but they should adopt the philosophy of sci-
ence, the only philosophy which is not a mere ingenious
dream, and possesses objective significance.

The philosophy of science is the philosophy. It is the
indispensable introduction to the study of any science and
furnishes the basis for scientific method as well as a general
survey of the assured results of all the several sciences.
If the philosophy of science had been better known, the
principle of relativity had at once been rightly understood
and the vagaries of many mystifying contentions would

have been avoided.

* * *

The purpose of this article is to set forth in general
outlines the truth and significance of the principle of rela-
tivity, not to present an exhaustive treatment of it in all
its phases and applications. We must bear in mind that
in dealing with the several innumerable problems of exist-

228 THE MONIST.

ence science introduces a method which possesses certain
limitations due to conditions which originate through some
fictions of an apparently arbitrary nature assumed for the
sake of isolating the object of investigation and concentrat-
ing upon it our attention.

We must bear in mind that we behold an object by
focusing our eyes upon it and that only thereby can we
form a picture of the object. It is a fiction to behold an
object as if it were a thing by itself and it is positively
impossible to see anything as it is in all its relations and
with all its changes, past, present and future. Nor would
such a comprehension of the object in all its entirety be
desirable, for in the omneity of its relations we would see
the whole universe while the special feature which concerns
us sinks into insignificance. The same is true of science.
Each of the several sciences selects its own field of investi-
gation and thus constitutes a definite domain of abstraction
for the sake of concentrating all attention upon it. For
mechanics and for the measurements of motion in space, we
need a reference point which must be able to be considered
stationary, and if that is not the case we must refer both
the movable place of observation, viz., the reference point
(R) and the object observed (O) to one common system,
which could be treated as, or must so far as R and O are
concerned, actually be, stable.

We conclude by repeating that there is nothing abso-
lute ; all real and actual existences, all concrete things and
happenings are relative, and if there is any thing that in a
certain sense deserves the name absolute it is the truth as
described in our mental fictions, the laws of purely formal
thought, the eternal uniformities of purely formal rela-
tions such as we know from mathematics and all the other
purely formal sciences; but even they are absolute only in
the sense of constituting an entire system the truth of
which is absolute, viz., it stands aloof and is founded in it-

THE PRINCIPLE OF RELATIVITY. 22Q

self as a world of necessary conclusions built up in the field
of anyness to serve as models for any conditions in any
world actual or imaginary. And this absolute, this system
of mental construction is after all a system of relations.

The more we ponder on the nature of existence, the
more we shall understand the sweeping significance of

relativity.

P. c.

INVENTORS I HAVE MET.*

AJY one who has been a professor of physics in a large
city for several decades, unless he has earned a repu-
tation for the crudest and densest Philistinism, must have
made the acquaintance of divers thinkers and inventors
who have taken counsel with him in their perplexities —
thinkers of all kinds, schooled and unschooled, sanguine
and timid, those that solve problems and those that create
them; thinkers, suspicious and confiding, ambitious and
practical ; inventors at any price, and inventors on occasion.
It is obvious that the number of actual or alleged in-
ventors in this company is greater than that of silent stu-
dious, self-centered thinkers. Practical discomfort is felt
more often and to a greater extent than the rarer purely
intellectual discomfort which is the heritage of men on a
higher spiritual plane. Many fruitless hours may be spent
in such consultations, but many a bit of psychological illu-
mination may be gained and many a glance into the em-
bryology of technique and science. We may add right
here that the unlettered, unschooled or wild thinkers and
inventors are the most interesting and instructive.

* * *

One day a gentleman was announced who had some-
thing of importance to communicate to me. He told me
that he had taken a narrow tube full of liquid, closed
at the upper end and open below, from which of course

* Translated from the German by Lydia G. Robinson.

INVENTORS I HAVE MET. 23!

nothing could flow because of the pressure of air; then
he gave it a charge of electricity, whereupon the liquid
began at once to flow. From this he drew the rash con-
clusion that the electric charge removed the air pressure.
I gave instructions that an appointment be made with this
gentleman for a free hour in the afternoon in order to make
the experiment. But since one can easily tell whether or
not a man is undertaking something from a purely theo-
retical interest, I said to the attendant in the laboratory,
"The gentleman probably thinks he can drive a railway
train with the electrical machine." In the afternoon con-
siderably before the appointed time the stranger put in an
appearance. "Are you thinking of driving a railroad
train ?" the attendant asked him by way of filling the inter-
val with conversation. Immediately and without losing
another word the gentleman seized his hat and was gone
forever. So I had guessed his purpose correctly, and had
deprived him of the pleasure of taking me into his con-
fidence in his alleged lucrative undertaking. Forty years
have passed since then, and the man has probably calmed
down in the meantime.

There are people who become greatly excited over every
scientific novelty, whose imagination busies itself at once
in a new field without any special participation on the part
of their intelligence, and whose desire it is to make an in-
vention or a discovery in this field at any cost. So after
the discovery of the Foucault rotation of the pendulum's
plane of oscillation many experiments were made known
by which it was thought this rotation could be perceived
in water standing in a cylindrical tub across whose surface
coal-dust had been lightly strewn ; or again in a horizontal
disk suspended by a thread, or in a scale-beam similarly
suspended.

232 THE MONIST.

But obviously these experiments are not sensible. For
instance, if a horizontal disk is actually at rest with ref-
erence to the earth it has of course the component of rota-
tion of the earth around the perpendicular corresponding
to geographical latitude ; therefore the disk can not hence-
forth alter its position with reference to its terrestrial sur-
roundings. Under other circumstances, however, it has an
angular velocity around the perpendicular due to some im-
pulse, to a draft of air, or the thread's momentum of rota-
tion, and hence has no connection whatever to the Foucault
rotation. One young man could not accept these reflec-
tions at all but persisted in repeating the experiment thus
described by which he gained the interest of an old gentle-
man who observed in them "sometimes" the genuine Fou-
cault rotation.

To be sure, Professor Tumlirz has recently performed
an experiment which, while externally similar to this, is
correct. By this experiment the rotation of the earth can
be imitated, if the utmost care is taken, by the direction
of the current of water flowing axially out of a cylindrical
vessel. Further details are to be found in an article by
Tumlirz in the Sitzungsberichte der Wiener Akademie,
Vol. 117, 1908. I happened to know the origin of the
thought that gave rise to this invention. Tumlirz noticed
that the water flowing somewhat unsymmetrically in a
glass funnel assumed a swift rotation in the neck of the
funnel so that it formed a whirl of air in the axis of the
flowing jet. This put it in his mind to increase the slight
angular velocity of the water at rest with reference to the
earth, by contraction in the axis.

The above-mentioned imaginative young man also con-
structed a telephone by a static electrical charge, and this
invention likewise proved a delusion. Experimenting within
the space of one room he had heard his own voice both as
transmitter and receiver at the same time. Very often an

INVENTORS I HAVE MET. 233

illusory invention bears witness simply to the ardent hopes
of its originator.

Another young man declared that the theories of Gali-
leo with regard to falling bodies and projectiles which he
had learned in school were false; that the projected stone
forms an entirely different problem from the falling stone ;
that the stone that is thrown is carried through the air
and in the projection gravity is overcome. To this man
the Aristotelian distinction between the natural falling
motion and the violent motion of throwing is still valid.
The fusion of the two primitive ideas into a unified whole
had not yet taken place in his understanding.

* * *

Such a reversion to the primitive condition of science
is not an isolated one. We may therefore conclude that
after a disturbing interruption of the development of civili-
zation science would again pursue almost the same course
of evolution it had previously followed, although this of
course would not preclude minor accidental discrepancies.
Science has also its own natural embryology which is re-
vealed through epistemology. Once I received an inquiry
from the United States about the hydrostatic paradox
which after Archimedes has been explained by Stevinus
and for the third time by Pascal. The American writer
declared that he could not understand how the pressure
at the bottom of a vessel could depend upon anything else
than upon the weight of the liquid resting on the bottom.
Of course this was a very natural idea. I now proceeded
to expound to the gentleman that the pressure at the bot-
tom can not depend on the weight of the liquid resting on
the bottom, but only on that portion of the weight which
must be lifted in lifting the bottom, not the whole vessel.
This seems to have met with comprehension at once. The

234 THE MONIST.

ingenious and spontaneous complacency of this American
was altogether charming and delightful to me. He an-
swered me in English since he knew no other language.
He lived in "Cosmopolis" — street and number were un-
necessary, simply the name of the writer sufficed. Hence
the place was probably not yet Cosmopolis, but for the
time being perhaps an embryo of five or ten houses which
had undertaken to become a cosmopolis.

Intercourse with born thinkers of this type is very
agreeable to me. Thus I would love to have known that
naive Chinaman who, pointing to the street-car in San
Francisco, the propelling force of which seemed incom-
prehensible to him, said (as my colleague B. Brauner tells
me), "No pushee, no pullee, but it runs — ."

One day I had a visitor whose external appearance
proclaimed him every inch a man conscious of successful
achievement. Without any doubt he was also intelligent,
a good observer who had used his own eyes and knew how
to turn his observations to practical account. He belonged
to the class of inventors on occasion who base their con-
structions on practical and local knowledge and not on the
fancy that something must be invented whether or no. He
certainly deserved the success of his great business which
extended over all Europe. But what surprised me was
that he manifested such high theoretical aims at the same
time. He felt like the laboratory assistant of Faraday
who performed experiments while the great man only
delivered the superfluous lecture about them. How could
this great lecture, called science, have many difficulties
for one who was so successful in his practical life, for that
is the proof of the sum? Then too his theory was not in
the least without foundation, for it rested on independent
observation, that is to say, on what is called the Leiden-

INVENTORS I HAVE MET. 235

frost experiment. But while he ascribed to this one ob-
servation an unduly enormous significance, he questioned
at the same time the Newton theory of gravitation and all
other possible theories, or undertook to base them on differ-
ent foundations. My word for it, his observation was
good, but onesided and incomplete, and therefore inade-
quate for a foundation of his theories and would not bear
much fruit. He had a strong desire to rush at once into
print. "If you wish to do that, my dear sir, I advise you
at least to publish anonymously or under a pseudonym.
In case you are ridiculed you can then join heartily in the
laugh without anxiety for your reputation." The sensible
man followed this advice and was splendidly successful in
his book selling, for there are plenty of imaginative people
who take pleasure in crazy theories. "Wisdom and ex-
perience in one field/' I said also in the course of our con-
versation, "do not protect us from folly in another. You
are efficient in your specialty and we will suppose that I
am in mine. Would we not both be astonished and con-
fused if you for instance would come out to-morrow as an
obstetrician and I the day after as a dentist ? And yet no
less schooling and experience are needed for the conquest
of a scientific specialty."

Many people feel that nothing else so cramps and limits
their imagination as certain principles in science which
are held to be firmly established and which others are used
to look upon as providing the most abundant aid. Such
a principle for instance is that of the equality of action
and reaction, and another is that of the impossibility of
perpetual motion.

Once I was urgently invited to visit a man who wished
to show me something very remarkable. When I arrived
he first told me the following story. He said that he had

236 THE MONIST.

never doubted the principle of the equality of pressure and
counter-pressure. But once he had heard a traveler tell
of an animal in South America that sprang with agility
from branch to branch without communicating the slightest
motion to the branches either as it left one or reached the
the other. This aroused his interest so greatly that he
went at once to South America in order to observe this
squirrel-like animal. Here he convinced himself that the
law of the equality of pressure and counter-pressure did
not hold good. Upon his return he succeeded in devising
an arrangement with which by means of cords fastened
to one and the same body a motor tendency was communi-
cated to this body. He showed me a ruler in which a motor
impulse would arise by means of threads crossed and
stretched in various directions between swivels. As he
held it in his hand he said, "Now I feel myself drawn over
there towards the door," whereupon he proceeded to step
in that direction. "If that is so, sir," answered I, "you
will easily be able to convince every one of the fact, if you
will let this ruler swim freely on the surface of water so
that it can move in a definite direction without your per-
sonal intervention." This he promised to do. I now felt
myself impelled toward the door and took my leave as I
began to feel somewhat uncanny. It was really very dis-
quieting to remain in a place where, because of the inequal-
ity of pressure and counter-pressure, a tied-up package
or a well-screwed piece of furniture would be able spon-
taneously and independently to get up and travel and fly
at my head. It is now about twenty years since I have
heard anything of this wonderful experiment.

There was an old gentleman of whom I was very fond
who took a great interest in the problem of perpetual mo-
tion. He held that an instance of it must eventually be

INVENTORS I HAVE MET.

237

found because it was necessary for the progress of human-
ity. The most diverse hydraulic and mechanical construc-
tions were undertaken. When they were complicated enough
so that they could not be seen through he thought he had
reached his goal, but each time was of course disillusioned.
Since he was an educated man I gave him Huygens's
Horologium oscillatorium to read in which these condi-
tions are set forth very clearly and simply, but it made
no permanent impression. Ever and again his imagination
overcame his judgment and ever and again triumphed the

Fig. i.

Fig. 2.

unshakable conviction of the necessity of this thing for the
good of humanity. Somewhat similarly must Aristotle
have thought with regard to the displacing of slave labor
by the use of machinery.

One of the constructions of the old gentleman I remem-
ber very distinctly. It may be easily understood as pre-
sented in Fig. i. A siphon ab dips into the vessel A and
at the other end with a bell-shaped expansion C into the
vessel D. If the openings a and e are left unobstructed
then, according to the expectation of the inventor, the

238 THE MONIST.

small mass of water in the tube ab would follow the large
masses of C and D and flow out at e. Instead of this, Cba
behaved like a normal siphon flowing in the direction indi-
cated by the letters, whereas a part of the water in D, to
be sure, descended through e so that a break occurred
between the water in C and in D, whereat the arrangement
had failed to perform its function.

* * *

When I was a boy I had heard so much about perpetual
motion that at a time when I had only a very superficial
knowledge of the law of the lever I zealously set to work
on the construction of a perpetuum mobile. The drawing
in Fig. 2 will make clear the construction and its error.
I was tempted to regard the horizontal bars with weights
as somewhat long and efficient levers, although in this
case there could be no question of levers and their rota-
tion. Nature does not allow itself to be outwitted like the
limited attention of man. To lift a weight P to the height
H absolutely requires a weight P' which reaches the depth
H', so that P'XH' is at least equal to PXH. I can not
say that this effort did me any harm. The mistake taught
me to understand machines better than books or instruction
could have done.2 If any theory is of practical value in
promoting civilization it is that of the limitation of avail-
able mechanical power, and no illusion is more harmful to
progress than the idea of its inexhaustibility.3

* * *

One of the most remarkable inventors whom I have
ever known was an old mechanic. At every detail he noted
some advantage in construction and at once applied his
idea. He reformed the handles and shape of beer glasses,

3 The collection of constructions of perpetual motion machines preserved
in the Technical Museum at Munich must be very instructive from a psycho-
logical point of view, as far as they can be deciphered.

8 Indeed one of the greatest advances made in natural science rests upon
the overthrow of this illusion through a fundamental employment of it.

INVENTORS I HAVE MET. 239

laundry mangles, theater curtains ; he constructed a clock
from a barometer-tube closed at both ends in which a short
column of mercury was placed at the side of a scale marked
off empirically to measure time. He was a funny old fel-
low who wished to do away with the figures on the tower
clock because "anyone would be a fool who would not be
able to tell the time by the position of the hands." He
was a born physicist. From his simple story I can not
doubt that by blowing away the sawdust from a circular
saw with perforations in the rim he discovered of his own
accord the principle of the disk-shaped siren and the law
of tone vibrations.

He was as extremely jealous of Cagniard Latour as
if the latter by his much earlier observation had robbed him
of the finest discovery. On the principle of the disk-siren
he based his invention of a new musical instrument which
he called a sirenophone. By means of a weight and a con-
tinuous cord a pedal set the system of the siren-disks in
uniform rotation and at the same time worked a bellows.
Piano keys, sunk more or less deeply with increased pres-
sure, opened one or more tubes which blew with varying
degrees of strength into the series of holes of the siren-
disks so as to swell individual tones. The difference in
pitch was obtained by the proportion of the radii of the
pulleys over which the cords of the disks were drawn. This
instrument made far more pleasant music than a har-
monium and it would be simply impossible for it to get out
of tune. It could be manufactured in perfect tune by a
simple method of stamping. When a young man proposed
to the inventor to sell his invention but keep its name, he
received the answer, "The invention is great but unsa-
lable." Hence he apparently preferred that it continue its
existence as unique and legendary rather than be a source
of profit. When a colleague once tried to play the instru-
ment the inventor fell upon him furiously and declared it

24O THE MONIST.

was a sacrilege. The inventor surrounded himself with
the mystery of a medieval wizard and conjurer. The orders
of the minor petty German princes for whom he had ar-
ranged various theatrical details he wore with ostentation
and listed them carefully upon his visiting cards. This
man's vanity greatly diminished the impression of his very
considerable talent and disturbed his relations with his
hardly less gifted brother.

In my institute I once had a very gifted young man D.
to whom I proposed that he carry on a piece of work in
physiological optics in which he made good progress. One
day I came to him with the question, "Well, what are you
doing?" "Nothing," was the answer, "because I haven't
any pasteboard to make a new disk." "Well, if that is all
it takes to put a stop to your research you will not get very
far," was my reply. This episode would not have remained
in my memory if D. had not reminded me of it years later.
But it is noteworthy that soon afterwards he completed
a series of fine tasks for which he had provided himself
with all necessary devices in the simplest way possible; he
almost never had need for anything from the materials
of the institute. He constructed a Jamin compensator by
cutting a slightly curved optical lens. I must add that I
have seen many similar accessories in the collection left by
Norrenberg in Tubingen. There stood whole cases full of
the cleverest optical apparatus made out of cork and glass.
Norrenberg let the endowment lapse and made his appa-
ratus himself in order not to have to write everything down
in the inventory book and keep a strict account of it. Every
curator of an institution is familiar with this burden which
always intrudes upon his most convenient time for work, or
on his vacation.

The young man D., who was the exact opposite of the

INVENTORS I HAVE MET. 24!

preceding one in seriousness and simplicity, soon became
my assistant and left with me a cheerful memory of his
dry humor. When I was demonstrating to beginners the
interference bands of the sodium flame by the greater
thickness of layers of air of the Newton glass and bade
them not to focus their eyes upon the flame but on the
glass, they did not all succeed in this at once. With averted
face the assistant scattered a few grains of salt over the
glass, with the words, "There now, look at the salt !" When
I pointed out the Talbot bands by covering half of the pupil
with a piece of mica many looked through the mica and
many looked past it. The assistant cut a small hole in a
piece of black paste board and covered the half with mica,
saying: "There now, look through the hole!" When I
called attention to the range of oscillation of a string which
vibrated the fundamental tone and the octave at the same
time, one of the class was almost misled into considering
it two strings. "Put your finger in between quick, then
you will have two !" said the assistant.

In this brief review we have not drawn any sharp dis-
tinction between inventors and thinkers, between invention
and discovery. Indeed there is no great difference. The
liberation from a practical discomfort by a new procedure
we call an invention. But if we feel an intellectual discom-
fort, in that for instance we can not follow in our thought
an unaccustomed fact and can not see through it, then we
call a serviceable guide of our thoughts which helps us to
do so a discovery. When a man fiinds he can not boil
water in a pumpkin shell because it catches fire he invents
the pot by surrounding the pumpkin with clay. When a
man can not understand the light and dark bands in con-
flicting rays of light from two identical sources because he
thinks of light as a uniform stream he discovers inter-

242 THE MONIST.

ference from the instruction to represent light with period-
ically changing properties. Discoveries and inventions may
be due to an accidental occasional observation, as is shown
in the above examples. In other cases they may be the
result of prolonged systematic work as has been illumi-
natingly presented by the Muscovite engineer P. K. v.
Engelmeyer in his essay Der Dreiakt ah Lehre von der
Technik und der Erfindung (Berlin, Heymann, 1910). 4
If an invention is to be made there must be the desire to
remove an inconvenience ; there must be the knowledge of
the means by which this can be done, and the ability to
make a practical application of them. This is the Dreiakt
of the purpose, the plan for attaining it and the material
performance which takes place mutatis mutandis also when-
ever a theoretical problem is put to a practical application.

ERNST MACH.
VIENNA, AUSTRIA.

4 See a further account of this work in the editorial in this number en-
titled "A New Theory of Invention."

THE NEW LOGICS.1

I. THE RUSSELL LOGIC.

TO justify its pretensions, logic had to change. We
have seen new logics arise of which the most inter-
esting is that of Russell. It seems he has nothing new to
write about formal logic, as if Aristotle there had touched
bottom. But the domain Russell attributes to logic is in-
finitely more extended than that of the classic logic, and
he has put forth on the subject views which are original
and at times well warranted.

First, Russell subordinates the logic of classes to that
of propositions, while the logic of Aristotle was above all
the logic of classes and took as its point of departure the
relation of subject to predicate. The classic syllogism,
"Socrates is a man," etc., gives place to the hypothetical
syllogism: "If A is true, B is true; now if B is true, C is
true/' etc. And this is, I think, a most happy idea, be-
cause the classic syllogism is easy to carry back to the
hypothetical syllogism, while the inverse transformation
is not without difficulty.

And then this is not all. Russell's logic of propositions
is the study of the laws of combination of the conjunctions
if, and, or, and the negation not.

In adding here two other conjunctions and and or,
Russell opens to logic a new field. The symbols and, or
follow the same laws as the two signs X and -f-, that is

translated by George Bruce Halsted.

244 THE MONIST.

to say the commutative, associative and distributive laws.
Thus and represents logical multiplication, while or repre-
sents logical addition. This also is very interesting.

Russell reaches the conclusion that any false proposi-
tion implies all other propositions true or false. M. Cou-
turat says this conclusion will at first seem paradoxical.
It is sufficient however to have corrected a bad thesis in
mathematics to recognize how right Russell is. The candi-
date often is at great pains to get the first false equation;
but that once obtained, it is only sport then for him to ac-
cumulate the most surprising results, some of which even
may be true.

ii.

We see how much richer the new logic is than the
classic logic ; the symbols are multiplied and allow of varied
combinations which are no longer limited in number. Has
one the right to give this extension to the meaning of the
word logic ? It would be useless to examine this question
and to seek with Russell a mere quarrel about words.
Grant him what he demands; but be not astonished if
certain verities declared irreducible to logic in the old
sense of the word find themselves now reducible to logic
in the new sense — something very different.

A great number of new notions have been introduced,
and these are not simply combinations of the old. Russell
knows this, and not only at the beginning of the first chap-
ter, "The Logic of Propositions," but at the beginning
of the second and third, "The Logic of Classes" and "The
Logic of Relations," he introduces new words that he de-
clares indefinable.

And this is not all; he likewise introduces principles
he declares indemonstrable. But these indemonstrable
principles are appeals to intuition, synthetic judgments
a priori. We regard them as intuitive when we meet

THE NEW LOGICS. 245

them more or less explicitly enunciated in mathematical
treatises; have they changed character because the mean-
ing of the word logic has been enlarged and we now find
them in a book entitled "Treatise on Logic"? They have
not changed nature; they have only changed place.

in.

Could these principles be considered as disguised defi-
nitions ? It would then be necessary to have some way of
proving that they imply no contradiction. It would be
necessary to establish that, however far one followed the
series of deductions, he would never be exposed to contra-
dicting himself.

We might attempt to reason as follows : We can verify
that the operations of the new logic applied to premises ex-
empt from contradiction can only give consequences equally
exempt from contradiction. If therefore after n opera-
tions we have not met contradiction, we shall not encoun-
ter it after n-fi. Thus it is impossible that there should
be a moment when contradiction begins, which shows we
shall never meet it. Have we the right to reason in this
way? No, for this would be to make use of complete in-
duction ; and remember, zve do not yet know the principle
of complete induction.

We therefore have not the right to regard these as-
sumptions as disguised definitions and only one resource
remains for us, to admit a new act of intuition for each
of them. Moreover I believe this is indeed the thought of
Russell and M. Couturat.

Thus each of the nine indefinable notions and of the
twenty indemonstrable propositions (I believe if it were
I that did the counting, I should have found some more)
which are the foundation of the new logic, logic in the
broad sense, presupposes a new and independent act of
our intuition and (why not say it?) a veritable synthetic

246 THE MONIST.

judgment a priori. On this point all seem agreed, but
what Russell claims, and what seems to me doubtful, is
that after these appeals to intuition, that will be the end
of it; we need make no others and can build all mathemat-
ics without the intervention of any new element.

M. Couturat often repeats that this new logic is alto-
gether independent of the idea of number. I shall not
amuse myself by counting how many numeral adjectives his
exposition contains, both cardinal and ordinal, or indefi-
nite adjectives such as several. We may cite however some
examples :

"The logical product of two or more propositions is

D .
.... ,

"All propositions are capable only of two values, true
and false";

"The relative product of two relations is a relation";

"A relation exists between two terms," etc., etc.

Sometimes this inconvenience would not be unavoid-
able, but sometimes also it is essential. A relation is in-
comprehensible without two terms ; it is impossible to have
the intuition of the relation, without having at the same
time that of its two terms, and without noticing they are two,
because, if the relation is to be conceivable, it is necessary
that there be two and only two.

v.

ARITHMETIC

I reach what M. Couturat calls the ordinal theory which
is the foundation of arithmetic properly so called. M.
Couturat begins by stating Peano's five assumptions, which
are independent, as has been proved by Peano and Padoa.

1. Zero is an integer.

2. Zero is not the successor of any integer.

3. The successor of an integer is an integer.
To this it would be proper to add,

THE NEW LOGICS. 247

Every integer has a successor.

4. Two integers are equal if their successors are.

The fifth assumption is the principle of complete induc-
tion.

M. Couturat considers these assumptions as disguised
definitions; they constitute the definition by postulates of
zero, of successor, and of integer.

But we have seen that for a definition by postulates to
be acceptable we must be able to prove that it implies no
contradiction.

Is this the case here? Not at all.

The demonstration cannot be made by example. We
cannot take a part of the integers, for instance the first
three, and prove they satisfy the definition.

If I take the series o, i, 2, I see it fulfils the assump-
tions i, 2, 4, and 5; but to satisfy assumption 3, it still is
necessary that 3 be an integer, and consequently that the
series o, i, 2, 3, fulfil the assumptions; we might prove
that it satisfies assumptions i, 2, 4, 5, but assumption 3
requires besides that 4 be an integer and that the series
o, i, 2, 3, 4, fulfil the assumptions, and so on.

It is therefore impossible to demonstrate the assump-
tions for certain integers without proving them for all;
we must give up proof by example.

It is necessary then to take all the consequences of our
assumptions and see if they contain no contradiction.

If these consequences were finite in number, this would
be easy; but they are infinite in number; they are the
whole of mathematics, or at least all arithmetic.

What then is to be done? Perhaps strictly we could
repeat the reasoning of number III.

But as we have said, this reasoning is complete induc-
tion, and it is precisely the principle of complete induction
whose justification would be the point in question.

248 THE MONIST.

VI.
THE LOGIC OF HILBERT.

I come now to the capital work of Hilbert which he
communicated to the Congress of Mathematicians at Hei-
delberg, and of which a French translation by M. Pierre
Boutroux appeared in I'Enseignement mathematique, while
an English translation due to Halsted appeared in The
Monist.2 In this work, which contains profound thoughts,
the author's aim is analogous to that of Russell, but on
many points he diverges from his predecessor.

"But/' he says (Monist, p. 340), "on attentive con-
sideration we become aware that in the usual exposition
of the laws of logic certain fundamental concepts of arith-
metic are already employed, for example the concept of
the aggregate, in part also the concept of number.

"We fall thus into a vicious circle and therefore to
avoid paradoxes a partly simultaneous development of the
laws of logic and arithmetic is requisite."

We have seen above that what Hilbert says of the
principles of logic in the usual exposition, applies likewise
to the logic of Russell. So for Russell logic is prior to
arithmetic; for Hilbert they are "simultaneous." We shall
find further on other differences still greater, but we shall
point them out as we come to them. I prefer to follow step
by step the development of Hilbert's thought, quoting tex-
tually the most important passages.

"Let us take as the basis of our consideration first of all
a thought-thing i (one)" (p. 341). Notice that in so do-
ing we in no wise imply the notion of number, because it
is understood that i is here only a symbol and that we do
not at all seek to know its meaning. "The taking of this
thing together with itself respectively two, three or more
times . . . . " Ah ! this time it is no longer the same ; if we

"The Foundations of Logic and Arithmetic," Monist XV, 338-352.

THE NEW LOGICS. 249

introduce the words "two," "three," and above all "more,"
"several," we introduce the notion of number; and then
the definition of finite whole number which we shall pres-
ently find, will come too late. Our author was too circum-
spect not to perceive this begging of the question. So at
the end of his work he tries to proceed to a truly patching
up process.

Hilbert then introduces two simple objects I and =,
and considers all the combinations of these two objects, all
the combinations of their combinations, etc. It goes with-
out saying that we must forget the ordinary meaning of
these two signs and not attribute any to them.

Afterwards he separates these combinations into two
classes, the class of the existent and the class of the non-
existent, and till further orders this separation is entirely
arbitrary. Every affirmative statement tells us that a cer-
tain combination belongs to the class of the existent ; every
negative statement tells us that a certain combination be-
longs to the class of the non-existent.

IV.

Note now a difference of the highest importance. For
Russell any object whatsoever, which he designates by x,
is an object absolutely undetermined and about which he
supposes nothing ; for Hilbert it is one of the combinations
formed with the symbols i and =; he could not conceive
of the introduction of any thing other than combinations
of objects already defined. Moreover Hilbert formulates
his thought in the neatest way, and I think I must repro-
duce in extenso his statement (p. 348) :

"In the assumptions the arbitraries (as equivalent for
the concept 'every' and 'air in the customary logic) repre-
sent only those thought-things and their combinations with
one another, which at this stage are laid down as funda-
mental or are to be newly defined. Therefore in the deduc-

25O THE MONIST.

tion of inferences from the assumptions, the arbitraries,
which occur in the assumptions, can be replaced only by
such thought-things and their combinations.

"Also we must duly remember, that through the super-
addition and making fundamental of a new thought-thing
the preceding assumptions undergo an enlargement of
their validity, and where necessary, are to be subjected to
a change in conformity with the sense."

The contrast with Russell's view-point is complete. For
this philosopher we may substitute for x not only objects
already known but any thing.

Russell is faithful to his point of view, which is that
of comprehension. He starts from the general idea of
being, and enriches it more and more while restricting
it, by adding new qualities. Hilbert on the contrary recog-
nizes as possible beings only combinations of objects al-
ready known; so that (looking at only one side of his
thought) we might say he takes the view-point of exten-
sion.

VIII.

Let us continue with the exposition of Hilbert's ideas.
He introduces two assumptions which he states in his sym-
bolic language but which signify, in the language of the
uninitiated, that every quantity is equal to itself and that
every operation performed upon two identical quantities
gives identical results.

So stated, they are evident, but thus to present them
would be to misrepresent Hilbert's thought. For him
mathematics have to combine only pure symbols, and a
true mathematician should reason upon them without pre-
conceptions as to their meaning. So his assumptions are
not for him what they are for the common people.

He considers them as representing the definition by
postulates of the symbol (=) heretofore void of all sig-

THE NEW LOGICS. 251

nification. But to justify this definition we must show that
these two assumptions lead to no contradiction. For this
Hilbert used the reasoning of our number III, without
appearing to perceive that he is using complete induction.

IX.

The end of Hilbert's memoir is altogether enigmatic
and I shall not lay stress upon it. Contradictions accumu-
late; we feel that the author is dimly conscious of the
petitio principii he has committed, and that he seeks vainly
to patch up the holes in his argument.

What does this mean? At the point of proving that
the definition of the whole number by the assumption of
complete induction implies no contradiction, Hilbert with-
draws as Russell and Couturat withdrew, because the diffi-
culty is too great.

x.

GEOMETRY.

Geometry, says M. Couturat, is a vast body of doctrine
wherein the principle of complete induction does not enter.
That is true in a certain measure; we cannot say it is en-
tirely absent, but it enters very slightly. If we refer to
the Rational Geometry of Dr. Halsted (New York, John
Wiley and Sons, 1904) built up in accordance with the
principles of Hilbert, we see the principle of induction
enter for the first time on page 114 (unless I have made
an oversight, which is quite possible).3

So geometry which only a few years ago seemed the
domain where the reign of intuition was uncontested is
to-day the realm where the logicians seem to triumph.
Nothing could better measure the importance of the geo-
metric works of Hilbert and the profound impress they
have left on our conceptions.

*2d. ed, 1907, p. 86; French ed. 1911, p. 97. G. B. H.

252 THE MONIST.

But be not deceived. What is after all the fundamental
theorem of geometry? It is that the assumptions of geom-
etry imply no contradiction, and this we can not prove
without the principle of induction.

How does Hilbert demonstrate this essential point ? By
leaning upon analysis and through it upon arithmetic and
through it upon the principle of induction.

And if ever one invents another demonstration, it will
still be necessary to lean upon this principle, since the pos-
sible consequences of the assumptions, of which it is neces-
sary to show that they are not contradictory, are infinite
in number.

XI.

CONCLUSION.

Our conclusion straightway is that the principle of in-
duction cannot be regarded as the disguised definition of
the entire world.

Here are three truths : ( i ) The principle of complete
induction; (2) Euclid's postulate; (3) The physical law
according to which phosphorus melts at 44° (cited by M.
Le Roy).

These are said to be three disguised definitions: the
first, that of the whole number; the second, that of the
straight line; the third, that of phosphorus.

I grant it for the second; I do not admit it for the
other two. I must explain the reason for this apparent
inconsistency.

First, we have seen that a definition is acceptable only
on condition that it implies no contradiction. We have
shown likewise that for the first definition this demonstra-
tion is impossible; on the other hand we have just recalled
that for the second Hilbert has given a complete proof.

As to the third, evidently it implies no contradiction.
Does this mean that the definition guarantees, as it should,

THE NEW LOGICS. 253

the existence of the object defined ? We are here no longer
in the mathematical sciences, but in the physical, and the
word existence has no longer the same meaning. It no
longer signifies absence of contradiction; it means objec-
tive existence.

You already see a first reason for the distinction I made
between the three cases; there is a second. In the appli-
cations we have to make of these three concepts, do they
present themselves to us as defined by these three postu-
lates?

The possible applications of the principle of induction
are innumerable; take for example one of those we have
expounded above, and where it is sought to prove that an
aggregate of assumptions can lead to no contradiction. For
this we consider one of the series of syllogisms we may go
on with in starting from these assumptions as premises.
When we have finished the nth syllogism, we see we can
make still another and this is the n+ith. Thus the num-
ber n serves to count a series of successive operations; it
is a number obtainable by successive additions. This there-
fore is a number from which we may go back to unity by
successive subtractions. Evidently we could not do this
if we had n=n — i, since then by subtraction we should
always obtain again the same number. So the way we
have been led to consider this number n implies a definition
of the finite whole number and this definition is the follow-
ing: A finite whole number is that which can be obtained
by successive additions; it is such that n is not equal to
n — I.

That granted, what do we do ? We show that if there
has been no contradiction up to the nth syllogism, no more
will there be up to the n-f-ith, and we conclude there never
will be. You say: I have the right to draw this conclu-
sion, since the whole numbers are by definition those for
which a like reasoning is legitimate. But that implies

254 THE MONIST.

another definition of the whole number, which is as fol-
lows : A whole number is that on which we may reason by
recurrence. In the particular case it is that of which we
may say that, if the absence of contradiction up to the time
of a syllogism of which the number is an integer carries
with it the absence of contradiction up to the time of the
syllogism whose number is the following integer, we need
fear no contradiction for any of the syllogisms whose num-
ber is an integer.

The two definitions are not identical; they are doubt-
less equivalent, but only in virtue of a synthetic judgment
a priori] we cannot pass from one to the other by a purely
logical procedure. Consequently we have no right to adopt
the second, after having introduced the whole number by
a way that presupposes the first.

On the other hand, what happens with regard to the
straight line? I have already explained this so often that
I hesitate to repeat it again, and shall confine myself to a
brief recapitulation of my thought. We have not, as in
the preceding case, two equivalent definitions logically ir-
reducible one to the other. We have only one expressible
in words. Will it be said there is another which we feel
without being able to word it, since we have the intuition
of the straight line or since we represent to ourselves the
straight line? First of all, we cannot represent it to our-
selves in geometric space, but only in representative space,
and then we can represent to ourselves just as well the
objects which possess the other properties of the straight
line, save that of satisfying Euclid's postulate. These ob-
jects are "the non- Euclidean straights," which from a cer-
tain point of view are not entities void of sense but circles
(true circles of true space) orthogonal to a certain sphere.
If, among these objects equally capable of representation,
it is the first (the Euclidean straights) which we call

THE NEW LOGICS. 255

straights, and not the latter (the non-Euclidean straights),
this is properly by definition.

And arriving finally at the third example, the definition
of phosphorus, we see the true definition would be: Phos-
phorus is the bit of matter I see in yonder flask.

And since I am on this subject, still another word. Of
the phosphorus example I said: "This proposition is a
real verifiable physical law, because it means that all bodies
having all the other properties of phosphorus, save its
point of fusion, melt like it at 44°." And it was answered :
"No, this law is not verifiable, because if it were shown
that two bodies resembling phosphorus melt one at 44° and
the other at 50°, it might always be said that doubtless, be-
sides the point of fusion, there is some other unknown
property by which they differ."

That was not quite what I meant to say. I should have
written, "All bodies possessing such and such properties
finite in number (to wit, the properties of phosphorus stated
in the books on chemistry, the fusion-point excepted) melt
at 44°-"

And the better to make evident the difference between
the case of the straight and that of phosphorus, one more
remark. The straight has in nature many images more or
less imperfect, of which the chief are the light rays and
the rotation axis of the solid. Suppose we find the ray of
light does not satisfy Euclid's postulate (for example by
showing that a star has a negative parallax), what shall
we do ? Shall we conclude that the straight being by defi-
nition the trajectory of light does not satisfy the postulate,
or on the other hand that the straight by definition satis-
fying the postulate, the ray of light is not straight?

Assuredly we are free to adopt the one or the other
definition and consequently the one or the other conclusion ;
but to adopt the first would be stupid, because the ray of
light probably satisfies only imperfectly not merely Euclid's

256 THE MONIST.

postulate but the other properties of the straight line, so
that if it deviates from the Euclidean straight, it deviates
no less from the rotation axis of solids which is another
imperfect image of the straight line; while finally it is
doubtless subject to change, so that such a line which
yesterday was straight will cease to be straight to-morrow
if some physical circumstance has changed.

Suppose now we find that phosphorus does not melt
at 44°, but at 43.9°. Shall we conclude that phosphorus
being by definition that which melts at 44°, this body that
we did call phosporus is not true phosphorus, or on the
other hand that phosphorus melts at 43.9°? Here again
we are free to adopt the one or the other definition and
consequently the one or the other conclusion ; but to adopt
the first would be stupid because we cannot be changing
the name of a substance every time we determine a new
decimal of its fusion-point.

XIII.

To sum up, Russell and Hilbert have each made a
vigorous effort; they have each written a work full of
original views, profound and often well warranted. These
two works give us much to think about and we have much
to learn from them. Among their results, some, many
even, are solid and destined to live.

But to say that they have finally settled the debate
between Kant and Leibnitz and ruined the Kantian theory
of mathematics is evidently incorrect. I do not know
whether they really believed they had done it, but if they
believed so, they deceived themselves.

H. POINCARE.

PARIS, FRANCE.

THE WEIRD OF LOVE AND DEATH.

"O inhabitant of Lebanon, that makest thy nest
in the cedars, how gracious shalt thou be when
pangs come upon thee, the pain as of a woman
in travail." — Jeremiah, xxii. 23.

"Then he brought me to the door of the gate of
the Lord's house, which was toward the north;
and behold, there sat women weeping for Tam-
muz." — Ezekiel, viii. 14.

"And there followed him a great company of
people, and of women, which also bewailed and
lamented him.

"But Jesus turning unto them said, Daughters
of Jerusalem, weep not for me, but weep for
yourselves and for your children.

"For, behold, the days are coming, in which
they shall say, Blessed are the barren, and the
wombs that never bare, and the paps which never
gave suck." — St. Luke, xxiii. 27, 28.

The author of the following verses makes no claim to be a
translator, but merely an interpreter of a chapter from the Brick
Bible of Babylon. He has relied upon the scholarship of others for
his letter, but has sought its spirit not only beneath the text, but in
the actual world of love and death. Special students of comparative
religions indeed know the truth of Shakespeare's 59th sonnet:

"If there be nothing new, but that which is
Hath been before, how are our brains beguiled,
Which, laboring for invention, bear amiss
The second burthen of a former child!"

258 THE MONIST.

But the author has seen no other English version, in poetic form, of
this oldest Semitic Gospel of the Resurrection, which, however old
it be, is itself a translation, like the Greek Christian Gospels, from
earlier originals.1 Adonis has his Greek Gospels also, but only the
apocryphal have come down to us, and these have found ample em-
bodiment in Shakespeare's "Venus and Adonis."

The author has welded to the story of the Descent of Istar, two
fragmentary hymns from the same literature invoking the Divine
Pair, which common invocation is confirmed by the passage of
Jeremiah (xxii. 18) whose Hebrew text should read, according to
Prof. T. K. Cheyne : "Alas, my Brother, alas, my Sister ! Alas, Adon,
[Lord] alas Dodah! [Beloved Lady: a title of Istar]."

The cult of Dumu-zi-abzu (Sumerian or Akkadian "True Son
of the Deep Water") whom the Hebrews alternately adored and ab-
horred as Tammuz, took, in its migration from the shore of the Per-
sian Gulf to the ^Egean and Sicilian coasts, only his Semitic title
of "Adon." But in the course of transit the divinity first became
obscured and then the human reputation. From a benign and mys-
terious power behind the process of spring, or a general symbol of
the life principle of which winter deprives nature and death bereaves
love, he became a demi-godlike huntsman and paramour of Aphro-
dite the goddess of beauty. Finally, in modern parlance, his epithet
has dwindled to signify a pretty youth. Though coming from further
east, the worship of Tammuz had its most famous seat at Aphaca
(now Afka) about fifteen miles from the Phenician coast near the
source of a torrent now called Ibrahim. In that ravine a crude but
grand cosmic hypothesis was narrowed to a vulgar superstition. The
site became a pagan Loretto or Lourdes, and developed a perverse
traffic in sacred things which gave to Constantinople in the fourth
Christian century the same reason or pretext for suppression that
English shrines in the sixteenth century afforded Henry VIII.

The swift stream was miraculously tinged each year with the
blood of the dying god whose title it then bore. It is said that the
same geologic conditions stll perform the annual miracle. In the
Vale of Aphaca the triumph as well as the agony of a divine victim
were localized, just as later they were at Jerusalem. From Aphaca
to Galilee it is but eighty miles by crow-flight, and to Nazareth less

1Dr. Alfred Jeremias has published the original text of the Descent of
Istar with a literal German translation. An English version founded on Dr.
Jeremias's translation, appeared in The Open Court. See Cams, "Babylonian
and Hebrew Views of Man's Fate After Death," XV, p. 357.

THE WEIRD OF LOVE AND DEATH. 259

than one hundred. Indeed, at Bethlehem (the "House of Bread")
which lies seventy miles further south, the adoration of Tammuz,
as an earlier fruit of the wheat than the Christian eucharist wafer,
lingered in the days of St. Jerome. Though an enormous ethical dis-
tance separates the personality of Jesus from the mythical boar-
chaser of Lebanon, the dogmas of Chaldea show that the traditions
of the church rest on more than one foundation. The Egyptian
Gospel of Osiris is another corner-stone.

The modest figure of the Virgin Mother Mary has little in
common with the proud and passionate image of Istar, Ashtaroth or
Astarte. Rather has the concept of her borrowed the attributes of
the gracious Egyptian Isis. Istar's exchange of curses with her in-
fernal sister, as told in clay, may nevertheless have stirred the re-
ligious feelings of her votaries among the fish-wives of Babylon.
But there remains something in the grief of the divine bride for her
lost bridegroom which forecasts the plastic pathos of Michelangelo's
"Pieta" and is echoed in the rich harmonies of Rossini's "Stabat
Mater Dolorosa."

To realm whence no echo is borne,

to region no pioneer showeth;
To the Castle of Darkness Substantial,

to Yesterday's shadowy shore,
Our Lady Astarte, whose beacon

for lovers and mariners gloweth
At morning and even, descended

and smote on the dust-laden door.

"Now open the gate unto me,

grim warden that keepest the marches!
I would enter the Kingdom of Death !"

cried Our Lady, the mystical Bride.
"Unless to my summons thou hearken,

thy gate I will rend from its arches,
Setting free to outnumber the living,

the spirits of men that have died !"

26O THE MONIST.

To Lady Astarte, the warden

that watcheth the entrance of Hades
Made reply: "Till I take to my mistress

thy word, prithee, Istar, forbear!"
(A feud for eternity lay

'twixt the lovely and terrible ladies,
So how should Death bid Love be welcome,

and ope to a rival her lair?)

To pitiless Queen of Irkalla

the seneschal doubtfully wended:
"Sov'reign Lady of Death, at the precinct

thy sister Astarte doth stand.
Methinks that in quest of the life-giving

water the Queen hath descended;
The bars of thy mansion are shaken

beneath her imperious hand/'

To him said Queen Allat: "O warden,

as grain from the scythe of a reaper
To the Dungeon of Dust falleth Istar

imploring the water of life!
Like lip of reed that is thirsty

her need is for Tammuz the Sleeper :
But what are her sorrow and yearning

to us, or her menace of strife?

"Quoth she: 'For the hero I mourn

that hath left his wife widow'd and lonely.
I lament for the bride whose embraces

her husband hath lost and deplored;
For fate of the innocent children

whose span bore the spring-blossom only;
So lend me the water of life,

For the healing of Tammuz my Lord!'

THE WEIRD OF LOVE AND DEATH. 26l

"Yet, warden, we grant her caprice!

Suffer Istar to enter our portal
In conformity strict to the letter

of Death's incompassionate law.
Deprive her of every adornment

as if she were humble and mortal;
Extinguish the glory of Istar

that filleth the heavens with awe!"

The warden returning, threw open

the porch of Irkalla to Istar.
"Thou art welcome to Death, O dread Lady!

Let Ghostland rejoice in its guest!
'T is mine to conduct thee, O Queen,

to the presence of Allat, thy sister!"
But as she stepp'd over the threshold

he plucked from her forehead the crest.

"My crown with the crescent and star

give back to me!" Istar besought him.
"Nay, my Princess, the code of the kingdom

of Death even thou must obey!"
Through Second Gate when they immerged,

as the ruler of Hades had taught him,
The warden of gloom took from Istar

The radiant ear-rings away.

And so at each barrier passed,

the Queen of her robe he divested,
And the necklace, the brooch and the belt

and the bracelets he claim'd as his prey.
Relentless and brutal he was;

When Our Lady Astarte protested,
Repeating: "Nay, Princess, the edict

of Death even thou must obey!"

262 THE MONIST.

So into the hall of the hopeless,

the court of Queen Allat the Dreary,
All dishevelled, discrowned and dismantled

Our Lady Astarte he led.
Though her aspect was that of despair,

for her trials were many and weary,
Not dumb was Our Lady at sight

of the sinister Queen of the Dead.

She cursed her with formula dire,

with a torrent of bitter invective,
And she wept more in rage than in sorrow,

recounting the insults of Death.
The face of the monarch of Hades

grew scornfully sweet and reflective,
Nor uttered she one interruption

till Istar expended her breath,

Then spake with a delicate malice

these ominous words unto Istar:
"Since thou quittest the world, not a beast

of the wilderness seeketh a mate,
Nor egg hath been hatched by a fowl,

O gentle and courteous sister
Who threat'nest my realm with invasion,

but leavest thine own desolate!

"The maids of the men are unconscious,

no men to the maids make advances;
And the cradles are empty and rock'd

by the hands of no mothers to-day;
Their music the forests have lost,

the cities are stilled of their dances;
The land of the living is stagnant

since Istar to Death came away.

THE WEIRD OF LOVE AND DEATH. 263

"My thralls thou hast sought to suborn,

by promising thou wdiildst deliver
From the dust of the grave to adore thee

again on thy double-horned throne —
In truth, O Astarte, it seemeth,

now Love hath discarded her quiver,
The task would be light for annexing

the Kingdom of Life to mine own!

"Ho, Namtar! Take Istar and plague her

with sixty-fold measure of illness!
Assail her with chastening agues

and darken the flame of her eyes!
Let agony reign in her bosom,

her ears have the horror of stillness!
Let clouds gather over her spirit!

Let languor her limbs paralyse!"

Through creation there mounted a shudder

to throne of the Father Eternal;
To the One whose dominion is screened

by the awful illusion of space.
All nature cried out at the tyranny

seized by the power infernal;
In conclave aghast at the rumor

the sons of God each took his place.

'T is June, but the leafage hath fallen;

't is summer, but rime crusteth over
All the meads of the planets with whiteness;

't is season for rain, but a drought
The field of ephemeral life

with a brown desolation doth cover;
The fire of Astarte is dim;

from the tomb cometh Tammuz not out!"

264 THE MONIST.

So Papsukal, angel of light,

unto Mardttk the Sun-god repeated,
Who arose and went up to his Father

and bowed in the Presence with tears.
The lord of the hours for grace

of the Infinite Spirit entreated
To call back Our Lady Astarte

from Death to her place in the spheres.

From mind of the Father Eternal

in likeness not man nor yet woman,
Did a messenger come to creation,

with countenance fair and serene.
By myriad titles invoked on the

stammering lips that are human,
Among them "Atsu-su-namir,"

and it meaneth "His Rising is seen."

"To realm whence no echo is borne,

to region no pioneer showeth ;
To the Castle of Darkness Substantial;

to Yesterday's shadowy shore
Descend!" quoth the Infinite One,

"for the calm of the tempest that bloweth
From Allat the Queen of Irkalla,

the dame of the seven-fold door!

"Command her, in name of her Father,

to give from the Fount of Revival
Unto Istar her captive a draught

for the raising of Tammuz the Slain.
If pity she will not bestow

on the need of her sister and rival,
Then warn her how fragile Death's fetter

the gods Love and Life to restrain!"

THE WEIRD OF LOVE AND DEATH. 26$

More swift than the flight of a star

was the radiant herald in falling,
Through the limitless ether conveyed

on the thought of the Uttermost God.
O'er the Sea of Oblivion borne

to the Island of Silence appalling
Where hinges of Hell broke asunder

at touch of a magical rod.

Yet Allat, the Queen of the Dead,

at the luminous shape hurl'd reviling:
"Though I may not deny nor delay

my Father's unwelcome behest,
Atsu-su-namir, with the face

that is evermore hopeful and smiling,
I curse thee, who bringest His will!"

and she beat her implacable breast.

"Go, Namtar, and knock at the pillars

that hold up the base of our dwelling;
Bid the gnomes in their cavern assemble

and sit on their benches of gold;
Let Istar the water receive

that in Fount of Revival is welling,
And bring back the goddess before us;

her boon we no more may withhold."

Though grudgingly made the release,

through the seven-fold gate Lady Istar
In her strength and her beauty renewed,

from the Castle of Darkness hath gone.
No warden might check or betray,

no padlock nor bar might resist her;
With mantle and jewels restored

her figure resplendently shone.

266 THE MONIST.

She bore in her hand a bright chalice

for wakening Tammuz the Sleeper;
For Adonis, the First-fruits of Death,

an immortal libation she poured;
While hymns from the farthest confines

of creation grew louder and deeper,
As flowers and fishes and beasts

with mankind her arising adored:

"In Valley of Life there is growing

a tree amaranthine and shady;
From the grail of the crystal abyss

the sap of its verdure is drawn;
In heart of the earth it is rooted,

its leaves form the nest of Our Lady
Whose star in the highway of Heaven

enlight'neth the dusk and the dawn!

"Enshrined in a mystery sweet

is Adonis the Beautiful lying
On the lap of the Mother Divine

who lamented him cruelly slain.
There bloometh the garden of love,

and the flower of life is undying,
Beyond the soft veil of the temple

that hideth the deities twain!

"O Tammuz, our Lord and our Shepherd!

Miraculous Bridegroom of Istar!
Thou hast conquered the stronghold of Death

and thou leadest thy people like sheep!
Thou wert as the wheat in the field

that a wind of the desert doth blister,
Like tree of acacia with root

that a treacherous river doth steep!

THE WEIRD OF LOVE AND DEATH. 267

"Our Lady, whose star in the sky

bringeth hope to the heart heavy-laden,
And whose justice on earth is a lion,

whose mercy a lamb at the breast,
O Queen of the House of the Shepherd,

O Mistress of Love ever-maiden,
May infinite joy be upon thee,

thy grief be forever at rest!"

EDWARD GILCHRIST.
SWATOW, CHINA.

CRITICISMS AND DISCUSSIONS.

THE REV. JAMES BRADLEY ON THE MOTION OF THE

FIXED STARS.
(Reprinted from the Philosophical Transactions of 1727.)

[The theory of the relativity of time and space, which is at present upper-
most in the minds of physicists, has come into the foreground mainly through
the differences of measuring at large distances the time it takes light to
reach the observer's eye which is further complicated by the motions of his
own standpoint. This happened for the first time in the history of science in
the year 1726 when Mr. Bradley discovered that the fixed stars possessed
a definite and peculiar motion of their own which was due to the motion of
the earth around the sun and depended on the time it takes the light to reach
the earth.

This classical exposition of his experiments was published in the form of a
letter sent to the Phil. Trans. (Vol. XXXIV, p. 637) and has naturally become
quite inaccessible. There is probably only one complete file of the Trans-
actions west of the Alleghanies, the fortunate possessor of which is the
Chicago Public Library. Considering the rarity of this essay we deem it
proper to republish it and render it accessible to our readers. We do not
doubt the very way in which Mr. Bradley approaches the problem will throw
much light on the principle of relativity. In fact this essay will prove suffi-
cient to explain its far-reaching significance, the need of its invention and
the limitations of its use. A consideration of the foundaton of this principle
and the history of its origin will clear it of the mysticism with which its recent
representations have surrounded its statements. — p. c]

A Letter from the Reverend Mr. James Bradley, Savilian Professor
of Astronomy at Oxford, and F. R. S., to Dr. Edmond Halley
Astronom. Reg. &c. giving an Account of a new discovered
Motion of the Fix'd Stars.
SIR,

You having been pleased to express your Satisfaction with what
I had an Opportunity some time ago, of telling you in Conversation,
concerning some Observations, that were making by our late worthy
and ingenious Friend, the honorable Samuel Molyneux Esquire, and

CRITICISMS AND DISCUSSIONS. 269

which have since been continued and repeated by myself, in order
to determine the Parallax of the fixt Stars ; I shall now beg leave
to lay before you a more particular Account of them.

Before I proceed to give you the History of the Observations
themselves, it may be proper to let you know, that they were at
first begun in hopes of verifying and confirming those, that Dr.
Hook formerly communicated to the publick, which seemed to be
attended with Circumstances that promised greater Exactness in
them, than could be expected in any other, that had been made and
published on the same Account. And as his Attempt was what
principally gave Rise to this, so his Method in making the Observa-
tions was in some Measure that which Mr. Molyneux followed : For
he made Choice of the same Star, and his Instrument was con-
structed upon almost the same Principles. But if it had not greatly
exceeded the Doctor's in Exactness, we might yet have remained
in great Uncertainty as to the Parallax of the fixt Stars ; as you
will perceive upon the Comparison of the two Experiments.

This indeed was chiefly owing to our curious Member, Mr.
George Graham, to whom the Lovers of Astronomy are also not a little
indebted for several other exact and well-contrived Instruments.
The Necessity of such will scarce be disputed by those that have had
any Experience in making Astronomical Observations ; and the In-
consistency, which is to be met with among different Authors in
their Attempts to determine small Angles, particularly the annual
Parallax of the fixt Stars, may be a sufficient Proof of it to others.
Their Disagreement indeed in this article is not now so much to be
wondered at, since I doubt not, but it will appear very probable,
that the Instruments commonly made use of by them, were liable
to greater Errors than many times that Parallax will amount to.

The Success then of this Experiment evidently depending very
much on the Accurateness of the Instrument that was principally
to be taken Care of: In what Manner this was done, is not my
present Purpose to tell you ; but if from the Result of the Observa-
tions which I now send you, it shall be judged necessary to com-
municate to the Curious the Manner of making them, I may here-
after perhaps give them a particular Description, not only of Mr.
Molyneux 's Instrument but also of my own, which hath since been
erected for the same Purpose and upon the like Principles, though
it is somewhat different in its Construction, for a Reason you will
meet with presently.

Mr. Molyneux's Apparatus was compleated and fitted for ob-

2/O THE MONIST.

serving about the End of November 1725, and on the third Day
of December following, the bright Star at the Head of Draco
(marked v by Bayer) was for the first Time observed, as it passed
near the Zenith, and its Situation carefully taken with the Instru-
ment. The like Observations were made on the 5th, llth and 12th
Days of the same Month, and there appearing no material Difference
in the Place of the Star, a farther Repetition of them at this Season
seemed needless, it being a Part of the Year, wherein no sensible
Alteration of Parallax in this Star could be expected. It was chiefly
therefore Curiosity that tempted me (being then at Kew, where the
Instrument was fixed) to prepare for observing the Star on Decem-
ber 17th, when having adjusted the Instrument as usual, I per-
ceived that it passed a little more Southerly this Day than when it
was observed before. Not suspecting any other Cause of this Ap-
pearance, we first concluded, that it was owing to the Uncertainty
of the Observations, and that either this or the foregoing were not
so exact as we had before supposed ; for which Reason we purposed
to repeat the Observation again, in order to determine from whence
this Difference proceeded; and upon doing it on December 20th, I
found that the Star passed still more Southerly than in the former
Observations. This sensible Alteration the more surprized us, in
that it was the contrary way from what it would have been, had it
proceeded from an annual Parallax of the Star: But being now
pretty well satisfied, that it could not be entirely owing to the want
of Exactness in the Observations ; and having no Notion of anything
else, that could cause such an apparent Motion as this in the Star;
we began to think that some Change in the Materials, &c. of the
Instrument itself, might have occasioned it. Under these Apprehen-
sions we remained some time, but being at length fully convinced,
by several Trials, of the great Exactness of the Instrument, and
finding by the gradual Increase of the Star's Distance from the Pole,
that there must be some regular Cause that produced it; we took
care to examine nicely, at the Time of each Observation, how much
it was: and about the Beginning of March 1725, the Star was found
to be 20" more Southerly than at the Time of the first Observation.
It now indeed seemed to have arrived at its utmost Limit Southward,
because in several Trials made about this Time, no sensible Differ-
ence was observed in its Situation. By the Middle of April, it
appeared to be returning back again towards the North; and about
the beginning of June, it passed at the same Distance from the
Zenith as it had done in December when it was first observed.

CRITICISMS AND DISCUSSIONS.

From the quick Alteration of this Star's Declination about this
Time (it increasing a Second in three Days) it was concluded, that
it would now proceed Northward, as it before had done Southward
of its present Situation; and it happened as was conjectured: for
the Star continued to move Northward till September following,
when it again became stationary, being then near 20" more Northerly
than in June, and no less than 39" more Northerly than it was in
March. From September the Star returned towards the South, till
it arrived in December to the same Situation it was in at that time
twelve Months, allowing for the Difference of Declination on account
of the Precession of the Equinox.

This was a sufficient Proof, that the Instrument had not been
the Cause of this apparent Motion of the Star, and to find one
adequate to such an Effect seemed a Difficulty. A Nutation of the
Earth's Axis was one of the first things that offered itself upon this
Occasion, but it was soon found to be insufficient; for though it
might have accounted for the change of Declination in v Draconis
yet it would not at the same time agree with the Phaenomena in
other Stars ; particularly in a small one almost opposite in right
Ascension to v Draconis, at about the same Distance from the North
Pole of the Equator: For, though this Star seemed to move the
same way, as a Nutation of the Earth's Axis would have made it,
yet it changing its Declination but about half as much as v Draconis
in the same time (as appeared upon comparing the Observations of
both made upon the same Days, at different Seasons of the Year)
this plainly proved, that the apparent Motion of the Stars was not
occasioned by a real Nutation, since if that had been the Cause, the
Alteration in both Stars would have been near equal.

The great Regularity of the Observations left no room to doubt,
but that there was some regular Cause that produced this unex-
pected Motion, which did not depend on the Uncertainty or Variety
of the Seasons of the Year. Upon comparing the Observations
with each other, it was discovered that in both the fore-mentioned
Stars, the apparent Difference of Declination from the Maxima, was
always nearly proportional to the versed Sine of the Sun's Distance
from the Equinoctial Points. This was an Inducement to think,
that the Cause, whatever it was, had some Relation to the Sun's
Situation with respect to those Points. But not being able to frame any
Hypothesis at that Time sufficient to solve all the Phaenomena, and
being very desirous to search a little farther into this Matter ; I began
to think of erecting an Instrument for myself at Wansted, that

272 THE MONIST.

having it always at Hand, I might with the more Ease and Certainty,
enquire into the Laws of this new Motion. The Consideration like-
wise of being able by another Instrument, to confirm the Truth of
the Observations hitherto made with Mr. Molyneux's, was no small
Inducement to me ; but the Chief of all was, the Opportunity I should
thereby have of trying, in what Manner other Stars were affected
by the same Cause, whatever it was. For Mr. Molyneux's Instru-
ment being originally designed for observing v Draconis (in order
as I said before, to try whether it had any sensible Parallax) was
so contrived, as to be capable of but little Alteration in its Direc-
tion, not above seven or eight Minutes of a Degree; and there
being few stars within half that Distance from the Zenith of Kew,
bright enough to be well observed, he could not, with his Instru-
ment, thoroughly examine how this Cause affected Stars differently
situated with respect to the equinoctial and solstitial Points of the
Ecliptick.

These Considerations determined me; and by the Contrivance
and Direction of the same ingenious Person, Mr. Graham, my In-
strument was fixed up August 19, 1727. As I had no convenient
Place where I could made use of so long a Telescope as Mr. Moly-
neux's, I contented myself with one of but little more than half the
Length of his (viz. of about \2\ Feet, his being 24 J) judging from
the Experience which I had already had, that this Radius would be
long enough to adjust the Instrument to a sufficient Degree of
Exactness, and I have no reason since to change my Opinion: for
from all the Trials I have yet made, I am very well satisfied, that
when it is carefully rectified, its Situation may be securely depended
upon to half a Second. As the Place where my Instrument was to
be hung, in some Measure determined its Radius, so did it also the
Length of the Arch, or Limb, on which the Divisions were made to
adjust it: For the Arch could not conveniently be extended farther,
than to reach to about 6J° on each Side my Zenith. This indeed
was sufficient, since it gave me an Opportunity of making Choice
of several Stars, very different both in Magnitude and Situation ;
there being more than two hundred inserted in the British Catalogue,
that may be observed with it. I needed not to have extended the
Limb so far, but that I was willing to take in Capella, the only star
of the first Magnitude that comes so near my Zenith.

My instrument being fixed, I immediately began to observe
such Stars as I judged most proper to give me light into the Cause
of the Motion already mentioned. There was Variety enough of

CRITICISMS AND DISCUSSIONS. 2/3

small ones; and not less than twelve, that I could observe through
all the Seasons of the Year; they being bright enough to be seen
in the Day-time, when nearest the Sun. I had not been long ob-
serving, before I perceived, that the Notion we had before enter-
tained of the Stars being farthest North and South, when the Sun
was about the Equinoxes, was only true of those that were near the
solstitial Colure: And after I had continued my Observations a few
Months, I discovered, what I then apprehended to be a general
Law, observed by all the Stars, viz. That each of them became sta-
tionary, or was farthest North or South, when they passed over my
Zenith at six of the Clock, either in the Morning or Evening. I
perceived likewise, that whatever Situation the Stars were in with
respect to the cardinal Points of the Ecliptick, the apparent motion
of every one tended the same Way, when they passed my instrument
about the same Hour of the Day or Night; for they all moved
Southward, while they passed in the Day, and Northward in the
Night ; so that each was farthest North, when it came about Six
of the Clock in the Evening, and farther South, when it came about
Six in the Morning.

Though I have since discovered, that the Maxima in most of
these Stars do not happen exactly when they come to my Instrument
at those Hours, yet not being able at that time to prove the con-
trary, and supposing that they did, I endeavoured to find out what
Proportion the greatest Alterations of Declination in different Stars
bore to each other ; it being very evident, that they did not all change
their Declination equally. I have before taken notice, that it ap-
peared from Mr. Molyneux's Observations, that v Draconis altered
its Declination about twice as much as the fore-mentioned small
Star almost opposite to it ; but examining the matter more particu-
larly, I found that the greatest Alteration of Declination in these
Stars, was at the Sine of the Latitude of each respectively. This
made me suspect that there might be the like Proportion between
the Maxima of other Stars ; but finding, that the observations of
some of them would not perfectly correspond with such an Hypoth-
esis, and not knowing, whether the small Difference I met with,
might not be owing to the Uncertainty and Error of the Observa-
tions, I deferred the farther examination into the Truth of this
Hypothesis, till I should be furnished with a Series of Observations
made in all Parts of the Year ; which might enable me, not only to
determine what Errors the Observations are liable to, or how far

274

THE MONIST.

they may safely be depended upon; but also to judge, whether there
had been any sensible Change in the Parts of the Instrument itself.

Upon these Considerations, I laid aside all Thoughts at that
Time about the Cause of the fore-mentioned Phaenomena, hoping
that I should the easier discover it, when I was better provided with
proper Means to determine more precisely what they were.

When the Year was compleated, I began to examine and com-
pare my Observations, and having pretty well satisfied myself as to
the general Laws of the Phaenomena, I then endeavoured to find
out the Cause, of them. I was already convinced, that the apparent
Motion of the Stars, was not owing to a Nutation of the Earth's
Axis. The next Thing that offered itself, was an Alteration in the

Direction of the Plumb-line, with which the Instrument was con-
stantly rectified ; but this upon Trial proved insufficient. Then I
considered what Refraction might do, but here also nothing satis-
factory occurred. At last I conjectured, that all the Phaenomena
hitherto mentioned, proceeded from the progressive Motion of Light
and the Earth's annual Motion in its Orbit. For I perceived, that,
if Light was propagated in Time, the apparent Place of a fixt Ob-
ject would not be the same when the Eye is at Rest, as when it is
moving in any other Direction, than that of the Line passing through
the Eye and Object; and that, when the Eye is moving in different
Directions, the apparent Place of the Object would be different.

I considered this Matter in the following Manner. I imagined
CA to be a Ray of Light, falling perpendicularly upon the Line BD ;
then if the Eye is at rest at A, the Object must appear in the Direc-

CRITICISMS AND DISCUSSIONS. 275

tion AC, whether Light be propagated in Time or in an Instant.
But if the Eye is moving from B towards A, and Light is propa-
gated in Time, with a Velocity that is to the Velocity of the Eye,
as CA to BA; then Light moving from C to A, whilst the Eye
moves from B to A, that Particle of it, by which the Object will be
discerned, when the Eye in its Motion comes to A, is at C when
the Eye is at B. Joining the Points B, C, I supposed the Line CB,
to be a Tube (inclined to the Line BD in the Angle DBC) of such
a Diameter, as to admit of but one Particle of Light; then it was
easy to conceive, that the Particle of Light at C (by which the ob-
ject must be seen when the Eye, as it moves along, arrives at A)
would pass through the Tube BC, if it is inclined to BD in the Angle
DBC, and accompanies the Eye in its Motion from B to A ; and that
it could not come to the Eye, placed behind such a Tube, if it had
any other Inclination to the Line BD. If instead of supposing CB
so small a Tube, we imagine it to be the Axis of a larger ; then for
the same Reason, the Particle of Light at C, could not pass through
that Axis, unless it is inclined to BD, in the Angle CBD. In like
manner, if the Eye moved the contrary way, from D towards A,
with the same Velocity ; then the Tube must be inclined in the Angle
BDC. Although therefore the true or real Place of an Object is
perpendicular to the Line in which the Eye is moving, yet the vis-
ible Place will not be so, since that, no doubt, must be in the Direc-
tion of the Tube ; but the Difference between the true and apparent
Place will be (cateris paribus) greater or less, according to the
different Proportion between the Velocity of Light and that of the
Eye. So that if we could suppose that Light was propagated in
an instant, then there would be no Difference between the real and
visible Place of an Object, although the Eye were in Motion, for
in that case, AC being infinite with Respect to AB, the Angle ACB
(the Difference between the true and visible Place) vanishes. But
if Light be propagated in Time (which I presume will readily be
allowed by most of the Philosophers of this Age) then it is evident
from the foregoing Considerations, that there will be always a
Difference between the real and visible Place of an Object, unless
the Eye* is moving either directly towards or from the Object. And
in all Cases, the Sine of the Difference between the real and visible
Place of the Object, will be to the Sine of the visible Inclination
of the Object to the Line in which the Eye is moving, as the Veloc-
ity of the Eye to the Velocity of Light.

If Light moved but 1000 times faster than the Eye, and an Ob-

2/6 THE MONIST.

ject (supposed to be at an infinite Distance) was really placed perpen-
dicularly over the Plain in which the Eye is moving, it follows from
what hath been already said, that the apparent Place of such an
Object will be always inclined to that Plain, in an Angle of 89° 56'-J ;
so that it will constantly appear 3'^ from its true Place, and seem
so much less inclined to the Plain, that way towards which the Eye
tends. That is, if AC is to AB (or AD) as 1000 to one, the Angle
ABC will be 89° 56'i, and ACB = 3'i and BCD ^ 2ACB = 7'.
So that according to this Supposition, the visible or apparent Place
of the Object will be altered 7', if the Direction of the Eye's Motion
is at one time contrary to what it is at another.

If the Earth revolve round the Sun annually, and the Velocity
of Light were to the Velocity of the Earth's Motion in its Orbit
(which I will at present suppose to be a Circle) as 1000 to one ; then
tis easy to conceive, that a Star really placed in the very Pole of the
Ecliptick, would, to an Eye carried along with the Earth, seem to
change its Place continually, and (neglecting the small Difference
on the Account of the Earth's diurnal Revolution on its Axis) would
seem to describe a Circle round that Pole, every Way distant there-
from 3'|. So that its Longitude would be varied through all the
Points of the Ecliptick every Year ; but its Latitude would always
remain the same. Its right Ascension would also change, and its
Declination, according to the different Situation of the Sun in respect
to the equinoctial Points ; and its apparent Distance from the North
Pole of the Equator would be 7' less at the Autumnal, than at the
vernal Equinox.

The greatest Alteration of the Place of a Star in the Pole of
the Ecliptick (or which in Effect amounts to the same, the Propor-
tion between the Velocity of Light and the Earth's Motion in its
Orbit) being known ; it will not be difficult to find what would be
the Difference upon this Account, the Difference between the true
and apparent Place of any other Star at any time ; and on the con-
trary, the Difference between the true and apparent Place being
given ; the Proportion between the Velocity of Light and the Earth's
Motion in its Orbit may be found.

As I only observed the apparent Difference of Declination of
the Stars, I shall not now take any farther Notice in what manner
such a Cause as I have here supposed would occasion an Alteration
in their apparent Places in other Respects ; but, supposing the Earth
to move equally in a Circle, it may be gathered from what hath been
already said, that a Star which is neither in the Pole nor Plain of

CRITICISMS AND DISCUSSIONS. 277

the Ecliptick, will seem to describe about its true Place a Figure,
insensibly different from an Ellipse, whose Transverse Axis is at
Right-angle to the Circle of Longitude passing through the Star's
true Place, and equal to the Diameter of the little Circle described
by a Star (as was before supposed) in the Pole of the Ecliptick ;
and whose Conjugate Axis is to its Transverse Axis, as the Sine
of the Star's latitude to the Radius. And allowing that a Star by its
apparent Motion does exactly describe such an Ellipse, it will be
found, that if A be the Angle of Position (or the Angle at the Star
made by two great Circles drawn from it, thro' the Poles of the
Ecliptick and Equator) and B be another Angle, whose Tangent is
to the Tangent of A as Radius to the Sine of the Latitude of the
Star; then B will be equal to the Difference of Longitude between
the Sun and the Star, when the true and apparent Declination of
the Star are the same. And if the Sun's Longitude in the Ecliptick
be reckoned from that Point, wherein it is when this happens ; then
the Difference between the true and apparent Declination of the
Star (on account of the Cause I am now considering) will be always,
as the Sine of the Sun's Longitude from thence. It will likewise
be found, that the greatest Difference of Declination that can be
between the true and apparent Place of the Star, will be to the Semi-
Transverse Axis of the Ellipse (or to the Semi-diameter of the
little Circle described by a Star in the Pole of the Ecliptick) as the
Sine of A to the Sine of B.

If the Star hath North Latitude, the Time, when its true and
apparent Declination are the same, is before the Sun comes in Con-
junction with or Opposition to it, if its Longitude be in the first or
last Quadrant (viz. in the ascending Semi-circle) of the Ecliptick;
and after them, if in the descending Semi-circle ; and it will appear
nearest to the North Pole of the Equator, at the Time of that
Maximum (or when the greatest Difference between the true and
apparent Declination happens) which precedes the Sun's Conjunc-
tion with the Star.

These Particulars being sufficient for my present Purpose, I
shall not detain you with the Recital of any more, or with any farther
Explication of these. It may be time enough to enlarge more upon
this Head, when I give a Description of the Instruments &c. if that
be judged necessary to be done; and when I shall find, what I now
advance, to be allowed of (as I flatter myself it will) as something
more than a bare Hypothesis. I have purposely omitted some mat-
ters of no great Moment, and considerd the Earth as moving in a

2/8 THE MONIST.

Circle, and not an Ellipse, to avoid too perplexed a Calculus, which
after all the Trouble of it would not sensibly differ from that which
I make use of, especially in those Consequences which I shall at
present draw from the foregoing Hypothesis.

This being premised, I shall not proceed to determine from the
observations, what the real Proportion is between the Velocity of
Light and the Velocity of the Earth's annual Motion in its Orbit;
upon Supposition that the Phaenomena before mentioned do depend
upon the Causes I have here assigned. But I must first let you know,
that in all the Observations hereafter mentioned, I have made an
Allowance for the Change of the Star's Declination on Account of
the Precession of the Equinox, upon Supposition that the Alteration
from this Cause is proportional to the Time, and regular through all
the Parts of the Year. I have deduced the real annual Alteration
of Declination of each Star from the Observations themselves ; and
I the rather choose to depend upon them in this Article, because all
which I have yet made, concur to prove, that the Stars near the
Equinoctial Colure, change their Declination at this time 1"£ or 2"
in a Year more than they would do if the Precession was only 50",
as is now generally supposed. I have likewise met with some small
Varieties in the Declination of other Stars in different Years, which
do not seem to proceed from the same Cause, particularly in those
that are near the solstitial Colure, which on the contrary have altered
their Declination less than they ought, if the Precession was 50".
But whether these small Alterations proceed from a regular Cause,
or are occasioned by any Change in the Materials &c. of my Instru-
ment, I am not yet able fully to determine. However, I thought it
might not be amiss just to mention to you how I have endeavoured
to allow for them, though the Result would have been nearly the
same, if I had not considered them at all. What that is, I will shew,
first from the Observations of v Draconis, which was found to be
39" more Southerly in the Beginning of March, than in September.

From what hath been premised, it will appear that the greatest
Alteration of the apparent Declination of v Draconis, on account of
the successive Propagation of Light, would be to the Diameter of
the little Circle which a Star (as was before remarked) would seem
to describe about the Pole of the Ecliptick as 39" to 40", 4. The
half of this is the Angle ACB (as represented in the Fig.) This
therefore being 20", 2, AC will be to AB, that is, the Velocity of
Light to the Velocity of the Eye (which in this Case may be sup-
posed the same as the Velocity of the Earth's annual Motion in its

CRITICISMS AND DISCUSSIONS. 279

Orbit) as 10210 to One, from whence it would follow, that Light
moves, or is propagated as far as from the Sun to the Earth in 8' and
12".

It is well known, that Mr. Romer, who first attempted to
account for an apparent Inequality in the Times of the Eclipses of
Jupiter's Satellites, by the Hypothesis of the progressive Motion
of Light, supposed that it spent about 11 Minutes of Time in its
Passage from the Sun to us : but it hath since been concluded by
others from the like Eclipses, that it is propagated as far in about
7 Minutes. The Velocity of Light therefore deduced from the fore-
going Hypothesis, is as it were a Mean betwixt what had at different
times been determined from the Eclipses of Jupiter's Satellites.

These different Methods of finding the Velocity of Lig*ht
thus agreeing in the Result, we may reasonably conclude, not only
that these Phaenomena are owing to the Causes to which they have
been ascribed; but also, that Light is propagated (in the same
Medium) with the same Velocity after it hath been reflected as
before ; for this will be the Consequence, if we allow that the Light
of the Sun is propagated with the same Velocity, before it is re-
flected, as the Light of the fixt Stars. And I imagine this will
scarce be questioned, if it can be made appear that the Velocity
of the Light of all the fixt Stars is equal, and that their Light moves
or is propagated through equal Spaces in equal Times, at all Dis-
tances from them: both which points (as I apprehend) are suffi-
ciently proved from the apparent alteration of the Declination of
Stars of different Lustre ; for that is not sensibly different in such
Stars as seem near together, though they appear of very different
Magnitudes. And whatever their Situations are (if I proceed ac-
cording to the foregoing Hypothesis) I find the same Velocity of
Light from my Observations of small Stars of the fifth or sixth, as
from those of the second and third Magnitude, which in all Proba-
bility are placed at very different Distances from us. The small
Star, for Example, before spoken of, that is almost opposite to v
Draconis (being the 35th Camelopard. Hevelii in Mr. Flamsteed's
Catalogue) was 19" more Northerly about the Beginning of March
than in September. Whence I conclude, according to my Hypothesis,
that the Diameter of the little Circle described by a Star in the
Pole of the Ecliptick would be 40", 2.

The last Star of the great Bear's tail of the 2d Magnitude
(marked >/ by Bayer) was 36" more Southerly about the Middle of
January than in July. Hence the Maximum, or greatest Altera-

28O THE MONIST.

tion of Declination of a Star in the Pole of the Ecliptick would
be 40", 4, exactly the same as was before found from the Observa-
tions of v Draconis.

The Star of the 5th magnitude in the Head of Perseus marked
T by Bayer, was 25" more Northerly about the End of December
than on the 29th of July following. Hence the Maximum would
be 41". This Star is not bright enough to be seen as it passes over
my Zenith about the End of June, when it should be according to
the Hypothesis farthest South. But because I can more certainly
depend upon the greatest Alteration of Declination of those Stars,
which I have frequently observed about the Times when they be-
come stationary, with respect to the Motion I am now considering;
I will set down a few more Instances of such, from which you may
be able to judge how near it may be possible from these Observa-
tions, to determine with what Velocity Light is propagated.

a Persei Bayero was 23" more Northerly at the beginning of
January than in July. Hence the Maximum would be 40", 2. a
Cassiopece was 34" more Northerly about the End of December than
in June. Hence the Maximum would be 40", 8. ft Draconis was 39"
more Northerly in the beginning of September than in March',
hence the Maximum would be 40", 2. Capella was about 16" more
Southerly in August than in Feb. ; hence the Maximum would be
about 40". But this Star being farther from my Zenith than those
I have before made use of, I cannot so well depend upon my Ob-
servations of it, as of the others ; because I meet with some small
Alterations of its Declination that do not seem to proceed from the
Cause I am now considering.

I have compared the Observations of several other Stars, and
they all conspire to prove that the Maximum is about 40" or 41".
I will therefore suppose that it is 40"^ or (which amounts to the
same) that Light moves, or is propagated as far as from the Sun
to us in 8' 13". The near Agreement which I met with among
my Observations induces me to think, that the Maximum (as I have
here fixed it) cannot differ so much as a Second from the Truth,
and therefore it is probable that the Time which Light spends in
passing from the Sun to us, may be determined by these Obser-
vations within 5" or 10" ; which is such a degree of exactness as
we can never hope to attain from the Eclipses of Jupiter's Satel-
lites.

Having thus found the Maximum, or what the greatest Alter-
nation of Declination would be in a Star placed in the Pole of the

CRITICISMS AND DISCUSSIONS.

28l

Ecliptick, I will now deduce from it (according to the foregoing
Hypothesis) the Alteration of Declination in one or two Stars, at
such times as they were actually observed, in order to see how the
Hypothesis will correspond with the Phenomena through all the
Parts of the Year.

It would be too tedious to set down the whole Series of my
Observations ; I will therefore make Choice only of such as are
most proper for my present Purpose, and will begin with those of
v Draconis.

This Star appeared farthest North about September 7th, 1727,
as it ought to have done according to my Hypothesis. The follow-
ing Table shews how much more Southerly the star was found to be
by Observation in several Parts of the Year, and how much more
Southerly it ought to be according to the Hypothesis.

to

to °2

to

to w

0 fc

o 55

0 K

O (Q

8§g

W Hj W

« 0 g

Sfc O
fe § H

8 ^ «

1§>

g g rt

5 H S

^ > £

S § 85

ill

W Q g

to § ^

to § W

§1

g.I!

«g§

w B

M ^ W

S « B

1727 D.

g «

B «

1728 D.

B S

Oct. 20

41

4i

Mar. 24

37

38

Nov. 17

m

12

April 6

36

361

Dec. 6

m

18i

May 6

28i

291

Dec. 28

25

26

June 5

Itt

20

1728

June 15

171

17

Jan. 24

34

34

July 3

ii*

111

Feb. 10

38

37

Aug. 2

4

4

Mar. 7

39

39

Sept. 6

0

0

Hence it appears, that the Hypothesis corresponds with the Ob-
servations of this Star through all Parts of the Year; for the small
Differences between them seem to arise from the Uncertainty of
the Observations, which is occasioned (as I imagine) chiefly by
the tremulous or undulating Motion of the Air, and of the Vapours
in it; which causes the Stars sometimes to dance to and fro, so
much that it is difficult to judge when they are exactly on the
Middle of the Wire that is fixed in the common Focus of the
Glasses of the Telescope.

I must confess to you, that the Agreement of the Observations

282

THE MONIST.

with each other, as well as with the Hypothesis, is much greater
than I expected to find, before I had compared them; and it may
possibly be thought to be too great, by those who have been used
to Astronomical Observations, and know how difficult it is to make
such as are in all respects exact. But if it would be any Satisfaction
to such Persons (till I have an Opportunity of describing my In-
strument and the manner of using it) I could assure them, that in
above 70 Observations which I made of this Star in a Year, there
is but one (and that is noted as very dubious on account of Clouds)
which differs from the foregoing Hypothesis more than 2", and this
does not differ 3".

This therefore being the Fact, I cannot but think it very prob-
able, that the Phenomena proceed from the Cause I have assigned,
since the foregoing Observations make it sufficiently evident, that
the Effect of the real Cause, whatever it is, varies in this Star, in
the same Proportion that it ought according to the Hypothesis.

But least v Draconis may be thought not so proper to shew the
proportion, in which the apparent alteration of Declination is in-
creased or diminished, as those Stars which lie near the Equinoctial
Colure: I will give you also the Comparison between the Hypoth-
esis and the Observations of -^ Ursa Majoris, that which was far-
thest South about the 17th Day of January 1728, agreable to the
Hypothesis. The following Table shews how much more Northerly

to w

to

to «

0 fc

0 g

s §

o 55

w & o

« fc 8

^ 55 M

g 0 H

O Q W

CJ Q £3

y o £j

« § 2

w S |S

i g I

w fc ^

w fc >

H fc ^

w S S

to J3 £

to § B

i a 1

i a w

p w o

MOW

§ a §

S « g

u a x

w 0 H

M 0 fx

y ® H

1727 d.

w «

B S

1728 d.

3 «

g S

Sept. 14

29*

28*

April 16

18*

18

Sept. 24

24*

25*

May 5

24*

23*

Oct. 16

19*

19*

June 5

32

31*

Nov. 11

11*

10*

June 25

35

34*

Dec. 14

4

3

July 17

36

36

1728

Aug. 2

35

35*

Feb. 17

2

3

Sept. 20

26*

26*

Mar. 21

11*

10*

CRITICISMS AND DISCUSSIONS. 283

it was found by Observation in several Parts of the Year, and also
what the Difference should have been according to the Hypothesis.

I find upon Examination, that the Hypothesis agrees altogether
as exactly with the Observations of this Star, as the former; for in
about 50 that were made of it in a Year, I do not meet with a
Difference of so much as 2", except in one, which is mark'd as doubt-
ful on Account of the Undulation of the Air &c. And this does not
differ 3" from the Hypothesis.

The agreement between the Hypothesis and the Observations
of this Star is the more to be reguarded, since it proves that the
Alteration of Declination, on account of the Precession of the Equi-
nox, is (as I before supposed) regular thro' all Parts of the Years;
so far at least, as not to occasion a Difference great enough to be
discovered with this Instrument. It likewise proves the other part
of my former Supposition, viz. that the annual Alteration of Decli-
nation in Stars near the Equinoctial Colure, is at this Time greater
than a Precession of 50" would occasion : for this Star was 20" more
Southerly in September 1728, than in September 1727, that is, about
2" more than it would have been, if the Precession was but 50".
But I may hereafter, perhaps, be better able to determine this Point,
from my Observations of those Stars that lie near the Equinoctial
Colure, at about the same Distance from the North Pole of the
Equator, and nearly opposite in right Ascension.

I think it needless to give you the Comparison between the
Hypothesis and the Observations of any more Stars ; since the Agree-
ment in the foregoing is a kind of Demonstration (whether it be
allowed that I have discovered the real Cause of the Phenomena or
not;) that the Hypothesis gives at least the true Law of the Varia-
tion of Declination in different Stars, with Respect to their differ-
ent Situations and Aspects with the Sun. And if this is the Case,
it must be granted, that the Parallax of the fixt Stars is much
smaller, than hath been hitherto supposed by those who have pre-
tended to deduce it from their Observations. I believe, that I may
venture to say, that in either of the two Stars, last mentioned, it
does not amount to 2". I am of Opinion, that if it were 1", I should
have perceived it, in the great number of Observations that I made
especially of v Draconis; which agreeing with the Hypothesis (with-
out allowing anything for Parallax) nearly as well when the Sun
was in Conjunction with, as in Opposition to, this Star, it seems
very probable that the Parallax of it is not so great as one single

284 THE MONIST.

Second ; and Consequently that it is above 400000 times farther from
us than the Sun.

There appearing therefore after all, no sensible Parallax in the
fixt Stars, the Anti-Co pernicans have still room on that Account,
to object against the Motion of the Earth; and they may have (if
they please) a much greater objection against the Hypothesis, by
which I have endeavoured to solve the fore-mentioned Phenomena;
by denying the progressive Motion of Light, as well as that of the
Earth.

But as I do not apprehend, that either of these Postulates will
be denied me by the Generality of the Astronomers and Philosophers
of the present Age; so I shall not doubt of obtaining their Assent
to the Consequences which I have deduced from them; if they are
such as have the Approbation of so great a Judge of them as Your-
self. I am

Sir, Your most Obedient

Humble Servant

J. BRADLEY.
POSTSCRIPT.

As to the Observations of Dr. Hook, I must own to you, that
before Mr. Molyneux's Instrument was erected, I had no small
opinion of their Correctness; the Length of his Telescope and the
Care he pretends to have taken in making them exact, having been
strong Inducements with me to think them so. And Since I have
been convinced both from Mr. Molyneux's Observations and my
own, that the Doctor's are really very far from being either exact
or agreeable to the Phenomena; I am greatly at a loss how to ac-
count for it. I cannot well conceive that an Instrument of the
Length of 36 Feet, constructed in the Manner he describes his,
could have been liable to an Error of near 30" (which was doubtless
the Case) if rectified with so much Care as he represents.

The Observations of Mr. Flamsteed of the different Distances
of the Pole Star from the Pole at different Times of the Year,
which were through Mistake looked upon by some as a Proof of the
annual Parallax of it, seem to have been made with much greater
Care than those of Dr. Hook. For though they do not all exactly
correspond with each other, yet from the whole Mr. Flamsteed con-
cluded that the Star was 35" 40" or 45" nearer the Pole in December
than in May or July : and according to my Hypothesis it ought to
appear 40" nearer in December than in June. The Agreement there-
fore of the Observations with the Hypothesis is greater than could

CRITICISMS AND DISCUSSIONS. 285

reasonably be expected, considering the Radius of the Instrument,
and the Manner in which it was constructed.

THE PRINCIPLE OF LEAST ACTION.*

REMARKS ON SOME PASSAGES IN MACHOS MECHANICS.

Ernst Mach in his Mechanics1 remarks,2 with reference to the
integral variational principles of Hamilton and of least action, that
other such principles are possible, which idea has been suggestive to
myselfy and, as I have obtained some results which throw light on
Mach's suggestions, I will try to describe the results here in not too
technical language.3

i.

We must first of all notice a slight historical inexactitude in
Mach's treatment of the principle of least action. "Maupertuis,"
we are told,* "enunciated, in 1747, a principle which he called lle
principe de la moindre quantite d 'action.' ''' Maupertuiss laid before
the Paris Academy on April 15, 1744, a memoir in which he ex-
plained the reflection and refraction of light by a hypothesis sub-
stituted for Fermat's principle of least time.6

Maupertuis, like a good follower of Newton, accepted the emis-
sion hypothesis of light, and, according to P. Stackel,7 the contra-

* Philip E. B. Jourdain, an English scholar who has devoted his life to
research in the line of modern logic, mathematics and pure mechanics, sub-
mits to us some remarks on Mach's Science of Mechanics. He is a devoted
and zealous student of Mach's works and is as familiar with them as a theo-
logian with his Bible. Being also well acquainted with the work of Georg
Cantor, Peano and Bertrand Russell he is especially fitted to explain the
theoretical aspect of pure mechanics. We are confident that his lucubrations
serve a good purpose and therefore deem it wise to submit them to specialists
by giving them space in our columns.

1 Die Mechanik in Hirer Entwickelung historisch-kritisch dargestellt, 4th
ed., Leipsic, 1901, pp. 395-413; Engl. transl. by T. J. McCormack under the
title The Science of Mechanics, a Critical and Historical Account of its Devel-
opment, 3d ed., Chicago, 1907, pp. 364-380. (This translation will be referred
to as Mechanics, and the above German edition as Mechanik.)

'Mechanik, pp. 399, 402, 413; Mechanics, pp. 368-369, 371-372, 380.

8 Cf. note on p. 78 of my paper "On the General Equations of Mechanics,"
Quarterly Journal of Mathematics, 1904, pp. 61-79.

* Mechanik, p. 395 ; Mechanics, p. 364.

* Cf . Mechanik, pp. 484-485 ; Mechanics, pp. 454-455.

6 Mechanik, pp. 454-457 ', Mechanics, pp. 422-425.

7 Encykl. der math. Wiss., IV, I, (1908), p. 49, note 125. Stackel wrongly
refers to the Berlin Mem., 1745, p. 276, for Maupertuis's application of the
principle of least action to the motion of light.

286 THE MONIST.

diction that Mach found in Maupertuis's application of the principle
of least action to the motion of light is due to Mach's mistaken sup-
position that Maupertuis worked on the basis of the undulatory
theory.

On Fermat's principle of least time and Maupertuis's principle
of least action, we will quote some passages from E. T. Whittaker's
lately published book, A History of the Theories of Aether and
Electricity from the Age of Descartes to the Close of the Nineteenth
Century.8

"Descartes's theory of light rapidly displaced the conceptions
which had held sway in the Middle Ages. The validity of his ex-
planation of refraction was, however, called in question by his
fellow-countryman Pierre de Fermat (b. 1601, d. 1665), and a
controversy ensued which was kept up by the Cartesians long after
the death of their master. Fermat^ eventually introduced a new
fundamental law, from which he proposed to deduce the paths of
rays of light. This was the celebrated Principle of Least Time,
enunciated I0in the form, 'Nature always acts by the shortest course.'
From it the law of reflection can readily be derived, since the path
described by light between a point on the incident ray and a point
on the reflected ray is the shortest possible consistent with the con-
dition of meeting the reflecting surfaces.11 In order to obtain the
law of refraction, Fermat assumed that 'the resistance of the media
is different/ and applied his 'method of maxima and minima' to
find the paths which would be described in the least time from a
point of one medium to a point of the other. In 1661 he arrived
at the solution.12 'The result of my work/ he writes, 'has been the
most extraordinary, the most unforeseen and the happiest, that ever
was; for, after having performed all the equations, multiplications,
antitheses and other operations of my method, and having finally
finished the problem, I have found that my principle gives exactly
and precisely the same proportion for the refractions which Monsieur

'London and Dublin, 1910, pp. 9-11, 102-103.

0 Renati Descartes Epistolae, Pars tertia; Amsterdam, 1683. The Fermat
correspondence is comprised in letters xxix to xlvi.

10 Epist. xlii, written at Toulouse in August, 1657, to Monsieur de la Cham-
bre; reprinted in (Euvres de Fermat (ed. 1891), Vol. II, p. 354.

"That reflected light follows the shortest path was no new result, for it
had been affirmed (and attributed to Hero of Alexandria) in the /ce^rfXcua
ruv ATTTIKUV of Heliodorus of Larissa, a work of which several editions were
published in the seventeenth century.

" Epist. xliii, written at Toulouse on Jan. i, 1662 ; reprinted in (Euvres de
Fermat, Vol. II, p. 457; Vol. I, pp. 170, 173.

CRITICISMS AND DISCUSSIONS. 287

Descartes has established.' His surprise was all the greater, as he
had supposed light to move more slowly in dense than in rare media,
whereas Descartes had (as will be evident from the demonstration
given above) been obliged to make the contrary supposition.

"Although Fermat's result was correct, and, indeed, of high
permanent interest, the principles from which it was derived were
metaphysical rather than physical in character, and consequently
were of little use for the purpose of framing a mechanical explana-
tion of light. Descartes's theory therefore held the field until the
publication in 1667*3 of the Micrographia of Robert Hooke (b. 1635,
d. 1703), one of the founders of the Royal Society, and at one time
its Secretary."

Further on, we read (p. 102) : " ---- the echoes of the old con-
troversy between Descartes and Fermat about the law of refraction
were awakened '* by Pierre Louis Moreau de Maupertuis (b. 1698,
d. 1759).

"It will be remembered that according to Descartes the velocity
of light is greatest in dense media, while according to Fermat the
propagation is swiftest in free ether. The arguments of the cor-
puscular theory convinced Maupertuis that on this particular point
Descartes was in the right; but nevertheless he wished to retain
for science the beautiful method by which Fermat had derived his
result. This he now proposed to do by modifying Fermat's prin-
ciple so as to make it agree with the corpuscular theory ; instead of
assuming that light follows the quickest path, he supposed that 'the
path described is that by which the quantity of action is the least';
and this action he defined to be proportional to the sum of the spaces
described, each multiplied by the velocity with which it is traversed.
Thus instead of Fermat's expression

(where t denotes time, v velocity, and ds an element of the path)
Maupertuis introduced

Jv.ds

as the quantity which is to assume its minimum value when the

path of integration is the actual path of light. Since Maupertuis's v,

which denotes the velocity according to the corpuscular theory, is

"The imprimatur of Viscount Brouncker, P.R.S., is dated Nov. 23, 1664.

14 Mem. de I'Acad., 1744, PP- 417-426 [or (Euvres de Mr. de Maupertuis, Vol.
IV, Lyons, 1756, pp. 3-18. To Maupertuis's work we will return on another
occasion].

288 THE MONIST.

proportional to the reciprocal of Fermat's v, which denotes the veloc-
ity according to the wave-theory, the two expressions are really
equivalent, and lead to the same law of refraction. Maupertuis's
memoir is, however, of great interest from the point of view of
dynamics ; for his suggestion was subsequently developed by himself
and by Euler and Lagrange into a general principle which covers

the whole range of nature, so far as nature is a dynamical system/'

* * *

In a memoir of 1746,Z5 Maupertuis extended his hypothesis
to all motions and called it the universal principle of rest and mo-
tion. By way of proving it, he derived the known laws of impact
of inelastic and elastic bodies, and of the lever ;l6 the motion of light
having been dealt with in the memoir of 1744. It is most important
to realize that, as A. Mayer1? pointed out, Euler's discovery, made
under the stimulus of the Bernoullis and published in the autumn
of 1744 in an appendix to his Methodus inveniendi, was independent
of Maupertuis, but that later on Euler's own tendency towards
metaphysical speculation and the influence of Maupertuis combined
to make Euler treat his principle in a less precise and more general
way.

ii.

Euler observed in 1744 that the differential equations of the
motion of a particle are given by the simple requirement that the
integral fv.ds, where for the velocity v is substituted its value
resulting from the principle of vis viva, and the integral is taken
between two positions of the particle, should be a minimum. Euler

15 "Les loix du mouvement et du repos deduites d'un principe metaphysique."
Mem. de VAcad. de Berlin, 1746, pp. 267-294. Vpss (Encykl. der math. Wiss.,
IV, i, p. 95, note 256) has 1745 as the date of this memoir. This memoir was
that analyzed by Mach (Mechanik, pp. 395-397; Mechanics, pp. 364-367). The
analogies that exist between the motion of masses and the motion of light,
which were noticed by Johann Bernoulli and by Mobius, were dealt with by
Mach (Mechanik, pp. 402-408, 410-413, 457-459; Mechanics, pp. 372-380, 425-
427). The principle of least action has been found very useful in optics, by
Laplace, for example, in the treatment of astronomical refractions; and the
mathematics of the theory of systems of rays built upon this one principle,
which was the earliest work of William Rowan Hamilton, were later (in 1834
and 1835) transferred by Hamilton to the general problem of dynamics. Cf.
P. Stackel, Encykl der math. Wiss., IV, i, 1908, pp. 489-493.

16 In a memoir called "Loi du repos des corps" (Mem. de I'Acad. de Paris,
1740, pp. 170-176; CEuvres, Vol. IV, pp. 45-63) Maupertuis remarked that the
work done when a final configuration of equilibrium is reached is generally
either a maximum or a minimum (see Mach, Mechanik, pp. 69-75 ; Mechanics,
pp. 68-73).

"Geschichte des Prinzips der kleinsten Aktion, Akademische Antritts-
vorlesung, Leipsic, 1877 ; cf. my notes in Ostwald's Klassiker, No. 167, pp. 31-37-

CRITICISMS AND DISCUSSIONS. 289

expressly emphasized, first, that his theorem only holds if the prin-
ciple of vis viva holds (and therefore cannot hold for motion in a
resisting medium), and, secondly, that we must express v in terms
of the attracting forces by quantities belonging to the orbit.18

Euler's work on this point was influenced adversely by his own
tendency toward metaphysical speculation and Maupertuis's dis-
covery— published some months before Euler's — of the obscure and
almost theological universal "principle of the least quantity of ac-
tion."1*

in.

Lagrange20 generalized Euler's theorem for the motion of any
system of masses in the following way:

Let mlt m2, mst. . . be masses which act upon one another in any
manner, and also, if we wish, move under the influence of any
central forces which are proportional to any functions of the dis-
tances; let slt s2, s3,. . . be the spaces which are described by these
masses in the time t, and let z\, vz, v3,. . . be their velocities at the
end of this time ; then21

Sw. §v.ds

is a maximum or minimum, and thus, by the principles of the cal-
culus of variations,

2m.f(Sv.ds + v.8ds) = 0 (1)

Lagrange eliminated the terms involving Sv by making use of
the equation

18Jacobi (see below), by direct generalization of Euler's theorem, reached
his theorem.

" The early history of the principle of least action is very fully dealt with
by me in my notes at the end of Ostwald's Klassiker der exakten Wissen-
schaften, No. 167.

""Application de la methode exposee dans le memoire precedent a la
solution de differents problemes de dynamique," Miscellanea Taurinensia for
1760 and 1761, Vol. II, pp. 196-298 ; (Euvres de Lagrange, Vol. I, pp. 365-468.
This memoir immediately followed Lagrange's first fundamental memoir on
the calculus of variations: "Essai d'une nouvelle methode pour determiner
les maxima et les minima des formules integrates indefinies," Misc. Taur.,
1760 and 1761 [published 1762], Vol. II, pp. 173-195; (Euvres, Vol. I, pp. 335-
362; Ostivald's Klassiker der exakten IVissenschaften, No. 47, pp.3~3O.

In Lagrange's first publication ("Recherches sur la methode de maximis
et minimis," Misc. Taur. for 1759, Vol. I; (Euvres, Vol. I, pp. 3-20), he an-
nounced (p. 15) his intention of deriving the whole of mechanics, by means
of the principle of the least quantity of action, from a method he had of in-
vestigating the maxima and minima of indefinite integral formulae.

a For convenience of printing, the suffixes to the 2, m, v, and s are here
omitted. Instead of the now more usual S Lagrange (see below) used S.

2QO THE MONIST.

2m.v.8v = SU ..................... (2)

got by varying (differentiating with 8) the equation of vis viva.

Thus the equation (1), in conjunction with the condition (2),
supposing that all the positions at the limits of the integral are given,
so that there the variations of the coordinates are zero,22 gives the
fundamental equation^

JSdm{ (d+Hdt)Bx + . . .! =0, • • (3)

where 118* + . . . = 8U,

and S is a sign of a definite integral which refers to the masses of
the system ; so that, if there are a finite number of masses m±, m2,
w3,.. .,

Sdm = 2m.

If there is an equation of condition <f> = 0 between the coordinates,
the equation 8<£ = 0 gives a relation between the 8*'s_, 83^5 and 8,2's
of (3) ; and then we can eliminate from (3) all of the variations
except a certain number which is the degree of freedom of the sys-
tem. If, then, we put the coefficient of every independent variation
equal to zero, we obtain the necessary number of differential equa-
tions for the solution of the problem.

An important point is that, as Holder2* remarked, Lagrange25
drew attention to the fact that, even when the expression for the
element of work is not a complete differential, and consequently
"8U" can only be regarded as an abbreviation, and not as a notation
for the variation of a force-function, that the formula (2), or

8T = 8U,

can be applied to get an extension of the principle of least action
even to non-conservative forces. This wider form was not treated
in Lagrange's later work in the Mecanique analytique on the prin-
ciple of least action.

Thus Mach26 is mistaken in stating that Lagrange "drew ex-
press attention to the fact that Euler's principle is applicable only
in cases in which the principle of vis viva holds." Euler had already
made this remark, and subsequently Jacobi strongly emphasized it;
but Lagrange, correctly, as we now know, first drew attention to

83 (Euvres, Vol. I, pp. 369-370.
*/«&, pp. 368, 406, 418, 435, 459-

84 Gott. Nachr., 1896, p. 136. In Ostwald's Klassiker, No. 167, last line on
p. 39, for "Helmholtz" read "Holder."

88 (Euvres, Vol. I, pp. 384-385.

86 Mechank, p. 401 ; Mechanics, p. 371.

CRITICISMS AND DISCUSSIONS.

the fact that the principle of least action, in the very general form
which he gave it, does not depend for its validity on that principle
of vis viva, which only follows from the general equations of mechan-
ics under special conditions.

There was no mention of this extension in Lagrange's later
works, and Hamilton, for example, only took from Lagrange the
narrower form of the principle of least action which was given in

the Mecanique.

* * *

Lagrange appears to have noticed that the integrand of (3), put
equal to zero, is an expression of d'Alembert's principle; and, in
that form, d'Alembert's principle is the fundamental formula of
Lagrange's analytical mechanics,27 and then the principle of least
action became, for Lagrange, merely a result of the laws of mechan-
ics, to be got by the integration of the simpler equation.

However, in the early memoir Lagrange had concluded from
his generalized principle of least action nearly all the great results
which later, in his Mecanique, he derived in another way; and so
Jacobi28 remarked that Lagrange's principle became the mother of
our whole analytical mechanics. 2$

87 D'Alembert's principle in combination with the principle of virtual dis-
placements appeared in the above variational form for the first time in a
prize essay of 1764 of Lagrange's on the libration of the moon (CEuvres, Vol.
VI, pp. 5-61) ; and then, more fully, in a memoir of 1780 (CEuvres, Vol. V., pp.
5-122).

The various editions of Lagrange's Mecanique are: Mecanique analitique,
Paris 1788, I vol.; second, greatly enlarged edition, Mecanique analytique,
Paris, Vol. I, 1811, Vol. II (posthumous), 1815; third edition, with notes by
J. Bertrand, 2 vols., Paris, 1853 and 1855 ; fourth edition, after the third, but
with additional notes by G. Darboux, in (Euvres de Lagrange, Vols. XI, and
XII, Paris, 1888 and 1889.

38 See Compt. Rend., Vol. V, 1837, pp. 61-67 (Ges. Werke, Vol. iy, .pp.
129-136) ; Vorlesungen uber Dynamik, gehalten an der Universit'dt zu Konigs-
berg im Winter semester 1842-1843 und nach einem von C. W. Borchardt
ausgearbeiteten Hefte herausgegeben von A. Clebsch, Berlin, 1866, p. 2 (2d
ed., revised by E. Lottner, in Jacobi's Ges. Werke, Supplementband). Cf. A.
Mayer, Geschichte des Prinzips der klcinsten Action, Leipsic, 1877, p. 26 (on
Mayer's errors see my notes in Ostwald's Klassiker, No. 167).

In this early memoir the problems treated by Lagrange were : the motion
of one body attracted by many fixed central forces ; general problem of many
attracting masses under any other forces; the finding of the orbits of two
attracting bodies with respect to a third; a body in a plane under forces and
drawing two other bodies by threads; a thread fixed at one end and charged
with as many heavy bodies as wished ; an inextensible thread, all the points being
under any forces; the same problem with an extensible and elastic thread;
motion of a body of any figure animated by any forces; laws of the motion
of non-elastic and elastic fluids.

28 However, Lagrange's method of multipliers (Mach, Mechanik, pp. 499-
500; Mechanics, p. 471) appeared first in the Mechanique analitique of 1788.

2Q2 THE MONIST.

After the publication of the Mecanique, the principle of least
action fell into the background of interest until Hamilton, in 1834,
showed that this principle had also a totally different title to our
consideration. The only really important contribution to the ex-
ceedingly interesting questions that rise a propos of the principle
of least action was an almost entirely neglected one made by Olinde
Rodrigues in 1816.

IV.

In Lagrange's derivation, the variation of v(=ds/dt) is not
carried out, but the terms m.v.8v are eliminated by the variational
equation obtained from the principle of vis viva. Thus it is not
necessary to decide whether t must be varied or not, whether we
must put

a d&s dscfct * dBs

OTJ = or Ov =

dt dt dt dt'

It is almost beyond doubt that Lagrange would have maintained
that the independent variable t was to be varied ;3° but Rodrigues
was the first explicitly to say that, in this case, t must be varied.

Lagrange had worked with a space integral f^m.v.ds, and had
only remarked, in a short addition to the section on the principle of
least action, made in the second edition of the Mecanique, that the
above space integral transforms into the time -integral fZT.dt,
where 2T is the vis viva (or, as we now say, double the kinetic
energy) of the system.^1 But Lagrange did not actually carry out
the calculation of the variation of this time-integral ; this was done
by Rodrigues.s2 Rodrigues, as E. J. Routhss .did later and appar-
ently independently, to find the variation of fT.dt under the con-
dition T = U + const, for the variation, so that 8T - 8U = 0, multi-
plied the left-hand side of this last equation of condition by an
undetermined factor, integrated it, added it to the variation of
fT.dt, put all equal to zero, and then determined the factor.

80 Cf. (Euvres, Vol. I, pp. 337, 345 ; and Ostwald's Klassiker, No. 167, p. 56.
"See Ostwald's Klassiker, No. 167, p. n.

M Correspondance sur I'Ecole polytech., Vol. Ill, 1816, pp. 159-162; German
translation, with notes on some errors of Rodrigues, in Ostwald's Klassiker,
No. 167, pp. 12-15, 41-42, 49-55-

"First in An Elementary Treatise on the Dynamics of a System of Rigid
Bodies, 3d ed., London, 1877, pp. 305-312, 560-562. This passage coincides in
essentials with The Advanced Part [Part II] of a Treatise on the Dynamics
of a System of Rigid Bodies, 6th ed., London, 1905, pp. 301-309.

CRITICISMS AND DISCUSSIONS. 2Q3

V.

The question as to whether the independent variable should be
varied in the calculus of variations is of great importance to our
conception of this calculus. According to Mach, 34 the first satis-
factory explanation of the meaning of the process of variation used
in this calculus was given by J. H. Jellett.35 The value of the
function y = <f>(x) can vary by an (infinitesimal) increment dx of
the independent variable, when we obtain the differential

or by the varying of the form </> of the function without x varying,
so that <f>(x) becomes

^(^(K^+oAOO,

where \f/ is an arbitrary function and c is, for the definition of an
infinitesimal variation, an infinitely small positive number. Then
the variation of y is defined by

*y = *i (*)-*(*).

Thus, if we keep, as is convenient, the term "variation" to denote
alterations of value brought about by alteration of the form alone
of the function, we see that the independent variable is unaffected by
our process of variation. On the other hand, Lagrange, as we have
seen, held that the independent variable also was to be affected
by the 8 of the calculus of variations. Indeed, his claim that his
method was more general than that of Euler rested partly on this
ground. But other mathematicians appear mostly to have accepted
that conception of a variation which Euler gave in a later memoir
on Lagrange's method, that a "variation" of a function is brought
about by a change in value of the constants occurring in that function.
Thus, Jacobi, in his Vorlesungen uber Dynamik?6 stated that the
variations 8q of the generalized coordinates q contain merely the
changes in value of the #'s which arise from changes in value of
the arbitrary constants occurring in the q's. Accordingly, he main-
tained37 that the independent variable is not to be "varied," so that
Bt = 0.38

"Mechanik, pp. 468-474; Mechanics, pp. 437-443.

85 An Elementary Treatise on the Calculus of Variations, Dublin, 1850, pp.
i, 5-6. Cf. A. Kneser, Lehrbuch der Variationsrechnung, Brunswick, 1900, pp.
1-2.

88 Werke, Supplementband, p. 145.

87 Ibid., pp. 50, 59, 146, 149.

88 Cf. similar views on the nature of a "variation" with Euler, Lagrange,
Lacroix, G. W. Strauch, M. Ohm, Cauchy, and Stegmann in I. Todhunter's

294 THE MONIST.

So Jacobi, in his Vorlesungen uber Dynamik^ stated that, in
the action integral f'Sm.v.ds, the time must be eliminated by the
principle of vis viva, and all be reduced to space-elements. This,
as Mayer remarked in his tract of 1877, was required by Euler in
the case considered by him. Thus JacobiV0 formulation of the
principle of least action was: If two positions of the system are
given (that is to say, if we know the values which, for x = a and
# = &, the remaining Zn-\ coordinates receive), and we extend the
integral

2w . ds2

to the whole path of the system from the first position to the second,
then its value is a minimum for the actual path as compared with all
possible (consistent with the conditions, if there be any, of the
system) paths.41

Mayer, in his tract of 1877,*2 accepted Jacobi's view that 8t = 0
and consequently that, by means of the principle of vis viva, we
must reduce all the quantities in the integrand to quantities which
refer to the path of the system ; and that the theorem of least action
without this condition is quite meaningless. Since Lagrange did
not eliminate the time, Mayer*3 concluded that Lagrange's theorem
was meaningless, and what Lagrange really meant by his theorem
was what is known as Hamilton's principle. This view had been
previously maintained by M. Ostrogradski.44

But, in a memoir of 1886 on the general theorems of the cal-
culus of variations which correspond to the two forms of the prin-
ciple of least action in dynamics, Mayer*s remarked, on the variation

work A History of the Progress of the Calculus of Variations During the
Nineteenth Century, Cambridge and London, 1861, pp. 2, 8, II, 13, 17-20, 31,
377, 378, 402, 413, 480-481.

89 Werke, Supplementband, p. 44 ; Ostwald's Klassiker, No. 167, p. 17 (on
pp. 16-26 is a reprint of Jacobi's sixth and part of his seventh lecture, which
relate to the principle of least action).

40 Werke, Supplementband, p. 45 ; Ostwald's Klassiker, No. 167, p. 18 (cf.
the note on p. 55).

"On the limitations to the minimum-condition, which were pointed out
by Jacobi (cf. Mach, Mechanik, p. 401; Mechanics, p. 371) see Werke, Suppl,
pp. 45-49; Klassiker, No. 167, pp. 18-22, 58.

41 See p. 24, and Klassiker, No. 167, p. 57.
48 Op. cit., p. 27.

"Klassiker, No. 167, pp. 57-58.

""Die beiden allgemeinen Satze der Variationsrechnung, welche den
beiden Formen des Prinzips der kleinsten Aktion in der Dynamik entsprechen,"
Berichte der math.-phys. Classe der K'on. Sachs. Ges. der Wiss. zu Leipzig,
Sitzung am 14. November 1886, Vol. XXXyill, pp. 343-355- The first person
correctly to show the importance of Rodrigues's memoir was Th. Sloudsky

CRITICISMS AND DISCUSSIONS. 295

of t with Rodrigues : "Now, from the point of view of dynamics, in
which we only permit variations from the instantaneous position
of the system under consideration, that is so very unusual that I did
not think at all of this possibility in my earlier work. But as soon
as we neglect a purely dynamical signification (Deutung), and vary,
not only the coordinates, but also the time, immediately that point
which always caused the greatest doubts in Lagrange's derivation
becomes clear. It is explained, namely, how the equation of vis viva,
if it is prescribed as an equation of condition, can yet leave the
variations of the coordinates quite unlimited/6 and we see then that
Jacobi's assertion that we must necessarily eliminate the time from
the action-integral by means of the theorem of vis viva is not so;
that, besides Jacobi's principle, there is a second, equally justified
form of the principle of least action ; and that it is this second form,
and not Hamilton's principle inaccurately formulated, which La-
grange proved correctly, though certainly not with his usual clear-
ness.

We may here remark that Routh,*? from 1877 onwards and
apparently independently of Rodrigues, also varied tf "by the funda-
mental theorem in the calculus of variations," and derived the prin-
ciple of least action as Rodrigues did.

If Ms to be varied, we must regard it, according to the con-
ception of a "variation" derived from Jellett, as a function of an-
other variable, 0, so that BO = 0 but 8t is not zero in general. This
was done explicitly by Helmholtz*8 in 1887.

Helmholtz also stated the view that Hamilton's principle is a
form of Lagrange's principle. The grounds for this view are, as
I showed in 1908,49 more clearly evidenced in an identity established
by Rethy under certain restrictions.

VI.

We have dealt with the question as to the relation of the prin-
ciple of least action to Hamilton's principle, and we have seen how
Lagrange, by working with a form which only contained the time
through the velocities, and in which the variations of the velocities

(1866) ; Bertrand, in his notes on Lagrange's Mtcanique, mentioned Rodrigues,
but put S(dq/dt) =d8q/dt.

** Cf. Klassiker, No. 167, pp. 43-44.

47 Cf. ibid., pp. 50-51.

*""Zur Geschichte des Prinzips der kleinsten Aktion," Sitzungsber. der
Berliner Akad., Sitzung vom 10. Marz 1887, pp. 225-236; Wiss. Abh., Vol. Ill,
pp. 249-263.

"Math. Ann., Vol. LXV, pp. 514-516.

296 THE MONIST.

could be at once eliminated by means of the varied equation of vis
viva, allowed it to remain doubtful whether t was to be varied in
the principle of least action, or not. We have seen how this question
has given rise to discussions and misunderstandings which are con-
nected with the principle of the calculus of variations, in the works
of Rodrigues, Jacobi, Ostrogradski, Routh, Mayer, Sloudsky, Ber-
trand, Helmholtz, and Rethy. We have seen, finally, that Lagrange
had attained to a very general formulation of the principle of least
action, in which the equation of vis viva does not hold, a force-func-
tion does not exist, and the equations of condition may depend ex-
plicitly on the time. Thus Lagrange's principle is far more general
than Jacobi's.

Of late years, the occurrence of differential and non-integrable
equations among the equations of condition of a problem has as-
sumed great importance. This happens in certain cases of rolling
motion, and systems with such equations of condition were called
by Hertz non-holonomous. The question arises as to whether the
principle of least action and Hamilton's principle can be so formu-
lated as to apply to non-holonomous systems. We shall see that
Otto Holder first succeeded in formulating extended forms of both
principles which were completely equivalent to d'Alembert's prin-
ciple. There were, of course, several points ' not dealt with by
Holder on which it was essential to be quite clear. Thus, the pro-
cess of "variation" used by Holder was not always the one to which
we are accustomed in the calculus of variations, and the transforma-
tion of the principles from rectangular coordinates — which alone
were used by Holder — to more general coordinates gives rise to
interesting questions. However, it seems to me that we have now-
reached a certain degree of finality in all these subjects, and we will
now present the researches whose object was to extend the prin-
ciples, in their proper order, and, where necessary, comment on
them.

VII.

The question as to the extent of the variational principles be-
gins with the publication, in 1894, of Heinrich Hertz's posthumous
Prinzipien der Mechanik.*0 "The application of Hamilton's prin-

80 Gesammelte Werke von Heinrich Hertz, Vol. Ill, Die Prinzipien der
Mechanik in neuem Zusammenhange dargestellt (edited by Ph. Lenard, with
a preface by H. von Helmholtz), Leipsic, 1894; English translation by D. E.
Jones and J. T. Walley under the title The Principles of Mechanics, London,
1899-

CRITICISMS AND DISCUSSIONS.

ciple," said Hertz^1 "to a material system does not exclude fixed
connections between the coordinates chosen, but it requires that these
connections can be exposed mathematically by means of finite equa-
tions between the coordinates ; it does not permit of such connections
as can be expressed only by differential equations. But nature itself
appears not simply to exclude connections of the latter kind; for
they occur if, for example, three-dimensional bodies roll upon one
another without slipping."

Hertzs* called a material system holonomous if between possible
positions all thinkable continuous passages are also possible. The
name was chosen to indicate that such a system is subject to integral
(oAos) laws (voVos), while material systems in general are subject
only to differential laws. If the differential equations of condition
of a material system can all be integrated, the coordinates of every
possible position must satisfy the finite equations. The differences
between the coordinates of two neighboring positions therefore
satisfy an equal number of homogeneous linear differential equa-
tions, and, since these latter cannot contradict the given differential
equations (in equal number) of the system, they satisfy the latter
too. Thus the displacement between any two possible positions
is a possible displacement, and thus the system is holonomous. In-
versely, if the system is holonomous, its differential equations of
condition allow an equal number of finite or integral equations be-
tween the coordinates themselves.

VIII.

Here we may digress to remark that the fact that cases of
rolling motion give rise to equations of condition which are not
integrable was observed by Routh, Ferrers (1873), and C. Neu-
mann (1888). 53 The usual form of Lagrange's equations then fails.
Of the extensions, what I have called, in the paper just quoted,
"Routh's form" is the most important form for our present pur-
poses. It involves Lagrange's multipliers, and is the only form of
equation valid for non-holonomous systems which can be got di-
rectly by development of one of the integral variational principles.
In deducing equations of motion from, say, Hamilton's principle,

61 Werke, Vol. Ill, pp. 22-25 ; Principles, pp. 19-21.

M Werke, Vol. Ill, articles 123, 132, and 133 (pp. 91, 95, and 96) ^Prin-
ciples, pp. 80, 84-85.

"* Cf. the note on p. 63 of my paper "On the General Equations of Mechan-
ics," Quart. Journ. of Math., 1904, pp. 61-79. Cf. the bibliography in P. Ap-
pell's little book on Les mouvements de roulement en dynamique, Paris, 1899.

298 THE MONIST.

we so to speak divide the material system into a holonomous and
a non-holonomous part. Suppose there are 3n rectangular -co-
ordinates of the system, k finite equations of condition between
these coordinates and the time, and / non-integrable equations of
condition. We form our integral for a system with 3n-k degrees
of freedom and then eliminate the / superfluous coordinates by La-
grange's method.

IX.

An important paper on the differential equations of mechanics
was written by A. VossS4 in 1884 and published in 1885. In this
paper, the equations of condition were used in their differential
form, and were not assumed to be integrable, although the problems
of rolling motion which caused such equations to be considered were
not mentioned. The part which especially concerns us here is where
Voss uses Hamilton's principle for the introduction of more general
coordinates. He saysss that, with non-integrable equations of condi-
tion, "the transformation can no longer be reduced to a problem
of variations properly so called, but the property of the system of
differential equations of condition of being a complete one forms
the necessary and sufficient condition for this."

x.

Hertz decided that his own fundamental law56 holds both for
holonomous and non-holonomous systems, and that from this law
result the principle of least actions? and Hamilton's principles8 only
under a limitation to holonomous systems. But this contradicts the
general conviction^ that Hamilton's principle is merely a trans-
formation of d'Alembert's principle, and that the latter holds gen-
erally, and is equivalent to Hertz's law.60 Thus arose the questions
as to whether the usual derivation of Hamilton's principle from that
of d'Alembert requires any limiting supposition. This question was
the origin of the researches of Otho Holder.61 The very kernel of

""Ueber die Differentialgleichungen der Mechanik," Math. Ann.. Vol.
XXV, 1885, pp. 258-286.

"Ibid., pp. 263-264.

" Werke, Vol. Ill, art. 309, p. 162 ; Principles, p. 144.

"Werke, Vol. Ill, arts. 347-356, pp. 174-176; Principles, pp. 155-157.

** Werke, Vol. Ill, arts. 358-362, p. 177; Principles, pp. 158-159.

69 See, for example, Mach, Mechanik, pp. 413-414 ; Mechanics, p. 381.

* Werke, Vol. Ill, art. 394, p. 186; Principles, p. 166.

""Ueber die Principien von Hamilton und Maupertuis," Nachr. von der
konigl Ges. der Wiss. zu Gottingen, Math. phys. Klasse, 1896, pp. 122-157.

CRITICISMS AND DISCUSSIONS. 2QQ

Holder's work is his conception of the "variation of the motion of
a system;" this it was which allowed him to give such a wide ex-
tension to the principles of least action and of Hamilton, so that the
reply to the above question is: If d'Alembert's principle holds gen-
erally, so also must that of Hamilton, in its completest form ; but
if we choose Hertz's view that the varied path be a possible one,
we get the limitation denoted by him. Holder's conception of a
varied motion is, then, paradoxical in so far that this "motion" need
not be a possible one, — need not satisfy the equations of condition.
It is, in Holder's own words, only a mathematical auxiliary con-
ception.

With Hertz, Holder understood by "the position of a system"
the totality of the positions of the material points of the system;
the motion consists in a continuous sequence of positions of the
system, which are passed through in a definite way with the time.
To vary this original motion, we first give every system-position
a small displacement, so that a new continuous sequence of positions
arises. If the original sequence gives one position twice, we have
two positions covering one another which can naturally be displaced
in different manners. The starting position A and the final position
B are to be fixed, and we refer each position on the varied path to
one on the actual path. This correspondence is necessary in order
that we may put the variation of an integral taken along the original
path equal to the integral of the varied elements. We coordinate
the identical initial positions to one another, and similarly with the
two final positions.

If we imagine both the actual62 and the fictitious motion to begin
simultaneously at A, then the systems need not arrive at B simul-
taneously. In this case the corresponding positions on the two paths
cannot all be passed simultaneously, and if the passage from an
actual position to the corresponding position on the fictitious path
be denoted by 8, so that, if the position P is actually reached at the
time t, the corresponding position P + 8P is reached at the time
t + Bt and 8(dt) = d(8t).

Now, in the most general manner of variation of the motion,
we can still choose the velocity at each point of the varied path.
This must be infinitely little different from the velocity at the cor-
responding position of the actual path, but is otherwise arbitrary.

Holder then found the expression for 8T in rectangular coordi-

MThus it is assumed that the mechanical problem has one solution and
one only.

3OO THE MONIST.

nates, t and dt being affected by the 8-process, integrated the identity
for 8T from t0 to f± (the times when the system, in the actual motion,
is at A and B respectively), and integrated by parts. Thus, two
parts are obtained: one integrated, which vanishes, since the varia-
tions of the coordinates at A and B vanish ; and the other uninte-
grated, and we see by d'Alembert's principle, that the integrand
of the last integral can be put equal to 8U where, as before, "8U"
only denotes the variation of a force function U in special cases —
provided that the variations of the coordinates represent virtual
displacements of the system.6^ Thus Holder obtained the result
that, where the 8-process is a process of giving every position P
between A and B a virtual displacement to P+8P, and the aggregate
of positions P+8P is conceived as a fictitious path, then the equation

/{2T.<*8f + (8T + 8U)df) =0, (4)

where the integral is to be taken between the limits t0 and tlt is
equivalent to d'Alembert's principle.

We cannot too strongly emphasize the nature of this varied path
of the system. It is not necessarily a path that the system, however
constrained, could take ; that is to say, the connections of the system
might have to be distorted from point to point. The displacement
8P must be virtual at the instant t, but the position P + 8P is
"reached" by the system, supposed to "move" on a fictitious path
in a perhaps impossible way, at the, in general different, time
t + 8t. In fact, the fictitious path is only a possible one, of course
under new constraints, if the equations of the condition are inde-
pendent of the time, and the system is holonomous.

This fictitious motion is a useful conception because it enables
us to see exactly why Hertz, for example, rather naturally limited
the scope of the principle of least action and Hamilton's principle to
holonomous systems ; and also it allows us to formulate these prin-
ciples in a perfectly general manner. That the conception of a
"variation" is not that of the calculus of variations did not escape
Holder. "At the first glance," he wrote,6* "the conception is perhaps
peculiar; and it has been already said to me that I have no problem
of variation properly so called. But that does not concern me. I
am only concerned with giving a clear signification to the variations
of the coordinates and the time which at the same time is such that

"That is to say, displacements consistent with the equations of condition
and possible, at the instant considered. Cf., for example, Mach, Mechanik, p.
58 ; Mechanics, pp. 49, 56.

84 In a letter to me of Jan. 15, 1904; cf. Quart. Journ. of Math., 1904, p. 75,
last note.

CRITICISMS AND DISCUSSIONS. 30!

the principles hold as generally as is possible." In conformity with
this, Holder spoke of an "altered" (abgednderte) instead of a
"varied" motion.

In the above general principle, we can, without detracting
from the equivalence to d'Alembert's principle, specialize the varia-
tions. Two ways at once suggest themselves:

(1) We may determine that corresponding positions are to be
passed at the same instant, so that 8t = 0, then (4) becomes a gen-
eralized Hamilton's principle;

(2) We may determine the velocity at each point of the varied
path by fixing that 8T = 8U, the variation of the time being, of
course, not zero ; that is to say, using a more restricted phraseology
for this wider case, the total energy is constant in a variation ; then
(4) gives the principle of least action in its most extended form.

XI.

There is one rather important point upon which Holder only
touched very briefly. I mean the introduction of other more general
coordinates into the development of equations of motion from the
above principles. Voss attempted to do this in 1900, but, as I have
shown, 6s he used a method previously used by Routh and Rethy,
which preserved the strictly variational character of the 8-process
used even when the equations of condition depend explicitly on the
time. Thus Voss unintentionally abandoned Holder's 8-process.
The application of Holder's process to the formulation of the prin-
ciples in general coordinates was first carried out by myself in the
above cited paper of 1904, and more clearly in a paper of 1908.66
Mathematically speaking, this formulation is not quite so simple
as some might suppose ; but here we are only concerned with the
advantages of Holder's 8-process over the strictly variational process
in the formulation of the principle of least action and Hamilton's
principle. The abandonment of the strict conception of a variation
may appear to be a disadvantage. But surely this is compensated
by greater simplicity ; while, in my case, when we come to deal with
non-holonomous systems we must abandon this strict conception,
as was pointed out — we have seen above — by Voss in 1884 and by
others later in somewhat different forms. 6? Further, unless the

"Math. Ann., Vol. LXV, 1908, pp. 517-525.
"Math. Ann., Vol. LXV, 1908, pp. 525-527.

67 C. Neumann (1888), Hertz (1894), Holder (1896), and Appell (1898);
see also Boltzmann, Vorlesungen iiber die Prinzipe der Mechanik, Teil II,
Leipsic, 1904, pp. 30-34.

3O2 THE MONIST.

equations of condition do not contain the time explicitly, the form
of Rethy and Voss requires a condition holding for St at the limits
of integration, whereas in Holder's generalized principle of least
action no such condition is required.

XII.

As we have said at the beginning, Mach has stated, with ref-
erence to the principles of least action and Hamilton, that other
such principles are possible. In this connection there are two in-
vestigations to which we must refer. The first was by Voss68 in
1901, and was inspired by Holder's work. Voss remarked that if
not only the coordinates, but also the time is varied in the most
general manner, 8t can always be determined subsequently so that
if we put the variation of the integral of any function of the co-
ordinates and velocities equal to zero, we get the equation of mo-
tion. The second was an attempt by myself6^ to solve the problem
suggested by Mach, by determining all the possible integral varia-
tional principles. For this purpose I inquired what was the most
general form of the integrand in order that the principle obtained
hence should be equivalent to Routh's extension of Lagrange's
equations. The result was to find that Holder's principle (4) was
the most general of its kind, and, as Holder had remarked, his
principle may be specialized into Hamilton's principle or the prin-
ciple of least action. These two principles are, in fact, two special
cases out of the manifold of the principles equivalent to d'Alem-
bert's principle and derivable from (4) by determining St generally
in all possible ways.

But there is another aspect of the matter. We have taken La-
grange's equations, or rather Routh's extension of them, as funda-
mental. But there are other forms of the equations of mechanics
involving other quantities than Lagrange's T and U, and which
sometimes present advantages over Lagrange's.?0 From these other
equations we can derive?1 other variational principles not contained
in Holder's form (4), but since the functions in the integrand now
involve differential coefficients with respect to t of the second

88 "Bemerkungen iiber die Prinzipien der Mechanik," Sitzber. der math.-
phys. Klasse der k. Bayer. Akad. der Wiss. zu Munchen, Vol. XXXI, 1901, pp.
167-182, especially pp. 171-175; Encykl der math. Wiss., IV, i, 1901, p. 94.

M Quart. Journ. of Math., 1904, pp. 76-78.

70 Cf. my paper on "Alternative Forms of the Equations of Mechanics/'
in the Quart. Journ. of Math., 1905, pp. 284-296.

n Cf. Ibid., pp. 290-295.

CRITICISMS AND DISCUSSIONS. 303

order, we must determine the varied path so that not only the
variations Sq but also the differentials d8q of these variations vanish
at the limits of integration. Analogous conditions as to the paths
arise, if the integrand contains higher differential coefficients than
the second.

XIII.

A curious result,72 by the way, is that if we vary the integral
of action f2T.dt, so that &tr means, as with Holder, a virtual dis-
placement of x, and vary t, we get exactly the same result as if we
had not varied t either in T or in dt: the extra terms we get from
varying t happen to cancel one another. Hence the faulty deriva-
tion, which we sometimes see, of Hamilton's principle from the
principle of least action leads to correct results. This derivation
is : Since 8T = 8U, we have

It should be noticed that the extra terms above referred to cancel
even if the equations of condition contain the time explicitly. Fur-
ther, we have seen that the identification maintained by Helmholtz
and Rethy of Hamilton's principle with the principle of least action
depended on the equations of condition not containing the time ex-
plicitly ; and that the other identifications were based on misunder-
standings. Finally, we have seen how in Holder's other work, the
true relation of the principles became clear, and how, at the same
time, the principle became generalized.

XIV.

This sketch of the development and gradual generalization of
a small part of the theory of mechanics gives us food for meditation.
It seems to be necessary, in order that it may be possible to state the
principles in question quite generally, to make use of a paradoxical
conception — the conception of a generalized, fictitious "motion." It
would be easy to say that the principles are, by the laws of logic,
valid only under certain conditions ; hence the paradox when we
attempt to widen those conditions. But the paradox is not logical ;
it is merely verbal. We speak of a fictitious "path" and "motion"
merely for the sake of picturesqueness : a mathematician no more
means to imply the existence, in a mystical region of thought, of an
impossible and fictitious path or motion, than he means to imply
anything more than striking analogies of expression when he speaks,

n Quart. Journ. of Math., 1904, pp. 78-79.

304 THE MONIST.

in analytical geometry, of "imaginary intersections" or "circular
points at infinity." No philosopher wishes to confute a mathemati-
cian because, in his technical language, the mathematician may
assert that some "real" numbers are not "rational."

PHILIP E. B. JOURDAIN.
THE LODGE, GIRTON, CAMBRIDGE, ENGLAND.

NOTES ON THE CONSTRUCTION OF MAGIC SQUARES

OF ORDERS IN WHICH H IS OF THE GENERAL FORM 4/M-2.

It is well known that magic squares of the above orders, i. e.,
62, 102, 142, 182, etc., cannot be made perfectly pandiagonal and ornate
with the natural series of numbers.

Dr. C. Planck has however pointed out that this disability is
purely arithmetical, seeing that these magics can be readily con-
structed as perfect and ornate as any others with a properly selected
series of numbers.

In all of these squares n is of the general form 4p + 2, but they
can be divided into two classes :

Class I. Where n is of the form 8/> - 2, as 62, 142, 222 etc.

Class II. Where n is of the form Sp + 2, as 102, 182, 262 etc.

The series for all magics of Class I may be derived by making
a square of the natural series 1 to (w+1)2 and discarding the numbers
in the middle row and column.

Thus, for a 62 magic the series will be:

1 2 3 - - 5 6 7
8 9 10 -- 12 13 14
15 16 17 - - 19 20 21

29 30 31 — 33 34 35
36 37 38 -- 40 41 42
43 44 45 — 47 48 49

The series for all magics of Class II may be made by writing
a square of the natural numbers 1 to (n+3)2 and discarding the
numbers in the three middle rows and columns. The series for a
102 magic, for example, will be:

CRITICISMS AND DISCUSSIONS. 305

1 2 3 4 5 ... 9 10 11 12 13

14 15 16 17 18 ... 22 23 24 25 26

27 28 29 30 31 ... 35 36 37 38 39

40 41 42 43 44 ... 48 49 50 51 52

53 54 55 56 57 61 62 63 64 65

105 106 107 108 109 ... 113 114 115 116 117

118 119 120 121 122 ... 126 127 128 129 130

131 132 133 134 135 ... 139 140 141 142 143

144 145 146 147 148 ... 152 153 154 155 156

157 158 159 160 161 ... 165 166 167 168 169

By using series as above described, pandiagonal magics with
double-ply properties, or associated magics may be readily made
either by the La Hireian method with magic rectangles, or by the
path method as developed by Dr. C. Planck.

Referring now to the La Hireian method and using the 6*
magic as a first example, the rectangles required for making the
two auxiliary squares will necessarily be 2x3, and the numbers used
therein will be those commonly employed for squares of the seventh
order, i. e., (6+1 )2, with the middle numbers omitted thus:
123 — 567
0 7 14 28 35 42

It may be shown that a magic rectangle having an odd number
of cells in one side, and an even number of cells in the other side
is impossible with consecutive numbers, but with a series made as
above it can be constructed without any difficulty, as shown in
Figs. 1 and 2.

Two auxiliary squares may now be made by filling them with
their respective rectangles. If this is done without forethought,
a plain pandiagonal magic of the sixth order may result, but if
attention is given to ornate qualities in the two auxiliaries, these
features will naturally be carried into the final square. For example,

306

THE MONIST.

by the arrangement of rectangles shown in Figs. 3 and 4 both auxil-
iaries are made magic in their six rows, six columns and twelve

Fig. 2.

0

42

0

42

0

**

3S

7

Jf

7

3S

7

zs

'4-

Zf

'4

z$

/4

0

42

O

4-2

o

4-2

3f

7

3$

7

3S

7

2<?

'4

2S

/*

2<?

'4

Fig. 4.

7

z

3

3

Z

7

/

6

<r

S

6

/

7

z

3

3

z

7

/

6

cT

&

6

/

7

Z

3

3

z

7

/

6

&

<?

6

/

Fig. 6.

7

z

6

7

z

3

/

6

<?

/

6

s

7

Z

3

7

z

3

/

6

f

/

6

&

7

2

J

7

2

<3

/

6

S

/

6

&

Fig. 3-

7

44

3

49

Z

4$

s^~~\

(36

\^ J

/3

40

/"~"\

* }

\^ ^/

4/

/Z

3S

/6

3/

Z/

30

'7

/~^
\^S

43

&

s^~\
%£

6

*7

42

3

3#

/4

*7

/o

'f ^\
&

ZO

33

r A
<*)

34

/&

Fig. 5-

o

42

0

^2

O

42

33T

7

35

7

35

7

ZS

/4

zs

'4

ZS

/^

2S

'*-

2#

'&

Z8

/^

3S

7

3S

7

3S

7

O

/+2

O

42

0

4.Z

Fig. 7-

diagonals, and they are also 4-ply and 9-ply. Their .complementary
couplets are also harmoniously connected throughout in steps of

CRITICISMS AND DISCUSSIONS.

307

3, 3. These ornate features are therefore transmitted into the fin-
ished 62 magic shown in Fig. 5. If it is desired to make this square
associated, that is with its complementary couplets evenly balanced
around its center, it is only necessary to introduce the feature of
association into the two auxiliary squares by a rearrangement of
their magic rectangles as shown in Figs. 6, 7 and 8, the last figure
being a pandiagonal associated magic.

36

42

/J

/6

20

'7

/o

4?

4'

34

8

Z/

Fig. 8.

The next larger square of Class I is 142, and it can be made
with the natural series 1 to (14-fl)2 arranged in a square, discard-
ing, as before, all the numbers in the central row and column.

The rectangles for this square will necessarily be 2x7 and the
numbers written therein will be those ordinarily used for a square
of the fifteenth order, (14+1)2, with the middle numbers omitted,
thus:

1234567 —
0 15 30 45 60 75 90 —

9 10 11 12 13 14 15
120 135 150 165 180 195 210

AT

Z

6

/Z

//

6

7

z/o

/s

30

/6e5T

/tt

/s-

90

/

/4

/3

4

JT

/o

&

o

/&s

/so

4&

60

/3S

/£0

Fig. 9-

Fig. 10.

Simple forms of magic rectangles for the auxiliaries are shown
in Figs. 9 and 10, but many other arrangements of the couplets will
work equally well.

The smallest magic of Class II is 102, the series for which is
given below. The rectangles used for filling the two auxiliaries of
this square are 2x5, and they can be made with the numbers which

308

THE MONIST.

would be commonly used for a square of the thirteenth order (10+3)a
omitting the three middle numbers in each row thus :

1 2 3 4 5 ... 9 10 11 12 13
0 13 26 39 52 ... 104 117 130 143 156
Figs. 11 and 12 show these two rectangles with a simple ar-
rangement of the numbers. The two auxiliaries and the finished 102

/J

2

//

<£

cT

/

/2

3

/o

3

/S6

/3

/30

39

<?£

O

/4$

26

"7

/04

Fig. ii.

Fig. 12.

magic are given in Figs. 13, 14 and 15. Fig. 15 is magic in its
ten rows, ten columns and twenty diagonals. It is also 4-ply and
25-ply. Like the 62 magic, this square can also be associated by
changing the disposition of the magic rectangles in the auxiliaries.

/J

/3

/2

/2

/ 2

/2

/2

/o

/o

/o

/o

S

S

S

/J

/2

/ 2

Z

/ 2

/Z

/O

/O

/o

/o

/o

Fig. 13.

The above examples will suffice to explain the general con-
struction of these squares by the La Hireian method with magic
rectangles. It may however be stated that although the series pre-
viously described for use in building these squares include the lower
numerical values, there are other series of higher numbers which
will produce equivalent magic results.

CRITICISMS AND DISCUSSIONS.

309

0

O

0

/3

/J

26

/SO

26

/SO

26

/SO

"7

"7

"7

"7

"7

SZ

o

0

0

O

/s6

o

/3

/3

'3

26

26

/SO

26

/so

26

/SO

"7

"7

"

7

39

"

7

sz

JZ

52

SZ

soy

Fig. 14.

/6o

/6s

/<$

22

39

3/

2$

30

S3S

//S

/ZO

40

/za

*?

"

7

//s

s6

63

/s

7

/z

/se

/o

/s

7

Z6

24

27

Z9

3*

S33

36

S39

/3O

S22

sz

sv

6z

S3

Fig. 15.

6/

3io

THE MONIST.

The following table illustrates another rule covering the selec-
tion of numbers for all magic squares of these orders.

ORDER
OF
SQUARE

NATURAL SERIES

DISCARDING NUMBERS IN

6th

1 to ( 6+1)2

the middle row and column.

10th

1 to ( 10+3) 2

the 3 middle rows and columns.

14th

1 to(14+5)2

the 5 middle rows and columns.

18th

1 to(18+7)2

the 7 middle rows and columns.

22nd

1 to (22+9) 2

the 9 middle rows and columns.

26th

1 to (26+1 1)2

the 11 middle rows and columns.

and so forth.

numbers of the natural series (

These figures show that this rule is equivalent to taking the

V n-4

) and omitting the central ^

rows and columns. In comparing the above with the rules pre-
viously given, for which we are indebted to Dr. C. Planck, it will
be seen that in cases of magics larger than 102 it involves the use of
unnecessarily large numbers.

The numerical values of the ply properties of these squares
are naturally governed by the dimensions of the magic rectangles
used in their construction. Thus the rectangle of the 62 magic
(Fig. 5) is 2x3, and this square is 22-ply and 32-ply. The rectangle
of the 102 magic being 2x5, the square may be made 22-ply and
52-ply, and so forth.

The formation of these squares by the Path method which has
been so ably developed by Dr. C. Planck,1 may now be considered.
The first step is to rearrange the numbers of the given series in
such a cyclic order or sequence, that each number being written con-
secutively into the square by a well defined rule or path, the re-
sulting magic will be identical with that made by the La Hireian
method, or equivalent thereto in magic qualities. Starting, as before,
with the 62 magic, the proper sequence of the first six numbers is
found in what may be termed the "continuous diagonal" of its magic
rectangle. Referring to Fig. 1, this sequence is seen to be 1; 2, 5,
7, 6, 3, but it is obvious that there may be as many different se-
quences as there are variations in the magic rectangles.

The complete series given on page 304 must now be rearranged

1 "The Theory of Path Nasiks," by C Planck, M.A., M.R.C.S., published
by A. T. Lawrence, Rugby, England.

CRITICISMS AND DISCUSSIONS.

in its lines and columns in accordance with the numerical sequence
of the first six numbers as above indicated. To make this arrange-
ment quite clear, the series given on p. 304 is reproduced in Fig. 16,
the numbers written in circles outside the square showing the numer-
ical order of lines and columns under rearrangement. Fig. 17 shows
the complete series in new cyclic order, and to construct a square
directly therefrom, it is only necessary to write these numbers con-
secutively along the proper paths. Since the square will be pandiag-
onal it may be commenced anywhere, so in the present example we
will place 1 in the fourth cell from the top in the first column, and
will use the paths followed in Fig. 5 so as to reproduce that square.

The paths may be written I 3, 2

(4,3

and since we can always write

/6

JO

/o

'7

6

zo

4*

7

Z9

36

30

/6

jr

J3

7

Z/

6

/O

4*

Fig. 16.
-(n-a) instead of a, we may write this

Fig.i;.
This only means

3,2
-2,3

that the numbers in the first column of Fig. 17 (which may be
termed the leading numbers) are to be placed in order along the
path (3, 2), as in the numbers enclosed in circles in Fig. 5; 'and
then starting from each cell thus occupied, the remaining five num-
bers in each of the six rows of Fig. 17 are to be written along the
path (-2, 3). It will be seen that this is equivalent to writing the
successive rows of Fig. 17 intact along the path (-2, 3), or (3, -2)
and using a "break-step" (1, -1), as in Fig. 18 where the first
break-step is shown with an arrow. The break-step is always given

by summing up the coordinates ; thus, the paths here being

3,2
-2,3

by summing the columns we get (1, 5), that is (1, -1). The re-
sulting square is, of course, identical with Fig. 5.

As previously stated, this square being pandiagonal, it may be

312

THE MONIST.

commenced in any of its thirty-six cells, and by using the same
methods as before, different aspects of Fig. 5 will be produced.
Also, since by this method complementary pairs are always sepa-

7

B

D

Fig. 18.

Fig. 19.

rated by a step (n/2, n/2), any of the thirty-six squares thus formed
may be made associated by the method described in The Monist,
Vol. XX, No. 3, page 443, under the heading "Magic Squares by

S3

/S

ZJ

/o6

/6

/so

7

/OS

/6o

22

26

sz

"7

6s

/z

zs

so

/£//

36

/Z2

Fig. 20.

Complementary Differences,"2 viz., Divide the square into four quar-
ters as shown in Fig. 19 ; leave A untouched, reflect B, invert C and

2 Errata in this article : p. 440, footnote, and p. 443, fourth line from top
of page, instead of "for all orders = 4^+2'' read "for orders wherein n is of
the general form 4/>+2."— Page 44, last line, for "order 8n" read "this class."

CRITICISMS AND DISCUSSIONS.

313

reflect and invert D. For this concise and elegant method of chang-
ing the relative positions of the complementary couplets in a square
we are indebted to Dr. Planck.

The next square in order is 1(X The series of numbers used
is given on page 305 and their rearrangement in proper cyclic order

"

7

/OS

66

/6o

s6

62

7

/o6

/SS

/z

/39

Z2,

'6s

/3S

20

/'S

/0

AT*

S2,

26

36

/OS

/£/

30

AT

$7

/sz

/22

"3

'26

,6

so

Fig. 21.

for direct entry may be found as before in the continuous diagonal
of its magic rectangle. The sequence shown in Fig. 11 is 1, 2, 3, 4,
9, 13, 12, 11, 10, 5, and the complete rearrangement of the series in
accordance therewith is given in Fig. 20. Various 102 magics may

be made by using this series with different paths. The paths

z/

z

3

¥

'7

/6

/s

<?

/£

/

20

/&

/<$

3~

6

7

'V

&

will produce Fig. 15, and

5, 2

2,5

5,4
-4,5

Fig. 22.

will make Fig. 21, which is equiva-

lent to Fig. 15 in its ornate features.

These squares and all similarly constructed larger ones of these
orders may be changed to the form of association wherein the com-
plementary couplets are evenly balanced around the center of the

THE MONIST.

square, by the method previously explained. It will be unnecessary
to prolong the present article by giving any examples of larger
squares of this class, but the simple forms of magic rectangles for

2$

2

Z/

^

fa

6

'7

<?

&

/o

'Z

/

22

<3

20

5-

/<?

7

/6

/&

'#

//

Fig. 23.

29

Z

*7

t

25

6

25

s

&

zo

//

/<?

/$

/

2#

3

26

c5~

2^

7

22

Zf

SO

/&

/z

//

Fig. 24.

182 and 222 and 262 magics, shown in Figs. 22, 23 and 24, may be
of some assistance to those who desire to devote further study to
these interesting squares.3

W. S. ANDREWS.

L. S. FRIERSON.

A NEW THEORY OF INVENTION.

A Russian engineer, P. K. von Engelmeyer of Moscow ( Peters-
burger Chaussee 42), has published a little book on invention and
its significance in our industrial life under the title Der Dreiakt (Ber-
lin, Carl Heymann's Verlag) in which he claims that man is not
only a political being (£<5o»> iroAmKov) as Aristotle claims, but also
and mainly a technical being (£woi/ TCXVIKOV), and he means it in the
same sense in which Franklin called man a "tool-making animal."1

Mr. Engelmeyer defines technique as the art of reproducing
artificially or intentionally certain desired phenomena (p. 17) and
he calls attention to the fact that we are surrounded by the products
of invention. Our clothes, the light and heat in our houses, our mode
of traveling, in short, all that is called culture and civilization has

"More generally, if p, q are relative primes, the square of order pq will
be magic on its pq rows, pq columns and 2pq diagonals, and at the same time
/>2-ply and #-2ply, if it be constructed with the paths I p, q I, and the period

I Q> P I

be taken from the continuous diagonal of the magic rectangle pXq- The limi-
tations are dictated by the magic rectangle. Evidently p and q must both be
> i, and consecutive numbers must fail if the order is = 2 (mod. 4) ; in all
other cases consecutive numbers will suffice. c. P.

1 See the author's The Philosophy of the Tool, p. i.

CRITICISMS AND DISCUSSIONS. 315

been invented at various times. Some inventions have been made
by conscious endeavor, others by accident.

Our author distinguishes four characteristics of invention: (1)
its artificial nature — man interferes with natural conditions and in-
troduces a human element into them: (2) teleology — inventions
must be designed, they must serve a purpose; (3) surprise, by
which word our author means that they must be something new or
original ; we do not call invention what is merely an application of
former experience; (4) unity — every invention is a kind of a sys-
tem, an organic whole, and the members must be integral parts of
a new entirety. Discovery is somewhat different from invention,
but there is a domain which belongs practically to both invention
and discovery. Newton's law of gravitation is a discovery, but
mathematical formulas are both.

Mr. Engelmeyer quotes Goethe approvingly when he says:
"man does not experience or enjoy without at the same time being
productive," thus implying that invention is an indispensable ele-
ment in human existence. There are three fields of human activity.
When man devotes his efforts to purposes of utility, the result is
called invention ; when his efforts are devoted to cognition, the result
is called discovery; when this result serves esthetical pleasure it is
called a work of art. Just as all three domains are ultimately one,
so there must be but one theory of invention which our author calls
by the Greek name "Heurology," and in so far as it expresses this
union he calls it an act of three, or in German Dreiakt.

This theory of the Dreiakt is the subject of the main part of
the book, and the author has consulted the patent laws of different
nations for details and illustrations. From the standpoint of his
conception he distinguishes between the product and the method
of an invention; the former is the effect accomplished, the latter is
the arrangement of parts, the combination of substances in definite
proportions, the way in which substances are treated to change their
nature. The patent lawyer must consider the principle which com-
prises the effect together with the way in which it is produced. Ex-
amples are furnished by the sewing machine, the bicycle, hydraulic
systems, aeronautics, fire arms, chemical inventions, cement, ex-
plosives, photography, Bessemer steel, etc.

The concluding chapter of the book is devoted to the applica-
tion of the Dreiakt to patent laws and technical instruction. The
universality of the principle of the Dreiakt finds appreciation in the
proposition that the human will itself is a Dreiakt. Our auther

316 THE MONIST.

gives credit to O. Schanze who has published his views on the
same subject under the title Beitrdge zur Lehre von der Patent-
fdhigkeit, fascicle 2, pages 243-255 (Berlin, Siemens, 1904). He
uses the term Dreiakt in a slightly different sense and speaks of three
fundamental energies: (1) intention or will, (2) reflection or knowl-
edge, (3) practical skill. These characterize every act of creation
as a Dreiakt, (1) the aim which constitutes the teleology of the
work, (2) the plan or design which logically determinates the work
and (3) its execution. Schanze applies them to practical problems,
especially to these three: a, Who among several collaborators is the
author of the invention and who merely an assistant; b, how far
in its application is an invention entitled to protection by patent;
and c, at what state of completion does an invention acquire the right
to be patented. p. c.

BOOK REVIEWS AND NOTES.

THE PERIPLUS OF THE ERYTHRAEAN SEA. By Wilfred H. Schoff. New York :
Longmans, Green and Company, 1912. Pp. 323. Price $2.00 net.

"Periplus" means circumnavigation and may be freely translated "log
book" or "description of a sea voyage." There are several antique books
which bear the same title, and the present work refers to that body of water
which in modern times is known as the Indian Ocean, together with the Red
Sea and the Persian Gulf. This record describes the voyage from place to
place of an ancient merchant vessel and is of great interest in the history of
trading. The book itself is not long. It contains only 28 pages of English
text, but the translation has been made with great care. Very full notes ex-
plain the terms used, the merchandise traded and the historical connections,
and these cover pages 50 and 282 ; tables are appended listing articles of trade
and rulers mentioned and dates variously assigned to the original, a map
indicates the ports touched at and helps the readers to understand the geog-
raphy of our travelers. The book is furnished with a very thorough topical
index covering thirty two-columned pages. The work is creditable to the
spirit of the Commercial Museum of Philadelphia, which has brought it out.
W. P. Wilson, the director of the Philadelphia museums, says in his foreword :

"The Periplus of the Erythraean Sea is the first record of organized trad-
ing with the nations of the East, in vessels built and commanded by subjects
of the Western world. The notes add great interest, giving as they do an ex-
haustive survey of the international trade between the great empires of Rome,
Parthia, India and China, together with a collection of facts touching the
early trade of a number of other countries of much interest." K

THE INDIVIDUAL AND REALITY. By Edward Douglas Fawcett. New York:

Longmans, Green & Co., 1909. Pp. 449.

The author writes as one having authority. He considers himself a free
lance, since he is independent of any school of philosophy or religion, and
therefore "free to ignore all traditions and conventions and go straight to
reality in the search for truth." The present volume is intended to supersede
a former one to which he refers as "my Riddle." This former work was read
with enormous satisfaction by the late Prof. William James, and the fact that
this same thinker considers his book "as a great and powerful agency in the
spreading of truth" is regarded by the author as sufficient justification for its
appearance. Mr. Fawcett credits the source of his thinking to the anti-

318 THE MONIST.

Hegelian thought of Schelling and Schopenhauer, being allied to the former's
"immemorial being" and Bain's doctrine of relativity. He has not read Berg-
son with whom his results in part seem to agree. In this later work he has
abandoned the monadology of his former production, replacing it with a new
form of idealism. Some of the novelties of the former work are here retained.
Part I is an introduction to metaphysics ; Part II treats of the individual and
his universe, appearances, and the individual in his relation to the organism,
nature as a whole, and to himself. Part III deals with ultimate questions,
such as the ground of appearance, the evolution of nature and individuals,
birth, death, destiny and God. p

PROTESTANT THOUGHT BEFORE KANT. By Arthur Cushman M'Giffert. New

York: Charles Scribner's Sons, 1911. Pp. 261. Price, 75 cents net.
In this volume dedicated to Adolf Harnack, the author's teacher and
friend, Professor M'Giffert, of Union Theological Seminary of New York,
traces the development of Protestantism from the time of its early workings
in medieval Christianity to that of the great Konigsberg philosopher. This
includes a discussion of the leaders of the Reformation in all countries, Zwingli,
Melanchthon, Calvin; also the radical anabaptists and socianians. The Prot-
estant phase of scholasticism is discussed, and pietism in Germany, England
and New England. The book closes with a chapter on rationalism in its var-
ious phases as found in England, France, Germany and America. Professor
M'Giffert's book is the sixth volume in a series entitled "Studies in Theol-
ogy" which are intended as aids to interpretation in biblical criticism, pri-
marily for the use of ministers and theological students, but still the needs of
the general reader are kept in view so that the works shall not become too
technical. P

UEBER KLASSIKER UND PHILOSOPHEN DER NEUZEIT. By Julius Rupp. Leipsic:

Eckardt, 1910. Pp. 796 . Price 6m.

This is the third volume of Rupp's collected works which are to appear
in twelve volumes, and have been edited by P. C. Elsenhans. Each volume
has a separate introduction by the editor. The present one on the classicists
and modern philosophers contains three different collections of Rupp's essays.
The first set, from Lessing to Hegel, are on subjects relating to Lessing, Kant,
Herder, Spinoza, Schiller, Fichte and Schleiermacher. The second collection,
bearing the general title "Contemporary Philosophy," discusses subjects re-
lating to natural science, controversies about the soul, macrocosm, and micro-
cosm, the relations of soul to body, philosophy, theology, religion of the
spirit; and devotes special chapters to Emerson, Gioberti and Alexander Bain.
This volume contains also Rupp's "Sketches of a Thinker." p

THE PHENOMENOLOGY OF MIND. By G. W. F. Hegel. Tr. by /. B. Baillie.

2 vols. London: Sonnenschein, 1910. Pp. 823. Price 21 s. net.
This translation of Hegel's Phenomenology is one number of Sonnen-
schein's "Library of Philosophy" edited by Dr. J. H. Muirhead. The object
of the series is to familiarize English readers with results of modern philo-

BOOK REVIEWS AND NOTES. 319

sophical thought, admitting that in this respect Germany has far excelled
England. The editor's purpose, however, besides bringing German philosophy
to English thinkers, is to furnish a systematized philosophical library in which
English philosophy will receive the consideration due it, as its significance
has been largely ignored by the German schools. />

DAVID HUME, HANS LIV OG HANS FILOSOFI. Af Anton Thomsen. Copenhagen :

Nordiske Forfatteres Forlag, 1911. Pp. 458. Price 1.65 kr.
Professor Anton Thomsen of the University of Copenhagen is preparing
an extremely comprehensive work on the subject of this great English phi-
losopher. The first volume appeared during last winter, and after a few
introductory pages calling attention to the bicentenary of David Hume's birth,
takes up in its first book the philosopher's life and works, and in the second
book his epistemology and psychology. The philosophical critique is made
with due reference to the contemporary thinkers of all lands in connection
with the philosophy of past centuries. p

DEVOLUTION DE LA MEMOiRE. Par Henri Pitron. Paris: Flammarion, 1910.
Pp. 360. Price 3.50 fr.

This book treats of the extent of the domain of the memory and the re-
lations of the phenomena of inorganic memory to those of psychic memory ;
of the forms which memory assumes in all the steps of the evolution of ani-
mals and the continuity of the series when passing from brute creation to
man; of the aspects and limitations of human memory, the cause of its diffi-
culties and its probable future. The discussion of these points is based on the
collection of facts actually established by objective psychology, human and
comparative.

The conclusion drawn is both pessimistic and optimistic: pessimistic, be-
cause it sees no chance for the memory of men regarded individually to in-
crease in capacity, and because the utilization of the traces left by collective
memory (i. e., presented by published material) seems likely to become more
and more difficult; optimistic, in that the conservation of many recollections
will become less and less necessary in the progress of scientific classification
which will make possible the substitution of the knowledge of a small number
of general laws for that of a large number of particular facts. p

DAS KUNFTIGE JAHRHUNDERT DER PsYCHOLociE. Von G. Heymans. Aus dem
Niederlandischen tibersetzt von H. Pol. Leipsic: Earth, 1911. Pp.
52. Price i m. 20.

Prof. G. Heymans, retiring rector of the Groningen University, has pub-
hished his oration in the translation of Mr. H. Pol, the German teacher ot
the same university. It bears the title "The Future Century of Psychology,"
and insists that while progress is rapid in other branches the development of
psychology ought not to be neglected because it is more important than our
progress in inventions. The main subjects of psychology refer to the nature
of our own self, our relation to others and toward the ultimate foundation of
the world. He finds that much is to be done and much has been neglected

32O THE MONIST.

in former ages. In opposition to the common view that competition and war
are necessary, that mankind is bad at the core, he quotes Frederick the Great
as having said of a prominent educator : "Ah, mon cher Sulzer, vous ne con-
naissez pas assez cette maudite race, a laquelle nous appartenons !" In oppo-
sition to the current view he expects that the future will more and more
restrict competition and war, and criticizes the idea that they are necessary
for the amelioration of the race; that if the principle were reasonable cattle
breeders and hunters might just as well introduce it into the artificial methods
of producing higher and better breeds, but what would we think of a hunter
who would make his hounds quarrel about a piece of meat in a fierce fight in
which half of them would lose their lives, and this simply for the amelioration
of the race? He ends his oration by quoting the words of a mystic thinker,
"I trust that all will yet be good." K

In Hamburg, the place of the first monistic congress, a free religious
society has been founded which proposes to do a propaganda for a rational
world conception. Their aims are through religious devotion to cultivate the
true, the good and the beautiful. In politics they favor separation of church
from state and of school from church. Their secretary is Bruno Heyer, and
their treasurer Adolf Dunkel. K

The well-known activity of the Leipsic publishing house of Diirr is seen
by constant additional contributions to its Philosophische Bibliothek, and the
value of its productions is attested by the height to which the number of its
editions reaches. Among its 1910 publications, besides the seventh edition of
Baensch's translation of Spinoza's Ethics, we have an edition by Johannes
Schubert of Wilhelm von Humboldt's selected philosophical writings and the
Definitions of Christian Wolff collected by Julius Baumann for the purpose of
serving as collateral reading in the study of Kant. The centennial of the
Berlin University has been celebrated by this enterprising house by a volume
introduced by Edouard Spranger and containing the addresses of Fichte,
Schleiermacher and Steffins on "The Nature of the University," written or
delivered at the time of its opening. A second edition of Dr. Otto Apelt's
German translation of Plato's Thcaetetus bears the date of 1911, and purports
to be an entirely new translation of the dialogue. (Baruch de Spinoza, Ethik,
iibers. von Otto Baensch; Fichte, Schleiermacher, Steffens uber das Wesen
der Universit'dt, her. von Edouard Spranger ; Wilhelm von Humboldts ausge-
wdhlte philosophische Schriften, her. von. Johannes Schubert; Wolff sche
Begriffsbestimmungen, her. von Julius Baumann ; Platons Dialog Theatet,
iibers. von Dr. Otto Apelt.) P

The scientific publishing house of A. Hermann and Son, at Paris, are
publishing a French translation of the sixth German edition of Prof. W.
Nernst's large work on theoretical chemistry. It is translated by A. Corvisy,
under the title Traite* de chimie gtnerale. The first part is issued this year,
dealing with the general properties of bodies and atoms and molecules, p

VOL. XXII. JULY, 1912. NO. 3

THE MONIST

THE PHILOSOPHY OF BERGSON,1

i.

~^HE classification of philosophies is effected, as a rule,
JL either by their methods or by their results: "empirical"
and "a priori'' is a classification by methods, "realist" and
"idealist" is a classification by results. An attempt to clas-
sify Bergson's philosophy in either of these ways is hardly
likely to be successful, since it cuts across all the recognized
divisions.

But there is another way of classifying philosophies,
less precise, but perhaps more helpful to the non-philo-
sophical ; in this way, the principle of division is according
to the predominant desire which has led the philosopher
to philosophize. Thus we shall have philosophies of feel-
ing, inspired by the love of happiness; theoretical philos-
ophies, inspired by the love of knowledge; and practical
philosophies, inspired by the love of action.

Among philosophies of feeling we shall place all those
which are primarily optimistic or pessimistic, all those that
offer schemes of salvation or try to prove that salvation is
impossible ; to this class belong most religious philosophies.
Among theoretical philosophies we shall place most of the
great systems ; for though the desire for knowledge is rare,
it has been the source of most of what is best in philosophy.
Practical philosophies, on the other hand, will be those

JThe abbreviations of the titles of the works of M. Bergson referred to
are: C.E., Creative Evolution; M. and M., Matter and Memory; Tand F. W.,
Time and Free Will. The references are to the English translations of M.
Bergson's books.

322 THE MONIST.

which regard action as the supreme good, considering hap-
piness an effect and knowledge a mere instrument of suc-
cessful activity. Philosophies of this type would have been
common among Western Europeans if philosophers had
been average men ; as it is, they have been rare until recent
times, in fact their chief representatives are the pragma-
tists and M. Bergson. In the rise of this type of philosophy
we may see, as M. Bergson himself does, the revolt of the
modern man of action against the authority of Greece, and
more particularly of Plato; or we may connect it, as Dr.
Schiller apparently would, with imperialism and the motor-
car. The modern world calls for such a philosophy, and
the success which it has achieved is therefore not surpris-
ing.

M. Bergson's philosophy, unlike most of the systems of
the past, is dualistic: the world, for him, is divided into
two disparate portions, on the one hand life, on the other
matter, or rather that inert something which the intellect
views as matter. The whole universe is the clash and conflict
of two opposite motions: life, which climbs upward, and
matter, which falls downward. Life is one great force,
one vast vital impulse, given once for all from the begin-
ning of the world, meeting the resistance of matter, strug-
gling to break a way through matter, learning gradually
to use matter by means of organization; divided by the
obstacles it encounters into diverging currents, like the
wind at the street-corner ; partly subdued by matter through
the very adaptations which matter forces upon it; yet re-
taining always its capacity for free activity, struggling
always to find new outlets, seeking always for greater lib-
erty of movement amid the opposing walls of matter.

Evolution is not primarily explicable by adaptation to
environment ; adaptation explains only the turns and twists
of evolution, like the windings of a road approaching a
town through hilly country. But this simile is not quite

THE PHILOSOPHY OF BERGSON. 323

adequate; there is no town, no definite goal, at the end of
the road along which evolution travels. Mechanism and
teleology suffer from the same defect: both suppose that
there is no essential novelty in the world. Mechanism
regards the future as implicit in the past, since it believes
the future to be calculable ; teleology also, since it believes
that the end to be achieved can be known in advance, denies
that any essential novelty is contained in the result.

As against both these views, though with more sym-
pathy for teleology than for mechanism, M. Bergson main-
tains that evolution is truly creative, like the work of an
artist. An impulse to action, an undefined want, exists
beforehand, but until the want is satisfied it is impossible
to know the nature of what will satisfy it. For example,
we may suppose some vague desire in sightless animals
to be able to be aware of objects before they were in con-
tact with them. This led to efforts which finally resulted
in the creation of eyes. Sight satisfied the desire, but
could not have been imagined beforehand. For this rea-
son, evolution is unpredictable, and determinism cannot
refute the advocates of free will.

This broad outline is filled in by an account of the
actual development of life on the earth. The first division
of the current was into plants and animals: plants aimed
at storing up energy in a reservoir, animals aimed at using
energy for sudden and rapid movements. "The same im-
petus/' he says, "that has led the animal to give itself
nerves and nerve centers must have ended, in the plant,
in the chlorophyllian function" (C. E., p. 120). But among
animals, at a later stage, a new bifurcation appeared: in-
stinct and intellect became more or less separated. They
are never wholly without each other, but in the main in-
tellect is the misfortune of man, while instinct is seen at
its best in ants, bees, and Bergson. The division between
intellect and instinct is fundamental in his philosophy, much

3^4

THE MONIST.

of which is a kind of Sandford and Merton, with instinct
as the good boy and intellect as the bad boy.

Instinct at its best is called intuition. "By intuition,"
he says, "I mean instinct that has become disinterested,
selfconscious, capable of reflecting upon its object and of
enlarging it indefinitely" (C. E., p. 186). The account of
the doings of intellect is not always easy to follow, but if
we are to understand Bergson we must do our best.

Intelligence or intellect, "as it leaves the hands of na-
ture, has for its chief object the inorganic solid" (C. E.,
p. 162) ; it can only form a clear idea of the discontinuous
and the immobile (pp. 163-4) ; its concepts are outside each
other like objects in space, and have the same stability (p.
169). The intellect separates in space and fixes in time;
it is not made to think evolution, but represent becoming
as a series of states (p. 171). "The intellect is character-
ized by a natural inability to understand life" (p. 174) ;
geometry and logic, which are its typical products, are
strictly applicable to solid bodies, but elsewhere reason-
ing must be checked by common sense, which, as Bergson
truly says, is a very different thing (p. 170). Solid bodies,
it would seem, are something which mind has created on
purpose to apply intellect to them, much as it has created
chess-boards in order to play chess on them. The genesis
of intellect and the genesis of material bodies, we are told,
are correlative: both have been developed by reciprocal
adaptation (p. 196). "An identical process must have cut
out matter and the intellect, at the same time, from a stuff
that contained both" (p. 210).

This conception of the simultaneous growth of matter
and intellect is ingenious, and deserves to be understood.
Broadly, I think, what is meant is this: Intellect is the
power of seeing things as separate one from another, and
matter is that which is separated into distinct things. In
reality there are no separate solid things, only an endless

THE PHILOSOPHY OF BERGSON. 325

stream of becoming, in which nothing becomes and there
is nothing that this nothing becomes. But becoming may
be a movement up or a movement down: when it is a
movement up it is called life, when it is a movement down
it is what, as misapprehended by the intellect, is called
matter. I suppose the universe is shaped like a cone, with
the Absolute at the vertex, for the movement up brings
things together, while the movement down separates them,
or at least seems to do so. In order that the upward mo-
tion of mind may be able to thread its way through the
downward motion of the falling bodies which hail upon
it, it must be able to cut out paths between them; thus as
intelligence was formed, outlines and paths appeared (p.
199), and the primitive flux was cut up into separate bod-
ies. The intellect may be compared to a carver, but it has
the peculiarity of imagining that the chicken always was
the separate pieces into which the carving-knife divides it.
"The intellect," Bergson says, "always behaves as if
it were fascinated by the contemplation of inert matter.
It is life looking outward, putting itself outside itself,
adopting the ways of inorganized nature in principle, in
order to direct them in fact" (p. 170). If we may be
allowed to add another image to the many by which Berg-
son's philosophy is illustrated, we may say that the universe
is a vast funicular railway, in which life is the train that
goes up, and matter is the train that goes down. The in-
tellect consists in watching the descending train as it passes
the ascending train in which we are. The obviously nobler
faculty which concentrates its attention on our own train,
is instinct or intuition. It is possible to leap from one train
to the other ; this happens when we become the victims of
automatic habit, and is the essence of the comic. Or we
can divide ourselves into parts, one part going up and one
down; then only the part going down is comic. But in-
tellect is not itself a descending motion, it is merely an

326 THE MONIST.

observation of the descending motion by the ascending
motion.

Intellect, which separates things, is, according to
Bergson, a kind of dream; it is not active, as all our life
ought to be, but purely contemplative. When we dream,
he says, our self is scattered, our past is broken into frag-
ments (p. 2i2),2 things which really interpenetrate each
other are seen as separate solid units: the extra-spatial
degrades itself into spatiality (p. 218), which is nothing
but separateness. Thus all intellect, since it separates,
tends to geometry, and logic, which deals with concepts
that lie wholly outside each other, is really an outcome of
geometry, following the direction of materiality (pages
222-4). Both deduction and induction require spatial in-
tuition behind them (p. 225) ; "the movement at the end
of which is spatiality lays down along its course the faculty
of induction, as well as that of deduction, in fact, intellec-
tuality entire." It creates them in mind, and also the order
in things which the intellect finds there (p. 228). Thus
logic and mathematics do not represent a positive spiritual
effort (p. 224), but a mere somnambulism, in which the
will is suspended, and the mind is no longer active. In-
capacity for mathematics is therefore a sign of grace-
fortunately a very common one.

As intellect is connected with space, so instinct or in-
tuition is connected with time. It is one of the noteworthy
features of Bergson's philosophy that, unlike most writers,
he regards time and space as profoundly dissimilar. Space,
the characteristic of matter, arises from a dissection of the
flux which is really illusory, useful, up to a certain point,
in practice, but utterly misleading in theory. Time, on
the contrary, is the essential characteristic of life or mind.
"Wherever anything lives/' he says, "there is, open some-

2 It is noteworthy that elsewhere Bergson speaks of dreams as. giving us
duration more pure than in waking life (T. and F. W., p. 126).

THE PHILOSOPHY OF BERGSON. 327

where, a register in which time is being inscribed" (C. E.,
p. 17). But the time here spoken of is not mathematical
time, the homogeneous assemblage of mutually external
instants. Mathematical time, according to Bergson, is re-
ally a form of. space; the time which is of the essence of
life is what he calls duration. This conception of duration
is fundamental in his philosophy; it appears already in his
earliest book Time and Free Will, and it is necessary to
understand it if we are to have any comprehension of his
system. It is, however, a very difficult conception. I do
not fully understand it myself, and therefore I cannot
hope to explain it with all the lucidity which it doubtless
deserves.

"Pure duration/' we are told, "is the form which our
conscious states assume when our ego lets itself live, when
it refrains from separating its present state from its former
states" (T. and F. W., p. 100). It forms the past and the
present into one organic whole, where there is mutual pene-
tration, succession without distinction (ib.). "Within our
ego, there is succession without mutual externality; out-
side the ego, in pure space, there is mutual externality
without succession" (p. 108).

"Questions relating to subject and object, to their dis-
tinction and their union, should be put in terms of time
rather than of space" (M. and M., p. 77). In the duration
in which we see ourselves acting, there are dissociated ele-
ments ; but in the duration in which we act, our states melt
into each other (M. and M., p. 243). Pure duration is
what is most removed from externality and least penetrated
with externality, a duration in which the past is big with
a present absolutely new. But then our will is strained
to the utmost; we have to gather up the past which is
slipping away, and thrust it whole and undivided into the
present. At such moments we truly possess ourselves, but
such moments are rare (C. E., pp. 210-211). Duration is

328 THE MONIST.

the very stuff of reality, which is perpetual becoming, never
something made (C.E., p. 287).

It is above all in memory that duration exhibits itself,
for in memory the past survives in the present. Thus the
theory of memory becomes of great importance in Berg-
son's philosophy. Matter and Memory is concerned to
show the relation of mind and matter, of which both are
affirmed to be real (p. vii), by an analysis of memory,
which is "just the intersection of mind and matter" (p.xii).

There are, to begin with, two radically different things,
both of which are commonly called memory ; the clear dis-
tinction between these two is one of the best things in Berg-
son. "The past survives," he says, "under two distinct
forms: first, in motor mechanisms; secondly, in indepen-
dent recollections" (M. and M., p. 87). For example, a
man is said to remember a poem if he can repeat it by
heart, that is to say, if he has acquired a certain habit or
mechanism enabling him to repeat a former action. But
he might, at least theoretically, be able to repeat the poem
without any recollection of the previous occasions on which
he has read it ; thus there is no consciousness of past events
involved in this sort of memory. The second sort, which
alone really deserves to be called memory, is exhibited in
recollections of separate occasions when he has read the
poem, each unique and with a date. Here there can be no
question of habit, since each event only occurred once, and
had to make its impression immediately. It is suggested
that in some way everything that has happened to us is
remembered, but as a rule, only what is useful comes into
consciousness. Apparent failures of memory, it is argued,
are not really failures of the mental part of memory, but
of the motor mechanism for bringing memory into action.
This view is supported by a discussion of brain physiology
and the facts of amnesia, from which it is held to result
that true memory is not a function of the brain (M. and M.,

THE PHILOSOPHY OF BERGSON. 329

p. 315). The past must be acted by matter, imagined by
mind (M. and M., p. 298). Memory is not an emanation
of matter; indeed the contrary would be nearer the truth
if we mean matter as grasped in concrete perception, which
always occupies a certain duration (M. and M., p. 237).

"Memory must be, in principle, a power absolutely in-
dependent of matter. If, then, spirit is a reality, it is here,
in the phenomena of memory, that we may come into touch
with it experimentally" (M. and M., p. 81).

At the opposite end from pure memory Bergson places
pure perception, in regard to which he adopts an ultra-
realist position. "In pure perception," he says, "we are
actually placed outside ourselves, we touch the reality of
the object in an immediate intuition" (p. 84). So com-
pletely does he identify perception with its object that he
almost refuses to call it mental at all. "Pure perception,"
he says, "which is the lowest degree of mind — mind with-
out memory — is really part of matter, as we understand
matter" (M. and M., p. 297). Pure perception is consti-
tuted by dawning action, its actuality lies in its activity
(M. and M., p. 74). It is in this way that the brain be-
comes relevant to perception, for the brain is not an instru-
ment of representation, but an instrument of action (M.
anl M., p. 83). The function of the brain is to limit our
mental life to what is practically useful. But for the brain,
one gathers, everything would be perceived, but in fact
we only perceive what interests us (cf. M. and M., p. 34).
"The body, always turned towards action, has for its essen-
tial function to limit, with a view to action, the life of the
spirit" (M. and M., p. 233). It is, in fact, an instrument
of choice.

We must now return to the subject of instinct or intui-
tion, as opposed to intellect. It was necessary first to give
some account of duration and memory, since Bergson's
theories of duration and memory are presupposed in his

330 THE MONIST.

account of intuition. In man, as he now exists, intuition is
the fringe or penumbra of intellect : it has been thrust out
of the center by being less useful in action than intellect,
but it has deeper uses which make it desirable to bring it
back into greater prominence. Bergson wishes to make
intellect "turn inwards on itself, and awaken the poten-
tialities of intuition which still slumber within it" (C. E.,
p. 192). The relation between instinct and intellect is
compared to that between sight and touch. Intellect, we
are told, will not give knowledge of things at a distance;
indeed the function of science is said to be to explain all
perceptions in terms of touch.

"Instinct alone, he says, "is knowledge at a distance.
It has the same relation to intelligence that vision has to
touch" (C. E., p. 177). We may observe in passing that,
as appears in many passages, Bergson is a strong visual-
izer, whose thought is always conducted by means of visual
images. Many things which he declares to be necessities
of all thought are, I believe, characteristic of visualizers,
and would not be true of those who think by means of
auditory images. He always exalts the sense of sight at
the expense of the other senses, and his views -on space
would seem to be largely determined by this fact. I shall
return to this question at a later stage.

The essential characteristic of intuition is that it does
not divide the world into separate things, as the intellect
does ; although Bergson does not use these words, we might
describe it as synthetic rather than analytic. It apprehends
a multiplicity, but a multiplicity of interpenetrating proc-
esses, not of spatially external bodies. There are in truth
no things : "things and states are only views, taken by our
mind, of becoming. There are no things, there are only
actions" (C. E., p. 261). This view of the world, which
appears difficult and unnatural to intellect, is easy and
natural to intuition. Memory affords an instance of what

THE PHILOSOPHY OF BERGSON. 33!

is meant, for in memory the past lives on into the present
and interpenetrates it. Apart from mind, the world would
be perpetually dying and being born again; the past would
have no reality, and therefore there would be no past. It
is memory, with its correlative desire, that makes the past
and the future real and therefore creates true duration
and true time. Intuition alone can understand this min-
gling of past and future: to the intellect they remain ex-
ternal, spatially external as it were, to one another. Under
the guidance of intuition, we perceive that "form is only
a snapshot view of a transition" (C. E., p. 319), and the
philosopher "will see the material world melt back into
a single flux" (C. E., p. 390).

Closely connected with the merits of intuition is Berg-
son's doctrine of freedom and his praise of action. "In
reality," he says, "a living being is a center of action. It
represents a certain sum of contingency entering into the
world, that is to say, a certain quantity of possible action"
(C. E., p. 276). The arguments against free will depend
partly upon assuming that the intensity of psychical states
is a quantity, capable, at least in theory, of numerical meas-
urement ; this view Bergson undertakes to refute in the first
chapter of Time and Free Will. Partly the determinist
depends, we are told, upon a confusion between true dura-
tion and mathematical time, which Bergson regards as
really a form of space. Partly, again, the determinist rests
his case upon the unwarranted assumption that, when the
state of the brain is given, the state of the mind is theoret-
ically determinate. Bergson is willing to admit that the
converse is true, that is to say, that the state of brain is
determinate when the state of mind is given, but he regards
the mind as more differentiated than the brain, and there-
fore holds that many different states of mind may corres-
pond to one state of brain. He concludes that real free-
dom is possible: "We are free when our acts spring from

332 THE MONIST.

our whole personality, when they express it, when they
have that indefinable resemblance to it which one some-
times finds between the artist and his work" (T. and F. W .,
p. 172).

In the above outline, I have in the main endeavored
merely to state Bergson's views, without giving the reasons
adduced by him in favor of their truth. This is easier than
it would be with most philosophers, since as a rule he does
not give reasons for his opinions, but relies on their in-
herent attractiveness, and on the charm of an excellent
style. Like the advertisers of Oxo, he relies upon pictur-
esque and varied statement, and an apparent explanation
of many obscure facts. Analogies and similes, especially
form a very large part of the whole process by which he rec-
ommends his views to the reader. The number of similes for
life to be found in his works exceeds the number in any
poet known to me. Life, he says, is like a shell bursting
into fragments which are again shells (C. E., p. 103). It
is like a sheaf (ib., p. 104). Initially, it was "a tendency
to accumulate in a reservoir, as do especially the green
parts of vegetables" (ib., p. 260). But the reservoir is to
be filled with boiling water from which steam is issuing;
"jets must be gushing out unceasingly, of which each, fall-
ing back, is a world" (ib., p. 261). Again "life appears in
its entirety as an immense wave which, starting from a
center, spreads outwards, and which on almost the whole
of its circumference is stopped and converted into oscilla-
tion: at one single point the obstacle has been forced, the
impulsion has passed freely" (ib., p. 280). Then there is
the great climax in which life is compared to a cavalry
charge. "All organized beings, from the humblest to the
highest, from the first origins of life to the time in which
we are, and in all places as in all times, do but evidence a
single impulsion, the inverse of the movement of matter,
and in itself indivisible. All the living hold together, and

THE PHILOSOPHY OF BERGSON. 333

all yield to the same tremendous push. The animal takes
its stand on the plant, man bestrides animality, and the
whole of humanity, in space and in time, is one immense
army galloping beside and before and behind each of us
in an overwhelming charge able to beat down every re-
sistance and to clear many obstacles, perhaps even death"
(C.E., pp. 285-6).

But a cool critic, who feels himself a mere spectator,
perhaps an unsympathetic spectator, of the charge in which
man is mounted upon animality, may be inclined to think
that calm and careful thought is hardly compatible with
this form of exercise. When he is told that thought is a
mere means of action, the mere impulse to avoid obstacles
in the field, he may feel that such a view is becoming in a
cavalry officer, but not in a philosopher, whose business,
after all, is with thought: he may feel that in the passion
and noise of violent motion there is no room for the fainter
music of reason, no leisure for the disinterested contem-
plation in which greatness is sought, not by turbulence,
but by the greatness of the universe which is mirrored. In
that case, he may be tempted to ask whether there are any
reasons for accepting such a restless view of the world.
And if he asks this question, he will find, if I am not mis-
taken, that there is no reason whatever for accepting this
view, either in the universe or in the writings of M. Berg-
son.

ii.

The two foundations of Bergson's philosophy, in so
far as it is more than an imaginative and poetic view of the
world, are his doctrines of space and time. His doctrine
of space is required for his condemnation of the intellect,
and if he fails in his condemnation of the intellect, the in-
tellect will succeed in its condemnation of him, for between
the two it is war to the knife. His doctrine of time is

334 THE MONIST.

necessary for his vindication of freedom, for his escape
from what William James called a "block universe/' for
his doctrine of a perpetual flux in which there is nothing
that flows, and for his whole account of the relations be-
tween mind and matter. It will be well, therefore, in criti-
cism, to concentrate on these two doctrines. If they are
true, such minor errors and inconsistencies as no philos-
opher escapes would not greatly matter, while if they are
false, nothing remains except an imaginative epic, to be
judged on esthetic rather than on intellectual grounds. I
shall begin with the theory of space, as being the simpler
of the two.

Bergson's theory of space occurs fully and explicitly
in his Time and Free Will, and therefore belongs to the
oldest parts of his philosophy. In his first chapter, he con-
tends that greater and less imply space, since he regards
the greater as essentially that which contains the less. He
offers no arguments whatever, either good or bad, in favor
of this view ; he merely exclaims, as though he were giving
an obvious reductio ad absurdum: "As if one could still
speak of magnitude where there is neither multiplicity nor
space!" (p. 9). The obvious cases to the contrary, such as
pleasure and pain, afford him much difficulty, yet he never
doubts or re-examines the dogma with which he starts.

In his next chapter, he maintains the same thesis as
regards number. "As soon as we wish to picture number
to ourselves," he says, "and not merely figures or words,
we are compelled to have recourse to an extended image"
(p. 78), and "every clear idea of number implies a visual
image in space" (p. 79). These two sentences suffice to
show, as I shall try to prove, that Bergson does not know
what number is, and has himself no clear idea of it. This
is shown also by his definition: "Number may be defined
in general as a collection of units, or, speaking more ex-
actly, as the synthesis of the one and the many" (p. 75).

THE PHILOSOPHY OF BERGSON. 335

In discussing these statements, I must ask the reader's
patience for a moment while I call attention to some dis-
tinctions which may at first appear pedantic, but are really
vital. There are three entirely different things which are
confused by Bergson in the above statements, namely : ( i )
number, the general concept applicable to the various par-
ticular numbers; (2) the various particular numbers; (3)
the various collections to which the various particular num-
bers are applicable. It is this last that is defined by Berg-
son when he says that number is a collection of units. The
twelve apostles, the twelve tribes of Israel, the twelve
months, the twelve signs of the zodiac, are all collections
of units, yet no one of them is the number 12, still less is it
number in general, as by the above definition it ought to
be. The number 12, obviously, is something which all
these collections have in common, but which they do not
have in common with other collections, such as cricket
elevens. Hence the number 12 is neither a collection of
twelve terms, nor is it something which all collections have
in common; and number in general is a property of 12 or
1 1 or any other number, but not of the various collections
that have twelve terms or eleven terms.

Hence when, following Bergson's advice, we "have re-
course to an extended image" and picture, say, twelve dots
such as are obtained by throwing double sixes at dice, we
have still not obtained a picture of the number 12. The
number 12, in fact, is something more abstract than any
picture. Before we can be said to have any understanding
of the number 12, we must know what different collections
of twelve units have in common, and this is something
which cannot be pictured because it is abstract. Bergson
only succeeds in making his theory of number plausible by
confusing a particular collection with the number of its
terms, and this again with number in general.

The confusion is the same as if we confused a particular

336 THE MONIST.

young man with youth, and youth with the general concept
"period of human life," and were then to argue that because
a young man has two legs, youth must have two legs, and
the general concept "period of human life" must have two
legs. The confusion is important because, as soon as it is
perceived, the theory that number or particular numbers
can be pictured in space is seen to be untenable. This not
only disproves Bergson's theory as to number, but also
his more general theory that all abstract ideas and all logic
are derived from space; for the abstract 12, the common
property of all dozens as opposed to any particular dozen,
though it is never present to his mind, is obviously con-
ceivable and obviously capable of being pictured in space.
But apart from the question of numbers, shall we admit
Bergson's contention that every plurality of separate units
involves space? Some of the cases that appear to contra-
dict this view are considered by him, for example succes-
sive sounds. When we hear the steps of a passer-by in the
street, he says, we visualize his successive positions ; when
we hear the strokes of a bell, we either picture it swinging
backwards and forwards, or we range the successive
sounds in an ideal space (T. and F. W ., p. 86). But these
are mere autobiographical observations of a visualizer,
and illustrate the remark we made before, that Bergson's
views depend upon the predominance of the sense of sight
in him. There is no logical necessity to range the strokes
of a clock in an imaginary space: most people, I imagine,
count them without any spatial auxiliary. Yet no reason
is alleged by Bergson for the view that space is necessary.
He assumes this as obvious, and proceeds at once to apply
it to the case of times. Where there seem to be different
times outside each other, he says, the times are pictured
as spread out in space; in real time, such as is given by
memory, different times interpenetrate each other, and can-
not be counted because they are not separate.

THE PHILOSOPHY OF BERGSON. 337

The view that all separateness implies space is now
supposed established, and is used deductively to prove that
space is involved wherever there is obviously separateness,
however little other reason there may be for suspecting
such a thing. Thus abstract ideas, for example, obviously
exclude each other : whiteness is different from blackness,
health is different from sickness, folly is different from wis-
dom. Hence all abstract ideas involve space ; and therefore
logic, which uses abstract ideas, is an offshot of geometry,
and the whole of the intellect depends upon a supposed
habit of picturing things side by side in space. This con-
clusion, upon which Bergson's whole condemnation of the
intellect rests, is based, so far as can be discovered, entirely
upon a personal idiosyncrasy mistaken for a necessity of
thought, I mean the idiosyncrasy of visualizing succes-
sions as spread out on a line. The instance of numbers
shows that, if Bergson were in the right, we could never
have attained to the abstract ideas which are supposed to
be thus impregnated with space; and conversely, the fact
that we can understand abstract ideas (as opposed to par-
ticular things which exemplify them) seems sufficient to
prove that he is wrong in regarding the intellect as impreg-
nated with space.

One of the bad effects of an anti-intellectual philosophy,
such as that of Bergson, is that it thrives upon the errors
and confusions of the intellect. Hence it is led to prefer
bad thinking to good, to declare every momentary difficulty
insoluble, and to regard every foolish mistake as revealing
the bankruptcy of intellect and the triumph of intuition.
There are in Bergson's works many allusions to mathe-
matics and science, and to a careless reader these allusions
may seem to strengthen his philosophy greatly. As re-
gards science, especially biology and physiology, I am not
competent to criticize his interpretations. But as regards
mathematics, he has deliberately preferred traditional er-

338 THE MONIST.

rors in interpretation to the more modern views which
have prevailed among mathematicians for the last half
century. In this matter, he has followed the example of
most philosophers. In the eighteenth and early nineteenth
centuries, the infinitesimal calculus, though well developed
as a method, was supported, as regards its foundations,
by many fallacies and much confused thinking. Hegel and
his followers seized upon these fallacies and confusions, to
support them in their attempt to prove all mathematics
self-contradictory. Thence the Hegelian account of these
matters passed into the current thought of philosophers,
where it has remained long after the mathematicians have
removed all the difficulties upon which the philosophers
rely. And so long as the main object of philosophers is to
show that nothing can be learned by patience and detailed
thinking, but that we ought rather to worship the preju-
dices of the ignorant under the title of "reason" if we are
Hegelians, or of "intuition" if we are Bergsonians, so long
philosophers will take care to remain ignorant of what
mathematicians have done to remove the errors by which
Hegel profited.

Apart from the question of number, which we have al-
ready considered, the chief point at which Bergson touches
mathematics is his rejection of what he calls the "cinemato-
graphic" representation of the world. Mathematics con-
ceives change, even continuous change, as constituted by a
series of states ; Bergson, on the contrary, contends that no
series of states can represent what is continuous, and that
in change a thing is never in any state at all. This view-
that change is constituted by a series of changing states
he calls cinematographic; this view, he says, is natural to
the intellect, but is radically vicious. True change can
only be explained by true duration; it involves an inter-
penetration of past and present, not a mathematical suc-
cession of static states. This is what is called a "dynamic"

THE PHILOSOPHY OF BERGSON. 339

instead of a "static" view of the world. The question is
important, and in spite of its difficulty we cannot pass
it by.

Bergson's position is illustrated — and what is to be
said in criticism may also be aptly illustrated — by Zeno's
argument of the arrow. Zeno argues that, since the arrow
at each moment simply is where it is, therefore the arrow
in its flight is always at rest. At first sight, this argument
may not appear a very powerful one. Of course, it will be
said, the arrow is where it is at one moment, but at another
moment it is somewhere else, and this is just what con-
stitutes motion. Certain difficulties, it is true, arise out of
the continuity of motion, if we insist upon assuming that
motion is also discontinuous. These difficulties, thus ob-
tained, have long been part of the stock-in-trade of phi-
losophers. But if, with the mathematicians, we avoid the
assumption that motion is also discontinuous, we shall not
fall into the philosopher's difficulties. A cinematograph in
which there are an infinite number of films, and in which
there is never a next film because an infinite number come
between any two, will perfectly represent a continuous mo-
tion. Wherein, then, lies the force of Zeno's argument?

Zeno belonged to the Eleatic school, whose object was
to prove that there could be no such thing as change. The
natural view to take of the world is that there are things
which change ; for example, there is an arrow which is now
here, now there. By bisection of this view, philosophers
have developed two paradoxes. The Eleatics said that
there were things but no changes ; Heraclitus and Bergson
said that there were changes but no things. The Eleatics
said there was an arrow, but no flight; Heraclitus and
Bergson said there was a flight but no arrow. Each party
conducted its argument by refutation of the other party.
How ridiculous to say there is no arrow ! say the "static"
party. How ridiculous to say there is no flight! say the

34O THE MONIST.

"dynamic" party. The unfortunate man who stands in the
middle and maintains that there is both the arrow and its
flight is assumed by the disputants to deny both; he is
therefore pierced, like St. Sebastian, by the arrow from
one side and by its flight from the other. But we have still
not discovered wherein lies the force of Zeno's argument.

Zeno assumes, tacitly, the essence of the Bergsonian
theory of change. That is to say, he assumes that when a
thing is in a process of continuous change, even if it is
only change of position, there must be in the thing some
internal state of change. The thing must, at each instant,
be intrinsically different from what it would be if it were
not changing. He then points out that at each instant the
arrow simply is where it is, just as it would be if it were at
rest. Hence he concludes that there can be no such thing
as a state of motion, and therefore, adhering to the view
that a state of motion is essential to motion, he infers that
there can be no motion and that the arrow is always at rest.

Zeno's argument, therefore, though it does not touch
the mathematical account of change, does, prima facie,
refute a view of change which is not unlike M. Bergson's.
How, then, does M. Bergson meet Zeno's argument? He
meets it by denying that the arrow is ever anywhere. After
stating Zeno's argument, he replies: "Yes, if we suppose
that the arrow can ever be in a point of its course. Yes
again, if the arrow, which is moving, ever coincides with a
position, which is motionless. But the arrow never is in
any point of its course" (C. E.., p. 325). This reply to
Zeno, or a closely similar one concerning Achilles and the
Tortoise, occurs in all his three books. Bergson's view,
plainly, is paradoxical; whether it is possible, is a ques-
tion which demands a discussion of his view of duration.
His only argument in its favor is the statement that the
mathematical view of change "implies the absurd propo-
sition that movement is made of immobilities" (C. E., p.

THE PHILOSOPHY OF BERGSON. 34!

325). But the apparent absurdity of this view is merely
due to the verbal form in which he has stated it, and van-
ishes as soon as we realize that motion implies relations.
A friendship, for example, is made out of people who are
friends, but not out of friendships; a genealogy is made
out of men, but not out of genealogies. So a motion is
made out of what is moving, but not out of motions. It
expresses the fact that a thing may be in different places at
different times, and that the places may still be different
however near together the times may be. Bergson's argu-
ment against the mathematical view of motion, therefore,
reduces itself, in the last analysis, to a mere play upon
words. And with this conclusion we may pass on to a
criticism of his theory of duration.

Bergson's theory of duration is bound up with his the-
ory of memory. According to this theory, things remem-
bered survive in memory, and thus interpenetrate present
things : past and present are not mutually external, but are
mingled in the unity of consciousness. Action, he says, is
what constitutes being; but mathematical time is a mere
passive receptacle, which does nothing and therefore is
nothing (C. E., p. 41). The past, he says, is that which
acts no longer, and the present is that which is acting (M.
and M., p. 74). But in this statement, as indeed through-
out his account of duration, Bergson is unconsciously as-
suming the ordinary mathematical time; without this, his
statements are unmeaning. What is meant by saying "the
past is essentially that which acts no longer" (his italics),
except that the past is that of which the action is past ? The
words "no longer" are words expressive of the past; to a
person who did not have the ordinary notion of the past as
something outside the present, these words would have no
meaning. Thus his definition is circular. What he says is,
in effect, "the past is that of which the action is in the past."
As a definition, this cannot be regarded as a happy effort.

342 THE MONIST.

And the same applies to the present. The present, we are
told, is "that which is acting" (his italics).3 But the word
"is" introduces just that idea of the present which was to
be defined. The present is that which is acting as opposed
to that which was acting or will be acting. That is to say,
the present is that whose action is in the present, not in the
past or in the future. Again the definition is circular. An
earlier passage on the same page will illustrate the fallacy
further. "That which constitutes our pure perception," he
says, "is our dawning action. . . .The actuality of our per-
ception thus lies in its activity, in the movements which
prolong it, and not in its greater intensity : the past is only
idea, the present is ideo-motor" (ib.). This passage makes
it quite clear that, when Bergson speaks of the past, he
does not mean the past, but our present memory of the past.
The past when it existed was just as active as the present
is now; if Bergson's account were correct, the present
moment ought to be the only one in the whole history of
the world containing any activity.

In earlier times there were other perceptions, just as ac-
tive, just as actual in their day, as our present perception;
the past, in its day, was by no means only idea, but was in its
intrinsic character just what the present is now. This real
past, however, Bergson simply forgets ; what he speaks of
is the present idea of the past. The real past does not
mingle with the present. Our memory of the past does
of course mingle with the present, since it is part of it ; but
that is a very different thing.

The whole of Bergson's theory of duration and time
rests throughout on the elementary confusion between the
present occurrence of a recollection and the past occurrence
which is recollected. But for the fact that time is so f amil-

* Similarly in Matter and Memory (p. 193) he says it is a question whether
the past has ceased to exist, or has only ceased to be useful. The present, he
says, is not that which is, but that which is being made. The words I have
italicized here really involve the usual view of time.

THE PHILOSOPHY OF BERGSON. 343

iar to us, the vicious circle involved in his attempt to deduce
the past as what is no longer active would be obvious at
once. As it is, what Bergson gives is an account of the
difference between perception and recollection — both pres-
ent facts — and what he believes himself to have given is
an account of the difference between the present and the
past. As soon as this confusion is realized, his theory
of time is seen to be simply a theory which omits time alto-
gether.

The confusion between present remembering and the
past event remembered, which seems to be at the bottom
of Bergson's theory of time, is an instance of a more gen-
eral confusion which, if I am not mistaken, vitiates a great
deal of his thought, and indeed a great deal of the thought
of most modern philosophers — I mean the confusion be-
tween an act of knowing and that which is known. In
memory, the act of knowing is in the present, whereas what
is known is in the past; thus by confusing them the dis-
tinction between past and present is blurred. In percep-
tion, the act of knowing is mental, whereas what is known
is (at least in one sense) physical or material; thus by con-
fusing the two, the distinction between mind and matter is
blurred. This enables Bergson to say, as we saw, that
"pure perception, which is the lowest degree of mind. . . .is
really part of matter/' The act of perceiving is mind,
while that which is perceived is (in one sense) matter;
thus when these two are confused, the above statement
becomes intelligible.

Throughout Matter and Memory, this confusion be-
tween the act of knowing and the object known is indis-
pensable. It is enshrined in the use of the word "image,"
which is explained at the very beginning of the book.4

4Bergson's use of the word "image" is made clearer by a very pene-
trating analysis of Berkeley in a recent article, "L'Intuition Philosophique"
(Revue de Metaphysique et de Morale, Nov. 1911). This article displays very
distinctly the profound influence of Berkeley on Bergson's thought. Berg-
son's "image" is practically Berkeley's "idea."

344 THE MONIST.

He there states that, apart from philosophical theories,
everything that we know consists of "images," which in-
deed constitute the whole universe. He says : "I call mat-
ter the aggregate of images, and perception of matter these
same images referred to the eventual action of one par-
ticular image, my body" (M. and M., p. 8). It will be
observed that matter and the perception of matter, accord-
ing to him, consist of the very same things. The brain, he
says, is like the rest of the material universe, and is there-
fore an image if the universe is an image (p. 9).

Since the brain, which nobody sees, is not, in the ordi-
nary sense, an image, we are not surprised at his saying
that an image can be without being perceived (p. 27) ; but
he explains later on that, as regards images, the difference
between being and being consciously perceived is only one
of degree (p. 30). This is perhaps explained by another
passage in which he says: "What can be a non-perceived
material object, an image not imaged, unless it is a kind
of unconscious mental state?" (p. 183). Finally (p. 304)
he says : "That every reality has a kinship, an analogy, in
short a relation with consciousness — this is what we con-
cede to idealism by the very fact that we term things 'im-
ages.' ' Nevertheless he attempts to allay our initial doubt
by saying that he is beginning at a point before any of the
assumptions of philosophers have been introduced. "We
will assume," he says, "for the moment that we know
nothing of theories of matter and theories of spirit, nothing
of the discussions as to the reality or ideality of the external
world. Here I am in the presence of images" (p. i ). And
in the new Introduction which he wrote for the English
edition he says : "By 'image' we mean a certain existence
which is more than that which the idealist calls a represen-
tation, but less than that which the realist calls a thing, —
an existence placed halfway between the 'thing' and the
'representation'" (p. vii).

THE PHILOSOPHY OF BERGSON. 345

The distinction which Bergson has in mind in the above
is not, I think, the distinction between the imaging as a
mental occurrence and the thing imaged as an object. He
is thinking of the distinction between the thing as it is and
the thing as it appears, neither of which belongs to the
subject. The distinction between subject and object, be-
tween the mind which thinks and remembers and has im-
ages on the one hand, and the objects thought about, re-
membered, or imaged — this distinction, so far as I can
see, is wholly absent from his philosophy. Its absence is
his real debt to idealism ; and a very unfortunate debt it is.
In the case of "images," as we have just seen, it enables
him first to speak of images as neutral between mind and
matter, then to assert that the brain is an image in spite of
the fact that it has never been imaged, then to suggest that
matter and the perception of matter are the same thing,
but that a non-perceived image (such as the brain) is an
unconscious mental state ; while finally, the use of the word
"image," though involving no metaphysical theories what-
ever, nevertheless implies that every reality has "a kin-
ship, an analogy, in short a relation" with consciousness.

All these confusions are due to the initial confusion of
subject and object. The subject — a thought or an image
or a memory — is a present fact in me; the object may be
the law of gravitation or my friend Jones or the old Cam-
panile of Venice. The subject is mental and is here and
now. Therefore, if subject and object are one, the object
is mental and is here and now ; my friend Jones, though he
believes himself to be in South America and to exist on his
own account, is really in my head and exists in virtue of
my thinking about him; St. Mark's Campanile, in spite of
its great size and the fact that it ceased to exist ten years
ago, still exists, and is to be found complete inside me.
These statements are no travesty of Bergson's theories of

346 THE MONIST.

space and time ; they are merely an attempt to show what
is the actual concrete meaning of those theories.

The confusion of subject and object is not peculiar to
Bergson, but is common to many idealists and many mate-
rialists. Many idealists say that the object is really the
subject, and many materialists say that the subject is really
the object. They agree in thinking these two statements
very different, while yet holding that subject and object are
not different. In this respect, we may admit, Bergson has
merit, for he is as ready impartially to identify subject with
object as to identify object with subject. As soon as this
identification is rejected, his whole system collapses: first
his theories of space and time, then his belief in real con-
tingency, then his condemnation of intellect, then his ac-
count of the relations of mind and matter, and last of all
his whole view that the universe contains no things, but
only actions, movements,, changes, from nothing to nothing,
in an endless alternation of up and down.

Of course a large part of Bergson's philosophy, prob-
ably the part to which most of its popularity is due, does
not depend upon argument, and cannot be upset by argu-
ment. His imaginative picture of the world, regarded as
a poetic effort, is in the main not capable of either proof or
disproof. Shakespeare says life's but a walking shadow,
Shelley says it is like a dome of many-colored glass, Berg-
son says it is a shell which bursts into 'parts that are again
shells. If you like Bergson's image better, it is just as
legitimate.

The good which Bergson hopes to see realized in the
world is action for the sake of action. All pure contempla-
tion he calls "dreaming," and condemns by a whole series
of uncomplimentary epithets: static, Platonic, mathemat-
ical, logical, intellectual. Those who desire some prevision
of the end which action is to achieve are told that an end
foreseen would be nothing new, because desire, like mem-

THE PHILOSOPHY OF BERGSON. 347

ory, is identified with its object. Thus we are condemned,
in action, to be the blind slaves of instinct: the life-force
pushes us on from behind, restlessly and unceasingly.
There is no room in this philosophy for the moment of
contemplative insight when, rising above the animal life,
we become conscious of the greater ends that redeem man
from the life of the brutes. Those to whom activity with-
out purpose seems a sufficient good will find in Bergson's
books a pleasing picture of the universe. But those to
whom action, if it is to be of any value, must be inspired
by some vision, by some imaginative foreshadowing of a
world less painful, less unjust, less full of strife than the
world of our every-day life, those, in a word, whose action
is built on contemplation, will find in this philosophy noth-
ing of what they seek, and will not regret that there is no
reason to think it true.

B. RUSSELL.
CAMBRIDGE, ENGLAND.

PSYCHOTHERAPIC CULTS:1

CHRISTIAN SCIENCE; MIND CURE; NEW THOUGHT.

most noteworthy religious event since the Refor-
_L mation is perhaps the appearance in the United States
of a number of religious movements which may be grouped
together under the designation of psychotherapic cults.
The foremost of them is "Christian Science," founded by
Mrs. Mary Baker Eddy.

I hasten to add that the value of these cults does not,
in my mind, belong to their "metaphysics/' considered as
a philosophical system. It is the product of ignorant and
ill-trained minds. Much of it defies logic and offends com-
mon sense. But the defects which in the eyes of many
wholly damn these movements might conceivably be re-
moved, and there would remain important elements of a
new religious faith acceptable to the modern world.

I shall try to show that the psychotherapic movements
in their essential teaching are popularized and distorted
formulations, on the one hand, of important truths re-
garding the "power of thought" over body to which psy-
chology has recently given added significance, and, on the
other, of a non-theistic philosophy allied to the absolute
idealism of modern metaphysics. Although they distort
contemporary thought, they do not intend to oppose it.
They wish rather to build upon it.

1A discussion of other contemporary movements will be found in the
author's book, A Psychological Study of Religion: Its Origin, Function and
Future, Macmillan, 1912.

PSYCHOTHERAPIC CULTS. 349

These new cults are forcible reminders of the fact that
belief in a saving power is a condition of the existence of
religion, and also that the desire for deliverance from
moral and physical miseries and for the realization of ideals
continues to be the motive of religious life, just as it was
in the days of Gautama the Enlightener, and of Jesus the
Healer.

The mind-cure books announce "the discovery of the
might of truth in the treatment of disease as well as of
sin/' "the vital law of true life, true greatness, power,
and happiness." They claim to be "systems of transcen-
dental medicine/' or of "psychic therapeutics." They pur-
pose to minister to those who "would exchange impotence
for power, weakness and suffering for health and strength,
pain and unrest for peace, poverty for fulness and plenty."
They proclaim "the birthright of every man born into the
world to be physically whole and mentally happy." Their
claims have an extravagant sound, but no more so than
those made for "faith" by the New Testament writers who
declared it would remove mountains and secure eternal
blessedness after death. Nothing but vital experiences could
have inspired the enthusiasm and the assurance with which
these modern zealots proclaim the abounding efficacy of
their "truth."

If they call themselves Christians, it is not in the tra-
ditional sense. Of traditional Christianity they speak re-
spectfully, but they want a new dogmatics. They say,
"The time for thinkers has come. Truth, independent of
doctrines and time-honored systems, knocks at the portal of
humanity."2 In another of their aggressive little books
one reads: "Unrest is universal. The old landmarks are
disappearing. . . .Creed and dogma are things of the past;

3 Mary G. Baker Eddy, Science and Health, 1908, Preface.

35O THE MONIST.

religious ceremonial and form no longer interest the

masses."3

The impression these cults have produced on thought-
ful religious people is well expressed in this passage:

"Renan with his usual intuition declared that if it [the
religion of the future] were already in our midst, few of
us would know it.

"The prediction has proved true. The new religious
movement Christian Science has spoken a language so for-
eign to cultivated ears, its interpretation of the Bible is so
false, it is so obviously committed to errors, illusions, and
aberrations of every sort, that the intelligent have been
disposed to shrug their shoulders in contempt and to ignore
it. And yet they have not been able to ignore it altogether.
Every once in a while this curious superstition proves its
existence with unexpected power. We see a hard-headed
business man totally devoid of religious sentiment undergo
a new kind of conversion which leaves him as devout and
ardent as a Christian of the first century. An ailing wife
or daughter whom no physician has been able to help,
through some mysterious means is restored to health and
happiness. The victim of an enslaving habit, apparently
with very little effort and without physical means, suffer-
ings, or relapse, finds himself free. We enter a home where
the new belief reigns and we find there a peace to which
we are strangers.

"All over the country solid and enduring temples are
reared by grateful hands and consecrated to the ideal and
name of Mrs. Eddy. And this strange phenomenon has
occurred in the full light of day, at the end of the nine-
teenth and at the beginning of the twentieth century, and
these extraordinary doctrines have propagated themselves
not in obscure corners of the earth, among an illiterate and
fanatical population, but in the chief centers of American

8 Charles B. Patterson, A New Heaven and a New Earth, Preface.

PSYCHOTHERAPIC CULTS. 351

civilization. Such facts may well cause the philosophical
student of religion to reflect.4

In these movements is restored the alliance between the
art of healing the body and the art of healing the soul,
which was always a leading characteristic of the higher
religions during their period of greatest vitality. To the
masses the most impressive aspect of religions has always
been their power to heal the body. It was so in the early
ministry of Christ and during the first Christian centuries.
It is so now with these psychotherapists. And this revival
acquires great significance from the fact that it can now
be grounded upon the deeper understanding of the inter-
relation of mind and body, which we owe to modern science.

Speaking of the "four noble truths" of Buddhism,
(Satyani), i. e., the four axioms or certainties : the existence
of suffering, the origin of suffering, the emancipation from
suffering and the path that leads to the emancipation from
suffering, Kern says: "It is not difficult to see that these
four Satyas are nothing else but the four cardinal articles
of Indian medical science, applied to the spiritual healing
of mankind, exactly as in the Yoga doctrine. This con-
nection of the Aryasatyas with medical science was appar-
ently not unknown to the Buddhists themselves/' And
concerning the twelvefold causal root of the evil of the
world, the twelve Nidanas (causes), he declares that they
stand to the four Satyas 'in the same relation as pathology
to the whole system of medical science/ Now the four
truths and the twelve causes are fundamental facts upon
which Gautama's scheme of deliverance is built/'5

# # #

My chief effort will be to get from the writings of the
leaders of these therapeutic schools a clear idea of the

*Elwood Worcester, Samuel McComb, Isador H. Coriat, Religion and
Medicine, New York, 1908, pp. 8-10.

B Kern, Manual of Buddhism, Grundriss der indo-arischen Philologie und
Altertumskunde, Vol. Ill, No. 8, pp. 46-47.

352 THE MONIST.

power with which they expect to regenerate humanity, and
then to consider its adequacy. Whatever their affiliations,
these writers practically agree on the points that most
interest us. I do not shrink from putting before my read-
ers, to begin with, brief quotations from two of the most
extravagant and crude of these authors ; for even they find
followers among people who prove themselves intelligent
and sensible in the affairs of life.

T. Troward, a leader of Mental Science (not a disciple
of Mrs. Eddy), late divisional judge in Punjab and Edin-
burgh Lecturer on Mental Science, teaches the existence
of an unlimited, impersonal, though intelligent power,
which man may press into service, or appropriate to him-
self. His view of man's relation to that power is curious.
The individual can call it into action and give it direction,
"because it is in itself impersonal though intelligent." "It
will receive the impress of his personality, and can there-
fore make its influence felt far beyond the limits which
bound the individual's objective perception of the circum-
stances with which he has to deal. It is for this reason
that I lay so much stress on the combination of two appar-
ent opposites in the Universal Mind, the union of intelli-
gence with impersonality. . . .How do we know what the
intention of the Universal Mind may be? Here comes in
the element of impersonality. It has no intention, because

it is impersonal Combining, then, these two aspects

of the Universal Mind, .... we find precisely the sort of
natural force we are in want of, something which will
undertake whatever we put into its hands without asking
questions or bargaining for terms, and which, having
undertaken our business, will bring to bear on it an intelli-
gence to which the united knowledge of the whole human
race is as nothing, and a power equal to this intelligence."6

6T. Troward, The Edinburgh Lectures on Mental Science, The Arcane
Book Concern, 1909, Chicago, pp. 66-68.

PSYCHOTHERAPIC CULTS. 353

I find it difficult to conceive an unlimited impersonal
intelligence which has no intention and which individual
intelligence may direct. But in fairness to the abstruse
judge, I must add that this difficulty is no greater than that
presented by Hegel's conception of the Absolute Mind.

In the work of W. F. Evans we meet a consistent pan-
theism. He strives to give to his opinions an impressive
background compounded of modern science, antique pan-
theism, and modern idealism. How vast and accurate is
his knowledge will appear in the following passage. I
quote it without apology as another instance of a type of
conception apparently rational enough to be accepted by
many intelligent people. "The soul of man is a part, so
to speak, of the anima mundi, the soul of the world." The
power of the healing thought "issues from the spiritual
world of which our minds are a part, for all ideas belong
to that boundless realm of life." "It is stored up in ex-
haustless and overflowing abundance in the bosom of na-
ture. . . .it can be controlled in its lower degrees of mani-
festation by the intelligent will of man, which is the highest
form of its development and expression." "This grand
whole .... the universal world of spiritual intelligence is
called in Sanskrit, Addi-Budda. In the writings of Paul
it is called the Christ. . . .It is identical with what is called
magnetism, and is also that which the philosophers have
called the divine nous."1

One of the ablest and sanest writers of New Thought,
Ralph Waldo Trine, in a book which has passed its seventy-
fifth thousand, also announces a pantheistic gospel of an
infinite power at the service of man. "The great central
fact of the universe is that spirit of Infinite Life and Power
that is back of all, that animates all, that manifests itself
in and through all ; that self-existent principle of life from

7W. F. Evans, The Primitive Mind-Cure: Elementary Lessons in Chris-
tian Philosophy and Transcendental Medicine.

354 THE MONIST.

which all has come, and not only from which all has come,
but from which all is continually coming."

"This Infinite Power is creating, working, ruling
through the agency of great immutable laws and forces
that run through all the universe, that surround us on
every side. Every act of our every-day lives is governed
by these same great laws and forces."

"In a sense there is nothing in all the great universe
but law." But the presence of laws indicates a force back
of them. "This Spirit of Infinite Life and Power that is
back of all is what I call God."

"God, then, is this Infinite Spirit which fills all the
universe with Himself alone, so that all is from Him and in
Him, and there is nothing that is outside. . . .He is. . . .our
very life itself." "In essence the life of God and the life
of man are identically the same, and so are one. They
differ not in essence, in quality ; they differ in degree."

" .... if the God-powers are without limit, does it not
then follow that the only limitations man has are the limi-
tations he sets to himself, by virtue of not knowing him-
self?"

"The great central fact in human life, in your life and in
mine, is the coming into a conscious, vital realization of our
oneness with this Infinite Life, and the opening of ourselves
to this divine overflow" This means simply "that we are
recognizing our true identity, that we are bringing our
lives into harmony with the same great laws and forces,
and so opening ourselves to the same great inspirations
as have all the prophets, seers, sages, and saviours in the
world's history, all men of truly great and mighty power. "s
He does not hesitate to use the term "God-man."

8 Ralph Waldo Trine, In Tune with the Infinite or Fullness of Peace,
Power, and Plenty, Thomas Y. Crowell and Co., New York, pp. 11-20.

PSYCHOTHERAPIC CULTS. 355

Christian Science.

It seems almost incredible that one professing to be a
Christian should teach the impersonality of the divine na-
ture. And yet this is undoubtedly what Mrs. Eddy does,
and in this respect she agrees with those from whom I
have just quoted. The term that she prefers as a name
for the Divine Power is Principle. As synonyms she uses
Life, Truth, Love, God. In the earlier editions of Science
and Health, it is written that God "is not a person, God is
Principle."9 This is undoubtedly the standpoint of her later
writings also. But in them, probably because of the pres-
sure of adverse public opinion, she insists less than at the
beginning of her career upon the impersonality of Prin-
ciple, and the word "person" appears more frequently.
"Once in 1898, Mrs. Eddy hints that God may be personal
'if the term personality, as applied to God, means infinite
personality/ and Mr. Farlow in 1907 assures the Rev.
Edgar P. Hill that Mrs. Eddy does believe that 'God is per-
son in the infinite sense.' ' ' I take the following passages
from the same book: "Principle in her theology gathers
up into itself all the concepts we habitually associate with
God, except the most important — personality. Before her
book appeared in 1875, she was telling her pupils, as two
of them informed me, that they could make no progress
till they had banished from their minds the thought of God
as a person. She instructed Richard Kennedy 'to lay spe-
cial stress' in healing patients on the impersonality of God.
This is the commanding thought that rings through the
first chapter of the first edition of Science and Health."

"Mrs. Eddy's pantheism is unnecessary, and yet its
origin was inevitable in a mind as literal as hers. Quimby
often spoke of God as Principle. In the Quimby manu-

9 Mary G. Baker Eddy, op. cit., 3d ed., 1881, I, 67 ; II, 27.
10Lyman P. Powell, Christian Science, the Faith and its Founder, pp.
139-140.

356 THE MONIST.

script from which, for several years, Mrs. Eddy taught,
no sentence is more startling than the sentence 'God is
Principle/ "

"For more than thirty years Mrs. Eddy has been sol-
emnly asserting that in 1866 she received a 'final revelation/
Now this 'final revelation/ which was finally as well as
first expressed in 1875, in Science and Health, is saturated
with thought that God is not a person. In the very first
chapter we are informed that 'God is Principle, not person/
[I do not find that expression in the first chapter of the
1908 edition, but it is in No and Yes, published in 1909]
that Jesus preached the impersonality of God, that the
error of believing in the personality of God crucified Jesus,
that the trouble with conventional Christianity to-day is
that it makes God a person. .. .' (Pages 137-140).

On the other hand, in the seventy-third edition of No
and Yes, published in 1909, a pamphlet intended "to cor-
rect involuntary as well as voluntary error," we read : "Is
there a personal Deity? God is Infinite. He is neither a
limited mind nor a limited body. God is Love ; and Love
is Principle, not person. What the person of the Infinite
is, we know not; but we are gratefully and lovingly con-
scious of the fatherliness of this Supreme Being. God is
individual, and man is his individualized idea .... Limitless
personality is inconceivable .... Of God as person, human
reason, imagination and revelation give us no knowledge.

"When the term divine Principle is used to signify
Deity it may seem distant and cold, until better appre-
hended. This Principle is Mind, Substance, Life, Truth,
Love. When understood, Principle is found to be the only
term that fully conveys the ideas of God, — one Mind, a
perfect Man, and divine Science."11 This Principle, though
not a person, "is intelligence."

Although she wrote, "God is All in all," and "All in all

11 Eddy, No and Yes, 1909, pp. 19, 20.

PSYCHOTHERAPIC CULTS. 357

is God,"12 she will not be called a pantheist. In the edition
of No and Yes already quoted, she claims that "Christian
Science refutes pantheism, finds Spirit neither in matter
nor in the modes of mortal mind. It shows that matter and
mortal mind have neither origin nor existence in the eter-
nal Mind. . . .For God to know, is to be; that is, what He
knows must truly and eternally exist. If He knows matter,
and Matter cannot exist in Mind, then mortality and dis-
cord must be eternal."13

Her pantheism is in any case not materialistic, since
she holds matter to be unreal, a deception of mortal mind.
Hers is an idealistic pantheism, such as an ignorant person
of a thoroughly optimistic temperament might evolve on
the basis of imperfect knowledge of absolute idealism and
from observation of the mastery of mind over body.

The writings of Mrs. Eddy's disciples reflect the un-
critical, pantheistic idealism of their leader. Their favorite
phrases are such as these: "God's presence is the presence
of love;" "God is life everywhere present;" "One life fills
all, it is the Perfect Life."

The similarity of the essential aspects of New Thought
and Christian Science to the mystical element in Christian-
ity is evident. Both give clear expression to the anti-isola-
tion motive, to a dynamic belief in oneness-with-the-whole,
and both feel the essence of the cosmic plasma to be love.
Man is steeped in all-embracing Love. He need only place
himself in unison with the everlasting, all-comprehending
life-force and the fulness of life will be his. How love can
be an attribute of an impersonal power does not seem to
give Mrs. Eddy one moment of uneasiness.

In their curative practices, the psychotherapic cults
have the benefit of the recent discoveries concerning the
effects of suggestion. Regarding their methods, I may

" Eddy, Science and Health, 1898, p. 7.
13 Eddy, No and Yes, pp. 15, 16.

358 THE MONIST.

say here merely that they tend to place the person, as do
the practices of the other ethical religions, in a state of
increased suggestibility, a state described in part by the
words relaxedness, collectedness, monoideism, meditation,
communion. This condition of the subject aids greatly in
the realization of the expected benefits. The efficacy of
these curative methods is sufficiently demonstrated by the
wonderful extension of the movements. In every walk
of life people bear witness to the saving grace that is in
Christian Science or in New Thought. The forces of a
new life have welled up within them; the burdens of
existence have lightened, nay, have disappeared ; and now
they walk through life contented, hopeful, and aggressively
benevolent.

The following is an example of what people find in
Christian Science apart from the cure of disease :

"I accepted Science and Health without expecting it to
offer more than a human theory about life, — even the name
did not lead me to expect it to be religious; in fact, the
chief incentive to my reading it at that time was the great
kindness and sincere sympathy evinced by my friend, who

placed a copy at my disposal I started timidly at first,

and prayerfully, lest it should be misleading, but before
I had gone very far I experienced that wonderful spiritual
quickening which is so often spoken of in our meetings.
I wish I could tell exactly what the experience meant to
me, the wonderful awakening I had ; how old things van-
ished and all things became new. . It seemed as if the bur-
dens, perplexities, doubts, and fears had all suddenly rolled
away; as if the sun had emerged from behind the clouds,
and everything was again bright and beautiful.

"And what a feeling of strength, hope, and courage
came! Those old troublesome questions, especially the
question of death, were explained, and I felt a wonderful
release to know that death was not of God. I read and

PSYCHOTHERAPIC CULTS. 359

reread the latter part of the chapter on Christian Science
Practice, where that glorious truth is explained ; it was so
beautiful, so natural, and so true. There was such perfect
joy to me in that freedom, that I used to declare over and
over again, of those who had just passed from us (the
members of our home circle), 'They are not dead;' and so
free was I made from the old bondage, that never since
then has the thought of that change affected me as it did
before."14

Unnecessary importance is attached by the critical pub-
lic to the vagaries of Christian Science and of New
Thought; for instance, to the denial of the reality of mat-
ter, and therefore of disease; to the wild hopes of some of
their prophets that "the time will certainly come when the
highly developed man will have the power to lay down or
take up his life through a conscious knowlege of the laws
of eternal being and the direct application of these laws
to his own life."

When I say "wild hopes," I speak as the prosaic man
that I am. No less a philosopher than Bergson has ex-
pressed that same hope of overcoming death.

An apologist of the psychotherapic sects would be justi-
fied in making the following claims :

1. The salvation they promise is first of all for this
life.

2. The soul is not saved independently of the body. The
nefarious asceticism of older faiths is impossible on the
principles of Christian Science.

3. Their ideal involves efficiency in the conduct of this
life.

4. Their conception of salvation is free from anything
miraculous. They dispense with the wonders of the Fall,

14 Christian Science Sentinel, Dec. 3, 1901.
"Charles B. Patterson, op. tit., Preface.

360 THE MONIST.

of the self-sacrifice of a divine personage, and of salvation
by his atonement.

5. They divert attention from the sense of guilt and
suffering, and direct it to an immediately accessible healing
and invigorating power.

6. Although they usually define the aim of life in terms
of power, happiness, and love, they cannot fairly be charged
either with insensitiveness to moral values, or with indiffer-
ence to the ethical advancement of mankind.

7. Despite its extravagance, their "metaphysics" may
be regarded as a formulation, crude and distorted, of a
Weltanschauung made unavoidable by modern knowledge,
—a Weltanschauung, opposed in several important respects
to the traditional but no longer acceptable Christian philos-
ophy.

8. These cults have proved their value by their results.
In estimating the chances of continued life of religious

movements, one should bear in mind that vitally beneficial
beliefs may carry a heavy load of error and even of ab-
surdity. The Christian religion was not destroyed by the
expectation of the second coming of the Lord and of the
end of the world, by extravagant notions of the power of
faith, by absurd or incomprehensible doctrines regarding
the means of salvation, the resurrection of the body, and
the like. There is enough substantial, practical truth in
Christianity to bear the enormous doctrinal dead weight
it carries even to this day. It may be possible for the psy-
chotherapic doctrines to be purified in a reformation which
would either remove entirely or drive into side-currents
most of the offensive tenets.

J. H. LEUBA.
BRYN MAWR COLLEGE, PA.

THE MYSTERY OF LIFE.

A POETIZATION OF 'THE HAKO"— A PAWNEE CEREMONY.

BY HARTLEY BURR ALEXANDER.

PREFATORY NOTE. The 22d Annual Report of the Bureau of American
Ethnology contains Alice C. Fletcher's record of "The Hako : a Pawnee Cere-
mony." This record is the foundation of the present work. Miss Fletcher, in
her rhythmic renderings of the Indian songs, has incorporated meanings given
in the explanations of the leader of the ceremony as well as the literal sense
of the Indian texts ; the result being a series of admirable translations, abound-
ing in telling phrases. The version here presented has drawn freely upon Miss
Fletcher's fine renderings; but as "The Mystery" was designed to emphasize
the universal elements in the Indian thought, it necessarily involved generali-
zation and amplification of the primitive expression, as well as rearrangement
of materials. — The piece was conceived as a dramatic pageant, with musical
accompaniment, as will appear from its form.

DESCRIPTION OF THE SYMBOLS.
The Persons:

The LEADER, a Priest. He wears leggings and moccasins, and a robe girt
about his body, leaving shoulders and arms bare ; in his hair is a feather
of white eagle's down; he carries the brown-plumed wand.

Five ACOLYTES, dressed like the Leader. They carry the ceremonial articles
and act as assistants to the Leader.

The CHORUS, consisting of

(A) The SEMI-CHORUS OF FATHERS, led by the CHIEF OF THE FATHERS. They
are dressed in leggings and moccasins and ceremonial shirts, ornamented
with blue and white. They wear bonnets of white eagle's plumes. The
Chief carries a calumet and his bonnet extends in streamers of plumes
down his back. In Part II the bonnets are left off, and all wear blan-
kets, symbolic of night.

(B) The SEMI-CHORUS OF THE CHILDREN, led by the CHIEF OF THE CHIL-
DREN. They are dressed like the Fathers, except that their colors are
green and red and their bonnets adorned with brown plumes. In Part
II they also leave off the bonnets and wear blankets.

362 THE MONIST.

The CHILD.

The PERSONATOR OF THE MORNING- STAR, dressed in red, and wearing a red
plume; spread wings are attached to his wrists.

The Powers :
The BLUE SKY, abode of the FATHER OF HEAVEN, the Mighty Power.

The POWERS OF HEAVEN: The MORNING STAR, Herald of Day; the DAWN,
Child of Heaven and of Night; the SUN, Father of Day and of Life;
the Four WINDS from the Four Quarters of the World, where are the
Paths from Earth to Heaven.

MOTHER EARTH, whose Child is the Green Vegetation symbolized by the CORN
SPIRIT, andfwho sustains life with the running Waters which are the
WATERS OF LIFE and symbolize the continuing generations of Mankind.

The EAGLE. Chief of the Birds who are the Mediators between the Mighty
Power and Man; Conductor of the Visions, dwelling in the lower
Heaven, down to Man ; Symbol of the care which the Father of Heaven
has for his Children, — the brown plumes being emblematic of the Fe-
male Eagle in her care for her nestlings, the white plumes of the pro-
tecting Male Eagle: the place of the white is always outermost.

Emblems and Ceremonial Articles:

The BROWN-PLUMED WAND, borne by the Leader: a hollow stem, painted
blue, emblematic of the Sky, and adorned with a fan of the brown
plumes of the Female Eagle; also, with a Duck's head and breast, one
end of the stem being thrust through the mandibles; with a tuft of
Owl feathers; with red and white streamers, emblematic of Sun and
Stars.

The WHITE-PLUMED WAND, borne by an Acolyte: like the preceding except
that the stem is green, symbolic of Earth, and the plumes are the white
plumes of the Male Eagle.

The SPREAD WINGS OF AN EAGLE, mounted like the wings on the caduceus
of Mercury, except that each wing is on a detachable staff so that they
can be held separately, simulating flight, or conjoined, forming a banner.

The CORN, a light sheaf of maize with unhusked ears, symbolic of the Corn
Spirit and of the Vegetation which is the offspring of life-giving Mother
Earth.

The BOWL, hewn from the living wood, a part of Earth's green covering, and
painted blue as symbolizing the blue Sky. In it is borne water from a
running stream, symbolic of the vigor and strength which Earth gives
in the Waters of Life and of the continuance of life in the on-flowing
generations of men.

A tray with implements for Fire-making; a tray with ceremonial Tobacco;
a tray with four cups, one containing red, one blue, and one green
paint, and one with oil and fat. Trays of bread; jugs of water; turfs
for building the hearth-altar.

THE MYSTERY OF LIFE. 363

The Place :

The PLACE is a sward of level green on the open prairie. Above is the blue
sky with a few fleecy clouds. At the Western side of the sward, form-
ing the background, is a hedge of greenery, with three openings or gates.

The Northern Gate is the Gate of the Fathers,— North is the side of Night
and of the need of protection.

The Southern Gate is the Gate of the Children,— the South is the Winter
home of the birds, the side of peace and of plenty.

The Middle Gate, facing the Place of Sunrise, is the Gate of the Leader and
Acolytes. It opens from the Holy Place.

Color Symbolism :

BLUE symbolizes the abode of the Powers Above and of the Father of Heaven ;
GREEN symbolizes the Earth and life-giving food; RED is the color of
Life, of the life-blood and of the Morning Star who is herald of light
and life; WHITE symbolizes Sunlight, the fleecy Clouds and the Winds,
and hence the breath of Heaven, the Breath of Life.

PART I. THE COMING OF THE CORN.
THEME I.

Orchestral Prelude. Enter from the Central Gate the Leader and Acolytes;
from the North Gate, the Fathers; from the South Gate, the Children.
The Acolytes and the Chorus remain at the Rear; the Leader advances
to the Forefront.

The Leader intones:

I.

Give heed ! Give heed !

Give heed, O ye People!

Unto the Abode of Life give ye heed,

And unto the Powers thereof

Let your hearts be turned in reverence ....

ii.

Lift up your gaze!
Unto the blue and doming Skies

Lift up your gaze, —
Where dwelleth the Father of Heaven,
Where dwelleth the Father of Life,
Yea, from everlasting to everlasting.

Lift up your gaze
Unto the Father!..

364 THE MONIST.

In the Circle of the Heavens He hath set

The manifestations of His glory, —

The bright and shining Sun,

Which giveth forth the Light of Day

And answereth the hymn wherewith His creatures

Waken at Morn, —

In the Circle of the Heavens He hath established the Sun

To be a sign of His presence by Day,

And the quiet Stars hath He set to be His nightly ministers ,

The Four Winds

From the Four Pathways of the Skies, —
East, South, North, West,—
Breathe forth His Word and His Life
Throughout the Lodge of Heaven:
Yea, the music of His Word
And the gladness of Life
Breathe they forth
Through the Four Quarters of the World ....

Lift up your gaze
Unto the blue and doming Skies ! . . . .

in.

Upon the Earth
Let your thoughts descend, —

Our Mother Earth !

From her dark and fruitful womb ye are sprung,
And at her nourishing bosom ye are fed :
She is the Great Mother
Who keepeth us in life
And at death receiveth us:

Think on the Mother!

Her garment is the fair and flowing green,
The verdure of the hills is her habiliment,
Whence they that move obtain their strength
And the Sons of Men their sustenance:
Who is the Giver of Food unto her children.

THE MYSTERY OF LIFE. 365

As milk streameth from the breast,
From her ancient hills
And the cool depths of her yearly snows
The clear and living Waters are poured forth,
To be for her children their drink and their refreshing:
Yea, unto them that thirst She giveth the Waters of Life.
Think on the Mother !

IV.

Upon the Earth

Let your thoughts descend in reverent heed :
Let them be lifted up

To the blue and doming Skies !

Upon Earth and upon Heaven let your thoughts be placed,
For they are the Abode of Life and of the Powers thereof. . .

THEME II.
Roll of drums. The Chorus advances a pace, crying in unison :

Look down! We gaze afar on your dwelling!
Ye Mighty Ones, look down!

During the orchestral development that follows, the Semi-Chorus of Fathers
advances to the center of the sward where they form a circle, with an
opening to the East and one to the West, thus simulating the circular
outline of the walls of an earth lodge. With their hands they indicate
the building of walls. .During this action they chant: .

Ye of the Winds, behold us!
Ye Thunder gods, behold us!
Wielders of Leven, behold us !
Bringers of Death, behold us !

Ye of the Rains, behold us!
Ye of the Clouds and the Soil !
Givers of Increase, behold us!
Givers of Life, behold us!

We establish here a dwelling, —
A Wall of Defense,
A House of Life,
A Place that is Holy !

366 THE MONIST.

Full Chorus:

Look down ! We gaze afar on your dwelling !
Ye Mighty Ones, look down!

Semi-Chorus of Children advances, from the Western opening, within the
circle — the symbolic lodge — formed by the Fathers. They carry turfs
which they build into an hearth-altar at the center of the circle as they
file past. They form into two half circles, North and South, within the
circle of the Fathers. During the action they chant:

Spirits of Heaven, behold us!

Spirits of Earth, behold us!

Ye Shining Ones, behold us!

Ye Darkling Ones, behold us!

Ye that measure out the ways of men ....

Here we build unto you an Altar,
Whereof the flame is the prayer of man
Ascending. . . .

The Leader enters the encircled space from the Eastern opening, three Aco-
lytes bearing fire-making implements enter from the West. At the
Altar the Leader lays a fire and sends up a pillar of smoke, like an
Indian signal smoke. The music is the music of fire and of prayer.
As the smoke ascends —

The Chorus:

See! The Pillar of Smoke ascendetK
Up to the dome of Heaven
Where God abideth

The Leader:

As riseth the smoke of the Altar,
So the spirit of man upstriveth,
So the cry of his heart upmounteth,
Unto the deeps of the Blue,
Unto the Silence of God. .

The Chorus:

Speed aloft!

Bearing our supplication,

Bearing our prayer!

THE MYSTERY OF LIFE. 367

THEME III.

The flutes strike in with the clear piercing music of the Eagle. The Leader
gazes into the Eastern Sky. He raises his arm impressively, crying:

Lo, where cometh His answer —
The Eagle of the Chief of Heaven !

The Chorus circles North and South, bringing their faces to the East, and
then, during continuous circling motion :

Behold, an Eagle now is circling, widely circling above us!

Semi-Chorus of Children, circling to the South :

As the mother-bird circleth her nestlings, careful for her

chicks,
She circleth us, hovering. . . .

Semi-Chorus of Fathers, circling to the North :
She is the Eagle of God!
Of Him who is Father of Heaven,
Who ruleth the quartered Earth,
And sendeth His Will by the Eagle
Over the windy Pathways
That lead from Man up to God ....

Semi-Chorus of Children :

She is the Eagle of God !

The sign that He hath sent us

That we are in His eyes

As to the mother-bird are her nestlings. . . .

Semi-Chorus of Fathers :

She is the Eagle of God!
Whose coming is sign of His blessing, —
Of the gift of Food to His children,
Of the gift of Life to His children,
As the mother-bird home circling
Beareth food and life to her nestlings ....

Full Chorus:

Helpless are we as are nestlings,

Naked as unfledged eaglets

Lone in their storm-beaten crag. . . .

368 THE MONIST.

Semi-Chorus of Fathers :

About them circleth the Eagle,

Strong to protect, ever watchful,

His plumes flashing white in the sunlight, —

The cloud-frothing winds are his coursers!

Semi-Chorus of Children:

Over them hovereth the Eagle,
She of the brown brooding pinions,
Bearing them food in her talons, —
As the Father of Heaven permitteth.

Full Chorus:

We men are as naked and helpless

As the storm-beaten chicks of the Eagle ....

He of the wide-encircling Heavens guardeth us,
And the Sun-Father watcheth over us ;
Mother Earth bareth Her bosom unto us,
Her bounty is our daily bread ....

Amid silence the Leader and the Acolytes retire through the Center Gate, as
into an Holy of Holies. The Chorus remains ranged in the North and
South Forefronts.

THEME IV.

The oboes and bassoons strike up the droning music of the Corn. The tivo
Chiefs step forward.

Chief of the Fathers :

Father, have pity upon our weakness,
Father, have pity upon our hunger :
We men are as infants before thee,
We men are as helpless children
Weeping for food ....

Chief of the Children :

Out of far distant days soft-stepping,
I beheld one coming, a Spirit coming,
Coming to comfort me ....

In the tender and caressing night

I beheld my comforter: :. -'

THE MYSTERY OF LIFE. 369

Her wings dropped the dews of fragrance;
With the softness of stars was her body beautiful ;
In her breast were the singing voices of the fields ....

There enter from the North Gate two Acolytes, one bearing a tray of bread,
one bearing a jug of water, and from the South Gate two, with bread
and water. The Acolytes with the bread offer the bread to the Fathers
and to the Children.

Chief of the Fathers:

Lo, they bring ye the Body of Mother Earth :
Take thereof, and eat.

While they partake of the bread, one after the other, the Acolytes with the
water advance, offering the water to the Fathers and the Children.

Chief of the Children:

Lo, they bring ye the Waters of Life :
Drink, and be refreshed.

The Fathers and the Children moisten their lips as the water is offered them.
The Acolytes pass forth as they entered.

The music becomes tense, vibrant and rapid. The Chorus sways to and fro
in a crescendic rhythm.

From the Center Gate enter: Two Acolytes each bearing a staff with a spread
eagle-iving attached; the Leader and an Acolyte bearing the plumed
wands; an Acolyte bearing aloft the sheaf of maize; an Acolyte with
the bowl. They range themselves, the Leader a little in advance and to
the South, the Acolytes abreast, the wings at the ends, the Corn in the
center, the white-plumed wand at the left hand of the Corn-bearer, the
bowl at his right hand.

The Chorus, in animated motion, bursts forth in a lyric Hymn to the Corn :

Daughter of Heaven, Earth's first-born,
Hail to thee! Hail to thee! Spirit of Corn!
Thou at whose bounteous feasts we are fed,
Who givest us life in giving us bread:
Hail to thee ! Hail to thee ! Spirit of Corn !

Thou who dost welcome the Sun-Father's glance
With tassel and spear flung aloft to His Morn,
With nodding of plume and waving of lance,
Thou who dost make the green gardens to dance
With joy of thee, joy of thee, Spirit of Corn!

37O THE MONIST.

Thou who dost gather the sunlight and rain
Till the body of Earth with Heaven is o'erlain, —
Life, life is thy largess, who givest us grain!
Daughter of Heaven, Earth's first-born,
Hail to the thee ! Hail to thee ! Spirit of Corn !

They cease with nodding plumes.

THEME V.

The grave music of the Way of Life enters as an undertone to the Corn music.
The Leader advances to the Altar. He signals to the Acolytes, who up-
lift the emblems. He addresses the Powers:

Behold us, where we are standing,

Uplifting these emblems, —

Ye Mighty Ones, behold us ! ....

Out of the Heavens, cometh a flash!

Out of the Heavens, the light of His seeing eye!

At a sign the five Acolytes, abreast, advance to the Altar, before the Leader.
They present the emblems to the East, crying:

Ye of the East, behold us !
Ye of the Dawn and the Day!

They advance sixteen paces, wheel, and elevate the emblems to the West,
crying :

Ye of the West, behold us!

Ye of the Storm and the Night!

They return sixteen paces, wheel to the left, advance eight paces south, and
elevate the emblems to the South:

Ye of the South, behold us!
Ye of the Path of the Sun !

They wheel and advance sixteen paces to the North, elevating the emblems to
the North :

Ye of the North, behold us !
Ye of the Mother of Day !

They return eight paces to their original station before the Altar, and once
more advance sixteen paces to the East. There they remain, abreast.

THE MYSTERY OF LIFE. 371

The Leader advances eight paces from the Altar, till he stands, as it were,
upon the heart of the human figure traced by the evolutions of the
Acolytes.

The Leader:

Ye of Heaven and Earth, behold us!
Ye Powers of Life, behold us ! ....
Who journey the way of man.

Ye have given us for our Strengthener, the Spirit of Corn :
Ye have given us for our Leader, the Spirit of Corn ! . . . .
Who journey the toilsome way.

As the Spirit draweth nigh, we bow our heads:
As the Spirit toucheth us, we bow our heads ....
Who journey the Way of Life.

While the music grows in depth and gravity, the Chorus moves, forming in
a phalanx behind the Leader.

Then the Chorus-.

Open our way, Spirit of Corn!
Open our way, Leader in Life !

The Leader:

Open is the Way!

We are led as were our fathers led

Down through the ages:

We follow as they did follow.

The Leader signals; the Chorus moves forward; the Acolytes, abreast, with
the emblems upraised, the Corn still at the center, lead the processional,
which circles the sward and finally retires, the Leader and Acolytes
through the Center Gate, the Fathers through the North, the Children
through the South. During this movement, in full choral, is sung the
Chant of the Way of Life.

I.

During the advance:

Follow on, O Brothers, follow on!
The Spirit of the Corn doth lead
And unto you at your need

Falleth her benison:
Follow on, O Brothers, follow on.
Whither your sires are gone ....

372 THE MONIST.

Your feet one rhythm beating,
Your tongues one song repeating,
Your hearts one boon entreating,

Follow ye on!
Forth of the ruddy Morn,

Into the glowing Day,
Where the Spirit of the Corn

Showeth the way :
Follow on, O Brothers, follow on,

Whither your sires are gone.

ii.

Circling East:

Lo. the Circle of the Earth

Is the circle of Man's domain,
And he buildeth his puny hearth

In the midst of her spreading plain,-
And Morning and Noon and Night
He kindleth his tiny light.

Circling North :

Heaven hath a myriad stars,

Heaven hath the burning Sun,
The Day and the Night are their bars,
And their course is never run :
In the hour where it began
Dieth light in the lodge of man.

Circling West:

Man walketh in ways unknown,

From the darkening East to the West-
As a fledgling that hath flown
Forth from the Eagle's nest
To journey the pathless skies
With the sun of Heaven in his eyes.

Circling South :

Man bareth his head to the rain,

His breast to the storm layeth bare,
And he stalketh athwart the plain
Blind in the lightning's glare;

THE MYSTERY OF LIFE. 373

And heavy on his soul

Falls the terrible thunder's roll.

IV.

Circling East:

As an infant that is led

Amid the paths of surprise
By the hand that giveth him bread —
The hand of the foolish or wise —
So is a man in Their care
Who measure the ways he must fare.

Circling North :

The herds of the prairies pass,

At the will of the South and the North,
On the trail of the greening grass,

Where the Spirit of Life floweth forth,-
So man taketh up from the sod
The sacrament of God.

v.

Withdrawing :

Follow on, O Brothers, follow on!
In the ways whereto ye were born,
While leadeth the Spirit of Corn

Granting her benison:
Follow on, O Brothers, follow on,

Whither your sires are gone ! . . .
Your feet one spirit guiding,
Your lives one fate abiding,
In the wisdom of One confiding,

Follow ye on!
Into the sombre Night,

Forth of the flashing Day,
To lands beyond your sight

Lieth the Way

Follow on, O Brothers, follow on,

Whither your sires are gone.

[Exeunt omnes.]

374 THE MONIST.

PART II. THE REVELATION.

THEME VI.

The music opens with an eerie prelude, full of whispering notes suggestive of
things supernatural The Chorus, as yet unseen, strike in with their In-
vocation to the Visions. They enter singing, the Children from the
South, the Fathers from the North. They wear no bonnets and they
are girt with blankets, symbolic of Night. They circle in opposite direc-
tions, passing and repassing, file by file.

The Chorus:

Holy Visions, hither come!
Ye who dwell in rainbow Skies
Hidden from our mortal eyes
By the lights of Paradise, —

Holy Visions, hither come!

Holy Visions, hither come!
To our troubled lives descend,
Draw anigh and o'er us bend,
That our hurts may have an end :

Hither, hither come!

Holy Visions, hither come!
If we wake or if we dream,
Where your flashing pinions gleam
There doth Heaven on us beam:

Holy Visions, come!

Holy Visions, hither come!
Gift of joy your presence brings, •
When the music of your wings
To the gladdened spirit sings:

Hither, hither come!

Holy Visions, hither come!
Glorified the spirit blooms
Where the splendor of your plumes
Like a sun its night consumes:

Holy Visions, come !

THE MYSTERY OF LIFE. 375

Holy Visions, hither come!
With the lightnings of your glance
Make the hearts of men to dance
In celestial radiance:

Hither, hither come!

Holy Visions, hither come!
Bearing with you Heaven's Peace,
Bearing every hurt's release
In your healing mysteries :

Holy Visions, hither come!

The Chorus, as the song closes, form a semi-circle facing eastward, the
Fathers to the North, Children to the South. They kneel and draw
their robes over their heads, as in vigil The two Chiefs stand, a little
in advance.

The music is weird and mysterious, with innumerable fluttering crescendos,
as of approaching wings.

Then the Chief of the Fathers :

Hark, the sound of their wings !
Like the wings of mighty eagles:
Like the whistling winds on the prairies :
Like the rushing rain on the corn ! . . . .
Hark, the sound of their wings!

A pause. Then the Chief of the Children:

Was it in dreams that our Fathers beheld them?
In winged dreams that they came revealing
Unto our sires the Vision of Life?

Chief of the Fathers :

Yea, in their dreams our Fathers beheld them:
In shining dreams they came unveiling
Unto our Sires the Vision of Life ....

A pause. Then the Chief of the Children:

Hark, the sound of their wings !
Mighty spirits hither flying:
Mighty spirits here revealing
Visions as in days of yore. . . .
Hark, the sound of their wings!

The mysterious music continues for a time; then dies away into the steady
beating of deep-toned drums. An utter silence.

376 THE MONIST.

THEME VII.

A burst of drum-beats. The Chorus throw aside their robes from their heads,
and rise, crying:

Awake, O Mother, from sleep ! The night is far spent.
Awake, O Earth, from your rest ! The hills and the valleys

stir.

Awake, O World, from your night ! Day summoneth Earth
and Sky.

The Chorus moves, in a flowing rhythm, while the Chief of the Children sings
the Song of the Dawning, the orchestra sustaining with a liquid and
lyric mood:

A Wind bloweth forth from the East,

The Wind of the wakening Dawn:

The clutches of Sleep are released

Where the Wind bloweth on, bloweth on ....

The liquid Wind of the East,

The living Breath of the Dawn!

Lo, from her crag-built nest

The Eagle glanceth afar!

She preeneth her golden breast,

And with sweep of her pinions doth soar

Over the world's dim crest

Where the lights of the Morning are.

See! In the Eastern sky,

As a herald that runneth swift,

As a chieftain who draweth nigh

With ruddy plume uplift,

One cometh .... and passeth by :

The tidings of Dawn are his gift!

Tis the Star of the Morn, of the Morn !

A runner whom none shall withstay,

Whose red-shining token doth warn,

As he courseth his luminous way,

That a Child from the Night hath been born:

The Dawn! who foretelleth the Day!

THE MYSTERY OF LIFE. 377

To the growing animation of the music, the Chief of the Fathers'.

Behold !
A light in the East!

Behold !

The whitening Dawn!
Unto their morning feast
The creatures of light move on:
In pasture and brake
The world is awake

With browsing herd and with wilding deer:
The Day is here!

The music is rapid and exultant. The Chorus is in swift, swinging motion,
with imitative action suiting the words of their choral. All about is an
incessant tinkling, as of castanets and little bells.

The Chorus-.

Day is here!

Day is here, is here, is here!

Day is here, is here!

Awake, awake ! On the hills the light is breaking !
Awake, awake ! The heavens are aglow !
The sleepers all, their coverts are foresaking;
The winds of morning freshen as they blow:
Athwart the plain the deer with antlers shaking,
Athwart the sky the singing wildwings go!
Awake, awake! While dewy Earth is making
The springs of life with morning gladness flow !

Day is here!

Day is here, is here, is here!

Day is here, is here!

The song ceases with the Fathers to the North of the Altar, the Children to
the South, all facing toward it, their parallel files forming a broad
avenue from the Center Gate to the Forefront.

THEME VIII.

The music becomes strong and broad, developing the motive of the creation

of light and life and the mystery of revelation.
From the Center there enter, in single file: An Acolyte bearing the spread

wings, carried as a banner; an Acolyte bearing the white-plumed wand;

378 THE MONIST.

an Acolyte bearing a tray upon which is fire and tobacco; at a distance,
the Leader, as one inspired. The three Acolytes advance to the Fore-
front; the Leader remains before the Altar.

The two Chiefs with their calumets go before the Acolytes. They take the
fire and the tobacco and offer a smoke-offering to Heaven. Then the
Acolytes, in single file as before, withdraw through the Center; the
Chiefs retire to their stations.

The Leader, with uplifted gaze, intones the Psalm of Revelation :

With brooding mystery.

As I lay sleeping,

As I lay dreaming,

Out of the distance came one advancing,

Out of the distance came one descending,

As cometh a star from the deep of Heaven,

As cometh a star in a pool of light,

Welling to fullness,

Welling in stillness,

Till resteth its ray

On the brim of the World.

As I lay sleeping,

As I lay dreaming,

Out of the distance one came flying,

Out of the distance, with whirring of wings ....

As I lay sleeping,

As I lay dreaming,

Over me drooped her glittering wings,

Over me drooped, while she chanted the mystic

Spell of the riddle that ruleth the World.

As I lay sleeping,

As I lay dreaming,

She sang me the Song of the Eldest of Mornings,

She sang me the deeds of the Father creative,

She sang me the cure of the leaderless life. . . .

As I lay sleeping,

As I lay dreaming,

She read me the riddle that ruleth the World.

THE MYSTERY OF LIFE. 379

II.

With austere solemnity:

How they that were above were in Darkness

And they that were below were in Darkness:

When over all things brooded the Night, heavily ....

Silent were all things,

All lay hushed.

Then the Father of Heaven breathed the Breath of Life ;

Then the Father of Heaven moved upon the face of Darkness,

Upon the Body of Night,

Upon the body of the Mother of Day,

Moved the Father of Heaven,

Breathing the Breath of Life.

A Child to the Night is born !
.Unto the Father of Heaven and unto the Night
Is born the Dawn ....
Whose breath is the Breath of Life,
Whose gift is the Gift of Life
Unto all things.

A Child to the Night is born !

Yea, the Dawn,

Whose father is the Father of Heaven

And whose mother is the Night ....

And all things above

And all things below

Are quickened into being.

in.
As at first:

As I lay sleeping,

As I lay dreaming,

She sang me the Song of the Eldest of Mornings,

She sang me the deeds of the Father of All.

IV.

Solemnly, but with enthusiasm :

Then the Father of Heaven created the Chieftain Sun :
Who is sire of the shining Day;

380 THE MONIST.

Who is leader of the Wardens of Light ;

Who holdeth the measures of the years.

His spouse is our Mother Earth,

His warmth is the warmth of all that live,

Gladness is his offspring:

Whom the Father created Chieftain of the Skies.

Yea, the Father of Heaven united Earth and Sun

In Holy Marriage,

Whereof are born her breathing Children —

Bird and beast and mortal men —

And all her living fruits :

The Father of Heaven united Earth and Sun,

Whose Child is mortal Life.

v.
As at first:

As I lay sleeping,

As I lay dreaming,

Lo, in a Vision one came revealing

The Mystery of Life.

VI. i

With exaltation :

Give heed ! Give heed !

Give heed, O ye People!

Unto the Abode of Life give ye heed,

And unto the Powers thereof

Let your hearts be turned in reverence ....

The Leader remains beside the Altar.

THEME IX.

The Chorus moves in stately alternation of the Semi-Choruses, chanting their
antiphon to Earth and Sun.

Semi-Chorus of Fathers:

Now behold! Hither cometh the ray of our Father Sun,
Over all the land, us to touch and give us strength !

Semi-Chorus of Children:

We think on Mother Earth who lieth here:
We know she giveth of her fruitfulness.

THE MYSTERY OF LIFE. 381

Semi-Chorus of Fathers :

Now behold! Where mounteth up our Father Sun!
Into the Lodge of Heaven he mounteth up.

Semi-Chorus of Children:

Behold on Mother Earth the growing fields:
Behold the promise of her f ruitfulness !

Semi-Chorus of Fathers :

Now behold ! Through all the World our Father Sun
Sendeth his rays, the Messengers of Light!

Semi-Chorus of Children:

We think on Mother Earth who lieth here:
We see the promise of her fruitfulness.

Semi-Chorus of Fathers :

Now behold ! How all the life of hill and plain
Is quickened by the rays of our Father Sun!

Semi-Chorus of Children:

Give thanks to Mother Earth for trees and streams ;
Give thanks to Mother Earth for growing fields;
Give thanks to Mother Earth for ripened corn;
Give thanks to Mother Earth for food and life!

Semi-Chorus of Fathers:

Now behold! Where goeth down our Father Sun,
Who of his strength this day of life hath given!

Semi-Chorus of Children:

We think on Mother Earth who lieth here:
Truly, her power she hath given us!

Semi-Chorus of Fathers :

Now behold ! Where sinketh low our Father Sun

Upon the margent of the glowing West ! . . . .

So is the life of man led forth

Out of the Night, through Morn and Noon and Eve,

To sink into the silent Night again !

Semi-Chorus of Children:

We think on Mother Earth who lieth here. .

382 THE MONIST.

THEME X.

The mysterious music of the inaugural is resumed, but with a deeper, more
austere meaning. The Chorus forms for the outgoing. Then the
Leader, with arms outspread:

There is none persuadeth Death!

The old men have not told how any hath found a way.

The career of a Leader is difficult!

Marching counter, as in their entrance, the Fathers and the Children circle
the sward and pass out at their respective gates, chanting :

Holy Visions, ye of yore
To our Fathers came revealing;
Hither come, O come once more,
To our troubled lives with healing!

Holy Visions, ye who bring
From the starlit Sky her glories,
Hither come on shining wing,
Pause ye where the open door is :

Pause ye at the open gate,
Enter at the silent portal,
Bless the hearts of them that wait
With the grace of light immortal:

With the grace of holy sight
To the dream-life of the dreamer
Ye shall come, and guide aright:
He shall know his life's redeemer.

Holy visions ! As of yore
To our Sires ye came revealing,
Come, O come to us once more,
With the mystery of healing!

[As the last of the Chorus is disappearing, the Leader retires, solitary.]

PART III. THE MYSTERY.

THEME XL

From the North and South Gates the Fathers and the Children, except their
Chiefs, who remain behind, enter in an animated and swift-scattering

THE MYSTERY OF LIFE. 383

movement, giving the effect of individual wheelings and circlings and
poisings over the whole plaza. The music is lively and full of bird
themes.

The Chorus :

Hark, hark! The birds!

The birds are a-wing!

Earth and Sky are alive

Where they flit, where they swing !

Where they dip, where they dive,

And down the winds drive,

Till with whir and with whing

Of thunderous wing

The volleying air

Is a-blare, is a-blare!

Rising, circling, dipping, fleeting,

Now they rest, and now they haste !
Coming, going, parting, meeting,
Bird to bird his cry repeating :

"Summer nest is Wintry waste!
"Winter stealeth Summer pleasure,

"Garb of green he turneth gray:
"Where the winds bear Summer's treasure,

"Thither, thither, haste away !"

Flutt'ring, flocking, flitting, flying,
Now they rest, and now they haste,

Bird to answering bird a-crying:
"Summer nest is Wintry waste!"

Individual singers, one by one, sing the songs of the birds, with mimetic
action.

The Song of the Nestling :

O'er the prairie, o'er the prairie,

Round about me as I walk,
How the shadows flit in circles —
Mischief shadows, making mock!

'Tis the birds above wide circling,
'Tis their shadows on the ground :

As when parent birds protecting
Feeble nestlings circle round.

384 THE MONIST.

Birds of Heaven, Birds of Heaven,
We, your nestlings, joyous cry

When His sign of care ye give us,
Wheeling in the azure sky !

The Song of the Wren :

Whe kee re re wee chee!
Whe kee re re wee chee!

Joy, joy, joy!
Singeth the tiny Wren:
And shall not men
Know joy?

The Song of the Duck :

Lo, the Finder-Out of Ways—
The Bird of the Emerald Crest—
The Bird who never strays,

But doth fare
In arrowy flight and ware
Over water and earth and air,

North and South,

East and West

Oh, the speeding Scout of the Skies
Knoweth their quartering ties :
As the Leader of Men must know
Where the paths of Heaven go!

The Song of the Owl:

He! HiriWahoru!

He! Hiri Wahoru!

Wide-eyed Bird of the Night,
Who seest invisible things
And spreadest thy shadowy wings
In dim and inaudible flight. . . .

He! HiriWahoru!

He! Hiri Wahoru!

Let ours be the gift of thy sight!

Full Chorus:

Oh, the Bird, the Birds!
The Birds are a-wing!

THE MYSTERY OF LIFE. 385

Like sky-blown herds
At the wintry sting
Which the North

Striketh forth

Where they come,

Where they go,

All the air

Is a-blare,

All the air is a-thrum,

As with beating of drum

And sounding of string

Where drawn is the bow

And the swift arrows sing ! . . . .

Oh, the Birds are a-wing!

Summer flown,
Nestlings grown,
Southward blown
Wide a-wing!

The Chorus ends its evolutions with the two divisions forming, as it were,
encircling wings, across the Forefront, and facing Northwest and South-
west, so as to view the gates.

THEME XII.

The temper of the music becomes more grave, with the flutes of the Eagle
dominant.

Semi-Chorus of Fathers :

Behold, an Eagle now is circling, widely circling above us !

Semi-Chorus of Children :

As the mother-bird circleth her nestlings, careful for her

chicks,
She circleth us, hovering. . . .

Full Chorus:

She is the Eagle of God!

Of Him who is Father of Heaven,

Who ruleth the zoned Earth

And sendeth His will by the Eagle

Over the windy Pathways

That lead from Man up to God ! . . . .

386 THE MONIST.

The motive of the music is the poignancy of human aspiration.

From the North Gate, the Gate of the Fathers, enter-. An Acolyte with the
Spread Wings, borne as a banner; an Acolyte with the Corn, one with
the Bowl, one with Tray and Cups; the Leader, with wand; an Acolyte
with the white-plumed wand. They march in single file, their path a
semi-circle from the North to the South Gate, around the Altar. At
the Altar they stop.

The Leader:

I know not if the voice of man can reach unto the Skies ;
I know not if the Silent One can hear me as I pray ;
I know not if my words be foolish words or wise ;
I know not if I walk in straight or crooked way.

I only know His power, Who hath made our mortal lot
An hurt and stumbling pace led outward through the dark ;
I only know his trust, Who lest He be forgot,
Hath weathered deep the soul of man with an immortal mark.

As they move on toward the South Gate, the Gate of the Children, the Aco-
lytes sing, in choral:

Father, unto thee we cry !
Father of all we hear and see,
Father of all we feel and hope,
Author of life's mystery:
Father, unto thee we cry !

They pass out.

THEME XIII.

The Fathers, pianissimo bass, sing :

With the dawn will I seek my child,
With the tenderly growing dawn ;
Where the breath of the morn floweth on
I will go seeking my child,
My little one, my son ....

With swelling music, the Children:

Father, come unto me here,
Here where I wait for thee, —
With bread and with morning cheer,
Father, come unto me!

THE MYSTERY OF LIFE. 387

The Fathers:

I come, my child, I come,
Seeking for thee ....
Abide me, and nothing fear:
On the wings of the dawn I come
Seeking for thee ....

The Children:

See!

The Eagle is flying o'er us!

In the sky above, from the Father's home !

The Eagle descendeth unto us

With the Father's cheer !

In the music is the note of the dawning Light. Then the Chorus :
Behold !

The Star of the East!
The Star of the bursting Morn!

From the Gate of the Children a runner, personator of the Morning Star, clad
all in red, the color of life, and in his hair a red plume, symbolic of the
breath of life. To his arms are attached spread wings. Sweeping past,
he cries:

A Child is born!

Unto Man a Child is born!

Unto Man is born a Son !

He passes forth by the North Gate, the Gate of the Fathers.
The Chorus:

A Child is born ! A Child is born !

An holy Child is born!

Stars of the Morning rejoice!

Life is renewed in the World !

The music swells with prophetic exaltation.

Enter from the Holy Gate: The Acolyte with the Spread Wings; the Acolyte
with the Corn, he with the Bowl, he with the Tray on which are the
four cups; the Acolyte with the white-plumed Wand; the Leader; the
Chief of the Fathers, carrying the Child; the Chief of the Children.

When all are entered the Leader takes the Child and holds him aloft, crying :
Behold the Child!

388 THE MONIST.

The Chorus:

Behold the Child!

Behold the Promised One!

The Leader returns the Child to the Chief of the Fathers, on either side of
whom the Acolytes range themselves, and leads the way to the Altar,
while the Acolytes sing :

Here we go singing, singing, ....

Looking on the Child —

The little Child who leadeth us,

Borne in his father's arms:

Here we go singing, singing. . . .

Looking on the Child.

THEME XIV.

At the Altar they form: the Leader a few paces in advance, at his left the
Chief of the Fathers zvith the Child and the Chief of the Children; the
Acolytes ranged before the Altar, the white-plumed Wand to the North,
the Spread Wings to the South.

The Leader spreads his hands, like spread wings, above the Child. He sig-
nals to the Acolyte with the tray and cups, who advances. The Leader
dips his finger into one of the cups and touches the Child, drawing a
semi-circle about his brow.

The Leader:

With the Blue of the Skies I anoint thee ....

The Chorus:

That thou may'st long abide beneath the Lodge of Heaven.

The Leader dips his finger into a second cup and draws it across the Child's
chin :

With the Green of the Earth I anoint thee ....

The Chorus :

That thy feet may be led amid fruitful fields.

Dipping into a third cup and touching the Child's cheeks:

With the Crimson of Life I anoint thee. . . .

The Chorus:

That strength and vigor shall be thine in youth and age.

THE MYSTERY OF LIFE. 389

Dipping into the fourth cup the Leader touches the Child's brow :
With Oil and with Fat I anoint thee ....

The Chorus:

That peace and plenty may follow thee all thy days.

The Acolyte retires; the Leader once more spreads his hands above the Child;
a second Acolyte advances, bearing the Corn. The Leader taking it,
strokes the Child's body :

I stroke thee with the ripened Corn ....

The Chorus :

So may thy body's needs be satisfied!

The Acolyte with the Bowl advances. The Leader sprinkles the Child:
I refresh thee with the clear and running stream ....

The Chorus :

So may thy generations run onward without ceasing.

The Acolytes retire. The Leader takes from his hair the white eagle-down
and fastens it in the Child's hair:

With this sacred token I thee adorn —
Symbol of the fleecy clouds above,
Symbol of the winds of Heaven,
Symbol of the living breath
Into the body of man
Breathed by the Father

After a pause, his hands resting on the Child's head:

Enter ye into the House of Life, consecrate.

He returns the Child to the Chief of the Fathers. Then triumphantly:
I know now that the voice of man can reach the skies ;
I know now that the Mighty One can hear me as I pray ;
I know our Father answereth his children's troubled cries,
And pace by pace assigneth us the token of the way.

Give heed ! Give heed !

Give heed, O ye People!

Unto the Abode of Life give ye heed,

And unto the Powers thereof

Let your hearts be turned in reverence ....

390 THE MONIST.

THEME XV.

The music becomes reminiscent of the Chant of the Way of Life. The Chorus
moves forward, forming a circle, the Children within, the Fathers
without, as in the figure of the lodge. The Leader advances beyond
the Altar and paces a small circle, or symbolic lodge. The two Chiefs
enter this circle while the Acolytes, with emblems raised as in blessing,
form a semi-circle behind.

The Chief of the Children takes the Child from the Chief of the Fathers.
Then the Chief of the Fathers moves forward and sings:

Within the House of Life man entereth
A little Child with slow and faltering feet:

The breathing Heaven is in his fluttering breath,
The pulse of Earth in his swift blood doth beat.

Within the House of Life man tarrieth,
As one who for a season taketh rest:

The Blue above, below the grassy Earth, —
An oriole within a wind-swept nest.

Within the House of Life man offereth

The simple tokens of his daily need,
His prayer for food and drink, in humble faith

That some dim distant Power shall give them heed.

Then from the House of Life he hasteneth. . . .

Aye, as an Eagle in his feathered mail
Battleth adown the blast with windy Death,

Speedeth the Warrior-Soul with battle-hail !

The Chorus is in motion, moving in a strange dance simulating the -flight of
eagles. They form in files and circle about the central group. They sing :

Come, ye Fathers!

Come, ye Children!

Come, ye People, —

Mortal men !

Into the House of Life, come enter!

Into the House — the Way is open :

Enter in, O mortal men ! . . . .

Like flocking birds,

Like shouting eagles,

Full of joy and lust of life,

THE MYSTERY OF LIFE. 39!

Swiftly, swiftly, swiftly come ye, —
Enter in, O mortal men ! . . . .
As your Fathers came before you,
As a little child doth come,
Where the Way is open, open,
Enter in, O mortal men ! . . . .

As they cease, the tzvo groups, the Fathers and the Children, are formed, on
the North and the South, like the spread wings of an Eagle. The two
Chiefs, in the center, are the bird's body; the Acolytes, with the em-
blems, have retreated, forming, as it were, the tail plumes; the Leader,
with the Child, has advanced to the head.

There falls an utter stillness. The Leader uplifts the Child, looking upward.
In a penetrating voice he cries :

Breathe on him!

Breathe on him!

Life thou alone canst give him :

Long life, we pray, O Father, give unto him !

Mid swelling music, like the march of the tribes and nations of men, exeunt
omnes.

THE END.

CRITICISMS AND DISCUSSIONS.

BERGSON AND RELIGION.

Henri Bergson is probably the most potential name in modern
philosophy. Prof. William James, who was by common consent our
most distinguished thinker, though he was much older, called Pro-
fessor Bergson "master and teacher." This, certainly, is high praise.

Aside from his speculative capacity, Professor Bergson is a most
interesting figure. He is an earnest student of physiology, biology
and psychology, and he brings to his philosophical theories a great
wealth of scientific illustration and proof. And unlike so many of
our great metaphysicians, he has literary power, the gift of musical
speech. Whether the Evolution creatrice is great art like the Corin-
thians of Paul, the Divine Comedy, "Lycidas," or "Les Miserables,"
it may be too soon to decide. But it is certainly a work of art, and
of no mean order. Professor Bergson is a personality, and his
thought is always suggestive and commands attention.

It is interesting to watch the flight of his speculative 'arrows,
even though we fail to see that they strike any target. Nevertheless,
in my judgment he has made one vital suggestion, which I shall
indicate in the course of this study. But first I shall attempt to
trace his theory of the universe and his theory of truth and show
their philosophical and religious meaning and influence.

As every one comes to a study with certain prepossessions, I
may say that I am not a materialist, idealist or pragmatist, but con-
ceive there are in man elements not mechanical and that he has,
within narrow limits, the power of choice.

Professor Bergson in his theory makes an immeasurable pri-
meval "super-consciousness" the source of all things, of life and
matter. This unique creative absolute has will, freedom, and an
impulse to create, but strange to say, though it has this consciousness
and spontaneity, it has not intelligence. It moves on and on, ever
unfolding, ever augmenting, with no design or purpose, seeking

CRITICISMS AND DISCUSSIONS. 393

no predetermined goal, for M. Bergson frowns upon all forms of
teleology.

This theory of a great life-river, if I may so describe it, ever
seeking to find new channels of creative opportunity, I found to
my surprise was similar to that of my friend, Prof. F. C. Doan,
published in the Journal of Philosophy about two years before the
"Creative Evolution" appeared. I learned, since commencing this
paper, that Professor James had made the same discovery. And I
may say that, leaving off certain naive features in the book of Gen-
esis, M. Bergson's theory of the origin of the world reminds me of
that great sentence : "In the beginning, God."

Whence comes this vast energy with its impulse to create, M.
Bergson does not tell. He asserts that from it spring both life and
matter and that every living thing, from the lichen on the rock to
the golden dandelion nodding in the south wind, from the ameba
to the man, possesses consciousness and freedom, and these qualities
enmeshed and entangled in matter, reduced or attenuated to the
finest threads, are never lost. At times Professor Bergson calls
matter "the enemy" of all good. It is ever to be resisted, it must be
transmuted into living organisms, it must be saturated with "con-
tingency."

Again he calls the resistance of matter a "stimulus." It is by
the reduction of the flesh, by the chastening of the senses, that men
become healthy, strong and beautiful.

It will be seen that in this dogma of the life-urge, M. Bergson
strenuously opposes the new naturalism so popular at the close of
the last century. He affirms that life always has in it the seeds of
freedom or contingency, that contingency grows greater as organ-
isms develop. He cannot believe that the high reason that has traced
the laws of the earth and measured the stars, that the hope, affection,
imagination which blossomed into the melodious words of the Ser-
mon on the Mount are the product of mechanical and unintelligent
forces — that blind physical atoms could in time stumble into an
orderly living universe !

Has Professor Bergson spoken a deep, living word? Has he
made a new synthesis? There are many who believe that he has.
He opposes the older idealism of Kant, Hegel and Fichte, and the
"absolute" of such teachers as Royce and Bradley in his theory of
time. For unlike them, he makes time a reality, and in time creation
begins. His theory of this original creative energy makes the uni-
verse of life and matter a great Mississippi life-river, ever flowing

394 THE MONIST.

on. Its course may be traced in the past and in the present, but its
course in the future, he says, no one, however wise, can trace.

That the future is impenetrably veiled (an idea I have long
contended for), Professor Bergson urges from the fact that the uni-
verse is not made but making. There is ever the condition of un-
certainty, of spontaneity, of contingency, and thence may come the
unexpected. We see now the leaf, the stalk, the bud, but of the
glory and beauty of the flower and fruit, none can know.

M. Bergson's opposition to materialism is seen in his radical
idea of freedom. He maintains that in all living organisms there is
something that cannot be accounted for by the laws of matter. There
is in them a power which draws from itself more than it receives,
"gives more than has been given to it." There is something free
in the violet, the bird, the man, not produced by reflex action. There
is a tiny will, a drop of beauty, of will, of love, of intelligence, which
is pure creation. There is ever the quality of the contingent, the new,
the unforeseen, for this is a "spiritual universe."

Of course the idealist will say that Professor Bergson's theory
destroys the timelessness and omniscience of the Absolute, and the
naturalist will ask for proof. He will inquire, why it was necessary
to invent a "superconsciousness" to start the universe. He will
say it is just as easy to think of life evolving from matter, as matter
from life; and the idealist will be alarmed at the thought of ad-
mitting into the universe the element of imperfection and the un-
foreseen.

But we must now come to the more original, and more radical
part of his theory, his theory of truth. The extreme radicalism of
his idea may be seen from the fact that M. Bergson makes "not
reason but instinct bring us into the closest touch, the directest rela-
tion with what is most real in the universe," to use the words of
Mr. Balfour. In this, I may say that Professor Bergson follows the
present tendency to distrust the power of the intellect to reach a
reasonable explanation of the universe — to prove the existence of
God, of freedom, of immortality. All questions of ultimates are
beyond intellectual search. The intellect is limited to the sphere of
experience.

Professor Bergson agrees with this distrust of the intellect, but
affirms that what is impossible to the intellect is possible to instinct.
The province of reason is not life, freedom, spirituality, but matter,
mechanics and space, "the waste products of the" life-urge. James
agrees with his teacher here, for he says that "the reason can know

CRITICISMS AND DISCUSSIONS. 395

only surfaces." But, one may ask, are not these statements purely
dogmatic, speculative?

Professor Bergson, while he admits the immeasurably wider
horizons of the human intellect, asserts that instinct, in ants and bees
in which it comes to its perfect flower, is in touch with a higher
order of truth. Maeterlinck makes a similar assertion in his work
on the bees.

But surely there lie innumerable difficulties in the path of this
fantastic theory. If the instinct of the Hymenopterae is the infallible
organ for the discovery of knowledge, why is it that they do not ad-
vance, but keep in the same monotonous round? With this great
power, why is their achievement so limited, their vision so narrow?
Why should they have so much of this divine power, and man, who
is so incomparably greater, have so little? With this great endow-
ment, wherein have they advanced beyond him?

Professor Bergson tells of a certain kind of wasp, the fossorial,
which, instead of killing its victim, stings it into unconsciousness
by a most delicate surgical act. This mechanical skill, he says, does
not come as the result of numberless experiments, and it would
be forever impossible^ to intelligence, but it comes through that in-
stinct which reveals to the wasp the secret of life itself.

Does it not seem fantastic, to say the least, that the instinct of
the fossorial wasp can reach a higher truth than the most sustained
efforts of a great intellect? Can the work or conquests of the ants
and bees compare with the magnificent achievements of the human
intellect in mathematical, physical and moral science? Do we come
into nearer touch with reality in the cell of an ant than in a painting
by Titian ?

It is true that the instincts are nearest the primeval forces, and
may guide us best in the things of the flesh. Instinct may, by a sort
of divine unreason, go straight to the heart of the lower truth, but to
solve the supreme problems, the meaning of life, the existence of
God, of freedom and of immortality must be an achievement of the
highest intellect.

But it would not be fair to M. Bergson, not to explain that these
mystical assertions, these speculative dreams, are enmeshed in a
profusion of scientific illustration. He shows a minute and wide
knowledge of physiology, biology and natural history, and in his
boldest speculative flights always makes his final appeal to concrete
facts.

But now I come to the question that will arise in many minds :

396 THE MONIST.

Is the philosophy of Professor Bergson religious in the highest
sense ? Does it make its appeal to our spiritual faith and aspirations ?

Though this philosophy is radically opposed to the mechanical
and atheistical tendencies of naturalism, many will say it cannot be
called religious, as M. Bergson certainly means it to be. It is true,
the Christian may see theism in the primeval life-urge, which is the
source of matter and all living things, and in the exaltation of the
instinct a recognition of the validity of the religious intuitions ; but
it will be difficult for the intelligent man to see a real theism in this
primeval creative consciousness, though it has the will to create and
freedom, but has no plan or purpose, nor directs the universe to any
intelligent goal.

And while in his theory of evolution he escapes the difficulty
or dilemma of the old metaphysical systems (that the imperfections,
the evil, the sorrows of the universe, had been known to God before
He created it, and were of His own selection), it does seem difficult
to feel the sense of worship in the thought of a universe ever evolv-
ing, yet ever unintelligible and unmoral.

In the pluralism of Professor James, though he calls himself
a pupil of Bergson, there is something for the common mind to
catch hold of. When he says that God is the deepest power in the
universe and is a personality, that "man and God have purposes
for which they care and each can hear the other's call," he makes
an appeal to the humblest believer. But I fear that the common
people will not see the religious element in the philosophy of Pro-
fessor Bergson. The saints who love and pray will cling to the
thought of a transcendent God, leading the world to a wise and
happy end, rather than believe in this impersonal life-force that
forever unfolds, goes on and on, but knows not whither it is going.

On the other hand, the scientist will have his own thoughts. He
sees that M. Bergson, to find an explanation, goes back to that primal
sea of life. He will say that he cannot discover wherein that is
different from the theologian's going back to God.

Yet, on the whole, I should say that the philosophy of Professor
Bergson is theistic rather than atheistic, and spiritual rather than
material and mechanical.

I said in the beginning of this study that Professor Bergson
had made, in my judgment, a vital suggestion, and that is his recog-
nition of the high function of philosophy. Although in his theory
he remands the intellect to a much lower place than instinct, he for-
gets it in practice when he affirms that the vital, the supreme ques-

CRITICISMS AND DISCUSSIONS. 397

tions, "What are we ; What are we doing here ; and whence do we
come and whither do we go?" are the very cause of philosophy's
existence', and that the future (italics mine) will give back to phi-
losophy its rightful place — the first.

Professor Bergson does not think that we can arrive at objec-
tive certitude or that we can force assent, but he suggests that the
collection of many facts and their interpretation may give us a direc-
tion, "a direction only." These "lines of facts" will give nothing but
a probability; "but all together, by converging on the same point,
may give us an accumulation of probabilities which will gradually
approximate scientific certainty."

It is a pleasure to see the view I have been contending for —
that to this present discredit of the intellect, of philosophy, there
will come a reaction — confirmed by the high authority of Professor
Bergson. How far the reality to be known may exceed the power
to know I cannot tell, but this seems reasonable, that the universe
has an intellectual answer to those intellectual questions with which
it continually confronts us. There is in us the indomitable belief that
the terror and mystery of the material world may be transformed
by a large knowledge into "transparent formulae." Should we not
have the same belief that the terror and mystery of the moral and
religious worlds may be also, by a larger intelligence, transformed
into "transparent formulae"?

My study must end here, and I am aware how imperfect it has
been, but I have tried to represent Professor Bergson kindly and
impartially. This task has not been easy for, as Mr. Balfour says,
there are parts of his theory, especially his theory of knowledge,
difficult to comprehend ; but I am sure all will consent that he has
broken open new ground, and we can admit even the exaggeration
of Professor James: "Open Bergson and new horizons loom on
every page you read. It is like the breath of the morning and the
song of birds."

JAMES G. TOWNSEND.

JAMESTOWN, N. Y.

THE ANTI-INTELLECTUAL MOVEMENT OF TO-DAY.

Never before in the history of the world has science played
such a prominent part and received more recognition as the main
factor of civilization. And in truth there is a general agreement as

398 THE MONIST.

to the hope that we stand at the threshold of the age of science,
which means that all problems of life will be solved by scientific
inquiry and the old superstitions will be swept away. This principle
has been applied to the several domains of- life, to transportation,
to sanitation, to the preparation of food and medical problems, the
building of our homes and public edifices, yea even to the sphere
of social and religious life. It is strange, however, that in these
very days there have repeatedly appeared philosophical movements
which are decidedly anti-intellectual, and treat science with a con-
tempt in favor of the instinctive promptings of sentiment, which is
only paralleled among the most old-fashioned dogmatists, in the
tendencies of religious faith by such men as Augustine and Luther
who treat reason as an enemy to faith, and endorse the old principle
Credo quiet absurdum.

We will here make a few comments in explanation of this move-
ment without taking sides either with the admirers or the critics of
the new fashion. The latter, the critical aspect, is most exactly
represented by Mr. Bertrand Russell, pages 321 to 347 of the present
number of The Monist; the other to some extent by the Rev. Dr.
James G. Townsend. Mr. Russell points out that "if he (Bergson)
fails in his condemnation of the intellect, the intellect will succeed
in its condemnation of him."

It seems rather strange that in the days of the dawn of an age
of science such movements should be so prominent, but it seems to
me that these movements are the natural reaction against the many
wrong aspirations of science, for it can not be denied that the
prominence which science has gained in our days has also produced
a number of narrow-minded scientists, who apply their narrow view
of science to the whole of life. To them science is either physics
or chemistry or biochemistry, or whatever their specialty may be,
and most of them are acquainted with science only in its lower
branches, mechanics or physics or some other domain which is
void of the higher development of man where it unfolds itself in
social and moral ideas. Psychology to such minds is a mere func-
tion of the brain, and the truly typical features of the soul are an
accidental by-play of its coarsest substratum, or to draw their ulti-
mate conclusion, mind is considered a function of matter. Their
view of nature is limited, and while they rob man of his nobility
they degrade him into an equality not only with the brute but even
with inanimate existence.

The expression of this kind of narrow-minded science which

CRITICISMS AND DISCUSSIONS. 399

is not true science but the lowest step in the development of science,
has caused a distrust in the true nature of science.

Anti-intellectualism has become fashionable in the philosoph-
ical world. Prof. William James made a great propaganda for it
and succeeded mainly by his amiable personality. He speaks in
the name of a certain common sense which stands up for unscien-
tific views and defends a pluralism as well as a subjectivism on the
ground that it is based on experience. For the same reason theory
is discredited for sheer love of single and unrelated facts. Facts,
however, are replaced by interpretations of a very primitive kind,
among which even belief in spirits plays an important part. This
incoherent system which abhors all moralism and actually represents
a reaction to the world-conception of savage life goes under the
name of pragmatism. It has made many conquests and gained many
brilliant adherents even in the stable circles of European scholar-
ship.

Another center of anti-intellectualism has been established in
France of which Henri Bergson has become the leader through his
unprecedented brilliancy of style and oratorical talent. He has
gained many adherents in his own country, France, and celebrated
high triumphs in conservative England. He is expected in the
United States, and we have no doubt that he will be welcome in the
circles of all who are dissatisfied with the quiet and unpretentious
method of patient inquiry and scientific research. Men of this type
possess great zeal and they will naturally welcome an ingenious
representative of their philosophic tendencies.

In the meantime the spirit of criticism is stirring in England,
and we have before us a book which with all soberness reviews the
significance of the new star which has risen on the philosophical
horizon. It is written by Hugh S. R. Elliot, LL. T., the editor of
The Letters of John Stuart Mill* Sir Ray Lankester, K. C. B.,
F. R. S., being invited to write a few words by way of preface to
Mr. Elliot's book, says :

"I am glad to do this, not merely because I think that the books
in which M. Bergson formulates those illusions are worthless and
unprofitable matter, causing waste of time and confusion of thought
to many of those who are induced to read them, but also because
an unmerited importance has been attached to them by a section of
the English public, misled by the ingenious and systematic advertise-

* Modern Science and the Illusions of Professor Bergson. By Hugh S. R.
Elliot London, Longmans Green & Co., 1912. Price $1.60 net.

4OO THE MONIST.

ment of M. Bergson by those who amuse themselves with metaphys-
ical curiosities. He has been introduced to us as a "great French
philosopher.' To those who in a thoroughgoing way occupy them-
selves in collecting and comparing and classifying all the absurdities
which have been put forward as 'metaphysics' or 'metaphysical specu-
lation' since the days of Aristotle, this latest effusion has, no doubt, a
kind of interest such as a collector may take in a curious species of
beetle. To the student of the aberrations and monstrosities of the
mind of man, M. Bergson's works will always be documents of
value. But it is an injustice as well as an inaccuracy to speak of
their author as 'great,' or 'French,' or a 'philosopher.'. . . .

"A main objection to M. Bergson's account of his own per-
formances in the dark chamber [of the metaphysical x\ is that he
is not content with asserting (and expecting us to accept his bare
assertion) that time is a stuff both 'resistant and substantial,' that
consciousness is not always dependent on cerebral structure, that in-
tuition is a true guide and the intellect an erroneous guide. Such
escapades in the dark room astonish and interest only those who
are unacquainted with M. Bergson's numerous predecessors in the
maddening hunt of the illusive black cat. It is, however, a speciality
of M. Bergson that having by mere assertion attempted to make us
believe that he has grasped the black cat, and at any rate has in
his hand some hairs from its tail — he proceeds in the same spirit
to make absolutely baseless assertions about the domain of scientific
fact — a domain 'tabooed' against him and his fraternity. He writes
of the facts of physical science with the same careless assurance as
that which we tolerate with indifference when he is disporting him-
self in the extra-territorial region of x. Having made his arbitrary
assumptions about x, he proceeds in an inaccurate way to write about
some of the well-ascertained facts of the structure of animals and
plants. He promulgates novel opinions about them with the air of
one who has given serious study to them, which, however, it is
abundantly evident he has not. By a light-hearted perversion of
the facts as to the structure of the eyes of animals and other such
things, he endeavors to make them appear as evidence in support of
his arbitrary and preposterous fancies about x\ In doing so he
ceases to be merely an amusing juggler with the harmless creations
of his own and other people's fancy: he becomes a maker of un-
truth, and for those who listen to him a harmful Confusionsmeister.

"M. Bergson is gifted with an admirable facility of diction, and
has succeeded in arresting attention. On that account, since he

CRITICISMS AND DISCUSSIONS. 4OI

has exceeded the limits of fantastic speculation which it is customary
to tolerate on the stage of metaphysics, and has carried his methods
into the arena of sober science, it is a matter of urgency that his illu-
sions and perversions should be exposed with uncompromising frank-
ness to the reading public who may be, on their side, under an illusion
as to the importance of his teaching. Mr. Elliot's book effects this
exposure in a masterly way."

M. Bergson proposes the strange doctrine that perception does
not reside in the brain of the perceiver, but in the object perceived,
— a proposition which is bewildering, and among his arguments he
declares it theoretically not inconceivable that matter should be per-
ceived without sense organs. Such doctrines belong to the corner-
stone of his philosophy, and as an instance of Mr. Elliot's critique
we will here quote some paragraphs discussing M. Bergson's theory
of pain and of memory. M. Bergson defines pain as an "effort to
repair damage." Mr. Elliot writes:

"Just as perception is located in the perceived object, so Berg-
son alleges that pain is located in that part of the body where it
appears to be felt. This is of course in opposition to the belief of
physiologists, who affirm that the pain is really located in the brain,
not at the nerve endings ; and who support their contention by point-
ing, for instance, to the pain which a patient feels and refers to
his foot after it has for years been amputated. I am not, however,
concerned to defend a well-established fact: I wish only to point
out Bergson's mode of refuting it. 'If [the pain] is not at the
point where it appears to rise, neither can it be anywhere else: if
it is not in the nerve, neither is it in the brain ; for to explain its
projection from the center to the periphery a certain force is neces-
sary, which must be attributed to a consciousness that is to some
extent active. Therefore, he must go further. . . .' Here we get a
chain of deductions, every ling of which appears to be false. Why
should any force be necessary ? Why should that force be attributed
to a consciousness? Why should that consciousness be active? It
was one of Huxley's chief gifts to biology to have largely banished
deduction from that science, by strongly insisting on the danger of
traveling outside ascertained facts. A succession of deductions like
this, in a physiological inquiry, is a priori almost certain to be
erroneous. To me a posteriori there seems not even prima facie evi-
dence in favor of any of them : and they are set against a fact ex-
perimentally arrived at!

"The doctrine of two kinds of memory is a complication of

4O2 THE MONIST.

natural facts that will not appeal to anybody. But the fundamental
objection to it is that so often raised already : that there are no facts
to support it. The Professor attacks the physiological view of mem-
ory : he adduces a number of facts, such as those of sensory aphasia,
in opposition to it ; and having destroyed it to his own satisfaction,
forthwith we are presented with a new theory which is assumed to
be true. This new theory is worked out in extreme detail ; it is
unaffected by sensory aphasia, but otherwise the only credentials it
can produce are those of extreme unintelligibility. We have already
had occasion to observe that a doctrine is safest from criticism when
it is most difficult to understand. The fog is so thick that the critic
is disarmed. I therefore make no specific attack upon it, beyond
insisting upon the complete absence of evidence. Moreover, the
attack on the physiological theory could scarcely convince ony one
but a metaphysician. 'If memories are really deposited in the cortical
cells, we should find in sensory aphasia the irreparable loss of certain
determined words, the integral conservation of others.' But it is
not so. Now, what would a man of science consider himself entitled
to deduce from this ? Nothing further than that words are not
represented in the brain in minute specific areas for each word, but
that they are, or may be, represented in some other way, possibly
still undiscovered. But what does Bergson infer? That the mem-
ories of words are not stored in the brain at all. He refutes a crude
physiological hypothesis ; he then assumes that the refutation applies
to all possible physiological hypotheses, and thence jumps to his
own theory. It would have been just as reasonable to found his
own theory upon a refutation of Gall's phrenology. For phrenology
was a thoroughly materialistic hypothesis ; it assumed absolute con-
nection between mind and brain, and definite localization of mental
faculties in the brain. Phrenology has long been exploded, but
no one (except a metaphysician) infers from that that there is no
connection between mind and brain. A belief in that connection is
in no wise shaken by the exposure of phrenology; nor is it shaken
by the criticism of other crude attempts to localize mental qualities.
These criticisms are effective only for the particular theories against
which they are levelled. Hence we see that Bergson's theory of
mind and matter is founded upon the same fallacy as that of the
vital impetus — the fallacy which we stigmatized as the mannikin
fallacy at the beginning of the chapter. In bald outline it is like
refuting Mahommedanism, and then arguing: (1) Mahommedan-
ism is untrue; (2) therefore all religion is untrue; (3) therefore all

CRITICISMS AND DISCUSSIONS. 403

morality is a superstition. We have only to point out that (2) does
not follow from (1), nor does (3) follow from (2). In Bergson's
works the second step (2) is invariably taken silently immediately

( 1 ) has been established. The great show of facts in his works are
all connected with step (1), the criticism of adverse theories. Step

(2) is then slurred over without a word of discussion, and the rest
of the philosophy is taken up with step (3), which is just a hypoth-
esis or guess, or intuition, having no connection with foregoing
facts, but set out with such a wealth of words and analogies that
the unwary reader quickly loses his way and is totally lost. In
alliance with the main paralogism is the copious misuse of analogies
and of words, the latter especially in the form of materializing ab-
stractions such as time, life, motion, memory. The medieval real-
ists could scarcely have gone farther.

"The tendency to attribute substantial reality to abstractions is
conspicuous not only in metaphysics but in the thinking of all primi-
tive races. Thus a Basuto will not walk by a river lest his shadow
falling on the water should be seized and devoured by a crocodile.
Nearly all children at one time or another attempt to evade their
shadows by jumping or running. Names likewise are looked upon
as material things : as among the Chinooks, one of whom thought
that Kane's desire to know his name proceeded from a wish to steal
it. Here, as elsewhere, Bergson does nothing more than systematize
and magnify, on an enormous scale, almost universal vices of
thought."

As an example of Bergson's method we will quote a few more
passages from Mr. Elliot's book. Bergson says:

' 'Instinct is knowledge at a distance. It has the same rela-
tion to intelligence that vision has to touch/ Why, then, do we
owe our knowledge of the stars to intelligence, and not to instinct?
Why has astronomy advanced by the gradual triumph of intelligence
over bigoted superstition ? . . . .

"Bergson's attempt to establish the preeminence of men and
hymenoptera takes, in one place, the following form: — 'It is un-
questionable that success is the most general criterion of superiority,
the two terms being, up to a certain point, synonymous. By suc-
cess must be understood, so far as the living being is concerned, an
aptitude to develop in the most diverse environments through the
greatest possible variety of obstacles so as to cover the widest pos-
sible extent of ground. A species which claims the entire earth
for its domain is truly a dominating and, consequently, superior

404 THE MONIST.

species. Such is the human species, which represents the culminat-
ing point of the evolution of the vertebrates. But such also are, in
the series of the articulate, the insects, and, in particular, certain
Hymenoptera. It has been said of the ants that, as man is lord of
the soil, they are lords of the subsoil.'

"Under this definition, birds ought to be a dominating group,
for their distribution is wider than that of men. And the most pre-
eminent species of all would not be men, or insects, or even birds,
but those simple unicellular creatures like ameba, which are found
everywhere all over the earth."

Mr. Elliot sums up the whole book with the following con-
clusion :

"Professor Bergson's philosophy is contained in three volumes.
I here summarize my main objection to the fundamental doctrine
of each:

"1. Time is a stuff both 'resistant and substantial.' Where is

the specimen on which this allegation is founded?
"2. Consciousness is to some extent independent of cerebral
structure. Professor Bergson thinks he proves this by dis-
proving a crude theory of localization of mental qualities.
Will he furnish evidence of its existence apart from cerebral
structure ?

"3. Instinct leads us to a comprehension of life, that intellect
could never give. Will Professor Bergson furnish instances
of the successes of instinct in biological inquiries, where
intellect has failed?

"I venture to think that, until these questions are answered, we
are not called upon to consider further the merits of Professor Berg-
son's philosophy." EDITOR.

KANT AND BERGSON.1

"It is an incorrect and perverted usage of the word
'symbolic/ but one which is accepted by modern logi-
cians, when it is set in opposition to the 'intuitive' mode
of thought ; for the symbolic is only a species of the
intuitive." — Kant, Critique of Judgment.

We have in Kant not only the founder of criticism as a sys-
tem or a method which would be appreciated for their positive
qualities ; but on the other hand the purely critical, or if you prefer
negative, element is for the most part considered from an historical
1 Translated from the German by Lydia G. Robinson.

CRITICISMS AND DISCUSSIONS. 405

point of view in its application against rationalism and against
Locke and Hume. At bottom, however, Kant himself has tire-
lessly given expression to the propaedeutic character of his critique
as among its most essential features. Therefore it seemed to him
most important once for all to demonstrate metaphysics, as he found
it and understood it, to be futile and impossible, in so far as it laid
claim to being a system of cognitions.

Whether or not Kant had come in actual contact with histor-
ical metaphysics alone makes no difference. He undoubtedly wished
to do away with metaphysics in itself. It may be objected that he
opposes his criticism to that kind of metaphysics which he himself
has constructed as the object of attack. Nevertheless his critique
has a far broader application inasmuch as it makes metaphysics in
general the object of investigation. Whoever maintains the mere
possibility of a metaphysics must in some way or other decide the
question which Kant himself stated and wished to have solved,
namely whether metaphysics is at all possible.

In solving this problem it is a matter of indifference whether or
not one employs the Kantian method of deducing the possibility
of the thing sought from its postulate, from the hypothetical as-
sumptions of the problem. Only in one way or another the critical
attitude must be brought to bear upon the question. Hence the
nature of metaphysics or its necessity must not be asserted and
presented before its possibility is proved. Therefore it is really im-
possible for a Kantian to admit the methods employed by Bergson
in founding a new kind of metaphysics. Nevertheless we shall first
accommodate ourselves to his mode of thought so that we can not
be subject to the charge of orthodox critique. Yes we will even
go one step further. We will hypothetically admit that Bergson's
definition of metaphysics is right. He asserts metaphysics to be
the science which gets along without symbols ; it is intuitive knowl-
edge.

According to Bergson himself intuition is a sort of mental
sympathy by means of which one may transfer himself into the
midst of an object. Bergson avails himself of still other senses in
order to make this kind of cognition comprehensible to us. It is a
kind of mental auscultationp an intellectual vision. My present task
is to investigate whether such an intuition is possible, whether it is
at all thinkable. Bergson is satisfied simply to make the assertion.
But I will first show that even granting its possibility it does not
accomplish what is claimed for it.

406 THE MONIST.

From the very beginning intuition is something more than
merely a kind of cognition. It is supposed to transfer us directly
into the very being of the object, but in this being is included
existence. A comprehension of existence is at the same time a
comprehension of the cause of existence. The play is ceaselessly
repeated, one direct leap carries us across the abyss of cognition,
perception and comprehension. In intuition existence itself is pos-
ited. The more intuition is built up upon being, upon existence,
the more creative and the more constructive does it itself become.
A second process, that of deepening, runs parallel to this develop-
ment of the concept of intuition. From a comprehension of the
object, from a sinking into a strange object, from a constantly
greater pouring out of the subject, intuition becomes more and
more an internal process; finally, in intuition the subject comes
more and more to comprehend itself, its creative nature, its most
profound existence.

The stages of this development are well known. Scholasticism
saw in intuition the cognition of existence or non-existence. "In-
tuitive knowledge of a thing is knowledge by means of which it may
be known whether a thing is or is not."2 The logical antithesis of
existence and non-existence indicates even beyond that the creative
cause of existence. It is only necessary for the factor of necessity
to be abstracted from its logical wrappings to make it clear that
a decision about existence or non-existence ultimately depends on
the foundation, the positing of existence. Existence once posited,
the cognition of its necessity is at the same time admitted.

Spinoza goes even one step farther:

"This kind of knowledge, i. e., intuitive knowledge, proceeds
from an adequate idea of the absolute essence of certain attributes
of God to the adequate knowledge of the essence of things."3 By
reference to God, existence is therefore established more securely
so that the scientia intuitive? latterly comes to include existence.
Intuitive knowledge as knowledge under the form of eternity com-
prises this, that the essentialities of things follow from the eternal
nature of God by eternal necessity.5 And if we must remove the

2 "Notitia intuitiva rei est talis notitia, virtute cuius potest sciri, utrum res
sit vel non sit." — William of Occam, in /. sent, prooem.

3 "Atque hoc cognoscendi genus (sc. scientia intuitiva') procedit ab adae-
quata idea essentiae, formalis quorundarum Dei attributorum ad adaequatam
cognitionem essentiae rerum." — Ethices, II, Propos. XL, Schol. 2.

4 Or cognitio intuitiva, Eth. V, Prop. 36 Schol.
*Eth. V, Prop. 25, 27, and Dem. 32.

CRITICISMS AND DISCUSSIONS. 407

factor of the creative, we must nevertheless emphasize with Spinoza
himself the power and the force of this third step in cognition from
which the amor intellectualis del arises.

The necessity of existence in the scientia intuitiva can not be
more emphatically expressed than in the words: "Therefore to
conceive things under the form of eternity is to conceive things in
so far as they are conceived through the essence of God as real
entities or insofar as they involve existence through the essence of
of God."6 The climax of this development of the concept of intui-
tion (Intuitionsbegriff) is Kant's interpretation of the nature of
intellectual intuition (Anschauung) . According to him it is a non-
sensual active "faculty" which produces its intuition directly and
at the same time the objects of that intuition by its spontaneous
activity. It seems that Kant saw in Plato's Ideas the objective
counterpart of this intellectual intuition, for in them as intuitions
a priori he posits the primitive cause of all things. ("Von einem
neuer dings erhobenen vornehmen Ton in d. Philosophic, Berliner
Monatsschrift, Mai, 1796.")

Kant shares with Spinoza the association of this intellectual in-
tuition with the divine. He differs from him in that he does not
admit with Spinoza that it is possible on the part of man.

I pass over entirely the concept of intuition as worked out in
mysticism. With this concept the intuition of Bergson has nothing
to do.

Granted that intuition is possible, what does it accomplish? It
transfers one directly into the midst of objects. What of objectivity
it gains it loses in subjectivity. Its climax is its coincidence with
the essence of the object, and thus is emphasized as something quite
distinct from it. But if it remains distinct then it must always be
outside of the center of the object. This transference into a strange
object is really only a purposeless example of speculative fancy, for
it is absolutely inconceivable how a subject could be so changed into
an object that it would take up the object into itself, make itself
equivalent to it and yet remain autonomous itself. And even if this
procedure were possible we would utterly reject the dualistic theory
and be satisfied with the admission that in the center of the essence
of an object there is such a comprehension of this center that exactly
this comprehension would always be meant and finally would be so

e"Res igitur sub specie aeternitatis concipere est res concipere, quatenus
per Dei essentiam ut entia realia concipiuntur sive quatenus per Dei essentiam
involvunt existentiam." — Eth. V, Prop. 30, Dem.

408 THE MONIST.

understood again, provided that this procedure could be represented
in any way.

The process of intuition can not be presented nor can it be con-
trolled. It withdraws from every attempt at presentation or control.
In secret depths there suddenly takes place an escape, a /^ra/Jao-is efc
KpyiJUL pursued and extended indeed with effort but in its origin and
course unknown and unknowable. Means are entirely lacking to
verify its necessity and validity beyond its reality.

Every intuition is isolated, yet we do not see how a methodical
and systematic connection can be possible in the sum total of in-
tuitions. Neither an ascent, an increasing deepening, a methodical
thought-action, nor a well-constructed systematic connection of cog-
nitions. But we might perhaps waive this: intuitions crowd to-
gether in one of the most important, in the intuitive attainment of
intuition itself. Thus we would have an undivided apex crowning
ihe structure of cognition. The cognitions themselves might be of
another kind. But when and in whom is this intuition to take place ?
Can any one attain it at any time by making sufficient effort and
striving to win it? If so, I should think that exactly these prelim-
inary conditions, the knowledge of the kind of our endeavors, would
greatly concern us, and intuition itself would let our endeavor fall
from us void of interest like ripe fruit. There is something infinitely
wearisome about intuition. At one stroke it tears away the veil
from the mystery of mysteries and then all work is performed for-
ever. And yet not for ever. It remains finally, to be sure, the
possession of its acquirer who is not in a condition to communicate
it to others though he can indeed arrange to put himself in pos-
session of it, but has the possession for himself without being able
to compare it or to communicate it. So from this point weighty
prospects open before us. We do not exactly see how intuition could
remain as a possession with its acquirer. He must ever seek to
acquire it anew, for in memory exactly that disappears which makes
it intuition, namely, the lack of the symbolic, an everlasting coming
and going of intuitive experiences without plan or method, without
connection or aim. For each one brings with it as the supreme
purpose of cognition, but only as an experience, the truth as it is
given, not as it is known, comprehended and perceived.

However, the deeper we descend into the inwardness of the sub-
ject which produces the intuition, the stronger is evidenced the char-
acteristic note of the personal life, and the more distinct becomes
the absolute in itself. Assuming too that we include in these depths

CRITICISMS AND DISCUSSIONS. 409

the real, the cosmical center of the spiritual life, then exactly this
personal element, this experience, gives it a particularly independent
garb. From this point it is quite unimaginable how being and
experience are to be associated together. The best we can do is to
assert that the Kantian problem of cognition becomes deepened and
broadened but it goes no further. Intuition, too, whose legal char-
acter and validity must be comprehended or intuitively perceived,
is not a datum or a reality; but it is a problem and one that has
validity.

What importance for intuition has the character of truth ? Since
it can not be determined either categorically or by means of ideas
and especially not by symbols, it can, to be sure, contain truth in
itself — yes, according to its concept it must contain truth; but how
and by what intrinsic necessity it contains truth can by no means be
expressed without symbols. Only no one needs to know that a
cognition or an experience contains truth (for this knowledge would
be either accidental or problematic) but only to know by what neces-
sity truth is bound to a cognition or an experience. Then too the
mere possession of truth is worthless so long as it is not known that
it has its roots in well-grounded associations.

Therefore intuition must be rejected as a postulate because it
cannot serve to give any one an accidental experience of finding
himself in the center of an object. The primeval dream of humanity
to be able to know finality, to be able to possess everything, to
penetrate into the innermost kernel of things, is in itself contra-
dictory and untenable. Of what use is it to me to be in the center
of an object if I do not have besides an intuition that this is the
case, that it actually is the case? Did not Descartes remind us of
the possibility that a conception could be produced in us arbitrarily
and delusively from an outside cause? He comes to the conclusion
that our fancy can actually transport us into a foreign object very
vividly and naturally without question, and yet with an easy effort
if not simultaneously we can have the consciousness that it was
simply an image of our fancy. In the moment when I by means of
certain efforts of the imagination live in a vividly portrayed char-
acter of romance I have nothing but this imaginative figure within
me and it is utterly impossible for me to accompany this process,
which likewise is reflected in the very threshold of consciousness,
with a particular act of consciousness which includes it as object
or even only with the mere idea of the ego. On the other hand it

4IO THE MONIST.

is ye*y possible to emphasize and to comprehend an act of imagina-
tion in a particular process of consciousness.

Accordingly since intuition is said to transfer one directly into
an object, this is analogous to throwing a piece of sugar into water.
The sugar is dissolved ; "it" is indeed in the water, but the "piece"
of sugar is not in it.

Intuition is a sort of absolute cognition. If intuition is possible,
if we could penetrate at even one point into the mystery of the
universe, the force of our cognition would be weakened forever
at this point. At the most we would still have to assert and com-
municate the endeavor and the achievement if we could — at best
the old traditionalism of the end of the eighteenth century. How-
ever, it is clear that intuition has already its results in great men,
exceptional personalities, and that definite institutions or school
buildings had them in charge. Then the incessant effort to attain
possession of these intuitions would always be simply in order to
gain the same possession. Of course Bergson himself does not in-
tend this, but it is implied in the consequence of this wearisome
intuition.

Bergson has foreseen the dangers that threaten, for instance,
his concept of intuition. He constantly asserts the activity of in-
tuition. There is no doubt that such an exceptional event as attain-
ing the absolute is accompanied and introduced by attempts and
efforts of an extremely energetic kind. But intuition itself is not
for this reason active in any sense, although it is accompanied by
activity. Exactly the last point, namely transference, in which the
absolute and the comprehending subject almost coincide, must also
stand on the lowest step of activity, otherwise the whole process of
identity would be incomprehensible.

Bergson will undoubtedly accuse every critic of trying to assail
his concept of "pure" intuition with symbols in an inadmissible way.
But what if the gift of intuition refuses to come to us in spite of all
our efforts? Then in Bergson's estimation we are indubitably lost
as metaphysicians. It seems to me that the appeal to intuition would
greatly resemble the appeal to the healthy human understanding
which Bergson to be sure also invokes (p. 40). But Bergson must
show us distinctly and precisely the ways and means that lead to
intuition.

The intellectual experience (Miterleben) of the real mobility
by which thinking is obliged constantly to reverse the work of
thought, is claimed to be accomplished methodically. Or, rather,

CRITICISMS AND DISCUSSIONS. 411

only the reversion is properly claimed to be performed methodically.
For does not Bergson see that we are -again under the spell of the
formulism of symbols which has just been rejected with the greatest
energy? Are not mobility, reversion and method symbols just as
much as cognition, validity, categories, etc.? Bergson himself sees
how difficult it is for "the intuition once attained to find a mode of
expression and application corresponding to our habits of thought
and offering us in firmly postulated concepts the secure supports of
which we are so in need."

But everything finally comes to this, that if one were constantly
to imagine that he could transfer himself directly into the midst of
an object by exerting a special energy, this procedure would remain
epistemologically and metaphysically valueless so long as it does
not succeed in establishing the scope and degree of its validity, its
internal truthfulness, the origin and structure of its composition, etc.
It never depends on the cognition or experience in itself, nor on its
kind which may be described as much as one wishes, but always on
laying the foundation of cognition on a firm interrelation. Upon
what is the certainty of an intuition, and necessarily of its contents,
based? In what consists the security that I actually grasp the es-
sence of a thing, that I really am in the center of the object?

Bergson thinks he possesses one means of comparison. He is
convinced that the consciousness we have of our own person in its
"continuous course leads us into the interior of one reality after
whose pattern we must construct the rest."

He also upsets Kant's theory of the unknowability of the ego.
.... "Accordingly I have no knowledge of myself, what I am, but
merely how I appear to myself."7

We nowhere find in Bergson any attempt formally to oppose
the well-known deductions of Kant. At the same time he arms
himself against Kant's proofs. He accuses Kant of "misconstruing
the union of the sciences and metaphysics with intellectual in-
tuition." It would have been more correct to say that Kant has
opposed it with all his energy. Kant did not in the least accuse
metaphysics of being empty speculation; he was even the first to
point out the necessity of the metaphysical impulse. But he has
undertaken to show that metaphysics could never stand as a system
of cognitions. His problem was formulated : Is metaphysics every-
where possible as a unity of cognition? and his answer was firm

1 Cr. of Pure Reason, II, p. 157, cf. 135, 399 ff., and also the alteration of
the first edition. Proleg., 136 ff.

412 THE MONIST.

and decided, Not at all. With equal energy he rejected intellectual
intuition as cognition. Whoever makes both assertions repeatedly
is obliged to shatter and overturn Kant's critique in its fundamentals.

But this is not the case since Natorp's and Cohen's system has
been called a "dream" (p. 52). Ultimately we will have to dispose
of the idea which ascribes to Kant such a dogmatism as even his
own opponents have not consistently perfected, which maintains that
after Kant "the main task of criticism is to determine what the
intellect is supposed to be and what the object" (p. 52). Equally
dogmatic is the postulate that is ascribed to Kant that the intellect
is incapable of doing anything but "Platonize, i. e., cast every pos-
sible experience into previously existing moulds" (p. 53).

To be sure we are no longer satisfied with the conception of
metaphysics as it appeared to Kant. Likewise is it far indeed from
us absolutely to deny its possibility as he did. We maintain that
greater depths of the soul, which Kant also divined (synthetic one-
ness of apperception) can become present to us, but not by the help
of intuition, of intellectual perception (Anschauung) , but in an
energetic apprehension, in an active realization of its infinite con-
tent. Hence we consciously abandon cognition and its ways and
means which Bergson desires to broaden and deepen anew. For
by means of intellectual perception we fall again and still deeper
into the miserable intellectualism in which we long enough have
lain imprisoned.

Intuition indeed is to be divested of all intellectuality. Apart
from the fact that it thus incurs the loss of all power of cognition,
it becomes in addition a kind of assimilation of the object which
repeats in some way or other its content, and is everything else, ex-
cept cognition or comprehension. And yet finally the resultant, the
sum total of the intuitive performance must be analogous to "ex-
perience." The bare object must be distinguished from the object
in the confusion of intuition. And right here lies the problem. For
that an object can be concerned with intuition would be possible
in itself. But who could undertake to find out by any other means
than through intuition what the characteristic feature of the object
is, and on the other hand the content of the perfected intuition?

Assuming the possibility of intuition, it does not accomplish
what is claimed for it. The leap into the thing buries the one who
takes it. Intuition assumes a thing which outside of and independ-
ent of itself does not exist. Intuition is not only unfruitful, it is even
impossible.

CRITICISMS AND DISCUSSIONS. 413

For this statement I hope to bring forward convincing proofs.
All the varied results and evolutions of modern epistemology pos-
sess the common feature of interpreting cognition as complete and
immanent. It deduces all single factors and elements from the
problems and laws of cognition itself but does not construct them
a priori upon metaphysical foundations. For although the con-
stitutive features of the nature of cognition might be based on
metaphysical relations yet that which makes cognition cognition
can be ascertained only by their surrender. Hence a kind of
cognition which assumes the "thing" as given according to its ex-
istence and its nature is self-contradictory. Cognition exactly im-
plies that it gains, attains, performs something. A mere trans-
migration into the center would either signify a mere presence in
the thing or a replacement of the objective central point by an
assimilating subject. In either case no decision is reached about
cognition itself.

The tendency of modern epistemology is to look upon every-
thing as under the law of cognition. Bergson tries to push the thing,
the ''inwardness" (Inncrc) of cognition, before it and place it out-
side. Moreover the "being in the center" is the characteristic fea-
ture of cognition. But while Bergson stops here the modern epis-
temologists begin to lay their foundation at just this point. The
method by which the center of the object is reached is most im-
portant. That cognition reaches this point is implied in its concept
and need not be so greatly emphasized. But how it attains it is
important, and it makes the matter rather easy if the proper cognitive
process in the mysterious leap into the center is allowed to plunge
undiscerned. The problem is not how one can be "in" a thing, but
how in this center he can be active, and of what kind is the assimi-
lation or establishment of the center.

Then too the idea of a "central point" is an uncertain one
because it makes the end disappear and yet holds fast to the goal
even though undetermined. Thus the methodical character of cog-
nition is entirely overlooked, and its infinite exertion does not come
to its own.

The interrelated cosmos of the objects of cognition is knocked
into nothing, and is firmly bound to unchangeable points. Intuition
wills everything and is itself nothing.

However greatly much in Bergson's work appeals to us, espe-
cially the significance of the real as something moveable (although
the last word does not seem to have been spoken even here), yet

414 THE MONIST.

we must take issue as energetically against the theory of intuition
as against his pragmatism (page 54).

I have not formulated the above considerations systematically
but have rather adopted the rhetorical style of the French in order
to remain as objective as possible. It seems to me the time has
riot yet come for a far-reaching reflective critique, since Bergson
has promised a more conclusive argument for his theory in the
future. In any case he must without question come to an under-
standing with Kant; for to uphold metaphysics according to Kant
is difficult, but to introduce intuition again is by far the most diffi-
cult.

DR. BRUNO JORDAN.

EINBECK, GERMANY.

MAUPERTUIS AND THE PRINCIPLE OF LEAST ACTION.

The present investigations are concerned with the history of the
Principle of Least Action in the hands of Maupertuis, Euler and
others. The subject is of great importance in the history of mechan-
ics, both because the principle of least action became, in the hands
of Lagrance, "the mother," as Jacobi expressed it, "of our analytical
mechanics," and because the animistic tendency displayed in the
search for a maximum or a minimum principle in physics undoubt-
edly had a great influence on such moulders of mechanical theory as
Euler, Lagrange (in his early work).1 Hamilton, Gauss, and, in

1 Besides Lagrange's early printed works, his correspondence with Euler
allows us to form some impression of the stimulating effect which the principle
of least action had on Lagrange's mind at the beginning of his career. La-
grange's correspondence with Euler extends from 1754 (probably: the year
is not given) to 1775 and is reproduced in the CEuvres de Lagrange, vol. xiv,
pp. 133-245. Already in 1754 Lagrange announces (ibid., p. 138) that he
has made "some observations about the maxima and minima which are in
the actions of nature." In a letter of August 12, 1755 (ibid., pp. 138-139) La-
grange informs Euler that he had a new and simpler method of solving iso-
perimetrical problems and (ibid., pp. 140-144) gives a full statement of it
(cf. Euler's reply, ibid., pp. 144-146). This discovery of what was afterwards
called "the calculus of variations" certainly gave the principle of least action
an additional attractiveness to Lagrange ; he speaks, in a letter of May 19,
J756, of his meditations "on the application of the principle of least action to
the whole of dynamics" (ibid., p. 155 ; cf. pp. 156, 158, 161, and the final sen-
tences of Lagrange's first printed paper in the first volume of his CEuvres}.
Lagrange's interest in the principle of least action seems to have evaporated
when he observed that, when developed, the integrand is the variational form
of d'Alembert's principle, and that it is simpler and equally effective to start
with the equations of motion divorced from the integration. This is La-
grange's point of view in 1788. The earliest date at which this change in
point of view is shown is, so far as I can find, 1764 (early memoir on the
libration of the moon). In a letter of Sept. 15, 1782, to Laplace, Lagrange

CRITICISMS AND DISCUSSIONS. 415

our own times, Willard Gibbs. I have avoided, as much as possible,
entering into merely biographical details and details of the great
controversy between Maupertuis, Konig, Euler, and Voltaire about
this very principle, in so far as they have no value in the history of
science. But I have been very careful to give accurate and detailed
references to the books and memoirs where everything relevant, so
far as I know, may be found. I mention this expressly, because
much in this chapter of the evolution of mechanics — one may even
say, of thought in general — has been misquoted or misunderstood
by even eminent authorities. Unless the contrary is stated, all the
books referred to have been consulted either by my assistant, Miss
Harwood, or by myself.2

Pierre Louis Moreau de Maupertuis^ was born at Saint-Malo in
1698 and died at Basel in 1759. He was the first French New-
tonian ;4 was the author of several papers on the figure of the earth
and the leader of that well-known French expedition which meas-
ured an arc of the meridian in Lapland, confirming the deduction
from the Newtonian theory that the earth is flatter at the poles ;5

says ((Euvres, vol. xiv., p. 116) that he has almost finished a mechanical
treatise uniquely founded on "the principle or formula" given in section i of
his memoir of 1780 on the libration of the moon.

2 Adolf Mayer (Geschichte des Princips der kleinsten Action. Akademische
Antrittsvorlesung, Leipsic, 1877, p. 7) reports that among the manuscripts left
by Jacobi are fragments of a history of the principle of least action of which
he has made use.

3 There is a biography of Maupertuis by La Beaumelle {Vie de Maupertuis
par L. Angliviel de la Beaumelle; ouyrage posthume, suivi de lettres inedites
de Frederic le Grand et de Maupertuis, avec des notes et un appendice, Paris,
1856). Cf. also Samuel Formey, Eloge de M. de Maupertuis (read in 1760),
reprinted, with additions and corrections by de la Condamine and Trublet, in
1766 in the Histoire de V Academic de Berlin for 1759, pp. 464-512; and Emil

du Bois-Reymond, Maupertuis; Rede , Leipsic, 1893 (on La Beaumelle' s

book, see pp. 72-81).

4 La Beaumelle, op. cit., p. 16; du Bois-Reymond, op. cit., pp. 17-18. See
Maupertuis's papers in the Paris Memoires for 1732-1736; and Discours sur
les differentes figures des astres, 'avec une exposition des systemes de MM.
Descartes et Newton, published anonymously at Paris in 1732 and again in 1742
(not seen), and the popular part of it is most conveniently consulted in the
(Euvres de Mr. de Maupertuis, Lyons, 1756, vol. i, pp. 79-170. Cf. La Beau-
melle, op. cit., pp. 23-34; I. Todhunter, A History of the Mathematical The-
ories of Attraction and the Figure of the Earth from the Time of Newton to
that of Laplace, London, 1873, vol. i, pp. 63-76, 93-102 (this also contains an
account of those works which come into the scope of the next note).

5 La Beaumelle, op. cit., pp. 34-64, 71-75, 457-458, 461-462, 467; Du Bois-
Reymond, op. cit., pp. 18-35; and a German translation with notes by myself,
of Clairaut's book of 1743 on the figure of the earth, which is soon to appear
in Ostwald's Klassiker.

4l6 THE MONIST.

and was Frederick the Great's President of the Berlin Academy6
(from 1746). With Maupertuis's geometrical works we are not
concerned here/ nor are we with those philological and anatomical
speculations of his, which were so ruthlessly and unjustly parodied
by Voltaire.

According to Du Bois-Reymond,8 Maupertuis's teleological ten-
dencies showed themselves early in his career in speculations as to
what grounds the Creator could have had for preferring the law of
the inverse square to all other possible laws of attraction.

Some words about Maupertuis's personal character are neces-
sary. When Maupertuis returned from Lapland, there was great
opposition in some quarters to the reception of his results. This
foolish opposition had a bad influence on Maupertuis : his never small
feeling of self-importance increased, and he became embittered.9 On
the other hand, he was given, as President of the Berlin Academy,
almost unlimited powers, even as regards the payment of the mem-
bers' pensions,10 and this may partly explain, as Carlyle suggests
in his Frederick the Great, the tiring chorus of praise that breaks
out in the Berlin Histoire whenever any of the members have occa-
sion to mention Maupertuis's name. In the course of our discussions,
too, we shall have, in order to correct a strange error about Mau-
pertuis and the principle of least action made by Lord Morley in his
well-known book on Diderot and the Encyclopedists, to touch upon
the question as to whether Maupertuis was a materialist or not."

ii.

Maupertuis read to the Paris Academy on the 20th of February,
1740, a memoir entitled: "Loi du Repos des Corps."12 He began
by remarking that demonstrations a priori of such principles as that

6 La Beaumelle, op. cit., pp. 65-68, 76, 91-98, 104; du Bois-Reymond, op.
cit., pp. 36, 38, 39-42.

7 La Beaumelle, op. cit., pp. 15-16. 18-19, 22-23, 460-461 ; du Bois-Rey-
mond, op. cit., p. 16 ; M. Cantor, Vorlesungen iiber Geschichte der Mathematik,
vol. iii, 2d ed., Leipsic, 1901, pp. 774-775, 786.

8 Op. cit., p. 18. The place where this speculation is given is in the Figure
des Astres ((Euvres, 1756, vol. i, pp. 166-170).

9 Du Bois-Reymond, op. cit., p. 33.

10 Ibid., p. 40 ; La Beaumelle, op. cit., p. 107.

11 In the course of this article, we shall refer to Mach's work on mechanics
as Mechanik and Mechanics, as we have done before (Monist, April, 1912).

12 Histoire de I 'Academic royale des sciences. Annee 1740. Avec les
Memoires de Math, et de Phys. pour la meme Annee, Paris, 1742, pp. 170-176;
(Euvres, 1756, vol. iv, pp. 45-63.

CRITICISMS AND DISCUSSIONS. 417

of the conservation of vis viva "cannot apparently be given by phys-
ics ; they seem to belong to some higher science."

Maupertuis sought for a general law in statics analogous to
the known theorem that, in any system of elastic bodies in motion,
which act upon one another, ^m.v'2 is constant, and found that: In
order that a system of bodies of which each is attracted to a center
by a force varying as the nth power of the distance from that center,
should remain in equilibrium, it is necessary that

Sw./.s"41,

where / is the intensity of the force which acts on m, and z is the
distance of the mass m from its center of force, is a maximum or a
minimum. In the proof, by showing the truth of the principle in
two classes of cases, he concludes that as, for equilibrium

Si«./.s*.<fcr=;0j
the above sum must be a maximum or a minimum.1 3

In an "Addition" added to the reprint in the (Euvrcs,14 Mau-
pertuis remarked that his law holds if the forces are proportional
to functions Z of the distances £, and then the law is that

Sw././Z.cte
must be a minimum.15

in.

Mattpertuis's first enunciation of the law of the least quantity
of action was in a memoir read to the French Academy on April
15th, 1744, entitled: "Accord de differentes Loix de la Nature qui
avoient jusqu'ici paru incompatibles."16 The laws in question ap-

13 If there is one constant force on all the masses, and its center is at an
infinite distance from the system, the center of gravity of the system must be
as far as possible from, or as near as possible to, this center, for equilibrium to
subsist.

14 Vol. iv, pp. 62-63. It should be remarked that Euler, in a paper quoted
below in the Berlin Histoire for 1751, pp. 171-173, had pointed out: (i) that it
is not necessary that the forces are proportional to like powers of the dis-
tances, provided that we do not neglect the coefficients i/(n+i) when they are
different for the different bodies on which the forces act (p. 171) ; (2) that
the forces need not be supposed to be proportional to functions (f auctions
quelconques) of the distances, and if the force is V instead of fsn, Zf.m.V.ds
will then be a maximum or a minimum — according to the kind of equilibrium
(p. 172) ; and (3) that the whole distance of each body from the centers of
forces need not be considered, but, if convenience of calculation requires it,
we need only consider the distances of the bodies from fixed points on the
lines of direction of the forces (pp. 172-173).

15 Maupertuis does not add: "or a maximum." The subject of this memoir
of 1740 and its connection with the principle of least action were afterwards
greatly developed by Euler. Cf. also Mach, Mechanik, pp. 69-75; Mechanics,
pp. 68-73.

16 Histoire de I' Academic; Annee 1744 (Paris, 1748), pp. 417-426; CEuvres,
1756, vol. iv, pp. 3-18 (with the addition referred to below).

4l8 THE MONIST.

pear1? to be those of the reflection and of the refraction of light.
When a ray of light in a uniform medium travels from one point
to another, either without meeting an obstacle or with meeting a
reflecting surface, nature leads it by the shortest path and in the
shortest time. But when a ray is refracted by passing from a uni-
form medium to one of different density, the ray neither describes
the shortest space nor does it take the shortest time about it. As
Fermat showed, the time would be the shortest if light moved more
quickly in rarer media, but Newton proved that, as Descartes had
believed, light moves more quickly in denser media. Maupertuis's
discovery was that light neither takes always the shortest path nor
always that path which it describes in the shortest time, but "that
for which the quantity of action is the least/'

"I must now explain," he went one,18 "what I mean by the quan-
tity of action. A certain action is necessary for the carrying of a
body from one point to another : this action depends on the velocity
which the body has and the space which it describes ; but it is neither
the velocity nor the space taken separately. The quantity of action
varies directly as the velocity and the length of path described ; it is
proportional to the sum of the spaces, each being multiplied by the
velocity with which the body describes it. It is this quantity of
action which is here the true expense (depense) of nature, and which
she economizes as much as possible in the motion of light."

Then Maupertuis found, as a consequence of his principle, that
the sine of the angle of incidence is to the sine of the angle of re-
fraction in the inverse ratio of the velocity of the light in each me-
dium. T9 After showing that the law of reflection also follows from

17 Maupertuis afterwards stated (see below, section V) that the agreement
was between the laws of the motion of light and mechanical laws. I have
given below my grounds for almost suspecting that this was not what Mau-
pertuis originally meant.

18 Histoire de V Academic, 1744, p. 423; (Euvres, vol. iv, p. 17. Notice that
here, in the general definition, mass is not mentioned. This is another reason
for believing that, at first, Maupertuis only considered the motion of light-
corpuscles, and not that of ordinary matter.

19 Cf. Mach, Mechanik, pp. 397-398 ; Mechanics, pp. 367-368. Using Mau-
pertuis's and Mach's figure, CRD is the horizontal refracting plane, AR is the
incident and RB the refracted ray (A and B being any points chosen on these
respective rays), m the velocity of light along AR and n the velocity along
RB. Then Maupertuis says correctly that, according to his principle, w.AR
+n.RB must be a minimum. That is to say

d[mV(AC2+CR2) + nV(BD2+DR2)] =o,

whence, carrying out the differentiations, observing that AC and BD are con-
stant, and rf(CR) — — rf(DR),

(CR/AR : DR/BR) : : n : m, or (sin CAR/sin RED) = (w/m),
which is correct on the corpuscular hypothesis; Mach's criticism that the

CRITICISMS AND DISCUSSIONS. 419

his principle of the least quantity of action, Maupertuis concluded :20
"We cannot doubt that all things are regulated by a supreme Being,
who, while he has imprinted on matter forces which show his power,

has destined it to execute effects which mark his wisdom ; "

And :21 "Let us calculate the motion of bodies, but let us also consult
the designs of the Intelligence which makes them move."

It is of interest, in connection with the dispute with Konig
which arose afterwards, to read the note which Maupertuis appended
to the reprint in his (Euvres:22

"When I read the preceding memoir in the Paris Academy of
Sciences, I only knew of what Leibniz had done on this matter by
what M. de Mayran says of it in his memoir on the reflection of
bodies in the Paris Memoir es for 1723. Like him, I had confused
this opinion of Leibniz's with that of Fermat. ..."

Then he gave,2^ after Euler,2* the full opinion of Leibniz.2*

Now we shall see below that Maupertuis in the Histoire for
1752 said that he had "adopted" Leibniz's definition of action. We
have no means of knowing how far, if at all, Maupertuis was in-
debted to the ideas of Leibniz.

IV.

There is nothing on the subject of the principle of the least
quantity of action in the Histoire de I' Academic de Berlin (which
contains the Memoir es of the various classes of the Academy) for
1745 ; but, in the Histoire for 1746, published in 1748, Maupertuis

reciprocal values appear instead of the actual ones is only true, as P. Stackel
observed in the Encykl. der math. Wiss., vol. iv, part i, 1908, p. 491, on the
undulatory theory, which Maupertuis, as a good Newtonian, did not adopt.

Further, Maupertuis's principle does state that w.AR-f-w.RB (which is
what $v.ds reduces to here) is to be a minimum. This was contested by
Mach (but cf. Mechanik, p. 406; Mechanics, pp. 375-376).

Du Bois-Reymond (op. cit)., pp. 48-49) speaks of the example of the
motion of light which Maupertuis chose in 1744 to illustrate his principle
being "not happily chosen," because experiments have proved that the velocity
of light in air is greater than that in water — the opposite state of things to
that which the emission theory required.

20 (Euvres, vol. iv, p. 21.

21 Ibid., p. 22.
"Ibid., p. 23.

23 Ibid., pp. 23-28. In the text of the memoir of 1744, Maupertuis (ibid.,
p. 15) thus mentioned Leibniz: "Leibniz wished to conciliate the opinion of
Descartes [that light moves more quickly in the denser media] with final
causes ; but he did this only by suppositions which could not be sustained, and
which did not square with the other phenomena of nature."

24 Hist, de I'Acad. de Berlin, vol. vii, 1751, pp. 205-209.

25 Acta Eruditorum, 1682 (not seen).

42O THE MONIST.

has26 a memoir: "Les Loix du Mouvement et du Repos, deduites
d'un Principe Metaphysique."

This memoir begins with the prefatory remark:2? "I gave the
principle on which the following work is founded on April 15th,
1744, in the public assembly of the Royal Academy of Sciences of
Paris, as the A eta of this Academy testify." Then Maupertuis refers
to Euler's Methodus inveniendi of 1744,28 and the special pleasure
that the Appendix gave him, "as," he says, rather patronizingly
and in words which led some29 to suppose that Euler merely applied
Maupertuis's principle, "it is a beautiful application of my principle
to the motion of the planets, of which this principle is in fact the
rule."

The memoir is composed of three parts: (1) Examination of
the proofs of the existence of God, which are drawn from the
wonders of nature ;3° (2) The thesis that these proofs must be sought
in the general laws of motion, and that the laws according to which
motion is conserved, distributed, and destroyed are founded on the
attributes of a supreme intelligence ;^r and (3) Investigation of the
laws of motion and rest.32 In the third part, Maupertuis^ states
the general principle that "when some change happens in nature,
the quantity of action necessary for this change is the smallest pos-
sible," and adds: "The quantity of action is the product of the mass
of the bodies by their velocity and by the space which they describe.
When a body is transported from one place to another, the action
is greater in proportion as the mass is greater, as the velocity is
greater, and as the path by which it is transported is longer." From
this principle, Maupertuis deduces the laws of impact of hard (or
inelastic) and elastic bodies,34 and of the lever.35

28 Pp. 267-294. The mathematical (third) part of this memoir is, in part,
identical with "Recherche des Loix du Mouvement" in the (Euvres, vol. iv,
pp. 31-42; the theological part is included in the Essai de Cosmologie to which
we will soon refer.

™ Histoire de VAcad. de Berlin, 1746, p. 267. This note was repeated in
Maupertuis's (Euvres, vol. i (see below).

28 See below, section IX.

29 For example La Beaumelle, op. cit., p. 85.
s°Histoire de VAcad. de Berlin, 1746, pp. 268-277.
31 Ibid., pp. 277-287.

™ Ibid., pp. 287-294.

33 Ibid., p. 290 ; CEuvres, vol. iv, p. 36.

34 Histoire, pp. 290-293; (Euvres, vol. iv, pp. 36-42.

a tlistoire, p. 294; not in the (Euvres. The explanation of this omission
given by Maupertuis ((Euvres, vol. i, p. xxvii) is that this problem is too lim-
ited (as the directions of the forces of weight are all supposed to be parallel
to one another and at right angles to the straight lever) ; but the "Loi du

CRITICISMS AND DISCUSSIONS. 42!

When treating of impact of hard (inelastic) bodies of masses A
and B, which move with the velocities a and b respectively in a straight
line and in the same sense, Maupertuis considers the spaces (a and
b) described in a certain time (the unit of time), so that m.v.s be-
comes m.v2, as Mach notices, and so he points out Maupertuis's
inconsistency .s6

Let A move faster than B, so that A catches B up and infringes
on it, and let the common velocity of A and B after the impact be x
(less than a and greater than b). "The alteration which has hap-
pened in the universe consists in that the body A which moved with
the velocity a and which in a certain time described a space equal to
a only moves with the velocity a and describes a space equal to x,
while the body B which only moved with the velocity b and described
a space equal to b moves with a velocity x and describes a space
equal to x. This change is, then, the same as would have happened
if, while A moved with the velocity a and described a space equal to
ttj it had been carried backwards through a space equal to a-x on
an immaterial plane moving with the velocity a-x, and while B
moved with the velocity b and described a space equal to b, it had
been carried forward through a space equal to x - b on an immaterial
plane moving with a velocity x — b. Now, whether A and B move
with their own velocities on movable planes or they are at rest there,
as the movement of these planes charged with bodies is the same,
the quantities of action produced in nature will be A (a — j*)2 and
B(^r — b)2, and their sum must be as small as possible." This gives

2.A.
whence

In this case, where the bodies move in the same direction, the
quantity of motion destroyed and the quantity produced are equal,
and the total quantity of motion remains, after the impact, the same
as it was before. If the bodies move towards one another it is easy
to apply the same reasoning ; or it is sufficient to consider b as nega-
tive with respect to a. Then the common velocity will be

If A and B are perfectly elastic, and move in the same direction
with velocities as before, except that a and ft are the respective

repos" of 1740, given in vol. iv of the CEuvres, is a general principle of statics
and "agrees so perfectly with the principle of the least quantity of action that
we may say that it is only the same thing."

MMechanik, pp. 395-396, 398; Mechanics, pp. 365-366, 368.

422 THE MONIST.

velocities after impact, "the sum or the difference of these velocities
after the impact being the same as it was before," then, by analogous
considerations on the change which has happened in nature, Mau-
pertuis arrives at the conclusion that the quantity of action is here

and this, when minimized, since

(3-a = a-b and thus dp = da,
gives

a= (Aa-Ba-2B&)/(A + B), 13= (2Aa+Ab-Bb)/(A + E).

Here the sum of the vires vivae is conserved on impact, but this
is not the case with hard (inelastic) bodies.

To find the law of the lever Maupertuis considers masses A
and B attached to the ends of an immaterial lever of length c, and
seeks the point, at a distance z from A, around which they are in
equilibrium. For this purpose he seeks the point around which, if
the lever receives some small movement, the quantity of action is the
smallest possible. Then A and B, on this movement being im-
parted to them, describe small arcs similar to one another and pro-
portional to the distances of these bodies from the point sought.
These arcs will be the spaces described by the bodies and at the
same time will represent their velocities. Thus the quantity of action
will be proportional to

and this, when minimized, gives

v.

In the "Avertissement" to the fourth volume of his (Euvres,
Maupertuis says of the memoir of 1744: "I show the agreement of
the laws which light follows in its reflection and its refraction with
those which all other bodies follow in their motion." In point of
fact, this is not quite the case: he shows how both the law of re-
flection and that of refraction could, on the corpuscular hypothesis,
be deduced from one principle ; but, in the whole memoir, other mo-
tions than that of light were only referred to shortly. The law that,
in a uniform medium, light moves in a straight line is common, he
says,37 to all bodies : they move in a straight line unless some external
force deflects them; and the law of reflection is the same as that
87 Paris Histoire, 1744, p. 418; CEuvres, vol. iv, p. 7.

CRITICISMS AND DISCUSSIONS. 423

followed by an elastic ball impinging on an unbreakable surface.
But no like explanation of the law of refraction had been given.

Later on, Maupertuis38 adds a note to his definition of the
quantity of action as 2s.v: "As here there is only one body, we ab-
stract from its mass."

VI.

Maupertuis's Essai de Cosmologie was published in 175 1,39 and
consists of three parts: (1) Examination of the proofs of the exis-
tence of God, which are drawn from the wonders of nature; (2)
Deduction of the laws of motion from the attributes of the supreme
intelligence; and (3) Spectacle of the universe. No part of the
work is stated mathematically, and the third part is a rhetorical
sketch of the solar system, in which the principle of the least quan-
tity of action is not mentioned.40 The two first parts are practically
the two first parts of the memoir of 1746.

38 CEuvres, vol. iv, p. 17. This note is not in the original memoir of 1744
(the paragraph in the text to which the note refers is on p. 423 of this mem-
oir), but was first added, as a marginal note, in the Essai de Cosmologie of
1751. These facts suggest that the mechanical applications of Maupertuis's
principle were, at least, not clear to Maupertuis in 1744. For my own part,
I cannot help almost having the impression from a study of the original
memoir of 1744 and its reproduction, with comments, in the CEuvres of 1756,
that the laws of nature referred to in 1744 are the laws of catoptrics and
dioptrics, whereas afterwards Maupertuis, because of the discovery com-
municated in his memoir of 1746, tried to persuade possibly himself and
certainly his readers that the laws were more general laws of nature. Cf.
Note 18, Section III, above.

Formey, in the Eloge quoted at the beginning of this paper, says (p. 496) :
"II y [in the memoir of 1744] etoit principalement question des loix qui suit
la lumiere, surtout lorsqu'elle passe d'un milieu diaphane dans un autre."

39 Essay de Cosmologie. Par M. de Maupertuis, Leyden, 1751. At the
end (pp. 81-104) is a reprint of the 1744 paper with the mathematics (the
note referred to in section V, last note, is put in the margin of pp. 97-98) ;
and on pp. 63-80 is a "Recherche mathematique des Loix du Mouvement et
du Repos," from, says Maupertuis, the Berlin Memoires for 1747 (a misprint
for 1746). The Essai was partly reprinted in the first volume of the CEuvres
de Mr. de Maupertuis (Nouvelle edition, corrigee et augmentee, Lyons, 1756, pp.
3-78, and the mathematical part, which was omitted in the previous editions
of Maupertuis's CEuvres, is included in vol. iv, pp. 18-19, 36-42. On pp. iii-
xxviii, is an "avant-propos" giving, among other things, an account of the
Koenig incident of 1751 and its consequences. On pp. xiv-xv is the same
notice about his own and Euler's works of 1744 that is at the head of Mau-
pertuis's paper in the Berlin Memoires for 1746. On d'Arcy's objections (see
section XV) Maupertuis (CEuvres, vol. i, p. xxvi) said that 'As the only
objection which appears to have some foundation rests on the fact that, in the
impact of elastic bodies, he has confused the change which happens to the
velocities (which is real) with the change of the quantity of action (which is
zero), I will make no other reply than the few words I have said about it in
the Memoires of our [Berlin] Academy for the year 1752" (see section XVI).

*° However, in the second part (CEuvres, vol. i, p. 45), we read: "What
a satisfaction for the human mind to find in the laws which are the principle

424 THE MONIST.

Maupertuis had a low opinion of the proofs of the existence of
God from the construction of animals. Thus, somebody^ found
evidence for this existence in the folds of the skin of a rhinoceros —
the animal could not move without these folds. Maupertuis^2 rather
appositely asked : "What would be said of a man who should deny
a Providence because the shell of a tortoise has neither folds nor
joints?" And -.43 "It is not in the little details, in those parts of the
universe of whose relations are known too little, that we must look
for the supreme Being, but in phenomena whose universality suffers
no exception and whose simplicity lays them quite open to our sight."

VII.

The reason why Maupertuis laid stress on the deduction from
the principle of the least quantity of action of the laws of the impact
of inelastic masses was that the law of the conservation of vis viva
fails in this case.44 Leibniz^s recognized Descartes's error in think-
ing that, in nature, the sum of the products of the masses into their
respective velocities is constant, and substituted in it the squares of
the velocities for the velocities, so that the sum is what is called the
vis viva of the system considered. But, in impact, the vis viva is
only conserved if the bodies are elastic ; and, according to Mauper-
tuis :«6 "When we make this objection to the Leibnizians, they pre-
fer to say that there are no hard (durs, inelastic) bodies in nature
than to abandon their principle. This were to be reduced to the
strangest paradox to which love of a system could reduce one: for
what can the primitive elementary bodies be but hard bodies?"

In vain, then, said Maupertuis,47 did Descartes and Leibniz, in

of motion of all the bodies of the universe the proof of the existence of the
governor of it !"

"•Phil. Trans., No. 470. [The paper referred to is entitled: "A Letter
from Dr. Parsons to Martin Folkes, Esq., President of the Roy. Soc., con-
taining the Natural History of the Rhinoceros," and is printed in the Phil.
Trans, for 1743, pp. 523-541].

42 CEuvres, vol. i, p. 12.

"Ibid., p. 21.

44 CEuvres, vol. i, pp. xvi-xvii, 44.

45 On Leibniz's mechanics (the conservation of vis viva, and so on), cf.
Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz, with an
Appendix of leading Passages, Cambridge, 1900, pp. 77-99, 226-238; esp. pp.
89-90. The concept of action with Leibniz was not mentioned by Russell ; on
it cf. du Bois-Reymond, op. cit., pp. 48, 51, 89-90; and Helmholtz, "Zur Ge-
schichte des Princips der kleinsten Action," Sitzungsberichte der Berliner
Akad., 1887, pp. 225-236, or Wiss. Abh., vol. iii, pp. 249-263. Cf. also L. Cou-
turat, La logique de Leibniz, 1901, pp. 229-233, 577-581.

48 Op. cit., p. xvii.
47 Ibid., p. xviii.

CRITICISMS AND DISCUSSIONS. 425

different ways, imagine a world which could dispense with the hand
of a Creator : no quantity which can be regarded as a cause in the
distribution of motion subsists unaltered. But "Action" is, so to
speak, created at each instant, and always created with the greatest
economy possible ; and by this the universe announces its dependence
on a wise and powerful author.

Maupertuis*8 said that, because he held that the conservation of
vis viva is not the universal principle of movement, the whole sect
of Leibnizians in Germany descended on him (je vis fondre sur moi
toute la secte que M. de Leybnitz a laissee en Allemagne), and then
mentioned49 Konig's having attributed some of Maupertuis's and
Euler's discoveries to Leibniz. Then followss° an account of the
incident.

As a justification of the word "action," MaupertuisS1 remarked
that he had found this word quite established by Leibniz and Wolff,
and did not wish to change the terms.

VIII.

When speaking of Diderot's Thoughts on the Interpretation of
Nature of 1754, John Morley,52 now Lord Morley, said :

"Maupertuis had in 1751, under the assumed name of Baumann,
an imaginary doctor of Erlangen, published a dissertation on the
Universal System of Nature, in which he seems to have maintained
that the mechanism of the universe is one and the same throughout,
modifying itself, or being modified by some vital element within, in
an infinity of diverse ways.53 Leibnitz's famous idea, of making
nature invariably work with the minimum of action, was seized by
Maupertuis, expressed as the Law of Thrift, and made the starting
point of speculations that led directly to Holbach and the System
of Nature s* The Loi d'Epargnc evidently tended to make unity

48 Ibid., p. xix.

"Ibid., p. xx.

50 Ibid., pp. xx-xxvi, cf. section XI below.

01 Ibid., pp. xxvi-xxvii, cf. Maupertuis's paper of 1752, described below in
section XVI.

52 Diderot and the Encyclopedists, vol. ii, London, edition of 1905, pp. 262-
263.

63 "As to the precise drift of Maupertuis's theme, see Lange, Gesch. d.
Materialismus, i, 413, n. 37. Also Rosenkranz, Diderot's Leben, 1866, vol.i,
P. I34-"

54 "In 1765 Grimm describes the principle of Leibnitz and Maupertuis as
'gaining on us on every side'. .. .Corr. Lit., iv, 186." [Under the date of Feb.
T5> J765, Grimm (Correspondance litteraire philosophique et critique de Grimm
et de Diderot depuis 1753 jusqu'en 1790, new ed., vol. iv, p. 186) speaks thus

426 THE MONIST.

of all the forces of the universe the keynote or the goal of philo-
sophical inquiry. At this time of his life, Diderot resisted Mau-
pertuis's theory of the unity of vital force in the universe, or per-
haps we should rather say that he saw how open it was to criticism.
His resistance has none of his usual air of vehement conviction.
However that may be, the theory excited his interest, and fitted in
with the train of meditation which his thoughts about the Encyclo-
paedia had already set in motion, and of which the Pensees Philo-
sophiques of 1746 were the cruder prelude."

Again :ss

"Diderot was in no sense the originator of the French material-
ism of the eighteenth century. He was preceded by Maupertuis,
by Robinet, and by La Mettrie ; and we have already seen that when
he composed the Thoughts on the Interpretation of Nature (1754)
he did not fully accept Maupertuis's materialistic thesis. Lange has
shown that at a very early period in the movement the most consis-
tent materialism was ready and developed, while such leaders of the
movement as Voltaire and Diderot still leaned either on deism and
scepticism. "s6

Lange'sS7 work was first published in one volume: Geschichte
des Materialismus und Kritik seiner Bedeutung in der Gegenwart
at Iserlohn in 1866. In the whole book, Maupertuis is only men-
tioned once. On page 224s8 it is said that people debated whether
the Marquis d'Argens (Jean Baptiste de Boyer) or Maupertuis or
some personal enemy of Albrecht von Haller, really wrote the
Homme machine which De la Mettrie ironically dedicated to Von
Haller.59

The fourth part60 is devoted to the materialism of the eighteenth
century, and consists of three divisions: De la Mettrie's Homme
machine of 1747 ;61 Holbach's Systeme de la Nature, ou des lois du
monde physique et du monde moral of 1770, published, according
to the title-page, in London, but really at Amsterdam, under the

of the Leibniz-Maupertuis principle of thrift, immediately after speaking of
the second volume of Robinet's De la nature, published in four volumes
1761-8.

On Holbach's System of Nature (1770), see Morley, op. cit., pp. 155-203.

55 Morley, op. cit., pp. 272-273.

58 Gesch. d. Materialismus, \, 309, 310, etc.

57 Friedrich Albert Lange.

58 Cf. the references below the second edition of Lange's work.

59 Lange, op. cit., p. 72.

60 Ibid., pp. 163-229.

61 Ibid., pp. 163-186.

CRITICISMS AND DISCUSSIONS. 427

name of Mirabaud who had been dead for ten years ;62 and the Ger-
man reaction against materialism.^

On the other hand, Maupertuis is often spoken of in the second
edition of Lange's work, published at Iserlohn in 1873 and 1875 in
two volumes under the same title,64 and it is to this edition that
Morley's citations refer. We will continue this reference to Lange's
book after having given some information about Maupertuis's work
of 1751, which Morley mentions.

In 1751 Maupertuis published at Erlangen, under the pseudo-
nym of "Baumann," a Latin dissertation under the title: Dissertatio
inaugurate metaphysica, de universali naturae systemata,6* in which

62 Ibid., pp. 186-214.

63 Ibid., pp. 214-229.

64 There is an English translation of this edition in three volumes, by E.
C. Thomas, published at London in 1877, 1880 and 1881 (History of Material-
ism and Criticism of its Present Importance'). The passages in this transla-
tion parallel to those of Morley's citations are given here.

65 Another edition, with a French translation and with neither the place
nor year of publication has been given; a third, only in French and entitled:
Essai sur la formation des corps organisees was published by 1'Abbe Trublet,
with a notice and conjectures about the author, at Berlin (really at Paris) in
1754; and the French version (Systeme de la Nature: Essai sur la formation
des corps organisees} was published, with a preface, in Maupertuis's (Euvres,
1756, vol. ii, pp. 135-168 (between pp. 160 and 161 are pages numbered 145*
to *i6o). Diderot's Pensees sur I' interpretation de la nature was published
anonymously at Paris in 1754 with "London" as the place of printing (Cf.
Karl Rosenkranz, Diderot's Leben und Werke, 2 vols., Leipsic, 1866, vol. i,
pp. 134-146; (Euvres completes de Diderot, ed. by J. Assezat, vol. ii, Paris,
1875, pp. 1-63 ; cf. Assezat's "Notice preliminaire," p. 3. Maupertuis's "Re-
ponse aux objections de M. Diderot," was printed in his (Euvres, 1756, vol. ii,
pp. 169-184 (between pp. 176 and 177 are pages numbered 161* to *I76). Cf.
on all this, La Beaumelle, op. cit., pp. 178-181, 200-201.

On Maupertuis's theories of generation, see La Beaumelle, op. cit., pp.
86-87, 98-103; du Bois-Reymond, op. cit., pp. 38-39, 44-45. The Venus phy-
sique of 1745 (anonymous) was republished in Maupertuis's (Euvres, 1756,
vol. ii, pp. 1-133. The statement that Maupertuis endeavored to explain the
formation of the foetus by gravitation is one of Voltaire's libels on Mauper-
tuis. The truth seems to be that Maupertuis, in his Venus and Systeme de la
Nature, as well as in one of his Letters ("Lettre xiv, Sur la generation des
animaux," (Euvres, 1756, vol. ii, pp. 267-282), tried to explain this formation
by the different attractions or (in the Systeme} psychical tendencies of the
"different parts. The Lettres de M. de Maupertuis (sur differ ents sujets} were
published in 1753 and again in the (Euvres, 1756, vol. ii, pp. 185-340, after
having been grossly caricatured by Voltaire in his Histoire du docteur Akakia
et du natif de Saint Malo ((Euvres completes de Voltaire, vol. xxiv, Paris,
1892, pp. 358-376). By the way, Letters X and XI ("Sur les loix du mouve-
ment" and "Sur ce qui s'est passe a 1'occasion du principe de la moindre quan-
tite de 1'action"; (Euvres, 1756, vol. ii, pp. 238-242 and 243-251 respectively)
refer to the principle of least action; and Letter XII (ibid., pp. 252-257; "Sur
1 'attraction") contains a short expose of Maupertuis's work in introducing
Newtonianism into France.

Maupertuis does not seem, by his published writings, to have been nearly
so ridiculous a person as Voltaire, for personal reasons, tried to make him
appear to be. And Voltaire's sarcasms have had great influence on the ideas

428 THE MONIST.

a hypothesis that the parts of matter have something similar to
what we call desire, aversion, and memory was advanced to explain
certain physiological facts. Maupertuis chose this pseudonymous
fashion of giving his thoughts to the public, partly because the
work of an unknown author would be less the butt of objections,
and partly in order that he should not be obliged to reply to them.
But he felt it necessary to reply to Diderot's Thoughts because his
doctrines were accused of having results contrary to religion. Then
he acknowledged the work: he had soon been recognized as its
author. What concerns us here is that the law of least action is
not mentioned in this work of Maupertuis's. Further, the Essai
de Cosmologie of 1751 was not published anonymously or pseudo-
nymously. Thus there seem to be no grounds for Morley's strange
error.

Lange shows that the Newtonian theory is a combination of
materialism in natural science with a religious faith in the spiritual
constructor of the material world-machine. "The magnificent phe-
nomena of the seventeenth century were renewed in increased splen-
dor, and to the age of a Pascal and Fermat succeeded with Mau-
pertuis and D'Alembert the long series of French mathematicians
of the eighteenth century, until Laplace drew the last consequences
of the Newtonian cosmology in discarding even the hypothesis of a
creator/'66

Maupertuis is classed with Robinet and La Mettrie as a mate-
rialist^ on the grounds of his Latin dissertation of 1751. The
English translation of the note (37) referred to by Morley is:68
"Comp. Rosenkranz, Diderot, i, 134 ff. The pseudonymous disser-
tation of Dr. Baumann (Maupertuis) I have not seen, and it may
be open to some doubt, according to Diderot and Rosenkranz,
whether it does really contain the materialism of Robinet — that is,
the unconditional dependence of the spiritual upon the purely me-
chanical series of external events — or whether it inculcates Hylo-

of Maupertuis formed by succeeding generations. Thus Mach (Mechanik, pp.
484-485, Mechanics, po. 454-455) gives, I think, Voltaire's version of some of
the things dealt with by Maupertuis in a Letter published earlier than those
just mentioned. Maupertuis's Lettre sur les pr ogres des sciences was pub-
lished at Berlin in 1752 and again in his CELuvres, 1756, vol. ii, pp. 341-399-
Here is the project of founding a town where only Latin should be spoken,
in order to preserve this most universal of languages (pp. 367-368), and a
plea (pp. 394-398) for "metaphysical" — or, as we would say now, psycho-
logical— experiments.

66 Lange, Geschichte, 2d ed., vol. i, p. 304; History, vol. ii, p. 16.

67 Lange, Geschichte, vol. i, p. 310; History, vol. ii, p. 25.

68 Lange, Geschichte, vol. i, pp. 315, 412-413; History, vol. ii, p. 31.

CRITICISMS AND DISCUSSIONS. 429

zoism — that is, modifications of the natural mechanism by the spirit-
ual content of nature according to other than purely mechanical
laws."

Again :69 "Bnffon began the publication of his great work on
natural history in the year 1749, with the first three volumes ; but
it was only in the fourth volume that he unfolded the idea of the
unity of principle in the multiplicity of organisms, an idea which
occurs again in Maupertuis in an anonymous work in 1751, in Dide-
rot in the Pcnsccs sur r Interpretations de la Nature, 1754, while we
find it developed with great clearness and distinctness by La Mettrie
as early as the L'Homme Plant e in 1748."

This, together with the passage referred to above, when we were
speaking of the first edition, about Maupertuis being considered by
some to be the author of L'Homme Machine,70 completes the list of
Lange's references to Maupertuis in the second edition of his book.

We must add that Maupertuis, in his writings and in his life,
showed the greatest respect for religion. He was by no means a
materialist and atheist/1 and the only reason, said he, that he had
for replying to Diderot's Thoughts on his dissertation of 1751 was
that Diderot stated that the dissertation, in spite of its carefully re-
ligious tone, led to conclusions which were subversive of religion.

IX.

This seems the best place to give some account of the work of
a man who will now take a prominent place in the development of
Maupertuis's ideas ; I mean Leonhard Euler.?2

The modern period of the discussion of maximal and minimal
problems begins with Johann Bernoulli's proposal of the problem of
the brachistochrone in 1696 and the consequent rise into importance
of the "isoperimetrical" problems. 73 The period 1696 to 1762 of

69Lange, Geschichte, vol. i, p. 328; History, vol. ii, p. 52.

70 Lange, Geschichte, vol. i, p. 398 ; History, vol. ii, p. 137.

71 Du Bois-Reymond, op. cit., pp. 43-44, 49-50.

72 On the older period of the history of such problems, see Mach, Mechanik,
PP- 453-457; Mechanics, pp. 421-425. This period is — like all early periods in
the history of branches of science — characterized by the fact that the maximal
and minimal problems are all isolated. This period extends as far as Newton
who in 1687 solved "the first problem of the calculus of variations," the deter-
mination of the figure of the solid of least resistance (cf. M. Cantor, op. cit.,
p. 291).

73 Mach, Mechanik, pp. 457-467 ; Mechanics, pp. 425-436. A German an-
notated translation of some works of Johann Bernoulli, Jakob Bernoulli, and
Leonhard Euler, from 1696 to 1744, is given by P. Stackel in No. 46 of Ost-
walds Klassiker. Cf. also M. Cantor, op. cit., pp. 237-241, 384, 446-458, 533,
846-848.

430 THE MONIST.

the history of such problems is distinguished by the names of Johann
Bernoulli, Jakob Bernoulli, and Leonhard Euler, and extends until
Lagrange, in 1762, brought all these interrelated methods under the
general and abstract analytical form of the calculus of variations.
It is to this period that the works of Maupertuis, Euler, and their
contemporaries, with which we are concerned here, belong. The
leading work published in this period was the famous Methodus in-
veniendi tineas curvas maximi minimive proprietate gandentes : sive
solutio problematis isoperimetrici latissimo sensu accepti which was
published at Lausanne and Geneva in 1744.74

Mathematicians found that various problems of mechanics might
be put into isoperimetrical form. Whether their tendency to do
this, which was very common at that time, was due to esthetic,
theological, or technical reasons, it is hard to say. Daniel Bernoulli
— a son of Johann Bernoulli — remarked that certain statical problems
can be treated with greater facility by isoperimetrical methods than
by the usual mechanical principles ; the feeling, too, that the dis-
covery that a problem about natural objects could be put in a max-
imal or minimal form had a connection with the way the Deity
managed things here below in making nature act by the shortest
or easiest or readiest paths, and so with what were then called "meta-
physical"75 questions, undoubtedly had an influence on others besides
Maupertuis — on Euler for example. But we shall see how piety and
humility led Euler, though accurate, judged by the mathematical
standards of those days, very cautious, and perhaps a little unimag-
inative/6 to accept and admire the bold and not always accurate
mechanical generalizations which Maupertuis professed to deduce
from "metaphysics." But probably the esthetic satisfaction which

74 An annotated German translation of a great part of this book was given
in No. 46 of Ostwalds Klassiker. However, the two appendices (on the
elastic curves, and on the motion of a particle round a center of force in a non-
resisting medium) with which we shall be especially concerned here were not
translated with the main body of the work. But the first appendix was trans-
lated, in another connection, in No. 175 of the Klassiker (see below, section
X). An account of Euler's book of 1744 is given in M. Cantor's Geschichte,
vol. iii, 2d ed., Leipsic, 1901, pp. 857-867.

75 In the eighteenth century, "metaphysics" stood for — at least among
mathematicians — a branch of learning which included theology, psychology,
and logic. Consider the "metaphysical experiments" advocated by Maupertuis,
and the "metaphysics of the infinitesimal calculus" (L. N. M. Carnot, Lagrange,
and others), which meant what we mean when we say: "the logical principles
of the calculus."

76 D'Alembert, in a letter of March 3, 1766, to Voltaire (quoted by Delam-
bre in his "Notice" in CEuvres de Lagrange, vol. i, p. xxi), says of Euler:
"c'est un homme peu amtisant, mais un tres grand geometre."

CRITICISMS AND DISCUSSIONS. 43!

arises from stating a problem in a maximal or minimal form in-
fluenced mathematicians the most.

However this may be, to this form come many problems of
statics, such as the catenary of Johann and Jakob Bernoulli,77 and
Jakob Bernoulli's problem of the elastic curve.78 From Daniel Ber-
noulli's letter to Euler and from Euler's first appendix to his book of
1744, we see with what interest Daniel Bernoulli and Euler reduced
this problem in the theory of elasticity to isoperimetrical methods.

These problems were all statical ones ; and it was Daniel Ber-
noulli who suggested to Euler the putting of a certain dynamical
problem into isoperimetrical form. It must be remembered that
Euler, by his papers published by the St. Petersburg Academy in
1732 and 1736/9 had placed himself at the head of the mathematical
world, in the treatment of isoperimetrical problems. We must now
say some words about Daniel Bernoulli and Euler and their rela-
tions to one another.

Daniel Bernoulli80 (1700-1782) was a son of the famous Jo-
hann Bernoulli (1667-1748) and was attached to the St. Petersburg
Academy from 1725 to 1733. From 1733 to 1782 he was Professor
of Anatomy and Botany, and later Experimental Physics and Specu-
lative Philosophy too, at Basel. His mathematical works81 are on
differential equations, the theory of numbers, the theory of prob-
ability, series, and mechanics82 — principally the theorem of vis viva**
the problem of vibrating cords,8* and hydrodynamics.8* Leonhard
Euler86 (1707-1783), whose name as a mathematician is too well
known for it to be necessary for us to refer further to his many
works, came to St. Petersburg in 1727, owing to the exertions on
his behalf of Daniel Bernoulli and Hermann, but left St. Peters-

77 Cf . Mach, Mechanik, pp. 75-77 ; Mechanics, pp. 74-76 ; Ostwalds Klas-
siker, No. 46, p. 19; M. Cantor, op. cit., pp. 219-220, 228, 235, 289, 384, 455,853.

78 Cf. M. Cantor, op. cit., pp. 220-221, and Johann Bernoulli's letter of
March 7, 1739, to Euler in Fuss's Correspondence referred to below, vol. ii,
pp. 23-25.

79 Cf. M. Cantor, op. cit., pp. 846-856.

80 M. Cantor, op. cit., pp. 89-90, 550; Encycl. Brit., 9th ed., vol. iii, 1875,
pp. 606-607.

81 Ibid., pp. 477-48i, 610, 630-632, 634-635, 640, 642-644, 688, 693, 707, 721,
851, 900, 904-906.

82 Cf. also Mach, Mechanik, pp. 43-49, 326 ; Mechanics, pp. 40-47, 293.

83 Cf . also Mach, Mechanik, pp. 374-379 ; Mechanics, p_ p. 343, 348.

84 Cf. also Mach, Die Principled der Wdrmelehre, 2d ed., Leipsic, 1900,
PP. 96-97.

85 Cf. Mach, Mechanik, pp. 440-453; Mechanics, pp. 403-420.

86 M. Cantor, op. cit., pp. 549-551.

432 THE MONIST.

burg in 1744 to become Director, of the Mathematical Class of
Frederick the Great's reformed Academy of Sciences at Berlin.
In 1727 Euler met Daniel Bernoulli and was stimulated by him to an
investigation on geodesic lines.8? The letters addressed by Daniel
Bernoulli to Euler — those from Euler to Bernoulli are unfortunately
lost — from 1726 to 1755 have been published in P. H. Fuss's Cor-
respondancc mathematique et physique de quelques cclebres gco-
nietres du XVIIIicme siecle.^ From this correspondence we will
now make the extracts which concern our present subject.

In a letter to Euler of January 28th, 1741, Daniel Bernoulli
asked whether it was not Euler's opinion that orbits about centers
of force could be deduced by an isoperimetrical method.89 As we
have said, Euler's replies are lost. In a letter of December 12, 1742,
Bernoulli has some further remarks on the same subject ;9° and in a

87 M. Cantor, op. cit., p. 843.

88 St. Petersburg, 1843, vol. ii, pp. 407-655. In these letters there is fre-
quently mention of isoperimetrical problems, but the first mention of a mechan-
ical problem treated by an isoperimetrical method is on pp. 456-457 (letter
of March 7, 1739) where the elastic curve, which requires a certain integral
which represents the "potential vis viva" to be a maximum, since Bernoulli
thinks "that an elastic lamina which takes a certain curvature of itself will
bend in such a way that the vis viva will be a minimum, since otherwise the
lamina would move," is referred to (other references are given on pp. 468-
469, 506-507, 512-514, 533-534. 536-537)- To this apparently refers what Ber-
noulli (p. 534) calls an a priori method — a speculation which contrasts oddly
with the passages quoted below which are rather anti-"metaphysical." The
first occurrence of a reference to a dynamical problem to be treated by an
isoperimetrical method is that given below.

It was Daniel Bernoulli who recommended that Bousquet of Geneva
should be chosen as the printer of Euler's "masterly" (herrlichen) treatise on
the isoperimetrical method — the Methodus printed in 1744 (letter of Feb. 9,
1743; ibid., p. 521; cf. pp. 524-525 (see extract below), 528, 529, 533 (see
extract below), 541, 550, 553, 578). In a letter of September 4, 1743, Bernoulli
(ibid., p. 536) says: "I regret that I could not read through your additions
to the treatise on isoperimeters ; but I have just (fugitive oculo) glanced at
them." This is important in view of Euler's account (section XII below) of
the date and circumstances under which these additions were made and
printed.

' "Von E\v. mochte vernehmen, ob Sie nicht meinen, dass man die orbitas
circa centra virium konne methodo isoperimetrica, wie auch die figuram terrae
pro theoria Newtoniana herausbringen" (Fuss, Correspondance, vol. ii, p. 468).

°"Man kann die principia maximorum et minimorum nicht genugsam
ausforschen; die trajectoriae circa centrum virium, vel circa plura centra
virium, miissen gleichfalls per methodurn isoperimetricorum konnen solviret
werden, obschon man das maximum vel minimum, quod natura affectat, nicht
einsiehet. Es haben also Ew. einen grossen Nutzen dadurch geschafft, dass
Sie die methodum isoperimetricorum so weit perfectionnirt haben. Meiner
Meinung nach ist dieses argumentum inter omnia pure analytica utilissimum,
und ist dieses ein wahres Exempel, dass vel sola propositio problematis, wenn
man auch die Solution nicht hatte, saepe maxima laude digna sey" (ibid., p.
513).

CRITICISMS AND DISCUSSIONS. 433

letter of April 23, 1743, speakss1 with praise of Euler's great treatise
on the Isoperimetrical Method, suggests the addition of a treatment
of the problem of the elastic curve and others like it, and then com-
ments on Euler's discovery that §v.ds is a minimum for central
orbits, that Euler has obviously communicated to him without proof,
as follows:

"The observation about trajectories that fjv.ds must be a maxi-
mum or minimum appears to me very beautiful and important ; but
I cannot see how this principle is demonstrated. Please let me know
whether the principle extends to trajectories about many centers of
forces. Perhaps it is only an observation a posteriori, owing to a
discovery you may have made that the trajectories have this prop-
erty, and you may not have been able to demonstrate it a priori"

In a letter of September 4, 1743, Bernoulli writes :92

81 Wegen Ew. herrlichen Tractat de isoperimetricis werde ich yorlaufig
mit demselben reden ; Sie belieben nnr denselben fertig zu halten. Sie konn-
ten das problema de elastica hac methodo invenienda und andere dergleichen
noch beyfiigen. Ich sehe leicht, dass man die curvaturam catenae et laminae
elasticae oscillantis auch darin reduciren kann ; auf den modum aber bin ich
noch nicht bedacht gewesen. Die meisten ciirvas mechanicas wird man auch
dahin reduciren konnen. Die Observation von den trajectoriis, dass ^v.ds
ein maximum oder minimum seyn miisse, diinkt mich sehr schon und von
grosser Wichtigkeit ; ich sehe aber die Demonstration dieses principii nicht ein.
Ew. belieben mir zu melden, ob sich solches auch ad trajectorias circa plura
centra virium erstrecke. Vielleicht ist es nur eine observatio a posteriori, in-
dem Sie angemerkt haben, dass die trajectoriae diese proprietatem haben, ohne
solche a priori recht demonstriren zu konnen" (ibid., pp. 524-525).

02 "Aus Dero Brief ersehe ich, dass ich in meiner Conjectur mich nicht
betrogen, wenn ich gesagt habe, dass Dero Observation circa orbitas plane-
tarum, in quibus ^v.ds vel \v.v.dt ein minimum ist, vielleicht nur a poste-
riori sey gemacht worden ; denn nach meinen principiis kann ich solches a
priori nicht einsehen. Der Herr Clairaut schreibt, dass solches auch schon
von einem Englander sey remarquirt worden. Es scheint, dass dieses nicht
sowohl ein principium, als eine proprietas sey, gleich wie es eine proprietas
ist elasticae, dass sie das maximum solidum generirt. Doch hab ich nicht
untersucht, ob die idea maximi solidi die elasticam in omni extensione be-
greife. Sie konnen mich dieser Miihe entheben, denn ich weiss, dass Sie alle
dergleichen Untersuchungen allbereits gemacht haben. Von meinem principio
a priori, dass die elastica das \ ds/rr ein minimum formire, hab ich mit
vieler Erkenntlichkeit ersehen, aber zugleich mit Beschamung, dass Sie in
Ihrem supplemento so honorificam mentionem thun. Dieses principium gehet
auch an in laminis inaequaliter elasticis, wenn man macht $eds/r.r ein mini-
mum. Die laminae naturaliter non rectae erfordern zwar einen andern calculum,
aber keine andere methodum ; wenn aber die laminae proprio pondere zu-
gleich incurvirt werden, so ist es schwer, das maximum oder minimum quod
natura affectat zu determiniren. Ich muthmaasse, dass man allhier muss ad
maxima maximorum recurriren, wenn zweyerley Considerationen zusammen
kommen. Quaeatur brevitatis gratia curva AC, quam lamina naturaliter recta
AB et uniformis proprio solo pondere incurvata accipiet : f ragt sich, ob nicht
curva AC talis seyn konnte, dass inter omnes eiusdem longitudinis, inter eos-
demque terminos positas curyas, eandemque f ds/rr habentes, das centrum
gravitatis infimum locum obtineat. Wir haben Beide diese curvam directe
determinirt; fragt sich also, ob man ex hoc principio eandem curvam finden

434 THE MONIST.

"From your letter I see that I was not mistaken in my conjecture
that your observation that §v.ds or fv.v.dt is a minimum for the
orbits of the planets was perhaps only made a posteriori ; for I can-
not see this a priori by the light of my principles. M. Clairaut writes
that this property has also been noticed by an Englishman. It
appears that this is not so much a principle as a property, just
as it is a property of the elastic curve to generate the maximum
solid. Still I have not investigated whether the idea of the maximum
solid includes that of the elastic curve in all its extension . . . . "

And in a letter of December 25, 1743, Bernoulli writes :$3

"I doubt whether one can ever show a priori that the elastic
curve must generate the maximum solid ; I consider this as a property
which is shown by calculation and that nobody could have foreseen
from first principles — as little as the identity of the isochrone and
the brachystochrone. Such properties are, as it were, discovered
through accident by our reason, and I consider the property ob-
served, that in orbits fu.ds is a minimum, to be on this level. I
was confirmed in this opinion by learning that you only observed
this property a posteriori and never would have found it if you had
not determined the orbit by other means."

Lastly, Bernoulli's anti-"metaphysical" tendency is still more
strongly shown in a passage94 of a letter to Euler of April 29, 1747:

"Herr Ramspeck has written to my father that you are engaged
in various public metaphysical controversies. You really ought not
to meddle with such matters, for from you we expect only sublime
things, and it is not possible to excel in metaphysics."

Euler, we know, had a strong reverence for "metaphysics" and

wiirde. Der calculus aber wird ohne Zweifel weitlaufig seyn, und bin ich von
diesem principio nicht convincirt, so dass Ew. sich schwerlich die Miihe werden
gebenwollen meine Conjectur zu untersuchen. Wenn solche aber richtigware,
wiirde es, wie ich glaube, leicht seyn, schier aller curvarum maxima et minima
a priori anzuzeigen" (ibid., pp. 533-534)-

83 "Ich zweifle ob man jemals a priori werde zeigen konnen, dass die
elastica miisse maximum solidum generiren ; ich betrachte solches als eine
Proprietat, die der calculus ausweiset, und die kein Mensch ex principiis novis
jemals wiirde haben konnen vorhersehen, eben so wenig als die identitatem
isochronae et brachystochronae. Dergleichen proprietates sind ratione nostri
gleichsam accidental, und auf diesen Fuss betrachte ich auch die observatam
proprietatem orbitarum, in quibus [u.ds ein minimum macht, worin ich um
so viel mehr confirmirt werde, als ich errathen, dass Sie diese proprietatem
nur a posteriori observirt haben und niemals wiirden gefunden haben, wenn
Sie nicht die orbitas aliunde determinirt hatten" (ibid., p. 543).

14 "Herr Ramspeck hat meinem Vater geschrieben, dass Sie in unter-
schiedenen controversiis metaphysicis publicis stehen. Sie sollten sich nicht
iiber dergleichen Materien einlassen; denn von Ihnen erwartet man nichts als
sublime Sachen, und es ist nicht moglich in jenen zu excelliren" (ibid., p. 621).

CRITICISMS AND DISCUSSIONS. 435

consequently attached to Maupertuis's a priori speculations a value
far above his own discovery. We shall see later that, in papers
published among the Mcmoires of the Berlin Academy, he empha-
sizes, as he apparently did to Daniel Bernoulli, the fact that he had
only discovered the minimal condition satisfied by orbital motion in
an a posteriori manner, as if this was rather a demerit. Nowadays
we would say that Euler's great caution in, for example, insisting, in
his Methodus, that the v in

fv.ds

is to be expressed in terms of ^ by the principle of vis viva, so that
his minimal principle cannot be extended to the case of motion in
a resisting medium, where the principle of vis viva does not hold, and,
in later publications, the careful enumeration of cases when testing
Maupertuis's statical principle, are merits. But the following ex-
tract from the first appendix on elastic curves to the Methodus of
1744 proves that more general "metaphysical" ideas were by no
means foreign to Euler:

"For since the plan of the universe is the most perfect possible
and the work of the wisest possible creator, nothing happens which
has not some maximal or minimal property, and therefore there is
no doubt but that all the effects in nature can be equally well deter-
mined from final causes by the aid of the method of maxima and
minima as from the efficient causes."95

x.

We will now return to the publications of the Berlin Academy.
The only paper concerning us here in the Histoire for 1747,

95 "Cum enim Mundi universi fabrica sit perfectissima, atque a Creatpre
sapientissimo absoluta, nihil omnino in mundo contingit, in quo non maximi
minimive ratio quaepiam eluceat; quamobrem dubium prorsus est nullum,
quin omnes Mundi effectus ex causis finalibus, ope Methodi maximorum et
minimorum, aeque feliciter determinari queant, atque ex ipsis causis efficienti-
bus, Methodus, p. 245, and cf. section XII below. (See Ostzvalds Klassiker,
No. 175, p. 18. Cf. Mach, Mechanik, p. 485; Mechanics,^. 455. Cf. also
E. Diihring, Kritische Geschichte dcr allgemeinen Principien der Mechanik,
3d ed., Leipsic, 1887, pp. 293-294, 296-299, 385-400). These reflections of
Diihring's are on the effects of philosophy on mechanics and Lagrange's anti-
"metaphysical" tendencies. Lagrange's own words are (Mechanique analitique,
Paris, 1788, p. 187): "....as if vague and arbitrary denominations [such as
the least quantity of action} made up the essential part of the laws of nature
and could by some secret virtue raise simple results of the known laws of

mechanics to the position of final causes"; and (p. 189) : " 1 regard this

principle [of least action] not as a metaphysical principle but as a simple and
general result of the laws of mechanics."

On the principle of least action with Fermat, Maupertuis, Euler, and
Lagrange, and its effect on Gauss, cf. Diihring, op. cit., pp. 100-102, 218-219,
287-302, 425-430.

436 THE MONIST.

published in 1749, is one in the class of speculative philosophy by
Samuel Formey,96 entitled : "Examen de la preuve qu'on tire des fins
de la nature, pour etablir 1'existence de Dieu" ; in which the author
comes, by a rather different way, to the same conclusions as Mau-
pertuis (1746).

In the Histoire for 1748, published in 1750, there are two papers
relating to our subject by Euler.0? The first is entitled : "Recherches
sur les plus grands et plus petits qui se trouvent dans les actions
des forces," and he quoted with approval Maupertuis's memoir of
1746, and remarked98 that Maupertuis had shown that in the state
of equilibrium of bodies, if some small movement were to happen to
them, the quantity of action would be the least. He himself, says
Euler, had discovered a similar law in the motion of bodies attracted
to one or many centers of forces; in this case §u.ds expresses the
quantity of action. In statics" this principle has been long recog-
nized. Thus, it is easy to see that a chain suspended by its ends
must take such a figure that the center of gravity of the chain is as
low as possible ; and thus, if x is the distance of the element ds
from an arbitrary horizontal plane, fx.ds will be a minimum for
the curve of the chain, and fjz.ds is the quantity of action.100 Many
other analogous cases were, according to Euler, treated by Mau-
pertuis; and Daniel Bernoulli remarked that the curve of an elastic
lamina has a minimal property, and this view was developed by
Euler in Appendix i of his Methodus inveniendi of 1744.101

There are, then, two ways of solving mechanical problems : one
is the direct method, and the other is, knowing the formula which
must be a maximum or a minimum, by the method of maxima and
minima ; the effect is determined by efficient causes and by final
causes respectively. But it is often very difficult to discover the
formula which must be a maximum or a minimum, and by which the
quantity of action is represented; and this investigation belongs

06 Pp. 365-384-

07 Pp. 149-188 and 189-218.

08 Ibid., p. 150.

09 Ibid., pp. 150-151.
100 Ibid., p. 151.

101 A convenient German translation of this Appendix, with critical and
historical notes by H. Linsenbarth, was given in No. 175 of Ostwalds Klassiker
(Abhandlungen uber das Glcichgewicht und die Schwingungen der ebenen
elastischen Kurven von Jakob Bernoulli (1691, 1694, 1695) und Leonh. Euler
(1744)). Very interesting are Euler's (pp. 18-20) theological remarks and
references to the frequency with which maximal and minimal problems ap-
peared in the mechanical work of the Bernoullis. (Cf. section IX above.)

CRITICISMS AND DISCUSSIONS. 437

rather to metaphysics than to mathematics. "I believe," says Euler,102
"that we are still very far from that degree of perfection where we
are able to assign, for each effect which nature produces the quantity
of action which is the smallest, and deduce it from the first prin-
ciples of our knowledge ; and that it will be almost impossible to ar-
rive at it unless we discover, for a great number of different cases,
the formulas which become maximal or minimal. Now, knowing
the solutions with which the direct method furnishes us, it will not
be difficult to find a posteriori formulas which express the quantity
of action, and then it will not be so difficult to prove their truth by
the known principles of metaphysics." With this end in view, Euler
investigated several problems as to the curve formed by a flexible
string in equilibrium.

Euler10^ arrived at the conclusion that the expression of the
quantity of action, which, when supposed to be a minimum, gives the
figure of the thread, is in perfect agreement with the Lazv of Rest
published by Maupertuis in 1740.

Euler's second memoir on the principle of least action in this
volume is entitled: "Reflexions sur quelques Loix generates de la
Nature qui s'observent dans les Effets des Forces quelconques." He
emphasizesI04 that he was only led a posteriori to the discovery of
the minimum in the case of the equilibrium of threads, and thenlos
remarks : "It is the figure which a fluid mass, all of whose particles
are attracted by any forces, which was the principal object of the
researches of M. de Maupertuis in order to discover the general law
of rest in the Paris Memoir es of 1740. Thus I too will consider a
fluid mass, all of whose particles are attracted to as many fixed
centers as is wished by forces proportional to any functions of the
distances to those centers, and I will investigate the figure of equi-
librium for this mass. Then I will try to discover what will be a
maximum or a minimum in this figure, in order to be in a better
state to determine what must be understood by the name of the
quantity of action of the attracting forces] and afterwards I will
show by some reflections the great importance of this quantity in
all researches concerning the effects produced by any forces." The
expression discovered in this way was again found to agree with
Maupertuis's law of 1740.

102 Op. cit., p. 152.

103 Ibid., p. 180.
104/Zmf., p. 190.

105 Ibid., p. 191 ; cf . p. 190.

438 THE MONIST.

XL

There is nothing relating to the principle of least action, nor
to mechanics (except in astronomy) in the Berlin Histoire for 1749
(published in 1751) ; but in that for 1750 (published in 1752) there
is106 an "Expose concernant 1'examen de la lettre de M. de Leibnitz,
alleguee par M. le Prof. Koenig10? dans les mois de Mars, 1751, des
Actes de Leipzig,108, a 1'occasion du principe de la moindre action"
by Euler, I09, with the note: "As will easily be seen by reading this
memoir, it is one of those whose publication may not be delayed."

Konig had denied the validity of the principle in the case of
equilibrium, and indicated some cases in which what, according to
the principle, ought to be a minimum really reduces to nothing. But,
says Euler,110 "this objection is not of great importance, since it
is sufficiently recognized in the calculus of maxima and minima
that it can often happen what is a minimum vanishes entirely. But
although that may be so in certain cases it by no means results that
one ought to extend it to all cases of equilibrium, as always neces-
sarily happening in that state ; on the contrary, there are numberless
cases in which this quantity of action is not zero but is really a
minimum ; and this puts beyond doubt that the aim of Nature is not
the nullity of action, but its minimity." Then Euler quotes the
example of the catenary, and says that the quantity of action reduces

106 Pp. 52-64.

107Johann Samuel Konig (1712-1757); Cf. M. Cantor, op. cit., pp. 599-
601. Konig was a pupil of Johann Bernoulli's at the same time as Maupertuis.
(Mayer, op. cit., pp. 17-18).

108 "De Universal! Principle- Aequilibrii et motus in Vi viva reperto deque
nexu inter Vim vivam et Actionem utriusque Minimo" (Nova Acta Erudi-
torum, 1751, pp. 125-135, 144, 162-176). Konig affirms that equilibrium is a
result of the nullity of action and vis viva (pp. 126, 164) that in some cases
the action is a maximum, and this would hardly be reconcilable with Mau-
pertuis's proof of the Creator's wisdom (pp. 126, 165) ; and that since action
is vis viva into the time, the principle is that vis viva is a minimum^ (p. 127).
Konig, like a thorough Leibnizian, praises the theorem of vis viva highly
("Censeo itaque, Theoremate Virium vivarum fundamentum universae Me-
chanicae contineri," p. 169), and deduces statistics from it. The extract from
the letter of Leibniz's is given quite at the end (p. 176) and is: "L' Action n'est
point ce que vous penses, la consideration du terns y entre ; elle est comme le
produit de la masse par le terns, ou du terns par la force vive. J'ai remarque
que dans les modifications des mouvemens elle devient ordinairement un
Maximum, ou un Minimum. On en peut^deduire plusieurs propositions de
grande consequence ; elle pourroit servir a determiner les courbes que de-
crivent les corps attires a un ou plusieurs centres. Je voulois traiter de ces
choses entr'autres dans le seconde partie de ma Dynamique, que j'ai supprimee;
le mauvais accueil, que le prejuge a fait a la premiere, m'ayant degoute."

109 As we learn from a note on p. 63 of the Histoire for 1750.

. 53-

CRITICISMS AND DISCUSSIONS. 439

to the distance of the center of gravity of the chain from the center
of the earth; and111 Daniel Bernoulli's and his own researches on
elastic curves.

As regards dynamics, Konig quoted from a supposed letter
written by Leibniz to Hermann, in which "action" was defined as
Maupertuis defined it and the property of being "ordinarily a maxi-
mum or a minimum" in dynamical problems remarked. Konig
could not produce the original nor could the original be found by
officials. It is not interesting now to follow the controversy much
further. Konig did not charge Maupertuis with plagiarism;112 but,
since the principle was considered by Maupertuis and others to be
of the greatest possible importance and to reflect great credit on
Maupertuis, its discoverer, the Berlin Academy, of which Maupertuis
was president, took up the matter with great zeal, and concluded,
like Euler's report, that, on internal and external evidences, the
fragment of the letter was forged, either to injure Maupertuis or
to exaggerate, by a pious fraud, the merits of Leibniz. "3 The re-
sult was an unjust expulsion of Konig from the Berlin Academy,
and the consequent culmination of Voltaire's ill-feeling towards
Maupertuis. "4

XII.

To return to the Plistoire for 1750. To the literature of the
controversy also belongs a "Lettre de M. Euler a M. [Jean Bernard]
Merian" of September 3, 1752.IIs Nowadays, the only interesting
part of this letter is where Euler116 gives some details about the publi-
cation of his Methodus inveniendi. The defenders of Konig stated that
they knew the Methodus had been in the publisher's hands at Lau-

. 54-
. 60.

113 Ibid., p. 62.

114 On the Konig incident, see La Beaumelle, op. cit., pp. 139-141, 143-145,
150-167, and, on Voltaire's part in it, pp. 167 et seq. Further du Bois-Reymond,
op. cit., pp. 35-36, 47, 50-66. It is now known that the fragment of Leibniz's
letter was probably genuine, and part of a letter to Varignon ; Cf. ibid., pp.
56-57, and the references to Gerhardt's paper in M. Cantor, op. cit., p. 599.

Even in 1877, Mayer (op. cit., p. 19) said that the letter was without
doubt forged; but Helmholtz in 1887 (op. cit.} showed that its genuineness
was probable.

It appears that Euler only made one separately printed contribution to
the discussion on Konig' s dissertation ; it is entitled : "Dissertatio de principio
minimae actionis una cum exaniinatione objectionum Cl. Prof. Konig contra
hoc principium factorum," Berlin, 1783. We have not seen this work, but only
quote it from the Bibliography in Fuss's Correspondance, vol. i, p. xciv.

™Ibid., pp. 520-532.

™Ibid.t pp. 525-526.

44O THE MONIST.

sanne since 1743, a circumstance which would give Euler priority
over Maupertuis. This, says Euler, is correct in so far as it con-
cerns the treatise itself, which he had finished some years before it
appeared, but he only made the additions since he had sent the
manuscript to Lausanne, and only shortly before the publication of
the book towards the end of 1744. Further, he had communicated
this supplement to nobody before printing it.

"When," says Euler,1 1? "I used the method of maxima and
minima to define the trajectories which are described by bodies at-
tracted by any central force, I do not pretend to have been beyond
what MM. Bernoulli and others have done when they determined
by the help of the same method the curvature of the catenary, that of
a piece of linen filled with liquid, and other curves of the same kind.
Such investigations only furnish particular principles which can
hardly be extended further than the cases to which they are applied.
On the other hand, it is a question here of a universal principle, from
which all the former principles should result, and which can be re-
garded as a Law established in all the phenomena of nature ; which
would render its discussion less the part (du ressort) of Mathe-
matics than of Metaphysics, on the principles of which this doctrine
should be founded. Also, although for long people have not doubted
that, in all natural effects, there is a maximal-minimal principle which
determines them, nobody before the Illustrious President of our
Academy has even suspected in what elements this principle was
contained and how it could be accommodated to all cases.118 As

117 Ibid., pp. 526-527.

118 Cf. Methodus, pp. 309, 320. The actual quotations are: (i) "Quoniam
omnes naturae effectus sequuntur quandam maximi minimive legem; dubium
est nullum, quin in lineis curvis, quas corpora projecta, si a viribus quibus-
cunque sollicitentur, describunt, quaepiam maximi minimive proprietas locum
habeat. Quaenam autem sit ista proprietas, ex principiis metaphysicis a priori
defmire non tarn facile videtur : cum autem has ipsa curvas, ope Methodi
directae, determinare liceat; hinc, debita adhibita attentione, id ipsum, quod
in istis curvis est maximum yel minimum, concludi poterit. Spectari autem
potissimum debet effectus a viribus sollicitantibus oriundus; qui cum in motu
corporis genito consistat, veritati consentaneum videtur hunc ipsum motum,
seu potius aggregatum omnium motuum qui in corpore projecto insunt, mini-
mum esse debere. Quae conclusio etsi non satis confirmata videatur, tamen,
si earn cum veritate jam a priori nota consentire ostendero, tantum conseque-
tur pondus, ut omnia dubia quae circa earn suboriri queant penitus evanescant.
Quin-etiam cum ejus veritas fuerit evicta, facilius erit in intimas Naturae
leges atque causes finales inquirere ; hocque assertum firmissimis rationibus

corroborare." (2) "Tarn late ergo hoc principium patet, ut solus motus

a resistentia medii perturbatus excipiendus videatur; cujus quidem exceptionis
ratio facile perspicitur, propterea quod hoc casu corpus per varias vias ad
eundum locum perveniens non eandem acquirit celeritatem. Quamobrem,
sublata omni resistentia in motu corporum projectorum, perpetuo haec con-
stans proprietas locum habebit, ut summa omnium motuum elementarium sit

CRITICISMS AND DISCUSSIONS. 44!

regards myself, I only knew in a sure manner a posteriori the prin-
ciple I used to determine trajectories ; and I have ingenuously con-
fessed that I was not in a position to establish its truth in another
manner. All that I have done is to deduce from it the same curves
that are commonly found by the direct method, starting from the
principles of mechanics. I have not even dared to extend its use
unless I could justify by calculation its agreement with known prin-
ciples. And that is what has led me to separate from this principle
motions in a resisting medium and other more complicated ones ;
for no way presented itself to my mind of discovering the truth
with regard to these motions."

Among the Memoircs in the Class of Speculative Philosophy in
the same volume (1750) of the Histoire, are two by Merian1^ en-
titled: "Dissertation ontologique sur 1'Action, la Puissance et la
Liberte," and "Seconde Dissertation sur TAction, la Puissance et la
Liberte"; in the first of which120 Maupertuis's explanation, in the
Essai de Cosmologie, of the generation of the idea of motive force
is quoted.

XIII.

In the Berlin Histoire for 1751, published 1753, there are five
memoirs we shall have to notice, and all of the Class of Mathe-
matics.121

The first is by Euler,122 and is entitled: "Harmonic entre les
Principes generaux de Repos de Mouvement de M. de Maupertuis."
Both principles of Maupertuis (of 1740 and 1744) rest, says Euler,
on the same foundation, so that if one is proved, the other cannot be

minima. Neque vero haec proprietas in motu unius corporis tantum cernetur,
sed etiam in motu plurium corporum conjunctim; quae quompdocunque in
se invicem agant, tamen semper sunima omnium motuum est minima. Quod,
cum hujusmodi motus difficulter ad calculum revocentur, facilius ex primis
principiis intelligitur, quam ex consensu calculi secundum utramque Metho-
dum instituti. Quoniam enim corpora, ob inertiam, omni status mutationi
reluctantur ; viribus sollicitantibus tamparum obtemperabunt, quam fieri potest,
siquidem sint libera ; ex quo efficitur, ut, in motu genito, effectus a viribus
ortus minor esse debeat, quam si ullo alio modo corpus vel corpora fuissent
promota. Cujus ratipcinii vis, etiamsi nondum satis perspiciatur; tamen, quia
cum veritate congruit, non dubito quin, ope principiorum sanioris Metaphy-
sicae, ad majorem evidentiam evehi queat; quod negotium aliis, qui Metaphy-
sicam prositentur, relinquo."

119 Pp. 459-485 and 486-516.

120 Ibid., p. 479.

121 In this volume, the memoirs in the Classes of Experimental Philosophy
and Mathematics are paged (pp. 1-356) separately from those in the Classes
of Speculative Philosophy and of Belles Lettres (pp. 1-154).

m Pp. 169-198.

442 THE MONIST.

doubted. Now, Maupertuis and Euler had established the truth of
the law of rest of 1740 by a multitude of different cases. Euler,
then, first deduced the principle of motion from that of rest,12^ and
then12* showed that all the elementary theorems of statics follow
readily from the law of rest.

The nerve of Euler's investigation is the deduction of the prin-
ciple of least action from the law of rest. Euler I25 called the in-
tegral fV.dv, where V is a central force acting on the body M and
v is the distance from M to any fixed point in the direction of V, the
effort (effort), so that Maupertuis's law is that the sum of all the
efforts is a maximum or a minimum.

"What is more natural," exclaims Euler,126 "than to maintain
that this same principle of equilibrium should also subsist in the
movement of bodies under like forces? For if the intention of
nature is to economize the sum of the efforts as much as possible,
this intention must extend also to movements, provided that we
take the efforts, not merely as they subsist in an instant, but in all
the instants together for which the movement lasts. Thus, if the
sum of the efforts is <£ for any instant of the motion, then, putting
dt for the element of the time, the integral f3?.dt must be a mini-
mum. If then, for the case of equilibrium the quantity 3> must be a
minimum, the same laws of nature seem to exact that, for motion
f®.dt should be the smallest.

"Now it is precisely in this formula that the other principle of
M. de Maupertuis, concerning motion, is contained, however differ-
ent it may appear at the first glance. To show this agreement, I
have only to remark that when a body moves under the action of the
forces V, V, V",. . . ., the effort <3> to which the body is subject ex-
presses at the same time the vis viva of the body — the product of
the mass M of the body and the square of its velocity (M)." Thus
the formula which must be a minimum is

Where v, v' , v", . . . . , are the distances of M from the centers

123 On pp. 181-182, Euler remarked that, if we wish, inversely, to deduce
the principle of rest from that of motion, "we must suppose the motion in-
finitely small, and this causes great obscurities (brou'illeries) in the conside-
ration of infinitely small velocities and of the spaces which are described in
an infinitely small time.

124/ZnU, pp. 183-193.

125 Ibid., p. 174.

126 Ibid. p. 175.

CRITICISMS AND DISCUSSIONS. 443

of forces V, V, V", . . . . , which are functions of these distances,
Euler12? gets the equation

Mu2 = const - 5 J* . dv - const - <E> ;

and:128 "the constant does not disturb this harmony between the
effort <3> and the vis viva M.w2 of the body; for if fj^.dt is a maxi-
mum or a minimum, fM.u2.dt or fM.u.ds will be so also, since
the term f const dt = const t does not enter into the consideration
of the maximum or minimum. And, besides that, as the effort <f>
is expressed by integral formulae, it already contains in itself any
constant, so that I could have neglected this constant entirely and
simply put Mu2 = -®, whence the identity would have been more
evident. However, if we take the above integrals on a fixed foot-
ing (sur un pied fixe'), so that the effort <i> receives a determined
value, the addition of the constant will be necessary; since the
velocity of the body at a certain point of its path depends on the
initial velocity, and by this initial velocity the constant must be de-
termined in each case proposed. But, of whatever quantity it may
be, the determination of the maximum or minimum is not affected."
Of course, as Mu2 is equal to the negative of <£, if fMu2.dt is a
minimum, f$.dt will be a maximum, and reciprocally.

Euler12^ then proved "the identity between the effort and the
vis viva" for two or more bodies, connected in any way with one
another to make a flexible body: the sum of the vires vivae of all
the elements of the body always reduces to the sum of the efforts
to which all the elements are subject in the same time, — in the case
of two bodies of masses M and N, distances to the1^0 center of force
considered x and y respectively, and the accelerating forces X (a
function of .v) and Y (a function of y) respectively,

remarked that there are cases of equilibrium in which
the sum of the efforts is a maximum and1^2 classes the cases of
equilibrium as of such natures that, if the sum of efforts is a
minimum, equilibrium reestablishes itself on an infinitely small dis-

. 177.
128 Ibid., p. 178.
™Ibid.} pp. 179-181.

130 Of course the proof extends to as many centers of force as wished.

131 Ibid., p. 194.

138 Ibid., p. 195. There is an example of the sum of efforts being a maxi-

mum on pp. 195-196.

444 THE MONIST.

placement being given to the system, whereas, if the sum is a maxi-
mum, this is not the case. ^3

XIV.

Euler's second paper in the volume for 1751 is entitled: "Sur
le Principe de la Moindre Action. "T34 This paper is concerned with
the opinion that there is a minimum in the actions of nature, with
Aristotle and his school, Descartes, Fermat, Leibniz,1^ Wolff, Engel-
hard, s'Gravesande, and others, and was occasioned by the Konig
affair. It is ridiculous, says Euler,^6 to suppose that Konig's frag-
ment was written by Leibniz, for it attributes to Leibniz a principle
opposed to that which he adopted publicly in the case of the motion
of light — that the product of the path described and the resistance
is a minimum.

Referring to his own discovery of the minimum of the action —
integral for central orbits, Euler's? remarks: "Besides, I had not
discovered this beautiful property a priori but (using logical terms)
a posteriori, deducing after many trials the formula which must be-
come a minimum in these movements; and, not daring to give it
more force than in the case which I had treated, I did not believe
that I had discovered a wider principle: I was content with having
found this beautiful property in the movements which take place
around centers of forces."

Euler's third paper in this volume is entitled: "Examen de la
Dissertation de M. Le Professeur Koenig, inseree dans les Actes de
Leipzig, pour le Mois de Mars, 175 1."1^8 In this paper Euler exam-
ined Konig's demonstrations with care and pronounced them to be
worthless. X39

The "Essai d'une Demonstration Metaphysique du Principe
general de 1'Equilibre" of Euler, printed in the same volume,1 4°
does not mention Maupertuis's name,141 and is concerned with the
deduction from indubitable axioms of the principle that, for equilib-

133 Cf . Mach, Mechanik, pp. 70-75 ; Mechanics, pp. 69-73.

134 Loc. cit., pp. 199-218.

135 Ibid., pp. 205-209.
™Ibid.,v. 209.
™Ibid., p. 214.

138 Ibid., pp. 219-239, "Additions," pp. 240-245.
159 Ibid., p. 220.
uo Ibid., pp. 246-254.

141 It is, however, Maupertuis's "Law of Rest" (Cf. also Mayer, op. cit.,
P- 23).

CRITICISMS AND DISCUSSIONS. .445

rium, where, P, Q, . . . . are forces and x, y, . . . . are measured on
their respective lines of action,

/P.rf.r+/Q. </y + ....
is a minimum.

Lastly, there is, in this volume a paper by Nicolas de Beguelin,142
tutor of Frederick the Great's nephew who was later Frederick
William II, entitled : "Recherches sur 1'Existence des Corps Durs/'14^
in which Maupertuis is called a great man144 and the illustrious
author of the principle of least action, I45 and the other conclusions
are just what Maupertuis would have wished.

xv.

In the Paris Memoires for 1749, the Chevalier d'Arcy146 pub-
lished some reflections on the principle of least action, which he
had long hesitated to publish, but that he did so in the interests of
truth. D'Arcy maintained: (1) That the action of a body is not
proportional to m.v.s, because this supposition, in a particular case,
leads to a result contrary to that which the laws of motion give;
(2) That, admitting Maupertuis's definition of action, the quantity
of it that nature employs in each change is not a minimum, and
that if in some cases this is so, the principle of least action cannot
serve to prove it; (3) that Maupertuis's law of equilibrium that
Maupertuis deduced from the principle of least action is only estab-
lished by the introduction of a foreign and gratuitous supposition ;
(4) that, in general, whatever may be the laws of nature, one could
always easily find a function of the masses and velocities which
would represent them when it is supposed to be a minimum, but
this property would not be enough to give the name of action to
this function nor to raise the principle thence obtained to the rank
of a metaphysical principle;147 (5) that, if we define the action of

143 Lived from 1714 to 1789. (Cf. Berlin Histoire, 1788-9 (not seen) ; M.
Cantor, op. tit., vol. iv, 1908, pp. 174 (article by F. Cajori), 227 (article by
E. Netto).

143 Ibid., pp. 331-355-

144 Ibid., pp. 344, 346.
"5 Ibid., p. 347-

146 "Reflexions sur le Principe de la moindre Action de M. de Maupertuis,"
Hist, de I'Acad. Roy. des Sci., 1749 (Paris, 1753), Memoires, pp. 531-538.
There is an account of this memoir in the Histoire, pp. 179-181. Patrick
d'Arcy was born on Sept. 18 (27), 1725, at Galloway and died on Oct. 18,
1779. ^ He was a count, a field marshal of France, and a "Pensionnaire-Geo-
metre" of the Paris Academy (Poggendorffs biog.-lit. Handwortcrbuch, vol.
i> P- 57)- Cf. M. Cantor, op. cit., vol. iv, 1908, p. 18 (article by S. Giinther).

™Ibid.t pp. 535-536.

446 THE MONIST.

a body around a point to be the product m.v.p, where p is the per-
pendicular drawn from this point on the direction of the body, then
the total action existing in nature at any instant around a given
point, being produced in one given body, the quantity of action of this
body will always be the same around this point,1*8 and from this
theorem are easily deduced the principle of the conservation of vis
viva, the case of rest, the centers of oscillation or of percussion, the
law of the refraction of light, and so on.

With regard to (1), d'Arcy1^ gave the following considera-
tions. "If two bodies produce equilibrium, that is to say, if rest fol-
lows from their direct impact, without our knowing to what the
action is proportional, it (the action) must necessarily be equal in
the two bodies ; for if not, then it would follow that an action was
in equilibrium with a lesser action, that is to say that different actions
produce the same effect. Now, can we imagine that two equal and
similar effects can be produced by unequal quantities of causes?
This does not imply that the effect is proportional to its cause, but
only that the same effect is always produced by the same quantity
of cause and vice versa.

"Let there be two hard bodies A and B perfectly equal and pro-
ceeding in opposite directions with equal velocities, then clearly rest
will follow their impact. If A, proceeding in the same direction
with the same velocity, is impinged upon by the body C of different
mass and velocity, but such that rest follows impact, I believe that
nobody can deny that the action of B is equal to that of C, since both
destroy the velocity of A. Can we have another idea of the equality
of two quantities than of our being able to substitute one for the
other without changing anything?" If B proceeds with double the
velocity of, and traverses double the space traversed by, C, the prin-
ciple of Maupertuis says that the mass of C is four times that of B ;
and this is contrary to what we find by the laws of motion. "Thus,"
concludes d'Arcy, "the action is not proportional to the mass multi-
plied by the velocity and by the space described."

With respect to (2), d'Arcy150 remarked that if two bodies A
and B proceed in the same direction with the velocities a and b,

148 This theorem was given by d'Arcy in the Paris Memoires for 1747
(published in 1752; pp. 348-356) under the title: "Principe general de Dyna-
mique, qui donne la relation entre les espaces parcourus et les temps, quelque
soit le systeme de corps que Ton considere, et quelles que soient leurs actions
les uns sur les autres." This memoir (read in 1746) is part of the paper (of
three memoirs) entitled: "Probleme de Dynamique" on pp. 344-361.

149 Loc. cit., pp. 532-533.

150 Ibid., pp. 533-534-

CRITICISMS AND DISCUSSIONS. 447

the action of the bodies A and B will be Aa2 + B&2. If after im-
pact they proceed with the velocities x and z, their action after
impact will be A.r2 + Bs2. isi Now the quantity of action after impact
will be either equal to or less than or greater than what it was before
impact: if it is equal we have the theorem of vis viva, which does
not hold for hard bodies ; if it is greater it will have increased by
the quantity

if it is smaller it will be diminished by the quantity

and this quantity is the real quantity of action lost, and consequently
is that employed by nature to produce the actual change; therefore

or, if we suppose dx-dz,

which is absurd. It is not, then, the destroyed part of this quantity
which is a minimum. Maupertuis's argument is: Suppose that the
bodies A and B proceed in the same direction with the velocities
a and b and that the plane on which they are moves with the velocity
x; evidently A will move on this plane with a velocity a-x and B
will move behind with a velocity x — b, x being greater than b and
less than a. Maupertuis finds that

A(a-*)2 + BO-£)2
will be a minimum when the velocity x is such that

A(a-*)=B(*-&),

that is to say, when the bodies are in equilibrium on this plane.
"I vow," said d'Arcy,J53 "that I do not know what consequence one
can deduce from this other than: AP2+BQ2 being a minimum and
P2 = CQ.dx and Q2= fA.of.r, we will have

and consequently if

A.Z = B.X,

where Z and X are functions of x, then AZ2 + BX2 will always be a
minimum, and vice versa; and this leads me to believe that, when
one has found that A.Z2 + B.X2 is a minimum, one knew that
A.Z = B.X."

1 "Since a, b, x and z express the spaces as well as the velocities."
152 For hard bodies x =. z and for elastic ones a — b = z — x.
163 Ibid., p. 534-

448 THE MONIST.

With regard to (3), when Maupertuis deduced the law of the
lever from his principle of least action, he made a gratuitous sup-
position, that the lever moves with a constant angular velocity.15*
To find the point of the lever (of length C) about which two bodies
of masses A and B at the ends of the lever produce equilibrium,
Maupertuis called Z the distance of A to the sought point, and an-
nounced that, to solve the problem, he would suppose the lever to
receive some small movement and then express that the quantity of
action is the smallest possible. If, remarked d'Arcy, we call V the
small velocity of A and suppose that A describes a space a, the
velocity of B and the space described by it will be, respectively,

V(C-Z)/Z and o(C-Z)/Z,
and the action of the bodies will be

AVo + BVa(C-Z)2/Z,

and the differential equated to zero, supposing that a and V are
constant, gives Z-C. Maupertuis gets the correct law by suppos-
ing that the lever moves with a constant angular velocity. But this
supposition, says d'Arcy, "seems to me absolutely gratuitous, since,
to each value of Z, the action or the time necessary for it to describe
the constant angle is different."

With regard to (5), d'Arcy155 remarks that his definition of
action is in perfect agreement with d'Alembert's:156 "The action is
the movement that a body produces or tends to produce in another
body."

D'Arcy 's principle is that the sum of the masses of a system,
each mass being multiplied by the sector which it describes around
a fixed point in the same time, less the sum of the sectors described
in the contrary sense, each being multiplied by the mass of the
body which describes it, is proportional to the time. The only dif-
ference from the principle that d'Arcy gave in this memoir of 1749
is that instead of (as in 1747) sectors multiplied by masses, were
used in 1749 the equivalent expressions m.v.p.

Let two bodies A and B move with the velocities a and b before
impact and with the velocities x and s after impact. By the above
principle the action of A and B round any point O will be the same
after as before the impact ; thus, where P is the foot of the perpen-
dicular from O on the line joining A and B,

™ Ibid., p. 535-
mlbid.tp. 536.
158 In the Encyclopedic (not seen).

CRITICISMS AND DISCUSSIONS. 449

and consequently

A(a-*)=B(*-&),

and this relation between the velocity lost by A and that gained by
B holds whether the bodies are elastic or not. In elastic bodies we
easily see that a-b-z-x, and hence, from the above equation

which is the property of vires vivae.157

If two bodies A and B strike the ends P and Q of a straight
lever with the same velocity a, to find the fulcrum-point C of the
bar such that A and B remain at rest after the impact, d'Arcy158 ob-
serves that the action of A round C must be equal to the action of
B round C, and thus C is the Center of gravity. By the same
method we find the centers of oscillation or of percussion, and so on.

When deducing the law of the refraction of light, I™ d'Arcy ob-
serves that, in his memoir of 1747, he had proved that it is the same
thing whether the bodies are attracted toward the point round which
the action is sought or not, as the quantity of this action is not altered
thereby. Let FG be the surface of a diaphanous and homogeneous
sphere of center C, M a point outside the sphere, and N a point in-
side. A ray of light — /A being the mass of a corpuscle of light —
travels from M to N, its velocity outside the sphere being v and
inside the sphere being u, meeting the surface at m. "The action
of the surface FG can only be towards the center C; for whatever
action this body may have on the corpuscle of light on one side of
the perpendicular to the surface, it will have the same action on the
other side." Thus we have

fjL.v.CR = fjL.u.Cr,

and this gives the known law of refraction of light. The case of
FG being plane instead of spherical is then treated, and d'Arcy
finally remarks that other examples of the application of his prin-
ciples are given in the memoir of 1747.

XVI.

The Berlin Histoire for 1752, published in 1754, contains among
the memoirs of the class of Speculative Philosophy a "Reponse a un
Memoire de M. d'Arcy insere dans le Volume de 1'Academie Royale

167 D'Arcy, loc. cit., p. 537.

158 Ibid.

™Ibid., pp. 537-538.

45O . THE MONIST.

des Sciences de Paris pour 1'annee 1749" by Maupertuis,l6° which
is headed by a notice,161 in italics, stating that the memoir (1744)
in which the principle of the least quantity of action was first com-
municated was received by the Paris Academy, Maupertuis "dares
to say, with some applause (applaudissment)." Then Maupertuis
refers to his paper of 1746, to his Essai de Cosmologie, to the attacks
of "un Professeur de la Haye" to whom, as he used libels, he will
never reply, and to d'Arcy who "attacks with so much politeness and
modesty," that Maupertuis thinks that he ought to reply to him. He
appears, says Maupertuis, "to be such a lover of the truth that I will
try to introduce him to it."162

(1) D'Arcy tried to show that Maupertuis is wrong to call
m.v.s action. Maupertuis believed that he had good grounds for
justifying the name; but, to cut matters short, Maupertuis said that
he had adopted Leibniz's definition. l6^ D'Arcy 's reason against
calling the above product action reduces to this: In the impact of
hard bodies, two different quantities of action reduce to rest one
and the same body moving with the same velocity. By the same kind
of reasoning, says Maupertuis, d'Arcy might object to the name vis
viva-, for two different vires vivae can reduce the same hard body
to rest." And in fact here the vis viva is the same as the action,
for here "the space is proportional to the velocity. "l6* Again, with
elastic bodies, if two unequal bodies with the same vires mortuae
(m.v) strike a third body at rest, different vires mortuae will come
into existence or perish.

(2) D'Arcy, to show that Maupertuis is wrong in holding that
the quantity of action necessary to produce any change in nature
is a minimum, confuses, when treating of impact, change of the
quantity of action with change of velocities. l6s The velocities can
change without the quantity of action changing, as is the case in the
impact of elastic bodies (when this quantity is the same as the quan-

™Histoire de I'Acad. de Berlin, 1752, T. VIII, pp. 293-298.

161 Ibid., pp. 293-294.

162 "....et paroit si Amateur de la verite, que je tacherai de la lui faire
connoitre" {ibid., p. 294).

103 ". .. .mais pour trancher court avec M. d'Arcy, je puis dire que ce n'est
pas mon affaire. Leibnitz, et ceux qui 1'ont suivi, ont appele ainsi le produit
du corps par 1'espace et par la vitesse; j'ai adopte une definition etablie, contre
laquelle on n'avoit point dispute, et que je n'avois aucune raison de changer;
voila ce qu'il me suffiroit de repondre" ; ibid., p. 295. Apparently this is upon
what E. du Bois-Reymond relies when he says {op. cit., p. 48) : "Maupertuis
borrowed, as he himself says, the concept and name of action from Leibniz. . ."
. 295-
. 296.

CRITICISMS AND DISCUSSIONS. 451

tity of vis z'iva) ; in the impact of hard bodies, the change of the
velocities is neither equal nor proportional to the change in the quan-
tity of action.

jf 166 {-fog bodies are elastic, the change is : A which moved before
with the velocity a moves afterwards with the velocity a, and the
corresponding velocities of B are b and ft. If then we wish that
afterwards A should move with the velocity a and B with the veloc-
ity b, we must transport the A-plane with the velocity a- a and the
B-plane with the velocity f$ — b\ and from this we must get the quan-
tity of action A(a-a)2 + B(/3-b)2 necessary to produce the change
in nature, and which is a minimum. If A and B are hard, and the
common velocity after the impact is x, and if we wish each body to
move with its original velocity, we proceed as before, and get, for
the quantity of action necessary to produce this change, A (a — ,r)2 +
B(,r-fr)2, the smallest possible.

(3) D'Arcy's criticism on Maupertuis's deduction of the lever
is mistaken, for Maupertuis supposed the lever to be in a state of
rest and infinitely little displaced from this state.167

Finally, Maupertuis168 mentioned the incompleteness of this
theory of the lever, which was not remarked by d'Arcy, but about
which we have read in connection with the reprint of the memoir
of 1740169 in Maupertuis's GLuvres.1"?0

XVII.

In the Paris Memoires for 1752 appeared a reply by d'Arcy171
to Maupertuis's paper in the Berlin Memoir es for 1752. After a
few preliminary words in which what looks like sarcasm is veiled in
words of compliment — Maupertuis's "modesty," "politeness," and
"simplicity" being praised, d'Arcy172 confesses that if he had need
of a proof of an arranging intelligence he would find it just as much
in the uniformity of the laws of generation of the vilest insects as
in the general laws of mechanics.

166 Ibid., pp. 296-297.

167 Ibid., pp. 297-298.

168 Ibid., p. 298.

169 Mapertuis here refers to this paper as being in the Memoires for 1743.
This is, of course, a misprint.

170 See section II above.

1 "Replique a un Memoire de M. de Maupertuis, sur le principe de la
moindre action, insere dans les Memoires de 1' Academic royale des Sciences
de ^Berlin, de 1'annee 1752," Hist, de I'Acad. Roy. des Set., 1752 (Paris, 1756),
Memoires, pp. 503-519.
172 1 bid., p. 503.

452 THE MONIST.

With regard to Maupertuis's (correct) classification of d'Arcy's
objections under three heads, d'Arcy'73 maintains that the first still
holds, for "when someone says that nature economizes action, he
clearly means that this quantity expresses this cause or the real
force," and d'Arcy'74 even accuses Maupertuis of falling back on
the authority of Leibniz. His argument depends for its validity
on the principle that a definition is something more than the mere
giving of a name.

With regard to d'Arcy's second objection, d'Arcy^s quoted
from the Encyclopedic1"?6 to show that Maupertuis's phrase "change
happened in nature" and that his own interpretation of this phrase
in the above simple case of impact as

which is to be a minimum, so that

is natural and also showed1 77 that Maupertuis himself implied this
interpretation.

Then d'Arcy^8 showed that the manner in which Maupertuis
used his principle in the case of the refraction of light is different
from that in which he used it in the case of impact. If we treated
the latter case like the former, we should have the result that

is a minimum, and hence that

Aa2 + B/?2 = 0.

In the case of light, it is the action before the change plus the
action after the change which is a minimum ; in impact it is the mass
by the velocity lost and by the space which will be described in conse-
quence of this velocity.

With respect to Maupertuis's reply to d'Arcy's third objection,
Maupertuis, says d'Arcy,I79 has misread the objection: there was not
said to be a supposition about an angular and constant motion but
about a constant angular motion. D'Arcy quotes objections nearly
the same as his of 1749 from the above cited article on "Cosmo-

173 Ibid., p. 504
™Ibid., p. 506.

™Ibid., pp. 507-508.

178 Article "Cosmologie," p. 196 [not seen].

177 D'Arcy, loc. tit., pp. 508-509.

178 Loc. cit., pp. 509-510.
178 Ibid., pp. 510-511.

CRITICISMS AND DISCUSSIONS. 453

logic" : "When Maupertuis applies his principle to the case of equi-
librium in the lever, certain suppositions must be made, amongst
others, that the velocity is proportional to the distance from the ful-
crum,180 and that the time is constant as in the case of impact. ..."

In the case of the reflection of light, d'Arcy181 shows that nature
is prodigal or avaricious of action as a mirror is more or less concave
respectively, and again quoted the article "Cosmologie" on this
point.

Finally, d'Arcy182 returned to his principle of 1747, which he
prepared to substitute for Maupertuis's principle. l8s

XVIII.

In the Berlin Histoire for 1753, published in 1755, the only
paperl84 relating to the principle of least action is an "Examen des
Reflexions de M. le Chevalier d'Arcy sur le Principe de la moindre
action" by Louis Bertrand. lgs Bertrand's paper was headed by a
note to the effect that, as the Paris Academy of Sciences had, con-
trary to its custom, hurried to publish in its Memoir cs of 1749 some
reflexions of d'Arcy which he had only given in 1752, the Berlin
Academy believed that it might publish this examination one year
before it ought to have appeared.

D'Arcy, says Bertrand,186 undertook to overthrow Maupertuis's
principle, but only succeeded in overthrowing the false ideas which
he had formed about it. In the first place, d'Arcy objected to Mau-

180 As d'Arcy expressed it, that the angular velocity is constant.

181 Ibid., pp. 511-513.

182 Ibid., pp. 513-519. On p. 513 he emphasized that the memoir containing
this principle was read to the French Academy in 1746.

183 On d'Arcy's memoirs see Mayer, op. cit., pp. 13-15, 21. It seems to me
that Mayer's view of these memoirs is too favorable. I will return to this
point in my criticisms.

184 The contrary was stated, owing to a wrong reading of A. Mayer, op.
cit., p. 17, by myself in Ostwalds Klassiker, No. 167, p. 36; but, of Euler's
five papers in this volume, one is on Daniel Bernoulli's papers on vibrating
cords (cf. M. Cantor, op. cit., vol. iii, ad ed., Leipsic, 1901, pp. 904-907), two
papers are on spherical and spheroidical trigonometry deduced from the
method of maxima and minima (cf. ibid., pp. 867-869), one on the law of
refraction of rays of different colors, and one on the paths of projectiles in
resisting media ; — and in none of these is any reference to the principle of least
action except in a passage (p. 306) in the last line but one of these papers,
where he refers to the convincing proof of the existence of a Deity given by
Maupertuis, and also to the argument from the wonderful structure of the
eye.

185 Pp. 310-320. Louis Bertrand (1731-1812) was then in Berlin and was
a friend of Euler's ; cf. Poggendorff, vol. i, p. 171 ; M. Cantor, op. cit., vol. iv,
Leipsic, 1908, p. 332 (article by V. Bobynin).

188 Op. cit., p. 311.

454 THE M ON IST.

pertuis's definition of action. This is a question of words ;l8? d'Arcy
required that the action of different hard bodies should be estimated
equal if each of these bodies is capable of reducing to rest the same
hard body endowed with a certain velocity, so that the action of a
body is measured by m.v. But, says Bertrand, it is well known188
that, in the impact of hard bodies, a part of the motion is destroyed
— that part which would be reproduced if the bodies were elastic:
"hence it follows that, if a hard body (A) of mass 1 and velocity
1 were reduced to rest both by a body (B) of mass 1 and velocity 1
and by a body (C) of mass % and velocity 2, we could only affirm
positively that the action of B is equal to that of C if we have pre-
viously proved that when B impinges on A it loses the same quan-
tity of motion as when C impinges on A. For if it were true that in
one case more motion were lost than in the other, the rest in this case
ought not to be attributed to the equality of action of the two bodies,
but to the greater loss of motion ; in fact, if this loss had not been
greater, some motion would have been left for the bodies which have
impinged, and thus rest would not have followed the impact.

"In order, then, that the reasoning by which M. d'Arcy has
wished to prop up his definition of action should be conclusive, it
would be necessary for him to prove that the same quantity of mo-
tion is lost whether B impinges on A or C impinges on A. Now
this he will never prove.

"Not being able to do anything in that direction, perhaps he
will claim that it is sufficient to attend to the change which happens
to the body A after the impact ; but, if <he only pays regard to the
effect produced on the body impinged upon, we can urge against
him the impact of elastic bodies, where a body A of mass and veloc-
ity both 1 is reduced to rest both by a body B of mass 1 and velocity
0, by a body C whose velocity and mass are both %, and by a body
D whose mass is % and velocity 1. Now, M. d'Arcy would con-
tradict his own definition of action if he claimed that the actions
of B, C, and D were all equal to one another. Thus the foundation
on which M. d'Arcy wished to support his manner of estimating
action absolutely lacks solidity." In d'Arcy's last paragraph on the
definition of action, he wrongly concludes, says Bertrand,18?, that
from Maupertuis's definition of action, follows that whenever the

™Ibid., pp. 311-312, 313-

188 " Cest une chose dont tons les Philosophies conviennent " (ibid.,

p. 312).

189 Ibid., pp. 313-314-

CRITICISMS AND DISCUSSIONS. 455

velocities and the masses of two hard bodies are such that rest follows
the impact of these bodies, the actions of these bodies are equal.

With regard to d'Arcy's attack on Maupertuis's principle, Ber-
trand190 remarks that Maupertuis expressly said that not the differ-
ence of the actions before and after the impact, but the quantity of
action necessary to produce this change is to be a minimum. The
quantity of action necessary to produce a change is not the difference
of the actions before and after the change ; but it is the product of
the mass of the bodies whose state is changed, the space that these
bodies describe in consequence of (en suite du) the change, and the
velocity with which they describe it, also in consequence of the
change.191

With regard to d'Arcy's strictures on Maupertuis's treatment
of the lever, Bertrand192 reproduces d'Arcy's supposition that A
moves with a small velocity V and describes a space a, whence the
velocity of B is V(c — z)/z, the space described by B is a(c — s)/z,
and the action of the whole system is

Then, before differentiating, d'Arcy supposed V and a constant ; and
Bertrand inquires why should the velocity of and space described
by A be supposed to be constant rather than those of and by B.
Maupertuis puts as constant the angle that A and B describe around
the fulcrum of the lever ; and this supposition does not affect one
of the bodies rather than the other, for this angle is the same for
both bodies. Still, this supposition appears gratuitous to d'Arcy
because for each value of z the action or the time necessary to make
A and B describe the angle supposed constant is different. But,
says Bertrand, if the action necessary to make A and B describe the
angle supposed constant were not different for each value of z, it
would be absurd to seek which of these actions is the least.

With regard to d'Arcy's assertion that, whatever the laws of
nature might be, it would always be easy to find a function of the
velocities and masses such that, when minimized, it would give these
laws, Bertrand19^ remarks that "that may be true of many particular
cases." Rather earlier in his paper, Bertrand19* remarks a propos

100 Ibid., p. 314-
1M/Wd., pp. 314-315-
102 Ibid., pp. 317-318.
**Ibid. p. 318.
194 7Md., pp. 315-316.

456 THE MONIST.

of d'Arcy's suggestion that Maupertuis knew the formula A(a-^r) =
B(JT — b) for impact and concluded that the action must be

A(a-.*-)2 + BO-&)2

in order that the known formula should result when the action was
minimized, and d'Arcy's attempted generalization, that, if Z and X
are functions of x, then, if AZ

will always be a minimum and vice versa, that this generalization
will always be false except when dZ + d*K = 0, — the case which he
wished to generalize.

The rest of Bertrand's^s paper is devoted to d'Arcy's own
principle. "This principle," says Bertrand,196 "can in a certain sense
be admitted, but it will never lead to important discoveries ; still
less will it show us, so to speak, the true ends in view of nature:
and these circumstances put it infinitely below that of M. de Mau-
pertuis."

With regard to the way in which Bertrand's paper is written,
it seems both magisterial and hasty : attempts at sarcasm against
d'Arcy and flattery — or perhaps sincere reverence — for Maupertuis
stand out too prominently. Bertrand was young when he wrote it,
so there is a greater chance that he was sincere. Still, he was of,
or was about to be of, the Berlin Academy.

XIX.

We will now give a brief retrospect of the development of views
on the principle of least action, and dispose of all historical questions
before trying to elicit what gains have resulted for knowledge by this
development.

A. Mayer19? says of Euler's formulations of the principle of
least action: "We shall see that this correct form [in the second
appendix to the Methodus of 1744] got lost to him in the course of
time, and that soon it lost as much in rigor as it appeared to gain
in generality." Mayer's198 grounds for this view were that Ja-
cobi's199 principle of least action was the "true" principle, owing to

195 Ibid., pp. 318-320. Just at the end is: "On pourroit faire encore nom-
bre de reflexions stir rinsuffisance de ce Principe applique a la refraction des
rayons^ de lumiere; mais il semble qu'il y auroit une sorte de mauvaise hu-
meur a examiner si rigoureusement se que M. d'Arcy paroit avoir voulu
trailer cavalierement." I have left the accents unaltered.

. 319-

197 Op. cit., p. 6.

198 Op. cit., pp. 6-1 1.

199 Cf. Monist, vol. xxii, April, 1912.

CRITICISMS AND DISCUSSIONS. 457

the difficulty there appeared to be200 if the time was not eliminated,
and this elimination had apparently to be done by the equation ex-
pressing the conservation of vis viva. Thus the principle of least
action is subject to the limitations implied by the subsistence of
the theorem of vis viva. Thus Euler, in the above mentioned appen-
dix, expressly pointed out that his theorem cannot hold for motion
in a resisting medium, and that, in the integrand, the velocity must
be expressed "ex viribus sollicitantibus per quantitates ad curvam
pertinentes.201 Consequently Mayer202 maintained that Lagrange's
(1760) generalization of the principle of least action is, in the form
in which Lagrange states it, meaningless, and the theorem which
he really had in his mind is that known as "Hamilton's principle"
given by Hamilton in 1835. We know203 that later on (in a publi-
cation of 1886) Mayer changed this view, owing to acquaintance
with a paper of Rodrigues's (1816) in which the time (the t in the
integrand) was varied by the 8-process of the calculus of variations,
and admitted that there are two forms of the principle of least ac-
tion : Jacobi's and Lagrange's. This view has been confirmed by
the later researches of H61der.2°4

Now Jacobi's principle may be considered to be a generalized
form of Euler's theorem, and Lagrange's principle a more precise
and generalized form of Maupertuis's. So it happens that Mau-
pertuis was right in thinking his theorem quite general, and Euler

200 Ibid.

^Methodus, p. 312. Cf. pp. 318-319 on the necessity for the principle of
vis viva.

202 Op. cit., pp. 26-29. Mayer (ibid., p. 24) also remarked that Euler's
later (Maupertuisian) form of the principle, in which the condition that all the
quantities in the integrand must be reduced, by means of the principle of vis
viva, to space-elements alone is not stated, is quite meaningless, for the forces
acting on the system, on which the path of the system depends, do not occur
in the integral of action. Here we will anticipate our criticism by pointing
out that in Lagrange's memoir the conditoin

ST = 5U,

where "T" and "SU" have the meaning already explained in The Monist, vol.
xxii, April, 1912, p. 290, is explicitly given, and what would now be written
in the same way was, tacitly or not, presupposed in all Euler's works.
Mayer said that the problem of variations only subsisted under the con-
dition

T = U + const.,

which implies the preceding equation, but, as Lagrange pointed out, is not
necessarily implied by it. And it is the preceding equation alone that we re-
quire to rescue the principle of least action from meaninglessness. Mayer's
remark (ibid., p. 27) that Lagrange completely leaves out the condition is
simply an error.

203 Cf. Monist, vol. xxii, April, 1912.

204 Ibid.

458 THE MONIST.

was right in doing what Mayer20 s complains of — in dropping the
condition about the theorem of vis viva holding.206 Of course, it
may have been, and probably was, the case that neither Maupertuis
nor Euler had any good grounds for believing that they were right.
Indeed, one is forced, against one's will, to the opinion that Euler
was in a position in which, as Mayer20? expresses it, "he could not
with propriety retort to the powerful President of his Academy."

The only reason why it is necessary to inquire closely whether
Euler really considered Maupertuis's principle to be valid seems to
me mainly to be the provision of an example to show the necessity
of an additional condition when we wish to deduce properties of
motion from the equation of the variation of the integral of action
to zero. There is also the possibility of our being given yet another
example of the greater power of instinctive beliefs or "metaphysics"
over the good man's mind than the love of scientific truth.208 If
we should have to conclude that Euler deliberately hid the truth for
the personal favor of Maupertuis, this conclusion will fill us with the
same regret and loathing that we feel for the weakness in Galileo's
character and the disgraceful exercise of the church's power on him,
respectively.

It seems to me true that Euler's love for "metaphysics" alone
could not lead him to forsake scrupulous honesty in his search for
the truth. It is difficult, but very possible, to acquit Euler of the
charge of veiled sarcasm against Maupertuis's principle. In a paper,
from which we have quoted above, in the Berlin Memoires for 1748,
he expresses his belief that we are still very far from being able to
assign, for each effect which nature produces, the quantity of
action which is the smallest, and from being able to deduce it from
the first principles of our knowledge. Indeed, Euler seems to have
no doubt that something must be a minimum, but he also thinks
that this something may be different — or at least seem to us, with-
out imperfect knowledge, different — in different cases.2°9 At any
rate Euler goes carefully through single statical cases and deter-
mines the equivalent in terms of the forces of "the quantity of

205 Op. cit., pp. 23-24. Euler did not, however, explicitly drop this condition.

206 Euler had presupposed in 1744 that the principle of vis viva held:
Maupertuis considered his principle applies to cases — such as the impact of
inelastic bodies — where the principle of vis viva does not hold.

*"Ibid., p. 17.

208 On Euler's "metaphysical" tendencies, cf. Mayer, ibid., pp. 21-23.

200 Cf. the remark of d'Arcy that, whatever the laws of nature might be
one could always find a function of the masses and velocities which, when
minimized, would represent them (cf. section XV).

CRITICISMS AND DISCUSSIONS. 459

action" in each case. Nowadays, we would say,210 of course, that
this inductive procedure was far more "reasonable" or scientific
than Maupertuis's ; but we must remember that then the opinion
was far more generally held than it is now that knowledge of
the truth could be attained by other than scientific methods.

It was, I think we must say, not merely love for "metaphysics"
which led Euler to sacrifice important details of his principle. Com-
parison of Daniel Bernoulli's letter to Euler of September 4, 1743,
with Euler's markedly different account in the Berlin Memoires of
1750 of the circumstances about the publication of the Methodus
of 1744, as well as Euler's obviously unjust attitude towards Konig,
points to a lower influence. If we dismissed — as we would like —
thoughts that this sort of influence came in, we would be faced
with the insoluble problem that Euler supported a principle which
was claimed to embrace cases where the theorem of vis viva fails
while he had convinced himself that the subsistence of this theorem
was a necessary condition for the validity of the principle. And
here the suggestion arises of itself that, since Euler, in his papers
in the Berlin Memoires, only committed himself to the mathematical
support — as distinguished from warmly expressed admiration — of
Maupertuis's principle in statical cases, he dared not affirm that the
action-integral was a minimum in nature even when the principle
of vis viva did not hold.211 This stop was reserved for Lagrange,
and perhaps it was on this account that Euler in a letter of Novem-
ber 9, 1762, congratulated Lagrange in the words:212 "What satis-
faction would M. de Maupertuis not have, if he were still alive, to
see his Principle of least action carried to the highest degree of
dignity of which it is susceptible.213 If this conjecture be true, we
must believe that Euler had a childlike faith that "metaphysics"
could generalize a theorem so far as to drop a condition which he
had satisfied himself, was necessary. We know now that this faith
— if indeed it existed — was justified.

PHILIP E. B. JOURDAIN.

THE LODGE, GIRTON, CAMBRIDGE, ENGLAND.

210 Like Mayer, op. cit., p. 23.

211 Indeed, where he refers to dynamical cases (in the Berlin Histoirc of
1751) he explicitly uses the principle of vis viva. Euler nowhere refers to
the problem of the impact of inelastic bodies, on which Maupertuis and others
laid such stress.

212 GELuvres de Lagrange, vol. xiv, p. 201.

213 "Quelle satisfaction n'aurait pas M. de Maupertuis, s'il etait encore en
vie, de voir son principe de la moindre action porte au plus haut degre de
dignite dont il est susceptible."

460 THE MONIST.

THE CAPTURE HYPOTHESIS OF T. J. J. SEE.1

In the opinion of Mr. See,2 the planets were not formed from
fragments of the solar nebula, nor did the moon originate from a
piece of that of the earth. He believes that the planets had a cosmic
origin outside of the solar nebula ; that they are foreign bodies cap-
tured by the sun while passing near it in their journey ; and that in
the same way the moon was captured by the earth at a certain remote
time.

How was this phenomenon accomplished? Mr. See thinks that
the sun was formerly surrounded by a vast atmosphere and that the
capture took place as the result of a resistance created by this at-
mosphere.

Let us therefore study the effect of the resistance of the medium
on the motion of a planet. 3 If there were no resistance the motion
would be Keplerian, the orbit would be an ellipse of any eccentricity
whatever. The density of the resisting medium being by hypothesis
very small, this orbit would vary slowly. We shall study the varia-
tions of this orbit by the method of the variation of constants.

First let us recall some formulas pertaining to the elliptical
motion of planets.

Calling the radius vector r and the true anomaly v, the equation

of the orbit is

/. i

1-f-^COSZ/

e denoting the eccentricity, and

(2) p = a(l-<?)

denoting the parameter of the elliptical orbit whose major axis is

2a. We have also the equation of the areas

the constant C of the areas having the value

C=

in which M represents the mass of the sun. (We disregard the

1 Translated by Lydia G. Robinson from the author's Lemons sur les hypo-
theses cosmogoniques, Chaps. VI and XIII. Paris, Hermann, 1911.

2 T. J. J. See, Researches on the Evolution of the Stellar Systems, Vol. II,
"The Capture Theory of Cosmical Evolution." Lynn, Mass., Nichols & Sons ;
Paris, Hermann, 1910.

3 See he. cit.t Chap. VII, pp. 134-158.

CRITICISMS AND DISCUSSIONS. 461

mass of the planet compared to the sun's mass.) The mean motion
n is connected with half the major axis a by Kepler's third law.
(3) »V = M.

Finally the equation of the vis viva gives

MM

r~ 2a
in which T is half the vis viva.

Differentiating equation (1) with reference to time, we have

dr pe sin v dv
dt~ (I+ecos v)2dt

pe sin v C

pe sin v C

= 7i~7 — \2^2
(1+ecos v)2P

C

= — • esrnv.
P

Now dr/dt is the component of velocity in the direction of the
radius vector. The component perpendicular to this radius vector
has for its value

dv C

r~dr~r

Q

= — (!+£ cos v).
P

From the two components of the velocity V, we derive the square
of this velocity,

In short, if we put
we shall have

The above formulas belong to Keplerian motion.

Now let us suppose that there is an atmospheric medium with a
resistance R directly opposed to the velocity and function of the

462 THE MONIST.

value V of that velocity. The constant of the vires vivae - M/2a
during the time dt will undergo a variation

M ,
Mda;

this variation will equal the work of the resistance R which is
Hence we have

p

whence we derive

da 2R/002

dt" A/M^'

replacing M and p by their values (2) and (3) in this last equation,
we obtain

(4) ^ =

dt

This is the equation which gives the variation of the major axis ; the
second member is necessarily negative. Hence the effect of the resist-
ance of the medium is always to diminish a and consequently according
to equation (3) to increase n. The angular velocity of the planet
increases4 at the same time that its mean distance from the sun
diminishes.

W shall now study the effect of resistance of the medium on the
eccentricity of the orbit.

First of all the derivative dC/dt of the areal constant C would
be equal to the momentum of the disturbing force R, with reference
to the center of attraction. Now this force R opposed to the veloc-
ity has for its components:
in the direction of the vector ray

dr
dt

-Rv'

perpendicular to the vector ray

4 Formula (3) even shows that na increases as a diminishes, whence we
have the curious result that resistance of the medium causes an increase in
the linear velocity of the planet.

CRITICISMS AND DISCUSSIONS. 463

dv

and the momentum of the force R with reference to the sun is

~dv

R * RC-

-~v": "Rv

Hence we have

dC RC
~dt= ""V~*
Remember that

c=

Taking the logarithmic derivatives of the two extreme members,
we have

Col i ? /

2\a 1— <r/

This equation makes it possible for us to obtain de since da and dC
have been computed. We find

2e de 1 da _2 dC
1 — F dt a dt C dt '

an equation which may be written by replacing da/dt and dC/dt by
their values (4) and (5),

2e de 2Rp 2R

^ ' T — ^"^=~ — r=r~'~"vr'

Let us now transform the second member of this equation. We
have previously found (page 461)

V = pJ^

na

hence the second member may assume the form

_2.R_ r i^i

~na^^' P J'

or again, by restoring the value of p2, this other form

2R 2e cos v+2<?

464 THE MONIST.

Finally equation (6) then gives

/ 1— \ CiC £ JA. A/ JL — €•* / \

(7) 3:= — -(tf + coszO.

dt nap

This is the equation which gives the variation of the eccentricity of
the orbit.

Formulas (4) and (7) make it possible to compute at any
instant the variations of the major axis and of the eccentricity.
But here it is only desirable to obtain their secular variations, and in
order to do this, to compute the value of da and de during the time
of a complete revolution.

Taking as an independent variable the true anomaly v we shall
have

da_da dt^
dv~~ dt dv

de__de_ dt_
dv dt dv'
Now the equation of the areas

(8)

(9) --

dv C

=P-

Formulas (4), (7) and (9) therefore make it possible to write the
values (8) of da/dv and de/dv which, integrated between 0 and 2?r
will give the variations of half the major axis and the eccentricity
during one revolution.

We may here offer certain hypotheses on medial resistance R.
This resistance increases as the velocity ; we shall suppose it pro-
portional to a certain power of the velocity V. It varies directly
as the distance r from the sun, for the density, and consequently the
resistance, of the sun's atmosphere increases inversely as the dis-
tance; let us suppose R proportional to a certain power (negative)
of r. In short let us put

10) R = AW-*f

h, a and ft being positive constants. Since V is proportionate to p,
and r to l/(l+e cosv), we can write formula (10) as follows:

R = £pa (l+«?cos v)* ,

k being a new positive constant.

In view of these hypotheses on R, the values (8) of da/dv and

CRITICISMS AND DISCUSSIONS. 465

de/dv, computed by means of the formulas (4), (7) and (9), may
be written

(11)

dv

where H denotes the positive constant

— /~v>

naC
bear in mind that in these values (11)

In order to study the secular variations of a and e we must
develop the second members of the values (11) in trigonometric
series according to the cosines of the multiples of v, and integrate
between v = 0 and v — 2?r. By integration all the cosines will be 0 ;
therefore we are interested in the constant terms of these trigono-
metric developments and especially the sign of these constant terms.

We already know that da/dv is necessarily negative, since da/dt
is always negative. Therfore we shall work only with de/dv. We
must develop in a trigonometric series the expression

Pa~l(l+ecos ^~2(^+cos v).

Now if we first develop the product of the two first terms we ob-
tain:

(12) pa-1(l+*cosz;)0-2 = Ao+ Ai cos z> + A2 cos 2z;-f ... .

We observe that A0 is necessarily positive because it is the mean
value of the first member both of whose terms are always positive.
Then multiplying the two members of formula (12) by (e + cosv)
we have

Pa~1(l+e cos v)f*~2(e+cos v) = ( Ao*+y ) +... ,

all the unwritten terms of the second member having their mean
value 0.

The second formula (11) therefore gives for the mean value
of de/dv during one revolution

(13) !=

Since the second member of equation (13) is generally negative
we conclude from it that the medial resistance has the effect of

466 THE MONIST.

diminishing the eccentricity of the orbit. This would be the case
particularly whenever Ax is positive. Now according to formula (12)
we have

2 C*
= -

TTj o

—
2 (1+^cos v)P~2cos vdv.

If at the same time

Aj will be positive, for of two elements of the integral correspond-
ing to the two values v and ir-v of the variable of integration, one
is positive and the other negative, but the positive element possesses
a greater absolute value than the negative.

In an analogous way we know that if the two inequalities

are satisfied, we shall likewise have

Ai>0.

If we suppose the eccentricity e to be so small that we can dis-
regard its square e~ we shall find more general conditions. The second
formula (11) is reduced to

-/ = -H [1+ (a-l)e cos z;+ (P-2)e cos v\ (<?+cos v);
dv

whence by retaining only the mean value of the second member we
derive

Then in order to diminish the eccentricity it is sufficient that

<*+/?>!.

In this case even if /3 = 0 (that is, if the resistance R does not vary
with the distance r from the sun) we need only have

that is to say, R increasing more rapidly than the simple power of
the velocity. Now we often grant as an approximation that a medial
resistance is proportionate to the square of the velocity.

This diminution of the eccentricity because of a medial resis-
tance might have been foreseen in general and without calculation in
the following manner. Suppose the resistance is not felt except in
the vicinity of the perihelion P (Fig. 1). In that case the planet

CRITICISMS AND DISCUSSIONS. 467

undergoes at this point P a sudden diminution of velocity which re-
sults in a decrease in the major axis. Since the perihelion remains
the same and the aphelion approaches it, it is clear that the eccen-
tricity is lessened. On the other hand, if resistance acts only at the
moment of the aphelion, the new orbit would have the same aphelion
as the former one, but its perihelion would be nearer that of the
sun, and the eccentricity would be increased. In fact the resistance
is felt all along the orbit, but two reasons combine to make it felt
more strongly at the perihelion: in the first place the velocity is
greatest at that point, since the atmosphere which is generally denser
nearer the sun offers a greater resistance near the perihelion.

To sum up, the effect of medial resistance on a Keplerian orbit
is to diminish both the major axis and the eccentricity.5 Therefore
if we agree with Mr. See that a resisting atmosphere originally
extended for vast distances around the sun, we can conceive that a

Fig. i.

body of cosmical origin when passing into the sun's sphere of in-
fluence might be able to modify its trajectory. Whether it was
parabolic or hyperbolic it now becomes elliptical, because the medial
resistance continues to diminish the major axis and the eccentricity
of the orbit which approaches the circular form. The resisting at-
mosphere is gradually absorbed by the sun, and when it finally dis-
appears the smaller body continues to revolve around the sun in its
orbit which is almost a circle. Such, according to Mr. See, is the
history of all the planets.

Just as the planets have been captured by the sun so also, ac-
cording to Mr. See, have the satellites, been captured by their respec-
tive planets.6

In order to study this capture we shall take up the comparatively
simple case called the restricted problem. The sun S and a planet J

8 It is easy to recognize that this resistance does not produce any secular
effect (at least at the first approximation) on the longitude of the perihelion.
To be sure it does not modify the plane of the orbit which retains the same
inclination and the same line of nodes with reference to a fixed plane.

8 Loc, cit., Chap. VIII, pp. 159-182; X, pp 211-236.

468 THE MONIST.

(e. g., Jupiter) each revolve around their common center of gravity
G in a circular orbit with a constant angular velocity w (Fig. 2). It
is required to study the motion of a small planet P whose mass is
negligible with reference to that of the principal planet J and which
consequently will not affect the motion of the latter. We will take
as origin the center of gravity G, of the system S - J ; as plane of
the coordinates xy, the plane in which S and J describe their circular
orbits ; and in this plane rectangular movable axes, the axis of x
being the straight line SGJ which connects the sun with Jupiter;
the axis of z is the perpendicular to the plane of the orbit at G. The
forces acting actually upon the point P (x, y, z) are the attraction
of the sun and of Jupiter. These two forces are derived respectively
from the two functions of forces7

Pi PZ

S G J

Fig. 2.

M!, M2 being the masses of the sun and Jupiter, plf p2 their distances
from P. Since the axes are movable we must add to these forces the
centrifugal force and the compound centrifugal force. The com-
ponents of the centrifugal force are

The components of the compound centrifugal force are

Hence the equations of the motion of the planet P with relation to
the movable axes are

7 We assume the mass m of the small planet P to be equal to unity. More
exactly, since this mass m is a factor in every case we shall not write it in
the formulas.

CRITICISMS AND DISCUSSIONS.

469

dt2 ~~ ds dz '
If we multiply these three equations

respectively, and add the results, we obtain a combination imme-
diately integrable which brings us to the following integral

)1VJ-1 jLVJ-2 / o o \ s-~\

= — + — + -0 (x2+y2)-C,
J Pi P2 2

known by the name of the integral of Jacobi.

Since the first member of this last equation is positive, the co-
ordinates x, y, z of the point P will satisfy the inequality

2+ 2)_c>0_

X.

Fig. 3-

Hence the projection (x, y) of the point P on the plane of xy
will be within the curve

in this equation pl and p2 denoting the distances of this projection
of the point P from the points S and J. For very great values of
the constant C this curve comprises two rings (denoted by 1 on
Fig. 3) surrounding the points S and J respectively. As C dimin-
ishes, these two rings become dilated and finally unite at a double
point A (Curve 2). Then when C is further diminished they finally
make only one curve (Curve 3) surrounding at the same time both
S and J.8 Hence when the constant C is not too great the small
planet is obliged to remain within Curve 3 but still is free to travel
in the proximity either of the sun or of Jupiter. On the contrary

8 We pay no attention here to certain portions of curves which are very
far removed from the origin.

470 THE MONIST.

if the constant C is very great the small planet will remain within
one of the rings 1 ; it will be a satellite either of the sun or of
Jupiter.

Now the effect of a passive resistance like that of a medium
is to increase the constant C of the second member of Jacobi's in-
tegral. Hence the curve encircling the small planet constantly con-
tracts. If it was originally Curve 3 at a definite moment it will
become Curve 2 with the double point. If at this moment the planet
is near the sun it will never return to the proximity of Jupiter; it
is captured by the sun. If on the contrary it is in the neighborhood
of Jupiter it will never return to that of the sun ; it will be captured
by Jupiter and from that moment will become one of his satellites.

The theory of Mr. See accounts for the smallness of the eccen-
tricities of the orbits of planets and satellites.9 But why are the
movements of almost all the heavenly bodies in a straight line, and
why have their orbits such small mutual inclinations? In the hy-
pothesis of Mr. See these two questions remain without any satis-
factory answer. To try to explain the smallness of the inclinations
we may suppose that the resisting atmosphere of the sun is of a
greatly flattened lenticular form ; hence a body whose orbit is greatly
inclined to the plane of this disk suffers a resistance much smaller
than a body moving in the very plane of the disk. The first body
has therefore much less tendency to be captured than the second,
and is in the plane of the disk in which the captures of the planets
are made.

We may also suppose that the resisting medium itself revolves.
It will then tend not to counteract the velocity of the planet revolving
within it but to impose upon this planet a certain velocity. Since
the resistance is no longer directly opposed to the velocity, the plane
of the orbit could vary and tend to diminish its inclination to the
equatorial plane of the solar atmosphere.

FORMATION OF SPIRAL NEBULAS.

In the work previously referred to,10 Mr. See is concerned with
the formation of nebulas, especially with the origin of spiral nebulas.

Let us imagine two masses of cosmical vapor N and N', almost
equal in size and traveling in opposite directions (Fig. 4a). As they

9 The diminution of the eccentricity because of a resisting medium is of
first importance not only in the theory of Mr. See ; it is taken into considera-
tion also in the theories of Faye and of Du Ligondes.

10 Op. cit., Chap. XIX.

CRITICISMS AND DISCUSSIONS. 471

approach each other their adjacent extremities will be prolonged
each in the direction of the other by mutual attraction (Fig. 46)
and may even end in uniting to form a single body (Fig. 4c) near
whose center attraction combined with friction will tend to produce
a condensation, a sort of central nucleus. The two masses of vapor
N and N' will turn in the directions of the arrows around this center
like two arms of a windmill.

Such, according to Mr. See, would be the origin of the spiral
nebulas. The central nucleus would tend to enlarge more and more

N

Fig. 4.

at the expense of the matter in the two spiral branches N and N'.
Hence we see that in the opinion of Mr. See the motion of the
matter in the two arms of the spiral nebula contrary to the usual
view would be centripetal and not centrifugal. Moreover whether
the motion is convergent or divergent the law of areas accounts
equally in both cases for the slowness of the arm's revolution around
its pivot, that is to say, the spiral form of both arms.

It may happen that the ends of the two masses of vapor N and
N' do not join as they approach each other, but are merely deviated
by attraction. Then the phase following phase 2 of Fig. 4. is not

N

Fig. 5-

phase c but phase d (Fig. 5) after which it assumes phase e. In
such a case we have the origin of an annular nebula like that of
Lyra. In the two diametrically opposed light portions seen in the
ring of Lyra, Mr. See finds an argument for the application of this
theory in that adjacent ends of the two masses of vapor N and N'
would not be perfectly united.

Hence Mr. See thinks that an annular nebula is formed by the
same mechanical process as spiral nebulas of which it thus proves
to be in some sense a particular case. But the annular form is

472 THE MONIST.

very rare because the conditions for the formation of a perfect ring
are not often realized.

One great objection may be offered to this theory. The tw«
arms of a spiral nebula are usually almost symmetrical. In the
ordinary hypothesis in which the movement of the arms is assumed
to be divergent this symmetry ma" be explained by the common
origin of the two arms. In the hypothesis of Mr. See there is no
wray to account for it, for the two masses of cosmical vapor N and
N' which give rise to the nebula and which have met accidentally will
not usually be equal. They ought then to give birth to an unsym-
metrical nebula.

Mr. See thinks that originally the solar system was a spiral
nebula of vast extent. The matter at its center first became agglom-
erated into particles which with the help of the resistance of the
medium were condensed into asteroids, according to the process ex-
plained above, and then into planets, which are further increased by
bombardment.11

Mr. See is led by analogy to believe that the spiral nebulas
which are less advanced in their evolution than the solar system are
composed of a vast number of very small bodies like the planets or
even the moon. If we can not analyze these nebulas it will be be-
cause of the extremely small size of their component parts and not
because these celestial objects are so excessively remote. Mr. Bohlin
has tried to measure the parallax of the nebula of Andromeda (which
is a spiral nebula of a continuous spectrum) and he has found it
equal to 0", 17, so that this nebula would be comparatively very near
us. But considering how little accuracy the points on the nebulas
admit of, can we regard this observation as conclusive and certain?

H. POINCARE.

PARIS, FRANCE.

NOTES ON THE CONSTRUCTION OF MAGIC SQUARES

OF ORDERS IN WHICH 11 IS OF THE FORM 8/> + 2.

Referring to the article in the last issue of The Monist by
Messrs. Andrews and Frierson, under the above heading, it was
shown that the minimum series to be used in constructing this
class of squares is selected from the series 1, 2, 3, (w+3)2, by

11 Mr. See sees in the lunar craters signs of a bombardment produced at
the surface of the moon by the fall of a large number of little satellites. He
compares these craters to the marks left by great drops of rain in the mud
(op. cit., p. 342, plate XII).

CRITICISMS AND DISCUSSIONS.

473

discarding 3 rows and columns from the natural square of the order
n + 3.

It is not necessary, however, to discard the three central rows
and columns, as was therein explained, there being numerous

variations, the total number of which is always equal to ( — -r— \

Fig. i.

Fig. 2.

Fig. 3-

Fig. 4.

Fig. 5-

Fig. 6.

Fig. 7- Fig. 8. Fig. 9.

therefore the 102 can be constructed with 9 different series, the 182
with 25 different series, the 262 with 49 different series, and so on.

In Figs. 1 to ,9 are shown all the possible variations of dis-
carding rows and columns for the 102, Fig. I representing the series
explained in the foregoing article.

The central row and column must always be discarded, the
remaining two rows and columns can be cast out symmetrically in
relation to their parallel central row or column and should be an

474

THE MONIST.

odd number of rows or columns from it. In other words, we cast
out the central row, then on each side of it we cast out the 1st, 3d,

vO
to

NO

to

VO
VO

•*

2

O

co

CM

s

vo

vO

-

ON

NO

^

NO

ON

S

ON

5

X

2

8

CM

vo

s

s

CM
vo

N

td

Ld

^

1

J

td

o

0

ON

id

o

o

ON

w

0

on

LJ

CM

<

td

co

H

jj

-

S

WJ

9

td

s

•*>

CO

U

td

to

vO

NO

0

a

on

CM

to

u.

10

*"*

CM

to

*J

ON

NO

o

£

O

ON

NO

to

O

CM

•*

(N

CM

2

2

O

•^HMM
MHHMM

o

0

•MMMM

~

2

^

^

~

T*

^

o

VO

ON

00

NO

0

NO

00

Ov

*

0

<

o.

to

CO

ON

ON

to

( )

td

00

.

td

CX5

rO

iii

(tl

[T}

— !

w

j

5

«*<

*

O

z

5

td

CO

s

^

5

Id

«

O

o

t_l

LM

m

u

NO

U

NO

u

to

CM

••*

on

to

CM

*^

ftS

vo

CO

••

UJ

a:

«

CO

_

CO

^

«

CO

^

CO

CM

c^

mmumrn

m*mmm*

l^iHB^

5th, or 7th, etc. rows from it, and irrespective of the rows, we do
likewise with the columns.

CRITICISMS AND DISCUSSIONS.

475

In a manner already explained, numbers are selected according
to the series desired and arranged in rectangles with which the
magic square is constructed.

A set of rectangles with their respective series is shown
Fig. 10, and the following table will give directions for their use.

in

SERIES

RECTANGLES (See Fig. 10)

Fig. 1

Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

A and X
B and X
C and X
A and Y
B and Y
C and Y
A and Z
B and Z
C and Z

Fig. ii.

For example, suppose we were to construct a square, using the
series denoted in Fig. 3. By referring to the table it is seen that we
must employ rectangles C and X. By using the La Hireian method
these rectangles are placed as shown in Fig. 11, care being taken to
arrange them in respect to the final square, whether it is to be asso-
ciated or non-associated.1

A non-associated square resulting from rectangles C and X is
shown in Fig. 12. Another example by Mr. Andrews, using the
path method is shown in Figs. 13, 14 and 15. Here a series corres-

1 See preceding article.

THE MONIST.

ponding to Fig. 8 has been selected and the natural square is shown
in Fig. 13, the heavy lines indicating the discarded rows and col-
umns. The rows and columns are re-arranged according to the nu-

6S

/07

S6

//3

SB

f/7

SS

/OS

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CRITICISMS AND DISCUSSIONS.

477

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1 See article in Monist of April, 1912.

478 THE MONIST.

In constructing the final square, Fig. 15, an advance move -4,
-5 and a break move 1, 1 was used.

It wiil be unnecessary to show examples of higher orders of
these squares, as their methods of construction are only extensions
of what has been already described. It may be mentioned that these
squares when non-associated can be transformed into associated
squares by the method given in Messrs. Andrews and Frierson's
article. HARRY A. SAYLES.

SCHENECTADY, N. Y.

POSTSCRIPT ON BUDDHISM AND CHRISTIANITY.

My article on the "Contributions of Buddhism to Christianity,"
which appeared in The Monist of October, 1911, called forth two
criticisms in the following number (January 1912). One was by
Albert J. Edmunds, "Buddhist Loans to Christianity," pp. 129 ff.,
and the other by Wilfred H. Schoff, "First Century Intercourse
Between India and Rome," pp. 138 ff.

Even before these criticisms reached me, I began to doubt
whether my standpoint that Buddhist influences were "not yet to be
found in the canonical Gospels, but first in the Apocryphal Gospels,"
could be maintained in this categorical form.1 The historical possi-
bility for the infiltration of Buddhist material into the canonical
Gospels I have never denied, but only its probability. I take pleas-
ure in using this opportunity to grant that by the lucid critique of
Edmunds the probability of the hypothesis of Buddhist loans in the
New Testament has increased in my opinion.

The connection of the Asita-Simeon parallel with the praise of
the heavenly hosts in both the Suttanipata and in the Gospel of Luke
has strongly impressed me even though I can not concede to Ed-
munds that this connection is an "organic" one on both sides. The
connection is organic only in the Pali source and not in Luke, where
in the second chapter the Simeon story does not stand in an intrinsic
connection with the angelic hymn but only near it. But even this
correspondence is certainly remarkable enough.

The exposition which Edmunds has given of the temptation
parallels ( Samyuttanikaya and Luke iv. 1-2) also decidedly increases
the probability of the loan hypothesis. Because of this the Buddhist
origin of some other New Testament stories, to which I have here-
tofore only with hesitancy granted a remote possibility that they

1 See my article, "Buddhistisches im Neuen Testament," in Das Freie
Wort, Frankfort, December 1911, pp. 674 ff.

CRITICISMS AND DISCUSSIONS. 479

might have been borrowed from India, also becomes of course more
probable.

Edmunds is entirely mistaken in his explanation of the Wander-
ing Jew (pp. 137-138). 2 Mark ix. 1 : "Verily I say unto you, There
be some here of them that stand by, who shall in no wise taste of
death, till they see the kingdom of God come with power," does not
in the least contain the germ of this legend but simply expresses
like the other passages on the Parousia ( Matt. x. 23 ; xvi. 28 ; Luke
ix. 27) the conviction of Jesus that the end of the world was at
hand.

The article of W. H. Schoff elucidates in a clear exposition
well-known facts about the commercial intercourse between India
and the Occident in the first century after Christ, but he brings no
positive proof that an exchange of ideas necessarily went hand in
hand with the extensive commercial intercourse. Especially, he, as
the translator of the Periplus, ought to have inferred from this text
that the mariners and traders of those days had but little thought
for anything but their merchandise. The author of the Periplus,
who describes his journey to India between 70 and 75 A. D., treated
only of what would be interesting to the merchant and mariner, but
otherwise shows that he was uninformed about the most common-
place things and says not one word about religion. Likewise the
Indian merchants who had settled in Alexandria were according to
the testimony of Dio Chrysostom (Orat. 35) ignorant people and
probably of Dravidian race. They would have taken no more inter-
est in religious questions than the Greek or Roman merchants of
their time.

When Schoff (page 141) describes the merchants as "bearing
ideas no less than goods," this is simply begging the question.

More important for our purpose than all reports of ancient
commercial relations seems to me the observation of Max Miiller
expressed in the following words:3 "Though we have no tangible
evidence of anything like translations, whether Oriental or Occi-
dental, at that time, we seem perfectly within our right when we
look upon the numerous coincidences between the fables of ^Esop
and the fables occurring in Sanskrit and Pali literature as proving
the fact that there was a real literary exchange between India, Per-
sia, Asia Minor and Greece beginning with the 6th century B. C."

TUBINGEN, GERMANY. R. GARBE.

2 Compare also Buddhist and Christian Gospels, 4th ed., II, pp. 264 ff.

3 In the article "Coincidences" in Last Essays, I, 269-270.

480 THE MONIST.

POINCARE'S COSMOGONIC HYPOTHESES.

Prof. H. Poincare has just published an important book1 which
treats the interesting problem of the origin of the world according
to the scientific views of modern philosophers and naturalists. Pro-
fessor Poincare in the first chapter discusses Kant's hypothesis and
subjects it to a critical analysis. The second chapter is devoted to
La Place; the third analyzes La Place's hypothesis and discusses
the work of La Roche, especially the theory of the stability of
rings and the formation of satellites. Subdivisions of this third
chapter treat the hypothesis of a uniform notation, the rings of
Saturn, the rupture of rings according to La Place and the forma-
tion of planets and satellites, and the author sums up the objections
to the theory of La Place.

The fourth chapter is devoted to the hypothesis of H. Faye,
according to which the earth is much older than the sun. Chapter
five discusses the hypothesis of du Ligondes who claims that Kant's
hypothesis stand in contradiction to the principle of the gases. The
sixth chapter treats the hypothesis of Prof. T. J. J. See, which will
be of special interest to American readers because he is a native
American and is the astronomer of the Naval Observatory, Mare
Island, California. This chapter together with the thirteenth is
reproduced in an English translation on another page of this issue.
The seventh chapter discusses the theory of Sir George Howard Dar-
win, his theory of tides, especially the internal tides of the earth,
the accelerative influence of cooling down, and his hypothesis of
the formation of the moon. The eighth chapter treats the theory
of solar and terrestrial heat, as well as the adiabatic equilibrium of a
perfect gas.

Chapter nine treats of the theory of Sir Norman Lockyer,
Chapter ten of Schuster and Chapter eleven of Arrhenius's theories ;
Chapter twelve compares the mass of the Milky Way with a gaseous
mass. Its substance is comparable to the radiant matter of Krookes,
rather than to a true gas. He then treats possible causes of the
flattening of the Milky Way and concludes with a consideration of
the star clusters of Kapteyn and Schiaparelli.

In the thirteenth chapter our author returns to Professor See
and discusses his view of the formation of the nebular spirals ; and
the last chapter is devoted to the hypothesis of Emile Belot. P. c.

1 Lemons sur les hypotheses cosmogonlques. Paris: Hermann, 1911. Price
12 francs.

VOL. XXII. OCTOBER, 1912. NO. 4

THE MONIST

FOR LOGISTICS.1

INTRODUCTORY NOTE. M. POINCARE AND M. COUTURAT.

Soon after Mr. Bertrand Russell's Principles of Mathematics of
1903 was published, M. Louis Couturat gave an exceedingly inter-
esting popular account of this and other works in the Revue de
Metaphysique et de Morale for 1904 and 1905, which was afterwards
published in book form in 19052 with an appendix on Kant's philos-
ophy of mathematics read at the celebrations in 1904 of the cen-
tenary of the death of Kant. Then M. Henri Poincare thought fit
to publish, in the above Revue t a series of articles of which this is
a list :

"Les mathematiques et la logique," Revue, Vol. XIII, 1905,
pp. 815-835; Vol. XIV, 1906, pp. 17-34; and ibid., pp. 294-314; "La
logique de 1'infmi," ibid., Vol. XVII, 1909, pp. 461-482.

In connection with some of the subjects so lightly and grace-
fully touched upon by M. Poincare appeared the following:

Mario Pieri, "Sur la compatibilite des axiomes de 1'arithme-
tique," Rev. de Metaphys., Vol. XIV, 1906, pp. 196-207.

Louis Couturat, "Pour la Logistique (reponse a M. Poincare)/'
ibid., pp. 208-250.

B. Russell, "Les paradoxes de la logique," ibid., pp. 627-650.

The writings of M. Poincare are well known to the readers of
The Monist. His criticisms are refreshingly light and gay and he
never allows profundity to obscure his wit. It is, however, un-
fortunate that his airy remarks on modern logic — which, by the
way, he confesses rather needlessly that he has not studied — have
been taken so seriously by many. It is, as newspaper editors know, a
tendency of the public to read with interest and even to accept un-
critically the opinions of an eminent person on matters about which
he is not an expert. The views of a well-known football player on

1 Translated by Philip E. B. Jourdain.

a Les principes des mathematiques avec un appendice sur la philosophic des
mathematiques de Kant.

482 THE MONIST.

the science of anatomy would no doubt be widely read, and the
views of M. Poincare on the philosophical questions at the root of
mathematics are not, in essentials, of a very different nature. It
is part of the business of anatomy to study deeply these faculties
which the athlete uses unconsciously. The analogy is quite evident.
M. Poincare is one of our greatest mathematicians, and centuries
have proved that a man who is a great mathematician need be
neither a great philosopher nor a great logician. We do not expect
such a combination of qualities, nor, as a rule, do we find them.

M. Louis Couturat gave a very full and adequate reply to the
first two of M. Poincare's articles. In spite of this M. Poincare re-
produced, in the same words, his refuted arguments in his lately
published book Science et Methode. The chapter entitled "Les
Mathematiques et la Logique" on pp. 152-171 of the book is almost
identical with pp. 815-824 of the first article; the chapter entitled
"Les Logiques nouvelles" on pp. 172-196, which is that translated on
pp. 243-256 of The Monist for April, 1912, is an abridged version
of pp. 826-835 of the first paper and the second article. The chapter
entitled "Les derniers efforts des Logisticiens" on pp. 192-214 re-
produces much of the less technical parts of his third article, and
this article, which is translated in the present number, was replied
to by Mr. Russell in his above cited paper.

The fourth article of M. Poincare is concerned principally with
a memoir on the theory of "logical types" published by Russell in
1908 and with one on the foundations of the theory of aggregates
published by Zermelo in the same year.

It is quite obvious that nobody should allow himself to speak
or write in terms of approval or disparagement of a branch of study
with which he has only a superficial acquaintance. Each of us is
free to dislike or like a particular subject and to leave it alone or to
cultivate it accordingly, and if he finds good reasons for so doing he
ought to publish them. But not even the most eminent can really
think that a brightly written condemnation of a subject, based on
a very superficial acquaintance with it, is of any real value. Indeed,
the more eminent a person is, the more able he generally is to
prevent us from seeing the truth. And then, besides the thought
of the efforts of others to perceive the truth, there is the very noble
sentiment with which M. Poincare begins his book La valeur de la
science : "The search for truth ought to be the aim of our activity ;
it is the only end which is worthy of it." Very nice, but with
regard to what the French call "logistics" or "mathematical logic,"

FOR LOGISTICS. 483

and everybody used to call "symbolic logic," M. Poincare has not
been as true to his lofty sentiment as his admirers have learned to
expect and demand.

Under these circumstances it seems only fair — I do not mean
to logistics but to the public — to give people the opportunity to
read M. Couturat's answer as well as M. Poincare's attack.

In the following translation, any bibliographical or other notes
which I have added are enclosed in square brackets. Where possible
I have abbreviated the translation and avoided the use of symbols.

There are a few passages in M. Couturat's article which may
possibly give rise to a wrong impression. Thus, he speaks of logical
demonstrations making true the chance finds of the intellect. Of
course the process of demonstration does not do this: It gives the
finder and other people certainty as to whether the find is true or
not. But we must not accuse M. Couturat of being a pragmatist on
the slender grounds of a loosely expressed sentence ; especially as in
other parts of this article he has protested in the clearest possible
way against the confusion between creation and discovery.

Near the end of the second section there is a reference to a
number of mathematicians who failed adequately to deal with the
paradox discovered by Burali-Forti, among whom are mentioned
Russell and myself. The article of Russell referred to contains,
implicitly, a criticism of certain views widely held by mathematicians
at that time and also — again implicitly — the solution of the paradox
and others like it. This of course was familiar to M. Couturat, but
the citation of Russell in that connection might mislead some people.
With regard to myself, at the time (1903-1904) that I wrote the
papers referred to I was hardly, as M. Couturat says, "totally a
stranger to logistics," but I freely grant that I was not as familiar
with it as is necessary even to grasp the full bearings of the ques-
tion. My attempt at the solution, though I believe it has one small
merit in distinguishing between what may be called entity and
existence, I have since then abandoned.

The discussion, in the third of M. Couturat's sections, of the
question of existence does not appear to me to be satisfactory, and
I have added a note referring to some former remarks of mine on
this subject in The Monist for January, 1910. p. E. B. j.

REPLY TO M. POINCARE.

I thank M. Poincare for the honor which he has done
me by taking me in particular as the subject of his articles

484 THE MONIST.

on "Mathematics and Logic/'3 but I must say that I do not
deserve this honor, for the ideas which I have presented are
not my own and I fear that M. Poincafe has done them a
great wrong by discussing them from a work in which they
are given at second-hand. In fact, as I have been care-
ful to warn my readers, my articles4 were mainly only
an account of Mr. Russell's book; and wherever I have
been led to add an analysis of the works of other logis-
ticians I have not omitted to refer to them. Now it is not
customary to criticize works of this class from a simple
analysis of them, above all when the value of these works
consists in the rigor of demonstrations, and these demon-
strations are necessarily absent from my summary exposi-
tion. For example, I have analyzed long memoirs of
Peano, Pieri and Whitehead by limiting myself to the enun-
ciation of their chief theorems, without the quotation of
a single demonstration. It is constantly assumed that the
reader who wishes to see the demonstration of such and
such a theorem has only to seek out the original memoirs,
and it would obviously be pointless to reproach me for not
having given it. Similarly I have thought I ought to
describe in my book, to complete one of my articles,
Peano's space-filling curve in an elementary and intuitive
form which is accessible to the first comer and without
speaking of the rigid analytical demonstration. What
would one think of a mathematician who, only knowing
this curve by my account of it, allowed himself to criticize
its construction, to doubt the rigor of the demonstration,
or to declare that this demonstration does not exist and
that the proposition in question rests on intuition ?

Also I had warned my readers that in my work I would

* [See Dr. G. B. Halsted's translation of "The New Logics" in The Monist
of April 1912, and of "The Latest Efforts of the Logisticians" in the present
number.]

* Published, with some corrections and additions, in a volume bearing the
title, Les principes des mathematiques, Paris, Alcan, 1905.

FOR LOGISTICS. 485

sacrifice rigor to clearness, not to that logical clearness
which is inseparable from rigor and which can only be
obtained by logistical symbolism, but to that clearness
in the common acceptation of the term which is called
intuition and which M. Poincare esteems so highly. It
must be granted that I am very badly rewarded for the
concessions which I have made to intuition, since M. Poin-
care profits by them to reproach me with a lack of rigor.
In any case, I wished to do the work of a commentator and
a popularizer and to compose for the use of the laity a kind
of introduction to the works of which I gave a short ac-
count. That is to say, it was not for M. Poincare that I
wrote, and I did not pretend to teach him anything about
these works. In all cases, a work of the kind I wrote may
serve — I hope so at least — to teach the elements of the
doctrines in question, but it cannot serve as a sufficient
basis to criticize these doctrines; to be just and effective,
the criticism ought to be on the original works from which
I drew my inspiration. What would M. Poincare say if
some one took it upon himself to discuss Hilbert's prin-
ciples of geometry5 from the analysis — however exact and
complete it may be — which he has given of it to the French
public ?

I might stop with these remarks, and perhaps I ought
to do so ; for if I have already compromised the doctrines
in question by my attempt at popularization, I run the risk
of compromising them still more by undertaking to defend
them against an adversary like M. Poincare. If I have re-
solved so to defend them, it is, on the one hand, because it
has pleased M. Poincare to substitute me for the masters
of logistics, and, on the other hand, because these masters
have believed that I would suffice for the task and have
left to me the care of justifying them. I thank them for

B [The Foundations of Geometry, trans, by Townsend. Chicago, The Open
Court Publishing Co.]

486 THE MONIST

their confidence ; but the reader ought to know that if there
is any thing good and enduring in my work it is to those
masters that I owe it, and that all that is feeble and defec-
tive comes from myself. If then I succeed in justifying
logistics against the criticisms of M. Poincare, so much the
better; if not, it will be my fault and will prove nothing
against logistics.

f I.

In the first place, we must not confuse logistics with
what M. Poincare calls "the logic of M. Hilbert." M. Pom-
care has not made this confusion, but many of his readers
may do so when they see him associate these two doctrines
in the same discussion and in a common condemnation.
Now it must be clearly realized that Hilbert is a complete
stranger to logistics and has never used any logical cal-
culus in his researches. If then the criticisms that M. Poin-
care makes against him are just, they have no bearing
against logistics, but rather tend to prove the superiority
of logistics over verbal reasoning and simple common sense.

It is important also to correct a historical error to
which the following phrase of M. Poincare may give rise:
"What Hilbert has done for geometry others wish to do
for arithmetic and analysis." We might believe from this
passage that the logisticians attack the subject of arith-
metic and analysis after the works of Hilbert on geometry,
and in imitation of them. The Grundlagen der Geometric6
of Hilbert were published in 1899. Now, ten years before
this (in 1889) Peano had published not only his Arith
metices principia nova methodo exposita but also / Prin-
cipii di Geometria logicamente esposti, both of which were
written in the symbolism which he had invented in the year
before. In 1891 he published in the first volume of the
Rivista di Matematica two articles on the concept of num-

6 [English translation as noted above.]

FOR LOGISTICS. 487

her which already contained the five fundamental axioms
of arithmetic. In 1894 he published in the fourth volume
of the same Rivista the memoir on the foundations of ge-
ometry which I have analyzed in Les Principes des Mathe-
matiques.7 Lastly, in 1899 Fieri published his logical re-
construction of projective geometry and of metrical geom-
etry in the Memoirs of the Turin Academy. These dates
are enough to prove that, if Hilbert has not wished to
profit by the works of the logisticians, the logisticians
could not have profited by his work and had no need of his
example not only in arithmetic and analysis but even in
geometry. Consequently M. Poincare commits a histor-
ical error in attributing to the "works of M. Hilbert"
the "triumph" of logistics in geometry. I content my-
self, on this point, with stating a fact: In 1900 Hilbert
elaborated for arithmetic a complicated system of eighteen
axioms,8 when eleven years before this arithmetic had been
built up on five axioms only, which Padoa in 1902 reduced
to four. Finally, to render to each person the "chrono-
logical" justice which is due to him, I should record that
Frege stated, in his Grundlagen der Arithmetik of 1884,
the theory of the integer number which Russell has adopted
in principle, and undertook to prove that the principles of
arithmetic are purely logical — analytical in Kant's sense.
M. Poincare writes : "This invention of M. Peano was
called pasigraphy," and adds : "This name exactly defines
its bearing." The first phrase contains an error of fact.
Never did Peano call his logical symbolism by the name of
"pasigraphy"; he always called it "mathematical logic".9
If I call it "logistics," it is first, because of the equivocal-

T Chap. VI, pp. 159-180.

8 "Ueber den Zahlbegriff," Jahresber. der deutsch. Math.-Ver., Vol. VIII,
1900. [This essay was reprinted in an appendix to the 3d German edition of
the Grundlagen der Geometric, Leipsic and Berlin, 1909, pp. 256-262.]

8 See all the editions of Peano' s Formulaire de Mathematiques, and the
Notations de Logique mathematique (Turin, 1894) which forms the introduc-
tion to the first edition.

488 THE MONIST.

ness of the expression "mathematical logic," and, secondly,
not because "this new name implies the purpose of revo-
lutionizing logic," but because this good old word, which
Vieta gave to algebra, indicates, by its very etymology,
the general art of reasoning and calculating. In this sense
it was employed in the eighteenth century by Lambert to
denote his own logical calculus.10 It was Schroder who
first called it "pasigraphy" in a communication made to the
first congress of mathematicians at Zurich in 1898, and
that probably with a depreciative intention." Now this
word is quite inexact, whatever M. Poincare may say.
People call any written universal language a "pasigraphy" ;
thus the international code of maritime signals12 is a
"pasigraphy." I myself formerly used this word when
speaking of Peano's symbolism but I corrected it at once :
"A system of pasigraphy or, better, of ideography" ;13 this
means that the symbols translate not words or phrases but
ideas. I concluded the same article by the words: "We
would restrict incorrectly the value of Peano's symbolism
if we only regarded it as a kind of stenography. It is
also and chiefly an instrument of logical analysis, of deduc-
tion and of verification" ; and I recalled, a propos of this,
the "universal characteristic" of Leibniz. It is, then, en-
tirely to misinterpret the nature and bearing of logistics
to regard it as a mere pasigraphy.

For the rest, M. Poincare speaks of logistics in the
way in which a bel esprit might speak of algebra or mathe-
matics in general. For example, he says: "The essential
elements of this language are certain algebraic signs which
represent the different conjunctions if, and, or, and then.
That these signs may be convenient is possible, but that

10"Versuch einer Zeichenkunst in der Vernunftlehre, Logische und philo-
sophische Abhandlungen, edited by John Bernoulli, Berlin, 1782.

11 Translated into English in The Monist for October, 1898.

13 Cf. Couturat and Leau, Histoire de la langue universelle (Paris, 1903),
preliminary chapter on "Les pasigraphies."

18 Bulletin des Sciences mathematiques, Vol. XXV, 1901.

FOR LOGISTICS. 489

they are destined to revolutionize the whole philosophy is
another question. It is difficult to admit that the word if
acquires, when it is written D, a virtue which it did not
have when it was written if." In the first place we must
not believe that logistical symbols are limited to the literal
translation of some words.14 The sign D translates if no
more than then, it expresses the idea of implication; the
same sign may translate and in certain cases and or in
other cases. Inversely, the word and has not the same
meaning in the three following cases: "Peter is rich and
happy," "Peter and Paul are rich," "Peter and Paul are
brothers" ; and consequently it is not translated by the same
logistical symbol. It is, then, quite unjust to consider "the
new language" as a mere tracing of ordinary language and
consequently as having no value and no utility of its own/5
M. Poincare believes that I attach "an exaggerated im-
portance which would astonish M. Peano himself" to the
use of symbols. I can reassure him on this point. M.
Peano writes to me on this subject : "I have always affirmed
the importance of symbolic notation in all mathematical
propositions, its great utility in difficult and delicate ques-
tions, and its indispensability in the study of principles.
That is written down in all the volumes of the Formulaire
. . . ."Everywhere and always he insists upon the necessity
of expressing every mathematical proposition and every
definition entirely in symbols.16

"Like the childish notations of Herigone, who wrote, for example, "5<"
for pentagon ; or like any system of analogous abbreviations that a mathematical
student may invent for taking notes.

"In 1895 Peano wrote: "Mathematical logic does not reduce merely

to an abbreviated symbolical writing, to a kind of tachygraphy; it allows us
to study the laws of these signs and the transformations of propositions. . . .
The two objects of mathematical logic, the formation of a symbolical script
and the study of the forms of transformations (or of reasoning) are closely
connected" ("Sur la definition de la limite d'une fonction," American Journal
of Mathematics, Vol. XVII). This memoir was meant (as its subtitle "Exer-
cice de logique mathematique" shows) to make the new logic known to mathe-
maticians. Mathematicians then cannot be excused for still ignoring it, and
it is doubly inexcusable for them to criticize it without knowing it.

18 Cf. his memoir printed at Paris in 1900 among those read at the first
international congress of philosophy.

49O THE MONIST.

However that may be, there was some one who had an
opinion which is as "exaggerated" as that of Peano and
myself of the importance of symbolism, and that was Leib-
niz. He went as far as to say that the discoveries in mathe-
matics that he had made arose solely from the fact that he
had perfected the use of symbols, and his discovery of the
infinitesimal calculus was, for him, only a specimen of his
char act eristic a universalis.17 In fact, we know that he did
not invent infinitesimal ideas ; he only invented a symbolism
to represent them and an algorithm to manipulate them.
We might say of him : "He only introduced two new signs,
d and /. That these signs may be convenient is possible;
that they could revolutionize the whole of mathematics is
incredible." We might also say of algebra: "It consists
simply in representing by signs the words plus, minus,
multiplied by, and divided by. But it is not to be seen
how it constitutes a progress beyond arithmetic ; it is diffi-
cult to admit that the word plus when it is written + ac-
quires a virtue that it did not possess when written plus."
And yet, could the theory of equations and the theory of
algebraic forms have been elaborated with words?

M. Poincare asserts that "pasigraphy does not preserve
us from error." Without doubt it does not, any more than
the rules of algebra or arithmetic do. Does it follow that
these rules are false or that we ought to defy them? Be-
cause we make mistakes in addition, must we condemn the
four rules of arithmetic and even the arithmetical signs,
and only count on our fingers or with little balls ? The mis-
takes which a logistician may commit do not weaken the
value of logistics any more than mistakes in calculation
shatter the certainty of arithmetic. It is enough that
logistics allows us to reason more easily and more surely
and to discover faults of reasoning more easily; and that

17 See Couturat, La Logique de Leibniz, pp. 84-85, the texts cited in the note
and the third appendix.

FOR LOGISTICS. 49 1

is what it does. In this sense it is, as Leibniz said, an art
of infallibility — not that logisticians are infallible, but they
are less exposed to error than those who trust to simple
common sense, that is to say to intuition.

Besides, M. Poincare forms quite a false idea of logis-
tics by considering it as a mechanism from which intelli-
gence is nearly excluded ; and his comparison of it with the
"logical piano" of Stanley Jevons is not exact. We must
first of all know that this logical piano merely concerns
logical classes and that it only effects the least important
— and the most mechanical — part of reasoning. Its office
consists in suppressing the elementary classes which are
annulled in virtue of the given premises. But it leaves
almost all the rest to be done; thus, on the one hand, we
have to put the logical problem into equations, and, on the
other hand, we have to combine the subsisting classes in
such a way as to obtain the consequences in the desired
form. Thus the algebra of logic does not reduce to a blind
mechanism. This is still more true of logistics which sur-
passes the algebra of logic and is much less "mechanical."

Another comparison is no happier: "Are the rules of
perfect logic the whole of mathematics ? We might just as
well say that the whole art of the player of chess reduces to
the rules for moving the pieces." But nobody ever asserted
that all mathematics reduces materially to logic, that is to
say that there is nothing more in a treatise on mathematics
than in a treatise on logic. We maintain only that all
mathematical reasonings are effected in virtue of the rules
of logic alone, in the same way that all the games of chess
that have been and can be played are effected according to
the rules of the game . . . . , otherwise the rules would be
worthless. The comparison returns then against the ad-
versaries of logistics, for it shows how a small number of
elements, combined according to some few fixed laws, can
generate an unlimited variety of consequences. People

492 THE MONIST.

have asserted that logistics put leading-strings on inven-
tion, and have urged against logistics the rights of genius.
How could mathematics constantly evolve and progress if
it is always condemned to rest on a small number of prin-
ciples and "logical constants" ? M. Poincare does not use
this argument and leaves on one side the question of in-
vention ; but it is clearly visible that the theory of "logical
constants" inspires in him an instinctive repugnance, and
that every attempt to catalogue the primitive notions and
principles of mathematics appears to him to be an insup-
portable pretension and a restriction on the "liberty" of the
scientific man. It is for that reason that he opposes to
logical and demonstrative reason the "sure instinct" of the
inventor and the "more profound geometry" which guides
him; and these kinds of considerations are very much in
fashion. It is, at the present time, fashionable to put the
"logic of nature and of life" in opposition to formal logic
that is disdainfully called "dialectical," "abstract," and
"verbal."

There is here a confusion which it is important to dissi-
pate. To oppose to logic the psychological fact of invention
is to commit the most gross ignoratio elenchi, Logic has
neither to inspire invention nor to explain it; it contents
itself with controlling it and verifying it in the proper sense
of the word (making it true). Do we reproach metrical
science for not giving poetical genius or the science of har-
mony for not conferring musical genius? And do we
therefore conclude that the rules of both have no value
and no utility? As for the theory of "logical constants,"
the liberty of the mathematical discoverer is no more re-
stricted by formulating the primitive principles and notions
on which his science rests than the libetry of the musician,
of the painter and of the poet is restricted by saying to
them in turn: "As for you, you will never be able to do
anything but combine the seven fundamental notes with

FOR LOGISTICS. 493

their accidentals; as for you, the seven colors of the spec-
trum, and as for you, the twenty-six letters of the alpha-
bet." That is exactly in what measure logistics clogs in-
vention and clips the wings of genius. People should really
stop throwing invention at the head of logicians, as if
invention could be contrary to logic. Besides, this "sure
instinct" and this "more profound geometry" which guide
the discoverer are only unconscious forms of the logical
reason and proceed according to the same laws. The rea-
son which invents is conformable, and at bottom iden-
tical, with the reason which demonstrates, and without
it the latter could not verify what the former has by
chance found; and these chance finds are only true on this
condition. It is, then, conformity with the laws of logic
"which alone gives value to the edifice which has been
built."

M. Poincare speaks of "the logic of Russell" and op-
poses it to the logic of Aristotle, as if Mr. Russell was the
first to go beyond the confines of the Aristotelian logic.
He appears besides to have an inexact notion of the Aristo-
telian logic when he says: "The logic of propositions of
Russell is the study of the laws according to which the
conjunctions if, and, or and the negation not are combined.
It is a considerable extension of the ancient logic." I can
assure M. Poincare that Aristotle was already acquainted
with the conjunctions if, and, or and negation, and that he
took account of them in his logic. All the classical logicians
knew and studied hypothetical judgments (where if fig-
ures), copulative judgments (where and figures), and
disjunctive judgments (where or figures) ; and classical
logic has always admitted negative judgments. If M. Poin-
care means that Mr. Russell is the first who has translated
these judgments into symbols and submitted them to an
algorithm he is at least half a century out of his reckoning :
for it is to Boole (without speaking of his fore-runners)

494 THE MONIST.

that this honor is due. It is, then, not Mr. Russell who has
"adjoined" to syllogistics "the conjunctions and and or"
and who has thus "opened up a new domain to logic."

M. Poincare believes that he can establish a funda-
mental difference between the two logics by remarking that
"the symbols are multiplied and permit of varied combina-
tions which are no longer Unite in number" and he adds :
"Have we any right to give this extension to the meaning
of the word logic?" It would, then, seem that for him
logic is characterized by the limited number of the com-
binations which it admits. But I do not see that there is a
radical difference. Besides, in what sense did the ancient
logic only admit a limited number of combinations? Is it
a question of the number of valid moods of the syllogism?
But modern logic, too, only admits a limited number of
simple types of reasoning. Is it a question, on the other
hand, of the infinite diversity of complex reasonings that
one can obtain by combining these types? But classical
logic too could form an infinity of reasonings by combining
syllogisms. In all cases the two logics have the same char-
acter and only differ in respect of the more or less. Be-
sides, how is the number relevant in this matter? If a
logical principle is true, whether it be the principle of the
syllogism or any other, is it not capable of justifying an
infinite number of reasonings just as well as a finite num-
ber? Does its demonstrative virtue by some chance be-
come exhausted after n applications ? Lastly, what means
this reproach addressed to logistics of admitting an in-
finite number of combinations, when, on the other hand,
it is reproached with only having a very limited number of
principles? Is it not, rather, for it, just as it is for geom-
etry (according to a well-known phrase), a glory to deduce
from so small a number of principles so great a number of
consequences ? How can this fact scandalize a mathemati-

FOR LOGISTICS. 495

cian who is familiar with the incredible fruitfulness of the
theory of combinations?

When M. Poincare opposes the old and the new logic
to one another and considers the latter as an enormous and
perhaps illegitimate "extension" of the former, he appears
to forget the fact that the domain of a science may receive
an extension — even a considerable one — without the notion
and the definition of this science changing. Otherwise we
could never speak of the progress of the sciences : M. Poin-
care seems to suppose by that that a science remains in
essentials identical with itself in the course of its historical
development. The reasoning of M. Poincare would serve
to prove that the infinitesimal calculus is not a part of
mathematics ; that electricity is not relevant to physics, and
that the theory of organic compounds is not relevant to
chemistry. Now it is for this reason that the extension
of the "field" of classical logic becomes an extension of
the "meaning of the word logic" M. Poincare says again :
"It seems that there is nothing new to write about formal
logic and that Aristotle saw to the bottom of it." If he
means by that (as Kant did) that logic has made no prog-
ress since Aristotle, it is nowadays a simple error of fact;
but if he means that logic ought to remain (or ought to
have remained) confined in the domain assigned to it by
Aristotle, he maintains implicitly that logic was perfect
and complete at its birth, and this is contrary to the analogy
of all the other sciences and to probability. We would
only smile at a man who claimed to reduce mathematics to
what it was in the time of Euclid, and physics to Aristotle's
physics. How then dare any one maintain or insinuate
that Aristotle has said the last word about logic and that
it is forbidden to develop this science beyond the narrow
limits assigned to it by its founder ?

Besides, if "the new logic is richer than the classical
logic," it is not so much by the extension of its domain as

496 THE MONIST.

by the deep study of the principles that have always di-
rected those reasonings which have been recognized as just
by that rational instinct to which M. Poincare attaches so
much value. He seems to reproach the logisticians with
"introducing" into logic indefinable notions and indemon-
strable principles. It would be more just to say that they
have discovered or recognized them; just as Aristotle did
not invent but discovered and recognized the principle of
the syllogism. M. Poincare is in too great a hurry to assert
that these indemonstrable principles "are appeals to intui-
tion, are synthetic a priori judgments." Perhaps he would
have been of another opinion if he had taken the trouble
to run through the enumeration of these principles. Why
should the principle of composition: "If a is b, and a is c,
then a is be" constitute an appeal to intuition rather than
the principle of the syllogism: "If a is b, and b is c, then
a is c" ? In what is the principle of simplification : "ab is a"
more synthetic than the principle of identity with which it
has been so often confused ? In any case, it has been con-
sidered by Kant as the type of analytic judgments. Is it of
these principles that M. Poincare said: "We regarded them
as intuitive when we met them, more or less explicitly
enunciated, in treatises on mathematics. Have they changed
character because the meaning of the word logic is en-
larged and we now find them in a book called Treatise on
Logic" ? In what treatise of mathematics has M. Poincare
seen them formulated? And his argument returns on him-
self, for even if they were put in a treatise on mathematics,
would that change their character as logical principles?
"They have not changed their nature, they have only
changed place" writes M. Poincare in italics ; but it is he
who has changed place. It is not enough that they should
be used in mathematical reasonings to call them mathe-
matical, and it is not enough that they are not found in
treatises on classical logic to refuse to them the title of

FOR LOGISTICS. 497

logical principles. Otherwise it would be necessary to say
that logical principles are, by definition, those which Aris-
totle and the schoolmen have discovered and formulated;
and that all the logical principles discovered by modern
logicians are intuitive. The distinction of the logical and
the intuitive would then reduce to a question of chronology.

Besides, the vague conception of intuition is out of
place as a weapon against the logicians, especially when
the intuition spoken of is not specified. Is intellectual in-
tuition meant, which bears upon the relations of ideas, or
sensible intuition, which necessarily clothes the spatial
form? These two intuitions are wholly different. All
logicians are ready to recognize that their principles pro-
ceed from intellectual intuition, that is to say they are
objects of immediate knowledge by the reason; but very
few will agree that they proceed from sensible intuition,
and rest, for example, as Lange has maintained, on spatial
schemata. For the rest, whatever the solution of this
"metalogical" problem may be, all the logical principles
ought to have the same fate ; and the traditional principles
of identity, contradiction and so on will be "appeals to
intuition" in the same sense and in the same measure as
the others. The logisticians then, must not be accused
of altering logic by introducing intuition into it ; for if this
accusation has any value, it is Aristotle who began this
introduction.

In any case it is inexact to say that "living" reasonings,
the only ones "in which our mind remains active," are
"those in which intuition still plays a part." Purely logical
reasonings need more mental effort and ingenuity than
M. Poincare believes, and, even with the mediocre aid of
Jevon's logical piano, a certain cleverness is necessary to
combine the brute results of mechanism and to draw the
conclusion wished. Besides, why reproach logistics with

498 THE MONIST.

making reasonings easier and more sure?18 If, like algebra,
it condenses into short formulae the result of long and
complicated reasonings, it is to relieve the powers of the
mind and to allow it to embrace a greater number of data
and to draw vaster and more distant conclusions. Con-
sequently, far from paralyzing the faculty of invention or
rendering it useless logistics lends it stilts or wings. The
discovering mind will always find something to exercise
itself upon, but it will do so on data which are more and
more complex. That is what happens in analysis, where
each new theory combines formulae which sum up the re-
sults of simpler and more elementary theories. M. Poin-
care may then be reassured: logistics does not exclude
genius.

M. Poincare makes a curious reproach to logistics:
"The part of intelligence is restricted to choosing among
a limited arsenal rules posited beforehand, and has not
the right to invent new ones." If we remark that the
"rules" are none other than the principles of logistics, this
phrase appears to me to mean that intelligence "has the
right" to invent new logical principles. It is a strange
conception of logic to consider it as always evolving and
as never finished.19 It evidently proceeds from the psycho-
logical confusion between the science and what we know
of it at a given moment. No one will ever "invent" new
rules of logic; some of these rules which had not been
noticed but were quite as "ancient" as the others and
equally "posited" beforehand, that is to say a priori, will
perhaps be "discovered." And the logisticians do not do
anything else. But then, why does M. Poincare reproach

""More sure," for M. Poincare confesses that in living reasonings "it is
difficult not to introduce an axiom or postulate which is unperceived." Must
we conclude from that that "life" is incompatible with logic ?

19 To use the favorite comparison of M. Poincare, what would we say of
a chess-player who wished to invent a new rule in the middle of a game, —
for example, to make his king move several squares when in check? Such an
"invention" would be called trickery and nothing else.

FOR LOGISTICS. 499

them with innovating ? With respect to the nine indefinable
notions and the twenty indemonstrable propositions of Rus-
sell, he says: "I believe that. . . .1 would have found some
more." He is quite at liberty to do so: the logisticians do
not ask for anything better, and will register his discoveries
— or, if he prefers to say, his inventions — with gratitude.
But what do these contradictory reproaches mean if not
that M. Poincare claims for himself "the right" to "invent"
logical principles at the very moment when he refuses this
right to the logisticians ?

For the rest, what good is it to discuss in abstracto the
qualities of logistics? M. Poincare grants that "pasig-
raphy can furnish us with a criterion to decide the question
which occupies us. If every treatise on mathematics can
be translated into the Peanian language, the logisticians
are right." Now the logisticians replied in advance, long
ago, to this ironical invitation. Ten years ago Peano pub-
lished the first edition of his Formulaire de Mathematiques,
whicfc is precisely a treatise or manual entirely written in
logistics; the fourth edition (1903-1904) comprises Logic,
Arithmetic, Theory of Numbers, Algebra, the Theory of
Real Numbers, the Theory of Definite Functions, the In-
finitesimal Calculus, the Theory of Complex Numbers, the
Theory of Circular Functions, the Geometrical Calculus
(comprising the theory of vectors and the theory of Qua-
ternions), and Differential Geometry; the "Additions" even
contain the elements of kinematics. The fifth edition of
the Formulaire is in course of publication.20 The principal
theorems are accompanied by their logistical demonstra-
tions. I will add that this mathematical manual is a collec-
tive work which M. Peano and his collaborators are in-
cessantly revising and perfecting. , Consequently the proof

20 Professor Peano has published, besides, a classical manual entitled :
Aritmetica generate e algebra elementare, drawn up in logistics (Turin, 1902).

5OO THE MONIST.

which M. Poincare requires of logisticians was given long
ago and is being completed from day to day.

It is true that M. Poincare soon seems to repent of his
rash concession and adds: "Again we must examine the
translation closely. It is not sufficient that we should be
presented with a single page where there are only formulae
and not a single word of ordinary language, in order that
we must bow down .... It will be necessary, when we are
in the presence of a pasigraphical reasoning, even when
this reasoning is correct, to examine if an appeal to intui-
tion is not hidden away in some corner." These reserves
are evidently very just in so far as they are counsels of
critical method. But why does M. Poincare not conform
to them ? It is not enough to express these general reserves
which are applicable to any demonstrative work, to weaken
the value of logistics and throw disfavor and suspicion on
the work of logisticians. The logisticians have given to the
public not "one page" but more than three hundred pages
of logistical formulae and demonstrations. Let those who
have doubts on the value of these demonstrations "exam-
ine" them as closely as they wish and let them point out
lacunae and errors, — for that is their right and even their
duty. But the burden of proof falls on them, and it is not
enough, in order to get rid of this burden, to shake their
heads with a smile of incredulity.

ii.

I pass on to the objections aimed at logistics in so far
as it is applied to mathematics. Here again I must say
that M. Poincare wrongs it by judging it merely from the
"popular" exposition which I have given of it. In effect,
the logistical formulae which constitute, as M. Poincare
says, a "new language" are sufficient by themselves and are
intelligible wholly by themselves; if it were necessary to
add to them a single word of ordinary language, it would

FOR LOGISTICS. 5OI

prove their incompleteness or defectiveness. Besides, this
"new language" was invented expressly to avoid the equiv-
ocation or the beggings of the question implied more or less
confusedly in ordinary language. Consequently the logis-
tical formulae are the only ones which can be exact, rigor-
ous and exempt from the above logical vices. Thus, when
an author thinks that he ought to translate them into ordi-
nary language, it is merely to make them more accessible
to the "laity" ; but it must be understood that this verbal
translation is always imperfect, approximate and by no
means allows the proper appreciation of the logical value
of the formulae. Just because language cannot equal
the precision and the rigor of the formulae, I have made
no scruples about introducing into my verbal translations
apparent beggings of the question in order to make them
more clear and more "French." What does an inexacti-
tude more or less matter when the logistical formula alone
counts from the logical point of view? I could not expect
that any one should judge and condemn these formulae
from the mere inspection of the verbal translation which I
gave of them for the use of novices. All translation is a be-
trayal; but that is still more true when the translation
makes exactly those qualities of the original on which study
and discussion bear vanish. It is exactly as if some one
wished to study the meter of Virgil in a French trans-
lation of the Aeneid.

Now, it is of these verbal translations, and only of these
verbal translations, that M. Poincare has taken account in
his criticism ; he does not appear to have noticed the logis-
tical formulae; "It is Greek, so it is unread." He may
then "amuse himself by counting how many numerical ad-
jectives my exposition contains" : that will prove absolutely
nothing against "pasigraphy." Nevertheless we will ex-
amine his arguments one by one in order to show better
that they all miss the point. On the subject of the logical

5O2 THE MONIST.

definition of zero, he says: "to define zero by something
null and something null by none is indeed to misuse the
richness of the French language." Then he recognizes
that I have "introduced an improvement in my definition"
(a double inexactitude, for this definition is not my own and
the "improvement" in question is due to Mr. Russell) by
writing "what," according to M. Poincare "means, in
French, zero is the number of objects which satisfies a con-
dition which is never satisfied. But as 'never' signifies fin
no case9 1 do not see that the progress is very great." I will
confine myself to recalling the verbal translation that I
have given of this formula : "if qur is always false, A is the
class of 4r's which verify qur." The verbal translation of
that is : A is the class of objects which satisfy a condition
which is always false, that is to say, false for all the values
attributed to x. Where is to be seen in this formula the
idea of the number zero or even of any number ? And are
we to be reproached for introducing into logic mathe-
matical notions, when classical logic was acquainted with
universal judgments and used the word all? To be able
to attribute to us a begging of the question — even one that
is simply verbal — M. Poincare has had to transform our
translation by replacing "always false" by "never true."
If, then, somebody here abuses the French language it is
not I.

But this reproach is even more undeserved if it is ad-
dressed to the logistician, who writes neither in French
nor in Italian nor in English but in a symbolism made ex-
pressly to liberate ideas from the tacit implications that
language introduces into them by custom. M. Poincare
himself says : "It is impossible to give a definition without
enunciating a phrase and difficult to enunciate a phrase
without putting in it a name of a number or at least the
word many or a word in the plural.21 And then the roof

* On the subject of the plural, it may be remarked that Peano has, follow-

FOR LOGISTICS. 503

is slippery and at every moment there is a risk of falling
into a begging of the question." These very just reflections
bear only on the logical defects of language and on the
faults that language can make us commit. It is precisely
to avoid these faults and to cure these defects that the
logisticians have invented their rigorously defined signs
which have no meaning but that which they are given by
definition.22 Put shortly, M. Poincare's argument comes
to this : "All those who reason with the words of ordinary
language are liable to commit beggings of the question;
now the logisticians use, not words, but symbols rigorously
defined ; consequently they too must commit beggings of the
question." The syllogism is not conclusive for it has four
terms. And even if it had only three, that is to say when
one could legitimately conclude from words to symbols,
the two words which I have italicized would still render it
invalid; the major says that we may commit errors; the
conclusion asserts that certain authors have necessarily
committed them.

The criticism of the definition of the number i is no
firmer. "One is the number of elements of a class of which
any two elements are identical"; such is the verbal trans-
lation that M. Poincare gives of this definition. "It is
more satisfactory. . . .in the sense that, in order to define
i, we do not use the word one] — but still the word two is
used" ; and M. Poincare rightly suspects that two can only
be defined by means of one.23 But he makes an unjust use
of the fact that I have used the word two to make a phrase
in ordinary language. The more exact translation of the
logistical formula is: "i is the class of classes u which are

ing Leibniz's recommendation, excluded it from the "uninflected Latin" which
he has given out as a form of international language, and which has been
adopted by many.

22 Cf. the beginning of the preface to Peano's Arithmetices principia of
1889.

23 By means of the general formula by which we define n + 1 by means of
n; cf. Les Principes des Mathematiques, Chap. II, § B, p. 59.

504 THE MONIST.

not null and such that if x is a u and y is a u then x is
identical with 3; whatever x and y may be." Where is there,
I do not say the word, but the idea of two in this formula ?
M. Poincare will say perhaps that two (problematic) ele-
ments x and y of the class u are made to appear in it ; but
the fact that they are two does not come into the question
in any way; and the proof of it is that in reality they are
only one: x and y are merely two names (excuse me,
names) for a single individual. This criticism obviously
has no bearing on another equivalent formula which I
have given,24 and which may be translated: "One is the
class of classes u which are not null and such that if x is a
u the class of the elements of u which are not identical with
x is null." That presupposes of course the definition of the
null class; but, as we see, there is no more even a prob-
lematical two elements of u, but only one, and we only ex-
press that there is no other.25

Will anybody say that, by the mere fact that an element
is spoken of, the number one is implied?26 But that is an
objection which M. Poincare does not formulate and to
which I have replied in advance in the following passage :
"We must not believe that the definition of the number
one constitutes a vicious circle, for the definition of the
singular class rests solely on the relation of identity. If
it is true that it implies in a sense the unity or rather the
individuality of the element considered, this unity cannot
be identical with the number one which is to be defined : for
this unity is a property of each element while the number
one is the property of a class .... consequently, in all cases

24 Ibid. I have logistically deduced this from the preceding one on p. 60.

26 Here is a more fundamental definition that Mr. Russell has communi-
cated to me : "One is the class of classes u such that the proposition : 'x is a u'
is equivalent, for all values of x, to (x is identical with c* is not false for all
values of c.' " Notice that this definition does not presuppose the notion of the
null class. As for the formula "x is a u", cf. its definition farther on.

26 [In French, the same word un stands for both an and one].

FOR LOGISTICS. 505

the units which constitute a cardinal number are different
from the number one."27

The confusion which exists in many minds between
these two ideas arises, I believe, from the double meaning
of the word for one, which is used both as the name of a
number and as an indefinite article.28 In the latter case
it would be better to use the word some as the logicians
do.29 This equivocalness exists in French and German,
but not in English. If then, somebody is inclined to invoke
it, he should take care to abuse not "the richness" but the
poverty of the French language. To sum up, it is not
enough to conceive any one object to conceive the number
one, nor to think of two objects together to have by that
alone the idea of the number two. From the fact that a
logical formula contains two or many symbols we must
not conclude that it implies by that alone the idea of two
or of some other number. When we say: "Peter and Paul
are wise," we mean to say: "Peter is wise and Paul is
wise"; we do not think the number two and we have no
need to think it nor to notice that that makes "two wise
men." In the same way when we say: "# and y are ele-
ments of the class w,"3° we do not think the number two
and no idea of number is implied in this proposition.31

m Les Principes dcs Mathematiques, Chap. II, § A, pp. 47-48. M. Pom-
care seems to propose or to accept such a justification when, after having
quoted the phrase of Hilbert: "Let us consider the object I," he adds: "Remark
that by doing this we by no means imply the notion of number, for it is under-
stood that i here is only a symbol. ..." Doubtless, but it is a symbol, that is
to say one object. Will M. Poincare say that that implies the number one?
Or will he grant to the logisticians the same liberty as to Hilbert ?

28 [Cf. note 26].

29 And also M. Meray, thus giving example in logic to other mathema-
tians.

30 Notice that it is only grammar which makes us use the sign of plural
in are elements.

81 Here is the rigorous definition of the proposition "x is a w," that Mr.
Russell has communicated to me: "x is a u" means: "The proposition: '<i>x
is true, and u has the relation of a class to the property which defines it' is
not false for all values of x" There is not here the shadow of the idea of
the number one, but, as in my enunciation, the purely logical notions of false,
negation and all. This definition was already given by G. Frege, Grundgesetze
der Arithmetik, Vol. I, 1893, P- S3-

506 THE MONIST.

These considerations reply to this objection of M. Poin-
care's : "A relation is incomprehensible without two terms ;
it is impossible to have the intuition of the relation without
having at the same time the intuition of its two terms."
That proves nothing, and M. Poincare adds : "And with-
out remarking that they are two, for in order that the
relation may be conceivable, it is necessary that they should
be two and two only." It is not the question to know—
and it is a psychological question — if we "remark" or not
that they are two, but if the notion of the relation implies
that of the number two. Now for that it would be neces-
sary that it implied the notion of the class formed by its
"two" terms; and that is obviously not the case. The
proposition : "x is the father of y" by no means implies the
idea of the class formed by x and 3;. Besides, it often hap-
pens that a relation (which is then called reflexive) exists
between a term and itself. Would it be maintained then
that it has still two terms ? That would be to say that x
is at the same time one and two.

The only logistical formula that M. Poincare has criti-
cized in itself and not in its verbal translation is one given by
Burali-Forti. M. Poincare says on this point: "I understand
thePeanian language too little to dare to risk a criticism."
This confession would disarm us if he did not "risk" this
criticism immediately afterwards : "I fear that this defini-
tion begs the question, for I see the figure i in the first
member and 'Un' in the second member." M. Poincare has
trusted too much to his "intuition," and it has deceived
him. Instead of "risking" this criticism on the mere wit-
ness of his eyes, he ought, conformably to the fundamental
rule of mathematical method, to have substituted for what
is defined the phrase which defines it; and to ascertain if
this definition really begs the question, he had only to refer
to the definition of the symbol "Un."

Now M. Burali-Forti defines "Un" as the class of sin-

FOR LOGISTICS. 507

gular classes, which in Russell's definition of the cardinal
number i. This definition is equivalent to the one which
I have given above and neither of them implies the idea
of that which is defined. As to the formula which M.
Poincare has criticised, it means: "i is the ordinal type
of the ordered classes of which the cardinal number is
unity." Thus it consists in defining the ordinal number i
by means of the cardinal number, and this explanation is
enough to do away with any appearance of a vicious circle.
So we see how "risky" the criticism of M. Poincare is.
He seems to consider as insignificant the formula

i E No

which M. Burali-Forti deduces from his definition. M.
Poincare translates it inaccurately as : "One is a number" ;
and then makes merry at the expense of pasigraphy, which
"is sufficient to demonstrate that one is a number." If he
had read the memoir of M. Burali-Forti — even in the "inter-
linear Italian translation" — more attentively he would have
known that "No" means ordinal number, and perhaps he
would have found the formula which teaches us that i is
an ordinal number less ridiculous. Even if this formula
"taught" nothing to M. Poincare, he had no grounds for
judging it to be insignificant, and that for two reasons.
On the one hand, this formula is sufficient to prove that the
class "No" exists, and this result is not to be despised, since
M. Poincare attaches so much importance to existence-
theorems and wrongly reproaches the logisticians with
neglecting them. On the other hand to prove that all the
finite whole numbers are ordinal numbers, we are obliged
to use the principle of induction, and for that purpose to
set out from the fact that i is such a number. However
evident or trivial this fact may appear to M. Poincare, it
was important to demonstrate it, and the formula at which
he mocks proves the conscientiousness and the rigor of the

508 THE MONIST.

logisticians. The pleasantries of M. Poincare are then
quite pointless.

As for the paradox discovered by M. Burali-Forti in
the theory of transfinite ordinal numbers, and from which
M. Poincare deduces an argument against logistics, I will
only say that this contradiction can by no means be im-
puted to the use of logical symbols ; and the proof of this
is that mathematicians who are total strangers to logistics
recognize it, discuss it, and have for years past spent vain
efforts to solve it.32 It is a purely logical difficulty which
resides in the principles of the logic of classes, that is to say
in the old and traditional part of logic. M. Burali-Forti,
in a communication made to me,33 believes that the contra-
diction arises from the different meanings that are given
to the word "ordinal number/' and that it depends, at bot-
tom, on the extension and the properties attributed to the
concept of class. Mr. Russell believes that it can only be
solved by restricting or even sacrificing the notion of class ;
broadly speaking, we must give up the principle — appar-
ently so evident and clear to intuition — that each concept
determines a class which is its extension.34 If logistics
has enabled us to discover this contradiction, it can only be
considered as a merit and not as a reproach for it proves
that it is an instrument of precision for thought. But M.
Poincare is more exacting. He summons logistics to re-

32 Bernstein, Math. Ann., Vol. LX; Jourdain, Phil. Mag., 1904-1905; Rus-
sell, Mind, 1905; Hadamard, Borel, Lebesgue, Baire, Bulletin de la Societe
Math, de France, 1905; Zermelo, Borel, Konig, Schonflies, Math. Ann., Vol.
LIX, LX.

88 [Cf. for fuller details pp. 228-229 of Couturat's original paper].

84 See Russell, "On some difficulties in the theory of transfinite numbers
and order types," Proc. Lond. Math. Soc. (2), Vol. IV, 1905, pp. 29-53. M.
Poincare concludes hastily: "Burali-Forti and Cantor have arrived at contra-
dictory conclusions ; thus one or the other is mistaken." It cannot be said
that one of them is mistaken if it is a question, as Russell shows, of a con-
tradiction of principle, of a kind of antinomy. Thus we can see how much
the conclusion is worth : "consequently pasigraphy does not preserve us from
error." For the rest, logistics is only a "method of infallibility" (as Leibniz
said) if certain premises are granted; it cannot be made responsible for a
contradiction inherent in the premises.

FOR LOGISTICS. 509

solve here and now the contradiction which has become
the crux of mathematicians. He says of Mr. Russell and
Dr. Whitehead: "If they could have .... purged it [the
theory of infinite numbers] of every contradiction, they
would have rendered us a signal service." The logisticians
are not obliged to solve difficulties which stop all mathe-
maticians, M. Poincare included, and — as if they were
modern Oedipuses — to reply to the riddles of all the
sphinxes which are encountered in science ; but if they suc-
ceed where others have failed, M. Poincare will be good
enough to remember this phrase, and do honor to logistics
for the solution.

in.

I now come to the special criticisms that M. Poincare
addresses to the logisticians on the subject of their philos-
ophy of mathematics and, in particular, of their theory of
whole number. In the first place, there are certain argu-
ments which it is astonishing to find him using, but which
fortunately are not likely to impress philosophers. For
example: "The definitions of number are very numerous
and very varied. . . .If one of them were satisfactory, no
new ones would be given." The same objection might be
urged not only to every philosophical speculation — and that
is the usual argument of sceptics and positivists — but to
every scientific theory ; M. Poincare knows this quite well.
If this argument had any value, it would be the negation
of all progress, even scientific progress. In mathematics
in particular there exist numerous definitions of the irra-
tional number, of the limit, of the definite integral, and so
on. Has ever any one concluded from this that all these
definitions are bad ? Certainly not, but simply that certain
ones are better than the others, without these others being
properly speaking defective or wrong. For the rest, if this
argument were to be taken literally, it would prove at the

5IO THE MONIST.

outside that all the definitions proposed are bad except one,
the last. Consequently, the argument has no bearing
against Mr Russell's definition as long as this definition
is the last proposed.

M. Poincare is surprised that the logisticians define
arithmetical addition by means of logical addition which
appears to him to rest on an act of intuition which is anal-
ogous but "more complex/' But in the first place if an
act of intuition is really necessary for one or the other of
these operations, is it not advantageous and meritorious
to define the one by the other, so as to reduce to a minimum
the number of acts of intuition ? Logical addition is not an
invention of the logisticians ; it has existed at all times and
in all minds. It is the combination which the conjunction
and expresses in the phrases, " the French and the Eng-
lish," "philosophers and mathematicians." Logic, even
classical logic, cannot dispense with it. Thus it is not ar-
bitrarily, as M. Poincare seems to believe, that this notion
is introduced "into the chapter headed 'Logic.' ' Given
that it is indispensable to logic, the whole question is to
know if it can be used to define arithmetical addition. This
idea is too natural for Peano and Russell to have been the
first to do it; it is already clearly expressed in the work of
Lambert. To refute it, M. Poincare ought to have shown
how and why arithmetical addition cannot be defined by
means of logical addition, and consequently ought to have
criticized Whitehead's35 formal definition of it. Or, if he
believes that the notion of logical addition is "more com-
plex" than that of arithmetical addition, he should try to
define the first by means of the second. That is the best
means of proving that mathematics is independent of logic.
Meanwhile, he ought to allow the logisticians to observe
the classical precept that principles must not be multiplied
without necessity.

"Amer. Journ. of Math., Vol. XXIV, 1902.

FOR LOGISTICS. 511

M. Poincare solemnly accuses the logisticians of hav-
ing violated two rules of method. The first consists in
this : Every mathematical definition supposes the existence
of the object defined and is only valid on this condition.
But this condition is by no means a necessary rule. It is
useless to invoke the opinion of John Stuart Mill, whose
authority is rather mediocre in the logic of mathematics.
The condition that M. Poincare wishes to impose on logis-
ticians is absolutely gratuitous and is not acknowledged
by the most rigorous mathematicians. A definition is no
more than the giving of a name; it by no means supposes
the existence of its object. We can very well define a prob-
lematical object, and then prove that it does not exist. Thus
Euclid denotes by a certain sign "the greatest prime num-
ber/' and then demonstrates that it does not exist. We
define the derivative or the integral of a function in gen-
eral, without supposing that every function has a derivative
or an integral. What M. Poincare wished to say or ought
to have said is, on the other hand, that a definition does
not imply the existence of the object defined, and this exist-
ence must be proved or postulated if we wish to be able to
use it in further reasonings. This36 is a well-known rule
of mathematical method, and it is enough to run through
Peano's Formulaire to see that each definition is accom-
panied, when there is occasion, by an existence-theorem
which usually determines the conditions under which the
object defined exists.

M. Poincare says that "in mathematics the word exists
can only have one meaning, it means 'is exempt from con-
tradiction.9 " I am sorry to contradict him on so elementary
and essential a point: logical — or mathematical, it is all
one — existence is quite another thing from the absence of
contradiction.37 It consists in the fact that a class is not

88 Cf. Les Principes, 39.

87 It is a curious thing that this conception of logical existence only appears
admissible in a panlogism analogous to that of Leibniz, and where the exten-

THE MONIST.

empty; that is to say that at least one member of it exists,
and this means by definition that the class in question is
not null. It is exactly for that reason that it is the custom
of mathematicians to prove the existence of a class by
giving an example, that is to say by indicating an individual
which belongs to this class ; and they have no other means
for proving an existence-theorem — unless they reduce it to
a preceding theorem or postulate of existence.38

But, it will be said, how is the existence of the individual
which is used as an example proved ? Must not this exist-
ence be established in order that the existence of the class
of which it is a part may be deduced ? Although this asser-
tion may seem paradoxical, the existence of an individual
as such is not demonstrated. The individuals, by the mere
fact that they are individuals, are always considered as
existing; or rather the question does not arise for them
since logical existence is a property of classes and not of
individuals.39 We never have to express that an individual
exists, absolutely speaking, but only that it exists in a class,
that is to say, is an element of it.40 When an individual
is defined by means of general terms, its existence is demon-
strated in two stages : This individual being defined as the
u (u being a certain class), we demonstrate that the class
u is not null, and then that it is a singular class. The defi-

sion of concepts would be absolutely determined by their comprehension. For
example, Leibniz and his disciples believed that if "No man is a stone," that
is to say, if no "men-stones" exist, it is because the concepts man and stone
respectively contain contradictory elements (such as living and not-living).

[On the following discussion of the "existence" of classes and individuals,
cf. my remarks in The Monist , Jan., 1910, Vol. XX., pp. 113-116. — Tr.]

88 It is enough to have a proposition of the form : "x is a member of «," to
be able to conclude that the class u exists.

89 Of course, classes themselves can be considered as individuals with
respect to classes of classes, but then they "exist" even when they are null.

40 M. Poincare thinks it necessary to add to Peano's postulate the follow-
ing: "Every integer has one which follows it." He does not see that this
postulate, which he believes new, is contained in the third postulate : "The
consecutive of an integer is an integer." In fact, this implies that the con-
secutive referred to exists as an individual of a class, and even that it is
unique, for otherwise we would say that the consecutives are contained in the
class of integers.

FOR LOGISTICS. 513

nition of the individual is then justified.41 But what we
really demonstrate is not the existence of the individual as
such but the existence of the class to which it belongs.42

In all of this there is no question of contradiction.
What then is the relation between the existence of a class
and the absence of contradiction in its definition? It con-
sists in this : If a definition is contradictory, no individual
fulfils its conditions, and consequently the corresponding
class does not exist. Contradiction is then a purely nega-
tive criterion of existence; it is the criterion of non-exist-
ence. And reciprocally, if a class exists, that is to say
contains an element, we can conclude from that, as M.
Poincare says, that its definition is not contradictory. Thus
existence appears as the criterion of non-contradiction.
But it is to be noticed that the relation between existence
and contradiction is exactly the inverse of that which M.
Poincare affirms; it is not non-contradiction that proves
existence, but it is existence that proves non-contradic-
tion.43

It is then arbitrary and misleading to maintain that a
definition is only valid if we first prove that it is not con-
tradictory. Besides, it would be interesting to know how
we could prove directly that a definition or a system of
postulates is not contradictory. The presence of a contra-
diction can certainly be proved, but the absence of every
contradiction is, like the innocence of an accused person, a
negative fact which cannot be proved directly. Hilbert

41 It must be noticed that, though the definition of a class has no need of
justification (as this class may be null) the definition of an individual must be
justified by the double demonstration of the existence and uniqueness. There
is, then, no contradiction here.

42 Cf. Russell, "The Existential Import of Propositions," Mind, July, 1905.
48 After having written these lines, I found the same doctrine stated by

G. Frege in his Grundlagen der Arithmetik, §§94, 95 (1884). "A concept is
admissible, even when its marks contain a contradiction ; only we must not
suppose that anything falls in its extension. But from the mere fact that a
concept does not contain a contradiction, we cannot conclude that something
falls in its extension...." (§94). "The non-contradiction of a concept can
only be established rigorously if we prove that something falls in its exten-
sion. The inverse would be an error" (§95).

514 THE MONIST.

stated in 1900 that we can find a direct demonstration of
the compatibility of the axioms of arithmetic;44 and in 1904
he believed that he had found such a demonstration.45 But
this demonstration is not satisfactory, in the opinion of M.
Poincare himself. If "M. Hilbert hides himself," it is not
"because the difficulty is too great," but because the prob-
lems which he has proposed to himself appear insoluble.
M. Padoa46 has already replied to Hilbert by recalling
that, in his own theory of algebraic numbers,47 he has
demonstrated, by the exemplary method which is the only
one possible, the irreducibility of his postulates and their
reciprocal independence. And he concluded with this
phrase : "The contradictions or the dependencies of propo-
sitions can only be demonstrated by deductive reasoning
while non-contradiction or independencies of propositions
can only be demonstrated by verifications (we verify that
properly chosen interpretation of the symbols satisfy or do
not satisfy the propositions in question)." In fact, a con-
tradiction or a dependence is translated by a proposition
of non-existence or by an implication ; while a non-contra-
diction or an independence is translated by a proposition
of existence or by a non-implication. And this difference is
equivalent to that of universal and particular propositions
in classical logic. We know that we can only establish
really universal propositions by demonstration, but that to
establish a particular proposition it is enough to cite a
single case in which it is true. In general we have no other
means, for we cannot deduce it from universal premises
without the adjunction of some particular proposition.

** Communication to the second international congress of mathematicians
at Paris in 1900; cf. Bulletin of the Amer. Math. Soc., 1902.

46 Communication to the third congress at Heidelberg in 1904 ; cf. Monist,
July, 1905. [Hilbert's paper is reprinted on pp._ 263-279 of the third edition of
his Grundlagen der Geometric, published at Leipsic and Berlin in 1909].

46 "Le probleme no. 2 de M. D. Hilbert," L'Enseignement mathematique,
Vol. V, 1903, pp. 85-91.

47 Bibliotheque du (ier) Congres int. de Philosophic, Vol. Ill, pp. 309-365 ;
Revue de mathematique s, Vol. VII, 1901, pp. 73-84.

FOR LOGISTICS. 515

Now, just as it is impossible to deduce a particular from
universal premises — that is to say a negation from many
affirmations — it is impossible to prove deductively an ex-
istence or a non-implication if we set out from non-exist-
ences or from implication. Thus the direct method that
Hilbert and Poincare recommend is impracticable. M.
Poincare has no right, then, to require of the logistician a
demonstration which Hilbert could not furnish. He might
just as well convict them of impotence by summoning them
to take a bite out of the moon.

In default of a direct demonstration M. Poincare sug-
gests a very curious method of verification. To prove that
a system of postulates is not contradictory, it would be
necessary, according to him, to compare two by two all
their consequences to prove that "there are not two which
are contradictory to each other." But, as he himself imme-
diately recognizes, this method is impracticable if the con-
sequences to be examined are infinite in number, as is the
case in arithmetic. I add that, in fact, it has never been
applied. Nobody has ever seen a mathematician spend his
time in comparing among themselves all the propositions
of a theory to assure himself that the definitions from
which he started do not contain some contradiction, and
that consequently the entities denned really exist. Where
would we be if we had to make such a verification for each
new definition ? But, it would be replied, it is the whole of
mathematics which constitutes this verification; it is a fact
that no contradiction between any two propositions has
ever been met. Very well, but this verification a posteriori
is as valid for logistics as for mathematics, since logistics
merely claims to formulate the primitive principles and
definitions of mathematics. For example, we may ask if
the postulates by which whole number is defined are not
contradictory. Logistics has only to reply: I deduce from
them all the theorems of classical arithmetic; vou have

516 THE MONIST.

never found the least contradiction in these theorems when
you made them rest on vague and confused intuitions ; why
do you wish that there should be any more contradiction
in them at the present time? They are the same proposi-
tions, merely reduced deductively to some principles. In
any case, the burden of proof falls on those who believe
that these principles are contradictory; for contradiction
may be proved, but non-contradiction may not.

The method in question is not only practicably inappli-
cable and unapplied in fact : it is logically illegitimate. In
fact, it is not enough to bring two propositions together,
to discover that they are contradictory, unless the contra-
diction is formal and explicit. For example, there is no
formal contradiction between the two propositions : "ABCD
is a non-rectangular parallelogram" and "ABCD is a quad-
rilateral which can be inscribed in a circle" ; the contradic-
tion only appears when we know the properties of the in-
scribable quadrilateral, that is to say, when the conse-
quences of the second proposition are deduced. To bring
to light the implicit and latent contradiction of two postu-
lates, it would be necessary, accordingly, to deduce all the
possible consequences (in number infinite) from these pos-
tulates. That presupposes the following definition : "Two
propositions are contradictory to one another when they
have consequences which are contradictory to one another."
But such a definition is illogical because it contains a circle.
Thus M. Poincare's criterion of non-contradiction implies,
not merely an infinite regress, but also a vicious circle.

M. Poincare well knows that the method which he pro-
poses is impracticable. He tries to correct it by means of
the principle of induction : "Perhaps there may be a means
of showing that a new reasoning cannot introduce contra-
diction, provided that we suppose that, in the series of pre-
ceding reasonings, we have hitherto met with none." No-
tice the very doubtful form in which this hypothesis is

FOR LOGISTICS. 517

stated. Indeed, it is a hypothesis in the air, which rests
on no example and on no precedent, and which seems to
be invented merely to charge the logisticians with a vicious
circle. Now, not only is it not true, that is to say, nobody
has ever used so strange a kind of reasoning, but it is im-
probable. To show this, let us see what further indications
M. Poincare gives. He supposes that "a series of syllo-
gisms" can be formed from the starting-point of the axioms
as premises; then, "when we have finished the nth syllo-
gism, we see that we can make a (n-f-i)th" ; lastly, we can
show that, "if there has been no contradiction at the nth
syllogism, there will not be at the (n+i)th." All these
hypotheses are absolutely gratuitous and contrary to all
probability. In the first place, mathematical reasonings do
not, in general, consist in a linear series of syllogisms;
otherwise the type of mathematical reasoning would be the
sorites. Must we repeat that the syllogism is by no means
the only type of deduction, and that there are many other
logical principles or rules which enter into reasoning?
Then, the simple deductions which compose a reasoning
to not arrange themselves in a linear series, as M. Poincare
imagines; the image of mathematical reasoning is not a
chain but rather a genealogical tree.48 What, then, does
the number of reasonings made at a given moment signify
if their linear order is always more or less arbitrary, and
arises solely from the practical necessity of enunciating
them in speech, because time has only one dimension? "The
number n serves to count a series of successive operations,"
says M. Poincare; what becomes of his argument if these
operations are not successive or are only so by accident?
Can we affirm that this number n exists at each instant and
that it is well determined? We can count simple deduc-
tions if they all reduce to the type of the syllogism; but

48 Cf. Les Principes, p. 286 [and the long note on p. 238 of M. Couturat's
article, which we have not here translated. It contains the detailed writing
out of a simple theorem in the mathematical logic of Peano].

518 THE MONIST.

how are we to count heterogeneous deductions which pro-
ceed from various rules ? Will it be said that each applica-
tion of a logical principle constitutes a unity ? But, besides
the fact that all the principles have not the same deductive
importance, it can happen that many principles occur at
once in an elementary deduction. That is what happens,
notably, when one intervenes as premise and the other as
a rule of deduction. All this proves that the number of
deductions, whether syllogistic or not, has no objective
reality, and that any numbering of them is arbitrary. Con-
sequently, how are we to admit that a proposition depend-
ing on this number can be established and concluded from
n to n-\- 1 ? And then M. Poincare relies on his hypothet-
ical case to attribute to the logisticians a vicious circle
which they have not committed. "With an if," says com-
mon sense, "we could put Paris in a bottle." It is with an
if that M. Poincare arrives at attributing a paralogism to
the logisticians.

Unfortunately, M. Poincare seems to forget elsewhere
all his if's when he asserts categorically that the principle
of induction is necessarily used in every demonstration of
the compatibility of the axioms of arithmetic or of any sys-
tem of axioms. For example, he says: "We must have
recourse to processes of demonstration where, in general,
we have to use the same principle of complete induction
which is the one to be verified." Would it not be believed
that the fantastic method which he proposes is in current
use? Elsewhere he cites it as one of the "possible applica-
tions of the principle of induction," as if this application
had been actually made. Finally he says, on the subject of
the theorem of Bernstein : "If ever another demonstration
is invented, it must still rest on this principle, since the pos-
sible consequences of the axioms which are to be shown to
be non-contradictory are infinite in number." Thus, it is
enough that we have to do with an infinity of propositions

FOR LOGISTICS. 519

(or of any objects) in order that, according to M. Poincare,
the principle of induction necessarily intervenes. He has
quite forgotten that the application of this principle pro-
posed by him is subject to extremely restrictive hypotheses.
At the bottom, he seems to confuse mathematical induc-
tion with induction pure and simple. For how are we to
conceive that from the absence of contradiction in a series
of reasonings we can infer the absence of contradiction in
the following reasonings ? Without doubt, if this inference
was certain and could be expressed by the precise formula :
"If no contradiction has been found in the first n reasonings
it will not be found in the n-\- 1 first ones," there would be
an occasion to apply the principle of induction, and the
conclusion would be equally certain. But the inference in
question can at most only be probable, and consequently it
only constitutes a common induction and not a mathemat-
ical induction. To borrow an example from M. Poincare,
the geometry of Lobachevski, since it only comprises a fin-
ite number of theorems, did not absolutely prove that the
postulate of Euclid is independent of the other geometrical
axioms (that is to say that its negation is compatible with
them) ; it only gave this proposition a probability which
was greater as the number of theorems of the new geom-
etry became greater. But there is always an abyss between
a probability, however great it may be, and an apodictic
certainty. Now, the results of common induction are char-
acterized by probability, while mathematical induction is
a rigorous process which engenders certainty. If then the
inference that is drawn from reasonings already made to
future reasonings has only a probable value (as common
sense — that "sure instinct" to which M. Poincare refers—
thinks), it rests on an induction pure and simple and not
on the principle of mathematical induction.49

*9[The fourth section of M. Couturat's paper occupies pp. 241-247, and con-
tains a detailed refutation of M. Poincare's remark that Mr. Russell had not
demonstrated the existence of the integers. M. Poincare's opinion rested

52O THE MONIST.

The second principal fault with which M. Poincare
charges the logisticians consists in that they surreptitiously
change a definition : "You give a subtle definition of num-
ber and then you think nothing more about it .... and when
the word 'number' is found farther on, you attach the same
meaning to it as the first comer would. . . .Here is a word
of which we have given an explicit definition A. We then
make use of it, in discourse, in such a way that it implicitly
supposes another definition B." That is a very serious re-
proach that must not be urged without proof against logi-
cians so rigorous and so practised as Peano and his collab-
orators. Now M. Poincare gives no proof and confines
himself to general reflections on method which affect logis-
ticians less than anybody else, for there is continually in
these reflections a question of "words" and of "phrases."
Mathematicians who reason with words and phrases are
doubtless liable to attribute to a term, instead of the
meaning assigned to it by its definition, the meaning which
current use gives it. But it is exactly to avoid these illog-
ical associations and implications that the logisticians use
symbols whose meaning is solely determined by their for-
mal relations, and which are manipulated in virtue of for-
mal rules of calculation. Has M. Poincare already for-
gotten that he reproached logisticians with reducing rea-
soning to a blind mechanism, that is to say, with neglecting
the meaning of their symbols ? "To demonstrate a theorem
it is not necessary nor even useful to know what it means" ;
"the mathematician has no need of understanding what he

partly on a misreading and partly on the fact that, in M. Couturat's popular
book, the question of existence was rather neglected in comparison with Mr.
Russell's work. However, in Mr. Russell's early work, while existence was
treated at length, the far more important question of entity was not con-
sidered. Thus the justification of Mr. Russell's early existence-theorems does
not now appear to be quite satisfactory, and accordingly is here left untrans-
lated. The second part of the fourth section is also untranslated here. It
contains a refutation of M. Poincare's hasty judgment that the principle of
induction is not the definition of finite number, and is slightly more technical
than the rest of M. Couturat's paper. What follows is, in essentials, M.
Couturat's fifth section.]

FOR LOGISTICS. 521

does." The two reproaches are contradictory; let M. Pom-
care leave to the logisticians at least the advantage of "the
logical correction of reasonings" which compensates for
its "formal" and almost "unintelligent" character. In any
case, all the general and vague reasons which he alleges
to support his criticism return against it, for they tend to
prove that the logisticians are exempt from the causes of
error which he points out.

I have long sought in the articles of M. Poincare for the
precise proofs of his accusation. I believe that I have
found one, and yet I am not quite sure. M. Poincare re-
proaches Mr. Russell with using two different formulae of
the principle of induction, and with confusing them illegi-
timately : "A number may be defined by recurrence ; on this
number we may reason by recurrence: these are two dis-
tinct propositions. The principle of induction does not
teach us that the first is true, it teaches us that the first
implies the second." He says again : "The principle of in-
duction does not mean that every whole number can be
obtained by successive additions ; it means that, for all the
numbers that can be obtained by successive additions, we
can demonstrate any property by recurrence." In the first
place, the expression "successive additions" is not precise.
The question necessarily arises, "How many additions?",
and the reply is, "a finite number" ; but the finite numbers
are characterized by the principle of induction. Conse-
quently, M. Poincare's proposed enunciation means: "For
all the numbers which can be defined by recurrence (or by
complete induction), we can demonstrate a property by
recurrence." Now that is a wholly analytical proposition,
and almost z. tautology: "All the numbers which verify
the principle of induction verify the principle of induction."
If this were the formula of the principle of induction, it
would be an analytic judgment, and not a synthetic judg-
ment as M. Poincare maintains.

522 THE MONIST.

But that is not the true formula of the principle of in-
duction, and it is incomprehensible how a mathematician
like M. Poincare could have made such a mistake. It is not
with him just an airy remark, for he returns to this impor-
tant question at the end of his second article and gives pre-
cise expression to his thoughts in the following terms : "A
whole number is that which can be obtained by successive
additions, it is that which can be defined by recurrence ....
A whole number is that on which we can reason by recur-
rence .... The two definitions are not identical ; without
doubt they are equivalent, but they are so in virtue of a
synthetic a priori judgment; we cannot pass from one to
the other by purely logical processes."50

Will it be said that the logisticians have invented a
new enunciation of the principle of induction, which they
set up against the classical enunciation? By no means,
they have only translated the traditional enunciation into
symbols. And what is still stronger, M. Poincare himself
quoted this traditional enunciation at the beginning of his
first article: "We know the enunciation of this principle.
If a property is true of a number i,SI and if we establish
that it is true of n-\-i provided that it is true of n, it will
be true of all the whole numbers." Now that is one of
the verbal translations of the formula of the principle of
induction.52 M. Poincare cannot then dispute the exactness
of the symbolic formula. Thus he accuses the logisticians
of surreptitiously changing a definition ; and it is he himself
who, in one and the same article, changes the definition,
or rather the enunciation, of the principle of induction!

BO[M. Couturat, on p. 249 of his article, formulates thr<^ two definitions
in symbols, and shows that the passage from one to the other is effected by a
process as analytic as the passage from the proposition, "Pompey is one of
the AT'S such that Caesar conquered x" to the pioposition, "Pompey was con-
quered by Caesar," or, "Caesar conquered Pompey."]

61 Or of the number o ; that comes tc the same thing here.
88 It is one of the verbal translations that I have given in Les Principes,
P. 55-

FOR LOGISTICS. 523

To prove his accusation he himself commits the paralo-
gism which he wrongly attributes to them, and all his
reproaches of illogicality fall on himself alone. If I had
the wit of M. Poincare, I would say that his "adventure"
is quite as instructive as that of M. Burali-Forti, and that
it ought to "warn" the adversaries of logistics of the neces-
sity of being circumspect.

I will not bring up the conclusion of the articles of M.
Poincare because I do not see the utility of carrying the
discussion into history where it is complicated by questions
of interpretation. The controversy is not "between Kant
and Leibniz,"53 but between M. Poincare and the logisti-
cians. Besides, the question, as M. Poincare has put it, is
not a question of general philosophy or of epistemology,
but of pure logic. Admitting the principles and the primi-
tive ideas of the logisticians, M. Poincare has maintained
that, setting out from these data, they cannot build up
mathematics without another postulate — an appeal to in-
tuition or a synthetic a priori judgment ; and he has thought
that he has discovered in their logical construction certain
paralogisms (beggings of the question or vicious circles).
I believe that I can conclude from the above discussion that
not one of these theses is proved, and that, in particular,
the logisticians have not committed any of the logical errors
that are so lightly imputed to them. I have too high an
idea of the wit and the character of M. Poincare not to be-
lieve that he will form a more just and more favorable
opinion of logistics . . . when he has studied it.

LOUIS COUTURAT.
PARIS, FRANCE.

63 [Monist, April, 1912, Vol. XXII, p. 256.]

THE LATEST EFFORTS OF THE LOGISTICIANS.1

THE logicians have attempted to answer the preceding2
considerations. For that, a transformation of logistic
was necessary, and Russell in particular has modified on
certain points his original views. Without entering into
the details of the debate, I should like to return to the two
questions to my mind most important: Have the rules of
logistic demonstrated their fruitfulness and infallibility?
Is it true they afford means of proving the principle of com-
plete induction without any appeal to intuition?

THE INFALLIBILITY OF LOGISTIC.

On the question of fertility, it seems M. Couturat has
naive illusions. Logistic, according to him, lends inven-
tion "stilts and wings," and on the next page : "Ten years
ago, Peano published the first edition of his Formulaire"
How is that, ten years of wings and not to have flown !

I have the highest esteem for Peano, who has done very
pretty things (for instance his "space-filling curve," a
phrase now discarded) ; but after all he has not gone fur-
ther nor higher nor quicker than the majority of wingless
mathematicians, and would have done just as well with his
legs.

On the contrary I see in logistic only shackles for the
inventor. It is no aid to conciseness — far from it, and if

1 Translated by George Bruce Halsted.

1 "The New Logics," in The Monist, April, 1912.

THE LATEST EFFORTS OF THE LOGISTICIANS. 525

twenty-seven equations were necessary to establish that i
is a number, how many would be needed to prove a real
theorem? If we distinguish, with Whitehead, the indi-
vidual x, the class of which the only member is x and which
shall be called 1 x, then the class of which the only member
is the class of which the only member is x and which shall
be called 11 x, do you think these distinctions, useful as they
may be, go far to quicken our pace ?

Logistic forces us to say all that is ordinarily left to be
understood; it makes us advance step by step; this is per-
haps surer but not quicker.

It is not wings you logisticians give us, but leading-
strings. And then we have the right to require that these
leading-strings prevent our falling. This will be their
only excuse. When a bond does not bear much interest,
it should at least be an investment for a father of a family.

Should your rules be followed blindly? Yes, else only
intuition could enable us to distinguish among them; but
then they must be infallible ; for only in an infallible author-
ity can one have a blind confidence. This, therefore, is for
you a necessity. Infallible you shall be, or not at all.

You have no right to say to us: "It is true we make
mistakes, but so do you/' For us to blunder is a misfortune,
a very great misfortune ; for you it is death.

Nor may you ask: Does the infallibility of arithmetic
prevent errors in addition? The rules of calculation are
infallible, and yet we see those blunder who do not apply
these rules \ but in checking their calculation it is at once
seen where they went wrong. Here it is not at all the
case; the logicians have applied their rules, and they have
fallen into contradiction; and so true is this, that they are
preparing to change these rules and to "sacrifice the notion
of class." Why change them if they were infallible?

"We are not obliged," you say, "to solve hie et nunc all
possible problems." Oh, we do not ask so much of you.

526

THE MONIST.

If, in face of a problem, you would give no solution, we
should have nothing to say; but on the contrary you give
us two of them and those contradictory, and consequently
at least one false ; this it is which is failure.

Russell seeks to reconcile these contradictions, which
can only be done, according to him, "by restricting or even
sacrificing the notion of class." And M. Couturat, dis-
covering the success of his attempt, adds : "If the logicians
succeed where others have failed, M. Poincare will remem-
ber this phrase, and give the honor of the solution to
logistic."

But no! Logistic exists, it has its code which has al-
ready had four editions ; or rather this code is logistic itself.
Is Mr. Russell preparing to show that one at least of the
two contradictory reasonings has transgressed the code?
Not at all; he is preparing to change these laws and to
abrogate a certain number of them. If he succeeds, I shall
give the honor of it to Russell's intuition and not to the
Peanian logistic which he will have destroyed.

THE LIBERTY OF CONTRADICTION.

I made two principal objections to the definition of
whole number adopted in logistic. What says M. Couturat
to the first of these objections?

What does the word exist mean in mathematics? It
means, I said, to be free from contradiction. This M.
Couturat contests. "Logical existence," says he, "is quite
another thing from the absence of contradiction. It con-
sists in the fact that a class is not empty." To say: a's
exist, is, by definition, to affirm that the class a is not null.

And doubtless to affirm that the class a is not null,
is, by definition, to affirm that a's exist. But one of the
two affirmations is as denuded of meaning as the other,
if they do not both signify, either that one may see or

THE LATEST EFFORTS OF THE LOGISTICIANS. 527

touch a's which is the meaning physicists or naturalists
give them, or that one may conceive an a without being
drawn into contradictions, which is the meaning given
them by logicians and mathematicians.

For M. Couturat, "it is not non-contradiction that
proves existence, but it is existence that proves non-contra-
diction." To establish the existence of a class, it is neces-
sary therefore to establish, by an example, that there is an
individual belonging to this class : "But, it will be said, how
is the existence of this individual proved? Must not this
existence be established, in order that the existence of the
class of which it is a part may be deduced? Well, no ; how-
ever paradoxical may appear the assertion, we never dem-
onstrate the existence of an individual. Individuals, just
because they are individuals, are always considered as ex-
istent .... We never have to express that an individual
exists, absolutely speaking, but only that it exists in a
class." M. Couturat finds his own assertion paradoxical,
and he will certainly not be the only one. Yet it must have
a meaning. It doubtless means that the existence of an
individual, alone in the world, and of which nothing is af-
firmed, cannot involve contradiction; in so far as it is all
alone it evidently will not embarrass any one. Well, so let
it be ; we shall admit the existence of the individual, "abso-
lutely speaking," but nothing more. It remains to prove
the existence of the individual "in a class" and for that it
will always be necessary to prove that the affirmation,
"Such an individual belongs to such a class," is neither
contradictory in itself, nor to the other postulates adopted.

"It is then," continues M. Couturat, "arbitrary and
misleading to maintain that a definition is valid only if we
first prove it is not contradictory." One could not claim
in prouder and more energetic terms the liberty of contra-
diction. "In any case, the onus probandi rests upon those
who believe that these principles are contradictory." Pos-

528 THE MONIST.

tulates are presumed to be compatible until the contrary is
proved, just as the accused person is presumed innocent.
Needless to add that I do not assent to this claim. But,
you say, the demonstration you require of us is impossible,
and you cannot ask us to jump over the moon. Pardon
me; that is impossible for you but not for us, who admit
the principle of induction as a synthetic judgment a priori.
And that would be necessary for you, as for us.

To demonstrate that a system of postulates implies no
contradiction, it is necessary to apply the principle of com-
plete induction ; this mode of reasoning not only has noth-
ing "bizarre" about it, but it is the only correct one. It is
not "unlikely" that it has ever been employed ; and it is not
hard to find "examples and precedents" of it. I have cited
two such instances borrowed from Hilbert's article. He
is not the only one to have used it and those who have not
done so have been wrong. What I have blamed Hilbert
for is not his having recourse to it (a born mathematician
such as he could not fail to see a demonstration was neces-
sary and this the only one possible), but his having re-
course without recognizing the reasoning by recurrence.

THE SECOND OBJECTION.

I pointed out a second error of logistic in Hilbert's
article. To-day Hilbert is excommunicated and M. Cou-
turat no longer regards him as of the logistic cult; so he
asks if I have found the same fault among the orthodox.
No, I have not seen it in the pages I have read ; I know not
whether I should find it in the three hundred pages they
have written which I have no desire to read.

Only, they must commit it the day they wish to make
any application of mathematics. This science has not as
sole object the eternal contemplation of its own navel; it
has to do with nature and some day it will touch it. Then

THE LATEST EFFORTS OF THE LOGISTICIANS. 529

it will be necessary to shake off purely verbal definitions
and to stop paying oneself with words.

To go back to the example of Hilbert : always the point
at issue is reasoning by recurrence and the question of
knowing whether a system of postulates is not contradic-
tory. M. Couturat will doubtless say that then this does
not touch him, but it perhaps will interest those who do
not claim, as he does, the liberty of contradiction.

We wish to establish, as above, that we shall never en-
counter contradiction after any number of deductions
whatever, provided this number be finite. For that, it is
necessary to apply the principle of induction. Should we
here understand by finite number every number to which
by definition the principle of induction applies ? Evidently
not, else we should be led to most embarrassing conse-
quences. To have the right to lay down a system of postu-
lates, we must be sure they are not contradictory. This is
a truth admitted by most scientists ; I should have written
by all before reading M. Couturat's last article. But what
does this signify? Does it mean that we must be sure of
not meeting contradiction after a finite number of propo-
sitions, the finite number being by definition that which
has all properties of recurrent nature, so that if one of these
properties fails — if, for instance, we come upon a contra-
diction— we shall agree to say that the number in question
is not finite ? In other words, do we mean that we must be
sure not to meet contradictions, on condition of agreeing
to stop just when we are about to encounter one? To state
such a proposition is enough to condemn it.

So, Hilbert's reasoning not only assumes the principle
of induction, but it supposes that this principle is given us
not as a simple definition, but as a synthetic judgment a
priori.

To sum up :

A demonstration is necessary.

530 THE MONIST.

The only demonstration possible is the proof by recur-
rence.

This is legitimate only if we admit the principle of in-
duction and if we regard it not as a definition but as a syn-
thetic judgment.

THE CANTOR ANTINOMIES.

Now to examine Russell's new memoir. This memoir
was written with the view to conquer the difficulties raised
by those Cantor antinomies to which frequent allusion has
already been made. Cantor thought he could construct a
science of the infinite ; others went on in the way he opened,
but they soon ran foul of strange contradictions. These
antinomies are already numerous, but the most celebrated
are:

1. The Burali-Forti antinomy;

2. The Zermelo-Konig antinomy;

3. The Richard antinomy.

Cantor proved that the ordinal numbers (the question
is of transfinite ordinal numbers, a new notion introduced
by him) can be ranged in a linear series, that is to say that
of two unequal ordinals one is always less than the other.
Burali-Forti proves the contrary; and in fact he says in
substance that if one could range all the ordinals in a linear
series, this series would define an ordinal greater than all
the others ; we could afterwards adjoin i and would obtain
again an ordinal which would be still greater, and this is
contradictory.

We shall return later to the Zermelo-Konig antinomy
which is of a slightly different nature. The Richard an-
tinomy (Revue generale des sciences, June 30, 1905) is as
follows: Consider all the decimal numbers definable by a
finite number of words; these decimal numbers form an
aggregate E, and it is easy to see that this aggregate is

THE LATEST EFFORTS OF THE LOGISTICIANS. 53!

countable, that is to say we can number the different deci-
mal numbers of this assemblage from I to infinity. Sup-
pose the numbering effected, and define a number N as
follows: If the nth decimal of the nth number of the as-
semblage E is

0, i, 2, 3, 4, 5, 6, 7, 8, 9
the nth decimal of N shall be :

1, 2, 3, 4, 5, 6, 7, 8, i, i

As we see, N is not equal to the nth number of E, and
as n is arbitrary, N does not appertain to E and yet N
should belong to this assemblage since we have defined it
with a finite number of words.

We shall later see that M. Richard has himself given
with much sagacity the explanation of his paradox and that
this extends, mutatis mutandis, to the other like paradoxes.
Again, Russell cites another quite amusing paradox : What
is the least whole number which cannot be defined by a
phrase composed of less than a hundred English words ?

This number exists; and in fact the numbers capable
of being defined by a like phrase are evidently finite in
number since the words of the English language are not
infinite in number. Therefore among them will be one less
than all the others. And, on the other hand, this number
does not exist, because its definition implies contradiction.
This number in fact is defined by the phrase in italics which
is composed of less than a hundred English words ; and by
definition this number should not be capable of definition
by a like phrase.

ZIGZAG THEORY AND NO-CLASS THEORY.

What is Mr. Russell's attitude in presence of these con-
tradictions? After having analyzed those of which we
have just spoken, and cited still others, after having given

532

THE MONIST.

them a form recalling Epimenides, he does not hesitate to
conclude: "A propositional function of one variable does
not always determine a class." A propositional function
(that is to say a definition) does not always determine a
class. A "propositional function" or "norm" may be "non-
predicative." And this does not mean that these non-predi-
cative propositions determine an empty class, a null class;
this does not mean that there is no value of x satisfying
the definition and capable of being one of the elements of
the class. The elements exist, but they have no right to
unite in a syndicate to form a class.

But this is only the beginning and it is needful to know
how to recognize whether a definition is or is not predi-
cative. To solve this problem Russell hesitates between
three theories which he calls

A. The zigzag theory;

B. The theory of limitation of size;

C. The no-class theory.

According to the zigzag theory "definitions (proposi-
tional functions) determine a class when they are simple
and cease to do so when they are complicated and obscure."
Who, now, is to decide whether a definition may be re-
garded as simple enough to be acceptable? To this ques-
tion there is no answer, if it be not the loyal avowal of a
complete inability: "The rules which enable us to recog-
nize whether these definitions are predicative would be ex-
tremely complicated and cannot commend themselves by
any plausible reason. This is a fault which might be rem-
edied by greater ingenuity or by using distinctions not yet
pointed out. But hitherto in seeking these rules, I have
not been able to find any other directing principle than the
absence of contradiction."

This theory therefore remains very obscure; in this
night a single light — the word zigzag. What Russell calls

THE LATEST EFFORTS OF THE LOGISTICIANS. 533

the "zigzaginess" is doubtless the particular characteristic
which distinguishes the argument of Epimenides.

According to the theory of limitation of size, a class
would cease to have the right to exist if it were too ex-
tended. Perhaps it might be infinite, but it should not be
too much so. But we always meet again the same difficulty ;
at what precise moment does it begin to be too much so ?
Of course this difficulty is not solved and Russell passes on
to the third theory.

In the no-classes theory it is forbidden to speak the
word "class" and this word must be replaced by various
periphrases. What a change for logistic which talks only
of classes and classes of classes ! It becomes necessary to
remake the whole of logistic. Imagine how a page of
logistic would look upon suppressing all the propositions
where it is a question of class. There would only be some
scattered survivors in the midst of a blank page. Apparent
rari nantes in gurgite vasto.

Be that as it may, we see how Russell hesitates and the
modifications to which he submits the fundamental prin-
ciples he has hitherto adopted. Criteria are needed to de-
cide whether a definition is too complex or too extended,
and these criteria can only be justified by an appeal to in-
tuition.

It is toward the no-classes theory that Russell finally
inclines. Be that as it may, logistic is to be remade and
it is not clear how much of it can be saved. Needless to
add that Cantorism and logistic are alone under considera-
tion; real mathematics, that which is good for something,
may continue to develop in accordance with its own prin-
ciples without bothering about the storms which rage out-
side it, and go on step by step with its usual conquests
which are final and which it never has to abandon.

534

THE MONIST.

THE TRUE SOLUTION.

What choice ought we to make among these different
theories ? It seems to me that the solution is contained in
a letter of M. Richard of which I have spoken above, to be
found in the Revue generale des sciences of June 30, 1905.
After having set forth the antinomy we have called Rich-
ard's antinomy, he gives its explanation. Recall what has
already been said of this antinomy. E is the aggregate of
all the numbers definable by a finite number of words,
without introducing the notion of the aggregate E itself.
Else the definition of E would contain a vicious circle ; we
must not define E by the aggregate E itself.

Now we have defined N with a finite number of words,
it is true, but with the aid of the notion of the aggregate
E. And this is why N is not part of E. In the example
selected by M. Richard, the conclusion presents itself with
complete evidence and the evidence will appear still stronger
on consulting the text of the letter itself. But the same
explanation holds good for the other antinomies, as is easily
verified. Thus the definitions which should be regarded as
not predicative are those which contain a vicious circle.
And the preceding examples sufficiently show what I mean
by that. Is it this which Russell calls the "zigzaginess" ?
I put the question without answering it.

THE DEMONSTRATIONS OF THE PRINCIPLE OF INDUCTION.

Let us now examine the pretended demonstrations of
the principle of induction and in particular those of White-
head and of Burali-Forti.

We shall speak of Whitehead's first, and take advan-
tage of certain new terms happily introduced by Russell
in his recent memoir. Call recurrent class every class con-
taining zero, and containing n+i if it contains n. Call

THE LATEST EFFORTS OF THE LOGISTICIANS. 535

inductive number every number which is a part of all the
recurrent classes. Upon what condition will this latter
definition, which plays an essential role in Whitehead's
proof, be "predicative" and consequently acceptable?

In accordance with what has been said, it is necessary
to understand by all the recurrent classes, all those in whose
definition the notion of inductive number does not enter.
Else we fall again upon the vicious circle which has en-
gendered the antinomies.

Now Whitehead has not taken this precaution. White-
head's reasoning is therefore fallacious ; it is the same which
led to the antinomies. It was illegitimate when it gave
false results ; it remains illegitimate when by chance it leads
to a true result.

A definition containing a vicious circle defines nothing.
It is of no use to say, we are sure, whatever meaning we
may give to our definition, zero at least belongs to the
class of inductive numbers ; it is not a question of knowing
whether this class is void, but whether it can be rigorously
deliminated. A "non-predicative" class is not an empty
class, it is a class whose boundary is undetermined. Need-
less to add that this particular objection leaves in force the
general objections applicable to all the demonstrations.

* * *

Burali-Forti has given another demonstration.3 But he
is obliged to assume two postulates: First, there always
exists at least one infinite class. The second is thus ex-
pressed :

#eK(K — iA) .D .u<vu.

The first postulate is not more evident than the prin-
ciple to be proved. The second not only is not evident, but
it is false, as Whitehead has shown; as moreover any re-
cruit would see at the first glance, if the axiom had been

•In his article "Le classi finite," Atti di Torino, Vol. XXXII.

536

THE MONIST.

stated in intelligible language, since it means that the
number of combinations which can be formed with several
objects is less than the number of these objects.

ZERMELO'S ASSUMPTION.

A famous demonstration by Zermelo rests upon the
following assumption: In any aggregate (or the same in
each aggregate of an assemblage of aggregates) we can
always choose at random an element (even if this assem-
blage of aggregates should contain an infinity of aggre-
gates). This assumption had been applied a thousand
times without being stated, but, once stated, it aroused
doubts. Some mathematicians, for instance M. Borel, reso-
lutely reject it; others admire it. Let us see what, accord-
ing to his last article, Russell thinks of it. He does not
speak out, but his reflections are very suggestive.

And first a picturesque example: Suppose we have as
many pairs of shoes as there are whole numbers, and so
that we can number the pairs from one to infinity, how
many shoes shall we have? Will the number of shoes be
equal to the number of pairs ? Yes, if in each pair the right
shoe is distinguishable from the left ; it will in fact suffice
to give the number 2n — i to the right shoe of the nth pair,
and the number 2n to the left shoe of the nth pair. No, if
the right shoe is just like the left, because a similar opera-
tion would become impossible — unless we admit Zermelo's
assumption, since then we could choose at random in each
pair the shoe to be regarded as the right.

CONCLUSIONS.

A demonstration truly founded upon the principles of
analytic logic will be composed of a series of propositions.
Some, serving as premises, will be identities or definitions ;
the others will be deduced from the premises step by step.

THE LATEST EFFORTS OF THE LOGISTICIANS. 537

But though the bond between each proposition and the
following is immediately evident, it will not at first sight
appear how we get from the first to the last, which we may
be tempted to regard as a new truth. But if we replace
successively the different expressions therein by their defi-
nition and if this operation be carried as far as possible,
there will finally remain only identities, so that all will re-
duce to an immense tautology. Logic therefore remains
sterile unless made fruitful by intuition.

This I wrote long ago; logistic professes the contrary
and thinks it has proved it by actually proving new truths.
By what mechanism ? Why in applying to their reasonings
the procedure just described — namely, replacing the terms
defined by their definitions — do we not see them dissolve
into identities like ordinary reasonings ? It is because this
procedure is not applicable to them. And why? Because
their definitions are not predicative and present this sort
of hidden vicious circle which I have pointed out above;
non-predicative definitions cannot be substituted for the
terms defined. Under these conditions logistic is not sterile,
it engenders antinomies.

It is the belief in the existence of the actual infinite
which has given birth to these non-predicative definitions.
Let me explain. In these definitions the word "all" figures,
as is seen in the examples cited above. The word "all" has
a very precise meaning when it is a question of an infinite
number of objects; to have another one, when the objects
are infinite in number, would require there being an actual
(given complete) infinity. Otherwise all these objects could
not be conceived as postulated anteriorly to their definition
and then if the definition of a notion N depends upon all the
objects A, it may be infected with a vicious circle, if among
the objects A are some indefinable without the intervention
of the notion N itself.

The rules of formal logic express simply the properties

538 THE MONIST.

of all possible classifications. But for them to be applicable
it is necessary that these classifications be immutable and
that we have no need to modify them in the course of the
reasoning. If we have to classify only a finite number of
objects, it is easy to keep our classifications without change.
If the objects are indefinite in number, that is to say if one
is constantly exposed to seeing new and unforeseen objects
arise, it may happen that the appearance of a new object
may require the classification to be modified, and thus it is
we are exposed to antinomies. There is no actual (given
complete) infinity. The Cantor ians have forgotten this,
and they have fallen into contradiction. It is true that
Cantorism has been of service, but this was when applied
to a real problem whose terms were precisely defined, and
then we could advance without fear.

Logistic also forgot it, like the Cantorians, and en-
countered the same difficulties. But the question is to
know whether they went this way by accident or whether
it was a necessity for them. For me, the question is not
doubtful; belief in an actual infinity is essential in the
Russell logic. It is just this which distinguishes it from
the Hilbert logic. Hilbert takes the view-point of exten-
sion, precisely in order to avoid the Cantorian antinomies.
Russell takes the view-point of comprehension. Conse-
quently for him the genus is anterior to the species, and
the summum genus is anterior to all. That would not be
inconvenient if the summum genus was finite; but if it is
infinite, it is necessary to postulate the infinite, that is to
say to regard the infinite as actual (given complete). And
we have not only infinite classes; when we pass from the
genus to the species in restricting the concept by new con-
ditions, these conditions are still infinite in number. Be-
cause they express generally that the envisaged object pre-
sents such or such a relation with all the objects of an in-
finite class.

THE LATEST EFFORTS OF THE LOGISTICIANS. 53Q

But that is ancient history. Russell has perceived the
peril and takes counsel. He is about to change everything,
and, what is easily understood, he is preparing not only to
introduce new principles which shall allow of operations
formerly forbidden, but he is preparing to forbid operations
he formerly thought legitimate. Not content to adore what
he burned, he is about to burn what he adored, which is
more serious. He does not add a new wing to the building,
he saps its foundation.

The old logistic is dead, so much so that already the
zigzag theory and the no-classes theory are disputing over
the succession. To judge of the new, we shall await its
coming.

HENRI POINCARE.

PARIS, FRANCE.

THE PHILOSOPHY OF RELATIVITY

IN THE LIGHT OF THE PHILOSOPHY OF SCIENCE.

Objectivity.

SINCE the dawn of civilization man has groped after
truth. He has investigated it ; he has pondered on it ;
he has made guesses and proposed hypotheses ; he has ap-
proximated truth by allegories, foreshadowing it in verse
and fable ; and since he began to count and to measure he
has reduced the results of his inquiry to exact statements.

All observations are necessarily subjective, but man
is not satisfied with subjective truth, he wants objective
truth and objectivity of statement is the ideal of science.

Is objectivity impossible? Must we abandon our ideal
of science ? It seems to us that science has more and more
in its various fields approached its ideal of objective truth.
Standard measures have been invented and perfected. Time
is measured by a pendulum of definite size, even apparently
trivial factors have been considered such as latitude and
altitude; and our precision machines testify to the in-
genuity of man's genius in his attempt to eliminate per-
sonal equations as much as possible. The reliability of
scientific computation has reached a marvelous degree, but
it is almost more astonishing that we are still dissatisfied
and that our measurements of minute fractions of the wave
lengths of light are no longer exact enough for our needs.

In the face of the enormous accomplishments of science
in approximating the ideal of objectivity, a new school has

THE PHILOSOPHY OF RELATIVITY. 54!

risen which goes so far as to deny all objectivity, and in-
sisting upon the truth of relativity, it would make us be-
lieve that objectivity is a phantom.

The relativity principle was first pronounced by Ein-
stein in the Jahrbuch der Radioaktivitdt (Vol. IV, pp.
411 ff., 1907). It was invented to account for certain diffi-
culties in the explanation of optical and electrical phenom-
ena by considering the relativity of the movements in a
system that is not at rest, called a disturbed system in con-
trast to quiet systems. In all quiet systems the common
laws of dynamics hold good and the proposition of the
relativity principle has been made for the sake of account-
ing for the laws of disturbed systems.

The principle of relativity is an a priori postulate from
which certain theorems are derived whose truth is to be
verified or refuted by experiment. Mr. Norman Camp-
bell says:1

"The principle is what is more often termed a 'theory'
— that is to say, it is a set of propositions from which ex-
perimental laws may be logically deduced. It can be proved
to be true or false in a manner convincing to everybody
only by comparing the laws so deduced with those found
experimentally; but a theory which never conflicted with
experiment might yet (as I hold) be judged objectionable
on other grounds, and, conversely, a theory which was not
in complete accord with experiment might yet be judged
satisfactory/'

Among the postulates of the principle of relativity there
is one, counted the second, which presents great difficulties.
It proclaims that "The velocity of light determined by all
observers who are not accelerated relatively to each other
is the same whatever may be the relative velocities of the
observer."

1 See "The Common Sense of Relativity" in The Philosophical Magazine
for April 1911, pp. 502 ff.

542

THE MONIST.

An unsophisticated thinker would naturally assume that
the velocity of light must be expected to increase or de-
crease according to the velocity of the observer. But the
relativist assures us that light is an exception; on his as-
sumption light is like a shadow whose motion depends upon
the motion of its body representing the observer. The
relation of the shadow to its body remains the same, how-
ever its body's (the observer's) velocity may change.

The question as to the velocity of light is a question of
physics, not of philosophy, and we will touch upon it later.
Here we will state only that the main objection to the
relativity principle is the inference which implicates our
objective ideal of science.

Not all the relativists agree on all points of their doc-
trine, and contradictory statements are not uncommon.
We can here only characterize the general tendency and
will not enter into the individual interpretations too closely.

Relativists try to avoid a difficulty which we grant
exists, but is not insurmountable. Idealists of former days
have used more subtle methods to dispose of the belief in
objectivity of things, of time, and of space. They have
produced only quibbles and the relativists have succeeded
no better ; only it is strange that the movement has origi-
nated among the physicists.

In a former article2 we have demonstrated the para-
mount importance of relativity, but for all that we see no
necessity for abandoning the old ideal of science. On the
contrary we feel inclined to insist on it more strongly than
ever. We do not deny the relativity of all existence
throughout and without exception, but we still cling to the
old scientific ideal of objectivity and we can not see that
the relativity principle, in the one-sided sense in which the
relativity physicists uphold it, is well established.

Having discussed in the article mentioned the part

""The Principle of Relativity," Monist, April, 1912.

THE PHILOSOPHY OF RELATIVITY. 543

which relativity plays in scientific method, we feel inclined
to add a few suggestions concerning the significance of
the recent movement among physicists who emphasize the
principle of relativity and prophesy that through it a new
era in the scientific interpretation of the world will have
to begin.

We have seen that many of the paradoxes which are
proclaimed by the relativity physicists disappear on close
inspection, for the contradictions resolve themselves into
purely verbal contrasts. The same object is not in itself
longer or shorter, but the result of measurement will be
different according to the conditions under which the meas-
urements take place. And further, although time can be
eliminated, although it may be treated as a function of
space, or even be treated as a kind of fourth dimension,
the conception of time will nevertheless still remain of
great convenience. The truth is that we must subsume
time and space under one common category which, with
Kant and other thinkers of well-established classical tra-
dition since the days of Aristotle, has been called "form."
We must always bear in mind the interrelation between
time and space and view the two as the forms of one and
the same reality. Time is the form of doing, of progressive
action, of change, of events, and space is the form of being,
of existence in its juxtaposition of parts. The former is
the order of procedure in which the latter is transformed.
Neither can be thought without the other, and the two are
one. The principle of simplicity requires us to consider both
in their interrelation. But for all that the traditional no-
tion of time still proves the best method for rendering
measurements of changes intuitively clear while an elimi-
nation of time as proposed by the Relativity Physicists is
apt to obscure the issue; and we come to the conclusion
that experience has not without good reasons found in the
proper terms "space" and "time" a very convenient, yea,

544

THE MONIST.

as it seems to me, the most appropriate, mode of represen-
tation.

It is strange that the relativity principle has been pro-
posed for the very purpose of approximating objective
truth with greater exactness, but instead of accounting
for inexactness or inaccuracies in results and for apparent
contradictions by taking into consideration the mistakes
in calculation on account of the shifting conditions of this
world which is a constant flux, a panta rhei, the leaders of
the new movement cancel the old ideal of science which
has guided us thus far and propose a new standard strongly
tinged with subjectivism, built upon the basis of the rela-
tivity of all existence.

All experience is a mixture of objectivity and subjec-
tivity : it is due to the interrelation between a sentient sub-
ject and the sensed objects. So far science has tried to
eliminate the subjective side, the personal equation, while
the relativity physicists deny the legitimacy of the ideal of
objectivity, or as they call it, the concept of the real. It
is true that in clinging to the facts of observation without
trying to eliminate the subjective elements and thereby to
unify our results in an objective statement, we simplify
our calculations, but it is very doubtful whether this proce-
dure can be generally applied to other than optical and elec-
trical phenomena. Relativists deem the theory justified if
they simplify their own line of labors. Mr. Campbell ex-
claims in his enthusiasm:

"Anything more beautifully straightforward it would
be hard to conceive. Not only is the result magnificently
simple, but it furnishes us with a mathematical instrument
of extraordinary power. In place of the elaborate calcu-
lations which have hitherto been necessary in dealing with
moving systems, all that we have to do now is to solve the
problem under consideration for the limiting case of infini-
tesimal velocity, and then effect a mere algebraical trans-

THE PHILOSOPHY OF RELATIVITY. 545

formation. The only objection that seems likely to be
raised is that the principle proves too much, that it appears
impossible that such far-reaching conclusions can be drawn
from such simple assumptions : the only difficulty, in fact, is
that the thing is too easy."

"The crudest arguments based on the oldest theory of
light lead to the conclusion that the rate of a clock as ob-
served by a certain observer must change with the relative
motion of clock and observer. For, it will be argued, the
observer does not see the clock 'as it really is at the mo-
ment/ but 'as it was a time T earlier, where T is the time
taken for light to reach the observer/ And on these lines
it is easy to show that the apparent rate of a clock moving
away from the observer with a velocity v is ( I — v/c)
times3 the rate of the same clocks observed at rest. It is
only the magnitude of the change concerning which the
two theories differ.

" 'Yes/ says our objector, 'that is all very well : of
course the apparent rate of the clock changes with motion,
but does the real rate change?' We immediately inquire
what the 'real rate' means. He is at first inclined to assert
that it is the rate observed by an observer traveling with
the clock, but when we inquire relative to what clock that
observer is to measure the rate he becomes uneasy. He
cannot compare another clock traveling with him, for if
the 'real rate' of one clock has changed, so has the 'real
rate' of the other ; and he cannot use a clock which is not
traveling with him, because he admits that he does not see
such a clock 'as it really is.'

"Pressing our inquiries, I think we shall get an answer
of this nature. 'If I take a pendulum clock to some place
where gravity is different, the rate of the clock will change.
It is a change of this nature which I call a change in the

8 c denotes the universal velocity whatever it may turn out to be. See ibid.
P. 508.

546 THE MONIST.

"real rate," and I want to know whether there is any
change of that kind, on the theory of relativity, when the
clock is set in motion/ Now why does our objector call a
change of the first kind a change in the 'real rate' ? The
reply is to be found in the history of the word 'real/ The
word is intimately associated with the philosophic doctrine
of realism, which holds that the most important thing that
we can know about any body is not what we observe about
it, but its 'real nature/ which is something that is inde-
pendent of observation.

Now, of course, a quantity which is wholly independent
of observation cannot play any part in an experimental
science, but there are quantities which are independent of
observation in the more limited sense that they are observed
to be the same by whatever observer the observation is
made. The term 'real' has come to be transferred from the
philosophical conception to such quantities. The 'real rate'
of the clock is said to change when it is transferred to a
place where gravitation is different, because all observers
agree that the rate of the clock which has been moved has
undergone an alteration relatively to that which has not
been moved.

"Now in the conditions which we are considering the
observers do not agree. If A and B, each carrying a clock
with him, are moving relatively to each other, they will not
agree as to the rate of either of their clocks relative to
A's standard or to B's standard or to any other standard.
The conditions which, in the case of the alteration of gravi-
tation, gave rise to the conception of a 'real rate' are not
present : in this case there is no 'real rate,' and it is as ab-
surd to ask whether it has changed as it would be to ask a
question about the properties of a round square. However,
some people, who in their eagerness to escape the reproach
of being metaphysicians have adopted without inquiry the
oldest and least satisfactory metaphysical doctrines, are so

THE PHILOSOPHY OF RELATIVITY. 547

enamoured of the conception of 'reality' that they refuse to
give it up. Finding that the observations of different ob-
servers do not agree, they define a new function of those
observations, such that it is the same for all observers, and
proceed to call this the 'real rate/ This function, according
to the principle of relativity, is $n' where n' is the rate of
the clock as seen by an observer relative to whom it is trav-
eling with the velocity v: according to that principle, if
we substitute in that function the appropriate values for
any one observer, the resulting number will always be the
same. So far no overwhelming objection can be raised."

What the relativists call "real" we would call objective,
and we deem the ideal of objectivity to be the goal of sci-
ence. Mr. Campbell has much to say on the concept of
reality :

"It is the great merit of the principle of relativity that it
forces on our attention the true nature of the concepts of
'real time' and 'real space' which have caused such end-
less confusion. If we mean by them quantities which are
directly observed to be the same by all observers, there
simply is no real space and real time. If we mean by them,
as apparently we do mean nowadays, functions of the di-
rectly observed quantities which are the same for all ob-
servers, then they are derivative conceptions which depend
for their meaning on the acceptance of some theory as to
how the directly observed quantities will vary with the
motion, position, etc. of the observers. 'Real' quantities
can never be the starting point of a scientific argument ; by
their very nature they are not quantities which can be de-
termined by a single observation : the term 'real' has always
kept its original meaning of some property of a body which
is not observed simply.

"All the difficulties and apparent paradoxes of the prin-
ciple of relativity will vanish if the attention is kept rigidly
fixed upon the quantities which are actually observed. If

548

THE MONIST.

any one thinks he discovers that that principle predicts
some experimental result which is incomprehensible, let
him dismiss utterly from his mind the conception of reality.
Let him imagine himself in the laboratory actually per-
forming the experiment: let him consider the numbers
which he will record in his note-book and the subsequent
calculation which he will make. He may then find that the
result is somewhat unexpected — to meet with unexpected
results is the usual end of performing experiments, — but he
will not find any contradiction or any conclusion which is
not quite as simple as that which he expected.

"There is one further point sometimes raised in con-
nection with the principle on which a few words may be
said.

"It is sometimes objected that the principle 'has no phys-
ical meaning/ that it destroys utterly the old theory of
light based on an elastic ether and puts nothing in its place,
that, in fact, it sacrifices the needs of the physical to the
needs of the mathematical instinct. That the statement is
true there can be no doubt, but the absence of any substitute
for the elastic ether theory of light may simply be due to the
fact that the principle has been developed so far chiefly by
people who are primarily mathematicians. It is well to ask,
can any physical theory of light be produced which is con-
sistent with the principle?

"The answer depends on what is meant by a 'physical
theory/ Hitherto the term has always meant a 'mechan-
ical theory/ a theory of which the fundamental propositions
are statements about particles moving according to the
Newtonian dynamical formulae. In this sense a physical
theory is impossible if the principle of relativity be accepted,
for the same reason that a corpuscular theory of light is
impossible, if the undulatory theory of light be accepted.
Newtonian dynamics and the principle of relativity are two
theories which deal in part with the same range of facts ;

THE PHILOSOPHY OF RELATIVITY. 549

they both pretend to be able to predict how the properties
of observed systems will be altered by movement. If they
are not logically equivalent they must be contradictory : in
either case an 'explanation' of one in terms of the other is
impossible. It can be easily shown that they are contra-
dictory: if the principle of relativity is true, Newtonian
dynamics must be abandoned."4

We start with "the facts of observation," and try to es-
tablish the objective state of things, called also "the real" ;
but relativists ignore the latter, and since every observer
has his own particular observation, they declare that there
is neither real time nor real space. The real is ruled out
from observation.

Suppose, however, that the clocks which the relativ-
ist observes wrere the heartbeats of the relativist himself
and the observer were the diagnosing physician, would the
relativist insist that the physician had better drop out of
sight the notion of reality, that there is as little sense in
asking for "the real rate" of his heartbeat as it is absurd
"to inquire whether, if all triangles had four sides, all
circles would be square"?5 If we can not attain an abso-
lutely correct objective statement, we keep at least the
ideal in view and this ideal is not an empty dream.

The relativity principle is a mathematical view of cer-
tain problems worked out for the sake of most minute
measurements; and the attitude of the relativists is stern.
If the facts can not be clearly represented by it, the worse
for the facts, and if the physicists declare that their phys-
ical theories are incompatible with it, a new brand of physi-
cists has to be manufactured who will inaugurate a rela-
tivist reform in physics.

*This conclusion is reached by Sommerfeld in a paper, Ann. d. Phys.,
XXXIII, p. 684, etc. (1910).

8 See Campbell, loc, cit., p. 509. The comparison is not appropriate.

550

THE MONIST.

Primary Concepts.

The relativity problem would never have originated
had the philosophy of science been clearly and distinctly
understood by physicists, but they have familiarized them-
selves very little with even the problems, let alone reached
proper solutions which explain the elementary concepts of
our scientific terms, the difference between substance and
form, between energy and matter, and the significance of
the purely formal sciences.

As mathematicians are in the habit of starting with ax-
ioms, so the relativists begin with postulates and these
postulates come in collision with the primary concepts such
as have been formulated among the orthodox physicists
and mathematicians of the present day.

A truly scientific view will brook neither axioms in
mathematics, nor postulates in philosophy, nor primary
concepts in physics.

There has been much talk about primary concepts, and
arguments have been offered why time is not a primary
notion or why we should let it pass as such. The truth is
that time as well as space are two methods of describing
definite relations. Time is not so much a fourth dimension
of space, though we might look upon it as if it were such,
time is the measure of motion and space is the scope of mo-
tion. Both time and space are presupposed in the idea of
motion. There is no time in itself, there is no space in
itself. What Newton and others with him call absolute
space is "space conception" and what they call absolute
time is "time conception." Such are the ideas which by
pure deduction on a priori arguments, physicists form of
time and of space, just as mathematicians formulate the
general conception of numbers, of distances and of other
relations, angles, areas, etc.

The idea of primary concepts is a very unfortunate de-

THE PHILOSOPHY OF RELATIVITY. 551

vice to lay a foundation for science. The faults of this
method will not show so long as specialists are concerned
about specialist problems, but the carelessness of taking
anything for granted shows itself as soon as any problem
broadens out into a general inquiry when its connection
with universal problems is questioned. Such primary con-
cepts are assumed to be undefinable and self-evident. That
opens the door to an arbitrary interpretation as to the na-
ture of space and time and energy, and gives a wide berth
to mysticism.

Science brooks neither axioms nor primary concepts.
Science starts with experience ; it quarries out of experience
the stones of the purely formal sciences which furnish all
the methods of both common sense knowledge and scien-
tific inquiry. The most general characteristic of experience
is activity. Activity manifests itself in change. Change
implies motion; it means either change of place, i. e., mov-
ing from here to there, or change of combination, viz., a
moving of particles among themselves. Change inter-
feres with existing relations, it modifies the old interrela-
tions and establishes new interrelations.

The nature of relations in one terse term is called form.
The word "form" comprises both outer shape and inner
structure, and all interrelations of things as well as thoughts
can be determined by the laws of pure form, arithmetic,
geometry, logic, etc. Under all circumstances change mod-
ifies relations and means "transformation." There is a
transformation in the juxtaposition of things or their parts,
and there is a succession of events. The scope of the former
we call "space," of the latter "time"; or better from the
former we deduce our notion of space, from the latter our
notion of time.

Physical inquiry is not helped by calling certain fea-
tures of experience "primary concepts" and least of all
(as has been done) should space, time and force, — these

THE MONIST.

highly complicated constructions of a priori thought — be
beclouded by this mystifying name. Both time and space
are features of the form of existence, and force is a general
term for that feature of existence which marks its activity
as motion, viz., as change of place, or rather as that which
causes changes and is measured by the resistance over-
come.

If we adopt the relativist principle to ignore the scien-
tific ideal of objectivity, i. e., if we define size as the result
of measurement and moments of time as determinations of
measurement by units of duration, without regard to the
ideal of coincidental happenings, and a common standard
of time, we may produce incredible statements against
which common sense rebels, and Professor Magie in his
Presidential Address,6 delivered before the Physical So-
ciety and Section B of the American Association for the
Advancement of Science, at Washington, D. C. (December
28, 1911), says in comment thereof:

"A description of phenomena in terms of four dimen-
sions in space would be unsatisfactory to me as an explana-
tion, because by no stretch of my imagination can I make
myself believe in the reality of a fourth dimension. The
description of phenomena in terms of a time which is a
function of the velocity of the body on which I reside will
be, I fear, equally unsatisfactory to me, because, try I ever
so hard, I can not make myself realize that such a time

is conceivable I do not believe that there is any man

now living who can assert with truth that he can conceive
a time which is a function of velocity or is willing to go to
the stake for the conviction that his 'now' is another man's
'future' or still another man's 'past.'

"One of the members of this society, recognizing our
present inability to conceive of relative time, and conceiv-
ing our intuitions of space and time to be the result of

6 Published in Science, February 23, 1912, pp. 281 ff :

THE PHILOSOPHY OF RELATIVITY. 553

heredity operating through many generations of men who
lacked the light of relativity, once proposed to me that
every one who could get even a glimmer of the notion of
relative time should persistently exercise his mind therein
and teach it to his students, in the hope that in a few gene-
rations the notion would emerge with the force of an in-
tuition. It would not be fair to leave the impression that
he was solemnly serious when he made this suggestion."

Form (i. e., relativity) is, as much as matter and energy,
an ultimate generalization and may be called a fundamental
concept (not a primary concept), and all the work of sci-
ence is a tracing of transformations.

It is essential for the measurement of space and time to
employ as measures uniform units, for space of distance
and for time of duration. In the same way we need uni-
form units to measure force.

Besides a quantitative analysis of experience, there is
a qualitative analysis which traces such transformations
as build up parts into a higher unit, whereby through the
interrelation or the interaction of the parts a new thing
originates possessed of properties which are absent in the
parts before their combination.7

The law of change is called causality. Cause is the
motion which starts the process of transformation; effect
is the result of the change ; and reason is the general rule
(formulated as a so-called law of nature) from which we
understand why the cause must have this effect.8

The so-called law of the conservation of matter and
energy is a deduction from the law of causality, which can
be made as soon as we understand that all happenings are
transformations, for if all changes are transformation, the

7 See for instance the author's exposition of the nature of quality in The
Monist, Vol. XV, p. 375. See also Philosophy of Form, p. 12.

8 This has been repeatedly discussed, e. g., in the author's Fundamental
Problems, pp. 79 ff.

554

THE MONIST.

amount of existence, its that, remains the same, only its
form changes.

While investigating the several problems of our ex-
perience, scientists assume that they deal with real occur-
rences and thus they implicitly grant the that of existence,
popularly denoted "matter" and "energy," viz., thingish-
ness (or with a Latin term "reality") and actuality. The
existence of ether is but an extension of the concept matter
and so physicists have so far believed in the existence of
ether ; but the relativity physicists, in their anxiety to pro-
pound original ideas, deny the existence of ether. Says
Prof. William Francis Magie in his above mentioned Presi-
dential Address:

"The principle of relativity in this metaphysical form
professes to be able to abandon the hypothesis of an ether.
All the necessary descriptions of the crucial experiments
in optics and electricity by which the theories of the uni-
verse are now being tested can be given without the use
of that hypothesis. Indeed the principle asserts our inabil-
ity even to determine any one frame or reference that can
be distinguished from another, or, what means the same
thing, to detect any relative motion of the earth and the
ether, and so to ascribe to the ether any sort of motion;
from which it is concluded that the philosophical course is
to abandon the concept of the ether altogether. I may
venture to say that in my opinion the abandonment of the
hypothesis of an ether at the present time is a great and
serious retrograde step in the development of speculative
physics. The principle of relativity accounts for the nega-
tive result of the experiment of Michelson and Morley,
but without an ether how do we account for the interference
phenomena which made that experiment possible? There
are only two ways yet thought of to account for the passage
of light through space. Are the supporters of the theory

THE PHILOSOPHY OF RELATIVITY. 555

of relativity going to return to the corpuscles of Newton ?
There is choice only between corpuscles and a me-
dium, and I submit that it is incumbent upon the advocates
of the new views to propose and develop an explanation
of the transmission of light and of the phenomena which
have been interpreted for so long as demonstrating its
periodicity. Otherwise they are asking us to abandon what
has furnished a sound basis for the interpretation of phe-
nomena and for constructive work in order to preserve
the universality of a metaphysical postulate."

The concepts substance, i. e., matter or mass, and en-
ergy are ultimate generalizations as much as form, but they
are very different from form. We could do without the
words "matter" or "ether" by the use of some other indi-
cation to be introduced in our formulas which denotes real-
ity; but that would not disprove the truth of the popular
view, which describes every concrete bodily existence as
material, nor is it likely that the old method of nomencla-
ture will be rendered antiquated or erroneous.

We must not forget what matter means. Matter is a
word which denotes that quality of objects which all of
them have in common, viz., objectivity. An object is a
thing that is objected to us, that offers us resistance, that
impresses itself upon our existence and thereby affects our
senses, and by objectivity we understand the general prop-
erty of concrete existence, the that of experience, or its
reality, viz., its thingishness. To deny the reality of the
real, the thingishness of things, is as ridiculous as the
opposite mistake, i. e., to think of reality, or objectivity,
or of matter as a mysterious entity in itself. There is no
reality in abstracto, for every that of existence is of a
definite form which acts somehow, and the activity of things
we call their actuality, or, as we call it in physics, energy.

The same problem presents itself in the domain of the
phenomena of ether, i. e., of light and electricity. There

556

THE MONIST.

are some good reasons to assume that concrete matter has
originated by a contraction or condensation of a more prim-
itive substance which for all we know may prove to be the
luminiferous ether, that thin substance which has been as-
sumed to be the mediuni of light and electricity. If it is
claimed by modern physicists that the principle of relativity
disposes of the ether, that we no longer need it and can dis-
card a belief in it as a superstition, that all physical phe-
nomena can be accounted for without the assumption of
an ether, we confront the same situation as in the theory
of energetics, where the claim is made "There is no matter,
all is energy."

The truth of this position, so far as we freely grant it,
is this, that all scientific explanation describes the trans-
formation of things; it traces the changes that take place
according to the laws of form (mathematics and mechan-
ics). In experience we are confronted with the fact that
it is so, but the scientist inquires into the factors how it
has become so, how it acts, and how it changes. By describ-
ing the how in formulas (so-called laws of nature) we de-
note the several factors with algebraic letters, such as g —
gravity, t — seconds of time, d = the distance traversed
by a falling body and v = the velocity of the fall, etc., and
express their interrelation in equations, as

v = gt and d = l/2gtz.

By this method the essential features of natural phe-
nomena are expressed in symbols, and he who has been
initiated into the secret meaning of the symbols and the
method of using them, will be able to predict the course of
events if he is in possession of the necessary data.

What we here call with one word "essential" Kirchhoff
characterizes in two words "most complete and most terse,"
or to use the common version "the most exhaustive and
simplest." We deem our term preferable, and we under-

THE PHILOSOPHY OF RELATIVITY. 557

stand by "essential" all that which is efficient to produce the
result, not more, not less.

We speak of the three laws of Kepler and of the con-
densed statements of the law of gravitation as "formulas,"
and this term truly expresses the nature of these general-
ized descriptions of certain types of uniformities. They are
reductions of events to their purely formal (i. e., purely
relational) conditions, and these purely formal conditions
are the determinant (i. e., the causative) factors in all pos-
sible phenomena of a special type.

This is not a new truth. How old it is may be inferred
from the Greek term "formal"9 which in its etymology
means "the causal" or "the causative" because the Greek
philosophers describe the formal factors as efficient in cau-
sation.

When we have traced the essential factors of a certain
type of changes, the scientist's work is finished. Whether
mankind will ever be able to complete a scientific compre-
hension of the world in all its details, must be regarded as
doubtful, but wherever science has succeeded in discovering
the essential factors and has reduced them to formulas, we
have been enabled to offer for every such phenomenon a
satisfactory explanation.

This procedure affords us an insight into the reason
\vhy the course of a certain phenomenon must be so, why
it can not be otherwise, and in this procedure the that is the
basis, the how is the method of cognition. There is no ex-
planation possible for the that, for the reality of the real,
for the actuality of the fact; all explanations refer to the
hozv. The that is a brutal fact, and the ultimate goal of
science is the how, the answer being the formulation of
laws of nature which explain to us by a use of the law of
pure form that under given circumstances definite trans-
formations will take place. Knowledge of the laws of na-

0 rb a/Ttw5« derived from a-lria. rr cause.

558 THE MONIST.

ture helps man to adapt himself to nature and also to adjust
his surrounding natural conditions to himself.

In our explanation we can omit the that as a matter of
course, for it is understood that reality is real. We can
describe the purely formal relations only, which are the
essential part of explanations. There is no sense in ex-
plaining the that. We have simply to state whether or not
a formula covers actual facts, but to deny the that and say
that there is only a how the world wags, but there is no
world, seems to us a proposition that misconceives the situ-
ation.

We must not forget that such a word as substance, de-
noting here both "matter" and "ether" or existence in gen-
eral, is a term that stands for objective reality. Ether is
the that of the phenomena of electricity and light, as matter
is the that of bodily objects, declaring that they are real,
that they are concrete, and the term "substance" covers
any kind of existence, it embraces both matter and ether
or whatever the ultimate world-stuff may be called. There
is no sense in denying their actuality, and all that may be
meant by such a denial can only be either the redundancy
of an express declaration that the formulas of physics refer
to real processes, or a denial of ether or of matter as exist-
ences in themselves apart from their manifestations in defi-
nite configurations or modes of motion — a proposition
which nowadays no one will seriously dispute.

A denial of the existence of substance (of matter and
ether) is a purely verbal quibble. We might as well deny
the existence of energy and declare that there is no energy,
that there are only changes of place. The truth is that the
faculty of existence which manifests itself in changes of
place is called energy. We must not conceive of energy

as something in itself.

* * *

I am told that my own view is the gist of the principle

THE PHILOSOPHY OF RELATIVITY. 559

of relativity, and if that be true, I would gladly hail a phi-
losophy of relativity as another name for the philosophy of
science. I have myself characterized the philosophy of sci-
ence as a philosophy of form, and form denotes the re-
lations in their totality. However, I would add that the
system in which I have formulated this philosophy of sci-
ence is simpler than the world-conception of the relativity
physicists, besides it rests on a more solid foundation and
is absolutely free from paradoxes.

While I deny that we can dispense with the idea of
objectivity (be it called matter, or ether, or substance) I
claim that we need make no mention of it in our formulas.
In this sense we can dispense with the mention of ether.
While I would not take the several paradoxes of time and
space as serious and deny their objective truth, I grant
that by a little confusion of thought in calling time or space
relations the results of our different measurements, we can
legitimately produce these paradoxes by exhibiting the in-
evitable discrepancies which originate through measure-
ments from different standpoints as objective contradictions.
Finally I consider it the ideal of a scientific philosophy
to reduce all possible occurrences to relations, to resolve
them into questions of form, to look upon them as trans-
formations, and therefore I say that the ultimate aim of
science is to describe everything in formulas. I see no ob-
jection to the relativist claim that this is a postulate of sci-
ence. In fact, I deduce this postulate directly from my
conception of reality which presents itself everywhere in
our experience as transformation. Thus we would justify
the principle of relativity on the basis of the old traditional
basis of exact science.

The main claim of the relativists is based upon their
simplification of the electromagnetic equations, and this is
granted even by the adversaries of the principle of rela-
tivity. Professor Magie says:

560 THE MONIST.

"It is surely true that if it were not for this demand of
simplicity, immediately attainable and at present expressed
in the electromagnetic equations, the chief incentive to the
development of the theory of relativity would be wanting/'

The one simplification of formulas is attempted by cer-
tain relativists by a generalization of time and space into
a higher four-dimensional system, and they call it a four-
dimensional space. We may note incidentally that Wag-
ner's Parsival has anticipated the doctrine of relativity,
for in his search he utters the mysterious words: "Zum
Raum wird hier die Zeit!" (Into space here changeth
time!) The relativists might as well have called their
four-dimensional space a four-dimensional time. We ab-
stain from giving it a name, but subsume time and space
under one and the same category as "form" which enables
us to view time and space as two inseparable factors of the
cosmic system of interrelations, and we deem it wise to re-
member that they are different. If the relativity physicists
have this in mind and do not mean ulterior mystifications,
I would not hesitate to join their ranks on this point.

* * *

We may add one more comment about simplification.
Logical possibilities are wider than actualized reality. Re-
ality is one instance among many others which are not
actualized. The fictions of fairy tales, of Gulliver's Trav-
els, and of religious myth are instances of it. But in the
domain of pure logic even actually absurd conditions pa-
rade as legitimate potentialities. Actual space has three di-
mensions, but metageometricians have invented more-di-
mensional spaces. Why not ? We have in the construction
of purely logical systems the undeniable right to general-
ize into the not actualized logical possibilities and mathe-
maticians can not be restrained from building up a pange-
ometry. While Euclidean space is homaloidal, they may

THE PHILOSOPHY OF RELATIVITY. 561

create all kinds of curved spaces, which are all legitimate
before the tribunal of pure logic, if they are but consistent
in themselves. The main gain derived from such construc-
tions which will naturally appear to the average man of
average common sense as gratuitous, if not positively non-
sensical, consists in rising to a higher level and understand-
ing from this higher point of view the actualized reality
better than if he remains on the terra firma of a limited
sense-experience.

It might help our comprehension of causality as a trans-
formation according to the laws of form to conceive the
chain of causation as reversible, that the condition of causes
are turned into effects and that the final factors that bring
about the effect become the causes. This view has been
humorously worked out by Fechner who for this purpose
assumes that the pendulum of events will go on for a while
in the direction it takes now, but the time will come when
it will swing back. And then it will appear to us as quite
natural and necessary that the decayed and waste material
from fields and polluted rivers pass into our bodies and are
changed in our bowels into juice to go forth from our
mouths on the dinner table as lovely fruit or cheese, with
bread and butter, and as roast venison or fish to go back
and constitute useful parts in the revived animal. It would
please us to see all this come about and the thought of the
resurrection of the lamb under the butcher's knife would
demonstrate that there is a purpose in the law of causation.
We would be accustomed to the outcome and deem it
natural. In fact some notions of an inverse world order
in the golden age when the lamb will feed on the wolf, when
the deer will hunt the hunter, when the rich shall be poor
and the poor rich, when the miserable will be comforted
while the fortunate will be tortured has now and then re-
ceived serious support in the religious hopes of the dis-
inherited classes of mankind, and we may find in the New

562 THE MONIST.

Testament an echo of this belief in those traditions which
come down to us from Ebionite sources, the parables of the
foolishness of the rich and the benediction of the poor.
Dives goes to Hell while Lazarus is carried by angels to
Abraham's bosom. Abraham says in Luke xvi: 25 : "Son,
remember that thou in thy lifetime receivedst thy good
things, and likewise Lazarus evil things: but now he is
comforted, and thou art tormented." No mention is made
that Dives was wicked and that Lazarus was good; the
only argument is that the other world must be reverted in
its order.

A view of this kind which generalizes the mechanical
constitution of the world and sees the possibility of an in-
verted causation, just as an engine may be reversed, may
widen our comprehension and simplify our formulas of
moral action, but we need not for that reason believe in
its actualization. It is simply an instructive lusus imagina-
tionis, an ingenious and helpful fiction — like our conception
of four-dimensional space.

The mathematician who limits his studies to the Euclid-
ean plane will understand his problems better if he becomes
familiar with the theorems of stereometry, or if he views the
figures of plane geometry as projections; or again if he re-
gards a certain set of curves as conic sections. And further
many problems of stereometry find a simpler formulation
if viewed from the more comprehensive, though purely
imaginary, view-point of a four-dimensional geometry. All
this indicates that the simplifications of which the relativity
physicists boast, may be (and I am inclined to believe that
they are) very harmless. For all I can say, judging merely
from the acceptance they have found, they must be true,
but I can not see why they should be subversive of the sci-
entific world-conception of the past.

A peculiar view of time which has been proposed in all
seriousness, although common sense might consider it as

THE PHILOSOPHY OF RELATIVITY. 563

absurd, is the concept of time and space as consisting of
discrete ultimate units. Do not our years, and days, and
our hours too begin at definite moments ? We become fifty
or sixty years old suddenly with the beginning of a definite
minute, According to this, time would run in jerks like
the jumping second hands, and it would ultimately consist
of infinitesimally small units of duration. Space also would
be stippled and not continuous. Every motion would have
to proceed in hopping from spot to spot, and the surface of
a plane would be not unlike a half-tone picture which pro-
duces the impression of a continuous level but consists in
reality of different dots more or less deeply tinged with
ink. Such conceptions of time and space are quite con-
ceivable although our classical and well-established views
of both present them as continua. If space and time were
actual entities endowed with positive qualities, if they were
not merely potentialities of motion, a scope in which we
move about, we could discover the nature of space by ex-
periment. However, as they are constructions made in the
abstract domain of anyness we should not refuse to con-
sider seriously all kinds of propositions as to the nature of
time and space.10

In comment on theories of this kind we would say that
duration is continuous, but time consists of discrete units
of duration ; and again the scope of motion shows us an un-
interrupted expanse while geometry exhibits definite lines

10 The present number of The Monist contains an article on "Atomic
Theories of Energy" by Mr. Arthur E. Bostwick, which will prove of great
interest even to those who do not accept this theory. In comment we would
say that Mr. Bostwick's defense of an atomic theory of energy is certainly
true of definite amounts of energy, and his theory holds good also in his
comparison of energy to amounts of money values deposited in a bank account.
If deposits were made in specie, we could trace every dollar of a deposit. It
is true we can not do so, but this we can not do only because no one cares to
receive definite and individual coins, but is satisfied with money in any form.
Therefore the bank is like a reservoir of water which receives and gives out
water as it happens to come. The bank gives credit for amounts received and
pays out amounts according to request. Thus the individual coin is lost sight
of as the many drops of water are definite and concrete masses, and every
dollar in a bank represents some concrete value somewhere.

564 THE MONIST.

of definite direction and of definite length. Geometrical
space in its classical Euclidean form is not stippled, never-
theless every construction is particular. Geometrical points
have no extension, but they possess a definite location, be-
ing determined, e. g., by two crossing lines. Thus space is
not the totality of all points, but the totality of our scope
of motion and anywhere in space points may be laid down.
In a word: Time and geometrical space are constructions
invented for the purpose of making measurements possible
in a scope of potentialities.

Actual existence is always definite, pure forms however
as well as purely formal thoughts, are always potential.

It seems as if the beginning of actuality must consist
in establishing something that is limited and concrete. In
this way it appears plausible that a potential world would
be continuous as an ocean of pure ether might be, but
an actual world ought to consist of a group of units, of
atoms, of definite particular specks of existence endowed
with definite amounts of energy, and we ought to be able to
trace every definite amount of existence through all the
changes which in the process of evolution it will undergo;
and this ought to be true as regards every amount of both
matter and energy.

SOME PHYSICAL PROBLEMS OF RELATIVITY.

The physical problems presenting themselves in the ex-
periments which have become connected with the move-
ment of relativity do not seem to have any direct bearing
on the principle of relativity itself. Relations are of a
purely formal nature and relativity therefore belongs to
the same kind of knowledge as arithmetic, geometry and
logic. Relativity can and must be applied to physics just
as much as there is an applied mathematics, but as the
Pythagorean theorem is independent from its applications

THE PHILOSOPHY OF RELATIVITY. 565

in experience, so applied relativity can neither establish
nor refute the principle of relativity. This is true above all
of the well-known and most important Michelson-Morley
experiment.

The instrument made in Berlin by Schmidt & Haensch
was so delicate that it was of no use in Berlin, and even
when placed upon the foundation for the pier of the equa-
torial in the Astrophysical Observatory at Potsdam the
fringe of interference rings disappeared by stamping upon
the pavement at a distance of about 100 meters. Every
detail of consequence was taken into consideration, not only
the motion of the earth through the ether but also the
motion of the whole solar system towards the constellation
of Heracles. The expansion of the brass arms of the in-
strument through a change in temperature, and also the
bending of the arms through rotation were duly considered
and the difficulties arising therefrom met. A scale ruled
on glass was employed in order to dispense with the mi-
crometer screw which here proved useless. Yellow light
was used, because its wavelength is least difficult to meas-
ure.

If the ether is at rest while the earth moves through
it, the time required for light to pass from one point to
another on the earth's surface would depend on the direc-
tion in which it travels. Two pencils of light that travel
over paths at right angles to each other will interfere; the
one traveling in the direction of the earth's motion will
travel 0.04 of a wave length farther than it would have
done were the earth at rest, while the other pencil at right
angles to the motion of the earth would not be affected.
The results of Professor Michelson's experiment are neg-
ative. He found very small displacements in the fringes of
his ray of light, so small that they must be accounted as
mere errors of the experiment. While we ought to expect

566 THE MONIST.

a displacement of 0.05 we have only such as lie between
0.004 and 0.015. Professor Michelson says:11

"The interpretation of these results is that there is no
displacement of the interference bands. The result of the
hypothesis of a stationary ether is thus shown to be in-
correct, and the necessary conclusion follows that the hy-
pothesis is erroneous.

"This conclusion directly contradicts the explanation
of the phenomenon of aberration which has been hitherto
generally accepted, and which presupposes that the earth
moves through the ether, the latter remaining at rest."

In another article Professor Michelson states his re-
sult thus:12

"The luminiferous ether is entirely unaffected by the
motion of the matter which it permeates."

Professor Michelson has varied the conditions of his
experiment by trying whether deviations could be detected
through a change of level, by throwing pencils of light
upward and by repeating it at different hours of the day,
but the displacements remained insignificant. One of Pro-
fessor Michelson's articles ends thus:13

"In any case we are driven to extraordinary conclu-
sions, and the choice lies between these three :

"i. The earth passes through the ether (or rather allows
the ether to pass through its entire mass) without appre-
ciable influence.

"2. The length of all bodies is altered (equally?) by
their motion through the ether.14

n "The Relative Motion of the Earth and the Luminiferous Ether" in The
American Journal of Science, Vol. CXXII, page 128.

12 "Influence of Motion of the Medium on the Velocity of Light," in The
American Journal of Science, Vol. CXXXI, page 386.

18 "The Relative Motion of the Earth and the Ether," The American Jour-
nal of Science, Vol. CLIII, p. 478.

14 This would be the case according to the theory of H. A. Lorentz, whose
views are mainly presented in the Encyclopadie der math. Wissenschaften.

THE PHILOSOPHY OF RELATIVITY. 567

"3. The earth in its motion drags with it the ether even
at distances of many thousand kilometers from its surface."

Another article by Professor Michelson on the same
subject is published in The American Journal of Science,
Vol. CXXXIV, p. 333-

What this famous experiment has to do with the prin-
ciple of relativity except in a most general way, is not yet
clear to those who have not joined the ranks of the rela-
tivity physicists; but the relativity physicists insist very
vigorously and dogmatically that it proves, or at least
favors, their theory. Professor Michelson himself has not
joined their ranks, though he recognizes the difficulties
of the situation.

It is strange that Michelson's experiment seems to
stand in contradiction to another and older experiment
made first by Bradley, which is known as the aberration
of light. If the earth passes through the ether with its
own velocity (e) while the rays of the sun come down
upon the earth with the velocity of light (/) there ought
to be a deflection of light amounting to e/l, viz., the veloc-
ity of the earth divided by the velocity of the light in its
path from the sun towards the earth, and though this rela-
tion is very small, it has actually been observed and de-
termined to amount to a trifle over twenty seconds.

This conclusion which could be anticipated according
to the logic of mechanics seems to be contradicted by
Michelson-Morley's experiment in which the attempt is
made to measure with a ray of light the motion of the earth
while passing through the ether.

The discrepancy between the two experiments will per-
haps find a proper explanation in the proposition that if
the source of light lies outside the earth as in the case
of the rays of the sun, they will show the deflection. As
is to be expected they would come down in straight lines
like raindrops falling in an absolutely quiet air which

568 THE MONIST.

would be caught by a moving body as if they came down
at an angle; but if the source of light moves along with
the earth there would be no difference whichever way they
turn, first towards the east or first towards the west, or at
right angles, and the sources of the light would partake of
the acceleration of the earth so as to show no difference,
as raindrops dripping down within the car would fall down
in straight lines from its top to the floor, assuming that the
doors and windows of the car are hermetically closed and
there be no draft which would deflect their perpendicular
dripping.

It almost seems as if some ether were carried along
by the earth to a considerable distance beyond its sur-
face while the other ether in outer space would remain at
rest, but it would be bold for any one but a specialist to
venture the proposition of any theory on so new a subject
of which few facts only have been ascertained. Yet most
assuredly the topic under investigation has nothing to do
with the principle of relativity, unless relativity is a mis-
nomer for the phenomena attributed to the luminiferous
ether.

The question of relativity is a philosophical problem,
but the Michelson-Morley experiment is of a purely phys-
ical nature, and so we must expect that the last word as
to its explanation should be given by physicists.

The other experiment which is assumed to verify the
principle of relativity is the one first made by Kauffmann,
and afterwards repeated in a modified form by Bucherer.
This experiment too has little or nothing to do with rela-
tivity. On the contrary it seems to prove the existence of
something absolute for it reaches a limit of velocity.

There is at present a tendency in the world of thought,
noticeable in pragmatism and other anti-intellectual move-
ments, which seems to annihilate the very existence of
objectivity, and with it science, man's endeavor after a

THE PHILOSOPHY OF RELATIVITY. 569

purely objective cognition. Everything is relative, and the
general belief has spread that an absolutely objective de-
scription is impossible. To speak of the size of objects
seems to have lost its sense, for size has become to the
present generation merely the result of measurement, and
thus an objective determination is in some quarters looked
upon as a superstition of prescientific tradition, an inheri-
tance from the dark ages. But it is not true that there is
no objectivity, for one of the greatest accomplishments of
Michelson was the establishment of a definite measure by
calculating the size of a meter in wave-lengths or red
cadmium light in a vacuum. The waves of light are ab-
solutely definite, and thus we have here a result of measure-
ment in truly objective terms. If the Kauffmann-Bucherer
experiments prove, as is claimed, that an increase of veloc-
ity means an increase of mass and that the limit which is
reached is the velocity of light, we only learn that rela-
tivity is not without bounds, and that on the contrary a
climax is reached which can not be surpassed. The high-
est velocity is the velocity of light.

The conclusion that the highest velocity is the velocity
of light seems to be contradicted by the facts of gravitation
for according to the Newtonian theory gravitation is pos-
sessed of a practically infinite velocity in that the gravity
of the sun exercises its influence upon the planets without
any perceptible difference of time. But this is no object-
tion, for consider : The action of gravity formulated in the
well-known law of falling bodies and of their acceleration
which describes true motions is very slow in comparison
to the velocity of light. The influence which is exercised
in the strain between two gravitating bodies, say between
the moon and the earth, is not a motion at all, but a con-
dition, and this condition is the same between the two cen-
ters of the thus interrelated bodies. It is a state of tension
and there is no transference of a wave motion either from

57O THE MONIST.

the moon to the earth or from the earth to the moon. The
tension is simultaneous. The misconception seems to rise
from the error that there are two bodies and there is a
third item which manifests itself as a passing from the
one to the other under the name of gravitation. We must
view the whole system as one field of action in which sev-
eral bodies in motion are balanced among themselves ac-
cording to their mass. Their mutual attraction is not
transferred motion but a simultaneous interaction. New-
ton retarded the general acceptance of the law of gravita-
tion, first definitely proposed by Hooke, for eighteen long
years because he could not make up his mind to believe in
an actio in distans, and when he was finally convinced, he
still expressed his misgivings how to overcome this objec-
tion, but is there any actio in distans at all? Is not the
whole system of the universe an interrelated whole and
does not a center of gravity (howsoever it may have origi-
nated) extend so far as its stress reaches? Where its
strain produces a tension, there it affects its surround-
ings. If we look upon the phenomena of gravitation in
this light we need not make the fantastical assumption
that gravity is possessed of an infinite velocity.

The relation between the increase of velocity and the
increase of mass promises to throw light on the ultimate
constitution of matter, but the result of the experiment
is only the first step to a solution of this tremendous prob-
lem, concerning which at the present stage of science we
can have only vague suggestions. When the man appears
who can read the facts aright, he may be able to point out
how by a mere stress the aboriginal world-stuff which,
for all we know, may be, or even must be, the ether, pro-
duces a tension within this mysterious infinitely elastic
and incredibly thin substance, and the tension between two
centers of such contraction would, like the strain between
nodes within thin tridimensional rubber, act in all direc-

THE PHILOSOPHY OF RELATIVITY. 571

tions according to the Newtonian formula of gravitation, as
being directly proportional to the product of their amounts
of contraction, and inversely proportional to the square
of their distance between two centers. Thus the origin of
matter would be due to an unknown force which with a
velocity only inferior to the velocity of light would drive
infinitely small corpuscles around in a whirling dance with
such a regulated speed that conglomerated multitudes of
such whirls would appear to us as solid masses.

Here again we would be confronted by an ultimate
limit. We would discover that objective reality, our world
of matter in motion, is built up of ultimate particles; or
perhaps better, of ultimate activities, that below the atom
there are smaller units, the hypothetical electrons, which
may be characterized as centers of force, and that they are
due to condensation which produces the phenomena of
gravitation. All further phenomena of physics and chem-
istry would have to be explained as the result of these ele-
mentary actions.

Formerly thinkers were inclined to see infinity all
around. They thought of the atomic structure not only
as infinitesimally small, but also as truly infinite ; the mole-
cules being analyzable into atoms and the atoms again
into still smaller units, say into electrons or monads, and
that the monads were again compounds of monadules and
so forth — all this being argued on the poetic notion that

"Great fleas have little fleas
Upon their backs to bite 'em,
And little fleas have lesser fleas,
And so ad infinitum"

The molecule is a kind of planetary system, with atoms
as satellites, so is the atom with its circling electrons ; why
should not the electron be of the same construction and
why should not the component parts of the electron be as-
sumed to be made after the same pattern world without

572

THE MONIST.

end? On the other hand our solar system is one among
uncountably many others of the Milky Way; and the
Milky Way in its turn is one universe of an enormously
larger system of many Milky Ways. This is the conclu-
sion which astronomy has deduced from actual facts. Why
then should not this in our opinion enormous system of the
many Milky Ways be only a tiny item in a still larger sys-
tem, and why should we not be justified in the assumption
that we are confronted with an infinite vista into both
directions toward the infinitely small and the infinitely
great?

This notion has been brought out in the second quatrain
which reads:

"And the great fleas themselves in turn
Have greater fleas to go on,
While these again have greater still,
And greater still and so on."

A vista into infinitudes, going out into the infinitely
small and the infinitely great, now seems to become un-
tenable, and definite limits loom up, which condition, so it
seems to us, would reveal, not a bottomless and undefinable
relativity but a definite world of an objective reality with
definite interrelations and limits. If there are definite limits
in either direction we may fairly well assume that they are
in both directions. Further, if the universe is definite in
its space relation, it should also be definitely limited in
time. The world may have originated in an immeasurable
ocean of uniformities as a definite commotion and may
terminate again in a general dissolution by dissipation.
If such be the case the relativity principle would not apply
to the whole. Relativity would mean the interrelationship
of all things, but the whole as a whole would be of a
definite particularity with definite boundaries while the con-
stitution of the world would exhibit a structure of ex-
tremely tiny ultimate units of a determinably definite size,

THE PHILOSOPHY OF RELATIVITY. 573

endowed with a definite velocity and at every given point
of a definite form of motion.

While the totality of existence, the sum total of our
Milky Ways, appears to have had a beginning and may
after the lapse of immeasurable ages come again to an
end, we do not deem it excluded that the same process
of world-formation may start again, as it probably was
repeated long before the origin of this our present uni-
verse. While thus everything existent, even the ether it-
self in its totality, would have to be regarded as particular
and concrete with definite boundaries and as being limited
to a definite time both in its beginning and in its end, there
would after all loom up in the background of this world an
infinitude of space, an eternity of time and an unfathom-
able wealth of potentialities as to new formations which in
spite of all the light which the most advanced science will
ever shed on the world problem will keep this great All of
existence with its inexhaustible resources and its myste-
rious order an object of constant \vonder and awe.

The relativity problem as such is a philosophical prob-
lem, but the relativity physicists have made a physical
problem of it, and the philosophical problem of relativity
is not a new problem, it is as old as science ; it is only the
lack of philosophical training which has led to the enun-
ciation of some baffling paradoxes which if they were true
would make objective science impossible, for they would
abolish definiteness of any kind and do away with objectiv-
ity. And strange to say, claims of this kind are upheld on the
ground of experiments which tend to establish the exist-
ence of an absolute, or as we would prefer to say, of some
ultimate, which would prove that our experience does not
float as a local tangle in an endless infinitude, but that
there is a beginning and end, and also a boundary of all
concrete reality at every definitely given moment. No mys-
ticism is needed. Infinitude and eternality are potential-

574 THE MONIST.

ities, not actualities. They are vistas of what may be, not
what is. They constitute the inexhaustible wealth of na-
ture and of life without robbing science of its validity.

There is a tendency in mankind to think of the present
moment as the climax of the past, which ushers in a new era
by being an unprecedented and unique start. Every new
generation passes through such a period of self-sufficiency
and of an intoxication with their own incomparable self-
hood. The old problems seem new to them, and trying to
formulate them in an original way, they applaud their own
mistakes as something extraordinary and wonderful.
Goethe characterizes this tendency in the young graduate
who has just taken his degree of Bachelor (See Faust,
Second Part, Act II) where this young man vents his am-
bitious conceit in these words:

"This is Youth's noblest calling and most fit!
The world was not, ere I created it;
The sun I drew from out the orient sea;
The moon began her changeful course with me ;
The Day put on her shining robes, to greet me ;
The Earth grew green, and burst in flower to meet me,
And when I beckoned, from the primal night
The stars unveiled their splendors to my sight.
Who, save myself, to you deliverance brought
From commonplaces of restricted thought?
I, proud and free, even as dictates my mind,
Follow with joy the inward light I find,
And speed along, in mine own ecstasy,
Darkness behind, and Glory leading me!"

It is apparent that the relativity physicists confront an
important problem, but they have not succeeded in solving
it ; they have not even as yet properly formulated the ques-
tion and their propositions are still in a state of fermen-
tation. It is difficult to say what will come of it. It is to
be hoped, however, that the movement will follow the usual
course of mental growth. The relativists will drop their
extravagant claims, they will mature the truth which they
grope after and will at last formulate it into clear state-

THE PHILOSOPHY OF RELATIVITY. 575

ments so as to justify the prophecy of Mephistopheles,
who comments upon the proud words of the young Bach-
elor thus :

"Go hence, magnificent Original ! —
What grief on thee would insight cast !
Who can think wise or stupid things at all,
That were not thought already in the Past?
Yet even from him we're not in special peril ;
He will, ere long, to other thoughts incline :
The must may foam absurdly in the barrel,
Nathless it turns at last to wine."

At the present state of our knowledge it would be fan-
tastical to suggest a solution of the physical problems con-
nected with the relativity movement, and we must leave
the discussion of them to the future, for ere we can ap-
proach a solution we must know much more about the
ultimate constituents of matter.

Who will furnish the key to the lock of the closed door
at which the relativity physicists are knocking?

CONCLUSION.

The details of the physical problems and their solution
have only a slight interest for philosophy. The philosopher,
however, expects that the physicist's solutions shall be con-
sistent and that our scientific world-conception shall tol-
erate no contradictions.

If we consider the all-importance of form and the
enormous significance which the formal sciences possess, we
are inclined to regard the philosophy of relativity as a
synonym and parallel development of the philosophy of
science — the philosophy of form. But before we can
definitely say so, we would expect the relativists to work
out their philosophical substructure in a conservative way,
to rid themselves of their paradoxical propositions, give up
false pretensions to originality, recognize the past tradi-
tions of science, and rather than abandon the past, join

576 THE MONIST.

their cause to the legitimate progress that follows from
the tendencies, the ideals and aspirations of the established
sciences.

We do not deny the relativity of all existence through-
out and without exception, but we still cling to the old
scientific ideal of objectivity and we can not see that the
relativity principle is well established.

The great question before the world of thinkers is this :
Is it possible to construct a philosophy of science? The
author of this essay has answered this question in the affir-
mative, and has worked in this field for fully a quarter of
a century. He has worked out the details of a philosophy
of science, and has submitted to the world in both The
Open Court and The Monist his answers to the several
philosophical questions. These questions are: the nature
of the soul ; the origin of sentiency and of thought ; the na-
ture of reason, especially in its origin and in its relation
to language, the mechanism with which reason manifests
itself; the nature of ethics and the foundation of morality
as it is found in the laws of the objective world; the sig-
nificance of the God-conception as the authority of conduct,
as the ideal of right and wrong, as the standard of truth
and error, as the object of devotion, of gratitude, of rev-
erence mainly as the factor which determines good and
evil. All these questions are not beyond the scope of scien-
tific inquiry and in the philosophy of science definite solu-
tions are propounded which, though based on radical prin-
ciples of unbiased thought, lead to a justification of the
historical growth of religion and science.

The whole scope of existence as it presents itself in
human experience can become an object of scientific in-
quiry, and all scientific problems admit ultimately of a defi-
nite solution without equivocation or prevarication, yet
at the same time science is only one attitude among several
others from which the world can be confronted. The noetic

THE PHILOSOPHY OF RELATIVITY. 577

conception is the ideal of understanding the world in its
pure objectivity represented in mental terms to the exclu-
sion of sentimental subjectivity. But man is not a child
of reason only. He is also endowed with sentiments, with
will and with artistic tendencies. While the scientific
world-conception is absolutely indispensable for the man
of thought who works for a constant elevation of mankind
upon a higher level, we must at the same time recognize
the rights of the large masses who naturally are non-
scientific and are swayed by sentiment, by devotion, by art,
by ethical aspirations, by a religious comprehension of life ;
and thus we see in artistic and religious conceptions ways
of treating the world problem which are by no means un-
justified and ought not to be repudiated on the ground that
they are non-scientific, sometimes unscientific, or even anti-
scientific and purely sentimental. Religious cosmogonies,
ecclesiastical ceremonies, religio - poetical fictions possess
values of their own which can not and should not be meas-
ured by the standards of scientific method. The mystic
also has his right to confront the world with his emotions
and visions. Nevertheless, even here the philosophy of
science will be capable of investigating various products
of these tendencies and has a right to evaluate their truth
or untruth by tracing the meaning of allegorical poetry
as well as the wholesomeness of ethical attitudes which they
encourage. In this way the philosophy of science as worked
out by the present writer has by no means been narrow but
has granted a free scope to all legitimate tendencies of the
human mind, and if the philosophy of science has been
properly understood, leaders of thought in the movements of
pragmatism, relativism, Bergsonianism and other modern
tendencies, would have been able to avoid at least some of
their aberrations, and could have devoted their energies to
efforts in the right direction. At any rate they would have
been better understood; instead of being classified with

578 THE MONIST.

philosophy, they would more properly have been regarded
as a new species of poetry, or as literary ebullitions. Such
they are ; as such they possess value. They are not philos-
ophy, certainly not philosophy in the strict sense of the
word; they are not scientific world-conceptions.

It may appear strange to class the movement which
proclaims the principle of relativity in the same category
with pragmatism and other antiscientific tendencies. We
do so because the relativists have much in common with
pragmatists, because both cancel the ideal of objectivity,
both identify truth with the subjective conception of the
real or with the observer's statement of facts. They iden-
tify size with result of measurement and think that the
traditional view of truth is an error.

We do not overlook the fact that the relativists are of
a highly intellectual type and employ scientific methods,
but their aim is after all a denial of the old ideal of science,
of the objectivity of truth, and of clearness of thought. All
this is surrendered for the sake of a purely subjective simpli-
fication of statement which recommends itself in their own
specialty. Certainly there is a great difference between
relativists and pragmatists, but we recognize in both a
subjectivist tendency and a subjectivist aim. Neither of
them feel the need of approximating objectivity and both
indulge in ideal constructions, both build air castles, the
former of mathematical fiction, the latter of philosophical
poetry.

All these modern anti-scientific isms may have origi-
nated through the one-sided tendencies of a misapplied
scientism or even through the lack of comprehension of the
principles and the significance of science among naturalists.
These isms emphasize therefore certain contentions which
have a nucleus of truth, by insisting on the rights of senti-
ment though they go too far when attacking science itself

THE PHILOSOPHY OF RELATIVITY. 579

and claiming a superiority for unscientific sentiment over
clear and methodical thought.

There is no question that all these modern movements
try each in its own way to satisfy legitimate tendencies, but
in doing so they have mostly gone astray ; partly they mis-
understand their own aspirations, partly they lack sufficient
depth of comprehension and width of horizon in encom-
passing the whole realm of human endeavor.

We do not expect that in this partisan scramble of var-
ious prejudices, the whole world of thinkers can be induced
to recognize the common ideal of philosophical thought,
but we hope that there will be enough minds to understand
the several movements, to appreciate them so far as their
aspirations are legitimate, and to discover their weak points
in which they stray away from the straight path that leads
forward to a truer, deeper and a broader conception of the
world.

EDITOR.

ATOMIC THEORIES OF ENERGY.

A THEORY involving some sort of a discrete or dis-
continuous structure of energy has been put forward
by Prof. Max Planck of the University of Berlin. The
various aspects of this theory are discussed and elaborated
by the late M. Henri Poincare in a paper entitled "L'Hypo-
these des Quanta," published in the Revue Scientifique
(Paris, Feb. 21, 1912).

A paper in which a discontinuous or "atomic" struc-
ture of energy was suggested was prepared by the present
writer fifteen years ago but remains unpublished for rea-
sons that will appear later. Although he has no desire to
put in a claim of priority and is well aware that failure to
publish would put any such claim out of court, it seems to
him that in connection with present radical developments
in physical theory the paper, together with some correspon-
dence relating thereto, has historical interest. Planck's
theory was suggested by thermodynamical considerations.
In the paper now to be quoted the matter was approached
from the standpoint of a criterion for determining the iden-
tity of two portions of matter or of energy. The paper is
as follows :

SOME CONSIDERATIONS ON THE IDENTITY OF DEFINITE POR-
TIONS OF ENERGY.

It has been remarked recently that physicists are now
divided into two opposing schools according to the way in

ATOMIC THEORIES OF ENERGY. 581

which they view the subject of energy, some regarding it
as a mere mathematical abstraction and others looking
upon it as a physical entity, filling space and continuously
migrating by definite paths from one place to another. It
may be added that there are numerous factions within
these two parties; for instance, not all of those who con-
sider energy to be something more than a mere mathemat-
ical expression would maintain that a given quantity of it
retains its identity just as a given quantity of matter does.
In fact a close analysis would possibly show that opinions
are graded very closely and continuously from a view
hardly differing from that of Lagrange, who clearly saw
and freely used the mathematical considerations involving
energy before the word had been invented or its physical
meaning developed, up to that stated recently in its ex-
treme form by Professor Ostwald, who would replace what
he terms a mechanical theory of the universe by an "ener-
getical" theory, and would dwell exclusively on energy as
opposed to its vehicles.

Differences of opinion of this sort very frequently re-
duce to differences of definition, and in this case the mean-
ing of the word "identity" or some similar word or phrase
has undoubtedly much to do with the view that is taken
of the matter. It may be interesting, for instance, to look
for a moment at our ideas of the identity of matter and the
extent to which they are influenced by the accepted theory
of its constitution.

Very few persons would hesitate to admit that the
matter that now constitutes the universe is identical in
amount with that which constituted it one million years
ago, and that any given portion of that matter is identical
with an equal amount of matter that then existed, although
the situations of the parts of that portion might be and
probably were widely different in the two cases. To assert
this is of course a very different thing from asserting that

THE MONIST.

the identity of the two portions or any parts thereof could
have been practically shown by following them during all
their changes of location or state. That cannot be done
even in the case of some simple changes that are effected
in a fraction of a second. For instance, if water from the
pail A be mixed with water from the pail B there is no
possible way of telling which pail any given portion of the
mixture came from or in what proportions, yet it is certain
that such portion is identical with a portion of equal mass
that recently occupied part of one or both pails.

How far our certainty as to this is influenced by our
ideas regarding the ultimate constitution of the water is
worthy of investigation. All who accept the molecular
theory, for instance, will regard our inability to trace the
elements of a mixture as due to purely physical limitations.
A set of Maxwell's "demons" if bidden to watch the mole-
cules of the water in pail A, one demon being assigned to
each molecule, would be able to tell us at any time the pre-
cise proportions of any given part of the mixture. But if
we should not accept the molecular theory and believe for
instance, that water is a continuum, absolutely homogene-
ous, no matter how small portions of it be selected, then
our demons would be as powerless as we ourselves now
are to trace. the constituents in the mixture.

We are now in a position to ask the question: Is the
matter in a mixture of two continua identical with that of
its constituents ? The identity certainly seems of a different
kind or degree from that which obtains in the first case,
for there is no part, however small, that was derived from
one pail alone. The mixture is something more than a
mere juxtaposition of elements each of which has retained
its identity; it is now of such nature that no part of it is
identical with any part of A alone or of B alone, nor of
A+B, where the sign + denotes simple juxtaposition. It
is identical, to be sure, with a perfect mixture of certain

ATOMIC THEORIES OF ENERGY. 583

parts of A and B, but this is simply saying that it is iden-
tical with what it is now, that is, with itself, not with some-
thing that went before.

Probably no one now believes that water or any other
kind of matter is a continuum, but the bearing of what has
been said may be seen when we remember that this is pre-
cisely the present stage of our belief regarding energy.

No one, so far as I know, has ventured to suggest what
may be termed a molecular theory of energy, a somewhat
remarkable fact when we consider the control now exer-
cised over all thought in physics by molecular theories of
matter. While we now believe, for instance, that a material
body, say a crystal, can by no possibility increase continu-
ously in mass, but must do so step by step, the minimum
mass of matter that can be added being the molecule, we
believe on the contrary that the energy possessed by the
same body can and may increase with absolutely perfect
continuity, being hampered by no such restriction.

It is not the purpose of this paper to discuss whether
we have grounds for belief that there is such a thing as a
minimum quantity, or atom, of energy, that does not sep-
arate into smaller parts, no matter what changes it under-
goes. Suffice it to say that there appears to be no a priori
absurdity in such an idea. At first sight both matter and
energy appear non-molecular in structure. But we have
been forced to look upon the gradual growth of a crystal
as a step-by-step process, and we may some day, by equally
cogent considerations, be forced to regard the gradual in-
crease of energy of an accelerating body as also a step-by-
step process, although the discontinuity is as invisible to
the eye in the latter case as in the former.

Without following this out any farther, however, the
point may be here emphasized that it is hardly possible for
one who, like the majority of physicists, regards matter as
molecular and energy as a continuum, to hold the same

584 THE MONIST.

ideas regarding the identity of the two. Efforts to show
that definite portions of energy, like definite portions of
matter, retain their identity have hitherto been made chiefly
on the lines of a demonstration that energy travels by defi-
nite and continuous paths in space just as matter does.
This is very well, but it would appear to be necessary to
supplement it with evidence to show that the lines repre-
senting these paths do not form at their intersections con-
tinuous blurs that not only forbid any practical attempt at
identification on emergence, but make it doubtful whether
we can in any true sense call the issuing path identical with
the entering one. Otherwise the identity of energy can be
admitted to be only that kind of identity that could be pre-
served by matter if its molecular structure did not exist.
One who can admit that this sort of identity is the same
sort that can be preserved by molecular matter may be able
to hold the identity of energy in the present state of the
evidence, but the present attitude of physicists would seem
to show that, whether they realize the connection of the
two subjects or not, they cannot take this view. In other
words, modern views of the identity of matter seem closely
connected with modern views of its structure, and the same
connection will doubtless hold good for energy.

Regarding the probable success of an attempt to prove
that energy has a "structure" analogous to the molecular
structure of matter, any prediction would doubtless be rash
just now. The writer has been unable, up to the present
time, to disprove the proposition, but the subject is one of
corresponding importance to that of the whole molecular
theory of matter and should not be entered upon lightly.

The writer freely acknowledges at present that the
illustrations in the foregoing are badly chosen and some of
the statements are too strong, but it still represents essen-

ATOMIC THEORIES OF ENERGY. 585

tially his ideas on the subject. No reputable scientific jour-
nal would undertake to publish it. The paper was then
sent to Prof. J. Willard Gibbs of Yale, and elicited the
following letter from him:

"NEW HAVEN, June 2/97.
"My DEAR MR. BOSTWICK :

"I regret that I have allowed your letter to lie so long
unanswered. It was in fact not very easy to answer, and
when one lays a letter aside to answer, the weeks slip away
very fast.

"I do not think that you state the matter quite right in
regard to the mixture of fluids if they were continuous.
The mixing of water as I regard it would be like this, if
it were continuous and not molecular. Suppose you should
take strips of white and red glass and heat them until soft
and twist them together. Keep on drawing them out and
doubling them up and twisting them together. It would
soon require a microscope to distinguish the red and white
glass, which would be drawn out into thinner and thinner
filaments if the matter were continuous. But it would be
always only a matter of optical power to distinguish per-
fectly the portions of red and white glass. The stirring up
of water from two pails would not really mix them but
only entangle filaments from the pails.

"To come to the case of energy. All our ideas concern-
ing energy seem to require that it is capable of gradual in-
crease. Thus the energy due to velocity can increase con-
tinuously if velocity can. Since the energy is as the square
of the velocity, if the velocity can only increase discontinu-
ously by equal increments, the energy of a body will in-
crease by unequal increments in such a way as to make
the exchange of energy between bodies a very awkward
matter to adjust.

"But apart from the question of the increase of energy

586 THE MONIST.

by discontinuous increments, the question of relative and
absolute motion makes it very hard to give a particular
position to energy. Since the 'energy' we speak of in any
case is not one quantity but may be interpreted in a great
many ways. Take the important case of two equal elastic
balls. One, moving, strikes the other at rest, we say, and
gives it nearly all its energy. But we have no right to
call one ball at rest and we can not say (as anything ab-
solute) which of the balls has lost and which has gained
energy. If there is such a thing as absolute energy of
motion it is something entirely unknowable by us. Take
the solar system, supposed isolated. We may take as our
origin of coordinates the center of gravity of the system.
Or we may take an origin with respect to which the center
of gravity of the solar system has any (constant) velocity.
The kinetic energy of the earth, for example, may have
any value whatever, and the principle of the conservation
of energy will hold in any case for the whole solar system.
But the shifting of energy from one planet to another will
take place entirely differently when we estimate the ener-
gies with reference to different origins.

"It does not seem to me that your ideas fit in with what
we know about nature. If you ask my advice, I should not
advise you to try to publish them.

"At best you would be entering into a discussion (per-
haps not in bad company) in which words would play a
greater part than precise ideas.

"This is the way I feel about it.
"I remain

"Yours faithfully,

J. W. GIBBS."

Professor Gibbs's criticism of the illustration of water-
mixture is evidently just. Another might well have been
used where the things mixed are not material — for instance

ATOMIC THEORIES OF ENERGY. 587

the value of money deposited in a bank. If A and B each
deposits $100 to Cs credit and C then draws $10, there is
evidently no way of determining what part of it came from
A and what from B. The structure of "value," in other
words, is perfectly continuous. Professor Gibbs's objections
to an "atomic" theory of the structure of energy are most
interesting. The difficulties that it involves are not over-
stated. In 1897 they made it unnecessary, but since that
time considerations have been brought forward, and gen-
erally recognized, which may make it necessary to brave
those difficulties.

Planck's theory was suggested by the apparent neces-
sity of modifying the generally accepted theory of statis-
tical equilibrium involving the so-called "law of equipar-
tition," enunciated first for gases and extended to liquids
and solids.

In the first place the kinetic theory fixes the number of
degrees of freedom of each gaseous molecule, which would
be three for argon, for instance, and five for oxygen. But
what prevents either from having the six degrees to which
ordinary mechanical theory entitles it ? Furthermore, the
oxygen spectrum has more than five lines, and the molecule
must therefore vibrate in more than five modes. "Why,"
asks Poincare, "do certain degrees of freedom appear to
play no part here ; why are they, so to speak, 'ankylosed' ?"
Again, suppose a system in statistical equilibrium, each
part gaining on an average, in a short time, exactly as
much as it loses. If the system consists of molecules and
ether, as the former have a finite number of degrees of free-
dom and the latter an infinite number, the unmodified law
of equipartition would require that the ether should finally
appropriate all energy, leaving none of it to the matter.
To escape this conclusion we have Rayleigh's law that the
radiated energy, for a given wavelength, is proportional
to the absolute temperature, and for a given temperature

588 THE MONIST.

is in inverse ratio to the fourth power of the wave-length.
This is found by Planck to be experimentally unverifiable,
the radiation being less for small wave-lengths and low
temperatures, than the law requires.

Still again, the specific heats of solids, instead of being
sensibly constant at all temperatures, are found to diminish
rapidly in the low temperatures now available in liquid
air or hydrogen and apparently tend to disappear at ab-
solute zero. "All takes place/7 says Poincare, "as if these
molecules lost some of their degrees of freedom in cooling
— as if some of their articulations froze at the limit."

Plank attempts to explain these facts by introducing
the idea of what he calls "quanta" of energy. To quote
from Poincare's paper:

"How should we picture a radiating body? We know
that a Hertz resonator sends into the ether Hertzian waves
that are identical with luminous waves: an incandescent
body must then be regarded as containing a very great
number of tiny resonators. When the body is heated,
these resonators acquire energy, start vibrating and con-
sequently radiate.

"Planck's hypothesis consists in the supposition that
each of these resonators can acquire or lose energy only
by abrupt jumps, in such a way that the store of energy
that it possesses must always be a multiple of a constant
quantity, which he calls a 'quantum' — must be composed of
a whole number of quanta. This indivisible unit, this
quantum, is not the same for all resonators ; it is in inverse
ratio to the wave-length, so that resonators of short period
can take in energy only in large pieces, while those of long
period can absorb or give it out by small bits. What is the
result ? Great effort is necessary to agitate a short-period
resonator, since this requires at least a quantity of energy
equal to its quantum, which is great. The chances are,
then, that these resonators will keep quiet, especially if the

ATOMIC THEORIES OF ENERGY. 589

temperature is low, and it is for this reason that there is
relatively little short-wave radiation in 'black radiation/. . .
The diminution of specific-heats is explained similarly:
When the temperature falls, a large number of vibrators
fall below their quantum and cease to vibrate, so that the
total energy diminishes faster than the old theories re-
quire."

Here we have the germs of an atomic theory of energy.
As Poincare now points out, the trouble is that the quanta
are not constant. In his study of the matter he notes that
the work of Prof. Wilhelm Wien, of Wurzburg, leads by
theory to precisely the conclusion announced by Planck
that if we are to hold to the accepted ideas of statistical
equilibrium the energy can vary only by quanta inversely
proportional to wave-length. The mechanical property
of the resonators imagined by Planck is therefore precisely
that which Wien's theory requires. If we are to suppose
atoms of energy, therefore, they must be variable atoms.
There are other objections which need not be touched upon
here, the whole theory being in a very early stage. To
quote Poincare again:

"The new conception is seductive from a certain stand-
point: for some time the tendency has been toward atom-
ism. Matter appears to us as formed of indivisible atoms ;
electricity is no longer continuous, not infinitely divisible,
it resolves itself into equally-charged electrons; we have
also now the magneton, or atom of magnetism. From this
point of view the quanta appear as atoms of energy. Un-
fortunately the comparison may not be pushed to the limit ;
a hydrogen atom is really invariable .... The electrons pre-
serve their individuality amid the most divers vicissitudes,
is it the same with the atoms of energy? We have, for
instance, three quanta of energy in a resonator whose
wave-length is 3 ; this passes to a second resonator whose
wave-length is 5 ; it now represents not 3 but 5 quanta,

590

THE MONIST.

since the quantum of the new resonator is smaller and in
the transformation the number of atoms and the size of
each has changed."

If, however, we replace the atom of energy by an
"atom of action," these atoms may be considered equal
and invariable. The whole study of thermodynamic equi-
librium has been reduced by the French mathematical
school to a question of probability. "The probability of a
continuous variable is obtained by considering elementary
independent domains of equal probability .... In the classic
dynamics we use, to find these elementary domains, the
theorem that two physical states of which one is the neces-
sary effect of the other are equally probable. In a physical
system if we represent by q one of the generalized coordi-
nates and by p the corresponding momentum, according
to Liouville's theorem the domain f fdpdq, considered at a
given instant, is invariable with respect to the time if p and
q vary according to Hamilton's equations. On the other
hand p and q may, at a given instant take all possible val-
ues, independent of each other. Whence it follows that the
elementary domain is infinitely small, of the magnitude
dpdq. . . . The new hypothesis has for its object to restrict
the variability of p and q so that these variables will only
change by jumps .... Thus the number of elementary do-
mains of probability is reduced and the extent of each is
augmented. The hypothesis of quanta of action consists
in supposing that these domains are all equal and no longer
infinitely small but finite and that for each ffdpdq=h,
h being a constant."

Put a little less mathematically, this simply means that
as energy equals action multiplied by frequency, the fact
that the quantum of energy is proportional to the frequency
(or inversely to the wave-length as stated above) is due
simply to the fact that the quantum of action is constant—
a real atom. The general effect on our physical concep-

ATOMIC THEORIES OF ENERGY.

tions, however, is the same: we have a purely discontin-
uous universe — discontinuous not only in matter but in
energy and the flow of time. M. Poincare thus puts it :

"A physical system is susceptible only of a finite num-
ber of distinct states; it leaps from one of these to the
next without passing through any continuous series of
intermediate states."

He notes later :

"The universe, then, leaps suddenly from one state to
another ; but in the interval it must remain immovable, and
the divers instants during which it keeps in the same state
can no longer be discriminated from one another ; we thus
reach a conception of the discontinuous variation of time
— the atom of time."

I quote in conclusion, Poincare's final remarks:

"The present state of the question is thus as follows:
the old theories, which hitherto seemed to account for all
the known phenomena, have met with an unexpected ob-
stacle. Seemingly a modification becomes necessary. A
hypothesis has presented itself to M. Planck's mind, but
so strange a one that one is tempted to seek every means of
escaping it ; these means, however, have been sought vainly.
The new theory, however, raises a host of difficulties, many
of which are real and not simply illusions due to the indo-
lence of our minds, unwilling to change their modes of
thought

"Is discontinuity to reign throughout the physical uni-
verse, and is its triumph definitive? Or rather shall we
find that it is but apparent and hides a series of continuous
processes ? .... To try to give an opinion just now on these
questions would only be to waste ink."

It only remains to call attention again to the fact that
this conception of the discontinuity of energy, the accept-
ance of which Poincare says would be "the most profound
revolution that natural philosophy has undergone since

592 THE MONIST.

Newton" was suggested by the present writer fifteen years
ago. Its reception and serious consideration by one of
the first mathematical physicists of the world seems a suf-
ficient justification of its suggestion then as a legitimate
scientific hypothesis.

ARTHUR E. BOSTWICK.
ST. Louis, Mo.

CRITICISMS AND DISCUSSIONS.

HENRI BERGSON, PRAGMATISM AND SCHOPENHAUER.

The history of philosophy is like one of the ancestral galleries
in ancient European castles. At first glance you find yourself before
a bewildering variety of individuals, but if you look closer you dis-
cover that certain family traits reappear again and again. In the
history of philosophy a similar variety of individual systems at first
confuses the student. But upon closer scrutiny he will find that
here too the bewilderment ceases, that certain outlines are typical
for the structure of a great number of systems and that almost
every individual system belongs to such a type of structure. Con-
sidered in this light the history of philosophy presents a few types
of thought which undergo slight changes and show a slow develop-
ment according to the intellectual conditions of the century in which
the philosopher moulded his system.

The systematic structure to be considered in this paper is a
very modern one, namely Henri Bergson's philosophy. From a
purely philosophical standpoint it was severely criticized in the last
number of this magazine.1 In this number it may be scrutinized
from a purely historical standpoint.

Among laymen Bergson's name carries with it a certain feeling
of mystic refinement. However little they may know about him,
they instinctively expect such an appeal to their artistic natures as
they would from a sculpture by Auguste Rodin or a drama by
Maeterlinck. They instinctively feel the kind of a man who is about
to confront them and their feeling is probably correct.

Feeling, however, is quite a different thing from knowing.
Strange to say, philosophers are greatly at variance as to the place
of Bergson's philosophy in the gallery of philosophical systems.

1 See "The Philosophy of Bergson" by Mr. Bertram! Russell, Monist, July,
1912. Cf. also in the same number, "Bergson and Religion" by Dr. James G.
Townsend, and "Kant and Bergson" by Dr. Bruno Jordan.

594 THE MONIST.

Here is the struggle of a man's mind, some philosophers say, which
can be compared in importance only with the philosophy of Kant,
while still very different. Others are reminded of Hegel and others
of Berkeley; while American pragmatists say that Bergson is a
pragmatist. Others again are of the opinion that it is quite out
of the question to compare Bergson at all with philosophers of any
other school. They say he is unique; he is no type, but has an
individuality of his own.

We shall see. It is certain however that it would be rather
strange if Bergson were not a type, notwithstanding his marked
individuality ; if his philosophy really bore no relation to philosophies
of former days. This would mean that in the development of
philosophical traditions a structure of philosophy had arisen no
likeness to which had ever been seen before, that a child without
ancestors had been brought to light; but this is not very probable.
To inquire therefore after the historical antecedents of Bergson's
philosophy would mean to ask whether its structure is entirely new
or only a transformation of what already existed, and in the latter
case the questions arise, who used this structure before Bergson?
Who among the philosophers of former days may be called nearest
akin to him? Which philosophical tradition is continued by Berg-
son's thought? These are the questions which I shall try to answer

in this paper.

* * *

Which philosophical tradition is continued by Bergson? "The
pragmatistic one," say the American pragmatists ; "Bergson is a
pragmatist." I do not hesitate to agree that Bergson really is a
pragmatist, and here are the proofs.

Pragmatism holds that what we call reality, world, object of
knowledge, is not something independent of us, but rather a man-made
picture, a raw material transformed into a complicated instrument
for action. "The world is only an opportunity to do our duty,"
Fichte was wont to say. "The world is only an expedient for our
action," the pragmatists of to-day tell us. Seeing, hearing, smelling,
touching the world, as well as considering it as a multitude of
atoms, electrons, ions, means nothing else than a preparation to
grapple with the world.

This doctrine becomes very evident in Bergson's philosophy.
For Henri Bergson the essence of man is life. What we call man
is not so much the human body nor a soul-substance within that
body, but rather a dramatic performance, a continual course of

CRITICISMS AND DISCUSSIONS. 595

events, of visions, sounds, feelings, images, thoughts and especially
of actions. Man means an elan vital, a life-current running along
seventy, eighty or ninety years.

If this is so, what is the business of that life-current? To
what purpose is that action acting? In agreement with the biol-
ogists Bergson would answer that the business of life is to find
its way among other life-currents. But if we look closer we shall
see that these other life-currents differ widely from one another,
that man treats them at least in very different ways, some of them
as matter only and others as matter but also as souls.

For the present we shall disregard life-currents treated as
souls. As far as their treatment as pure matter is concerned,
Bergson is among the pragmatists. Man is different from most
animals in that he has hands and uses them not only for climbing
trees as the monkeys do but for providing instruments. It would
not be too bold to say that man has made his hands longer and
stronger by utilizing matter for instruments. The axe, the arrow,
the target are such artificial hands, not to mention the enormous de-
velopment of inventions during the last centuries, all tending to
the same end.

This leads to the question of how this mechanical point of view
influences our knowledge of reality. The answer is very simple.
Since man intends to use reality for instrumental purposes it appears
to him entirely as an object of action — either to act upon or to act
with.

We seldom realize how much difference such a point of view
makes in our knowledge. A desk in my study may serve as a
simple instance. Everybody agrees that it is a desk. But "desk"
means an instrument either to put a manuscript on, to read a book
on, to fit a lamp on, etc. In other words, from the very beginning
we all acknowledge a certain piece of wood as a practical object
destined for practical purposes, and it would be surprisingly hard
for us to free ourselves from this impression, to look at that object
and not identify it with a desk. But desk means instrument and in-
strument means possibility of action. I shall return to this point
very soon.

Meanwhile another reflection may serve to clear up this situa-
tion still further. I say that to all of us the desk appears as a desk.
We cannot help it. Still the impression of the desk is by no means
the same to all of us, for in addition to its being acknowledged as a
desk it may be recognized in many other ways. Let me suppose

596 THE MONIST.

that a dealer in woods happens to examine my desk. He will see
many features in it which other people do not observe. He will not
only infer but actually see the quality of the wood and probably tell
its cash-value off-hand; while all that other people see is that it is
"apparently of oak" and possibly that it looks "rather nice." The
merchant being a connoisseur actually sees more than other people.
Now perhaps a carpenter looks at the desk, then an artist, then a
botanist, then a chemist, then a physicist. The layman would
simply laugh when the botanist says that the desk is a conglomera-
tion of cells, or the physicist that it is a heap of molecules, or the
chemist that it is a multitude of atoms. Still these are the ways
in which the desk would be regarded by these men. It is only the
point of view which is different.

In other respects however we all are taking the same point of
view, for to all of us, whether layman, merchant or physicist, the
desk appears as a desk, and if it does not appear as a desk, it would
at least appear as a table. And if it does not appear as a table it
would at least appear as a "thing," and "thing" always means, if we
believe Bergson, something to act upon or to act with.

It is only the point of view which is different. In other respects
however all are taking the same point of view, for to all of us,
whether layman, merchant or physicist, the desk appears as a desk,
or if not as a desk, at least as a table. And if it does not appear
as a table it would at least appear as a "thing," and "thing" always
means, if we believe Bergson, something to act upon or to act with.

Hence, in considering the world as an accumulation of things
we have already taken a certain limited point of view; we are on
the way to treat the universe as an object and eventually as a means
of action. We have taken the decisive step, and cannot now go
back. We have made the start in our calculation and it will proceed

accordingly.

* * *

It is interesting that Bergson considers three-dimensional space
as one of the most important elements in the method by which the
world is conceived as a means for action. To see things in space
means to consider them as objects to act upon. Space is a kind of
uniform which we put upon the world in order to control it, for to
control things we cannot care what they are in themselves ; we must
care what they may be to us. Hence we deprive them of their very
essence; we treat them by a scheme, which enables us to divide
things up quite at will — while according to Bergson things in them-

CRITICISMS AND DISCUSSIONS. 597

selves are indivisible, although, as he expresses it, they have a cer-
tain "ballast" of that scheme.

Our three-dimensional space is a scheme for division and noth-
ing else; its very homogeneity is the means by which we divide
things. This is most apparent in theoretical physics where all
plurality of our pluralistic world is eliminated and only shadowy
colorless sections of space remain where before we saw blue and red
and green and yellow, where we heard noise and music, smelled
odors and tasted sweet and bitter. Theoretical physics is space
triumphant, which means it is a triumph of practical handling of the
world. Plurality once eliminated from the world there is no limit
for divisions. We may divide indefinitely, and dividing will doubt-
less contribute much toward our practical control over the world.

* * *

It is a very significant fact that we treat time in a similar way
again and again; we spatialize it. If somebody knocks at the door
three times in succession and we try to recall that succession of
knocks, we discover in ourselves a certain inability to do so. Instead
of representing the three knocks as a real sequence in time we find
ourselves fancying them one beside or behind the other, quite as
though they were three pearls on a cord or three blots on a line.
We are almost compelled to do so; for to recall something means
to see it all at once, and to see all at once is precisely not to see
one part after the other in succession, but to perceive them simul-
taneously. Hence we spatialize time, and in so doing we are tend-
ing again towards its homogeneity. Of course we are not treating
time as three-dimensional space — that would not do; but modern
scientists treat it as a "fourth dimension" of space, and common
sense regards it as a one-dimensional line. The next step in this
procedure will be to eliminate all plurality of concrete experience
from that line, to divide up time quite as arbitrarily as space and
to deal with time too, regardless of its contents, as suits our purpose.
The dial on a watch is nothing but a graphic demonstration of such
a one-dimensional time-line, its straightness being turned into a
circle.

Bergson's idea of the business of understanding is now suffi-
ciently clear. Understanding is an instrument by which human life
works its way through its surroundings. Moreover it is an instru-
ment by which human life continually makes use of homogeneous
schemes, treating simultaneous impressions by space and successive
impressions by spatialized time. This threefoldness of understanding

598 THE MONIST.

— practical use, homogeneous space and spatialized time — may still
become important for our later discussion. For the present it suf-
fices to state that understanding is to Bergson an instrument for
practical use. This is the reason why in America he is called a

pragmatist.

* * *

And now in seeming contradiction to my own words, and in
open contradiction to the theory of most American philosophers, I
say that Bergson is not a pragmatist. He is the very foe of the
pragmatists ; for to tell the truth, what pragmatism advocates, Berg-
sonian philosophy opposes. It is one of the main features of this
philosophy to disregard the whole realm of understanding as a realm
for practical use. To Bergson's mind it is precisely the pragmatic
attitude that hinders understanding from entering philosophy — and
Bergson is after all a philosopher. He leaves to pragmatism the
realm of science and common sense, but in philosophy he protests
against it.

To Bergson's mind philosophy begins where pragmatism ceases.
To be a Bergsonian philosopher I must rid myself of pragmatistic
habits. It is pragmatistic to look at everything from the point of
view of action, hence it is philosophic to discard that point of view.
It is pragmatistic to consider the world as wrapped in space, hence
it is philosophic to free the world from space. It is pragmatistic
to spatialize time, hence it is philosophic to remove that spatiali-
zation.

A -Bergsonian philosopher is a thinker freed from all prag-
matism. He no longer looks for the practical use of things, but
looks to things for their own sake. His mind no longer works to
make headway for life, but it turns itself round and looks at life
itself as it goes on within him. Bergsonian philosophy is conscious-
ness of life itself freed from its practical service.

* * *

And now our thoughts do not leave Bergson in passing over
to Schopenhauer and attempting to throw light on Bergson's ideas
by the philosophy of Schopenhauer and on Schopenhauer's ideas
by the philosophy of Bergson.

Like Bergson, Schopenhauer is a pragmatist; like the prag-
matism of Bergson, that of Schopenhauer holds good for understand-
ing only; and as for Bergson, so for Schopenhauer, philosophy be-
gins just where understanding and pragmatism cease.2

aCf. Schopenhauer, Werke (ed. Grisebach), I, p. 242.

CRITICISMS AND DISCUSSIONS. 599

Thus understanding plays quite a similar role with Schopen-
hauer as with Bergson. It is very significant that Bergson and
Schopenhauer use the same simile. Both call understanding "a
lantern" which life has kindled in order to find its way through the
world. For both this "lantern," originally used for a limited ser-
vice, has extended its light more and more until now it shines over
the whole universe, or at least what it calls a "universe."

Now the "universe" over which this lantern sheds its light
is matter. Our earth and all that lives on earth is matter. The
moon, the sun, the planets, all solar systems are matter. But for
Bergson as for Schopenhauer "matter" is nothing but reality treated
by the methods of understanding, covered with three-dimensional
space, put into spatialized time and considered pragmatically for
the single purpose of action.

For Bergson matter is simply correlative to understanding; it
is the only means by which understanding knows reality. Schopen-
hauer takes exactly the same position. "Matter," he writes, "and
hence the appearance of the whole universe, is there for under-
standing only. Understanding is its support, the condition of its
very existence; it is its necessary correlatum."3

It is important to realize that this coincidence between Bergson
and Schopenhauer is not insignificant, but indicates a very interesting
and far-reaching identity in the main structure of their systems.
That understanding is limited to matter and matter limited to under-
standing is of decisive consequence for the whole development of
both philosophies.

* * *

But the coincidence between Bergson's and Schopenhauer's
idea of understanding goes much farther than this; for precisely
the same three functions of understanding with regard to matter
pointed out by Bergson are likewise pointed out by Schopenhauer.
If Bergson declares that the only aim of understanding is to have
the possibility of acting upon its environment, and that this is the
reason why it materialises everything, Schopenhauer would say
that causality is the only category of understanding, for under-
standing is there solely to act upon its environment. That is the
service forced upon understanding by the all-powerful will to live,
and that too is the main reason why understanding transforms
everything into matter. In other words, Bergson's pragmatism of
understanding and Schopenhauer's doctrine of causality as the only

8 Werke, II, p. 160.

600 THE MONIST.

function of understanding tend precisely towards the same point,
a point of greatest consequence, in fact a cornerstone in the structure
of both systems.

For Schopenhauer as for Bergson understanding stands for ac-
tivity and for activity only. Its functions to provide for space and
time, are subordinate to that main function. They are the means
by which understanding succeeds in materializing the world for the
purpose of action.

When Bergson says that in order to handle the world for action
understanding covers it with three-dimensional homogeneous space,
Schopenhauer would say that three-dimensional homogeneous space
is one of the two indispensable intuitions a priori of understanding.
That space is a priori for Schopenhauer and possibly a posteriori for
Bergson is of no consequence for this part of our comparison. But
it certainly is of very great consequence that in the philosophy of both
understanding uses space as its most important instrument in mate-
rializing the world for the purpose of action.

The other instrument by which understanding materializes the
world is time. Bergson says that for this purpose time is spatialized.
Schopenhauer declares that time is the other of the two "intuitions
a priori" of understanding. Now there is apparently no similarity
at all between the ideas of Schopenhauer and Bergson; and still,
on looking closer, a careful observer will discover that there is a
similarity, and indeed a far greater one than would be suspected.
I venture to call special attention to this point.

What distinctive feature of space makes it appear to Bergson
particularly adapted for the practical purpose of understanding?
Certainly not that space is three-dimensional, but that three-dimen-
sional space is homogeneous. Space is fit for action solely because
of its homogeneity. With homogeneity arbitrary divisibility is pos-
sible, and with arbitrary divisibility understanding finds its way
to handle reality instrumentally — that is all.

Let us pass to time. What distinctive feature of time makes
it appear to Bergson as being particularly adapted for the practical
purposes of understanding? Bergson finds this distinctive feature
in the fact that we "spatialize" time. But what does he mean by
spatializing time? Again nothing but an attempt to treat time
like space, namely as a homogeneous something. It is not the one
dimension nor the straightness of the line, that "spatializes" time;
but its uniformity, its homogeneity, its divisibility at any point, and
hence its possibility to be handled instrumentally. Homogeneity,

CRITICISMS AND DISCUSSIONS. 6OI

divisibility at any point, is the only quality for which understanding
cares. It is wholly indifferent to everything else in space and in
spatialized time.

Passing to Schopenhauer we discover that the reason why he,
like his master Kant, considers space and time as "intuitions a
priori" is again their all-embracing homogeneity. The reader re-
members Kant's demonstration of this in his Critique of Pure Rea-
son. Space and time have the peculiarity of not being "concepts,"
but "intuitions," because they are spread out with absolute uniform-
ity, with absolute homogeneity, which does not allow the distinction
between different (three-dimensional) "spaces." Furthermore these
"intuitions" are a priori because they are necessary ; they are neces-
sary because they are supposed to cover everything; and they are
supposed to cover everything once more because they are absolutely
homogeneous — a uniform scheme which nothing can escape. Space
and time are for Schopenhauer and Kant intuitions a priori in so far
only as they are homogeneous schemes, to be placed over a world
of immediate images.

Schopenhauer's idea of time, as an "intuition a priori" is the
idea of a homogeneous scheme to be placed over a world of immediate
images. But this is exactly what Bergson calls spatialized time.
Therefore when Bergson contends that understanding as the cor-
relative of matter and an instrument for action makes use not only
of space but also of "spatialized time," and Schopenhauer contends
that understanding as the correlative of matter and an instrument
for action makes use not only of space but also of time as an
"intuition a priori" they mean the very same thing. They only use
a different vocabulary. It is essential for both that space and time
are homogeneous schemes and belong to understanding as means of
turning immediate images into matter and of handling matter prac-
tically. I shall very soon return to this point.

In the meantime I venture to sum up the result, thus far reached
in our investigation, in the statement that the theories of Bergson
and Schopenhauer with regard to understanding, matter, space and
time are essentially the same. And since half of the entire structure
of the philosophies of these two men is constituted by those theories,
their sameness means a corresponding sameness of half that struc-
ture.

* * *

We now proceed to the second half of that structure. Opposed
to understanding and matter there stands in Schopenhauer's philos-

6O2 THE MONIST.

ophy the "will to live." Opposed to understanding and matter there
stands in Bergson's philosophy a "life-current" the "elan vital"

For Bergson as well as for Schopenhauer the world of under-
standing is only a world of "appearance." It is not true reality, but
reality prepared for action. Hence, by understanding we are not in
a position to penetrate into the essence of reality. We are getting
only to the surfaces. We go around things, but cannot enter them.

We previously noted that Bergson used a simile originally used
by Schopenhauer. Both compare understanding to a "lantern" which
life has kindled in order to find its way through the world. Now
we discover for a second time that Bergson and Schopenhauer use
one and the same simile in precisely the same way. Schopenhauer
writes with regard to the inability of understanding to enter life:
"We see that it is impossible to reach the inner essence of things
by external means ; however much we thus investigate we find only
images and empty names. We are like the man who walks around
a castle, looks in vain for an entrance into it and in the meantime
sketches its walls"* Compare with this Bergson's account of under-
standing trying in vain to enter life : "It is like the work of an artist/'
he writes, "who traveling through Paris sketches a tower of Notre
Dame. . . .This designer replaces the true inner essence of the object
by an external schematic reproduction."*

It is the way of understanding to approach its objects by exter-
nal means only, and in doing so it tries to comprehend the life inherent
in them by dividing the object up into small parts. This, however,
is in vain. Understanding can never enter life in this way, for
the only true way of coming into contact with life is by feeling it
instinctively.

Schopenhauer illustrates this by an impressive simile : "Abstract
knowledge," he writes, "compares with instinctive feeling as a
mosaic compares with a painting by Van der Werft or Denner ; for
however nicely the mosaic may be put together, the outlines between
the stones remain and no continual transition from one shade of
color to another is possible."6 Bergson holds the same view, and it
is surprising that in another context, which however carries the
same meaning, he again uses the very same comparison originally
used by Schopenhauer. "A gifted artist paints a picture," he writes.

* Werke, I, p. 150.

'Bergson, "Introduction a la philosophic," Revue de metaphysique et de
morale, 1903, p. 10.

6 Werke, I, p. 98 f .

CRITICISMS AND DISCUSSIONS. 603

"We could imitate his picture by many colored stones. The more
nicely our stones are put together the more manifold and different
they are in color, the better we shall be able to reproduce their
curves and shades. But we should need an infinite number of in-
finitely small and infinitely differentiated stones in order to reproduce
the picture exactly."7

The idea in common, expressed by Schopenhauer and Bergson by
exactly the same simile, is that life cannot be perceived by external
dissection and recomposition but only by instinctive feeling. This
idea is of decisive importance for Bergson's own thought as well
as for Schopenhauer's, and our discovery that Bergson and Schopen-
hauer use the same similes in this context several times indicates
that their coincidence is more than a mere curiosity.

* * *

For Schopenhauer as for Bergson life is an object not of under-
standing but of instinct. In fact, Schopenhauer's philosophy might
well be headed "A Study in Instinct" as well as Bergson's. It is
therefore quite characteristic for both of these thinkers that they
are so greatly concerned with instinct as a biological fact; that both
of them pay special attention to insects, because in them instinct is
most developed. For Bergson as for Schopenhauer life is not only
"the object" of instinct. It would be more just to say that to them
instinct is the living of life ; it is life itself ; it is really as it is
seen directly, while the knowledge of understanding is neither life
nor reality but only an indirect way of preparing reality for practical
use.

For Schopenhauer as for Bergson the world of instinct as a
world of reality and life stands opposed to the world of under-
standing as a world of appearance and death. This distinction is
of greatest importance for Schopenhauer's philosophy as well as
for Bergson's.

So Bergson writes: "If one compares the definitions of meta-
physics and of the Absolute he observes that all philosophers in
spite of their controversies are at one in distinguishing two abso-
lutely different ways of knowing. The one way stops at the relative ;
the other penetrates to the Absolute, where it is approachable ....
The Absolute is perceived by intuition, everything else by analysis.
I call intuition the instinctive sympathy by which we put ourselves
into the heart of an object in order to unite with its particular in-

7 Bergson, loc. cit., p. 2.

604 THE MONIST.

expressible essence."8 With this introduction Bergson plunges the
reader into what he considers one of the most central points of his
philosophy.

Precisely the same way of "knowing the Absolute" is called by
Schopenhauer "the philosophical truth /car3 e£oxr?v" for his own sys-
tem,9 and Bergson and Schopenhauer furthermore agree that this
central truth of philosophy, instinctive knowledge as a key for life,
is limited at first to the knower's own being. "There is at least one
reality," Bergson tells us, "which we all perceive from the inside
by intuition. . . .that is we, ourselves."10

It is the instinct of our own life of which we are thus aware ;
but unfortunately this instinct is the only reality of which we dis-
pose directly. We have to transfer our own living instinct to the
external world in order to conceive the entire life of the universe.
This indirect way of knowledge set forth by Professor Bergson is
one of the chief principles of Schopenhauer's philosophy. What
Schopenhauer calls "will" is nothing else but what Bergson describes
as man's own life immediately experienced by instinctive feeling as
the "one reality which we all perceive from the inside," and then
transferred to the external world. "Will" is a determinate) a potion
for "what we immediately experience as the innermost essence" of
our own life, Schopenhauer declares,* and furthermore contends that
"to him who knows the most immediate datum of consciousness is
will .... this conviction will become the key for a knowledge of the
inmost essence of all nature. For he will now transfer his imme-
diate experience of life to all those objects which are not given to
him in immediate experience."11

From this it will be more evident why Schopenhauer's "will"
and Bergson's elan vital are precisely the same thing. The reason
is that both are brought forth by the same "philosophical truth Kar
e|o^v." Both "will" and elan vital are philosophical expressions
for instinctive feeling conceived as "the living of life" and thence

transferred to the external world.

* * *

In this world of "will" or elan vital the problem of time again
appears. We have already dealt with this problem as far as under-

* Bergson, loc. cit., p. i.

9 Werke, I, p. 154.

10 Ibid., p. 4.

* Werke, I, p. 164.
u Werke, I, p. 162.

CRITICISMS AND DISCUSSIONS. 605

standing is involved in it; we have now to deal with it as far as it
extends to the instinctive feeling of life.

In this latter realm the problem takes up the form of an an-
tithesis. Life as instinctively felt is according to Bergson, duree
reelle, true duration, true time, and to Schopenhauer it is "timeless."
Here Bergson and Schopenhauer evidently seem to contradict each
other, but as in our former discussion the contradiction is rather in
words than in thought. "True duration" means for Bergson time
freed from its specialization. "Timelessness" means for Schopen-
hauer time freed from past and future. It means "eternal pres-
ence."

It certainly is interesting to compare this conception of Schopen-
hauer's with Bergson's duree reelle. If you ask Bergson why we
spatialize time, he would answer that we do so in order to bring
past and future to the same level; in order even to conceive of a
future and of a past. Hence duree reelle, as time freed from its
spatialization, is time deprived of the conception of past and future.
But that is precisely what Schopenhauer calls "timelessness." If
consistently carried out, Bergson's duree reelle viewed from the
point of view of the being himself who exists in duree reelle is
adequately represented only by Schopenhauer's idea of "timeless-
ness" or "eternal presence." Bergson and Schopenhauer, contra-
dicting each other in their expressions, are logically bound to agree
in the fact. Schopenhauer's "timelessness" is duree reelle, and Berg-
son's duree reelle ought necessarily be conceived as timelessness.

It is very probable that Professor Bergson himself would con-
tradict this statement. He would point to the obvious fact that
again and again he has characterized duree reelle as involving both
past and future, and hence as something entirely different from
Schopenhauer's timelessness. This is very true. But it is no less
true that if meant as an objection to Schopenhauer's timelessness
Bergson's statement would be very inconsistent.

There are two points of view which should not be confounded.
Either duree reelle is viewed by an observing outsider or by the
being himself who exists in duree reelle. An outsider can realize
that what this being experiences involves past and future, the being
himself however can not. The simple reason for this is that ac-
cording to Bergson's own doctrine spatialization of time is necessary
in order to conceive, however vaguely, of any past or any future.
But spatialization of time is not duree reelle. Hence a being existing
in duree reelle does not realize that what he experiences involves

606 THE MONIST.

past and future. He does not know either "past" or "future." He
lives in timelessness, because he lives in duree reelle.

Duree reelle or "timelessness," viewed from the point of view
of an outsider, leads towards the conception of evolution. Learning
that his own doctrine of evolution was very much like that of
Schopenhauer,12 Professor Bergson thought this coincidence "a happy
inconsistency" on the part of Schopenhauer because of the latter's
doctrine of "timelessness"; while in truth the apparently missing
coincidence in the doctrine of "timelessness" and duree reelle was an
unhappy inconsistency on the part of Professor Bergson. There
can be no thought of evolution from the point of view of the being
who himself lives in duree reelle, for no evolution can be thought
of except in spatialized time. But, in full compliance with the
philosophy of Schopenhauer as well as of Bergson himself, an ob-
serving outsider may see a very obvious evolution where the being
existing in duree reelle sees "timelessness" only.

* * *

I return from the problem of timelessness, duree reelle and evo-
lution to the main idea of Schopenhauer's and Bergson's thought,
to their "philosophical truth K<IT' e^ox^v." True reality, life, is the
instinctive feeling of one's own life-current transferred to the outer
world and the world of philosophy as a world of instinct and life
is opposed to the dead world of understanding.

This philosophical truth icar' C^GX^ is founded on the instinctive
feeling of everybody's own life. Hence everybody is a philosopher
in so far as he is aware of his own life. He only does not try to
express his feelings in conceptual language. Technical philosophy
therefore is essentially constituted of everybody's instinctive and
intuitive feelings enlarged, systematized and changed into knowl-
edge.

Here again Schopenhauer and Bergson express themselves in
a very similar way. So Schopenhauer writes: "By intuition or in
concrete everybody is conscious of all philosophical truths, but to
demonstrate them in abstract concepts and reflective thought is the
business of philosophy."13 Compare with this Bergson's words:
"Every lasting system of philosophy is enlivened by intuition at

"Compare the very interesting article of Prof. Arthur O. Lovejoy of
Johns Hopkins University in The Monist, XXI, pp. 216 ff.

18 Werke, I, p. 491.

CRITICISMS AND DISCUSSIONS. 607

least in some parts. Dialectic is necessary to demonstrate intuition,
to mirror it in concepts and to communicate it to others."14

The similarity between Bergson's and Schopenhauer's idea is
striking even in its expression. Indeed both philosophies belong
to the same well-known type of thought that calls itself "intuitive."
Every intuitive philosophy somewhat despises abstract concepts.15
Still when intuition becomes a philosophy abstract concepts are
needed, and they are generously used in the writings of our two
thinkers in spite of their contention that nobody enters the Absolute
in this way. The gulf between understanding and instinct, theoret-
ically established, is practically bridged by philosophic discourse.
There the work of understanding is enlivened by instinct, and the
life of instinct is expressed in terms of understanding. None the
less instinct and understanding remain theoretically entirely different
for both Bergson and Schopenhauer, and it is not their difference
but their combination which by the latter is considered as the "riddle
of the universe."

This riddle of the universe, and corresponding to it the "philo-
sophical truth Kar* eloxV of Bergson and Schopenhauer, fairly sums
up what I wanted to state in this part of my paper, namely, that
these two philosophies are no less similar in the second half of their
structure than they were in its first half. A theory of understand-
ing common to both constitutes the first half, a theory of instinctive
life as opposed to understanding no less common to both constitutes
the second half of their systems. Thus the entire structure of the
thought of both is identical in its main outlines.

* * *

It would be possible to show how in some corollaries further in-
structive similarities between Bergson's and Schopenhauer's philos-
ophy spring up from that main identity.

I shall allude only to Bergson's theory of evolution, which, as
Prof. Arthur O. Love joy has pointed out in his very interesting
paper, exhibits a striking similarity to Schopenhauer's evolution-
ism.16 Bergson's doctrine of the unity of life is strangely similar to
Schopenhauer's doctrine of the unity of will. For both thinkers
this unity forms the basis of their evolutionism. On the other hand
it has been pointed out in this paper that Bergson's theory of dis-

14 Bergson, Evolution creatrice, p. 259; "Introduction a la philosophic,"
Revue de metaphysique et de morale, 1903, p. 4.

" The only true language of intuition is silence.
18 See note 12.

608 THE MONIST.

section as opposed to the unity of life goes back also to Schopen-
hauer.

Another point of similarity is to be found in the theory by
which Bergson and Schopenhauer explain laughter. Both find its
main cause in the sudden perception of a discord between torpid
understanding and flexible life.

In their theory of art both lay stress on the artist's power to do
away with the pragmatistic narrowness of understanding and to
bring man into immediate contact with life itself.

And Schopenhauer's theory of freedom although apparently very
different from that of Bergson is likewise founded upon the idea that
causality exists only in the realm of understanding and appearance,
while life in itself, will, is free and may manifest its freedom to the
living being — although the realization of this freedom is conceived
very differently by Schopenhauer and Bergson, the former being far

more consistent in this respect as in others.

* * *

Professor Bergson is by no means a consistent thinker. On the
other hand it is well known that although more consistent than Berg-
son, Schopenhauer too has justly been accused of great inconsistency.
This is one of the chief reasons why in spite of their striking simi-
larity the philosophies of Schopenhauer and Bergson differ widely
in more than one respect. Schopenhauer's Kantianism and Neo-
Platonism, which are incongruous with the rest of his system, are
happily avoided by Bergson. On the other hand Bergson's incon-
sistencies with regard to his activism and the confusion of his ter-
minology with regard to time and some minor points are avoided
by Schopenhauer. That Schopenhauer was more pessimistic than
Bergson is of much consequence for the external appearance but of
comparatively little consequence for the inner structure of both sys-
tems.

Important, however, is the fact that Schopenhauer is far more
systematic than Bergson. His philosophy is an attempt to furnish
an all-embracing Weltanschauung from the point of view of the will
to live and its servant, understanding. Bergson's philosophy con-
sists rather of several specific investigations, more or less loosely
connected. That is the reason why on the whole Schopenhauer's phi-
losophy is much more imposing and in almost all details much
richer than Bergson's thought, while Bergson has the advantage of
being less dogmatic and possibly still more stimulating than Schopen-
hauer.

CRITICISMS AND DISCUSSIONS. 609

As to elegance of style, figurative language and happy choice
of comparisons no modern philosopher can equal either Schopen-
hauer or Bergson. They rival each other and both are unsurpassed.
However, it seems to me that Professor Bergson's style, especially
his figurative language and his predilection for comparisons, is not
quite independent of the stilistic habits of Schopenhauer. Our dis-
covery that Bergson uses three similes originally used by Schopen-
hauer is a strong indication in that direction. Bergson carries a
stilistic habit of Schopenhauer to an extreme; but this is only a
symptom of a general feature of Bergson's style which is far more
onesided and far less varied, but at the same time still more sur-
prising and stimulating, than Schopenhauer's. Thus the differences
of thought in the two men are peculiarly mirrored in the differences

of their style.

* * *

This leads to the question as to the psychological background
for the similarity between Bergson's and Schopenhauer's thought.
When Bergson worked out his thought did he plagiarize Schopen-
hauer? The only answer to this very natural question of a layman
in the history of philosophy would be an unmistakable "Certainly
not!"

Personally I have good reasons to contend that Professor Berg-
son is not even aware of most of these similarities, and very likely
never was. He himself is probably inclined to think that most of
what he actually took from Schopenhauer is his own original thought
— original in the popular sense of "creation."

In fact, however, Bergson's thought appears to be "original"
not in the popular, but only in the Bergsonian sense of creation.
Popular creation is creation out of nothing; Bergsonian creation is
the past prolonged into the future. For Bergson all life is creative
because it is saturated with the life that has preceded it. Bergson's
own philosophy certainly is Bergsonian life par excellence. Hence it
is creative, because it is saturated with preceding life ; and I contend
that the preceding life with which it is saturated is Schopenhauer's
philosophy.

This is not very difficult to prove, for Bergson himself tells us
that he formerly studied Schopenhauer's philosophy closely. More-
over, when Bergson was at the most impressionable and decisive
stage of his mental development a Schopenhauer craze was preva-
lent in France, and Schopenhaueristes were seen even in literature
and society. Finally, Bergson's teacher Ravaisson was a follower

6lO THE MONIST.

of Schelling. Indeed some residua of Schelling's philosophy — espe-
cially with regard to his theory of matter — are easily discoverable in
Bergson's thought. But what is still more important for our in-
vestigation, there was no better way to prepare Bergson for Schopen-
hauer's philosophy than by a knowledge of Schelling, out of whose
thought Schopenhauer's own ideas emerged, just as to-day there is
perhaps no better way to prepare a mind for Bergson's philosophy
than by a knowledge of Schopenhauer, out of whose thought Berg-
son's ideas have emerged.

* * *

All this leads us back to where we started. The history of
philosophy is like one of the ancestral galleries in ancient European
castles. Certain family traits reappear again and again in the struc-
ture of philosophical systems and Henri Bergson's philosophy bears
the family traits of Schopenhauer's "World as Will and Idea."

But Schopenhauer's own philosophy shows family traits as well.
It emerged out of the philosophy of Schelling and the general trend
of German romantic thought in the early 19th century, and German
romanticism again owed a great deal to Herder and Goethe. Indeed
I know a passage by Goethe which contains Bergson's entire thought
in a nutshell. Using "reason" for "intuition" according to the ter-
minology of his time Goethe says to Eckermann: "The godhead is
active in the living, but not in the dead; it works in the growing,
the developing, but not in the finished, the torpid. Therefore reason
with its tendency for the Divine has to do with the growing, the
living; understanding with the finished, the torpid that it may use
it for practical purposes."17 Change Goethe's terminology into the
language of Bergson, and the thought expressed by Goethe is almost
as Bergsonian as Bergson's own.

This Bergson-Schopenhauer-Schelling-Goethe-Herder type of
philosophy could easily be traced back to the old German mysticism
and still further back to the ancient philosophy of the Vedanta, with
both of which Schopenhauer and most of his German predecessors
knew that their own thought was more or less closely connected.

Viewed from its first beginning to its present stage the develop-
ment of this type of thought goes on exactly in the way which
Bergson himself terms evolution creatrice. As a living process it
enters the thought of a philosopher in the shape last given to it by
the preceding generation. As a living process it is itself "creative,"
i. e., it assumes a new shape different from what it had before ; and

17 Conversations with Eckermann, Febr. 13, 1829.

CRITICISMS AND DISCUSSIONS. 6ll

in the brain of the following generation it certainly will change
again as a creative power.

Bergson's philosophy proceeds from an elan vital of thought.
This explains why it is saturated with the past and, as we may hope,
pregnant with the future. The past with which it is saturated, how-
ever, is neither pragmatism nor any American nor English philos-
ophy, for all these mean typical work of "understanding," while
for Bergson philosophy begins where understanding ceases. The
elan vital in Bergson's own philosophy is German and characteristic
of the close affinity between German and French philosophy — an
affinity which may be traced back all through the history of human
thought. In former ages the influence of French thought on Ger-
many preponderated over the influence of German thought on France.
Since the beginning of the nineteenth century it is the influence of
German thought on France which has preponderated because there
was a feeling that the elan vital of German thought is creative and
pregnant with a future. Never was its creative power developed
with more splendor and force than in Henri Bergson's philosophy.

GUNTHER JACOBY.

THE UNIVERSITY OF GREIFSWALD.

HENRI POINCARE: OBITUARY.

On July 17, 1912, the world lost the great French mathema-
tician whom Karl Weierstrass — one of the greatest mathematicians
of the nineteenth century — when writing to Sophie Kowalevsky,
specially singled out as one of the most eminent of the school of
younger French mathematicians.1

Jules Henri Poincare was born at Nancy on April 29, 1854.
He came of a family of which various members have risen to emi-
nence. His father was professor in the Faculty of Medicine at
Nancy, and wrote, among other works, on neurology at a time at
which such researches were only pursued by a small number of
scientific men. An uncle, Antoni Poincare, wrote on meterology;
and, of his two sons, one is M. Raymond Poincare, the present
President of the Ministerial Council, and the other is M. Lucien
Poincare, who is Director of Secondary Education and Minister of
Public Instruction. Henri Poincare's only sister married M. Emile

1Cf. G. Mittag-Leffler, Compte rendu du deuxitme congres international
des mathematiciens tenu a Paris 7900, Paris, 1902, pp. 145-148.

6l2 THE MONIST.

Boutroux, the distinguished philosopher, and their son, M. Pierre
Boutroux, is a well-known mathematician.

Henri Poincare was precocious, intellectually, and entered the
Ecole Polytechnique in 1873, and in 1875 the School of Mines as
engineering pupil ; in 1879 he gained the degree of Doctor of Mathe-
matical Sciences at the University of Paris; in the same year he
joined the Service of Mines as engineer; in 1881 he became pro-
fessor at the Faculty of Sciences in Paris; in 1887 he was elected
a member of the Academy of Sciences; and in 1908 he was elected
one of the forty "immortals" of the French Academy.

A biography of Poincare and a bibliography of his works has
been published by Ernest Lebon.2 Poincare's first original researches
were in pure mathematics. In 1880 the Academy of Sciences pro-
posed the theory of differential equations as the subject of the great
prize. Poincare sent in a sketchy memoir with the title "Non
inultus premor" — that of the town of Nancy — which did not gain
the prize but which Charles Hermite mentioned encouragingly in
his report. From the beginning of 1881 the subject — the integration
of certain linear differential equations — was developed with sur-
prising genius and rapidity in a series of papers presented weekly
to the Academy of Sciences. Weierstrass, who admired these papers
so warmly, thought it a pity that Frenchmen published their dis-
coveries in a succession of little papers. But surely the psychological
interest is heightened by this mode of publication. We know that
Poincare worked almost subconsciously, and often had no idea of
what he was going to discover. Gauss's motto was, Pauca sed
matura, and even now almost every publication of his is an almost
perfect and complete classic ; and yet how greatly do we feel the need
of some indication as to how these discoveries grew. Weierstrass
reminds us in many respects of Gauss. His works, too, were never
quickly published, and very many important things he found or
views he held were either not published at all, or only long after
he announced them, and then by his pupils. The case is different
with Poincare. One of the many reasons for which he will live is
because he has made it possible for us to understand him as well as
to admire him.

Poincare's name is associated, for the pure mathematician, with
the "Fuchsian," "Thetafuchsian," and "Zetafuchsian" functions. We
now call them, after Felix Klein, "automorphic" functions. But we

Paris

a Henri Poincare: biographie, bibliographie analytique des ecrits; 26. ed.,
s, Gauthier-Villars, 1912 (collection "Savants du Jour").

CRITICISMS AND DISCUSSIONS. 613

can only refer to his other researches on the theory of functions and
his allied work on the theory of numbers, and will now turn to his
works on astronomy and physics.

Poincare's investigations on the form taken by a gravitating
mass of fluid in rotation (1885-1901) led him to interesting theories
on the parting of the earth and moon and the formation of variable
stars. His researches on the stability of the solar system, which con-
sisted in the revision of Laplace's calculations and the carrying of
them to a higher order of approximation, showed that Laplace's
theory of 1784 was quite just. These and other results are con-
tained in Poincare's three volumes on the new methods of celestial
mechanics.3 Here we must also refer to his works on the tides and
on the problem of three bodies. On mathematical physics, Poincare
published many volumes of lectures given at the University of Paris
and elsewhere on light, electricity — including the theory of Maxwell
— capillarity, vortices, potential, thermodynamics, the theory of the
conduction of heat, elasticity, and the theory of wireless telegraphy.
Besides these, his lectures on the calculus of probabilities and on
various subjects in celestial mechanics have been published.

Some very interesting psychological and physical details about
Poincare were published in 1900 by Dr. Toulouse as the second
volume — the first was chiefly occupied by a study of Emile Zola —
of his Enquete medico-psychologique sur la superiorite intellectuelle*
The help given to the scientific answering of the question : "Le genie
est-il une nevrose?" by such studies is, of course, immense; but
most of my readers are more concerned with the qualities associated
with the great mathematical capacities of a man who took such a
keen interest in questions on the border-line between mathematics
and philosophy.5 It is impossible to read Dr. Toulouse's book with-
out gaining a very vivid picture of the personality of Henri Poin-
care. It is always deeply interesting to read authentic accounts of
the methods of work of mathematicians, and for some years past,
MM. H. Fehr, Th. Flournoy and E. Claparede have conducted an
inquiry on this subject in the columns of L' Enseignement mathe-
matique. Poincare himself, in a well-known article published in
1908, has made some striking observations on his own process of
mathematical discovery. And we must, I think, bear in mind, when

8 Les Methodes nouvelles de la Mecanique celeste, Paris, 1892-1899.
* Henri Poincare\ Paris, Ernest Flammarion.

8 Poincare's work in this direction is well known to readers of The Monist
by the translations of George Bruce Halsted.

614 THE MONIST.

reading Poincare's articles on the logic of mathematics, that they
are the work of a man who was primarily — perhaps almost exclu-
sively— interested in the faculties of invention. When mathematical
logicians asserted that the whole of mathematics follows by logical
principles alone from concepts which can be logically defined and
from the primitive propositions of logic alone, Poincare and many
other mathematicians objected that "intuition" was left out of ac-
count. There is a great likelihood that this is not really Kantianism
in mathematics ; only phrases make it seem so. Kant clearly recog-
nized the distinction between the question as to whether a truth B
is logically implied by a truth A and that as to whether B is dis-
covered by a certain person who starts from the premise A alone and
uses only purely logical considerations. The mathematical logicians
do not deny to the seeker of truth either genius or the creative power
— if such exist — of the artist ; they are concerned with an epistemo-
logical question, and psychological objections are irrelevant there.
The case is analogous to this: If someone were to point out that
the properties of logarithms are simple consequences of the con-
ception of one number as a power of another, he would not be con-
futed by the remark that Napier did not invent logarithms in that
way; or again, it is not relevant to the student of Keats's poetry,
as such, to know what porridge John Keats ate.

If this interpretation of the attitude of the "creative" mathema-
ticians is correct, their position with respect to mathematical logic
is easily explained. That the interpretation is correct seems sup-
ported by Poincare's last controversial work on mathematical logic
which he gave this year as a lecture to London University, and which
has just been printed in Sciential In the previous discussions on the
use of the infinite in mathematics, in which Poincare joined, each side
kept on repeating the same arguments. There seems, in fact, a
fundamental difference in mentality among mathematicians. Some,
whom Poincare called "pragmatists," believe that the infinite is
derived from the finite, and all verification and all definition is per-
formed with a finite number of words ; others, the "Cantorians,"
believe that there are objects and truths which cannot be defined or
demonstrated in a finite number of words. The Cantorians are
realists and believe that the truth of a proposition does not depend
on its verification by us. It is not difficult to place Poincare, on the

6 "La Logique de rinfini," Scientia (Rivista di Sciensa), July, 1912, pp.
i-n.

CRITICISMS AND DISCUSSIONS. 615

grounds of some of his writings, among those whom he not inap-
propriately calls "pragmatists."

When Poincare was five years old, he had a severe attack of
diphtheria, and partial paralysis. All this made him rather weak for
a long time, and perhaps was the origin of his lifelong clumsiness.
Of his absence of mind, many stories are told. Once during a walk,
he was suddenly surprised to find a wicker bird-cage in his hand.
He had unconsciously removed it from a wayside stall.

As regards religion, at the moment of his first communion he
was a believer ; then belief left him gradually, and, from the age of
eighteen he was a sceptic. In politics he was a republican ; he held
to the principle of personal property ; he believed in political equality
and the political rights of women, — but here he feared clerical in-
fluence.

In mathematics, he cannot be said to belong to any school. In
a short life not without physical drawbacks, he has, by regular work,
produced about 500 writings — some of them of the very first order.

PHILIP E. B. JOURDAIN.

THE LODGE, GIRTON, CAMBRIDGE, ENGLAND.

HENRI POINCARE: AN APPRECIATION.

The foremost of Frenchmen is no more. When Laplace was
asked to name the greatest German mathematician he answered,
"Pfaff." "But how about Gauss?" said the inquirer. "Ah," replied
Laplace, "he is the greatest of all mathematicians." Similarly we
might modify our first statement and declare that the foremost of
all men is no more. For on July 17, having apparently recovered
almost completely from a surgical operation undergone only a few
days before, Henri Poincare, while dressing himself in the morning,
was suddenly smitten with an embolism and fell dying in the arms
of his wife. While the delegates of learning from all quarters of the
globe were assembling in London to celebrate the 250th anniversary
of the Royal Society, instantly the brightest star in the galaxy of the
sciences was eclipsed forever. The sad intelligence was at once
flashed around the world, but the details as set forth in the Paris
journals of the 18th are but lately at hand.

Commanding the homage, and admiration of all, so generous,
so pure-hearted, so noble-minded was Poincare that he aroused the
envy and jealousy of none. If "Freedom shrieked when Kosciusko
fell," with far more propriety may universal Science, may Philosophy

6l6 THE MONIST.

herself, weep at the passing of her illustrious son. For Poincare
was not a mere specialist, an isolated summit of technical learning,
but rather a mountain range of knowledge. His Andean intellect
traversed the whole continent of science. In physics, in mathematics,
in astronomy, in logic, in philosophy even, he strode from peak to
peak in the heights of thought, and wherever his feet touched, there
was a blaze enkindled. His compatriots say that France has borne
no equal in a hundred years, not since d'Alembert and Laplace. To
a foreigner it may be questionable whether the limit may not be
pushed much further back, even to the days of Descartes. For while
the mind of Poincare did indeed cast off no single orb of thought
to match at once in largeness and in luster the Mecanique celeste,
or still more the Theorie analytique des probabilites, yet it has studded
the firmament of exact science with a host of splendors. Scarcely
if at all inferior to Laplace or even to Lagrange as analyst, as geom-
eter, as physicist, as astronomer, Poincare was what they were not
— he was a logician of the first order and a philosopher, profound,
penetrating, and spiritual. Nor was this all; for his genius in ex-
position allied him with Clifford and brought him into livelier sym-
pathy with the lay intellect than almost any of his peers in the realm
of pure science, while his fine artistic nature and literary sense ex-
pressed themselves in a style at once clear and concise, nervous,
vivid, picturesque and animated. As subtle as Hume, as compre-
hensive as Helmholtz, he was least of all a dry-as-dust savant; the
keenest of logicians, he did not disdain the graces of rhetoric, but
poured out for his fellows the divine draughts of his thought in
golden goblets of speech.

It was not, however, as mathematical physicist, as analyst of
Fuchsian functions, not as student of the stability of the solar system,
not as discoverer of unsuspected figures of equilibrium, not as master
of metageometry, not as preeminent logician of science, not as any
nor as all of these, that Poincare rendered his highest service to
humanity. It is his supreme merit to have recognized explicitly the
inalienable rights of the human spirit, to have opposed firm as Gib-
raltar the rising tide of naturalism and the pride of knowledge
which, intoxicated with the triumphs of physical science and its ap-
plications, refuses to see any mystery beyond sense remaining in the
world, and boldly aspires by means of mind to pull down mind from
its throne and to reduce the universe to a molecular maelstrom, to
a wisp of granulated ether. When Napoleon asked Laplace about
having written so great a book without once naming the name of God

CRITICISMS AND DISCUSSIONS. 617

therein the savant replied, "Sire, I have no need of that hypothesis."
Lagrange, a finer spirit, on hearing of this commented: "But it is
a beautiful hypothesis that explains many things." In his famous
mot Laplace has declared his kingship and at the same time defined
his kingdom. True, in the realm of matter he had no need of the
beautiful hypothesis ; in the kingdom of causality, of mass and mo-
tion, there is no purpose, no reason, and hence no need of God, the
Reason of all. But Poincare saw through all the phantasies of
"scientists," as the astronomer sees through the nebula in Orion,
and beheld far behind the phenomena of time and space the eternal
realities of self and of soul; while peering into the processes of
physical nature deeper even than Laplace himself, he never forgot
that they are after all an unsubstantial pageant, that

"On earth is nothing great but man,
In man is nothing great but mind."

So he became in a sense the moderator of the assembly of the
sciences. As no other living man he could say, "Thus far and no
further ;" for he spake as one having authority. Even the Germans,
who are seldom over-quick to acknowledge the hegemony of others
in the ranks of thought, forgot all national and racial prejudices in
the presence of Poincare and freely declared him to be "the first
authority of this age" (die erste Autoritat von dieser Zeit).

The savant closed his eyes at the age of fifty-eight in the full
flush of his powers, at the fever-heat of his intellectual activity.
What more he might have done, who knows? But assuredly his
mantle will fall upon worthy if not upon equal shoulders ; in the
paths he has broken there will follow increasing throngs. It is our
human form of speech to deplore an irreparable loss. But in some
larger, deeper and higher, though indefinable, sense there is perhaps
only gain forevermore.

"One accent of the Holy Ghost
The heedless world hath never lost."

Le roi est mort : vive le roi. Poincare is dead : but deathless is
Poincare.

WILLIAM BENJAMIN SMITH.
TULANE UNIVERSITY.

6l8 THE MONIST.

THE CAPTURE THEORY OF COSMICAL EVOLUTION

CONFIRMED BY THE LATEST RESEARCHES ON

THE ORIGIN OF STAR CLUSTERS.

Introductory Remarks.

It is a very remarkable fact that since the epoch of Sir William
Herschel little serious consideration has been given to the origin of
star clusters, until within the last few years. Accordingly the
thoughtful suggestions thrown out by that unrivaled man long
proved largely if not entirely barren of fruitful results for the de-
velopment of a science of cosmogony, because his early ideas were
lost sight of or forgotten. We have labored under a strange delu-
sion, of preferring the theories of Laplace to those of Herschel,
but have at last found the way from darkness to light, from error
to truth. And it happens that of all the investigations yet made in
cosmogony those relating to the neglected subject of star clusters
are the most convincing and least open to objection.

In a paper entitled "Dynamical Theory of the Globular Clusters
and of the Clustering Power Inferred by Herschel from the Ob-
served Figures of Sidereal Systems of High Order," recently com-
municated to the American Philosophical Society held at Philadel-
phia, and just published in the Proceedings of that illustrious
society, I have examined the whole problem of the origin of clusters
in a somewhat exhaustive manner. By the use of mathematical
methods of rigorous character, I was able to develop the most con-
vincing proofs that these aggregations of stars have arisen by the
process of capture in the course of millions of ages. It will be the
main purpose of this article to discuss the results arrived at in this
general investigation of the origin of star clusters; but before tak-
ing up this subject in detail it will be allowable to treat briefly of the
conclusions reached by the illustrious Poincare in his Leqons sur les
Hypotheses Cosmo goniques, 1911, and to notice also the unimportant
objections advanced by Prof. Charles Andre in Scientia, No. 2, 1912.

The Views of Poincare.

In his Legons sur les Hypotheses Cosmo goniques, 1911, M.
Poincare gives a summary of the various theories of cosmogony,
and in two chapters discusses results arrived at in my Researches
on the Evolution of the Stellar Systems, Vol. II, 1910.* He exam-

* These chapters appeared in translation in The Monist of July, 1912.

CRITICISMS AND DISCUSSIONS.

ines and adopts the proof therein given that the roundness of the
orbits of the planets and satellites is due to the secular effects of
the action of a resisting medium. He concurs in the capture of
satellites, as well as in the new theory of spiral and ring nebulae.
M. Poincare especially remarks how well the resisting medium ex-
plains the roundness of the orbits of the planets and satellites ; and
altogether is favorable to the recent development of cosmogony into
a new science of the starry heavens.

One point in my work, however, has been slightly misunderstood
by Poincare, and I will therefore dwell upon it here. After out-
lining the leading principles of the Capture Theory he adds that
while it fully explains the roundness of the orbits, it does not give
a satisfactory explanation of the inclinations of the planetary orbits.
But here he has evidently lost sight of the nature of the spiral nebula
from which our solar system is supposed to have arisen.

The Capture Theory means primarily that all revolving bodies
are added on from without, — the planets being added to the sun
and the satellites added to the several planets ; but it is not held that
the entrance into our system was from all directions over the celes-
tial sphere and thus entirely at random. On the contrary it is care-
fully explained in my work that the system from the beginning had
a fundamental plane of maximum areas, due to the fact that a spiral
nebula is formed by two principal streams coiling about one another ;
and the plane of maximum areas is the plane determined by these
predominant streams.

In the condensation of a nebula an infinite number of minor
streams probably are involved ; but the whirling motion is made
possible only by two predominant streams, as shown in photographs
of spiral nebulae. That is to say, there is more matter in the two
large streams than in the smaller ones ; and this gives a fundamental
plane to the system when it becomes mature, just like that in which
the planets of the solar system are found to move. The planetary
orbits ought not to lie exactly in the same plane, but near an in-
variable plane, such as Laplace in 1784 proved to exist in every
system of bodies subjected to the mutual gravitation of its parts.

The comets or smaller masses of nebulosity naturally should
be inclined at all angles to the invariable plane ; but as they intersect
that plane twice in their orbital motion about the sun, they will sooner
or later pass near a planet revolving in an orbit lying near the fun-
damental plane of the system, and their orbits are thus subjected to
profound changes of position as well as of form and extent. Count-

62O THE MONIST.

less comets are destroyed in building up the planets; so that much
matter not originally lying in the plane of the planets is finally cap-
tured and drawn into that plane, as the masses of the planets grad-
ually augment, and they are drawn nearer the sun in orbits becom-
ing ever smaller and smaller, and rounder and rounder.

Thus on the one hand the resistance of cometary matter reduces
the. size of the planetary orbits and makes them rounder, while on
the other hand the growth of these masses increases their mutual
attraction; and if they were originally near the plane of the pre-
dominant streams, in time they come to move almost exactly in one
plane, as now observed in our actual planetary system.

For as our system has shrunk, and the original orbits were
hundreds of times larger than at present, the nuclei at the outset
were not necessarily very near the plane in which they now move,
but may have departed from it considerably. Mutual inclinations
of a few degrees now found in our system are magnified at hundred-
fold primordial distances into very great absolute distances; so that
the original streams need not have been at all compressed, but may
have been exceedingly diffuse, just as actual nebulae appear to be.

Accordingly it is a remarkable fact that the theory which ac-
counts for the roundness of the orbits of the planets also explains
the small mutual inclinations of their orbits, and the rotation of the
sun about an axis nearly perpendicular to the plane in which the
planets revolve. The explanation of the origin of our system from
a spiral nebula thus appears to be entirely satisfactory.

The Views and Objections of Andre.

The objections to the Capture Theory advanced by Andre are
easily shown to be without the slightest foundation. It is quite
unnecessary to consider most of them, and I will therefore content
myself with the three chief ones, which will sufficiently show the
weakness of the rest.

1. Andre claims that the spherical expansion in Babinet's cri-
terion as I have used it is not strictly in accordance with Laplace's
theory, because Laplace did not imagine the sun's atmosphere to be
expanded in a spherical form, but rather in the form of a flat disc.
This objection is quite devoid of foundation, as will appear from the
following simple considerations.

a. If the expansion be spheroidal, as a flat disc, more of the
matter is at greater distance from the center, for given volume,
than in a spherical expansion; so that the moment of inertia is in-

CRITICISMS AND DISCUSSIONS. 621

creased, and with constant moment of momentum the angular veloc-
ity is therefore decreased. Hence a discoidal expansion of the sun
is more unfavorable to Laplace's hypothesis than the spherical ex-
pansion used by me. For in case of a sphere the moment of inertia
is shown in works on the calculus to be 2/5 (Mr2), where r is the
radius and M the mass ; in an ellipsoid with equatorial axes a and b
it is M/5(a2 + b2), and when a-b} as in an ellipsoid of revolution,
this becomes 2/5 (Ma2), a being the equatorial axis.

b. To reduce this to numbers I took ellipsoids with meridian
sections of eccentricity 0.10, 0.25, 0.5, and 0.8, giving oblatenesses
of 0.00501, 0.03176, 0.13397, and 0.40000 respectively; and found
a2 = 1 .00336r2 ; a2 = 1 .0217r2 ; a2 = 1 . 1525r2 ; a2 = 1 .4057r2. This
shows how the moment of inertia increases as the oblateness in-
creases, and thus proves a corresponding decrease of the angular
velocity of rotation below that published in my tables of Babinet's
criterion. The objection of Andre therefore has not the slightest
foundation, because my calculations are more favorable to Laplace's
theory than those based on the theory of an oblate spheroid.

2. Andre dwells on the fact that Laplace imagined only the
atmosphere of the sun expanded to the orbits of the planets. But
as the sun itself when so expanded becomes much rarer than most
atmospheres we are familiar with, it is readily seen that this point
is not well taken. When the sun is expanded to Neptune's orbit,
the average density of the nebula is 260 million times less than that
of air at sea level. Nothing more need be said on this point. Such
a medium could exert little or no hydrostatic pressure from the
center, and Laplace's theory of the detachment of zones of vapor
under conditions of hydrostatic pressure implies that he overlooked
the rarity of this medium, which makes such a thing as hydrostatic
pressure quite impossible. No alteration of central arrangement
of density would materially change this result, and we may thus
dismiss it without further comment.

3. As the centrifugal force, by Babinet's criterion, is only a ten
millionth part of that required to detach the earth, and a three hun-
dred millionth of that required to detach Neptune, while the hydro-
static pressure likewise is insensible, it is clear that no such detach-
ment as Laplace imagined ever took place. Andre, Ligondes and
other French writers are simply injuring the memory of Laplace
by presenting to the Paris Academy of Sciences conclusions which
would be immediately rejected by Laplace himself if he were living
to-day.

622 THE MONIST.

After having studied the works of this great master of celestial
mechanics from the days of my youth, I believe I have followed
his spirit in rejecting what is now known to be false. Professor
Andre is in the unfortunate position of having written books favor-
able to the abandoned theory of Laplace ; but he should aim at truth
rather than perpetual consistency, and modify his views to meet the
latest discoveries in science. For a true philosopher does not aim
at supporting his earlier writings, but at gradually attaining the
truth, even if his first work has to be modified or entirely abandoned.
The successors of Laplace obviously should act upon this laudable
principle.

4. Even if the retrograde satellites and a multitude of other
phenomena did not tell us unmistakably that all the satellites have
been captured, and we still tried to explain these bodies by the de-
tachment theory of Laplace, we should remain quite in the dark as
to the origin of the observed rotations. They would be simply
assumed, and not explained ; and so we should have no rational
theory of the formation of the solar system; whereas the Capture
Theory gives a simple and natural explanation of the rotations and
obliquities as well as the orbital motion of the satellites, and the
variations of their brightness, the lunar craters and maria and kin-
dred phenomena ; and all the phenomena are so woven together that
it is impossible to doubt the truth of the new theory.

In the same way, even if the solar nebula could have rotated
rapidly enough to detach zones of vapor as Laplace imagined, it
would still be impossible to account for so rapid a rotation. For-
tunately Babinet's criterion shows that no such rapid rotation for the
detachment of zones of vapor ever took place ; and that Laplace was
deceived by the roundness of the planetary orbits, which we now
recognize to be due to the secular action of the nebular resisting
medium formerly pervading our solar system.

Necessity for Wider View of all Sidereal Systems.

It requires no elaborate argument to convince any philosophic
investigator that the laws of cosmical evolution can best be deduced
from the study of nature in the widest sense. The narrowness of
the cosmogony of Laplace arose from the fact that it was based
wholly on our solar system, and that too before the system was
fully understood. The roundness of the orbits of the planets and
satellites and the survival of a ring about Saturn led to the idea

CRITICISMS AND DISCUSSIONS. 623

that all these bodies had originated by the detachment of rings.
Yet as soon as the orbits of the double stars were determined, they
were found to have eccentricities of every degree, between the round
orbits characteristic of the planets and satellites and the very elon-
gated orbits characteristic of the comets. The development of double
stars obviously could not have been by the formation of rings as im-
agined by Laplace.

Accordingly without such a comprehensive view of the different
types of systems it would be vain to hope for the deduction of a
general law of nature. The folly of adhering to the old methods
of Laplace based on an imperfect knowledge of the solar system
alone is thus apparent ; and after what is now shown, from Babinet's
criterion, as to the impossibility of detaching masses or rings, there
is no course open to us but to reject Laplace's hypothesis once for
all. It does not give us a general law of nature, and is not true
even for the special case of the solar system.

Our hope for finding the law of nature must be based on the
study of double and multiple stars, and sidereal systems of higher
order. Now it happens that of the various sidereal systems known
to the astronomer, the globular clusters are the most complex, and
at the same time the most symmetrical and regular in their consti-
tution. If therefore any light can be obtained on the formation of
sidereal systems of such high order, it might be possible to derive
principles which could be applied to less symmetrical systems of
lower order. This is what I have done in my recent investigation of
the origin of clusters. Having deduced the law of nature from the
highest and most complex systems, with wonderful regularity of
figure, I have proceeded to apply it also to systems of the lowest
type, as the solar system and the double and multiple stars. This
new method of procedure is so important, that it becomes advisable
to explain it in some detail.

Nature of Clusters, Average Distance of the Stars Apart, Increase
of Density Towards Center.

Sir William Herschel always considered the globular clusters
to be the most wonderful of all sidereal systems. He never ceased
to marvel at the existence of these swarms of stars, which were
known to be aggregations of suns; and he inferred that at length
they had been moulded into the spherical form by the action of cen-
tral powers.

624 THE MONIST.

Even in the time of Herschel it was recognized that the clusters
are very far from the earth, and thus that the component stars are
not really close together, but separated by intervals which are very
great compared to those which separate the planets from the sun.

More modern discovery has confirmed the sagacious conjectures
of the great Herschel. The latest investigation of the profundity
of the Milky Way, which I finished in November, 1911, and have
just published in the Proceedings of the American Philosophical
Society at Philadelphia, shows that the remotest clusters are re-
moved from us by at least a million light-years. Indeed this deter-
mination of the depth of the Milky Way shows that the remotest
stars may be removed from us by distances of five or ten million
light-years; but even with most of the clusters at distances of hun-
dreds of thousands of light-years, it is possible to say with certainty
that the average space between the stars in globular clusters is of
the order of a light-year, which is 63275 times the distance of the
earth from the sun. We thus have the spectacle of systems of stars
separated by great intervals, but so remote as to be drawn together
by perspective into a small angular space on the surface of the sky.

The density in these masses of stars was found by Herschel
to be always greatest towards the center; and in fact to be in
excess of that corresponding to the supposition of equal scattering.
Herschel therefore inferred that the accumulation in the centers
of the clusters must be due to the secular action of a clustering
power, which he believed to be nothing else than universal gravi-
tation working over millions of ages. He remarked that the Milky
Way presented the aspect of a clustering stream traversing the
heavens as an irregular band of milky light; and as he had found
the sidereal universe to be greatly extended in the direction of the
plane of the Milky Way, he correctly inferred that the clustering
stream thus presented to the eye was the effect of distance and of
local aggregations of the stars into star-clouds and clusters. The
stars are spread out into a comparatively thin stratum, and at great
distance the effect is to give the appearance of the Milky Way,
which thus appears as a clustering stream several degrees in width.

How the Stars are Captured in Clusters.

In the memoir above referred to I have established the capture
of stars by a cluster, and the secular shrinkage of the cluster, by
the use of Green's theorem for the transformation of a triple in-

CRITICISMS AND DISCUSSIONS. 625

tegral appropriate for space into a double integral over the surface
of the cluster. By showing that the surface shrinks as the result
of close appulses among the stars, and also as the outcome of mutual
gravitation, even when no close approach occurs, it is found that
the cluster becomes more and more compressed, with density ac-
cumulating towards the center.

The attraction of members of a cluster is analogous to surface
tension in working to decrease the volume of a bubble, or in round-
ing up a drop of dew, to give minimal surface for a given volume.
In the same way gravity tends to make a planet perfectly round,
except as modified by rotation into an oblate figure. Herschel used
such analogies in his argument for a clustering power, which he
inferred to be moulding the figures of clusters. And recently I have
tested his suggestion mathematically, and found a conclusive proof
that the argument is correct.

To give a simple analogy for the capture of stars in clusters,
with known processes in the solar system, we may remark that
Jupiter captures the comets crossing over his orbit, and transforms
their paths till they lie wholly within that of the planet. In this
way he has captured quite a family of comets and thrown their or-
bits within his own orbit. Now in the memoir above referred to
I have shown that a shell of stars in a cluster acts very much as
Jupiter does on the comets — and thus tends to reduce the path of an
oscillating star till it comes within the confines of the shell.

Accordingly if a star from without once enters a cluster, and
thus begins to traverse the series of shells of which the cluster
is made up, it will never quit the swarm but be gradually drawn in,
and captured, during one or more complete oscillations. The ex-
tent of its outward journey from the cluster, if any occurs, will be
decreased, until finally it is dragged down to the level of the shell,
and becomes a member of the cluster. This is one of the most re-
markable results of our dynamical theory of clusters. The Cap-
ture Theory being thus verified for these globular masses of stars,
it naturally may be expected to operate in systems of lower order.

No Possible Origin of Clusters Except that Outlined by the Capture

Theory.

The globular clusters are so perfectly symmetrical that they
become of high interest in elucidating the problems of cosmogony.
For it is not conceivable that systems of such large mass, great

626 THE MONIST.

extent and perfect symmetry, can have arisen, except by the gather-
ing together of stars from a wider extent of space.

No process of collision, for example, would account for the
globular clusters; for by impact the matter of two hypothetically
disrupted masses would neither be symmetrically distributed nor
dispersed over such a vast space as that now occupied by the thou-
sands of suns composing a cluster. Then, again, to be effective
such hypothetical collision would have to be between approximately
equal giant suns; and there are too few stars of such enormous
mass for pairs of them ever to come into bodily collision.

Accordingly, a little consideration shows us, on the one hand,
that such giant collisions would not occur; and, on the other, that
even if they could take place such widely diffused and symmetrical
swarms of stars could not arise by this process. The globular
clusters therefore are due to the aggregation of stars once symmetri-
cally and widely distributed in space. This gives us a good illus-
tration of the Capture Theory on the most stupendous scale. Simi-
lar views were reached by Herschel, without mathematical investi-
gation of the subject, such as I have recently developed; and it
may be remarked that he found the evidence of a clustering power
most convincing.

The New General Catalogue of Nebulae and Clusters, published
by the Royal Astronomical Society of London in 1888, contains a
list of more than one hundred globular clusters, mostly distributed
along the course of the Milky Way. The clustering of the stars
into great systems about so many centers shows how general and
widespread this tendency is in nature.

If now we recall that only the oldest sidereal systems can have
attained a state of perfect symmetry, it is obvious that a larger
number of sidereal systems might be expected to have an irregular
and unsymmetrical aspect. The globular clusters are therefore only
a part of the aggregations of stars exhibiting the effect of the
clustering power; but the perfection of this type of system renders
it eminently adapted to disclosing the process by which all clusters
are formed. For if the law of nature can be deduced from the
perfect type of sidereal development, it may with equal certainty
be inferred to operate in those sidereal systems which have not yet
attained to full maturity. By investigating the different types of
sidereal systems our studies may thus disclose the general law of
cosmical evolution and embrace phenomena extending over millions
of ages!

CRITICISMS AND DISCUSSIONS. 627

The Law of Nature Embraces also Systems of Lower Order, and

Therefore the Planetary System and the Systems

of Double and Multiple Stars.

Those who believe in the uniformity and continuity of the laws
of nature, as laid down by Newton in the Principia, 1687, will
quickly realize that the law of cosmical evolution established for
the globular clusters should necessarily hold also for systems of
lower order. Rule I: "We are to admit no more causes of natural
things than such as are both true and sufficient to explain their
appearances." Rule II: "Therefore to the same natural effects we
must, as far as possible, assign the same causes."

Accordingly, in line with these rules of Newton, I have shown
that the Capture Theory will explain the formation of the solar
system, as well as the double and multiple stars: and having found
the principle to be the same throughout the sidereal universe, I have
inferred that nature's law everywhere is one of adding on from
without. The component stars are added to the clusters, and drawn
nearer and nearer the center; the planets added to the sun and
made to revolve in smaller and smaller and rounder and rounder
orbits. Likewise the satellites were added on to their several plan-
ets, and the moon captured by the earth. The double and multiple
stars were formed on the same principle — the nuclei having origi-
nated in the distance, and subsequently approached the centers about
which they now revolve. This gives us a general law of nature of
the utmost simplicity.

And not only is the generality of the law proved by force of
analogy, but also by direct mathematical demonstrations in the solar
system, deduced from Babinet's Criterion; while in the clusters the
proof is so obvious that it need scarcely be emphasized. The demon-
stration of this law in the double and multiple stars is similar to
that available in the solar system; and moreover is supported by
the analogy of the clusters, into which the multiple stars merge
by insensible degrees, when the number of bodies in a group is in-
creased indefinitely.

Accordingly nothing is more certain than that the law of cos-
mical evolution now recognized is the true law of nature. It does
not even resemble the abandoned theory of Laplace, but has con-
siderable resemblance to the general outline of the nebular hypoth-
esis as traced by Sir William Herschel. In particular Herschel's
theory of clusters, as originating by the aggregation of isolated

628 THE MONIST.

stars is deserving of attention; for this is the earliest outline of a
process of capture similar to that now worked out in detail and
shown to be applicable to all types of systems observed in the sidereal
universe.

In conclusion it seems advisable to close this discussion by the
following summary quoted from my latest memoir on The Dynam-
ical Theory of Clusters.

Summary and Conclusions.

Without attempting, in this closing section, to recapitulate the
contents of this memoir in detail, it may yet be well to draw atten-
tion to some of the most significant conclusions at which we have
arrived.

1. As intimated in the first section of this paper the problem of
w-bodies, under ideal dynamical conditions, remains forever beyond
the power of the most general methods of analysis ; but the dynam-
ical theory of clusters gives us the one secular solution of this prob-
lem found under actual conditions in nature. For when n is of the
order of 1000, so as to give rise to a cluster, the clustering power
observed by Herschel operates to exhaust the mutual potential en-
ergy of the system, and bring about increasing accumulation in the
center, so that the cluster finally unites into a single mass of enor-
mous magnitude. Probably the giant stars of the type of Canopus
and Arcturus have arisen in this way.

2. And since attendant bodies of every class — as satellites, plan-
ets, comets, double and multiple stars — tend everywhere to approach
the centers about which they revolve, as an inevitable effect of the
growth of the central masses and of the action of the resisting
medium over long ages, it follows that the secular solution of the
problem of clusters is more or less valid for all cosmical systems.
They finally end by the absorption of the attendant bodies in the
central masses which now govern their motions.

3. The dynamical theory of globular clusters shows that the
clustering power inferred by Herschel is nothing else than the action
of universal gravitation ; and that it operates on all sidereal systems,
but does not produce the cumulative effect which Herschel ascribed
to the ravages of time inside of millions of ages.

4. The globular clusters are formed by the gathering together
of stars and elements of nebulosity from all directions in space ; and
this points to the expulsion of dust from the stars of the Milky Way,

CRITICISMS AND DISCUSSIONS. 629

and its collection about the region of the formation in such manner
as to give essential symmetry in the final arrangement of the cluster,
which doubtless has some motion of rotation, and originally a ten-
dency to spiral movement.

5. The stars and smaller masses are captured by the mutual action
of the other members of the cluster, and worked down towards the
center of the mass. This gives a central density in excess of that
appropriate to a sphere of monatomic gas in convective equilibrium
(A. N. 4053 and A. N. 4104).

6. The density of the clusters is greater on the outer border
than in a globe of monatomic gases, which shows that stars are still
collecting from the surrounding regions of space. The starless
aspect of the remoter regions about clusters is an effect of the rav-
ages of time, as correctly inferred by Herschel in the course of his
penetrating sweeps of the starry heavens.

7. And just as clusters under the mutual gravitation of the com-
ponent stars contract their dimensions, with time, chiefly owing to
the growth of the central masses, so also do other systems, whether
the mass-distribution be single, giving a system made up of a sun
and planets, or double, triple and multiple, giving binary, triple or
multiple stars, or sidereal systems of still higher order. The ten-
dency everywhere is from a wider to a narrower distribution of the
large bodies ; while the only throwing off that ever occurs is of par-
ticles driven away from the stars by the action of repulsive forces.

8. The orbits of the stellar and planetary systems are decreased
by the growth of the central masses and rounded up by the action of
the nebular resisting medium. And in like manner all clusters tend
to assume spherical or globular figures, so as to justify the expression
of Plato, that the Deity always geometrizes; or Newton's remark
that the agency operating in the construction of the solar system was
"very well skilled in mechanics and geometry."

9. Newton required the intervention of the Deity to give the
planets revolving motion in their orbits, because in the absence of
repulsive forces he could not account for the dispersion of the matter
so as to produce the tangential motions actually observed. By means
of the theory of repulsive forces, however, it is now possible to
explain these projectile motions, which Herschel likewise pointed to
as the chief agency for the preservation of sidereal systems. The
only assumption necessary is an unsymmetrical figure of the primor-
dial nebula, giving a whirling motion about the center as the system
develops ; and since the dust gathers from all directions it is certain

630 THE MONIST.

that this lack of perfect symmetry will always develop, as we see
also by the spiral nebulae.

10. It is this unsymmetrical form of the spiral nebulae produced
by the gathering of the dust from the stars, or the slight relative
tangential motion of stars formed separately but finally made to
revolve together as a binary system, that gives the projectile forces
with which they are set revolving in their orbits. In no case have
they resulted from the rupture of a rotating mass of fluid under
conditions of hydrostatic pressure as formerly believed by Darwin,
Poincare and See.

11. Even if the rotation could become rapid enough to produce
a separation, under conditions of hydrostatic pressure, by rupture
of a figure of equilibrium, there would still be the equal or greater
difficulty of explaining the origin of the primitive rapid rotation.
This last difficulty escaped notice till we came to assign the cause
of rotations, and found that mechanical throwing off was impossible
under actual conditions in nature. It is therefore recognized, from
the definite proof furnished by Babinet's criterion in the solar sys-
tem, that such a thing as a throwing off never takes place ; but that all
planetary and stellar bodies are formed in the distance, and after-
wards near the centers about which they subsequently revolve.

12. This gives us a fundamental law of the firmament — the
planets being added on to the sun, the satellites added on to their plan-
ets, the moon added on to the earth, and the companions added on to
the double and multiple stars — which now is found to be beautifully
confirmed by the dynamical theory of the globular clusters. It is
not often that such a great law of nature can be brought to light, and
it is worthy of the more consideration from the circumstance that it
explains all classes of stellar systems by a single general principle.

13. As sidereal systems of lower order are conserved by projec-
tile forces, it is probable that the clusters likewise have a spiral
motion of rotation, with similar projectile forces tending to counter-
act simple progressive collapse. The period of the orbital revolution
of the stars of a cluster is found to be common to all, without regard
to the dimensions of the elliptical orbits described; and thus the
whole system may have a common period of oscillation, after which
the initial condition is perfectly restored. This possibility in the
dynamics of a cluster is exceedingly wonderful and results from the
central attraction depending directly on the distance.

14. The equality of brightness in star clusters shows that some
process of compensation between the attractive and repulsive forces

CRITICISMS AND DISCUSSIONS. 63!

has produced stars of wonderful uniformity of luster. Thus the
present investigation confirms the previous researches on the evolu-
tion of the stellar systems, which have laid the foundations for a New
Science of the Starry Heavens.

15. Accordingly the Capture Theory of cosmical evolution being
now firmly established for the clusters, where the nature of the
process is entirely clear, it becomes at once a guide to us in dealing
with systems of lower order; and we see that the law of nature is
uniform and everywhere the same, the large bodies working in
towards the centers of attraction, while the only throwing off that
ever takes place is of small particles driven out of the stars by the
action of repulsive forces. All planetary bodies are formed in the
distance, and have their orbits reduced in size by increase of the
central masses, and rounded up by moving in a resisting medium.
This is a perfectly general law of the sidereal universe. It verifies
the early conjectures of Plato and Newton concerning the stability
of the order of the world and shows that these illustrious philosophers
were quite justified in concluding that the Deity always geometrizes.
The spiral nebulae tend to develop systems with rounder and rounder
orbits, and the clusters made up of thousands of stars assume globu-
lar figures with minimal surfaces and internal density so arranged
as to give maximum exhaustion of the potential energy.

16. This is geometry of the most marvelous kind, as we find it
impressed on the systems of the sidereal universe ; and the perfection
of this most beautiful science of celestial geometry may be considered
the ultimate object of the labors of the astronomer. The philo-
sophic observer is not and never can be content with mere observa-
tions of details which do not disclose the living, all-pervading spirit
of nature.

17. If, then, the mystery of the gathering of stars into clusters
is now penetrated and traced to the clustering power of universal
gravitation, so also is the mystery of the converse problem of starless
space, which was a subject of such profound meditation by the
great Herschel.

18. This incomparable astronomer likewise correctly concluded
that the breaking up of the Milky Way into a clustering stream is
an inevitable effect of the ravages of time ; but we are now enabled
to foresee the restorative process, under the repulsive forces of na-
ture, by which new nebulae, clusters and sidereal systems of high
order will eventually develop in the present depopulated regions of
starless space.

632 THE MONIST.

19. If there be an incessant expulsion of dust from the stars
to form the nebulae, with the condensation of the nebulae into stars
and stellar systems, while the gathering of stars drawn together
by a clustering power operating over millions of ages gives at length
a globular mass of thousands of stars accumulating to a perfect
blaze of starlight in the center, but surrounded externally by a desert
of starless space resulting from the ravages of time, certainly the
building of these magnificent sidereal systems may well engage the
attention of the natural philosopher.

20. The foremost geometers of the 18th century, including La-
grange, Laplace and Poisson, were greatly occupied with the prob-
lem of the stability of the solar system ; and in his historical eulogy
on Laplace the penetrating Fourier justly remarks that the researches
of geometers prove that the law of gravitation itself operates as a
preservative power, and renders all disorder impossible, so that no
object is more worthy of the meditation of philosophers than the
problem of the stability of these great celestial phenomena.

But if the question of the stability of our single planetary system
may so largely absorb the talents of the most illustrious geometers
of the age of Herschel, how much more justly may the problem of
the stability of clusters, involving many thousands of such systems,
claim the attention of the modern geometer, who has witnessed the
perfect unfolding of the grand phenomena first discovered by that
unrivaled explorer of the heavens?

The grandeur of the study of the origin of the greatest of side-
real systems is worthy of the philosophic penetration of a Herschel !
The solution of the dynamical problem presented surpasses the
powers of the most titanic geometers, and would demand the in-
ventive genius of a Newton or an Archimedes!

Yet notwithstanding the transcendant character of the problem,
and the hopelessness of a rigorous solution in our time, even an im-
perfect outline of nature's laws may aid the thoughtful astronomer,
in penetrating the underlying workings of the sidereal universe, and
thus enable him to perceive the great end subserved by the develop-
ment of the cosmos. If so, he may well rejoice, and exclaim with

Ptolemy :

"Though but the being of a day,
When I the planet-paths survey,
My feet the dust despise;
Up to the throne of God I mount
And quaff from an immortal fount
The nectar of the skies."— Transl. by W. B. Smith.

T. J. J. SEE.

CRITICISMS AND DISCUSSIONS. 633

THE PROGRESS OF BUDDHIST RESEARCH;

WITH SOMETHING ABOUT PENTECOST.

Since the writing of my note on the "Buddhist-Christian Miss-
ing Link" in the fall of 1911 (Open Court, Chicago, and MaM
Bodhi Journal, Colombo, both for January, 1912), great events have
happened in the field of Buddhist learning. We are now hot on
the trail of the Missing Link, if we have not yet found it. For, be-
sides the selected documents, to be presently described, there are
thousands more reposing in the libraries of Pekin, London, Paris and
Berlin, which we know to contain many more canonical Sutras trans-
lated into Sogdian,1 and there are doubtless more forthcoming in
Bactrian also.2

In a book published in 1908, I said this :

"Menander, in the second century before Christ, showed an
interest in, and a knowledge of, the Buddhist scriptures which may
have been founded upon a knowledge of Pali; but even then one
would expect such a patron to have some specimens of the lore he
admired translated into Greek, or into some vernacular. Strabo
says that nearly the same language pervaded Media and parts of
Persia, Bactria and Sogdiana. Strabo also says that the Corybantes
had come from Bactria, and Euripides pictures them as passing
the Bactrian Gates. When Buddhist ideas were carried westward,
they would as surely be translated as the Bacchic had been."

These words were written not later than 1907, and since then
my prediction has been abundantly verified. We have actually
found fragments in Chinese Turkestan of Buddhist scriptures both
in Bactrian and Sogdian, the latter coming from a Chinese library
that was closed up in 1035, while documents from a near-by tower
were dated A.D. 1 and A. D.20 !3 Bactrian or Tokharish was the
language of ancient Tukhara, i. e., northern Afghanistan and parts
of Chinese Turkestan. Sogdian was spoken in Russian Turkestan,
where the city of Samarkand had been the center of a Greek civili-
zation since the time of Alexander.

In Tokharish we have found Pacittiya 92 of the Vinaya, in the
recension of the Sarvastivadins, thus confirming the words of Yuan

1 M. Aurel Stein, Ruins of Desert Cathay. London, 1912, Vol. II, p. 213.

" Sylvain Levi, in Le Temps, Paris, May 19, 1911. Reprinted in the Revue
Archeologique.

* Stein, Ruins of Desert Cathay. Among these documents, though un-
dated, are some Sogdian epistles in Aramaic letters, now being read by Gau-
thiot.

634 THE MONIST.

Chwang, who said that all Tukhara was Sarvastivadin. In Sogdian
we have found the Vessantara Jataka, that great favorite about the
Bodhisat prince who gave all he had away.4 It was this very Jataka
that was graven upon the Great Tope at Anuradhapura, when vis-
itors from Alexandria came to see the opening ceremonies, in the
second century before Christ.

Other portions of scripture — the Nidana and Dasabala Sutras,
the Dharmapada — and a patristic hymn, have been found in San-
skrit ;5 while fragments of patristics have also turned up in Eastern
Turkish, written in characters of Syrian origin, side by side with a
Christian legend about the Wise Men from the East in the Gospel
of Matthew !8

All this means that in the early centuries of the Christian era
the religion of the Buddha was actively at work in languages spoken
by the Medes and Parthians who were present at Jerusalem in the
thirties of the first century (Acts ii. 9) : "Parthians and Medes and
Elamites, and the dwellers in Mesopotamia, in Judea and Cappa-
docia, in Pontus and Asia." It is to be noted that Judea, in this
verse, is tautological, for the scene narrated is laid in Judea. As
foreign countries are being represented, we must probably read
India, though Dean Alford defends our present text on geograph-
ical grounds. Now the New Testament writer who tells us this is
Luke, the Antioch physician, the author of a Gospel whose aim was
to take Christianity outside the narrow pale of Judaism and put it
into line with the Gentile religions. It is Luke alone who has the
story of the Penitent Thief, corresponding to the Angulimalo of
the Sutras.7 And in order to introduce this story into the Gospel,
Luke is compelled to violate the text of his master Mark, who says
that both the malefactors reviled the Lord. A scholar of the Eng-
lish church, in a recent number of the Hibbert Journal, has shown
that Luke was utterly unscrupulous in literary matters, and again
and again did violence to his sources to carry out his aims. I have
suggested, both in my Tokyo edition (1905) and in my Philadelphia
edition (1908) that Luke did violence to the text of Mark on purpose
to introduce these Buddhist legends wherewith he was familiar.

It is true that our present Bactrian and Sogdian manuscripts

* Gauthiot, in the Paris Journal Asiatique, January-February, 1912.

' Journal Asiatique, Nov.,-Dec., 1910.

9 Abhandlungen of the Royal Academy of Berlin, 1908 and 1911: article
"Uigurica," by F. W. K. Muller.

7 Middling Collection, No. 86, in the Pali ; but in the Numerical Collection
in Chinese,

CRITICISMS AND DISCUSSIONS. 635

are probably to be dated between the third century and the eighth.
But this is in Chinese Turkestan, whither their archetypes had been
brought from regions to the westward. We know, from coins and
from Buddhist history, that the religion was flourishing in Bactria
both at and before the time of Christ; and the inference is irresis-
tible that, when the missionaries began their Chinese translations
in the sixties of the first century, they had already acquired ex-
perience as translators in the tongues of the Parthian empire. The
only difference is, that the well-established civilization of China, and
the continuance of Buddhism therein, have preserved and dated the
Chinese versions, whereas the extinction of Buddhism by Islam in
Afghanistan and elsewhere has destroyed those older ones.

What we have actually found of them is due to Chinese care,
in Chinese dominions ; but we are entitled to infer a whole lost
literature in Bactrian, Sogdian AND GREEK,8 which was the
vehicle of Buddhist propaganda in the days of the Christian Evan-
gelists.

We do not need to wait until a Greek Sutra is dug up in Af-
ghanistan, as I have hitherto anticipated. We now have actually
in our hands a series of Buddhist documents translated by mission-
aries into languages that were understood by the very people whom
Luke records as present at a feast which his authorities had wit-
nessed. Could we but find, in these languages, the Buddhist An-
gelic Heralds and their Hymn, as recorded in the Sutta-Nipato ; the
Lord's Three Temptations, viz., to transmute matter, to assume
temporal power and to commit suicide, as recorded in the Classified
and Long Collections; the Penitent Brigand aforesaid; and the
Charge to the Sixty-one Missionaries, so like Luke's Charge to the
Seventy, we should have in our hands the key to the riddle which
Max Miiller said he had spent his life in trying to solve; viz., the
indebtedness of our proud religion of humility and peace, which
has been spread over the planet by the swords of Europeans, to the
meek and lowly cult of our brown brethren across the sea — that
cult which, alone among the faiths of mankind, has never dipped
its hands in the blood of animals or men.

ALBERT J. EDMUNDS.

PHILADELPHIA, PA.

"There is little doubt that in Bactria, Buddhist literature was actually
translated into Greek." (Buddhist and Christian Gospels, 4th ed., Philadel-
phia, 1908-1909. Vol. I (1908), p. 154). See also my remarks on "that lost
version of the Sutras which traveled westward." (Buddhist Texts in John,
1906, pp. 26-28.

636 THE MONIST.

BUDDHIST LOANS TO CHRISTIANITY.

WITH SPECIAL REFERENCE TO RICHARD GARBE.

SECOND ARTICLE.

To my remarks in The Monist and The Open Court for January,
1912, I should like to add a few words to congratulate Professor
Garbe upon the conclusion of his learned monograph. His final
summary I heartily endorse, except that I would modify one state-
ment. The following is the paragraph referred to (Monist, April,
1912, p. 187) :

"As we have seen, Christian influences upon the development
of Buddhism are limited to secondary products of a late day; just
as inversely Buddhist influences upon Christianity may be pointed
out only in non-essential particulars and from times in which the
doctrine of the Christian faith was established as a firm system. [ ]
All identities and similarities in the teachings of these two great
world-religions have, so far as essential matters are concerned, orig-
inated independently of one another, and therefore are of far greater
significance for the science of religion than if they rested upon a
loan."

These are essentially my own conclusions, stated many times
since February, 1900 ; but I would add, at the brackets, the words :
[except a few passages of minor import which found their way from
organized and aggressive Buddhism into formative Christianity.}

The passages especially in my mind are the Angelic Heralds
and their Hymn in Luke ii ; the Lord's Three Temptations in Luke
and Matthew ; two texts in John expressly quoted as Law and Scrip-
ture, but not found in the Old Testament or any other Jewish book
(John vii. 38; xii. 34) ; and the phrase (eon-lasting (or "eternal")
sin at Mark iii. 29 — a phrase so foreign to Christian ideas that the
copyists altered it to "eternal damnation," as Dean Alford admitted.
Moreover, as said in Buddhist and Christian Gospels (Ed. 4, vol. 1,
p. 157), Luke was probably influenced by such stories as the Charge
to the Sixty-one Missionaries (his "Seventy") and the Penitent
Brigand. As shown in my Tokyo edition (p. 48: the only impor-
tant passage not repeated in the Philadelphia one) each of these
stories of Luke is demonstrably fiction, and he moreover can be
proved to have altered the Marcan or Synoptic tradition to suit his
own ideas (as in Mark xvi. 7 = Luke xxiv. 6). To my mind the
case is precisely analogous to that of the moons of Uranus being
perturbed by the presence of Neptune.

CRITICISMS AND DISCUSSIONS. 637

When in Philadelphia last fall, Franz Cumont told us that there
is a set of technical phrases in ancient Greek books on astrology
which have now been shown to be literal translations from the
Babylonian. In precisely the same way, such Buddhist phrases as
(^on-lasting sin and others gained similar currency among the an-
cients, who persistently sought out the distinctive teachings of the
great nations, just as we do now.

With these reservations, I wish, as a student of Buddhism, to
give my most cordial adhesion to the conclusions of the learned
Brahmin scholar, who has dealt with a knotty problem in a masterly
manner and summarized the researches of many specialists.

PHILADELPHIA, PA. ALBERT J. EDMUNDS.

A POSTSCRIPT TO INDO-ROMAN RELATIONS IN THE
FIRST CENTURY.

In The Monist for December, 1911, Professor Garbe denied the
existence of Buddhist loans to canonical Christianity, and gave as
one of his reasons the following question and answer:

"Do the evidences of intercommunication at all permit the
assumption* that as early as the first century after Christ, or
earlier, Buddhist legends and ideas had found their way into

Palestine?

"They are not apt to raise this possibility to a serviceable
degree of probability for as early a period as the first post-
Christian century."

To this assertion I replied in the following number, avoiding
reference to the canonical literature, which was simultaneously con-
sidered by my friend Mr. Albert J. Edmunds, but assembling various
evidences of a large, important and rapidly increasing intercommuni-
cation between Rome and India during the first century of the Chris-
tian era, as indicating the possibility of the assumption which Pro-
fessor Garbe had outlined.

In The Monist for July, 1912, in a postscript to his most in-
structive discussion, Professor Garbe acknowledges the probability
of closer intercommunication than he has heretofore admitted, and
accepts one of the canonical parallels offered by Mr. Edmunds ; but
he thinks that I "beg the question" by assuming the possibility of an
interchange of ideas as well as goods.

To this objection I would reply that I was but addressing my-

1 Italics mine.

638 THE MONIST.

self to the assumption which he had declared to be unwarranted ; so
that if there has been any begging of the question it would seem to
have been in the same degree on each side of the discussion.

Professor Garbe objects to any citation of the Periplus because
it does not mention religion; but the citation was merely to show
the existence of an active commerce, and it is well known that the
missionary and the trader have gone close together in many ages
of the world. They have not always respected one another, but they
have usually followed the same paths. Surely Professor Garbe would
not expect a future historian of our own times to deny the assump-
tion of Christian missions in China because some surviving consular
report on the Shanghai trade might omit a reference to the Nicene
Creed!

Professor Garbe objects, also, that the Hindu traders to the
Roman Empire were Dravidians and stupid, and therefore not likely
to talk of their religion. But in the first century of our era they
were increasingly Indo-Scythian, from a portion of India that pro-
fessed a liberal and proselytizing Buddhism, and I repeat that for
that date and race, a spreading of ideas together with an interchange
of goods, was not only a possible assumption, but a probable fact.

The extent of such intercommunication is made much more
evident by Mr. J. Kennedy's paper "The Secret of Kanishka," begun
in the Journal of the Royal Asiatic Society for July 1912. The long-
drawn discussion as to the so-called Vikrama era of 58 B. C. seems
brought to a reasonable conclusion through Mr. Kennedy's brilliant
assembling of Chinese and numismatic evidence. It was the era
of the second Buddhist Council and of the Kushan king Kanishka.
His power over northwestern India, built up by his control of the
transcontinental silk-trade, was fortified by his becoming the pro-
tector of the Buddhist faith ; and under him and his immediate suc-
cessors, just before the Christian era, it is highly probable that his
faith was expounded to the east as far as Turfan, and to the west
as far as Charax Spasini, Antioch and Alexandria.

The truth is, that during the period between 50 B. C. and 100
A. D., approximately, India was a leading factor in the world's
thought, industry, commerce, and wealth; and, this being the case,
to repeat Professor Garbe's own words, "the evidences of intercom-
munication permit the assumption of the migration of Buddhist
legends and ideas into Palestine as early as the first century after
Christ." WILFRED H. SCHOFF.

PHILADELPHIA, PA.

BOOK REVIEWS AND NOTES.

THE RELIGION OF THE IRANIAN PEOPLES. By C. P. Tide. Part I (From the
German). With Darmesteter's Sketch of "Persia," and Goldziher's "In-
fluence of Parsism on Islam" (From the French). Translated by G. K.
Nariman. Bombay: Parsi Publishing Co., 1912.

G. K. Nariman, who is known to readers of the Revue de I'Histoire des
Religions and other magazines, is a Parsi scholar who is also acquainted at
first-hand with Buddhism, both from its Pali and its Sanskrit sides. Indeed,
one of the features of this excellent translation is an appendix by the trans-
lator entitled, "Some Buddhistic Parallels." The subjects dealt with are: (i)
the triple formula: body, speech and mind; (2) Buddhist allusions to con-
sanguineous marriages; (3) Hindu exposure of the dead, as described in the
Pitakas; (4) Mara and Ahriman; (5) questions addressed to Mazda and
Buddha; (6) the idea of a counterfeit creation (Parsi) or a counterfeit re-
ligion (Buddhist) ; (7) the use of the name Ormazd by Turanian Buddhists;
(8) the killing of noxious creatures by the Kambojas; and some other points.

The following note on the Turkish Buddhist literature recently found in
Central Asia deserves reprinting:

"Ein in turkischer Sprache bearbeitetes buddhistisches Sutra, by Radloff
and Stael-Holstein (St. Petersburg, 1910). This important work is typical of
the avoidable Babel which Western philologists seem unfortunately determined
to create in their otherwise fascinating field of marvelous investigations. The
original text is in the, up to now, almost unknown Uigurian, which the Russian
scholars have made accessible to us through a German translation; but the
transliteration is in Russian character, and the interesting notes on the Brahmi
gloss are made unserviceable to the average student of Buddhism by the
introduction of two sets of unknown alphabets, besides Chinese, Arabic and
Nagari scripts. Eastern students, however, must be grateful to the Imperial
Academy of Sciences, St. Petersburg, for the employment of the Nagari char-
acter in the publication of its admirable series of Bibliotheca Buddhica"

It is studies like this which help to break down the former provincialism
of religious treatises, wherein (to borrow a phrase of Cumont's) each religion
was regarded as an experiment in a closed vessel.

We could wish that the learned translator had had a little more regard
to the naturalization of Oriental adjectives, and so given us the familiar Eng-
lish forms Achcemenian, Sassanian, instead of Achcemenide , Sassanide. The
lack of diacritical marks is also confusing. But such small flaws by no

640 THE MONIST.

means detract from the great value of Tide's able essay in an English dress,
accompanied by the other essays indicated, which make the little book an
interesting companion for the student of Comparative Religion.

ALBERT J. EDMUNDS.

ALTUTONISH (PANGERMAN). BEI ELIAS MOLEE. TaCOma, IQII. PagCS 32.

The advocate of a new language called "altutonish" or "pangerman" to-
gether with an abolition of all capital letters is vigorously continued by
"elias molee, ph. b., 1554 'd' street, tacoma, wash., u, s. a." by sending out a
pamphlet containing exercises in his new language which he characterizes
as " ein (a) union spiek (language), makn up ov deuch, english, skandinavish
and hollandi, for to agenfererein (re-unite) al tutonish folka (people) into
ein spiek mitin (within) feivti (50) jiera (years)."

He believes that the world is mainly Teutonic and that a combination of
all Teutonic languages should be the best international language. As a motto
he selects a word of Victor Hugo, who has said somewhere: "The German
character hovers over the nations," or as it reads in German: "Die deutsche
Natur schwebt ilber den Volkern"

Such a combination might have been possible at the time the English
language originated after the Norman conquest through the breakdown of the
literal Anglo Saxon; but times are changed through the wide-spread use of
written and printed language which has added power to the resistance of the
established language such as was impossible in the times when language was
still purely speech, when it was limited to the spoken word which is more
flexible and would admit easily of radical changes. K

Readers of The Monist will be interested to hear that Prof. Hugo de Vries
is making another visit to the United States this autumn. He reached New
York about September 12, where he was to give a lecture at the Botanical
Garden on September 14. From there he goes to the University of Pennsyl-
vania to see the work which Professor Davis is doing with Oenotheras, and
then spends a short time in Washington. His next objective point is Dixie
Landing, Ala., where he goes with Professor Tracy to visit the type locality
of Oenothera grandiflora to study its possible mutants in its original habitat.
He then goes to Biloxi, Miss., where he will make his headquarters while
visiting the "mud lumps" near the mouth of the Mississippi River, and a
number of islands near Biloxi. After that he and Professor Tracy will go
to San Antonio, Brownsville, and other points in southern Texas, where
Professor de Vries goes to study the relation of the flora to the geological and
geographical conditions. On October 14, Professor de Vries is to deliver the
dedicatory address of the Rice Institute, at Houston, Texas.

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v.22

The Monist

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