THE SCIENCE OF LOGIC

THE

SCIENCE OF LOGIC

AN INQUIRY INTO THE PRINCIPLES OF
ACCURATE THOUGHT AND SCIENTIFIC METHOD

P. COFFEY, PH.D. (LOUVAIN)

PROFESSOR OF LOGIC AND METAPHYSICS, MAYNOOTH COLLEGE, IRELAND

IN TWO VOLUMES

VOL. II.
METHOD, SCIENCE, AND CERTITUDE

NEW YORK

PETER SMITH

1938

FIRST PUBLISHED, 1912

REPRINTED 1938 BY

SPECIAL ARRANGEMENT WITH

LONGMANS, GREEN AND CO., LONDON

FEB 1 6 1948

PRINTED IN THE UNITED STATES OF AMERICA

CONTENTS OF VOLUME II.

PART IV.

METHOD : OR THE APPLICATION or LOGICAL PROCESSES TO
THE CERTAIN ATTAINMENT OF TRUTH.

CHAPTER I.
GENERAL OUTLINE OF METHOD.

PAGE

200. Transition to Part IV i

201. Logic and Method 2

202. Synthesis and Analysis 7

203. General Rules of Method 10

204. Didactics : Analysis and Synthesis in Teaching 14

205. Scholastic Methods of Exposition and Debate 16

CHAPTER II.

INDUCTION IN ITS VARIOUS SENSES. INTRODUCTORY AND HISTORICAL
NOTIONS.

206. The Problem of Induction : Ascent from the Particular to the Universal 23

207. The so-called " Inductive Syllogism " : or " Induction by Simple

Enumeration of Instances" — "Complete" and "Incomplete" . 27

208. Scientific Induction as Treated by Aristotle and the Mediaeval Scholastics 32

209. Lord Bacon's Novum Organon : The Two Ideals of Generalization . . 37

210. Modern Conceptions of Induction : Newton, Whewell, J. S. Mill, Jevons 41

211. Analysis and Illustration of the Process of Scientific Induction . . 44

212. Scientific Induction and Deductive Inference 48

213. Relation of Antecedent to Consequent in Induction and in Deduction:

The Latter Considered as an " Inverse Process " .... 53

CHAPTER III.

PRESUPPOSITIONS OF INDUCTION : CONCEPTS OF " REASON " AND " CAUSE ".

214. Justification of Chapters III. and IV 56

->I5. "Reality" and the " Principle of Sufficient Reason " .... 58

vi TABLE OF CONTENTS

PAGE

216. The "Principle of Causality" in Induction: Aristotle's Classification of

Causes . . 61

217. "Purpose" or "Design": "Final Causes" and "Law" in Physical

Nature 66

218. Contrast between Traditional and Empiricist Conceptions of Efficient

Causality 70

219. The Sensist or Empiricist View of Causality : Mill's Teaching . . 75

220. Causality, Sequence in Time, and Contiguity in Space .... 80

221. "Plurality of Causes": "Reciprocal" and "Non-Reciprocal" Causal

Relation 84

222. Science and the Discovery of " Causes " and " Laws " .... 86

CHAPTER IV.

PRESUPPOSITIONS OF INDUCTION : UNIFORMITY OF NATURE.

223. Interpretations of the Principle of Uniformity in Nature 93

224. Ultimate Rational Grounds ot our Belief in Uniformity : The Scholastic,

Empiricist, and Idealist Views 99

225. Relation of the Principle to Induction and to Deduction . . . .113

CHAPTER V.
HYPOTHESIS: ITS NATURE, FUNCTIONS, AND SOURCES.

226. Functions of Scientific Hypothesis 120

227. Scientific Value of Various Kinds of Hypothesis 122

228. Nature and Verification of Causal or Explanatory Hypotheses . . 127

229. The R61e of Analogy in Verification : Ultimate Systematic Conceptions 135

230. Verification by Cumulative Evidence 141

231. " Postulates " and their Justification : " Truth " of Verified Hypotheses . 142

232. Theism as a Verifiable Hypothesis 145

233. Summary of Logical Requirements for a Legitimate Hypothesis . . 148

234. Sources of Scientific Hypotheses : Analogy ... . . 151

235. Worth of .Analogy : Its Function in Verification 155

236. The Argument from " Example " in Aristotle 158

237. "Analogy" as understood by Aristotle 160

CHAPTER VI.

METHOD OF DISCOVERING CAUSAL LAWS BY ANALYSIS OF FACTS :
OBSERVATION AND EXPERIMENT.

238. Observation and Selection : Initial Precautions 162

239. Experiment : its Relations to Observation 164

240. The Function of Experiment : Difficulties of Analysis .... 165

241. The "Rules" or "Canons" of Inductive Analysis; "Methods" of

" Agreement " and " Difference " 172

242. Combination of " Agreement " and " Difference " 179

243. Method of " Concomitant Variations ". Measurement. Statistics. . 186

244. Method of" Residues," "Conjunction of Causes," and " Intermixture of

Effects" 193

245. Scope of the " Methods " : Use of Symbols .... . 197

246. Quantitative Determination : Modes of Measurement . . . .201

247. " Empirical Laws " and their Explanation : Transition to Part V. . .205

TABLE OF CONTENTS vii
PART V.

THE ATTAINMENT OF SCIENCE AND CERTITUDE.

CHAPTER I.
SCIENCE AND DEMONSTRATION.

PAGE

248. Elementary Notions Defined: Truth, Ignorance, Error, Evidence,

Certitude, Opinion, Probability, Doubt 210

249. Three Kinds of Certitude ; Metaphysical, Physical, and Moral . . 214

250. Necessary Truth of Metaphysical Laws ; Contingent Truth of Physical

Laws and Facts 217

251. Aristotle's Ideal of " Scientific " Knowledge 223

252. Nature and Conditions of Demonstration 225

253. Restricted Scope of Aristotelean " Science " 229

254. Principal Kinds of Proof 232

255. Demonstration and Scientific Explanation. " Popular Explanation " . 235

256. Limitations of Scientific Explanation 239

257. An Erroneous View of Explanation 241

258. Discovery and Proof of Truth by Induction and by Deduction . . . 243

259. Moral Certitude in the " Human " Sciences .... . 248

260. Belief on Authority 250

261. Historical Science and Certitude : Its Criteria and Sources . . . 253

CHAPTER II.
OPINION AND PROBABILITY.

262. Nature of Probability : Cumulative Evidence : " Practical " Certitude . 260

263. Probable Arguments : The Aristotelean Enthymeme .... 263

264. Estimation of Probability : The Concept of " Chance " . . . .268

265. Conditions for the Mathematical Estimation of Probability . . . 272

266. Rules for Estimating Probability 276

267. Inverse Probability : Bernoulli's Theorem : Elimination of Chance . . 278

268. Application of the Calculus of Probability to Natural and Social

Phenomena 282

269. Function of Statistics and Averages : Their Right and Wrong Interpre

tations 285

CHAPTER III.
ERROR AND FALLACIES.

270. Logical Treatment of Error and its Sources 294

271. Error and Fallacy 296

272. Some Attempted " Classifications " of Fallacies : " Formal " and

" Material " Fallacies 298

273. Fallacies Incident to Conception 303

274. Fallacies Incident to Judgment and Immediate Inference . . . 308

275. Fallacies Incident to Method 315

QUESTIONS 338

GENERAL INDEX 343

PART IV.

METHOD ; OR THE APPLICATION OF LOGICAL PRO
CESSES TO THE ATTAINMENT OF TRUTH.

CHAPTER I.
GENERAL OUTLINE OF METHOD.

200. TRANSITION TO PART IV.— We have now completed
our examination of the formal aspect of the reasoning process,
and of the rules that guarantee its formal correctness or validity
(Part III.). But the object of all reasoning, of all science and
philosophy in fact, is to arrive at a certain knowledge of truth ;
and, to secure this, it is not enough that our reasoning processes
be correct or valid formally : the judgments involved in them
must, furthermore, be all both true and certain.

Truth is, as we saw (9, 79), contained in the mental act of
judgment, to which the operations both of inference and of
conception are thus subsidiary. An analysis of the material or
" truth " aspect of inference will therefore, of necessity, direct our
attention once more to the judgments of which our inferences
are composed, and to the concepts or ideas which enter into
our judgments (Parts I. and II.). After having separately
examined each of the three mental operations, of conception,
judgment, and inference, our next concern is to inquire how we
reach true judgments, especially those true universal judgments
which constitute scientific knowledge : how, in other words, we
are to exercise those three mental operations on the data of
knowledge to the best advantage for the acquiring of truth : how
we are to regulate and co-ordinate those mental acts, conception,
judgment, and reasoning, in exploring the various departments
of the knowable universe. This portion of logical doctrine is
variously described as applied logic, methodology, or the science
of logical method.

VOL. II. I

2 THE SCIENCE OF LOGIC

In all logical inference, our reason for assenting to the conclusion
is its evident connexion with premisses to which we have already
assented. But how do we come to assent to these latter ? Either
because they are self-evident — like the universal axioms involved
in all inference (193), — or derived by demonstrative evidence from
such self-evident truths, or generalized by induction from observed
facts. The general truths of the sciences may, then, be roughly
divided into these three classes : (a) self-evident axioms or
principles, such, for example, as " The whole is greater than its
part " : these are reached by a comparatively simple process of
intellectual abstraction and intuition, involving Definition and
Division of concepts, and their mutual comparison in judgment ;
(£) general truths that are not self-evident, but which have been
generalized by Induction from observed facts ; (c) conclusions
inferred by Demonstration from truths of classes (a) or (£).

Before the inductive method was developed, attention was largely de
voted, in the traditional Aristotelean logic, to definition, division, and
demonstration — the tres modi sciendi as they were called.1 Definition, by
analysing our concepts of things into the simplest possible notions, gives rise
to certain primordial, self-evident relations between these notions. These
relations are formulated in judgments and propositions which furnish the
foundations of the scientific edifice— the principles of the sciences. While
definition thus analyses our concepts, and gives us information about the
nature of their objects, it thereby also shows us wherein those objects agree
in thought and wherein they differ from one another. The process of
differentiation, or classification, or division, is thus the indispensable con
comitant of definition.

According as the mind becomes equipped with its elementary ideas and
judgments by means of sense observation, and intellectual abstraction and
intuition, it has recourse to the third mode of procedure, demonstration :
it draws certain and evident conclusions from self-evident principles, and from
these conclusions still further conclusions, and so on. The employment of
those various functions or factors of science, for the advance of knowledge,
is what the Scholastics called METHOD.

The process of (real) definition, understood in the Scholastic sense as an
explanation of the nature of a thing, and the concomitant process of (real)
division or classification, were always regarded in Aristotelean philosophy as
material processes, involving observation and analysis of facts, abstraction,
generalization, comparison, and even inference and verification of hypotheses
— in a word, all the processes nowadays described as " subsidiary to in
duction ". These made up the analytic stage of the Scholastic method, as
demonstration constituted its synthetic stage.

20 1. LOGIC AND METHOD. — Before investigating the method

1Cf. ZIGLIARA, Logica, (13), (44).

GENERAL OUTLINE OF METHOD 3

or methods of applying the mental processes we have been
mentioning, to the pursuit of truth, it will be useful here to take
a glance by anticipation at the main departments of human
knowledge which the logician may have in mind, and from
which he may draw his illustrations, in investigating such
methods.

We have pointed out already, in common with all logicians,
that it is not the function of logic to explore the provinces of
the special sciences in order to expound the various modes of
procedure peculiar to each. This is the function of the special
sciences themselves : each has, or ought to have, its own special
methodology. Logic ought to confine itself to an exposition
of those guiding laws and principles of reasoning and research
which are so universal that the mind must conform to them
always and in every department of rational investigation.1 In
thus limiting its field, logic will not be aiding the study of the
special sciences so directly as it will aid the study of philosophy
proper ; for philosophy presupposes a general knowledge of all
the special sciences and endeavours to synthesize their results ;
and in this arduous work it is guided by no other " rules of philo
sophizing" than the general canons and laws laid down in logic.
Indeed, if there be any science to which logic should serve as a
special introduction, it is philosophy, the " general science," and
not any of the special sciences.

But it is difficult to carry out in practice what is so simple in
theory. Just because philosophy does take up, interpret, collate,
and harmonize — as far as possible — the assumptions and conclu
sions of all the special sciences — mathematical, physical, natural,
anthropological, social, economical, ethical, etc. — it is not easy in
practice to say where the work of each special science ceases and
that of philosophy begins. And so it is, too, with regard to the
scope of logic. This may easily deviate into the investigation
of methodological details proper to special sciences ; or — which is
a more serious mistake — it may, by losing sight of some depart
ments of human experience and falling unduly under the influence
of others, set forth, as general canons of philosophical investiga
tion, methods that may be valid only within the narrower pre
suppositions of some special science or group of sciences. These

1 " Logica tradit communem modum procedendi in omnibus aliis scientiis.
Modus autem proprius singularum scientiarum, in scientiis singulis circa principium
tradi solet."— ST. THOMAS, In II. Metaph. lect. 5.

I *

4 THE SCIENCE OF LOGIC

are mistakes which writers on inductive logic since the time of
Mill have not successfully avoided. Nor is it difficult to one
looking back, to see why such mistakes were, humanly speaking,
almost unavoidable.

At different epochs men engaged in the investigation of those
higher and deeper problems which lie along the confines of philo
sophy and the special sciences, have been very differently impressed
as to the relative values of these latter in advancing human know
ledge. At one time the attention of scholars is drawn more
exclusively to one group of sciences, and again to another group :
and the logic of each period will be found to reflect faithfully the
then prevailing attitude, by its fuller consideration of the methods
and data of the dominating group.

Thus we see that, broadly speaking, the Middle Ages wit
nessed an exhaustive development of the logic of Deductive
Reasoning. This was because men were then more satisfied with
their principles of knowledge, and perhaps more religiously-minded ;
because they set greater store on a knowledge of man's nature
and destiny than on a knowledge of the external universe ; be
cause for progress in the former they relied on (deductive) reason
ing from great, broad, general principles and truths that were
universally accepted at the time — some on the authority of God
as being revealed by Him, others as self-evident, others again as
sufficiently established partly by their intrinsic evidence and partly
by the common assent and authority of the learned of past ages.

Then came the period of the Renaissance, a period of doubt
about hitherto received principles, of revolt against authority and
rejection of traditional views and methods. On the one hand,
the hitherto accepted teachings of philosophy and religion were
critically re-examined ; and this new analysis had finally the
effect of adding to the traditional logic an extensive discussion
on the possibility and grounds of human certitude, and on the
ultimate criteria or tests of truth (17). On the other hand, a
closer attention to the study of external nature led to a wonder
ful progress in the domain of the physical sciences. The cultiva
tion of this fertile field of research has been rewarded by rich and
useful discoveries ; the physical universe is being eagerly explored
and made to yield up its secrets ; and the general laws and con
ditions according to which its phenomena unroll themselves are
the keys by which its most hidden agencies are brought to light
and utilized by human enterprise. Hence the high degree of

GENERAL OUTLINE OF METHOD 5

importance that has been attached to general truths of the physical
order — in contrast with these other general truths that have to
do with man's religion, natural or supernatural, with his moral
conduct in life, with the inner nature of his own mind and soul,
with the ultimate purpose of his existence, and with his final
destiny.1 Hence, too, the very large and prominent place devoted
in modern treatises on logic to an analysis of the method and
processes by which general truths about the physical universe can
be securely and certainly established : as if these were the only
general truths of importance, or, anyhow, of most importance, to
man ; as if physical induction were the only or the chief method
of reaching a certain knowledge of the weightiest truths to which
the human mind can hope to attain.

The modern logician of induction invites us into chemical, physical and
physiological laboratories ; he familiarizes us with test-tubes and balances,
with boilers and engines and dynamos, with microscopes and telescopes ; he
teaches us how to observe and experiment, how to detect analogies between
physical phenomena, how to construct hypotheses foreshadowing the laws
according to which these phenomena take place ; he lays down canons which
will help us to simplify our data by elimination of the unessential, and so to
test or establish — or, it may be, to reject or to modify — our hypotheses, until
we thus finally discover and generalize some abstract law about the conditions
requisite for the occurrence and the recurrence of some physical event.

But the general truths we reach about the external universe, as distinct
from man himself, by the application of such methods, constitute only one
department of human knowledge— an important one, no doubt, yet by no
means the most important. There is, for instance, the wide and fertile, if
more difficult, department of human research which has for its object the
phenomena of human activity in the individual, in the family, and in the State :
the domains of anthropology and psychology, of the social, economic, and
political sciences. The methods of discovering and establi shing general truths in
these sciences should have no smaller degree of interest for the logician than the
method of reaching, say, the law of universal gravitation. Yet the modern
logician tells us comparatively little about the former : about statistics and
averages and the canons of probability : the various means of reaching another
class of general truths or laws which may have immense practical interest for
us, even though we can have only moral, and not physical or metaphysical,
certitude concerning them.

And what about the innumerable truths, or supposed truths, some of which
inform us of particular facts in human history, such as the conquest of Gaul
by Caesar, or the crucifixion of Christ ; others of which embody generalizations
such as that " Moral excellence in men and nations results from their posses
sion of deep and true religious beliefs " ; and all of which are accepted and
believed, by nine-tenths of those who do accept and believe them, on the
authority of their fellowmen, on the strength of historical evidence? If the

1 C/. JOSEPH, op. cit., pp. 344, sqq.

6 THE SCIENCE OF LOGIC

logician thinks it a part of his duty to teach us how to measure masses and
motions of matter by the " method of means," the " method of least squares," 1
etc., may we not reasonably expect from him an equally detailed code of
directions in the task, let us say, of estimating the value of the historical evi
dence for and against the alleged fact— so momentous in human history — that
Christ rose from the dead after His crucifixion ?

The logician is no more debarred from dealing with the methodology of
" metaphysical," or "ethical," or "historical" truth, than he is from investi
gating the methods of discovering and establishing " physical " truths. Truths
and theories, facts and phenomena, whether real or alleged, whether "re
ligious " or " scientific," forming, as they all do, the common data of philosophy,
fall equally within the sphere of logic. They are all subjects of human investi
gation : and it ought to be, therefore, the function of general logic, not to
teach us how to explore the hidden recesses of any particular department, but
rather to give us a general training in the method of discovering and proving
truth : a training which will help us equally well all round, which will aid us
in determining whether God exists and has spoken to us through Christ, no
less than in determining whether radium cures cancer, or whether alleged
" telepathic " phenomena are mere coincidences.

The logician must, of course, ultimately use his own discretion in deter
mining whether he ought in a general way to indicate the main methods in use
in this or that special department of science ; and it is just here, in judging
which departments are worthy of a more detailed attention, that he will be
influenced, consciously or unconsciously, by the general trend of intellectual
activity in his own time and country. In this way he is exposed to the danger
of unduly emphasizing the scope and import of certain special methods of
scientific research, or even of setting them up as the only methods of attain
ing to scientific truth.

Now, modern inductive logic shows pretty clear evidence of suffering from
an undue bias of the sort just outlined : it has concerned itself somewhat too
exclusively with the mathematically exact quantitative methods of the physical
sciences, and it has thus fostered an unwholesome tendency to conceive and
treat all human experience as amenable to the laws and methods of mechanics.
It has been more or less obsessed by the rigid determinism of the "mechanical
theory of the universe," which was so much in vogue about half a century
ago.

There is something one-sided in this tendency to cultivate the positive,
physical sciences, on the lines of mechanically exact, quantitative laws, and to
develop, in logic, a corresponding methodology of them — to the exclusion of
the human sciences, the knowledge of man's nature, origin, and destiny, of
his conduct and religion, of his social activity and its history. The intellectu
ally cogent evidence of the "exact " sciences — mathematics, whether pure or
applied to physics — lends itself, of course, most readily to clear, logical
treatment. But the " exact " sciences are not the only sciences, nor is the
assent which is given on intellectually cogent evidence the only assent that
deserves to be called scientific. Assents that are freely given may be scientific
and certain, provided that the evidence is as strong as can be reasonably ex
pected in the matter under consideration. And even where these assents do fall

1 Cf. WELTON, Logic, ii., § 158; JOYCE, Logic, p. 368.

GENERAL OUTLINE OF METHOD 7

short of certitude, the general method of weighing the evidence on which they
are based forms the proper object of logic.

It must be borne in mind that many of the processes to be hereafter de
scribed as subsidiary to induction find their application very extensively outside
the merely physical sciences, although they are for the most part illustrated
by examples drawn from the domain of these latter.1

202. SYNTHESIS AND ANALYSIS. — Method (peOoSo^ means
mode or manner of procedure, and may be defined as the proper
arrangement of our mental processes in the discovery and proof of
truth. If a truth needs proving, we cannot be said to have fully
discovered it until we have proved or established it as a truth ;
antecedently to this it is only a postulate or hypothesis. The
method which thus leads to science is sometimes called inventive
or constructive, to distinguish it from the method of teaching or
expounding truths already established, this latter being known as
didactic method (204).

In scientific method it is customary to distinguish the influ
ence of two great mental functions, analysis and synthesis ; and
according to the predominance of either of these over the other
in any department of scientific investigation, the latter is desig
nated an analytic or a synthetic science.

When a science sets out from a few simple ideas and a few
necessary, universal principles, and proceeds to combine these
elementary notions and relations, in order to deduce from them
other new, less simple, more complex relations, its progress is
synthetic (nrvv-riffii/ju). It goes from the simple to the complex,
from the more general to the less general. It employs the
method of composition, the synthetic method. Such a science is
called a rational, deductive, abstract science.

Pure mathematics, for example, sets out from a few neces
sary and universal principles (" in materia necessaria "), with which
the mind equips itself by the simple abstraction of a few element
ary concepts from the data of sense, and by direct intellectual
intuition of certain self-evident relations between those concepts.
These relations it combines and multiplies successively, thus
gradually forming definitions of the various thought-objects with
which it deals, divisions of these objects into groups or classes,
and demonstrations which show the relations, ever more and
more complex, between these objects. It is thus ever and
always discovering new abstract objects of thought, com-

1 C/. JOSEPH, Logic, pp. 472 sqq.

8 THE SCIENCE OF LOGIC

pounding, or building uf> its conceptions, so to speak, into more
and more complex wholes, synthesizing its gradually acquired
truths into a logical, harmonious, and progressive system.

Throughout this whole work of elaboration, the student of the
pure deductive sciences has no need to call in the aid of sense
experience, of observation or experiment : he might conceivably
become the greatest pure mathematician in the world without
ever leaving his library. He would, of course, need charts or
blackboards to aid his imagination in establishing the complex
spatial or numerical relations he might desire to examine between
the notions with which he deals. But it is from the primary
notions, not from the figures or symbols before him, that he de
duces even his remotest and most complex conclusions.

If, however, it is true that such quiet seclusion and abstract
speculation can produce a great mathematician, is it not equally
true that they can never produce a great physical scientist ? A
knowledge of the physical world implies actual, positive contact
with Nature and its activities. The discovery of its laws is con
ditioned by the observation of its concrete phenomena, and even
by experimenting with these latter. It is the result of a long
analytic process that has been called Induction : hence the designa
tion, physical or positive or inductive sciences.

When a science thus starts with concrete facts, with the data
of observation and experiment, and aims at discovering general
truths and formulating general laws, about those tacts, its progress
is from the complex to the simple, from the particular to the
general. This is the analytic method (ava\v(o) ; it finds its place
mainly in the experimental sciences.

We have already distinguished the reasoning by which we
thus ascend to higher and wider laws, as regressive, in opposition
to the progressive reasoning which is characteristic of the deductive
sciences (187). Professor Welton * thus illustrates the distinction :
" Instead of starting from an axiom of the widest generality, in
physical science it more frequently happens that the highest and
most general principles are the last to be discovered. ' Certain
general propositions are first discovered (e.g. the laws of Kepler)
under which the individual facts are syllogistically subsumed.
The highest principles are discovered later (e.g. the Newtonian law
of Gravitation) from which those general propositions are neces-

1 Logic, i., p. 392.

GENERAL OUTLINE OF METHOD 9

sary deductions ' (Ueberweg, Logic, p. 465). . . . A demonstration
of this kind is, therefore, called . . . Analytic".

It is usual to draw a distinction between the two scientific
methods : the synthetic, or that of the rational, deductive sciences ;
and the analytic, or that of the experimental, inductive sciences. -
There is reason for such a distinction : but only in this sense, that
synthesis is the predominant feature of the former, and analysis of
the latter ; not in the sense that either feature belongs exclusively
to either group. No such separation of analysis from synthesis is
possible in actual thought. As a matter of fact, the self-evident,
a priori axioms of the rational sciences necessarily presuppose the
mental analysis of some few elementary observations, by which the
mind is equipped with the concepts that form those rational prin
ciples. On the other hand, the general laws that are reached by
the long and laborious analyses and inductions of the experimental
scientist furnish us, in turn, with principles or starting points for
synthetic or deductive reasoning processes.

In reality, therefore, there is one and only one scientific method :
the analytico-synthetic, or combined inductive and deductive method.1

Whether analysis or synthesis will predominate in any parti
cular science, or at any particular stage in the growth of a science,
will depend on whether the subject-matter is best approached
from the side of the abstract universal, or of the concrete particular.
But the two methods are not essentially opposed ; rather they
"differ only as the road by which we ascend from a valley to a
mountain does from that by which we descend from the mountain
into the valley, which is no difference of road, but only a difference
in the going".2

This, moreover, is what we should expect when we reflect on the unity of
human nature ; and it is confirmed by the findings of psychology. Man derives
his abstract ideas from data furnished by his senses. Sense observation must,
therefore, be the forerunner of all rational speculation. The formation of
abstract concepts from the data of sense experience involves analysis of the
latter. These abstract concepts are in turn combined in manifold ways by
the activity of the intellect, and are being constantly reapplied to the facts of
sense observation. Thus it is that rational speculation is ever returning to those
same sense realities which first awake its activity. All science is " of the uni
versal and necessary " (to use the language of Aristotle) ; but it is no less true
that all science must aim at explaining the contingent, individual facts of our
sense experience. It must not only ascend by analysis and abstraction from
the particular to the universal, from fact to law, from effect to cause, but it

1 C/. MELLONE, Introd. Text-Book of Logic, pp. 383 sqq.

*Port Royal Logic, p. 314, quoted by Professor Welton, Logic, ii., p. 212.

io THE SCIENCE OF LOGIC

must also, by a regressive movement of thought, apply its abstract principles
again to concrete facts, and by means of the former explain the latter. This
combined and alternating use of analysis and synthesis will be more fully
illustrated in connexion with the treatment of Induction, Demonstration, and
Scientific Explanation. It is commonly employed in the physical sciences, and
it is the only method by which a reliable philosophy of man and the universe
can be constructed.1

There have been, in different ages, philosophers such as Descartes
(1576-1650) and Spinoza (1632-1677), who have thought it possible to build up
a philosophy by the purely synthetic or deductive method, on the basis of a few
self-evident fundamental truths. Such projects are chimerical, for philosophy
is expected to offer an intelligible interpretation of universal human experience,
and must, therefore, set out from an analysis of this latter.

The method of philosophy, too, like the methods of the sciences, is largely
influenced by the prevailing general views and standpoints of each successive
period : synthesis predominating in one school or in one epoch of philosophic
development, analysis in another : the former, for instance, in Plato and Neo-
Platonism, in St. Augustine and the early Middle Ages ; the latter in " scien
tific " and " inductive " philosophy since the Renaissance ; and neither, perhaps,
asserting undue supremacy in Aristotle, or in Scholasticism among its best
accredited representatives, whether mediaeval or modern.

A system of philosophy aims at working out and establishing some definite
world-view, some interpretation of human experience as a whole. The method
or methods that may be involved in the elaboration of such a thought-system
will themselves usually imply assent to certain fundamental judgments, whether
these be put forward as axioms or as postulates (203, 231). And hence it is
that systems of philosophy are to be judged not only by their explicit positive
teaching or contents, but also by their methods, for these too imply doctrines.'2
Indeed, it has been said that metaphysical systems differ merely in the stand
points from which they approach the interpretation of experience. This is only
an exaggeration of the undoubted truth that every such system is largely in
fluenced and characterized by some predominating point of view. Thus, the
idea of a process of Development, a tendency towards the realization of an
ideal, as pervading not only thought but reality, has always exercised more or
less influence on the trend of philosophical speculation. But the scientific
discoveries of the last few centuries in regard to organic evolution among the
forms of life, have led many to suspect the existence and operation of an all-
pervading law of Evolution, and to adopt, in all departments, only methods of
research directly based on this postulate. The wisdom of this procedure is
questionable. If it is really unsound, results will in due time reveal its
deficiencies.

203. GENERAL RULES OF METHOD. — Various rules or
canons, of more or less practical utility, have been laid down for
observance in the pursuit of truth, under the title of General
Rules of Method. They are of the nature of counsels. A full

1 Cf. MERCIF.R, Logique, p. 374 : Pratique de 1'analyse et de la synth&se en
philosophic.

2 Cf. DE WULF, Scholasticism Old and New, pp. 190-200.

GENERAL OUTLINE OF METHOD u

discussion of their grounds and significance would not be con
venient at the present stage of our investigations. For the purpose
of enumeration we may conveniently reduce them to the follow
ing:—

I. We should select as starting point the simplest, easiest, most
familiar objects of thought. What is simplest and easiest to un
derstand, will, however, depend on the amount and kind of
knowledge already possessed by the seeker ; and will, therefore, be
relative and variable. Each must determine, from his own know
ledge, what element or elements of the particular subject-matter
under investigation may be most easily grasped by him.

Whether what is simplest in itself is simplest for us, will be
largely determined by the nature of the subject-matter in hand.
Looked at in itself, the abstract, universal principle or law is
simpler, less complex in content, than any concrete fact under it :
e.g. the law of gravitation than the fall of an apple ; * but it is not
always this simple, abstract aspect of reality that comes first
under our notice or is most familiar to us. Of some aspects of
reality it is the widest and most general truths that are most
easily grasped, as in the case of the axioms of the rational
sciences ; and then the method employed will be mainly syn7
thetic. Oftener, however, it is the concrete, complex, many-
sided fact of sense with which we are most familiar^ as in the
data of the inductive sciences ; and then the method employed
will be mainly analytic.

II. We should proceed from the known to the unknown, GRADU
ALLY, step by step, in an orderly, logical sequence of thought, and
not hastily, irregularly, " PER SALTUM".

To secure this, we must observe carefully all the canons of
definition, division, reasoning, demonstration, etc. Failure in
the observance of these canons will usually expose us to error,
and will inevitably involve inversion, repetition, and consequent
confusion. Innumerable examples of those defects have been
instanced from the order followed in Euclid's elements of
geometry.2 The importance of explicitly examining and test
ing every step of our progress cannot be exaggerated. In no
other way can thoroughly scientific knowledge be either secured
or retained in the mind : whereas, on the other hand, a clearly
perceived, logical, organic connexion between truth and truth is
necessarily a powerful aid to memory.

1 WELTON, op. cit., p. 216. " ibid., p. 225.

12 THE SCIENCE OF LOGIC

Moreover, it is by careful separation of a problem or subject
into its various parts and details that we are enabled to distin
guish betweeen the accidental and the essential, and to avoid
being misled by superficial resemblances and seeming connexions.
Habit, association, familiarity, are apt to lead us astray. We
very easily mistake invariable sequence for causality, and ap
parent reasons for real ones.1 The principal sources and classes
of such mistakes will be enumerated in the sections on Fallacies.

III. While, on the one hand, we must never accept anything as
true which we do not clearly know to be so, on the other hand, we
must not expect the same degree of certitude, or the same cogency of
evidence, in all the sciences. Disregard of the second portion of
this rule has led many, especially in modern times, into scepticism,
i.e. doubt about the capacity of the human mind to attain to
certitude about anything. Taking too narrow a view of " science,"
they expect cogent evidence in the concrete subject-matter of the
human sciences — social, economic, and ethical — evidence which,
of their very nature, these sciences cannot be expected to yield.-
And when it is not forthcoming they drift into scepticism. One
would imagine that St. Thomas Aquinas was writing for the
twentieth century, rather than the thirteenth, when he penned these
sentences : " There are some who will not receive anything that
is told them unless it is mathematically proved. This is usual
with those who have had a mathematical training, because custom
is second nature. But it may be also due to the possession of a
strong imagination, combined with an undeveloped judicial faculty.
Others there are who will not receive anything unless there is
put before them some illustration of it that can strike their senses.
This, too, results either from habit, or from the predominance of
the influence exerted over them by their senses, or from want of
intellectual discrimination. . . . Others, however, there are who

1 " An Englishman resident in some city in South America sees united in the
inhabitants a profession of the Catholic religion, a great laxity of morals, and an
absence of all energy, fortitude or perseverance. Neglecting our rule, he comes to
the conclusion that there is a necessary connexion between Catholicism and the
vices around him. . . . Or, again, we may have observed in the newspapers that a
larger number of persons lose their lives by drowning on a Sunday than on any other
day. On this fact the Scotch Presbyterian makes the remark that it can only be
explained by the anger of God with all who take their pleasure on His Holy day :
quite overlooking the circumstance that it is on Sunday that a great number ot
excursionists of the middle and lower classes, who are unskilled in the use of boats
and can rarely swim, take their pleasure on the water."— CLARKE, Logic, pp. 469,
470.

2 Cf. JOSEPH, Logic, p. 489.

GENERAL OUTLINE OF METHOD 13

wish that everything offered them should be based on certitude,
that is, as the fruit of diligent rational inquiry. This is the atti
tude of a sound understanding in judging, and of sound reason in
investigating : provided always that [such certitude] be not sought
in matters where it cannot possibly be found" *

IV. We must keep before us, as dearly as we can, the end to
be attained in our inquiry or argument, and suit our method to the
attainment of this end. Of course, when the end in view is the
discovery of new knowledge, as distinct from the communication
of knowledge already possessed, to others, we cannot have a clear
or definite conception of what we are looking for : if we had, our
inquiry would be superfluous. Still, we must have some general
suspicion of it : otherwise we should not think of looking for
it at all. Discoveries are, no doubt, sometimes made haphazard,
by groping in the dark ; but this is the exception. As a rule,
our progress in knowledge is guided by hypotheses, based on
analogies with what we already know.

Besides those general canons of method, special rules are sometimes
formulated for the synthetic method, and special rules for the analytic. In the
chapters dealing with Induction we shall examine the latter method at some
length, and we shall there see that although the process by which we rise
from the perception of concrete, individual facts of sense, to the apprehension
of general truths, is one of very great importance, yet it is scarcely possible
to formulate any mechanical set of guiding rules for it.

It is the synthetic method that systematizes the truths discovered by
analysis, and explains concrete reality by applying to the latter analytically dis
covered laws. The rules laid down by some logicians for its employment are
almost too obvious to need special statement. For instance, we are reminded
that we must start either from axioms that are indisputably self-evident, or
from general truths already proved. The usual error here is by defect, by
taking for granted what is neither sufficiently simple to be self-evident, nor
has been clearly proved — the fallacy known as Undue Assumption of Axioms.
But philosophers, nowadays, not unfrequently err by excess, by demanding
proof for what is so clearly self-evident as to be indemonstrable. They call
into question the claim of any principles, however self-evident, to our uncon
ditional intellectual assent. They doubt or deny that such abstract, self-evid
ent axioms give us any insight into the real nature of things, confining the
validity of such axioms to the sphere of subjective mental appearances, and
according them at most a merely provisional acceptance as " assumptions "
or " postulates " which may perhaps be some day verified as objectively
valid, or may perhaps be destined to remain as mere " directive " or
" regulative " principles of our thought-processes. It is, of course, a grave
mistake thus to confound self-evident truths about the data of our ex
perience with those mere " working hypotheses " and " methodological

1 Lect. V. in Metaph. 2.

I4 THE SCIENCE OF LOGIC

assumptions " l which all investigators have sometimes to make, and which
are perfectly legitimate in their proper sphere ; but an inquiry into the grounds
of this erroneous tendency in modern philosophy would not be opportune
here.

Aristotle and the Scholastics examined in minute detail the requirements
of the synthetic processes through which we advance by demonstrative rea
soning from simple, self-evident first principles to more complex scientific
conclusions. Their teaching will be outlined in the chapter on Demonstration.

The remainder of the present chapter will be devoted to the application
of analysis and synthesis to the teaching or exposition, as distinct from the
discovery and proof, of truth.

204. DIDACTICS: ANALYSIS AND SYNTHESIS IN TEACHING.— When
our object is not to discover truth as yet unknown to us, but to communicate
what we know already to others, our method will be no longer constructive or
inventive, but instructive or educative ; instructive if it aims merely at the
communication of knowledge to the intellect ; educative if it aims at the
formation of right mental habits and character as well. The latter is the
scope of the art of Pedagogics ; the former alone, that of Didactics. This
latter, therefore, is the sole concern of the logician.

What, then, is the proper method of teaching or exposition ? Broadly-
speaking, it is laid down that while the analytic method is the great method of
discovery the synthetic method is the great method of instruction. And in
general terms this is correct. But the statement needs to be carefully limited
and qualified.

The analytic method is not exclusively the method of discovery ; as witness
the many discoveries of pure and applied mathematics. Nor, similarly, is the
synthetic method always the best method of exposition. It is, of course,
obviously the best in teaching the pure deductive sciences ; for in these the
abstract principles, being simpler than their complex applications and
conclusions, are more easily grasped by the beginner. But even here we
need initial observation of concrete facts or instances as an aid to the abstrac
tion of the simple notions, and to the intuition of the principles from which
these sciences start. This initial stage is analytic in its character. The teacher
familiarizes his pupils with concrete instances, facts, models, embodying the
abstract principles he wishes them to grasp. In dealing with children
especially, it is necessary to dwell at length on concrete things : these are more
familiar : and the child's power of grasping even the simplest abstract
principles, and reasoning from them, is comparatively undeveloped. The
aim, at this early stage, will rather be to awaken the child's powers of obser
vation and intuition, to arouse its curiosity and stimulate its interest by pre
senting to it simple but attractive facts, combined with judicious interrogations
and suggestions, calculated to draw out the pupil's powers of observation,
comparison, and inference.2

1 Cf. JOSEPH, op. cit., p. 523. Cf. infra, 237.

2 Professor Willmann, in Germany, has published, under the title of Didaktik
als Bildungslehre, a work of the highest merit on intellectual training. Habrich, a
pupil of Willmann's, has supplied the teachers of intermediate education in Germany
with a useful treatise on psychology, " Paedagogische Psychologic" in harmony with
the principles of scholastic teaching. From another standpoint, cf. Herbert Spencer's
works on Education.

GENERAL OUTLINE OF METHOD 15

Moreover, the pupil should be trained, as far as possible, to discover,
himself, the reasons and causes of the things observed by him. This involves
the use of the analytic method, and develops the spirit of analysis in the
learner. Such initiation into the method of independent personal investigation
constitutes the immense difference there is between intellectual education
proper and mere instruction.

This method of teaching by suggestion, of drawing out the learner's
powers by judicious questioning, is called the Socratic method, after the
Grecian sage who made such a fruitful use of it. He, himself, appropriately
called it the /iaievruoj Tt^vij, the art of intellectual obstetrics or mental mid
wifery '.*

This stage of analysis and observation is a necessary step towards ab
straction of ideas and intuition of first principles. These notions and
principles become in turn the explanatory reasons of the facts in which they
are realized. The learner will next be taught, by an application of the
synthetic method, to make use of those principles and laws for the under
standing and explanation of concrete phenomena.

Thus he will be taught to make use both of observation and of abstraction,
both of analysis and of synthesis. The former without the latter would lead
to narrowness of view, to the shortsighted philosophy of Positivism ; the latter
without the former, to barren, empty speculations, and to the substitution of
mere verbal explanation for real science. The sciences of observation develop
the spirit of specialized research ; the mathematical and metaphysical sciences,
the deductive, speculative turn of mind.

It will be seen, therefore, that as a rule the method employed in exposition
is the same as that employed in discovery ; that the art of teaching must
follow nature ; that the mind of the learner must follow substantially the
same path, whether he discover truth on his own account or be guided into
the knowledge of it by one who is already in possession of it.

Of course, when the exposition " is intended for well-prepared adults —
as when one writes a text-book, the most appropriate method is, generally
speaking, that of synthesis, as by that method the necessary relations of the
parts of the subject to each other are most clearly shown." 2 But even here
it is well to remember that the abstract, universal principle or law is not always
the easiest to grasp at the starting-point. In an example from chemistry,
given by Father Clarke in his Logic? we are told that "in each of these
opposite processes [analysis and synthesis], the rule ... of commencing with
what is more familiar, and thence proceeding to what is more remote and

] Socrates used to seek from others the knowledge they imagined they possessed,
and which he himself pretended not to possess. His arguments took the form of
dialogues, each in two parts. In the first, his " irony " confounded his interlocutor
and convinced the latter of the weaknesses and drawbacks of his position. In the
second, Socrates gradually drew from him a new and truer definition, a better under
standing, of the matter in dispute. After silencing his opponent in the first or de
structive stage of his discourse, he would begin by another series of questions to
construct a new solution- of the problem — to substitute for the exploded error, or
"spurious offspring," the " veritable fruit " of a " new-born " truth. The conclu
sion of the dialogue thus became the " fruit of their personal reflection," the " child
of their thought ".— C. PIAT, Socrate, pp. 106-109, Paris, Alcan, 1900.

8 WELTON, Logic, ii., p. 214. app. 471-74.

1 6 THE SCIENCE OF LOGIC

unfamiliar, is observed by the chemist. In his investigation he commences
with that which is most familiar to ordinary mortals (nobis notiora), the water
of the spring where thousands have drunk or bathed, and thence proceeds to
the various chemical agents it contains which are to us a mystery, though in
themselves they may be so simple as to admit of no further analysis. In im
parting to others the results of his experiments he begins from what is simpler
in itself and therefore more familiar to nature (naturae notiora), and thence
proceeds to the complex results with which ordinary men are familiar, however
complex they may in themselves be." But, if the audience is composed of
" ordinary mortals " to whom the elements — however much simpler and more
knowable they may be in themselves — are so many " mysteries," would not
the lecturer be better advised to commence his exposition with the more
familiar water, and to lead his audience along substantially the same path as
he himself had followed in the first instance ?

It seems rather a mistake, therefore, to apply the synthetic method
exclusively, to the exposition of the subject-matter of those sciences in which
analysis has been the main instrument of discovery. It is rightly used in the
teaching of the pure deductive sciences such as mathematics ; but the
exposition— at least the early stages of the exposition — of those sciences in
which analysis, observation, and experiment have played a conspicuous part,
should be rather analytic than synthetic. For example, the method followed
by Maher and Mercier in their well-known treatises on psychology — the
analytic or empirical phase leading up to the synthetic or rational one — is very
much superior to the exclusively synthetic method adopted by many Scholastic
writers in their Latin treatises on the subject. In accordance with the Scholastic
axiom, Operari sequitur Esse, we ought to commence by examining and
analysing the data on which our scientific knowledge of man is based, -viz, his
activities, to arrive next at a knowledge of his faculties, and ultimately of
his nature, origin, and destiny.

We are only following nature in adopting such a course of analytico-
synthetic exposition. The manner of using analysis in teaching will, however,
be slightly different from the manner of using it in discovery.1 In the
process of discovery, our analysis is necessarily slow, tedious, tentative, guided
merely by analogy and hypothesis, often erratic owing to our being misled by
false analogies and wrong hypotheses ; our experiments are necessarily multi
plied and often practically blind, though seldom quite aimless. But in the
process of exposition it is manifest that, having traversed the way before, and
being now in possession of the scientific knowledge which was our goal, our
didactic analysis may be much more direct and definite. We may exclude
all the gropings and deviations that occurred in the first search after the truth,
the misleading analogies and wrong hypotheses ; we may carefully select the
most appropriate instances and experiments for disclosing the law in question
to our pupils, and thus shorten the road for them : but we shall be travelling
substantially the same road and employing the same method as previously.

205. SCHOLASTIC METHODS OF EXPOSITION AND DEBATE. The mediaeval
Schoolmen followed the advice of the founder of the Lyceum : " Before you
try to solve any problem," wrote Aristotle, " set forth clearly the reasons or
difficulties that militate against the solution you are about to propose. In that

1 Cf. WELTON, ii., p. 220.

GENERAL OUTLINE OF METHOD 17

way you will see better where is the heart or kernel of the question, the exact
point in dispute ; you will fix your attention on it, and you will retain a firmer
conviction of what you have seen to stand successfully the shock of the de
bate." l

Open the Summa Theologica of St. Thomas, that monumental synthesis
of mediaeval wisdom " ad eruditionem incipientium" ." At the beginning of
each Question (Quaestio) or Sub-question (Articulus] will be found a resume"
of all the arguments, from reason and authority, that can be brought against
the intended solution. They are introduced by the familiar " Videtur quod
non . . . >}. Next comes the doctrinal affirmation of the thesis or solution,
introduced by the words " Sed contra . . .," and usually illustrated rather
than proved by some quotation from Scripture or from the Fathers. Then
comes the body of the article (Corpus Articuli), introduced by the phrase
" Respondeo dicendum quod . . ., " and containing the principle on which the
solution is based, together with its main proofs in the usual syllogistic form.
Finally, we have the further application of this same principle to the solution
of each of the various difficulties proposed against the thesis at the commence
ment : " Ad primum dicendum quod . . . " " Ad secundum . . . ," etc.

At the public debates that were held in the mediaeval universities at certain
fixed intervals during the year, usually before Christmas and Easter ("Zto-
putationes Quodlibetales" as they were called), the procedure was slightly
different. Any auditor might raise a question and indicate in a general way
the arguments in favour of the solution that had his preference. The " re-
spondens" i.e. the candidate for degrees, or his master, formulated their view,
and based it on some fundamental argument. This position was at once
attacked by the objector, and so the debate was opened. On the morrow, or
one of the following days, the master repeated, arranged, and " determined,"
or settled definitively, the various questions discussed. These " Determina-
tiones " have come down to us in the copious volumes of mediaeval philosophy
and theology known as " Quodlibeta ".:i

The method of carrying on academic debates in Scholastic philosophy and
theology, still in use in schools, colleges, and universities, where these subjects
are taught, is the same in principle as the above, if somewhat different in de
tail. The exercise is strictly syllogistic, and it undoubtedly gives the student

1 Metaphysics iii., i ; Nicomachaean Ethics, vii., i. Here is the comment of
St. Thomas : " Postis his quae videntur probabilia circa praedicta, prius inducamus
dubitationes, et sic ostendemus omnia quae sunt maxime probabilia circa praedicta
. . . quia si in materia aliqua dissolvantur difficultates et relinquuntur ut vera ilia
quae sunt probabilia, sufficienter est determinatum." — loc. cit., lect. i.

2 " Quia catholicae veritatis doctor non solum provectos debet instruere, sed ad
eum pertinet etiam incipientes erudire, propositum nostrae intentionis in hoc opere
est ea quae ad Christianam religionem pertinent, eo modo tradere, secundum quod
congruit ad eruditionem incipientium." A few brief sentences next tell us why he
undertook the work : to rid theology of many useless questions, and to give an orderly
exposition of it for the benefit ol learners; and in what spirit: "cum confidentia
divini auxilii." Those few simple sentences form the whole preface or prologue to
one of the greatest works that human genius has ever produced.

3 Cf. DE WULF, History of Medieval Philosophy, p. 258, note from Mandonnet's
Siger de Brabant, etc.

VOL. II. 2

1 8 THE SCIENCE Of LOGIC

an invaluable training in exact reasoning. The following outline may be
found helpful to academic disputants.

The professor fixes upon a thesis, appoints a pupil to " defend " it, and
one or more others to " object " to it. At the appointed time the defender
(" defendens" " respondens ") enters the pulpit or bema, announces the thesis,
adding, if desirable, a very brief exposition and proof. The objector (" ob-
jiciens ") then asserts the contradictory of the thesis, proving his assertion by
a syllogism. The defender resumes with the introductory phrase, " Sic argu-
mentaris, Domine " (" This is your argument, Sir "), repeats the syllogism
slowly and clearly, deliberating on the way in which he ought to deal with
each premiss, the consequence, and the conclusion. Having repeated the
syllogism, and also the introductory phrase, he again takes up and repeats
once more the major, and now passes judgment on it : "I grant the major "
(" Concedo majorem "), if he considers it true ; " I distinguish the major "
(" Distinguo majorem "), if he sees in it a true sense and a false sense, which
two he will separate by the addition of some well-chosen technical phrase to
show the true sense and the false one, qualifying the false by " I deny "
("Nego"), and the true by "I grant" (" Concedo ") ; "Please prove the
major " (" Faveas probare majorem "), if he considers the major entirely
false ; " Let the major pass " (" Transeat major "), if he considers it irrelevant,
or does not wish to pass definite judgment on it. In general, the objector
should so construct his syllogisms that the major will not admit of total denial.
Should the defender thus request his adversary to prove the major, the former
need not proceed to the minor of the original syllogism, but listen to and deal
with the proof brought forward for the major. If the defender has granted,
or " distinguished " the major, he proceeds to repeat the minor, and either
" denies " or " centra-distinguishes " it (" Nego minorem " or " Contra-dis-
tinguo minorem "). It is only when he " denies " either premiss, or " distin
guishes " .one and " contra-distinguishes " the other, that he has a right to
" deny " the " consequence " or probative force (consequentia\ and therefore
also the conclusion (consequens), of the syllogism ("Nego consequens et
consequentiam "). To " centra-distinguish " the minor is to introduce the
same distinction into it as into the major, granting the member correspond
ing to that denied, and denying the member corresponding to that admitted,
in the case of the major. It may sometimes be necessary to introduce
a further distinction into either or both members of a distinction in order to
sift fully the true from the false : this process is called " subdistinguishing "
(" Subdistinguo ").

The objector then continues the debate by proceeding to prove syllogis-
tically the proposition denied by the defender, in the sense in which it was
denied, commencing by the words, " I prove the major (or minor) denied "
[" Probo majorem (or minorem} negatam "] ; and the defender proceeds to
deal with the new syllogism as before.

The objector may, at any stage, request or allow the defender to explain
the precise force of the distinctions he has made in an answer : which the
defender does as briefly and clearly as possible, introducing his explanation
by the words, " I explain the distinction (distinctions) introduced " [" Et explico
distinctionem datam (distinctiones datas) "]. Various courses may here
present themselves to the objector.

GENERAL OUTLINE OF METHOD 19

He may, notwithstanding the explanations offered, urge some proposition
in the sense in which it has been denied. " But . . . Therefore the difficulty
remains ". " Atqui . . . Ergo stat difficultas "). To which the defender
replies, " I deny what you subsume " [" Nego subsumtum "]. The objector
must then proceed to prove the proposition in the sense in which it has been
denied. [" Probo subsumptum"~\

Or, again, the objector may urge the difficulty in a modified way, owing
to some concessions made by the defender in his explanation ; which he does
by commencing, " But I insist . . .," or, " But I urge the difficulty from your
own admissions " (" Atqui insto . . .," or, " Atqui ex concessis urgeo
difficultatem ". )

The real point of the difficulty ought to be kept in the minors as far as
possible : the distinctions made ought to be real, not merely verbal, i.e. ex
pressive of the same syllogism in different terms : quibbling and sophisms
ought to be rigorously excluded : the questions selected ought to be the more
serious ones, and the difficulties likewise : if the objector really feels the
difficulty he is putting, so much the better ; waste of time, vain display
of acuteness in making distinctions, or syllogisms more subtle than solid,
should not be tolerated : the number of syllogistic steps leading up to the
full solution of any difficulty will, of course, depend on the nature of the latter,
but need not usually exceed four or five, unless, indeed, a modified phase
of the difficulty, or a practically new difficulty, arises in the course of its solu
tion : exactness, lucidity, brevity in the formation of syllogisms and distinctions,
ought to be insisted on : and therefore, also, the necessary means to this end,
viz. familiarity with the technical tertninology of the philosophical problems
under discussion, and of philosophical terminology in general.

Such are the principal canons laid down for observance in those exercises.1
There is no reason why they should not be conducted in the vernacular if
necessary, rather than in Latin. The method is not wedded to any language ;
and philosophical thinking would be much less erratic and illogical than it is
at the present day if such disciplines formed an essential part of philosophical
training.

The Scholastic system of philosophy is identified with constructive and
didactic methods which are nowadays eliciting a more accurate and sympa
thetic appreciation from scholars, after a long period of prejudice and mis
understanding. It took shape in the early mediaeval schools of Europe under
the combined influence of St. Augustine, Plato, and a few of the logical
writings of Aristotle. But the introduction of the latter's works into the
Western schools towards the close of the twelfth century gave Scholasticism
its predominantly Aristotelean character in the thirteenth.2 To its preponder
ating use of synthesis as a constructive method we have already referred (201).
Its elaborate system of teaching, too, has had a profound influence on the
development of learning during many centuries. While recognizing its
limitations, we are bound in the interests of historical truth to give it credit for
many excellences. In general, we may say that the Scholastic method,

1 C/. ZIGLIARA, Logica, (46), De methodo disputandi.

2C/. DE WULF, History of Medieval Philosophy, pp. 101-48; Scholasticism
Old and New, pp. 19-88, 168-82.

20 THE SCIENCE OF LOGIC

whether constructive or didactic, trains the mind to careful reflection and
develops the critical faculty.

In the first place, it certainly gives one the habit of disentangling and
clearing up his ideas, of arranging them in order, of introducing rigorous
logical sequence among them.

Then, secondly, it teaches us to distinguish certainty from probability,
truth from appearances, science from plausible theorizing, and established
conclusions from unverified hypotheses.

Thirdly, it inculcates a spirit of disinterested inquiry after the truth. In
Scholastic philosophy truth is regarded in its native, unadorned beauty, so to
speak ; it is sought for its own sake, and with a dispassionate calm : to the
Scholastic, rhetoric makes no appeal : mere rhetoric excites the imagination
and emotions, disturbs the balance of judgment, begets confusion of ideas, and
hasty, ill-considered views. An inflammatory discourse that will arouse an
untrained audience to the highest pitch of passion or enthusiasm may not be
able to stand the test of a cold analysis, or the logic of the syllogism. The
language of Scholasticism is the very antithesis of rhetorical. It " simply and
solely expresses the intellectual concept, abstracting from all its relations to
the other faculties of the soul, and from the reactions it may call forth in them.
All possible obstacles between the mind and the objective truth are pitilessly
set aside. Its style, stripped of all ornament, free from all feeling and senti
ment and all the artifices of rhetoric, and hence so often accused of crudeness
and barbarism, has all the exactness and precision of a mathematical formula
or proposition ; it is pre-eminently truthful and clear. It was methodically
and most successfully shaped into the aptest possible instrument for the
systematization of thought : the instrument that was to build up the great
Summae, whose materials lay scattered for generations through a whole
world of literature. Reduced to the simple form and proportions of proposi
tion and syllogism, those truths could be logically moulded into an organic
whole in which each part received a prominence due to its relative import
ance." 1 We are often nowadays reminded of what Plato said : We ought
to tend to the truth with our whole soul — avv 6X17 rfj faxd • • • «»f TO Sv
<at TOV ovros ro (fravoTorov . . . TOUTO 8' (ival (fraptv TayaBov.* The Schol
astics receive those words with respect, but .also with caution. When the
truth is known, yes, by all means, let us love it, embrace it with all the ardour
of our souls, act up to it, work for it, suffer for it if needs be, and if duty
demands the sacrifice. But in searching for the truth our chance of finding
it will be in proportion to the degree in which our intellect succeeds in laying
aside all considerations foreign to the truth itself. At bottom, the truth is
always good, always truly useful, therefore ; of that there can be no doubt.
But this or that doctrine, which is subjectively judged to be useful, may not be
so in reality ; and some other, judged to be dangerous, may be the only one
truly useful in the long run, because it happens to be the one that is really
true.

Fourthly and finally, the Scholastic method counteracts the narrowing
influence exerted on the mind by a constant and exclusive contact with the

1 P. RICHARD, Etude critique sur le but et la nature de la scolastique (Revue
Thomiste, May and November, 1904).

2 PLATO, Republic, vii.

GENERAL OUTLINE OF METHOD 21

concrete, positive facts of sense ; it nourishes in the soul what we may call
the craving for the universal, the desire to grasp the idea in the fact, the
abiding law in the contingent phenomenon.

In a word : clearness, precision, severe logic, method ; a sense or percep
tion of the true ; love of the truth simply for its own sake ; elevation of thought
and a fresh and speculative turn of mind : such are the qualities developed by
the Scholastic method in those who are formed upon it. Many great philo
sophers have placed on record authoritative eulogiums of the syllogism.1
Such a writer as Huxley, who is certainly free from the suspicion of partiality
in this matter, pays a willing tribute of admiration to " Scholastic philosophy,
that marvellous monument of patience and genius, constructed by the human
mind to give a logically unified answer to the problems raised by the spectacle
of the universe ".a

But the Scholastic method is not without its limitations. A method, being
a means to an end, becomes useless, or even injurious, when wrongly employed.
The Scholastic method exercises mainly the speculative reason : it is primarily
explicative, synthetic. It accustoms one to understand how a conclusion is
connected with certain premisses, how conclusions follow from principles ;
but it develops very little, if at all, the habit of observation ; it gives little or no
stimulus to personal initiative in the discovery of new truth. A training in
the positive sciences is, therefore, the necessary complement of a " Scholastic "
formation or discipline of the mind. To round off and perfect this latter
training, nothing is more efficacious than contact with facts ; since the
intellect must derive all its ideas from external or internal sense experience, no
mere verbal descriptions of phenomena can equal the direct and immediate
perception of these latter. By his example and by his works, Aristotle is no
less the master of scientists than of philosophers. Not only Roger Bacon,
but Albert the Great, St. Thomas, Duns Scotus, were faithful to his method.
Pope Leo XIII. has recommended us expressly, in his encyclical Aeterni
Patris, to "receive with a willing and grateful mind every word of wisdom,
every useful thing by whomsoever it may have been discovered or planned ".
It must also be of very great utility to supplement a training in the Scholastic
method by reviewing the history of scientific progress, so as to realize what
provisional hypotheses and theories, what guesses and approximations, what
deviations and errors even, the human mind has had to pass through in its
journey towards the discovery of every new truth.

Again, the importance attached by Scholasticism to certain science in
clines its disciple to depreciate the value of the merely probable and provi
sional. To the " Scholastic " mind, the slowness of experimental work is
irksome : it easily becomes impatient of the problematic character of most
historical, sociological, political, and economic inductions, and of the many
reserves with which the materials of the special sciences must be employed.3
But, while it is very right and proper to seek for certitude, and very praise
worthy to look for demonstrative reasons, it is wrong to expect the impossible ;
where certitude cannot be had it is unreasonable to demand it.4

1 Cf. Leibniz, Nouv. Ess., iv., 17, § 4. — apud WELTON, op. cit., i., p. 411.

2 HUXLEY, Animal Automatism and Other Essays, p. 41.

3 Cf. MERCIER, Origines de la psychologic contemporaine, pp. 450 sqq.

•» Sunt aliqui qui omnia volunt sibi dici per ccrtitudinem. . . . Et hoc contingit

22 THE SCIENCE OF LOGIC

Furthermore, exclusive preoccupation with the true, exclusive attention
to the relation of things to the intellect alone, may disturb the harmony that
ought to regulate the development of our faculties. The Scholastic method in
terprets reality by referring the latter to intellect alone. Avowedly, and on
principle, the standpoint of its research is above and beyond the domain of
emotion and will ; it brings into action the intellect alone. Now, no one may,
with impunity, submit himself exclusively to any such purely intellectual
regime.1 It perfects and develops one side only of our being, the side that
is fundamental and essential, no doubt, but which, nevertheless, is not the
whole man. The mind that is excessively given to such a discipline develops
an unduly abstract and speculative turn, and loses very largely all just ap
preciation of the great complexity of concrete, actual things.2 All exclusive
preoccupation with a special order of truths entails, of necessity, the incon
venience just referred to. All specialists are prone to contract a peculiar sort
of " mentality " that tends to make them narrow, and suspicious of truths out
side their own chosen circle.

Finally, there is hardly any need to point out that the excessive use —
that is, the abuse — of the Scholastic method, may make one insensible to form,
to elegance of expression. A literary culture alone will counterbalance this
danger of an exclusively abstract, logical, and " intellectualist " mental dis
cipline.

MERCIER, Logique, pp. 271, 294-96, 371-84. WELTON, Logic, vol. ii.,
bk. vi. MELLONE, Introd. Text-Book of Logic, pp. 291, 383 sqq. DE WULF,
History of Medieval Philosophy, pp. 137, 254 sqq.; Scholasticism Old and
New, pp. 19-31. ZIGLIARA, Logica, (44), (45), (46).

propter bonitatem intellectus judicantis, et rationis inquirentis ; dummodo non qua-
ratur certitude in his, in quibus certitude esse non potest. — ST. THOMAS, In II.
Metaph., Lect. 5. Cf. supra, 203.

1 Cf. RICHARD, Revue Thomiste, Nov.-Dec., p. 564.

a Compare what Newman says in his Grammar of Assent about Inference, and
about what he calls the Illative Sense; also Pascal's striking passage (Pensees,
section i, p. 318. Brunsch. edit.) on the esprit geometrique and the esprit de finesse :
" The reason why certain practically shrewd people (csprits fins) are not great geo
metricians is because they are utterly unable to give their minds to the principles of
geometry. But the reason why geometricians are not shrewd (fins) is because they do
not see what is under their eyes ; accustomed to the clear truths of geometry, and to
reasoning from well-grasped, tangible principles, they get lost in small things (chases
de finesse) where the principles are not at all tangible. Here the principles are hardly
seen at all, but rather felt ; they can only with the greatest difficulty be impressed
on those who do not happen to feel them themselves ; and things of this sort are
so delicate and so numerous that it requires an exceedingly keen and delicate faculty
to feel them, and to judge them rightly according to this feeling, when, as happens
oftenest, we cannot demonstrate them in geometrical order, seeing that we have not
their principles in that way, and that it would be undertaking infinite labour to try
to get at them so. We must, as it were, see the thing at a glance rather than by
progressive reasoning, at least in a certain measure. And hence it is rarely we find
shrewd geometricians . . . because they wish to treat complex things (chases fins)
geometrically, and make themselves ridiculous by commencing with definitions and
principles : which is not the way in that sort of reasoning. It is not that the mind
does not reason ; it does, but tacitly, naturally, without art, in a way which none
may mechanically express, and with which few indeed are adequately endowed."

CHAPTER II.

INDUCTION IN ITS VARIOUS SENSES. INTRODUCTORY AND
HISTORICAL NOTIONS.

206. THE PROBLEM OF INDUCTION: ASCENT FROM THE
PARTICULAR TO THE UNIVERSAL.— In the foregoing chapter we
have gleaned some general notions about method, and about the
processes of analysis and synthesis involved in method. We
now purpose to deal with the analytic method and the doctrine
of Induction. To the main problem of induction we have referred
already (194, 198). How do we, from particular facts of sense
experience, attain to a knowledge of necessary, universal truths?
Such universal judgments we have seen to be essential not only to
all deductive, but to all mediate, reasoning whatsoever (193, 195).
We have called them abstract, general, universal, generic judg
ments (92). They are likewise called logical and scientific prin
ciples, axioms, laws of thought, laws of physical nature, etc.
We have expressed them both categorically : " M as such is P " ;
" All Ms are P" ; "Whatever is M is P" etc. — and hypotheti-
cally : " If anything is M it is P" ; " If 5 is M it is P" etc.
And now we have to analyse the conscious processes by which,
from the apprehension of particular facts, instances, cases (con
taining S, M, P, etc.), we reach a certain knowledge of such
general truths or laws. Since, moreover, the essential merit and
excellence of "scientific" knowledge lies in the fact that it is
a knowledge of the universal truth, principle, law, etc. — and,
through this, of the particular phenomena or instances under it,
— the importance of clearly understanding the process by which,
and the rational grounds on which, we give our assent to the
universal truth, will be at once apparent.

We have distinguished three kinds of universal truths
(195). There are, firstly, those absolutely necessary, self-evident
axioms such as the laws of thought, metaphysical principles
such as the principle of causality " Whatever happens has a

24 THE SCIENCE OF LOGIC

cause" ethical principles like " Virtue is praiseworthy" geo
metrical and mathematical axioms such as " Two and two are
four" ; and the whole vast body of truths that can be derived
from such principles by pure demonstration. These truths are all
in materia necessaria ; they have to do with abstract essences, or
objects of thought considered in a possible state, apart from the
changing conditions of actual existence in time and space.

The process by which we come into possession of truths of
this class presents no logical difficulty. It is simply a process
of forming abstract and universal concepts ; of analysing and
comparing these with one another ; of thus seeing intellectually
self-evident, necessary relations between them ; of generalizing
these relations and formulating them in necessary or analytic
propositions. The process embraces conception and judgment, but
does not involve logical inference or reasoning proper. It is from
sense observation of a few instances that we form the concepts :
we need such observations in order to get, for example, the
notions of "whole," and "part," and "greater". But having
once abstracted these intellectual notions from sense experience,
and compared them with one another, we have an immediate
intellectual intuition of the necessary truth that " the whole is
greater than its part " : and this truth we see to apply to every
whole, actual arid possible, known and unknown : we assent to it
not because we have examined all the instances — for we have
not — but because we perceive the relation to be universal because
it is necessary.^

Now, this simple process of abstraction, intuition, and general
ization, by which we attain to a knowledge of self-evident,
necessary principles, through the notions which we abstract from
sense experience, is sometimes called Induction. But this is
using the word in such a wide sense as to make it embrace every
mental process by which we ascend from or through the particular
to the universal. Aristotle used the equivalent Greek term in
this wide sense : ' ETraywyrj rj cnro rwv icad' eKacrrov eVt ra tca66\ov

e(f>o8o<?.2

1 Cf. JOSEPH, Logic, pp. 356, 363 (2), 508 sqq,

*Top. i. 12. Truths oi the- class with which we are dealing are described in
Scholastic philosophy as per se notae (86), i.e. knowable in themselves, by a full
analysis of tlie notions involved in them. In some of these truths the notions are
so simple as to be within the reach of all who are endowed with ordinary intelli
gence. These are said to be per se notae quoad omnes. In other cases, however,
the notions may be so complex — as, for instance, in the remoter mathematical con
clusions — that although the truths embodying them are knowable in themselves

INDUCTION IN ITS VARIOUS SENSES 25

The processes we have just described as abstraction, intuition^
and generalization, of simple, self-evident, necessary axioms, are
usually described by modern logicians as "geometrical" or " mathe
matical" induction}" And the reason assigned for the superior
cogency of the evidence and certitude we have in regard to these
truths, as compared with those we reach by "physical" induc
tion, is stated to be this : that in the former the objects compared,
being abstract, have their essential qualities fixed for certain by
ourselves, in the definitions we impose upon them ; while in the
latter the essential qualities of the objects — which are now con
crete things and agencies existing and acting in physical nature —
are not fixed by definitions which we impose on them, but "have
to be discovered and proved ". Thus Dr. Mellone writes : 2

"The universality of the result [that "the angles at the base of an isosceles
triangle are equal "] depends upon our being absolutely certain of what are
the essentials of the kind of triangle in question ; and we can be certain of
these because in geometry definitions have not to be discovered. The geome
trician can frame his own definitions, and change them, if necessary . . . the
mathematician makes his own definitions of what is essential and argues from
them. But in Nature the essential conditions have to be discovered and
proved. This is the great difference between mathematical and physical in
duction, and all the difficulties of physical induction result from it."

This explanation of the difference between metaphysically or
absolutely necessary and universal truths on the one hand, and
physically or contingently necessary and universal truths on the
other, differs from the scholastic account of them only in one par
ticular, but one which is all-important. Our definitions of the
abstract objects of thought with which the mathematical sciences

(quoad se), yet we may not have grasped the intension of the notions sufficiently to
see the necessity of the connexion between them : they may not be clear to us
(quoad nos) (C/.MAHER, Psychology, p. 289, n. 33 ; JOYCE, Logic, p. 239). The truth
of these we learn by Demonstration, i.e. by gradually tracing their rational, logical
connexion with the former ones.

The demonstration of a remote geometrical conclusion is simply the process of
showing how and why it is true, by revealing the rational connexions it has with
simpler antecedent truths, and ultimately with first principles (195). This process
is essentially deductive : a diagram may be necessary in order to help the imagina
tion, and to serve as a concrete illustration or instance : but it is not from the
diagram, from the instance, but, through it, from wider and simpler necessary prin
ciples that the conclusion is derived. It is only by an improper use of language
that this process can be described as "Geometrical Induction". Cf. Palaestra
Logica, pp. 103-104.

1 It is in the mathematical sciences we find the simplest and most obvious
examples of such axioms. Cf. MELLONE, op. cit., pp. 265-70. On the nature of
mathematical reasoning, cf. JOSEPH, op. cit., chap. xxv. ; infra, 258.

2 ibid. pp. 267, 269.

26 THE SCIENCE OF LOGIC

are concerned are just as really and truly discovered by us in
Nature, i.e. in the world revealed to our senses, as our " physical"
definitions, our concepts of the nature and activities of physical
agencies, are. They represent reality just as surely as the latter
do. The " abstract objects " which they define are really em
bodied in the world that is revealed to our senses, i.e. in the
physical universe. These objects and these definitions are not
arbitrary creations of our minds, fictions which we may modify at
will. If they were so, the pure deductive sciences would give us
no knowledge about reality, no real knowledge : they would be a
mere dream about the unreal.

Besides the analytic, absolutely necessary, and universal
judgments we have just examined, there are, secondly, those that
we have called physically necessary and universal, and thirdly,
those that we have described as morally necessary and uni
versal. The judgments of these two latter classes are syn
thetic ; and it is the process by which we reach these — more
especially the physical truths or laws (201) — that most properly
deserves the name of " induction " or " physical induction ".
The discovery and proof of such laws is the aim of all
the physical, natural, or positive sciences ; for in these laws lies
the explanation of the facts and phenomena of those vast domains
of sense experience. To determine the laws according to which
those phenomena happen ; to get at the nature of the things of
experience ; to understand phenomena by the laws that govern
them, and individual things by the natures which abide and act in
them : such is the ambition of the physical scientist. He sets out
from the observation of complex, varying phenomena, to extract
from them their common principles and abiding laws : his work
is mainly a work of decomposing, dividing, analysing : his method
is called analytic ; and his whole process of ascent from particular
facts to general laws is called " scientific" or "physical" Induction.

The doctrine of induction has been developed from, and largely based
upon, the remarkable growth of knowledge which the last few centuries have
witnessed in the physical sciences. In these sciences, especially, it finds its
application. From them, therefore, it naturally draws its aptest illustrations,
and we need not be surprised to find treatises on inductive logic often read
like pages from a handbook on some natural science (201). Nevertheless, it
is important to remember that induction is equally applicable to the data of
the social, anthropological, and philosophical sciences, as well as to physics :
and, moreover, it is only in so far as it is thus universally applicable that it
falls strictly within the scope of logic.

INDUCTION IN ITS VARIOUS SENSES 27

207. THE SO-CALLED " INDUCTIVE SYLLOGISM," OR " INDUC
TION BY SIMPLE ENUMERATION OF INSTANCES"—" COMPLETE"
AND " INCOMPLETE." — Since induction is an ascent from par
ticular instances to general truths, from " some " to "all," it has
been rightly described as a process of generalization. But we
have already repeatedly distinguished between the mere concrete,
collective, enumerative universal, and the really scientific universal
which is an abstract judgment, embodying some more or less
necessary principle or law (92, 195). It is this latter that scien
tific induction proper aims at establishing. Before dealing with
this, however, it will be convenient to examine the process by
which the collective judgment is reached. This process, too, has
been called " induction " : " induction by complete enumeration"
" formal," " perfect " : to distinguish it from the other or " scien
tific " induction, which has sometimes been described as " incom
plete," " material," " imperfect ". The induction of the collective
judgment from a complete enumeration of its constituent instances
is " formal " and " perfect " merely by reason of the absolute cer
titude which we necessarily possess about the sum-total when we
have examined all the instances. But to call scientific induc
tion, which attains to the general law by an analysis of some
instances, " incomplete " and " imperfect," is singularly unfor
tunate and misleading ; for it insinuates that this is a partial appli
cation of the former process, that it, too, attains to the universal
by enumeration, and that its result is " imperfect " or uncertain,
inasmuch as the enumeration is " incomplete ". As a matter of
fact, it does not reach the universal by enumeration at all. This
we shall see later on.1 Let us here examine the process by which
the collective judgment is reached : the so-called " inductive syllo
gism ". " Induction by complete enumeration " may be defined
as the process by which we predicate about a whole class or collection
of things what we have already predicated of each thing separately.'''

1 C/. JOSEPH, Logic, pp. 467-68; infra, 209, 211.

2 Father Joyce (Principles of Logic, p. 228) confines this " inductive syllogism "
to the " logical parts" (species} of a " logical whole" (genus). It applies equally
well to the " individuals " of a " lowest class," when these are limited in number and
can be exhaustively enumerated. Its principle, " Whatever can be predicated of each
of the parts successively can be similarly predicated of the whole," is not to be re
garded as the reciprocal of the Aristotelean Dictum de omni et nullo : for this latter
must be interpreted to refer to an abstract, not to a concrete, universal : and, in pass
ing from the abstract " M as such'1 to the " All M's" of the Dictum, we postu
late the principle to be discussed below (223-25) called the Uniformity of Nature,

cf. 253-54-

28 THE SCIENCE OF LOGIC

It is described by Aristotle in his Prior Analytics}* It is the
simple summing up of separate instances into an actual collec
tion. He speaks of it as in a certain sense the opposite of the
syllogism ; Kal rpoirov riva avri.K€i,rat r) eTraywyrj rat (rv\\o<yiarfi(a)
inductio quodammodo opponitur syllogismo. The syllogism essen
tially implies a comparison of two extreme terms (S, P} with a
third middle term (M}. Enumerative induction has no middle
term different from the minor extreme? The middle term (M] in
the syllogism must be, at least once, strictly universal : the cor
responding term, which stands as minor extreme in enumerative
induction, is not a strict universal — applicable equally to an in
definite number of realizations — but an actually complete collec
tion, a collective, actual whole ; and the so-called minor extreme
(S), which stands as middle term in enumerative induction, is a
consecutive enumeration of the individual instances, equal in point
of actual extension to the middle term. An example or two will
make this clear : —
S is P |l Saul, David, Solomon were men of remarkable

achievements ;
S is M Saul, David, Solomon were all kings of the whole of

Palestine ;
. : M is P I . '. All the kings of the whole of Palestine were men of

remarkable achievements.

Or, again, to take Aristotle's own example : 3

5 is P
S is M
. : M is P

Man, horse, mule, etc., are long-lived.
Man, horse, mule, etc., are bile-less.*
.•. All bile-less animals are long-lived.

From these examples we can understand Aristotle's definition
of the "inductive syllogism " as " proving the major term of the
middle by means of the minor," i.e. proving the universal, which
stands as major of the deductive reasoning, " M is P" — proving
that P can be predicated of the whole collection (AT) — by predicat
ing P of each member individually (5). The class or collection is

1 Anal. Prior, ii., 23 (25). *ibid.

3 Aristotle's " individuals are not particular individual things, but species, which
he combines under a genus. . . . He regarded an exhaustive summation of the
species which compose a genus as quite feasible." — WELTON, Logic, vol. ii., p. 33.
Cf. JOYCE, Logic, p. 228.

4 By bile-less animals Aristotle meant all those species of quadrupeds that have
no excess of choleric humours — a list which he considered it quite possible to com
plete. Cf. JOSEPH, Logic, p. 351 n.

INDUCTION IN ITS VARIOUS SENSES 29

symbolized by M as being greater in point of possible extension
than the individuals enumerated (S\ though actually equal to
them, and naturally less than the genus characterized by the
attribute P.

What is to be said about the value of this process ?

Firstly, it will not be valid unless the enumeration is com
plete. The enumeration must be Bia Trdvrwv, as Aristotle
expresses it ; else the argument will be fallacious : there will be
an illicit process of the subject of the conclusion. St. Thomas
likewise insists that as long as we base our conclusion on enumera
tion the latter must be complete.1 So long then as we concentrate
our attention on the mere enumeration of instances, and disregard
their nature, we can never be certain of our conclusion until we are
certain that our enumeration is actually complete : " opportet sup-
ponere quod accepta sint omnia ". Now we can practically never
be certain, in regard to the occurrence of natural phenomena, that
our enumeration of instances is complete : and this is the first
obvious limitation of the process as a means of reaching certain
knowledge. Mere " enumerative " induction, then, has only a pro
visional value. It enables us to say that so far as our actual
knowledge goes, such or such an enumeration may be regarded as
complete ; that it is complete we usually have no warrant to affirm
categorically. There are, of course, cases in which an incomplete
enumeration of instances may yield a very high degree of proba
bility for a universal conclusion, viz. when we are dealing with
phenomena such that if an instance contrary to those examined
existed we should in all probability have encountered it. The
truth of such a generalization cannot reasonably be doubted so
long as no negative instance turns up.2

Secondly, even where the enumeration of instances is complete,
the process does not lead to scientific knowledge, i.e. the knowledge
of a strictly universal conclusion embodying what can be called a
law. And the reason is manifest. The conclusion expresses a
simple addition of instances, and is, therefore, simply a collective
proposition whose subject is an actual whole ; whereas the strict

1 " Opportet supponere quod accepta sint omnia quae continentur sub aliquo
communi ; alioquin inducens non poterit ex singularibus acceptis concludere uni-
versale. . . . Patet quod inducens facta inductione quod Socrates currat et Plato et
Cicero, non potest ex necessitate concludere, quod omnis homo currit, nisi detur sibi
a respondente, quod nihil aliud contineatur sub homine, quam ista quae inducta
sunt " (In II. Anal. Post., lect. 4).

2 Cf. JOSEPH, Logic, p. 491 ; MELLONE, op. cit., p. 251, referring to Aristotle,
Top., viii., 8.

3o THE SCIENCE OF LOGIC

universal proposition, the abstract universal, can be reached only
by generalization of the abstract judgment which establishes some
sort of necessary connexion of attributes between subject and predi
cate. Adding parts to parts, to form a natural whole, gives us a
collective idea. Considering an object in the abstract, apart from
its individualizing characteristics, putting it into relation with its
concrete realizations, actual or possible, indefinite in number,
seeing that it is predicable of all, is to universalize and to make
scientific progress. For " all science is of the universal and
necessary";1 i.e. it is expressive of necessary, and therefore uni
versal, relations between the objects of our thought. The strict
universal is no mere actual collection ; it is applicable to an
indefinite number of instances. Therefore, this kind of induction
does not put us in possession of scientific or necessary truth.

It assumes, as we have seen, the external form of a syllogism
in the> third figure, but it is no more a true syllogistic process
than is the apparent syllogism whose premisses contain no true
universal, but only collective propositions. In fact it is just the
reverse of the process which John Stuart Mill erroneously put
forward as the true type of syllogistic reasoning (195).

To observe successively that each of the planets describes an elliptical
orbit around the sun, and then to say that all the planets describe such an
ellipse, is simply to group together isolated observations in a formula to aid
the memory, but this is not ascending from the particular to the universal.
Similarly, to conclude that, because the senses a, b, c, d, e, are each an occasion
of error, therefore all the senses are an occasion of error, is certainly not to go
through a scientific reasoning process : but rather through an arithmetical
process which simply tells us that five times one are five.

Examples might be multiplied indefinitely. They all point to the same
conclusion : that observation pure and simple puts us in possession of par
ticular facts, and that the grouping together of those facts in a collective
notion may help the memory and abbreviate the expression of thought, but
will not lead to scientific knowledge of any necessary truth or law.

Aristotle distinguished clearly between the formation of an actual whole
from its parts and the elaboration of a universal notion ; " Even if we succeeded
in showing separately," he writes,2 "whether by the same or by separate
proofs, that equilateral, isosceles, and scalene triangles have each their in
terior angles equal to two right angles, we should not yet have any right to
assert the universal proposition ; ' The triangle, as such, has its interior
angles equal to two right angles'." The separate proofs would not neces
sarily have given us a universal knowledge ((cafldAov) of the triangle as such.
Hence, we should not yet know whether the attribute, " having their interior

1 'H \t.\v bnarriW «ta0<$A.ov /coi 5i' ivayicalw.— ARISTOTLE, Post. Anal., i., 33.
* Post. Anal., i.t 5(5-7).

INDUCTION IN ITS VARIOUS SENSES 31

angles equal to two right angles" belonged to the triangle as such, and,
therefore, to all possible triangles.

Nor, even when we see that the three species, equilateral, isosceles, and
scalene, are exhaustive of the genus triangle, can we be said to know scien
tifically that the latter as such has the sum of its interior angles equal to two
right angles : unless we have proved this attribute to belong to each of the
three species, not on different grounds peculiar to each case, but on some
common ground inherent in their common nature as triangles : " f i ravrov rfv
rptywi/o) tlvcu. KOI IcroirXtvptf rj e»cdcm» rj iracriv — si eadem sit row esse ratio tn-
angulo et aequilatero, aut cuique trianguli speciei aut omnibus."1 In order
that such a conclusion be anything more than an enumerative judgment " it
would be necessary to show that the reason for the inherence of P is the same
in regard to all the parts of J/".2

But mere enumeration of the individuals of species (or of the species of a
genus) cannot of itself reveal to us anything in their common nature to serve
as a sufficient and necessary ground for predicating any attributes found in
all the examined individuals (or species), about the species (or genus) as such.

That Aristotle was acquainted with the true method of arriv
ing at such a scientific or necessary knowledge of the nature of
things we shall presently show (208). That he realized the in
ability of an incomplete enumeration as such to prove a really
general principle, is manifest from what he says of the so-called
" inductive syllogism " described above. When he speaks of it as
a way of "proving the major term of the middle by means of
the minor"3 i.e. of proving the universal principle " M is P"
11 If anything is M it is P" which stands as major in the demon
strative syllogism in the first figure, he does not mean "proving"
in the strict sense of demonstration (aVoSet^t?), for strict demon
stration is always by syllogisms in the first figure. He only means
that the inductive syllogism is a way of illustrating, making
clearer by instances or examples (BrjXouv ; TriOavvTepov, <ra<f>eaT€-

1 ibid., (6).

2 JOYCE, Logic, p. 229. The author observes that Euclid is usually able to do
this in cases where he proves successively that something is true of each of all the
possible instances of a logical whole. Cf. JOSEPH (op. cit., p. 503) : " The peculiar
nature of our subject-matter [here] enables us to see that no other alternatives
are possible within the genus than those which we have considered ; and therefore
we can be sure that our induction is ' perfect '. The nature of our subject-matter
further assures us that it can be by no accident that every species of the genus
exhibits the same property ; and therefore our conclusion is a genuinely universal
judgment about the genus, and not a mere enumerative judgment about its species.
We are sure that a general ground exists, although we have not found a proof by
it." No doubt, if we are assured that the species exhibit the same property, "by
no accident," our conclusion is universal ; but, even then, we only know that it is so,
not why it is so : until we can " show that the reason for the " property " is the
same in regard to all " triangles.

" Anal. Prior, ii., 23, (25).

32 THE SCIENCE OF LOGIC

pov, TToieiv},1 the general principle. " It is a mode of arranging a
deductive argument so as to enable us to realize psychologically,
the truth of the general principle (apx^i) which is the real major
premise — a mode of illustrating the principle by bringing forward
instances. Of course we cannot get ' all ' the instances, except
where the number is limited ; but this fact does not vitiate an
illustrative ' induction ' such as Aristotle had in view (cf. Anal,
Post,!., 4, 73<*33)-"2

If, therefore, Aristotle regarded the conclusion of any enumer-
ative induction as a strict, generic universal, he regarded the
knowledge of this as reached not by enumeration, but by analysis.3

As long as we have any doubt about the completeness of our
enumeration — which is nearly always, — and still rely on it alone
for our conclusion, we can only have provisional and probable, not
absolute and certain, knowledge, of the truth of the latter as a really
general proposition. But both the process and the conclusion
have in such cases this amount of utility, that they suggest to us,
more or less forcibly, the existence of some natural law, i.e. some
necessary natural connexion between the attribute predicated and
the class of things in question. When we find that a, b, c, d, e, are
P ; and know already that a, b, c, d, e, are 6" (whether all S or
only some S, does not matter much), the surmise inevitably
suggests itself that there may be something (say M~) in the
nature of S (and therefore in all S's, whether examined or not)
which is the natural ground for P. In other words, the conclusion
''Every S may, in virtue of the M that is in it, be P" suggests it
self as an hypothesis worthy of investigation. Thus, our attention
is drawn away from the number of S's ; and the tendency asserts
itself not to aim at completing the enumeration — which is usually
impossible, — but to examine the nature of the phenomena in ques
tion, (the S's], and to seek in them for some natural attribute or pro
perty (M} that will be the ground or reason for our predicating P
of them. This marks the passage to scientific induction, whereby
we are able, without a complete enumeration of instances, to rise from
particular facts to the conception and discovery of some universal
natural law.

208. SCIENTIFIC INDUCTION AS TREATED BY ARISTOTLE
AND THE MEDIAEVAL SCHOLASTICS. — We have seen that the
general conclusion, when derived from an incomplete enumeration

1 Cf. Anal. Prior, ii., 23 ; Top., i., 12 ; Anal. Post, i., 31.

3 MELLONE, op. cit., p. 247. 3 Cf. JOSEPH, Logic, pp. 356-57.

INDUCTION IN ITS VARIOUS SENSES 33

of instances, is never certain, and that such induction is called
"imperfect". We find it sometimes stated by modern logicians
that the only way of ascending from the particular to the general,
explicitly treated by Aristotle, and the only way known to the
mediaeval Scholastic logicians, was that of enumerative induction,
"complete " and " incomplete " ; that we find in these authors no
trace of the method of modern scientific induction, the method of
attaining to the universal by analysing a limited number of in
stances and seeking therein a connexion of content, of attributes,
a causal connexion, in the nature of the phenomena considered.
Thus, Professor Welton writes : * " The scholastic logicians . . .
made the essence of induction to consist in enumeration " ; and
Dr. Mellone : 2 " With the mediaeval logicians induction became
simply a process of counting particular things ". And these authors
merely give expression to a traditional misconception, the origin
and growth of which are clearly and succinctly accounted for by
Father Joyce, in his Logic (p. 233):

" The error seems to have arisen from the fact that the most famous of
the Scholastics (St. Thomas, Albert the Great, Scotus) do not employ the term
induction as the distinctive name of the inference by which we establish uni
versal laws of nature. Following the terminology of Aristotle . . . they called
it proof from experience (e'^Treip/o, experimentum, experientia). The signi
ficance of the term induction was somewhat vague. It covered all argument
from the particular to the general \cf. 206]. Hence (as e.g. in Scotus, Anal.
Prior., ii., q. 8) it might include this meaning among others. But it was more
usually employed to denote the formal process of perfect induction [207]
arranged as an inductive syllogism. Moreover, it was sometimes pointed out,
that our argument might be thrown into the form of an inductive syllogism :
for, though the enumeration was incomplete, yet in these few instances we
have equivalently seen all \cf. infra, 209]. It was by a later generation that
the term induction was restricted to its present signification. Incautious
readers, finding in certain passages the inductive syllogism described as the
formula of inductive argument, jumped too hastily to the conclusion that the
mediaeval philosophers rested their knowledge of the laws of nature on no
basis but enumeration."

Now, from the very fact that Aristotle and the Scholastics
considered it possible to reach a truth about "#//," actual and
possible, known and unknown, by an acquaintance with "some,"
they must have recognized a method of ascent to the " all" other
than enumeration. And so they did : viz. the method nowadays
known as Physical or Scientific Induction.

When, therefore, we hear it stated that Scientific Induction is

1 op. dt., p. 33. ao/>. dt., p. 247.

VOL. II. 3

34 THE SCIENCE OF LOGIC

an achievement of the modern mind, we must not infer that it
was entirely unknown to the ancients. That to modern thought
the honour was reserved of seizing upon the full significance of
the method, and of applying it with such marked success, even
the most ardent defenders of Aristotle and the Scholastics need
not deny.1 But that the principle of this method was known
to the latter, their works give unmistakable evidence.
And, firstly, let us turn to Aristotle himself: —

"Repeated sensations," he writes, "leave impressions in the memory,
and these engender experience (tpnfipia) ; experience suggests abstraction,
which separates from the particular instances the one in relation with the
many (TO iv napa ra TroXXa), that is to say, the universal. But the abstract
put in relation with an indefinite number of individuals, is a principle of
science and of art".2

Turning, now, to St. Thomas's full and lucid commentary 3 on
the passage just quoted, it would be difficult to find a plainer
illustration of the modern inductive Method of Agreement : A
physician has learned by repeated experiences that a certain herb has
cured several patients of fever. From these experiences he
ascends to the apprehension of the universal principle that " this
kind of herb cures patients afflicted with this kind of fever". St.
Thomas does not explicitly state the principle, or examine the
process by which the ascent is made ; obviously, however, it is
not made by enumeration of instances, complete or incomplete.

1 Ueberweg rightly remarks that " The recognition of the full significance of
the inductive method in the sciences was reserved for modern times " (System der
Logik, § 127).

3 Post. Anal., ii., 19, (5).

3 " Ex memoria multoties facta circa eamdem rem in diversis tamen singulari-
bus, fit experimentum : quia experimentum [^uirtipfa] nihil aliud videtur, quam accipere
aliquid ex multis in memoria retentis. Sed, tamen, experimentum indiget aliqua
ratiocinatione circa particularia, per quam confertur unum ad aliud, quod est pro-
prium rationis. Puta, cum talis recordatur quod talis herba multoties sanavit
multos a febre, dicitur esse experimentum quod talis herba sit sanativa febris.
Ratio autem non sistit in experimento particularium ; sed ex multis particularibus
in quibus expertus sit, accipit unum commune quod firmatur in anima, et considerat
illud absque consideratione alicujus singularium, et hoc accipit ut principium artis
et scientiae. Puta, diu medicusconsideravit hanc herbam sanasse Socratem febrien-
tem, et Platonem, et multos alios singulares homines ; cum autem sua consideratio
ad hoc ascendit quod talis species herbae sanat febrientem simpliciter, hoc accipitur
ut quaedam regula artis medicinae " (St. Thomas, in loc. cit.). It will be observed
that there is no mention here of " Inductio " but only of " Experimentum ". It is
significant, too, that these passages from Aristotle and St. Thomas are from the
Posterior Analytics, i.e. from that part of the Organon which treats of Certain Science,
while the passages quoted above in reference to enumerative induction — complete
and incomplete — are taken from the Prior Analytics and the Topics, i.e. the parts
that refer, the one to the formal side of reasoning, the other to probable arguments.

INDUCTION IN ITS VARIOUS SENSES 35

But another leading Scholastic, Duns Scotus, has analysed
with a good deal of precision the procedure by which the general
ization is effected. When a phenomenon occurs repeatedly under
the influence of a cause that is not free, we must conclude, he
teaches, that the effect in question has a " natural " connexion
with the cause. . . . For it is impossible that a necessary cause
produce the same effect regularly, unless it is determined by its
natural tendency — its directive principle or form, as he calls it — to
produce this effect. The effect must spring from the nature of
that cause and not from any accidental, concomitant agencies ;
for accidental agencies do not produce regular effects. And that
any such regular series of effects is due to the nature of a certain
cause, we know from experience : because we have seen this cause
followed by these effects, when acting now in one set of conditions,
again in a different set, and altogether in many varieties of cir
cumstances,1 Thus, Scotus points out as the rational, self-
evident basis of induction, the judgment that what REGULARLY
results front the action of NON-FREE causes cannot be the result
of mere CHANCE, but must have a necessary connexion with the
NATURE of those causes ; and he furthermore points to the neces
sity of varying our experiences, in order to separate, from the
changing and accidental circumstances that accompany the ap
pearance of the phenomenon in question, the one agency or group
of agencies on which it is really dependent, which forms its real
cause : a plain application of the modern Method of Agreement.

Why, then, it may be asked, did the Scholastics of the Middle Ages, if
they knew the theory of scientific induction, and the principle underlying it, not
proceed to apply the method, and so anticipate by centuries the wonderful

1 " De cognitis per experientam dico, quod licet experientia non habeatur de om
nibus singularibus, sed de pluribus, nee quod semper, sed quod pluries ; tamen
expertus infallibiliter novit, quod ita est, et quod semper et in omnibus ; et hoc per
istam propositionem quiescentem in anima : QUIDQUID EVENIT UT IN PLURIBUS AB

ALIQUA CAUSA NON LIBERA, EST EFFECTUS NATURALIS ILLIUS CAUSAE. Quae pro-

positio nota est intellectui, licet accepisset terminos ejus a sensu errante, quia causa
non libera non potest producere ut in pluribus effectum, ad cujus oppositum ordinatur,
vel ad quern ex forma sua non ordinatur . . . sed causa casualis ordinatur adprodu-
cendum oppositum effectus naturalis, vel non ad istum producendum, ergo nihil est
causa casualis respectu effectus frequenter producti ab eo, et ita si non est libera, est
naturalis. . . . Quod autem iste effectus evenit a tali causa producente ut in pluribus,
hoc acceptum est per experientiam ; quia inveniendo nunc talem naturam cum tali
accidenie. nunc cum tali, inventum est, quod, quantumcumque esset diversitas acci-
dentium talium, semper istam naturam sequebatur talis effectus. Ergo non per
aliquod accidens, per accidens illius naturae, sed per naturam ipsam in se conse-
quitur tallis effectus" (In. /. Sent. dist. iii., Q. iv, 9).

3*

36 THE SCIENCE OF LOGIC

strides which physical science has made since the Renaissance ? Many good
reasons may be assigned.

One is that in those ages philosophers were more preoccupied with the
philosophy of mind than with that of external nature, with the application of
reason to principles accepted on authority, with the explanation of revealed
religion and the unfolding of the contents of the Divine deposit of Revelation
by means of philosophical principles and methods (203). And, as the full mean
ing and proper understanding of those great truths and principles are arrived
at by the application of the deductive or synthetic method, the attention of
those philosophers was not arrested ^y the possibilities of knowledge that
might have been opened up through a more careful analysis of the complex
phenomena of external nature.1

But another, and more important, consideration is that they had not the
means of prosecuting such an analysis. They knew the method theoretically,
but this knowledge in itself was of little use. When there is question of estab
lishing a law of Physical Nature — such as the laws of the planetary motions,
or of the refraction of light — it is not enough to know that " a non-free cause
cannot regularly produce an effect that is opposed to its natural tendency, an
effect it is not determined by its nature to produce," — " causa non libera non
potest producere ut in pluribus effectum, ad cujus oppositum ordinatur, vel
ad quern ex forma sua non ordinatur ". This abstract, hypothetical principle
merely asserts that if " necessary " or " non-free " causes exist, causes predis
posed by an internal tendency ("forma ") to produce definite effects, the latter
will occur with the regularity of a " law " ; but it does not of itself authorize us
to assert categorically that there are such internal tendencies or principles of
finality in nature, that there are causes predisposed to manifest such fixed,
unchanging activities (cf. 223) ; and still less to affirm with certainty that this
or that oft-observed combination of particular phenomena is the expression
of some one of those causal tendencies existing in nature.

Such a categorical conclusion as the latter can be justified only by a dili
gent observation of the natural phenomena to which it refers. And nature is
infinitely complex : so that the establishment of a certain conclusion that this
series of phenomena reveals this universal physical law, necessarily presup
poses a detailed and accurate weighing, reasoning, analysing, and comparing
of all the elements that enter into the phenomena in question. The phe
nomena of physical nature exist in space and time : accurate quantitative
measurement is, therefore, at the basis of all experimental research : and hence,
the discovery of instruments for delicate measurement was an indispensable
condition for the progress of the physical sciences. But Aristotle and the
mediaeval Scholastics had neither the clock for the accurate measurement of
time, nor the balance for the exact estimation of weight, nor the thermometer
for measuring temperature, nor the barometer for measuring atmospheric
pressure, nor the telescope to observe the heavens, nor the microscope
to reveal the mysteries of the minute structure and composition of organic
tissues. It is true, indeed, that the sagacity of great genius, the patience of
long reflection, and disinterested zeal in the pursuit of truth, can contribute
much, even with the aid of mere ordinary observation, to the development
of scientific speculation : witness the wonderful perfection of the Ptolemaic

1 Cf. CLARKE, Logic, p. 480.

INDUCTION IN ITS VARIOUS SENSES 37

astronomy. Indeed the superior powers of Aristotle, and of his mediaeval
Christian commentators, in the domain of ordinary, unaided observation, are
undisputed at the present day. But it would be wrong to arrogate to them
an honour they would be themselves the first to disclaim,— the honour of creat
ing sciences which could not possibly have arisen without the invention of the
special instruments of observation and measurement just referred to.

Accurate experimentation was impossible in the Middle Ages, in the
absence of those delicate means of weighing and measuring that are the inven
tion of a more modern era. The thirteenth century, however, — the golden age
of Scholasticism — produced at least one exceptional and extraordinary man,
whose name cannot be passed over in connexion with the rise of scientific in
duction. Roger Bacon, a Franciscan monk, who lived through the greater
part of that century, dying at Oxford in 1 294, rose far above the commonplaces
of his time in his advocacy of the experimental method. His life was one im
passioned and even fanatical plea for the positive sciences. Nor did he con
tent himself with pleading : he set an example by devoting his great genius to
conducting scientific experiments and inventing instruments for that purpose.

He distinguished four possible ways of gaining a knowledge of nature :
authority, (a priori) reasoning, observation, and experiment. And he tells us
that of these four the first ranks lowest in worth : " auctoritas debilior est
ratione " ; the second, dialectic reasoning, does not satisfy the mind : " non
certificat " ; nor the third, which is ordinary, superficial observation. The
fourth alone — " internal " or " intrinsic " experience — is convincing, and that
owing to the aid it receives from mathematics and geometry. He anticipated
more renowned and more modern philosophers in an attempt to establish one
general science that would submit to mathematical principles all the varied
interactions of the bodies that make up the physical universe.1

209. LORD BACON'S " NOVUM ORGANON": THE Two
IDEALS OF GENERALIZATION. — The English monk of the thir
teenth century understood the nature and method of experimental
science as well as, if not better than, his namesake of the six
teenth. Francis Bacon, Lord Verulam (1561-1626), is commonly
regarded as the " founder of the inductive method ". Wrongly,
however ; because, in the first place, his method of " interpreting
nature " has never been adopted : " The value of this method,"
writes Jevons,2 " may be estimated historically by the fact that
it has not been followed by any of the great masters of science."

Bacon blamed his predecessors, the " deductive " philosophers,
for "anticipating" nature instead of " interpreting " it. After
enumerating four great sources of such fallacious " anticipations "
— the " Idola " or Phantoms : (a) of the Tribe (common to all men),
(fr) of the Cave (due to personal idiosyncrasies), (c] of the Market-

1 Op. maj., p. iv., dist. i., c. iii., dist. ii.-iv. ; Opus tertium, c. 29-37, etc. ; cf.
DELORME, Dictionnaire de theologie catholique, s.v. Bacon,

2 Principles of Science, p. 507.

38 THE SCIENCE OF LOGIC

Place (due to public catch-cries, shibboleths, etc.), (</) of the
Theatre (due to fashion) — he goes on to expound his own
" method ". He appears to have regarded all physical phenomena
as collections and combinations of sensible properties of matter,
each of the latter being a simple thing, a " simple nature," and
each due to some "form," i.e. to some essential constitutive
principle1 of the material agencies in which such sensible pro
perties are revealed. This is merely a statement of the scholastic
principle that the properties of an agent reveal its specific nature
or " formal cause ". But Bacon conceived it to be the duty of
the scientist to draw up a complete catalogue of all the sensible
properties exhibited throughout all nature, and of all the "forms"
to which these could be due : an utterly impracticable under
taking. Next, in order to facilitate the process of tracing each
property to its " form," or cause, tables or catalogues were to be
drawn up, exhibiting the relations of conjunction or concomitance,
separation, and variation, between the forms and the properties :
a still more arduous and unpromising task. Bacon never at
tempted to carry out these schemes himself. The first grave
defect of his " method " is, therefore, its inutility.

Next, assuming the possibility of compiling such data, he
pointed out that the cause, or " form," of a given sensible
property could be best detected by a process that would suc
cessively eliminate all the other rival " forms," and thus bring to
light the proper one. Every "form*' which is present when the
property in question is absent, or absent when the latter is present,
or which does not increase and decrease concomitantly with the
latter, is to be rejected as not being the "form " causally connected
with the latter. Such is the principle on which the method pro
ceeds, the principle of elimination, or exclusion of the non-causal
or casual concomitants of a phenomenon. It is theoretically
sound: "where you cannot (as in mathematics) see that a pro
position must universally be true, but have to rely for the proof
of it on the facts of your experience, there is no other way of
establishing it than by showing that facts disprove its rivals".2

1 The tendency of the science of Bacon's time to substitute for the qualitative
conceptions of the Scholastics, quantitative, picturable, measurable conceptions, is
revealed in his changing and uncertain ways of conceiving " form ". He appears
to have finally fixed upon the notion of something measurable in terms of " spatial
and temporal relations of bodies " (WELTON, op. cit., ii., p. 36), something which has
been described in present-day scientific language as a " principle of corpuscular
structure" (JOSEPH, Logic, p. 364).

a JOSEPH, op. cit., p. 366.

INDUCTION IN ITS VARIOUS SENSES 39

We shall see this principle applied later on by J. S. Mill, and uni
versally adopted. But, for its safe application we do not need,
as Bacon. taught, to have antecedently elaborated a completely
exhaustive catalogue of all the " forms " and " sense-qualities "
in the universe. It will suffice to eliminate all the possible
pertinent alternatives, suggested by a careful analysis of the matter
under investigation.

But, owing to the enumerative character of the process as
conceived by Bacon, and to the practical impossibility of a com
plete enumeration of the alternative factors involved, the process,
so applied, could never reach a necessary and universal law : for
(to use Bacon's own words) when " the axiom being established
is more extensive and broader " than " those particulars out of
which it is extracted " (Novum Organon, i., 105, 106) — and this is
what happens as long as his impossible "catalogues" are not
complete and absolutely reliable — he fails to indicate any prin
ciple (other than enumeration) which might justify him in drawing
a universal conclusion from such a defective enumeration of alter
natives. This, then, is a second serious defect of the " method ".

Next, it must be pointed out that although he says " In
duction which proceeds by simple enumeration is a puerile thing
and concludes uncertainly" (i., 105), and that "the syllogism is
not applied at all to the principles of science" (i. , 13), yet, as
a matter of fact, his whole process is a simple application of the
categorical syllogism in the second figure, combined with the
modus tollendo ponens of the mixed disjunctive syllogism ; in which
latter, moreover, the disjunctive major is assumed to be complete,
even though his catalogues of forms and qualities remained incom
plete throughout. Bacon's own example will illustrate this.

Let / be the " form " of heat (the " form " we are en
deavouring to detect or select from among all the known
"forms"). Let h represent the sensible quality of heat. Let
A, B, . . . Y, Z, represent the whole collection of " forms " or
" natures " in the universe. Then :

/is either A or B or C or . . . X or Y or Z ;

(1) But A is not present with h,
And / is present with h,
Therefore /"is not A ;

(2) And B is present in the absence of h,
While /is not present in the absence of ht
Therefore /is not B ;

40 THE SCIENCE OF LOGIC

(3) And C does not vary concomitantly with h,
While /"does vary concomitantly with ht
Therefore/ is not C ;

and so on, until all the "forms" except one, say Z, are thus
eliminated by syllogisms in Cesare or Camestres. Then we have,
finally, this mixed disjunctive argument in the modus tollendo
ponens, verifying the form of heat as Z : —

/"is either A or B or C or . . . X or Y or Z ;
But/is neither A nor B nor ... X nor Y ;
Therefore /"is Z.

This latter form of argument is regarded by many as the
typically " inductive " inference.1 The various arguments, (i), (2),
and (3), by which we apply various methods of elimination, sug
gest that instances (of the circumstances accompanying heat) are
no longer being merely enumerated, but that the nature of their
connexion (with heat) is being sifted by experiment. This marks
the transition from enumerative to scientific induction.

As was pointed out already, two possible tendencies may
arise from an incomplete enumeration of instances. The first,
with which many of the Scholastics, and Bacon himself, seem to
have been preoccupied, is to realize, somehow or other, the ideal
of a complete enumeration. To realize it actually is, for the most
part, chimerical, and moreover, it does not lead us to the true
universal. To realize it virtually, i.e. by falling back on some
rational principle which might justify us in saying : " and so on of
the unexamined instances " — " et sic de ceteris " — is to yield in
reality to the second tendency, while under the traditional sway
of the first : the second tendency being to abandon the mere
enumeration of the instances, to concentrate attention on their
material side, on the quality, the nature of the facts we are
dealing with, and to ask ourselves : Is it not possible and per
missible to rise to the conception and enunciation of a strictly
universal physical law from an examination of some instances only ?
It is possible to do so; and the difficulty of the process of
physical induction, by which we accomplish this ascent, is not a
difficulty of principle or method, but rather of application : it is a
difficulty that belongs not to the logical, but to the practical,
order.2

The ancient Greek philosophers, and the Scholastics of the
Middle Ages, were quite as well aware as any modern exponent
1 Cf. 197 ; JOSEPH, op. cit., p. 405. 2 C/. JOYCE, op. cit., p. 217.

INDUCTION IN ITS VARIOUS SENSES 41

of the inductive method that (i) Explanation of the phenomena
of physical nature consists in a thorough knowledge of their
connexion with their respective causes ; (2) that physical causes
act regularly, uniformly ; (3) that, therefore, if we could be sure
of having discovered and fixed upon the natural cause of a given
phenomenon, amid all its complex surroundings (by a process of
abstraction], we could at once (by generalization] formulate the
physical law that always and everywhere this cause will act in the
same way and produce this same phenomenon. But the difficulties
that beset the work of bringing to light with certitude the causal
connexion — the work of observing, analysing, experimenting,
etc. — were so great that neither the ancient nor the mediaeval
nature-philosophers had the courage and perseverance to grapple
with them. Hence, they made little or no serious effort to test the
worth of the probable conclusions which they based upon an incom
plete enumeration of superficially observed instances. The scientists
of the seventeenth and eighteenth centuries, Galileo, Torricelli,
Pascal, Descartes, Newton, etc., were making practical efforts in
many directions to scrutinize and question physical nature more
closely, long before logicians attempted to formulate and interpret
the theory of these researches. Lord Bacon's attempt at the
conscious formulation of a theory was a failure. Sir Isaac Newton
(1642-1727) was conspicuously successful both in theory and in
practice. Since the latter's day, many workers, both in the natural
and in the mental sciences, have sought to formulate the Theory of
inductive research. But those sciences are so progressive in their
methods, and views so fundamentally divergent as to the nature
of knowledge are propounded by philosophers, that there is still
comparatively little uniformity of treatment in the domain of
inductive logic.1

210. MODERN CONCEPTIONS OF INDUCTION: NEWTON,
WHEWELL, J. S. MILL, JEVONS.— Newton taught that in the
pursuit of knowledge we must start with an analysis of observed
facts: that we must suppose and formulate some general law
suggested by these facts : that we must, by synthetic or deductive
reasoning, derive consequences from this law, thus to determine
whether the law coincides with all observed facts or not.

Indeed, most writers on induction agree in recognizing certain
well-defined steps or stages in our progress from particular facts

1 For varieties of treatment cf. VENN, Empirical Logic, pp. 353 sqq. ; WELTON,
op, cit., ii., bk. v., chap. ii.

42 THE SCIENCE OF LOGIC

to general laws : the formulation of an hypothesis suggested
somehow or other by an initial observation of phenomena ; the
moulding, remodelling, generalizing of this hypothesis, by suc
cessive eliminations and exclusions — under the guidance of certain
canons of more or less practical utility, commonly known (after
J. S. Mill) as the "experimental methods" or "inductive
methods"; the final "verification" or "establishment" of the
hypothesis as a " law " ; the attempted " explanation " of this law
by wider laws ; the commencement of the synthetic or deductive
stage by the application of the established law to particular facts
for the " explanation" of these latter.

Not all writers, however, attach the same importance to the
various stages. Whewell,1 for instance, lays great stress on the
invention of hypotheses, or, in his own language, the " colligation
of facts by means of an exact and appropriate conception," 2 as
the most important step in the discovery of scientific truths. To
the subsequent process of generalizing the abstract hypothesis,
of remoulding and remodelling and verifying it by the application
of fixed canons, he devotes much less attention. Its verification
or proof 'he holds to consist in deducing consequences from it, and
ascertaining whether it thus foretells phenomena, at least those of
the same kind as the phenomena for the explanation of which
it was invented. Should an hypothesis, invented to explain " one
class of facts," be also found " to explain another class of a
different nature," it is more firmly established than by any other
means : this Whewell calls Consilience of Inductions?

J. S. Mill, on the other hand, almost entirely ignored the
theory of the initial step of conceiving an hypothesis. He ad
dressed himself to the process of generalizing directly from
particulars — a process quite impossible apart from the abstract
conception of some guiding hypothesis, — and to the establishment
of rules or canons for the correct carrying out of this process.
No doubt, this latter stage lends itself to methodical treatment,
while the former stage does not ; and Mill tried to justify his
mode of treatment by the plea that as a logician he was con
cerned only with the proof of general truths, not with their
discovery. There does not seem to be much force in such a plea.

1 Flourished 1794-1866; among his writings are the History of the Inductive
Sciences (3 vols., 1837; 2nd edit. 1847; 3rd, 1857) and a Philosophy of the Inductive
Sciences (2 vols., 1840 ; 2nd edit. 1847 ; 3rd, in three vols., bearing separate titles, of
which one was called Novum Organon Renovatum, 1858-60).

2 apud WBLTON, op. cit., ii., p. 50. » ibid., p. 51.

INDUCTION IN ITS VARIOUS SENSES 43

A truth cannot be said to be discovered in the full and complete
sense of the word until it is thoroughly verified, or proved to be
a truth. It may be formulated and held as true with more or
less probability — as the result of an enumerative induction or of an
analogical argument, as an hypothesis or as an "empirical general
ization," — but it cannot be fairly said to be fully "discovered"
until we have both " verified " it, or proved that it is true, and
"explained" it, or shown why and wherefore it is true, by
connecting it necessarily with already known and established
truths. In any case, Mill de facto regarded his " inductive
methods " as methods of discovery as well as of proof, and de
scribed induction itself as " the operation of discovering and
proving general propositions".1

Finally, we may mention Jevons,2 as an author who takes a thoroughly
enumerative view of induction, making the whole process consist in a succes
sive enumeration and determination of all the mathematically possible hypo
theses that might account for a given result or phenomenon. Obviously, in
this view certitude about our inductive conclusions is practically never attainable,
for the ideal of a perfect enumeration of instances is beyond our reach.3 The
method is open to the same objections as Bacon's method, which Jevons him
self criticizes. In the " infinite ballot-box " of nature, the determination of the
chances of an invariable sequence of any two " balls " is a problem in the
mathematical theory of probability, the solution of which cannot of its nature
give us certitude (267). Nor can the result of this " inverse problem " be made
any more certain or definite by arbitrarily limiting the elements in the ante
cedent to those contained in the consequent, nor, indeed, by arbitrarily limiting
them in any way. " If, for instance, we ... say : Given that certain com
binations of A, B, and C, are the existent ones, find a solution in terms of A,
B, C, and nothing else, from which this result shall follow, no complaint can
be made. The problem is a very limited one, but it may be useful. . . . But
to make the same restriction when the problem is, Given that dew is copious
on a cold, clear night, or given that a magnetic needle is deflected by an electric
current, find a solution which shall introduce no fresh terms into the statement
of the phenomena, would be a mere parody of physical investigation."4 In
deed, the only way of reaching certitude is that precluded by Jevons's view of
induction ; namely, by abandoning the enumerative ideal and addressing our
selves to an analysis of the nature of the phenomena in question, on the rational
assumption that constant coexistences or sequences of phenomena have their
explanation in the existence of fixed natures, of stable tendencies and lines of
action, in the phenomena themselves, and with the conviction that these fixed

1 Logic, iii., I., § 2.

2 Flourished 1835-1882 ; Logical writings : Principles of Science (2 \ols. 1874;
2nd edit, i vol. 1877) ; Elementary Lessons in Logic (1870) ; Primer of Logic (1876)
Studies in Deductive Logic (1880).

*Cf. JOSEPH, Logic, p. 487. <VENN, Empirical Logic, pp. 360, 361.

44 THE SCIENCE OF LOGIC

natures, these stable tendencies, have their ultimate explanation in the omni
potent will of an all-wise ruler of the universe (224).

The views of an individual author on these latter ultimate presuppositions
and foundations of induction are pretty sure to influence and colour his concep
tion of the various steps in the mental process itself by which the mind moves
inductively from particular to general, from fact to law. Some such views,
propounded by recent writers, will be examined in due course.

211. ANALYSIS AND ILLUSTRATION OF THE PROCESS OF
SCIENTIFIC INDUCTION. — From the preceding paragraphs of the
present chapter we can gather what the main problem of induc
tion is, and what its method of procedure ought to be. It seeks
a scientific knowledge of the concrete, particular phenomena of our
experience, i.e. a knowledge of them through their causes and
laws, a knowledge, which, bringing to light their nature, their
origin, the purpose of their existence or occurrence, will lay hold
of what is universal, permanent, abiding, in them. Amid the
changing and chaotic elements that make up our world of unanal-
ysed and unexplored sense experience, induction will try to trace
the permanent connexions of cause and effect, to eliminate the
variable conditions and surroundings of each phenomenon, and to
lay bare its connexion with its real ground or cause. Now, in
order to do this, we must not merely observe with accuracy the
phenomenon we wish to explain ; but next, and necessarily, we
must suppose that amid all its immediate conditions and surround
ings some element or elements constitute its determining cause,
and yield the law of its occurrence ; and then we must proceed
to test or verify our supposition by deducing consequences from the
latter, and comparing our conclusions with actual facts, analysed
by further observation and experiment. This process of testing
we must prosecute until we reach a full conviction that the sup
posed cause of the phenomenon is the necessitating and indispens
able, and therefore the true or real, cause, of the facts examined.
When we have thus established an isolated law, we may on the
one hand endeavour to explain this law itself by seeking its
connexions with other already known laws, and on the other
hand apply the law itself to the explanation of all facts that come
under it.

(i) Preliminary observation of facts; (2) supposition as to
their cause ; (3) verification of our supposition ; (4) explanation,
and (5) application, of the established law : such are the essential
steps in the inductive discovery and proof of scientific truths.
The deductive application of the general law to the facts is the

INDUCTION IN ITS VARIOUS SENSES 45

final step, by which we reach a scientific knowledge of those facts
in the observation of which the whole process had its origin.1

The method here outlined is recognized by Mill :2 he calls it
" deductive," admitting its application only to the more complex
phenomena due to a combination of causes ; yet he is forced to
allow that it is to this method " the human mind is indebted for
its most conspicuous triumphs in the investigation of nature ". 3
The advocacy of this method by many of our more recent induc
tive logicians, Bosanquet, Sigwart, Welton, Joseph, etc., is a
wholesome reaction against the Empiricism of the school of Mill.

The various steps indicated above will form the subject-matter
of subsequent chapters. The whole process, however, is based
upon certain fundamental principles and postulates which call for
explanation and justification at the outset (Chaps. III. and IV.).
With an example 4 to illustrate the inductive process, and a com
parison of the latter with deductive inference, we may conclude
the present chapter.

" Let a chemist take some hydrogen, a gas without colour, taste, or smell ;
which burns with an intensely hot bluish flame ; which is 14-4 times lighter
than air, 23-326 litres weighing 2 grammes. Let him take another and very
different sort of gas, chlorine ; of a yellowish colour and an unpleasant,
suffocating smell ; density 2-44, weighing 35-5 times more than hydrogen,
22-326 litres weighing 71 grammes.

" Let the chemist mix those two gases in a glass vessel, and place it in the
sunlight : a violent combination will suddenly take place, disengaging 22
thermal units or calories of heat ; after which the chemist finds in the vessel a
new body, whose distinctive properties have acquired for it the name of hydro
chloric acid. This new body will attack most of the metals and combine with
them to form various salts ; it will combine with the aqueous vapour of the
atmosphere to form a colourless, acid solution, etc.

" So far he has observed a fact [first step]. Next, how is it to be explained ?
Why did it happen ? What is its cause ? He supposes that it is due to some
law of nature [second step] ; he supposes the formation of hydrochloric acid
to be due to some property inherent in those two gases, acting in certain con
ditions, still to be determined. This suspicion of his is an hypothesis, which he
must now proceed to verify.

" For this latter purpose [third step] he will multiply and vary his ex
periments. For example, he will let the sunshine act on a mixture of chlorine
and oxygen ; supposing a priori that they too will combine ; but he finds that
they will not. It is not every two gases, therefore, that will combine under the
action of the sunlight. But, perhaps, at least any quantities whatever of
hydrogen and chlorine will combine ? A priori, again, the supposition is
permissible ; but again it is negatived by the facts. For repeated experiments

1 C/. 252: Regressive Demonstration. 7 Logic, iii., xi. and xlv.

3 ibid, xi., § 3. 4 From Mercier's Logiqtie, pp. 300 iqq.

46 THE SCIENCE OF LOGIC

establish that they will combine only in the proportion of I to 35-5 by
weight, or— which is the same— of i to I by volume. When those proportions
are brought together under the influence of sunlight— no matter how little or
great the absolute quantities may be, milligrammes, centigrammes, decigrammes
— the combination will take place. On the other hand, when those proportions
are not maintained, the quantity of the one which is in excess of its due propor
tion to the total quantity of the other, will remain over, unaffected by the
combination.

" Here, then, are other facts in presence of which the observer finds him
self : Two definite gases, mixed in definite proportions of i to i by volume
or i to 35-5 by weight, combine under the action of sunlight— the absolute
quantities of each being indifferent to the result and indefinitely variable.
Neither of these gases, mixed with any other gases, combine with the latter in
the same conditions and proportions ; if mixed with each other in any other
proportions than those indicated, they will not combine completely, but will
leave the surplus above the proportion unmolested. Further, the chemist
remarks that, after the combination, one volume of hydrogen and one volume
of chlorine, combining under definite conditions of temperature and pressure,
yield two volumes of hydrochloric acid gas.

" Are all those facts — which recur repeatedly in similar circumstances —
the result of mere chance coincidences of disconnected and indifferent causes ?
They are not : they cannot be. Reason will not admit that any such complex,
harmonious, stable series of facts could be due to chance. They must be the ex
pression of a law ; they must find their sufficient reason in the nature of the
combining bodies.

" The chemist finds this sufficient reason in what he calls the ' affinities '
of the reacting bodies ; the metaphysician, in 'properties inherent in the
nature ' of those bodies, and indicative of the energies of those natures. The
language is different, but at bottom the idea is the same : There are in the
world such complex, harmonious, stable series of facts as cannot be due to
chance activities, but must be the result and expression of natural laws ; and
the formation of hydrochloric acid from hydrogen and chlorine is a mani
festation of such a law.

" Thus it is that, from the total complex groups of circumstances in which
he has witnessed the formation of hydrochloric acid, the chemist abstracts or
gathers by induction the truth that hydrogen and chlorine have the property
of combining in the proportions indicated, with a disengagement of 22 calories
of heat for the formation of each molecule-gramme of hydrochloric acid. The
combination being, moreover, found to be independent of the particular place
and time, and of the absolute quantities of the bodies used, he can foretell
with certainty that always and everywhere those gases will combine in those
definite proportions to form the compound body, when submitted to the action
of the sunlight under the same general conditions.

" In a word, the law of hydrogen and chlorine is to combine, always and
everywhere, under the above-mentioned conditions. The chemist who has ob
served all the facts and extracted that law from them has made an induction."

"Thus, the chemist has verified his hypothesis that the two gases,
hydrogen and chlorine, have the natural property of combining in the definite

INDUCTION IN ITS VARIOUS SENSES 47

proportions of i to 35-5 by weight. They have an innate, inherent, intrinsic
tendency to do so, in certain recognized conditions and under the influence of
certain known natural agencies. Such is the law of their nature ; for, as St.
Thomas profoundly remarks, the law of a being is the ' natural inclination
which carries it towards the end it has to realize in the universe '.*

" Of course, the knowledge of that law does not exhaust all that is know-
able about the nature of the bodies in question. By no means. It merely lifts
a corner of the veil. The chemical property discovered simply shows us the
natures of the bodies that possess it, under one of their aspects."

Writers on induction do not usually emphasize the next step, which is the
deductive application of the verified law to facts. Yet, if we regard in
duction as the total process by which we reach a scientific knowledge of the
individual phenomena of nature, this deductive step is essential. The
utility of our abstract knowledge of law will always lie in its applicability to
concrete facts. " It is a natural property of hydrogen and chlorine to com
bine in certain proportions under certain conditions to form hydrochloric acid ".
Such is our abstract law. " Here are quantities of those gases in the due
proportions ; therefore if submitted to the action of sunlight, they will form
a certain quantity of hydrochloric acid with a disengagement of a certain
quantity of heat." Such is our deductive application. It will be seen at
once, therefore, how induction contributes to that " knowledge of things by
their causes " which is the only knowledge dignified by Aristotle with the title
of " scientific ". It will be easy, likewise, to see wherein lies the difference
between the method of the rational or deductive sciences and that of the
inductive sciences, and what is their point of contact (202). In the former,
deduction is immediately possible after the conception of a few definitions or
first principles, seen intuitively on a simple analysis and comparison of a few
very simple concepts (206). In the latter, on the contrary, deduction from the
general law cannot commence until the law •. has been established by a process
that is often tedious and difficult.2

Hence, if we give the name of Induction to that whole method of pro
cedure by which we establish the conclusions of the positive sciences, we must
distinguish two phases in it (202) : one deductive, which gives us science, in
the Aristotelean sense of the word, i.e. the explanation of observed facts by
their causes ; the other, preliminary to this explanation, the stage in which
the general law is reached, and which alone modern logicians call Induction,
in the special and restricted meaning of this term.3

Whether this strictly inductive phase of the whole procedure — the side by
which we ascend from concrete, particular facts to abstract, universal laws —
involves any reasoning process which is not syllogistic or deductive (192),
a comparison of induction with deduction will now enable us to determine.

1 Stimma Theologica, ia, iae, q. 93, a. 7 sqq. Cf. infra, 217.

2 "In the former [mathematical], generalization is unnoticed because it is all-
pervading; for the relevant conditions are distinguished from the first. In the
latter, generalization comes to an end and attracts attention as the result of a long
effort ; for all our task is to distinguish the relevant from the irrelevant conditions."
— JOSEPH, Logic, p. 509.

*C/. MELLONE, op. cit., 382-86.

48 THE SCIENCE OF LOGIC

212. SCIENTIFIC INDUCTION AND DEDUCTIVE INFERENCE.
— We have already compared Induction with Deduction, under
standing these terms as descriptive of Method (202 ; cf. 187).
They are sometimes contrasted with each other as forms of
logical inference. But, since induction is not a form of logical
inference at all,1 such a comparison is misleading. The so-
called " Induction by Complete Enumeration " we have shown
to be as unworthy of the name of a reasoning process as is the
so-called " syllogism " understood in the sense attached to this
term by John Stuart Mill (207). Both processes deal with mere
collective propositions, and are simply additions of actual parts
to form an actual whole (" induction "), or redistribution of that
whole into its parts (" syllogism "). The one process is the
reverse of the other, but neither is a reasoning process : the one
is summation of individuals into a group ; the other, distribution
of the group into its members : neither reaches the abstract,
universal judgment. Complete enumerative induction, therefore,
cannot be compared with the genuine syllogism in any figure.
Incomplete enumerative induction, however, in so far as it shows
a connexion between two objects (M and P} to be possible, and
suggests that the connexion may be necessary and universal, is
naturally formulated, as we have seen, in the third figure of
syllogism (172, 207) ; but it is, in a certain sense, the opposite of
the scientific syllogism (in the first figure) : inasmuch, namely, as it
seeks to establish a general principle from instances, while the
latter applies an already established principle to instances.

Does scientific induction, however, admit of any comparison
with deduction, or deductive inference, or the syllogism ? With
deduction as a method, yes. If we take both as methods, and
understand by induction the method whereby we ascend from the
consideration of particular facts to the establishment of some
general truth, in this meaning it is, of course, the reverse of the
whole deductive method, by which — in the mathematical sciences,
for example — we descend from the conception of some simple
and general truth to the understanding of some less simple and
less general one in the light of the former (202). The two
processes move in opposite directions: they view things from
opposite standpoints : they lead the mind along reality and into
the understanding of it by presenting opposite aspects of it : in

1 Cf, supra, 197. JOYCE, Logic, p. 217.

INDUCTION IN ITS VARIOUS SENSES 49

the one case the concrete and particular aspect comes first, in the
other the abstract and universal aspect.

In the positive sciences, or sciences of observation as they
are called, the ascent to the general is difficult ; the descent to
the explanation of familiar facts by applying the principle is
comparatively easy ; in the abstract, rational sciences, the ascent
from particular to general is easy, the descent from the general
to its applications is difficult (202). Here, however, the contrast
between induction and deduction ceases. As mental processes
they are both essential to the attainment of science ; for this is
the knowledge of fact by law, of effect by cause, of particular
by general.

But, apparently owing to Aristotle's conception and treatment
of enurnerative induction as a sort of syllogism without a middle
term, and to the fact that induction aims at generalizing from
particular experiences, some logicians have sought to represent
induction as a special form of logical inference, distinct from, and
in contrast with, those forms of inference which they conceive as
deductive. Now, to represent induction as simply a form of
inference is rather a misleading simplification of what is in
reality a whole series or combination of processes, some of which
" are not processes of reasoning- at all ".l Others of them, no
doubt, are logical inferences ; but not of any new form, distinct
from the various forms of mediate inference, categorical, hypothe
tical and disjunctive, that were known and analysed in logic
prior to the modern development of induction. These are the
only forms of inference known to induction ; and a glance at the
various steps in the inductive process (21 1) will show how far
they enter into it. The preliminary observation of the facts to
be investigated, and of all their surrounding circumstances, is, of
course, not a logical inference of any sort, though it may indeed
involve inferences, both immediate and mediate (238, 263). The
conception of an hypothesis as to the general law connecting the
facts with their causes, is not itself an inference either. But the
verification of an hypothesis may be expressed in a series of
inferences, each taking the form of a mixed hypothetical syllogism :
" If this hypothesis is true, certain events ought to follow from a
certain combination of agencies ; but (by observation or experi
ment we proceed to find that) they do follow (or do not, as the

JOSEPH, op. cit., p. 482.
VOL. II. 4

5o THE SCIENCE OF LOGIC

case may be) ; therefore the hypothesis is probably true (or cer
tainly false, as the case may be)." From this we see that the modus
tollens efficaciously disproves, and so eliminates, all hypotheses
that are unable to account for the facts under investigation. No
single application of the modus ponens, however, can verify the hypo
thesis with certitude. Nor, indeed, strictly speaking, could any ac
cumulation of them give us certitude about the antecedent,
regarding the matter from the point of view of formal inference ;
though often, as we shall see, hypotheses are sufficiently verified
in this manner (230). We usually try to verify our hypothesis
by showing not only that it will account for the facts, but that
no other hypothesis will account for them. We may sometimes
be able to do this by showing the facts to be such that they
necessarily involve the cause supposed in our hypothesis : " If
this hypothesis were not true, the facts could not be such and
such ; but they are such and such ; therefore, the hypothesis is
true." * It is rarely, however, we can directly show the facts to
be such that of their nature they necessarily involve the supposed
cause : for the most part we have to be content with showing
that they must involve it for the reason that no other conceivable
supposition can account for them. That is to say, we verify our
hypothesis by eliminating all competing alternatives. Now, this
process naturally assumes the form of a mixed disjunctive syl
logism in the modus tollendo ponens : —

" The cause of x is either a or b or c or d . . . or z

JIn his admirably clear exposition of Newton's researches on gravitation, Mr.
Joseph (Logic, pp. 477-82), illustrating the various stages of the inductive process,
says that "the final argument, in which the agreement of the facts with the results
of this hypothesis and of no other is shown to require the acceptance of this
hypothesis, is inductive" (p. 482). The term "inductive " cannot here be used in
a sense opposed to syllogistic, for the argument to which he applies it is a mixed
hypothetical syllogism. It is as follows : " Assuming that the continual deflexion
of the planets from a rectilinear path is due to an attractive form [force?], their
actual motions, if my statement of the law of attraction is true, would be thus and
thus ; if it is false, they would be otherwise : but they are thus and thus, and there
fore my statement is true" (ibid.). It may be symbolized thus : " If A then C, and
if not A then not C ; but C ; therefore A ". The standard syllogism, embodying the
axiom applied in this reasoning, and analogous to the standard syllogisms applying
the Dictum de omni, etc., in 192, might be expressed thus : " If a supposed cause
accounts adequately for any real fact, and is the only cause which can account for
it, then that supposed cause is real ; but (by analysis of the facts, through observa
tion and experiment) we see that this supposed cause, and it alone, can adequately
account tor this real fact ; therefore this supposed cause is real ". The author
applies the term " inductive " to reasonings which are not explanatory, which merely
convince us that a judgment must be true, without giving us any insight into the
reason why it is true.

INDUCTION IN ITS VARIOUS SENSES 51

It is not b or c or d . . . or z
.: It is*"1

— where a, b, c, . . . z are supposed alternative causes of the
phenomenon x. This reasoning is, as Mr. Joseph observes,2 " in
form very simple ; but the discovery of proper premisses is very
hard ". How is the investigator to determine the extent of the
major premiss, the field of pertinent alternative hypotheses? —
since he cannot realize Bacon's ideal of cataloguing all the
causes in the universe (209). Obviously, it is to be defined by
prudence rather than by inference. Then he must verify the
minor premiss " piecemeal by hypothetical arguments that rest
upon one or other of the [usual] grounds of elimination ".3

Finally, when, having verified our hypothesis, we apply it to
the explanation of facts, or when we explain itself by the appli
cation to it of wider laws, our reasoning is obviously syllogistic
and deductive.

Is any of the forms of inference outlined above, so characteristic of the
inductive method as to merit the title of " inductive reasoning " ? It matters
little whether we so describe any of them, provided we bear in mind that
" Induction " is much more than any of them : that it involves many pro
cesses other than mere inference. And, indeed, the same may be said of the
title " Deduction " as applied to forms of inference rather than to method. We
have already seen (192) that there is no uniformity of usage in the application
of the titles " deductive " and " syllogistic " to forms of inference. A " de
ductive " inference is perhaps most commonly understood to signify an infer
ence in which it is sought to subordinate some special cases (or classes of
cases) under some wider principle or law. This would be chiefly characteristic
of syllogisms in the first figure, whether categorical or hypothetical. But then,
syllogisms in the second or third figures would not be deductive in this sense ;
for in them there is not usually any subordination of instances to a rule.
Mathematical reasoning, too, proceeds in large part from known principles not
to subordinate cases, but to other co-ordinate and coextensive principles : in
these sciences the cognate truths are so related that very often either of a
pair, a and b, can be used equally well to prove the other : the related truths
are reciprocal ; and yet mathematical reasoning is universally regarded as
deductive.4 Hence, the subordination or subsumption of a case under a rule is
hardly a satisfactory criterion of " deductive " inference.

Mr. Joseph's treatment of the contrast between deduction and induction
is instructive. " Inductive Logic," he rightly remarks, " has not really laid bare
any new forms of reasoning ; we have already seen that Bacon's Induction is
a disjunctive argument ... Or if anyone likes ... to call inference deductive
when it proceeds from conditions to their consequences, and inductive when it
proceeds from facts to the conditions that account for them, he will find

JOSEPH, op. cit,, p. 406. *ibid. sibid.

4 C/. JOSEPH, op. cit., p. 368, 369 n. 2 : also pp. 503 sqq.

4*

52 THE SCIENCE OF LOGIC

" a. that the two processes cannot be kept rigidly apart. Whoever infers
from the facts of experience the conditions which- account for them must at the
same time in thought deduce those facts from those conditions.

" b. that what has been called Deductive Logic, what Inductive Logic has
been contrasted with, analyses forms of inference which, if the antithesis
between Induction and Deduction be thus understood, must be called in
ductive." 1

He himself regards the mixed disjunctive argument as a typically induc
tive form of inference, owing to the use that is made of it in verifying an
hypothesis by the exclusion or elimination of alternative hypotheses. But he
suggests a deeper distinction between deductive and inductive inference : " The
true antithesis is, as Aristotle saw, the antithesis between Dialectic and Demon
stration ; or in more modern phrase, between Induction and Explanation ".2
Inductive inference, then, would be the inference which convinces us that a
proposition is true (because certain facts are incompatible with any other
alternative), without, however, explaining -why it is true, without demonstrating
it ; while deductive inference would not only prove that a proposition is true, but
would also explain or demonstrate it, or, in other words, show us why it is
true. This is an intelligible and useful distinction ; but, obviously, it is based
on the matter of our inferences : it cannot be regarded as a distinction between
forms of inference, except in so far as some of the recognized forms of logical
inference are found to be more naturally applicable to matter in which we can
demonstrate our conclusions, and others to matter in which we can only set
up our conclusions as de facto true, without seeing why they are so. Now,
the disjunctive form of reasoning is, as we have seen, the form into which the
inductive verification of an hypothesis naturally falls. And to verify an hypo
thesis in this way is merely to show that it is true, without further explaining
it or showing why it is true : " the essence of inductive reasoning lies in the
use of ... facts to disprove erroneous theories of causal connexion. It is
... a process of elimination. The facts will never show directly that a is the
cause of x ; you can only draw that conclusion, if you show that nothing else is." '

" You establish a particular hypothesis about the cause of a phenomenon,
by showing that, consistently with the relation of cause and effect, the facts do
not permit you to regard it as the effect of anything else (and mutatis mutandis
if you are inquiring into the effect of anything). It is this which makes the
reasoning merely inductive. If you could show in accordance with known or
accepted scientific principles that the alleged cause was of a nature to produce
the effect ascribed to it, your reasoning would be deductive ; . . . you would
be applying them to produce a conclusion which you see to be involved in
their truth ; and if we suppose the principles to be of such a nature that we
can see they must be true, then the conclusion will appear necessary, and a
thing that could not conceivably be otherwise." 4

1 C/. JOSEPH, op. cit., p. 369.

2 ibid., p. 369. " The two antitheses." he adds, " are not quite identical, because
some dialectical arguments are not inductive, and explanation is not demonstrative
unless the premisses from which it proceeds are known to be true. The reasoning
from those premisses is however the same, whether the premisses are known or
only believed to be true." — ibid. n. i.

3 ibid., p. 395. 4ibid., p. 399.

INDUCTION IN ITS VARIOUS SENSES 53

" There is an enormous number of general propositions, which we accept
for no better reason than that the facts are inconsistent with our denying them,
and not because in themselves they have anything which could have led us to
suppose them true, antecedently to our experience. When it is said that we
ought always to follow experience, it is meant that we ought not to trust our
notions of what seems antecedently fit to be true, or mere guesses as to the
connexions that subsist in nature, but accept only those connexions which our
experience forces us to accept because it is inconsistent with any alternative.
Such reasoning is called a posteriori, because it starts from the facts, which
are conceived as logically dependent on, or posterior to, their principles, and
thence infers the principles on which they are dependent. Conversely,
deductive reasoning is often called a priori, because it starts from the
principles or conditions, which are conceived as logically prior to the con
sequences that follow from them l. . . . But it is an error to suppose that all
general principles are arrived at a posteriori or by process of merely showing
that facts are not consistent with any other. . . . Still it is true that in the
inductive sciences the vast majority of our generalizations are reached either
in this a posteriori manner, or by the help of deductions from other general
izations so reached. And it may be well to show by one or two examples how
generalizations that rest merely on induction present as it were a blank wall
to our intelligence, as something at which we cannot help arriving, but which
we can in no way see through or make intrinsically plausible." 2 The author
goes on to cite examples " to illustrate . . . what Bacon would call the
' surd and positive ' character of conclusions resting only on induction ".3 One
of these examples will be sufficient here : " Facts show that the excision of
the thyroid gland dulls the intelligence : could any one see that this must be
so ? Explanation may show that on a contribution which the gland, when
properly functioning, makes to the circulating blood depends the health of the
brain ; but that comes later than the discovery of the effects of excision ; and
even so can we understand the connexion, which facts establish, between1 the
state of the mind and the health of the brain ? " 4

These extracts will show a clear and intelligible distinction between two
ideals of the knowledge we aim at by inference : the knowledge that ceitain
things are so, and the further knowledge why they are so ; and, by way of
consequence, between " inductive " forms of inference, which naturally sub
serve the former ideal, and " deductive," " demonstrative," " explanatory "
forms of inference, which subserve the latter ideal. Some of these points will
receive further notice later, in the chapter on Explanation.

213. RELATION OF ANTECEDENT TO CONSEQUENT IN DE
DUCTION AND INDUCTION : THE LATTER CONSIDERED AS AN
" INVERSE PROCESS ". — We have seen that the logical inferences
involved in the inductive process assume one or other of the forms
commonly recognized in " formal " or " deductive " logic ; and that

1 " Or, in another sense, illustrated inmost mathematical reasoning, because the
premisses, without being more general than the conclusion, or giving the cause
why it is true, are not based upon an appeal to facts which might conceivably have
been otherwise."

3 JOSEPH, op. cit.t pp. 400, 401. 3»6»<f., p. 402. *ibid., p. 401.

54 THE SCIENCE OF LOGIC

the whole ascent from particular to general cannot be intelligibly
described as an " inductive syllogism," or as the opposite of the
" deductive syllogism ". We may, however, regard both pro
cesses in a light which will admit of their being compared and
contrasted. The relation of premisses to conclusion in the
syllogism is identical with the relation of antecedent to consequent
in a hypothetical proposition (134, 148, 165); the premisses or
antecedent being regarded as a "ground" or "reason" whose
affirmation gives us a right to affirm the conclusion or consequent,
though not as the sole, exclusive, only possible ground for affirming
the latter. Hence, given the antecedent, we may infer the conse
quent, though we cannot, conversely, affirm the antecedent if we
are given the consequent (140). In other words, a given logical
antecedent is regarded as necessitating some definite consequent,
while this same logical consequent is not regarded as definitely
necessitating that antecedent. Now, if we regard deduction as the
passage of thought from logical antecedent to logical consequent
(understanding these terms in the sense just indicated), deduction
may be described as a direct or definite process, reaching a de
finite result. And if we regard induction as the passage of
thought from the real consequent or effect, regarded as logical
consequent, to the real antecedent or cause, regarded as logical
antecedent, induction will appear to be an inverse or indefinite
process, reaching only indefinite results: since, for any given
effect, considered as logical consequent, there may be a plurality
of causes, considered as logical antecedents. This leads us to the
consideration of induction as an " inverse problem," or " inverse
process," in comparison with deduction regarded as a " direct
problem," or " direct process ".

In what sense, then, may induction be fairly described as an
" inverse process," the inverse of deduction? It has been some
times so described by logicians. The term is borrowed from
mathematics, and there it has a quite intelligible meaning. A
direct process is one by which, given certain data and laws of
inference, we arrive at a definite conclusion : the inverse process
is that by which, given the conclusion, we try to get back to the
data. While the former always gives a definite result, the latter
may yield very indefinite ones. For example, given 4x4, what
is the product? Answer (definitely): 16. Given the product
1 6, what number multiplied by itself yields this product ? Answer
(indefinitely): plus 4, or minus 4. Or again, of what factors is

INDUCTION IN ITS VARIOUS SENSES 55

1 6 the product? Answer (indefinitely) : 2 x 8, or 4 x 4 (inverse
processes).

Transferred to logic, this character of indefiniteness in the in
verse process is further emphasized. Given the conclusion of a
syllogism, find the premisses. An entirely indefinite problem, this,
since any one out of an immense number of middle terms may con
ceivably mediate the conclusion : and the inventio medii, the finding
of a real or true, as opposed to an imaginary, middle term (167),
like the invention and verification of an hypothesis, is amenable
to no law or method. The specifying of a middle term would
remove some of the indefiniteness, leaving only the possible moods
of the syllogism to be determined ; the assigning of one whole
premiss would leave the other premiss (definitely) to be deter
mined.1 Something like this Professor Welton must have in mind *
when he agrees, with Jevons, that " induction is ... an inverse
process ; it is the finding major premisses when the conclusions
are given ". But why major premisses ? The inductive problem
seems rather that of finding the whole (proper and correct)
antecedent (major and minor], given the consequent or conclusion.
Given certain facts or effects, construct and verify an hypothesis as
to their cause. And from what we have already said about the
indefiniteness of the passage from a given effect or consequent to a
definite cause or antecedent, as compared with the direct process of
arguing from cause to effect, from antecedent to consequent, it
will easily be understood why the former process has been de
scribed as inverse, and the latter as direct. Yet, by describing
induction as an inverse process, the impression may be conveyed
that it reaches, de facto, only indefinite results. Such an impres
sion would be erroneous ; for the aim of induction is precisely to
eliminate this indefiniteness by proving some one of the conceiv
able alternative antecedents to be the real antecedent : which it
does, as we have seen, by the indirect method of disproving the
other alternatives.

JOSEPH, Logic, chaps, xviii., xx., xxiii. MELLONE, op. cit., pp. 244 sgq.,
265 sqq. JOYCE, Logic, chap. xiv. WELTON, op. cit., bk. v., chap. ii. VENN,
Empirical Logic, chap. xiv. MILL, Logic III., ii., iii. MERCIER, Logique,
pp. 298-307.

1 C/. VENN, Empirical Logic, pp. 359 sqq,
a Logic, vol. ii., p. 59 (italics ours).

CHAPTER III.

PRESUPPOSITIONS OF INDUCTION : CONCEPTS OF « REASON "
AND "CAUSE".

214. JUSTIFICATION OF CHAPTERS III. AND IV.— Since the
days of Lord Bacon, many conflicting theories on the nature and
grounds of induction have been advocated by logicians. Seeing that
induction is the method by which we attain to a knowledge of uni
versal truths about the nature and activities of the things of the
visible universe, animate and inanimate, it is easy to understand
the importance of the whole subject. Before, therefore, we proceed
to analyse more closely the process of ascent from phenomena
to their laws, we must examine the rational principles that underli-
the process. Modern logicians have analysed these principles
in great detail, thus importing into the logic of induction long
disquisitions which would, perhaps, find a more appropriate place
in psychology, criteriology, and cosmology.

No doubt, the logic of induction cannot be understood with
out a statement of the principles which underlie the process. But
a treatise on logic is hardly the proper place for their full ex
position and vindication ; nor is it our intention to go into them
here at any great length. We shall endeavour to confine our
selves to a brief explanation of the rational foundations of the
inductive process, i.e. the principles that justify us in rising from
particular facts to the conception of a general law ; and to a brief
criticism of some current views that seem more or less erroneous,
regarding those principles. In doing this, however, we cannot
avoid some reference to numerous notions which must be left for
fuller treatment to more suitable branches of philosophy. What
these notions are, will be at once suggested by any ordinary
example of a natural phenomenon that calls for interpretation
from us. Let us take an instance.1

This morning, for example, at half-past eight o'clock, the ash-

1 Adapted from Mercier's Logique, pp. 298 $qq.
56

CONCEPTS OF " REASON " AND « CA USE " 5 7

tree on the hill in front of my window was struck by lightning,
its foliage withered and burned, and its trunk rent asunder. This
individual event has happened once. With its own peculiar train of
circumstances, it had never happened before and it will never happen
again. But, at other times and places, other trees — and houses and
people — have been similarly struck by lightning. We examine
the effects produced by lightning in such cases. We try to find
out under what conditions exactly they have been produced. How
is it that the brilliant flash, which dazzles our eyes in the storm,
is accompanied by such effects? If our search be successful, we
shall learn the nature of the lightning, the law (that is, the how?
the quomodo ?} of its action, and we shall then understand, " by their
causes" the effects produced.

To understand things by a knowledge of their causes is the aim
of all science. Now, even the most superficial observation of
the phenomena of nature convinces us that their variability is
bounded and ruled by a certain general sameness, or fixity, or
uniformity. The things of nature differ, no doubt, in many ways
from one another ; yet each of them belongs to a certain class, in
virtue of some common attributes — else how or why would they
have common class names ? Each belongs to some specific type,
inorganic, vegetable, animal, human, whose fundamental uni
formity, and relative fixity, are ever conspicuous throughout the
incessant evolution and change of circumstance to which the
transient individuals of the class are subject. And what is true of
" things " is equally true of " events ".

It will be observed, from the expressions italicized in the
foregoing paragraphs, that in the inductive process by which we
rise from facts to laws we are seeking for reasons, or explana
tions, for the how and the why of some phenomenon : we
regard this latter as an effect, and look for its cause : we observe
similarity amid variety : we study the conditions and circumstances
in which the phenomenon takes place: we analyse the causes
that lead up to it, and try to find out the nature of these causes
and the law according to which they act. Obviously, therefore,
our understanding of the inductive process will depend on our
manner of conceiving cause, reason, law, uniformity, identity, etc.
Hence, some explanation of the principles of " Sufficient Reason,"
and "Causality," and "Uniformity of Nature," and of their
bearing on the inductive process, is evidently called for at the
present stage. And first as to the Principle of Sufficient Reason.

58 THE SCIENCE OF LOGIC

215. "REALITY" AND THE "PRINCIPLE OF SUFFICIENT
REASON V — Among the presuppositions of induction, many
authors set down in the first place the Principle of Sufficient
Reason : that " whatever is judged to be true must have a reason
in our thought for being so judged ; and whatever is or happens
in the real order must have a sufficient reason or cause for so
being or happening ". As a matter of fact, this principle is a
presupposition not of induction alone, but of all search whatever
after truth. It simply postulates that reality is intelligible, and
its explanation attainable — at least to some extent. Unless we
assume that we can discover truth, it is idle to seek for truth.
All actual search after truth presupposes that some truth can be
found, and the gradual discovery of truth justifies the assumption.
The postulate is, therefore, reasonable and necessary. But at the
outset its meaning is essentially vague, and it is only by progress
in the discovery of truth that we can gradually attach definite
meanings to the terms "sufficient reason," "intelligible," "ex
planation," etc.

The principle refers to two orders, the logical and the real.
In the logical order, the order of thought, the premisses are the
sufficient reason of the conclusion, the antecedent of the conse
quent, until finally we come to some antecedent which, being
self-evident, has the sufficient reason of its truth in itself; that
is, in the reality which the judgment in question interprets by
means of two concepts carrying in them the evident ground for
the relation which the mind sets up between them. So, too, in
the real order, in the order of things, everything that exists,
every fact that happens, must have a sufficient reason, either
beyond itself — in that its happening or inception is the effect of a
cause distinct from it, — or in itself — in that it exists necessarily and
of itself , and is itself the explanation of its own existence.

But the two orders — of thought and reality — are not mutually
isolated and independent: the "objective evidence" which is the
logical ground or reason of first principles, is simply REAL
BEING put into relation with the MlND.2 " Objectum Intellects
est Ens": "The object of Intellect is Reality". This maxim
of scholastic philosophy is the assertion, against subjective

J C/. brochure entitled " The Inductive Sciences : An Inquiry into some of their
Methods and Postulates" by the present writer (Dublin : Browne & Nolan Ltd.,
1910), pp. 10 sqq.

3 i.e. ontological truth. C/. 248.

CONCEPTS OF « REASON " AND « CA USE " 59

phenomenism, of the power of the human mind to reach real,
objective truth.

The Principle of Sufficient Reason is, therefore, not merely
formal 'but raz/(i6). Not only can we not judge of a thing without
a sufficient reason in the thing itself for that judgment ; but also,
the thing itself, the reality itself, which is the object of our
thought, cannot be what it is, and as it is, unless it have a
sufficient reason in itself, or connected with itself, why it is, or
why it is so and not otherwise.

But when we ask what shall we be obliged to regard as the ultimate
"sufficient reason" or "explanation" of our experience as a whole, the
answer will obviously depend upon the view which careful and prolonged re
flection on that experience will lead us to form about the nature and meaning
of all reality. And the conclusions we may reach on this fundamental
question will, of course, determine our interpretation of the exact scope and
significance of the principle under consideration. Two erroneous interpreta
tions of the principle, based on erroneous views about the nature of reality,
may be noticed here, in contrast with the scholastic interpretation which is
based on the philosophy of theism.

One is variously known as Empiricism, Sensism, Positivism, Agnosti
cism. It is a mistake in method, no less than an error in fact, to assume, even
in regard to the inorganic universe, that no judgment about the latter can be
accepted as true without the same sort of cogent evidence which compels in
tellectual assent in the mathematical science of abstract mechanics ; that
a fact is " intelligible " or " knowable " only in so far forth as it illustrates the
laws of mechanical motion and inertia ; that the introduction of " purpose,"
" design," " intelligence," " final causes," as factors to help in explaining the
processes of physical nature, is " unscientific " inasmuch as these factors
cannot be " computed " in terms of the laws and principles of mechanics, and
are, therefore, themselves not scientifically " intelligible ". Any such narrow
ing of the concept of what is " knowable " or " intelligible " is entirely
gratuitous and unwarranted. Yet the Positivist philosophy, which has been
popular in modern scientific circles, insinuates this misleading interpretation
of what is in itself a true and reasonable principle. For this philosophy would
have us believe that what is beyond the range of sense experience is " un
knowable " (Agnosticism) ; and that the phenomena of sense experience are
" knowable " or " intelligible " only in so far as their uniform coexistences
and sequences throughout space and time exemplify and constitute the " laws "
of mechanics (Mechanical Atomism). Reality may surely be " knowable,"
even though not amenable to any such laws ; and there may be some reality
within the reach of our intellect, even though it be beyond the reach of our
senses.1 It was the misfortune of English philosophy, under the influence of
such men as Hume and Mill, to sink into this Sensism. By declaring all
reality to be, in ultimate analysis, a flow of sensations in the individual con
sciousness, they really declared all " knowledge," all " rational explanation " of

1 Cf. JOSEPH, Logic, pp. 382 sqq.

60 THE SCIENCE OF LOGIC

human experience, to be impossible. We shall see an illustration of this in their
futile attempts to explain and justify men's belief in the Uniformity of Physical
Causation. The Positivism which endeavours to interpret all human ex
perience as a process ruled by mechanical necessity has for its obverse side
Agnosticism— that is, a declaration of inability to assign any ultimate rational
ground that will explain human experience as a whole. This, like all
scepticism, is really an abandonment of the principle of sufficient reason ; for
it says, in effect, " We believe certain things, but, ultimately, we do not and
cannot know why we believe them ". The empiricist so interprets experience
as to end in agnosticism about the suprasensible, and in inconsistency about
what he calls the " scientific laws or generalizations " of sense phenomena.
In his attempt to account for the reliability of those generalizations, their
stability, their characteristic of necessity, he really explains this away, and
leaves no rational ground for human certitude (cf. 219, 224).

Another extreme and erroneous interpretation of the principle of sufficient
reason, another narrow view about the " intelligibility " of experience, and the
possibility of " explaining " the latter, is that of Hegelian Idealism. This is
the very antithesis to Empiticism. The latter fails to account for the " must"
the element of necessity, which characterizes, in varying degrees, our judg
ments about reality ; the former errs by attributing the same absolute intel
lectual necessity to all our judgments about reality. In a word, it claims that
the world as a whole is " intelligible " and capable of " rational explanation "
only on the assumption that it is one vast self-contained and self-explain
ing system of ideas, or thought-relations, which reveal themselves to in
dividual minds as endowed with the same metaphysical necessity which
characterizes our abstract judgments about the possible essences of things.
This, too, is an assumption which unduly narrows the scope of " explanation "
and the sphere of what is " knowable " or " intelligible ". If we reduce the
reality of things, in this fashion, to a mental fabrication of thought-relations,
if we make reality a ' theory? a mere mental ' constitution? a "determina
tion " of things " by each other as constituents of one order, a determination
which only exists for thought " ; if we say : " It is not that there is first the
reality of things,1 and then a theory about it. The reality is a theory " ; 3 if,
we contend that " mere feelings . . . except as related to each other through
relation to thought, are not facts at all," 3 that it is only by thinking them we
make them real and give them a nature : 4 are we not setting up a mental
creation, a system of abstract thought-relations, in the place of reality, and
ignoring the claims of that sense experience which certainly puts us into con
tact with reality ?

This Idealistic Monism misinterprets reality. Nor is the postulate involved
in it a necessary one : the postulate that all reality is one great mental or
intellectual system, one great thought or idea, unfolding itself in individual
minds according to necessary laws of logical thought ; for, surely, we can make

1 But surely there is some reality in the " things " themselves ? Surely reality
does not lie exclusively in any " determination " of relations established by thought
between those " things " ?

3 GREEN, Philosophical Works, vol. ii., p. 269; — apud WELTON, ii., p. 2.

3 ibid., pp. 385-86.

4C/. HERSCHEL, Nat. Phil., ioq\—apnd WELTON, ibid.

CONCEPTS OF « REASON " AND " C4 i/5^1 " 61

progress in knowledge without the aid of such an assumption ; and, besides,
there is at least this other alternative postulate — the postulate of Theism — that
the sense world reveals itself to the human intellect not as the self-evolution,
at once logical and real, of a Sole Being that is at once thought and reality,
but, rather, as a distinct system, dependent no less on a Supreme Will for its
actuality than on a Supreme Intelligence for its intelligibility.

This, then, is another possible alternative, and it is the true one : that the
whole world of human experience (including the human mind itself) is the
creation of a Supreme Free Will, governed by laws laid down by a Supreme
Intelligence {Philosophy of Theism] ; and not the logically necessary unfold
ing or evolution of one Sole Idea-Being (Idealistic Pantheism) ; or the ob
verse and unknowable background of the transient panorama which con
stitutes the individual man's sense consciousness (Empiricism, Agnosticism).

These are three alternative points of view — there are others also — from
which individual writers on inductive logic may proceed to lay down principles
for the guidance of the student in his search after truth, whether in science, in
philosophy, or in theology. The differences between them are revealed in the
respective ways in which writers of each of these schools treat of causality,
hypothesis, and generalization (based on the law of Nature's Uniformity), as
well as in the different ideals they set up regarding Scientific Explanation and
Physical Certitude. In the chapters that follow, we shall, therefore, have oc.
casion to recur repeatedly to the views we have just mentioned ; and the
principle itself of sufficient reason will arise again explicitly, in connexion with
the theory of Demonstration and Scientific Explanation.

2 1 6. THE PRINCIPLE OF CAUSALITY IN INDUCTION: ARIS
TOTLE'S CLASSIFICATION OF CAUSES. — When applied to contin
gent things, to the phenomena of nature around us, the principle
of sufficient reason resolves itself into the Principle of Causality.
This latter is an a priori, self-evident principle, like the former.
Cause and effect being correlative, to say that " Every effect has
a cause" is to state a truism. The principle is usually stated
thus : " Whatever happens (occurs, takes place, begins to be)
has a cause ". The axiom ' Ex nihilo nihil fit' is a negative
statement of the same principle. And another statement of it,
"Whatever is contingent (i.e. whatever does not contain in itself,
in its own essence, the sufficient reason of its actual existence)
has a cause," shows the connexion of the principle of causality
with the principle of sufficient reason. Being that is necessary
and self-existent has no cause. It is itself the reason of its own
existence ; whereas all contingent being is caused. The principle
of causality is evidently a necessary principle in regard to con
tingent being, i.e. it is essentially involved in our very concept
of contingent being. Nothing can happen without a cause:
whatever happens has necessarily a cause, i.e. something which

6a THE SCIENCE OF LOGIC

brings it about, which makes it happen, whether this cause be
free (i.e. self-determining) or not, in its mode of action.

Now, induction being mainly concerned with the discovery
of the causes which bring about the phenomena that constitute
our experience, it is important to have a clear understanding in
the first place about what scientists, logicians, and philosophers
mean by a " cause ".

What we may call the common and traditional notion of
" cause " is that of "anything which contributes in any positive
way to the existence or happening of something else ". Aristotle
distinguished between two intrinsic causes, the " formal " and the
"material," which constituted that "something," and two other
causes, the "efficient" and the "final," extrinsic to the "some
thing," and in regard to which the latter is properly called an
" effect ". The notions of " formal " and " final " causes are
closely connected with the Aristotelean view of nature as re
vealing Purpose and Design (217). We shall see that modern
science and philosophy are not the better for discarding these
notions.1 Inductive logicians confine their attention almost ex
clusively to the study of efficient causality ; and of this many
have perverted, or rather abandoned, the traditional notion.

The popular idea of " efficient cause " is that of an agent or
agency — something which by means of perceptible action, motion,
or change, produces some new state or condition of things. Thus
understood, a cause is clearly distinguished from a condition ; the
latter being anything which, though necessary for the happening
of the effect, does not contribute positively thereto: windows, for
instance, being the condition, not the cause, of the daylight in a
room. Most logicians of induction, however, ignore this distinc
tion 2 : the reason being that, so far as physical science is concerned,
it is of no importance. Nor indeed is it, provided we assume
that the duty of the physical scientist as such is merely to discover
all the antecedents, positive and negative, of whatsoever sort,
which are sufficient and indispenable for the happening of any
given phenomenon, without troubling himself about the manner
in which they contribute thereto.8 But not all are willing to set
such limits to the scope of physical science ; though, of course,

1 Cf. VENN, Empirical Logic, pp. 47-62, as an example of the attitude of the
empirical school of logicians towards them.

3 Cf. WELTON, op. cit.t ii., p. 19, where " cause " is defined as the " totality of con
ditions " requisite to the happening of a phenomenon.

* Cf. JOYCB, Op. Cit., p. 221.

CONCEPTS OF " REASON " AND « CA USE " 63

philosophers of the positivist school claim that when physical
science has discovered the invariable antecedents of a pheno
menon nothing further remains for investigation. Moreover, the
logician of induction should not confine his investigations to the
data of the physical sciences alone ; he must investigate our
thinking processes about all conceivable data. The distinction,
therefore, between condition and cause, need not be altogether
ignored.

We must next consider that the same thing or reality, the
same phenomenon or agency, may evidently be the effect of cer
tain efficient causes, and itself the efficient cause of other effects :
looked at in one connexion, from one point of view, it is an effect ;
in another connexion and from another point of view it is an
efficient cause. Thus we see, in physical nature, innumerable
series or chains of efficient causes, wherein each link has others
depending on it while itself in turn depends on others : whether
each follows the other in time or all exist simultaneously. Every
event in nature is the result of a long series of causal antecedents
stretching indefinitely backward and outward in time and space,
or rather of the convergence and co-operation of many such series.
It is precisely owing to this fact that inductive research for the
" efficient causes " of the phenomena of nature constitutes such a
difficult problem. When can we be said to have discovered in
ductively the group of agencies which are to be regarded as the
" total " efficient cause of any phenomenon ? What portion of all
the converging series of influences are we supposed to bring to
light explicitly, and to designate as the total efficient cause of an
event ? How far backward and outward from the event, and how
far forward and inward towards the event, are we to proceed in
our analysis of its concomitant and antecedent circumstances ?

Let us take, as an instance of natural causation, the formation
of water from oxygen and hydrogen. If we draw through the
process a line of demarcation (220) at the moment the water
begins to appear, and regard the appearance of the latter as the
effect to be explained, we shall evidently need to examine the
antecedents down to this very line itself, lest any indispensable
factor escape our notice. And in the backward direction, in enu
merating remoter antecedents which were indispensable steps lead
ing up to the final result, where are we to stop? Are we to in
clude not only the necessary heat, but the source of the latter —
the electric machine? and its maker? Are we to include not

64 THE SCIENCE OF LOGIC

only the gases, but the vessels containing them ? and the agencies
that produced them ? and those that brought them together in
the proper proportions ? Evidently not. We must, clearly, draw
the line limiting our backward search somewhere. And from the
region between it and the line bordering on the effect we must
set aside all the individual modes and circumstances which may
indeed be essential for this individual instance of the effect, but
which are indifferent and irrelevant so far as the production of this
kind of effect is concerned : * for it is not with the individual effect,
but with the kindvi effect, the production of water as such (i.e.
with the abstract and universal], that science is concerned. We
must, therefore, confine our attention to a limited group of ante
cedents in close proximity to the effect, analyse this group, and
set forth, as the " total proximate cause " of the phenomenon, only
that collection of factors which we regard as the sufficient (or
necessitating) and indispensable PROXIMATE factors in its production.
Moreover, the scientist, in enumerating these, will omit, and usually
does omit, such factors as are obviously necessary for the result :
he assumes it to be universally understood that they are present.
His concern rather is to detect some one factor (or collection and
collocation of factors) which immediately precedes the effect, and
which actually determines the effective co-operation of the existing
forces in the production of this specific kind of effect.2 This
factor he usually calls the " determining cause (or condition)" of the
phenomenon. All the factors in this proximate collection — all
the proximate factors sufficient and indispensable for the effect —
constitute what the scientist regards as the "proximate (efficient)
cause " of the phenomenon in question.

Although the principle of causality refers primarily to efficient
causes, i.e. causes which, by means of action, of real change or
motion, produce their effects ; and although modern writers on in
duction have concentrated their attention almost exclusively on
physical efficient causes — i.e. those which are, in themselves or
their action, perceptible to the senses — as being the more capable
of exact physical investigation, and even of mechanical measure
ment : still, the scope of inductive logic must necessarily embrace
the investigation of material, formal, and final causes, no less than
of efficient causes.3 To know a thing scientifically, we must know

1 Cf. JOYCE, op. cit., p. 221. a Cf. JOSEPH, op. cit., p. 393.

3 On this point we may refer the reader to a suggestive article by W. J. ROBERTS
in Mind (N.S., no. 32, October, 1909), connecting the theory of induction with
Aristotle's doctrine on formal cause. — Cf. JOSEPH, Logic, p. 457.

CONCEPTS OF " REASON " AND " CA USE " 65

not merely its efficient cause or causes, but its inner nature, its
formal and material causes. But its specific nature, or formal
cause, is revealed by its sensible energies and properties : it is only
by studying these — which are nearer and more familiar to us,
whose knowledge comes through the senses — that we can know
that which is more remote from us, though prior and simpler in
itself, viz. the specific nature, the ground of the universal law.
The principle underlying this progress of thought is expressed in
the Scholastic aphorism : Operari sequitur esse, or, Qua/is est
operatic ', talis est natura : As a thing is so it acts: Action is the
index of essence. And a knowledge of the formal cause or specific
nature of a thing helps to bring to light its purpose or function in
the universe, i.e. its final cause, the reason why it exists and acts,
the design it accomplishes in nature. Without a knowledge of the
" why and wherefore " of a thing, our knowledge of it is incomplete.

When, for example, Pasteur's experiments demonstrated that fermentation
is due to the action of a living microbe, or that every living cell has its origin
from some other living Cell, he discovered in the microbe the efficient cause
of fermentation, in the parent-cell the efficient cause of the younger cell.

Again, the chemical elements combine to form compounds in certain
definite proportions by weight. The components, hydrogen and chlorine, enter
into the formation of hydrochloric acid in the proportion of i part of hydrogen
t° 35-5 parts of chlorine by weight. Those definite quantities are material
causes of the various combinations into which these elements enter, for the
material mass or quantity is independent of specific change, i.e. change of
substance or substantial " form," and attaches to the material cause or prin
ciple in corporeal substances and agents.

Again, the combination of hydrogen and chlorine to form hydrochloric
acid is seen to depend on the chemical affinities of the two reacting bodies for
each other. These affinities being themselves specific properties of the
respective components, the formation of the acid is the result of the specific
natures of these components. But the specific nature and the specific pro
perties of a body depend on, and are determined by, its specific, essential or
substantial "form": its " formal" cause. So that when we determine the
law of a chemical combination, i.e. the fixed, uniform mode of action of the
substances involved— elements or compounds, — we are bringing to light the
formal causes, the specific constituent principles, the specific natures, of
those substances.

Again, the peculiar affinities of the chemical elements determine the
combinations which their respective natures incline them to realize. Hence,
to detect the affinities of these elements, and to characterize the latter by
those affinities, is to discover the innate tendencies which incline these
elements to form certain combinations. In other words, it is to discover the
internal purpose of the reacting bodies. The establishment of the laws of a
chemical combination is, therefore, the discovery not merely of the formal, but
VOL. II. 5

66 THE SCIENCE OF LOGIC

also of the final causes, of such combination. That is to say, it shows the
realization or formation of the compound as the internal reason why the
bodies in question combine in that way ; it reveals the finis operis, the intrinsic
aim of that activity which is the product and complement of their respective
natures or formal causes.

In some cases, the final cause is even the primary object of inductive re
search. This occurs very commonly in physiological investigations into the
functions of living organs — as, for example, in the efforts of physiologists to
discover the functions of the thyroid gland, or of the vermiform appendix.

217. "PURPOSE" OR "DESIGN" : " FINAL CAUSES" AND

"LAW" IN PHYSICAL NATURE. — It is intelligible that when
inquiring into the causes and reasons of phenomena that may be
due to human activity we should seek for their final causes, i.e. the
motive, the design, the end in view in their production ; but
the meaning of seeking for final causes in the natural agencies
even of the inorganic world may not be at first apparent : for,
how can an agent devoid of perception and appetite, nay, even of
life, act "for an end"? Such agents cannot, of course, act "for
an end " in the same way as men (" electivJ"\ who, by free will,
elect or choose the ends for which they act ; or in the same way
as animals (" apprehensive r"), which are conscious of the ends
towards which their appetites move instinctively ; but the inani-
. mate agencies of the physical universe can and do act, each "for
an end," effectively or equivalently (" executive""\ i.e. in such a way
as to make it clear that they are directed or oriented in their
action by a ruling intelligence, and for a purpose. That this
is so in fact, we are convinced by the manifest order, harmony,
regularity of natural phenomena. We know by experience that
the causes at work in the whole vast physical universe act each
in its own fixed way, uniformly, regularly : whence we conclude
that every such agency must have impressed on its very essence,
on its inner constitution, by the Creator, a definite " bent " or
" tendency " or " inclination " (" appetitus naturalis ") to act along
certain definite lines, and so to discharge its appointed function
in the universe. This inner principle of uniform action (which is
its substantial or specific formal cause] we call the nature of the
agent in question : and when it acts in the ordinary, normal way,
we speak of its acting " according to its nature" or " according
to the law of its nature ". By the nature of a cause or agent we
therefore primarily mean the inner directive principle of its activity :
its essence regarded as a source or principle of orderly, intelligible

CONCEPTS OF " REASON " AND « CA USE " 67

activity. * When we speak of Physical Nature, or the Order of
Nature, or the Course of Nature, or External or Visible Nature, we
use the term " Nature," in a collective sense, to signify the sum-
total of all the created agencies that make up the visible (i.e.
sensible, perceptible) material universe.

Hence, the extension of the concept of purpose from the do
main of rational or human agents to the animal, vegetable, and
inorganic kingdoms of nature, by Aristotelean and Scholastic
philosophers, is no mere > verbal metaphor. There is a true and
proper sense, as these philosophers contend, in which all created
agencies act in fulfilment of purpose, in which "ALL agents act
for an end " : " OMNE agens agit propter finem ".

The conviction is gradually forced in upon us by our experi
ence of natural phenomena, that every agency in nature must
have some fixed, intrinsic principle of activity, in virtue of which
it acts uniformly, and concurs with other physical agencies, not
capriciously or indifferently, but along certain prearranged and
predetermined lines ; so that " exceptions " to this uniformity
must be due in reality to the influence of some unknown natural
causes, or, possibly, to the intervention of the First Cause. Here,
at all events, is the great fact we gather from sense experience :
that very complex combinations of numerous natural agents re
peatedly concur to produce uniform series of effects. Of this
great fact there can apparently be one, and only one, rational in
terpretation : that which conceives the proximate causes of such
uniform series of phenomena as endowed each with a fixed natural
inclination or tendency to act steadily and consistently along de
finite lines, as having each an internal law which dominates it,
and in conformity with which it will act always and everywhere.
This innate, stable tendency is what the mind grasps when it
apprehends the law of the Uniformity of Nature. The great fact of
experience revealed in the regular, constant, harmonious concurrence
of numerous and varied forces and agencies to produce uniform series
of results, finds its sufficient reason and explanation only in a

1 The Essence of a thing (" Essentia " or " Quidditas ") is that which makes
the thing what it is (" id quo res est id quod est " : the answer to the question " Quid est
ilia res'} "). The Nature (" Natura ") is the essence itself looked on as the directive
principle of the thing's activities (the " principium operationis "). It was conceived
by the Scholastics as the impression of a divine directive plan or design on the inner
constitution of the created agency : "Stabilis inclinatio vel appetitus finis, rebus a
Deo inditus" or again, " Ars quaedam Divina indita rebus, per quam ad fines pro-
prios non solum ducuntur sed quodammodo vadunt." — St. Thomas, Q(^. DD. De
Veritatc, Q. xxii, a. i.

5*

68 THE SCIENCE OF LOGIC

fixed NATURAL INCLINATION or tendency of the agents which pro
duce such results. The expression " natural inclination " embodies
a fundamental doctrine of Aristotelean philosophy ; it implies
that the agencies whose effects or manifestations we observe in
the world around us are not, as the advocates of mechanical de
terminism (215) would have them, mere efficient agents capable
of producing any or every result indifferently, but that each of
them is endowed with an internal tendency in virtue of which it
manifests a manner of being and acting proper to itself; which
manner is called a property of the substance, and reveals the
specific nature of this latter.

This view of the universe, as the expression of a divine plan,
— hence called ideological, — renders intelligible the use of a term
that is constantly recurring in the logic of induction : the term
Law (Lex). Law means primarily an order, mandate, precept,
emanating from the will of a superior (the legislator), and imposed
upon a community subject to him.1 The law, as abiding in
their minds and hearts, by their knowledge of it and submission
to it, secures a certain uniformity in their conduct: it becomes
the immediate source and principle, in them, of a series of similar
acts. Next, the term Law came to be applied to what was
really its effect, to this uniform series of similar acts. It was then
extended, in this latter sense, from the domain of human activity
to the domain of physical, even inanimate, nature ; and here it
is now used, as, for example, in all the " physical " and " natural " 2
sciences, to denote any uniform series of connected phenomena,
whether the connected elements exist simultaneously (" coexist
ences ") or successively (" sequences "). The general propositions
or statements which formulate such connexions are commonly
referred to as "laws of physical nature": e.g. "Water seeks
its own level," " All bodies fall with the same acceleration in a
vacuum," "At a given temperature the volume of a given
quantity of gas varies inversely as the pressure it sustains,"
" Heat can produce mechanical work, and vice versa, in definite,
measurable proportions," "The strength of an electric current
varies directly as the electromotive force and inversely as the
resistance," "Every living cell has its origin from some other
living cell," "Fermentation is due to the action of microbes".

1 Cf. The Inductive Sciences, etc., pp. 70 sqq.

a These terms are commonly regarded as synonymous ; when they are distin
guished, the former refers to the sciences of inorganic, inanimate nature, the latter
to those of the living universe,

CONCEPTS OF "REASON" AND "CAUSE" 69

Most of these "laws" are merely formulae descriptive of con
stant connexions which have been discovered to exist between
phenomena, and of the conditions and circumstances in which
such connexions are found to obtain. But those uniform happen
ings must, after the analogy of the uniform conduct of a com
munity subject to the law of a superior, be themselves due to
fixed principles of action inherent in the constitution of the natural
agencies which manifest those uniform activities. Now, if we
bring to light the agencies which are operative — and co-operative
— in producing those regular coexistences and sequences, the
mode of action and interaction of the efficient causes that are
at work, the inner constitution or nature of those agencies, i.e.
their material and formal causes, and the scope or purpose of
those activities, we can formulate explanatory or causal laws, i.e.
laws which will not merely express the existence of uniformities,
but which, furthermore, will give us an insight into the "how"
and the "why" of such uniformities (222).

The Aristotelean conception and classification of causes, and the Scholastic
view of physical nature as a " cosmos," revealing purpose, design, intelligence,
and subject to " law " in the sense just explained, have been almost completely
ignored by modern exponents of the logic of induction.1 Some of these
latter have substituted a purely mechanical view of the universe, eliminating
the notions of " design " and " efficiency " as superfluous, and retaining merely
the notions of " invariable " or " necessary " " sequences " and " coexistences "
of material phenomena, as the ultimate factors of a rational explanation of the
universe. These writers have been induced by a rather superficial materialism
to abandon, and even to ridicule, the r61e of final causes in philosophical
research. Yielding too hastily to the natural craving for a simple solution of
the problems raised by the universe, they have thought to satisfy themselves
and others by proclaiming the sufficiency of physical efficient causality, i.e.
of invariable connexions between masses of matter in motion, for the adequate
explanation of all things. The attempt was necessarily futile, and is nowadays
generally recognized as such. " The mechanical theory of the universe,"
writes Professor Welton,2 " is simple, but inadequate even in inorganic nature ;
in organic nature it must be supplemented by the principle of development,
and finally by the conception of rational purpose." To which we may add
Mr. Joseph's testimony,3 that " to a physical theory of the world consciousness
remains unaccountable ; such a theory therefore cannot be complete or final ".

We shall see later (219, 224) that the "necessity" of those "uniform con
nexions " or " laws " can have no rational basis in the " mechanical " view of
nature. Neither, however, does it receive a satisfactory explanation on the
Hegelian, idealist view, that nature is merely a system of thought-relations ; and
that its "necessities" are identical with the necessities of thought (215).

1 Cf. VENN, Empirical Logic, pp. 47-52.

8 Logic, ii., pp. 206, 210; cf. p. 30 (italics ours). sop. cit., p. 384.

70 THE SCIENCE OF LOGIC

Writers who support this latter view bring out very clearly the shortcomings of
Empiricism ; l but, though they rightly include the concept of " final cause " i.e.
of purpose, design, in their philosophical explanation of natural phenomena,
they still fail to recognize explicitly the " formal " and " material " causes, as
distinct from the "efficient causes," of phenomena, and are thus led to
identify the cause with the process, and this latter with the effect.

In most of the physical sciences we are mainly concerned with the dis
covery and explanation of processes, changes, motions, activities, actions and
interactions between material agencies : and our main concern here must be
to find out what are the proximate agencies at work in a given process, to
separate these from irrelevant and accidental surroundings, to detect the total
(proximate) agens and the total (proximate) pattens in question, and to discover
and understand the connexion of physical efficient causality between these.

But the discovery of a connexion of efficient causality, of action and
interaction, between physical agents, is the discovery of active and passive
powers or properties in these agents : and the discovery of such properties or
powers leads to a knowledge of the intrinsic constitution, the nature, of these
agents. As a thing acts, so it is : Qua/is operatic, talis natura. All the
insight we have into the inner nature and constitution of things is got by
inference from their observed activities : Operari sequitur esse. And our
knowledge of the inner nature and constitution of a physical cause, of the
manner and conditions of its activities, will help us to understand its raison
d'etre, its function or role in the universe, the purpose it serves, the end it is
designed to fulfil, the final cause of the processes in which it plays a part.

Thus we see that the search for any one class of cause is by no means
incompatible with a search for the others. When one line of inquiry cannot
be prosecuted, another may ; and each often helps the others.

2 1 8. CONTRAST BETWEEN TRADITIONAL AND EMPIRICAL
CONCEPTIONS OF EFFICIENT CAUSALITY. — When the word
"cause" is used without qualification "efficient cause" is meant.
Used in this sense, the term " cause " has almost completely changed
its traditional signification ; and with very confusing results.
We must, therefore, note these changes of meaning carefully.

The traditional notion of efficient cause is that of " anything
which positively contributes by way of action or change or motion
to the production or happening or existence of anything else".
Positive influence by way of action is what we mean by the "effici
ency " of a cause. This traditional conception of efficiency, or
efficient causality, we can find no reason or justification for abandon
ing. We shall therefore retain it. Furthermore, we must dis
tinguish between the individual, substantial cause or agent itself
(" the agens" the " principium quod agit ") ; the power, faculty,
force, potential energy, of that cause (the "principium quo agens
agit"); and the action ("actio") by which it produces its effect.

1 Cf. Professor WELTON'S criticisms of Mill, op. cit., passim.

CONCEPTS OF " REASON " AND " CA USE ' ^ i

And, of efficient causes themselves, we may distinguish several
kinds : the First or Uncreated Cause, and second or created causes ;
the free cause — which has the power of choice to act or not to
act, which can determine itself to act or not, which has "do
minion " or control of its act, — and the non-free or necessary or
" natural" cause, — which, when placed in a definite set of circum
stances, does always act, because it must act, because it has no
power or control over its own act, but is by its very nature so
constituted (by the First Cause) that (unless the First Cause
miraculously interferes) it will, by a necessity of its nature, always
act in those circumstances.

Now, most modern writers on induction have come to use
the terms cause, and efficient cause, in the sense of a non-free or
necessary l cause. This in itself is not surprising, seeing that
they have mainly, if not exclusively, in view the physical universe,
inorganic and organic, exclusive of man ; and they may, perhaps,
regard the adjective " physical," applied to " cause," as a suf
ficient indication that they are dealing only with causes under
stood to be connected "naturally" or "by a necessity of their
nature " with their effects.2 With this usage, then, we will not
quarrel, provided it be distinctly understood that there are, or
may be, in existence, free causes. Where ambiguity would be
likely to arise, we should use the adjectives " free " or " necessary ".

An unfortunate result, however, of identifying efficient causality
with the uniform causality of necessary causes, calls for notice
here. It is the confusion of two quite distinct principles, the
"principle of causality " (216) and the "principle of the uni
formity of nature" (223), under the common title of the "law
of universal causation ".3 But it is one assertion that " The
same causes, acting in similar circumstances, will always produce
the same effect " ; it is another and quite a different assertion
that " Whatever happens has a cause ". The former, which is
known as the " principle of the uniformity of physical nature,"
is not universally true, of all causes : as we shall see later (223),
it applies, strictly speaking, only to "necessary" or "non-free"
causes ; though it is often stated by modern writers in such a
way as to insinuate that it is of universal application : which, of
course, is tantamount to a denial of human free will. Similarly,

1 The term " necessitating" would convey the idea better than " necessary ".
The latter term, however, can claim universal usage in this context.

8 Cf. JOSEPH, op. cit., p. 373. 3 Cy. MBLLONK, op. cit., p. 281.

72 THE SCIENCE OF LOGIC

the latter assertion — the self-evident principle of causality :
" Every event necessarily has a cause " — is not to be confounded
with this other altogether different assertion, that " Every event
has a necessary cause ". This latter statement is not evident ;
nay, it is not even true. Effects produced in the universe by the
free activity of man have, manifestly, not necessary but free causes.

Nevertheless, there are many modern writers on inductive logic, who in
sinuate—perhaps unconsciously — in their whole doctrine of causality that the
only concept of cause which is at all intelligible or amenable to scientific treat
ment is the concept of a necessary or necessitating cause. Thus, Dr. Mellone
refers to the self-evident principle of causality under the title of the Law of
Universal Causation, and rightly remarks that it refers to " cause " in the
widest sense : Every event must have some sort of cause, either a " necessary "
(or " uniformly acting ") cause, or a " capricious " cause, or — he might add —
a cause which, though free, is not " capricious," and about the operation of
which we can consequently generalize with some degree of safety.

" This principle [he writes] may be shown to be implied in all thinking.
Even children and the lower races of men, though they do not think of it,
think according to it. If the savage were content to leave any event unex
plained, he would not imagine that all events are controlled by spirits,
malevolent or benevolent. It is in fact IMPOSSIBLE TO THINK OF AN EVENT
WITHOUT REFERRING IT TO A CAUSE, known or unknown. Even if we had
a state of affairs where the past gave scarcely any assurance as to the future,
our way of conceiving it would not be contrary to the principle of the universality
of causation. We should think that some capricious power had added itself
to the conditions, turning them now this way and now that." J

All that is quite true ; for the word " cause " is clearly taken to include
conditions, agencies, influences, and powers, of whatsoever kind, capricious and
free no less than regular and necessary : on no other supposition indeed would
the statement that " every event has a cause " be a self-evident axiom.

But Dr. Mellone goes on immediately to say that the principle of the
Uniformity of Nature, or " Uniformity of Causation" as he prefers to call
it — that " the same cause must have the same effect "—a principle which will
be shown to refer properly only to necessitating causes (223)— is included in
the previous principle of the universality of causation, that " every event has a
cause ". Surely this is not so. The universality of the law of causation
throughout all contingent being, does not in itself imply that this causality is
necessarily uniform. The self-evident principle of causality— that nothing
can happen without a cause, ex nihilo nihil fit — understands " cause " in the
widest conceivable sense of any real principle, whether free or mechanical,
capricious or regular, which brings about the event : it has nothing to do with
the question of repetition or regularity at all. Whereas Uniformity of Causa
tion, even understood in the hypothetical sense in which Dr. Mellone takes it,"
bears exclusively upon regularity of repetition, and is self-evident only in re
gard to non-free, or necessary causes, which are by nature so constituted

1 MELLONE, Introductory Text-book of Logic, pp. 280-1.
*ibid., p. 282.

CONCEPTS OF « REASON " AND " CVf £/.S£ " 73

and so endowed with one fixed tendency that in similar circumstances they
must always produce similar effects. And yet Dr. Mellone continues : —

" The student will see on reflection that this principle is included in the
principle of universal causation ; for by cause is at least meant a condition
on which the effect always follows. If it sometimes followed and sometimes
did not, there would be no object in trying to discover it ; you would simply
not have a cause at all." 1

No doubt we are free to define a cause as " a condition [or group of con
ditions, agencies, influences] on which the effect always follows," and indeed
this is the narrower sense in which the term is usually understood when we
speak of the non-free causes that operate in external nature, the causes to
which the principle of uniformity properly applies. But it is certainly not
identical with the wider sense in which Dr. Mellone had rightly used the word
when formulating the self-evident law of universal causation, that " every
event has a cause," for in this latter context the term " cause " included free
and even " capricious " causes.

His final statement, that if the effect " sometimes followed and sometimes
did not, . . . you would simply not have a cause at all," is quite too sweep
ing. What is true, of course, is this, that we can infer or generalize about the
operation, beyond experience, of any cause, only in so far as we are warranted
in assuming its operation to be regular, not capricious. But if Dr. Mellone's
statement were true, it would follow that man is not the cause of what he does
freely, and that no science of human conduct is possible. This is one unsatis
factory result of discarding the traditional notion of physical efficient causes as
agencies or powers inherent in physical phenomena and productive of physical
change, for the empiricist notion of such causes as " invariable and uncon
ditional antecedents," i.e. phenomena or groups of phenomena " sufficient [or
necessitating] and indispensable " for the appearance of other [consequent]
phenomena.

The " efficiency " of causation is quite a distinct concept from the
" necessity " of causation. Yet these are sometimes confounded. Professor
Welton, for example, criticizing Mill's account of causality, writes 2 that the
latter " finds cause in a set of conditions whose existence necessitates that of
the effect," and he adds immediately that " greater efficiency than this no one
would wish to establish ". But efficiency is not necessity. A cause may be
efficient and yet not be necessitating, but free. In fact it is from our con-

1 MELLONE, ibid., p. 281. Mr. JOSEPH (op. cit., pp. 370 sqq.) adopts the same
view : " There is no need then to distinguish the law of causation from the
uniformity of nature ; for — bating the possible exception of the causality of the
human will — a cause which does not act uniformly is no cause at all ; and if we are
looking for the presuppositions of inductive inference it is plain that the only con
nexions whose existence would justify such inference are uniform connexions"
(P- 376)-

'2 Logic, ii., p. 19. Mr. Joseph makes a similar mistake about the verb produce :
" to say that anything may produce anything is to empty the verb ' produce ' of all
its meaning. For the causal relation is a necessary relation, such that if you have
one thing you must have another. To add that it does not matter what the other
is, destroys the force of the must " (p. 374). No doubt it destroys the force of the
"must"; but surely "must" is different from "produce," and this again from
" necessarily produce ".

74 THE SCIENCE OF LOGIC

sciousness of our own free volitional activity that we derive the notion of
efficiency in the first instance. Efficiency we conceive as positive influence in
the production of changes or effects by the exertion of power or force. The
earliest efficient causality of which we become aware is our own free efficient
causality. Then we come to conceive external nature as also endowed with
powers or forces, as efficient in the production of changes or effects. Of course
there have been and are philosophers who maintain that belief in real efficiency
in nature is an illusion ; and some have extended their denial even to the
domain of mind as well. Occasionalists take up this attitude on the ground
that efficient causality is essentially an attribute of the Creator, incom
municable to the creature. This view does not concern us here. Our present
purpose is merely to emphasize an obvious distinction between the notion of
efficient cause — whether free or necessary— and the notion of uniform con
nexion — whether of coexistence or sequence — between phenomena ; and to
point out that it is exclusively to the latter concept Empiricists apply the terms
" causation " or " causality ".

For the rest, as far as the theory of physical induction is concerned, this
later usage is not without its conveniences ; for in the first place, it is regularity,
uniformity, invariability of the connexion between physical causes and their
effects, that forms the real objective ground of our generalizations and inferences
about them : 1 not the inner nature of that connexion itself. And secondly,
I if the physical scientist sets up as his ideal the discovery of the perceptible ante
cedents, or groups of antecedents, which are sufficient and indispensable for the
production of certain phenomena — so as to be able to apply this knowledge in
bringing such phenomena about— as in engineering and the other applied
sciences— the ideal is a perfectly legitimate one.2 Only, if he is himself thus con
tent with the discovery of proximate, perceptible antecedents, he must not deny
l the possibility of prosecuting the search for remoter, non-perceptible agencies.3
And if he bestows on those visible groups of" invariable and unconditional ante
cedents " the title of "causes," we need not object to this — for they are de
facto " causes,"— though we have, perhaps, some reason to complain that he is
changing the traditional meaning of an important term without sufficient justifica
tion : even were there no such things in existence as causes in the traditional
sense of the term, he would not refute the traditional belief by merely changing
the definition of the name.

We agree with Mr. Joseph that the freedom of the human will is a difficult
problem, not to be argued here.4 And the same may be said of " efficiency ".
But to deny to free will the title of " cause " does not solve the problem or
prove free will to be a fiction. At all events men generally believe that they
are free agents, and that they freely " cause " or '•'•produce " effects. In the
face of this fact we see no adequate reason to justify the logician in asserting
absolutely and without qualification that " causa! connexions are necessary and
universal," or that " to assert causation is to assert uniformity of connexion ".6
The logician must take into account not merely the domain of physical nature,

lCf. VENN, Empirical Logic, pp. 50, 51, 93; MILL, Logic, iii., v., § 2.

"Cf. JOYCE, op. cit., p. 223.

. 3" I premise, then, that when ... I speak of the cause of any phenomenon,

^ I do not mean a cause which is not itself a phenomenon." — MILL, Logic, iii., v., § 2.

*op. cit., p. 373. *ibid., p. 375 (italics ours).

CONCEPTS OF " REASON " AND " CA USE " 75

but likewise the domain of human activity (201). Nor should he identify
physical science with science simply : " If the non-mechanical conditions upon
which physical changes depend (supposing that such there are) cannot be as
certained and formulated in a way which enables physical science to take ac
count of them, it will treat them as non-existent. It is of no use to regard a factor,
whose mode of action is unascertainable. It must remain for science — what the
will is upon one theory of human freedom — a source of purely incalculable and
to it irrational interference. But irrational interference is just what cannot be
supposed to occur. No doubt an interference which admits an explanation
according to law is not irrational ; but if the law is unascertainable, it is as
good as irrational. And this attitude of physical science has the practical justi
fication, that if events are once admitted to occur in the material order whose
conditions are unascertainable within that order, there is no point at which we
can draw the line. Only by assuming that it can explain everything is it possible
to find out how much it can explain in physical terms." 1 For the credit of
physical science itself we should be sorry to find any of its students claim such
pretensions for it as the author here attempts to justify (201). The physical
scientist may, of course, legitimately abstract from the existence of " non-
mechanical conditions," but he may not gratuitously deny their existence.
Surely, too, a " factor " may be " unascertainable," in the sense of being
" incalculable " in terms of material atoms and motion, may not admit of
" explanation according to " mechanical " law," and yet need not be, or
be called, " irrational," or " as good as irrational ". Is that alone "rational "
which is " mechanical " ? or is there no " law," no " explanation," for what
is not mechanical ? Surely this is a vast and gratuitous assumption for
anyone to make, whether in the name of physical science or on any other
pretext. We fail to see why the physical scientist must deny that " events "
may and do " occur in the material order whose conditions are unascertainable
within that order ". The man who ventures on such a denial would evince
more daring than science. Finally, can science " find out how much it can
explain " only " by assuming that it can explain everything " ? Again we
must confess our failure to see the necessity of any such extraordinary
assumption.

Bearing those few cautions in mind, we may now glance at the growth of
some prevalent views about physical causality.

219. THE SENSIST OR EMPIRICAL VIEW OF CAUSALITY:
MILL'S TEACHING.— John Locke (1632-1704) had taught that
causality, or the power to produce change, was not " contained
in the real existence of things, but . . . extraneous and super
induced " — i.e. by the consideration of the mind. But causality
in things seems to be as real as their substantiality, nay, as their
very existence. Accordingly, either causality is real or all
reality is simply a subjectively fabricated idea. The latter alter
native was practically accepted by David Hume (1711-1776),
who reduced all reality to a series of subjective feelings or states

lop. cit., p. 386.

76 THE SCIENCE OF LOGIC

of consciousness ; causality thus becoming a mere feeling of ex
pectation of invariable succession in certain of those states — a
conviction or belief resulting from the association of repeated
experiences.

Though some of Hume's followers renounced the subjectivity
of this view, all alike clung to the notion of invariable sequence of
phenomena in time as constituting the essence of causality. " The
cause" [of any physical fact, event, phenomenon], writes John
Stuart Mill1 (1806-1873) "is the sum total of the conditions,
positive and negative taken together . . . which being realized,
the consequent invariably follows. . . . The negative conditions
. . . may be all summed up under one head, namely, the absence
of preventing or counteracting causes." Here we have the
cause of a phenomenon described as that total group of antecedents
which, whenever it is realized, is always followed by that pheno
menon.

But day is invariably followed by night ; yet we do not call
it the " cause " of night. Nor do we call night the " cause " of
day, though it has been invariably followed by day. This is so,
Mill goes on to say, because the 'sequence here is not absolutely
or unconditionally invariable : it is invariable only conditionally
upon the conduct or activity of other things — upon the rising and
setting of the sun in the case contemplated. But invariable
sequence is not causality, he tells us, unless the invariability arises
wholly and entirely from the nature of the phenomena themselves,
is unconditioned by anything extrinsic to the latter, is altogether
independent of "whatever supposition we may make with regard
to other things," and will therefore obtain "under all imaginable
circumstances " : that is, of course, " as long as the present con
stitution of things " 2 endures. Such kind of invariable sequence
he terms " unconditional " ; 3 and he then goes on to give his final
and scientifically exact definition of " the cause of a phenomenon "
as " the antecedent or concurrence of antecedents on which it
[the phenomenon] is invariably and unconditionally consequent ".

By thus defining causation as sequence which is invariable, not

1 Logic, III., v., § 3. Mill properly points out that popular usage generally fixes
on some prominent one among those antecedents and applies to it exclusively the title
of " cause ".

2 By this expression Mill tells us that he means " the ultimate laws of nature
(whatever they may be) as distinguished from the derivative laws and from the col
locations ". — op. dt., III., v., § 6.

3 Notwithstanding the condition just set down about the permanence of the
" present constitution of things ".

CONCEPTS OF " REASON " AND " CA USE " 77

by reason of any extrinsic conditions, but unconditionally and by
reason of the nature of the phenomena themselves which constitute
the sequence, Mill evidently intended to convey that an antecedent,
in order to be a "cause," must have a "necessary" connexion
with its consequent. This conception of the "cause" of a
phenomenon — as something which, of itself, of its own nature,
and not by reason of any extrinsic conditions, is invariably
followed by that phenomenon — is precisely what had suggested
the traditional notion of a necessary as opposed to a free cause :
we are prompted to regard a cause as necessarily productive of an
effect by observing it to be always and in all circumstances
followed by that effect. By making the invariability of the con
nexion independent of all other conditions, and thus, as the only
alternative, dependent on the nature of the connected phenomena
themselves, Mill believed that he was giving intelligible ex
pression to

" what writers mean when they say that the notion of cause involves the idea of
necessity. If there be any meaning which confessedly belongs to the term
necessity, it is unconditionalness. That which is necessary, that which must be,
means that which will be, whatever supposition we may make in regard to all
other things. The succession of day and night evidently is not necessary in
this sense. It is conditional on the occurrence of other antecedents. That
which will be followed by a given consequent when, and only when, some
third circumstance also exists, is not the cause, even though no case should
ever have occurred in which the phenomenon took place without it. ... Let
me add that the antecedent which is only conditionally invariable, is not the
invariable antecedent [in the full sense of absolutely invariable — in the future as
in the past ?]. Though a fact may in experience have always been followed by
another fact, yet if the remainder of our experience teaches us that it might
not always be so followed, or if the experience itself is such as leaves room for a
possibility that the known cases may not correctly represent all possible cases,
the hitherto invariable antecedent is not accounted the cause ; but why ?
Because we are not sure that it is the [really, absolutely, unconditionally] in
variable antecedent "-1

But the idea of " necessity " is not the idea of actually uni
form and unvaried sequence, though it is derived from our ex
perience of the latter ; or of invariable sequence, except we take
invariable to mean not only that which has not varied and does
not and will not vary, but that which cannot vary. And in
variability in this latter sense need not be at all unconditional in
order to be described as " necessity," for the " necessity " itself
may conceivably be conditional : we can quite conceive a sequence

i ibid., 6.

78 THE SCIENCE OF LOGIC

which must remain unaltered so long as certain conditions are ful
filled. This, in fact, is the only necessity experience warrants us
in attributing to the sequences of nature ; and, as we shall
presently see, Mill's so-called " unconditional " invariability re
mained always ultimately " conditional ".

How, then, it may be asked, from actual, limited experience of unvaried
sequence in the past, can we get the idea of a sequence that is invariable — i.e.
which " cannot " vary, which is " necessary " ? Let us first recall the tradi
tional Scholastic account of " physical necessity," which is simple and intelli
gible. " Necessity " may be either intellectual, hypothetical, abstract,
connecting possible essences together in thought ; or it may be volitional,
categorical, concrete, connecting actual things or occurrences together in
reality. With this latter we are concerned here. When we speak of " that
which must be " in reference to things or events, when we say that one thing
must follow another, we can only mean that they are so constituted and
circumstanced that by their very nature or constitution, and collocation, they
cannot help following each other.1 Whatever Mill may say, no mere addition
or multiplication of " was " and " is " and " will be " can ever generate an
absolute or unconditional " must be ". What is there, then, in the observed
unvaried uniformity of nature in the past, to warrant us in thinking not only
that it will, but that it must, continue unvaried ? There is this : there is abundant
evidence (of which the fact of observed uniformity itself forms a part) to warrant
us in concluding with certitude that nature is the work of an All-Wise Creator
and Ruler, who has so constituted and arranged its agencies that they will and
must continue to exist and act, each in its own fixed, uniform way, as long as
He chooses in His wisdom to preserve and sustain it in existence. Such is
the uniformity, invariability, necessity, we ascribe to physical agencies : condi
tional on the Will of an All-Wise, All-Ruling Providence.2 There is the ulti
mate rational basis which analysis of human experience reveals for wx physical,
conditional certitude about the general laws of physical science.

Now let us observe and contrast the alternative offered by the empiricist
philosophy of Mill and his school. The physical cause of a phenomenon, he
writes, is that which has always " been followed by " that phenomenon in past
experience, provided this experience does not leave any " room for a pos
sibility that the known cases may not correctly represent all possible cases ".
But if, as Mill's own philosophy teaches, we have no faculties of knowledge
beyond our external and internal senses, whose only objects are sense-
phenomena, associated, compounded, and otherwise modified in consciousness,
how can the combination of past and present sense experience give us any

1 We abstract here, for the sake of simplicity, from the conditional necessity,
called moral obligation, to which the conduct of free, responsible agents is subject. To
these the Creator has given the power to act as they choose ; but He imposes on
them a necessity by which they must (freely choose to) act in a certain way if they
are to attain their end. But every non-free cause in animal, vegetable, and inor
ganic creation, He has endowed with such a nature and constitution as categorically
directs it to attain the end He has freely intended it to reach.

2 For a fuller development of these views on the necessity of physical laws and
causes, cf. infra, Chap. IV., 224.

CONCEPTS OF " REASON " AND " CA USE » 79

degree or kind of certitude, anything beyond a mere feeling of expectation
that " all possible cases " will resemble the observed cases ? And even for
this feeling of expectation Mill can offer us no rational ground whatsoever.
He states that our actual experience enables us somehow to make up our
minds that a given observed antecedent of a phenomenon will continue to be
the antecedent of the latter unconditionally : which means " whatever sup
position we may make about other things," or " under all imaginable circum
stances ". But this he immediately limits and qualifies by saying that the
antecedent will continue so only " as long as the present constitution of
things endures" or as long as, and on condition that, " the ultimate laws of
nature (whatever they may be)," do not -vary. So, after all, the "uncondi
tional " invariability turns out to be conditional. Our sense experience of
an unvaried sequence only enables us, therefore, to believe that the latter
will continue unvaried, z/and as long as " the present constitution of things,"
" the ultimate laws of nature," will remain unaltered. And what rational
ground\&.vt we, according to Mill, for believing that " the present constitution
of things " will continue stable, and their " ultimate laws " unaltered ? He
does not tell us ; and for a good reason : his philosophy affords none. It
limits our knowledge to phenomena of sense ; it is agnostic : it informs us that
we can know facts, but nothing about the inner nature and ultimate causes of
those facts. And thus the empirical theory of induction, as of knowledge
generally, destroys all certitude by rearing the whole edifice of physical science
on the basis of an underlying confession of helpless and hopeless ignorance.

In giving his final description of " cause " as the " uncondition
ally " invariable antecedent, Mill explained that the " cause "
must be not merely the hitherto invariable antecedent, but some
thing which is the antecedent in "all possible cases". By this
he has been commonly interpreted to mean that the " cause " in
in the strict sense is the antecedent (or group of antecedents)
which is not merely " sufficient " 1 but " indispensable " for the ap
pearance of the consequent : not only the antecedent which is
invariably followed by the consequent in question, but by which
alone the consequent is invariably preceded : so that the invaria
bility is on both sides, the relation is a reciprocal one, and
inference can proceed from effect to cause as well as from cause
to effect.

Thus we may distinguish, in Mill's account of causality, (i)
the looser scientific concept of "cause" as the antecedent (or
group of antecedents) which, when present, is always followed
by a certain consequent ; (2) the still looser popular concept of
" cause " as denoting some one prominent element of that group
(abstracting from the others) ; (3) the stricter and more exact

1 In the sense of " necessitating ". This is the meaning commonly attached to
the word in regard to physical causes. A free cause may be " sufficient " (in the
ordinary sense of the word) to produce an effect, and yet not necessitate that effect.

8o THE SCIENCE OF LOGIC

scientific concept of " cause " as the antecedent which is not
only always followed by the consequent in question, but which
is the only antecedent so followed : not only the sufficient, but
the indispensable, antecedent of that consequent.1

220. CAUSALITY, SEQUENCE IN TIME AND CONTIGUITY IN
SPACE. — Mill's account is intelligible so far as it goes. He has,
of course, never succeeded in assigning any ultimate rational ex
planation of the fact that natural causes and their .effects are
connected in the uniform, unchanging, " invariable " manner in
dicated by him. Apart from this defect, however, which is due
to his empiricist theory of knowledge, there is the erroneous im
plication that time sequence is essential to causality, that two
phenomena cannot be related as cause and effect unless they
succeed each other in time.

Now, efficient physical causality does not necessarily imply
that the cause must totally precede the effect in time. Even
popular thought, which seizes on one prominent, partial element
in the total cause — often a remote element — and on a similar
element in the effect, does not regard " cause " and " effect " as
separate, successive events, but only as distinct : the immediate
cause and the immediate effect are always thought of as con
nected. The link connecting them — the causation, action, change,
or process, as it is variously called — goes on in time and occupies
time. The immediate cause, therefore, cannot entirely precede,
but must also coexist with, the immediate effect. The producing
cause and the produced effect must be simultaneous, for they are

1 C/. JOSEPH, op. cit., pp. 64, 65 — " When we call one thing [i.e. kind of thing]
the cause of another, the real relation between them is not always the same ... we
say that molecular motion is the cause of heat, that the heat of the sun is the cause
of growth, that starvation is sometimes the cause of death, that jealousy is a fre
quent cause of crime. We should in the first case maintain that the cause and
effect are reciprocally necessary ; no heat without molecular motion and no molecular
motio^ without heat. In the second the effect cannot exist without the cause,
but the cause may exist without the effect; for the sun shines on the moon but
nothing grows there. In the third, the cause cannot exist without the effect, for
starvation must produce death, but the effect may exist without the cause, since
death need not have been produced by starvation. In the fourth case we can
have the cause without the effect, and also the effect without the cause ; for jealousy
may exist without producing crime, and crime may occur without the motive of
jealousy. It is plain, then, that we do not always mean the same thing by our
words, when we say that two things are related as cause and effect ; and any one
who would classify and name the various modes in which two things maybe causally
related would do a great service to clear thinking." And the author adds : " that is
the sort of service that Aristotle attempted in distinguishing the heads of predic-
ables ". C/. also op. cit., c. xxii.

CONCEP TS OF « RE A SON " A ND " CA USE " 8 1

correlative. If the cause ceases to act, then the effect ceases to be
produced; for the "action" (actio, facere] of the cause and the
" production " (passio, fieri) of the effect are one and the same
process of real change. Hence the Scholastic axiom " Cessante
causa, cessat effectus ".

The act of " taking poison " may have ceased long before
" death " occurs ; but the poison, once introduced into the
system, continues to exist and to operate, effecting changes
which in turn cause other changes, until finally a condition of the
organism is reached, which is so striking, familiar, and significant
that it has received a special title to indicate it, viz. death. The
first " act," and the final " state " or effect, are, therefore, connected
by a continuous process of natural causation, each stage of which
is both an effect (of the preceding one) and a cause (of the subse
quent one) ; and wherever we draw a line of distinction in this
process of change, the state of things on the one side of the line
is the immediate cause, of which the contiguous state on the other
side is the immediate effect.

" Cause and effect," writes Dr. Mellone,1 " are divided by a simple mathe
matical line — a line destitute of breadth — which is thrown by our thought
across the current of events ; on one side we have the cause, on the other the
effect. There is no pause in reality ; the whole process is continuous ; the
immediate cause conies into full action only at the very moment when the
effect begins to be produced. The point to be borne in mind is the continuity
of cause and effect."

The whole process of change in the occurrence of any physical
phenomenon is, therefore, continuous : there is one continued
" motus " or motion throughout : this motion may be regarded
either from the point of view of its origin, or from that of its
termination : it will be called action (" actio ") when looked at from
the side of the cause or agens from which it originates, and "passio "
when looked at from the side of the effect or pattens in which
it terminates. The Scholastics marked and emphasized their
appreciation of the unity and continuity of the whole process by
crystallizing their view in the dictum " Actio et passio sunt idem
numero motus" : " Acting" and " being acted on " are one and the
same real "motion," looked at from different standpoints.

But the Scholastics were at N the same time careful not to
confound the actual process of change (" fieri ") either with the
efficient causes themselves on the one hand, or with the stable

1 op. dt., p. 273.
VOL. II. 6

82 THE SCIENCE OF LOGIC

result of the change (the effect "in facto esse"} on the other.
They rightly distinguished in every such process the (material)
substances or agents at work (substantial causes), the forces or
powers (proximate principles of action) through which those
agents or causes act, and the action or process of change itself
(218). They distinguished, furthermore, between the extrinsic
causes (efficient andjinaf), which they called " causes of the actual
change" (i.e. of the "fieri" ex production of the effect), and the
intrinsic causes (formal and material] which they called (con
stitutive) causes of the produced result or effect, in its completed
state (" in facto esse ".) *

Ignoring those distinctions, modern writers have fallen into the error of
actually identifying the " efficient cause " with its " effect," by regarding
each as a mere aspect of the process of change itself, and this latter, ap
parently, as the sole reality. For example, Professor Welton2 arrives at this
conclusion : " Cause and effect are not two but one. That they are in
separable is indeed recognized by the relativity of the very terms themselves.
A cause without an effect or an effect without a cause is a contradiction in
terms and unthinkable. But we must go farther and say that in content they
are absolutely identical. It is only in form that they can be distinguished
and then we may speak of the one as determining and of the other as deter
mined. Thus the combination of hydrogen and oxygen in the quantitative
ratio of two to one determines that the effect shall be water, and the character
of that effect is determined by the character of the elements which are com
bined, but the combined elements and the water are one and the same
identical substance, and this substance is the content both of the cause and of
the effect."

This is indeed going very far ; much too far. To identify the efficient
cause with its effect, the "producer" with the "produced," is not only setting
popular thought and belief at defiance, but even espousing the implicit contra
diction that an effect can produce itself.

When, therefore, we come to reflect on the immediateness of the cause to
the effect, we see that while the scientist must indeed aim at grasping the former
as closely as possible to the latter, in order to be sure of including every indis
pensable factor in the former, and so attaining as closely as he may to the ideal
of a reciprocal causal relation, he must guard equally against identifying the
cause with the effect, under pain of making all experimental search for " causes "
meaningless and impossible. For, if the effect is identical with the cause, then
when we know the effect we know the cause, and there can be no meaning in
searching for the latter. Our " reciprocal relation " appears to have become
a mere tautology ; " The statement that cause and effect are ' identical ' . . .
becomes an extravagant paradox if taken seriously and applied to any particu
lar case of causation determined by scientific experiment ".3

1 C/. ST. THOMAS, Summa Theol., i., q. 101, Art. i \-apud JOYCE, op. cit.t p.
248.

*Op. cit. ii., p. 25. * MELLONB, op. ctt., p. 274.

CONCEPTS OF " REASON " AND " CA USE " 83

This confusion of cause with effect arises from losing sight of the categoiy
of substance, and of the all-important Scholastic distinctions between agent and
action, and between extrinsic (efficient) and intrinsic (formal and material)
causes l (216, 218). These distinctions are real; they are in the reality ; they
are not merely mental or logical, different ways of regarding one and the same
reality. In all processes of physical change the formal and material causes
are intrinsic to, and identical with, the interacting agents, because they con
stitute these latter. In the change by which oxygen and hydrogen produce
water, the two former are materially identical with the latter, but then they
differ formally (in their " formal " or " specifying " causes) from the latter and
from each other. " The combined elements and the water are one and the
same identical substance " ; but if they are, they are really different from the
separate elements, for these on combining, on becoming water, on assuming
the " form " or " specifying principle " of water, lost the " forms " of oxygen
and hydrogen respectively. If the water were really identical with the oxygen
and hydrogen, the change would not have been real but merely mental : that
is to say, the processes of external nature would not be real but illusory : the
only real change taking place would be the change involved in the logical
process of the thinking mind. And this, in fact, is what the advocates of
Hegelian idealism profess to believe (215).

Similarly, physical causes occupy space and act in space, but that con
tiguity in space, direct or indiiect contact, is essential to their activity, is not
clearly evident. That there is and must be a connexion of some sort, in
reality as well as in thought, between cause and effect, is undeniable. But
is actio in distans, i.e. across empty space or vacuum, metaphysically 01
physically impossible ? We know too little about the nature of matter, space,
and material action or motion, to give a categorical and decided answer to either
part of the question. " How can a body act where it is not ? " Professor Wei-
ton repeats the old puzzling query,2 and hazards an answer. But would it not
be as well honestly to confess our ignorance of the " how " — remembering
that this does not prove impossibility — as to say that the body is there, where
its influence is felt, "in one very true and important sense of its reality " —
in the sense of exerting influence there — while it is not present there, but
absent from there, and present in another place, " in another sense of its
reality — the sense in which reality is identified with visible and tangible
form and tangible resistance "? What then is space? — if different "senses"
or " aspects " of a body's reality may be in different parts of it ? The author
does not inform us ; though, a few pages further on,3 he seems to reduce all
physical efficient activity to local motion, and this latter to change of " spatial
relations ". This reduction of even qualitative and substantial changes in
physical nature to mechanical or local change has only its simplicity to

1 Cf. JOSEPH, Logic, p. 451. 2o/>. cit., pp. 20, 21.

3 ibid., p. 24 : " When it is said in this connexion [in mechanics, regarding the
conservation of energy] that 'the cause equals the effect,' the 'cause' spoken
of is not a thing but the efficient action of a thing, and this action reduces itself to its
permanent attributes in a certain spatial relation to the object on which it acts ".
The efficient action of a physical cause is thus analysed into certain permanent at
tributes of that cause, plus certain spatial relations between it and the "object"
upon which it is conceived to " act ".

6*

84 THE SCIENCE OF LOGIC

recommend it (217). It explains nothing adequately ; and it is in fact rejected
as inadequate by the author himself in a subsequent chapter of his logic.1

221. " PLURALITY OF CAUSES " : " RECIPROCAL " AND " NON-
RECIPROCAL" CAUSAL RELATIONS. — We have seen, so far, that
the term " cause " has a multiplicity of kindred meanings : that
besides the " formal " and " material " causes, or intrinsic consti
tutive principles of the visible, material agencies in nature, and
besides the " final " causes, " ends " or " purposes " for which
these act, there are also these agents themselves, which we have
called ' ' efficient " causes. We have distinguished between these
efficient causes and the " action " or " motion " or " process " by
which they produce their effects. We have also distinguished
between efficient causes that are " free " or " self-determining "
and efficient causes that are " necessary " or " necessitating " ; and
we have seen that we can lay down general propositions about
the mode of operation of efficient causes throughout space and
time only in so far as we are convinced that those causes
act uniformly beyond the range of our own actual sense ex
perience (218); observing that this uniformity, though not
absent from the domain of free causes, is much more prevalent
and reliable in the domain of " necessary " causes — that is, in the
physical sciences, with which induction is mainly concerned (218,
cf. 223). We have seen too that, generally speaking, every class
or kind of phenomenon in nature results from the convergence
and combination of numerous influences, agencies, and condi
tions, which are collectively "sufficient" (or "necessitating")
and severally "indispensable" for the production of that special
kind of phenomenon (216). The multiplicity and variety of these
conditions, and their inseparable connexion with conditions not
needed for the production of this kind of phenomenon, render
it difficult for science to sift out and group together as the
" cause" of the phenomenon, just those influences and those only
which are sufficient and indispensable for its production. Com
bined with this difficulty of bringing to light the " cause" in this
narrower and stricter sense of reciprocal cause (cf. 213), we have
the consideration that from the practical point of view — i.e. of
producing or preventing effects — acquaintance with a plurality
of alternative " causes," in the wider sense of " sufficient " though
not "indispensable" modes of producing that sort of effect, is
more important and more desirable than an exact knowledge of
1 op. cit., pp. 209, 210. Cf. JOSEPH, op. cit., p. 382.

CONCEPTS OF "REASON" AND "CAUSE" 85

the one "reciprocal" or "commensurate" cause of that effect.
Hence the question arises, whether Science ought to aim at the
discovery of reciprocating causal relations, or merely of causal
relations such that although the "cause" will necessitate the
" effect," this latter will not necessitate the former, but admit of
a " Plurality of Causes " (cf. 138).

If we take a " physical "or " necessary " " cause " in the
popular sense of some prominent or striking event which, when
it happens, is always followed by another remarkable event (the
"effect"), it will be evident that though the same natural cause,
acting in similar circumstances (e.g. administering deadly poison),
always produces the same effect (e.g. death), nevertheless the same
effect (death) need not be always produced by the same cause
(poison) : that although " effect " can be inferred from " cause "-
"posita causa, ponitur effectus" — still the converse, " cause " from
" effect " — "posito ejfectu, ponitur causa " — cannot be lawfully in
ferred. And the reasdn is that in this sense of the term " cause,"
the same " effect " may be produced by different " causes " : that one
and the same effect — death, for example — may be due to any
one or more of an indefinite multitude of " causes ". We speak
popularly of an agency as the "natural cause" of a given result
or effect, provided that this agency be sufficient (or necessitating] —
even though it be not indispensable, in the sense of being the only
possible agency — for the production of such an effect. And formal
logic, recognizing this mode of thought and expression, and ap
plying the Law of Parsimony (94), prohibits the simple conver
sion of the conditional proposition, which connects cause with
effect as logical antecedent with consequent, as reciprocal (140).
If, therefore, we take the terms "physical cause" and "effect" in
this practical meaning, the former as that which always and
necessarily produces the latter, and the latter as that which is
produced, no doubt, by the former, but which is or may be produced
otherwise as well, then it will be true to say that one and the
same " effect " may have a plurality of " causes," though one and
the same (natural or necessary) " cause " cannot have a plurality
of " effects "-1

1 Evidently, the co-operation or " composition " of many partial causes may
contribute to the production of one single effect : e.g. a person's death may be due
to a complication of diseases no single one of which would separately have proved
fatal (cf. 244). But " composition " of (partial) causes is quite a different thing from
"plurality of causes". The latter means that one and the same effect (death)
may, in different instances, be produced by entirely different total causes (poison,
shooting, smallpox, old age, etc.).

86 THE SCIENCE OF LOGIC

On the other hand, were we to understand by the " cause " of
a given kind of event not any and every factor (or group of fac
tors) capable of producing it, but that precise factor (or group),
and that only, which (being present in all modes of producing it)
is itself capable, and alone capable, of producing the event, then
this kind of event can be produced by that one " cause," and by
it alone. In other words, no event can have a "plurality of
causes " in this stricter sense of the term " cause V The doctrine
that the same effect can have a " plurality of causes " holds good
"as long as the 'cause* is understood in the popular way. The
plurality disappears before any exact scientific investigation"?
The subtraction of any factor from the " total cause " in this
strict scientific sense, or the addition of any new factor to it, must
necessarily modify the effect : no other factors or combinations
of factors .could produce this sort of effect exactly and identically.
This is but a simple application of the principle of identity. E
is an effect whose total cause (or, the totality of whose sufficient
and indispensable antecedents) is a + b + c. But, if it is so, it
cannot at the same time, being and remaining identical with it
self, be the result of a + b + c + d, or of a + b + d, or of a + 6,
or of m + b + y, or of any other conceivable combination.3

222. SCIENCE AND THE DISCOVERY OF "CAUSES" AND
" LAWS ". — In popular thought, therefore, the notion of " physical
cause " usually includes elements not indispensable to the pro
duction of the effect, though the notion of the " effect " does not
include any element which is not necessitated by some element
or other of the cause.4 The reason for this peculiar difference

1 The mediaeval Scholastics discussed " plurality of causes " in connexion
chiefly with the individual effect, and the principle or ground of its individuation ;
proposing the problem in terms like these : " Would Alexander the Great have been
the same individual had he been born of other parents than Philip and Olympia ? "
Their answer was usually in the negative. C/. ZIGLIARA, Ontologia (46), vii.

2MELLONE, op. cit., p. 277. 3Cf. JOSEPH, op. cit., pp. 377-8.

4 We say "usually," for there are evidences that the popular mind is quite
familiar with some applications of the scientific conception itself: for instance, with
the procedure at coroners' inquests, and with the convictions of criminals on circum
stantial evidence. " The popular idea of the non-reciprocal character of the axiom
of causation," writes Professor Welton, " is due to the fact that the ' cause ' is much
more frequently analysed than the ' effect ' — using those words in the popular
sense of temporal antecedent and consequent phenomena. Thus, when Mill says
in support of his doctrine of the Plurality of Causes, ' Many causes may produce
death' (op. cit., Bk. III., ch. x., § i), he is obviously speaking very loosely. Death
is not the whole effect. Moreover, death can never be death in general, but only
some one particular kind of death, and the death caused by a bullet through the
heart is not the same kind of death as that due to drowning, and both again differ

CONCEPTS OF " REASON " AND « CA USE » 87

between "cause" and "effect," in the popular sense of these
terms, is not far to seek : it arises from the practical attitude of
people in real life towards causality. When they want to pro
duce some one given kind of effect (death, for example), it may
matter little to them what particular, individual farm or character
this effect may assume, but it will evidently be of the greatest
importance for them to have a large number of distinct alter
native, individual " causes," or modes of producing the generic
effect, to choose from. Hence, while people regard the " effect "
in the abstract, contenting themselves with one generic name
for it in all its varied individual manifestations, and care little
to distinguish between these latter in the concrete, they behave
in quite the opposite way towards the " cause " : noting and dis
tinguishing carefully, and often naming separately, its various
concrete, individual modes or forms, and calling each of these a

" The reason," writes Dr. Venn, " why we look out for a cause is not to
gratify any feeling of curiosity, at least not primarily, but because we want to
produce some particular effect. . . . What the savage mostly wants to do is to
produce something or to avert something, not to account for a thing which has
already happened. What interests him is to know how to kill somebody, not
to know how somebody has been killed. Of course the past must interest him
to some extent, because what has happened once may come to pass again, but
this is a comparatively indirect or remote reference. What holds good of the
savage does so also, though to a somewhat less extent, of the great majority
of ordinary people : the explanation of the past will rationally be far sub
ordinate in interest to the prediction of the future. . . . When we want to
explain a fact an offer of several alternative solutions affords very little help.
. . . The scientific student of early culture vexes his mind to ascertain in
which of various possible ways fire was first produced, and employed by man ;
whether by lightning, by friction of boughs of trees, by sparks from flint chips,
or so forth. But for those whose only care was to make a fire when they
wanted it, such plurality of causes was all in their favour." 1

And Dr. Mellone thus happily illustrates the same truth : " Sometimes
what is practically most important is scientifically least important : it may be of
great importance to know what circumstances will produce an event without
knowing how they produce it. For instance, it may be of importance to clear

from death by poison, and so on. The effect as a totality differs in each case from
that in every other case, and the very existence of the enquiries of coroners' in
quests is a practical assertion of even popular belief in the reciprocity of the causal
relation, as it assumes that by a careful analysis of the total ' effect ' the cause is
arrived at, and this assumption can be only justified on the ground that this totality
could have had but one cause." — WELTON, op. cit.t pp. 27-8. Cf. JOSEPH, op. cit.,
pp. 446-47.

1 VENN, Empirical Logic, pp. 56, 63, 64.

88 THE SCIENCE OF LOGIC

the premises of rats ; traps, strychnine, phosphorus, and terriers are various
' causes ' between which we must choose : but we do not as a rule hold post
mortems on dead rats." 1

What Dr. Venn says of the savage and of the ordinary man
is also largely true of the scientist : he, too, has a practical as
well as a speculative aim in his researches. It is not his sole
concern to explain an effect by bringing to light its necessitating
and indispensable antecedents, i.e. its reciprocal or commensurate
cause : he also wants to discover all the alternative combinations
of existing agencies and conditions which embody the indispen
sable factors (in inseparable conjunction, perhaps, with many
superfluous or indifferent elements) — combinations which con
stitute so many practical alternative modes of producing the
effect in question.

" Properly speaking," writes Mr. Joseph, " to give the cause of anything is
to give everything necessary, and nothing superfluous, to its existence. Never
theless we should often defeat our ends if we gave precisely this ; if our object
in seeking the cause of a thing is that we may be able to produce or prevent it,
and if something is necessary to its existence which is a property of an object
otherwise superfluous, it would be of no use specifying the property necessary
unless we specified the otherwise superfluous object in which it was found."
This the author illustrates by remarking : " It may be the texture of the
pumice-stone that fits it to remove ink-stains from the skin ; but it would be of
more use to tell a man with inky fingers to get a piece of pumice-stone, than
to give him a description of the fineness of texture which would render a body
capable of making his fingers clean " 3. Similarly, with regard to the
" elasticity " of the air (or other elastic medium) as a cause of the transmission
of sound : " We want to know what possessed of the necessary elasticity is
present when we hear at a distance ; nor could anyone without knowing that
prevent the transmission of sound by removing the elastic medium ; for he
would not know what to remove ".3

In so far, then, as the scientist has this practical aim before
him, he will rest content with discovering " causes " in the wider
sense of this term — the sense in which an effect can have a
" plurality of causes," i.e. of alternative modes in which it may
be produced. Under the influence of this " practical " view of
inductive science, Dr. Venn regards this wider conception of
cause as " the most serviceable for purposes of inductive logic ".*
And in this he is undoubtedly right. But he goes farther, and
asserts that the stricter concept of cause — that which makes the
causal relation reciprocal —

*ofi. cit., p. 275 ; cf. JOSEPH, Logic, p. 446. *ibid., n.

8 ibid, * Empirical Logic, p. 71.

CONCEPTS OF "REASON" AND "CAUSE" 89

" necessarily results in rendering it useless for any purposes of inference ".
" Make it perfectly complete and accurate," he continues, " and you make it at
once hypothetical and the statement of what is to all intents and purposes a
mere identity." l [Such an over- refinement of the law of causation] " renders
that law suitable only for hypothetical conclusions, in other words, renders it
useless for positive inductions about matters of fact ". a

Now, it is of course true that if we make our concepts of
"cause "and "effect" so comprehensive and closely connected
as to involve each other reciprocally, we are not likely to get
beyond the hypothetical " If A then C and vice versa" to the
categorical "This A will always involve this C and vice versa".
It is true, too, that knowledge of the one immediate, indispensable
" cause " of C is of less practical utility than knowledge of the
numerous alternative groups of antecedents in which this one
" cause" is operative. But it is likewise true that if we want a
scientific, even though conditional, knowledge of C, a knowledge of
how it is produced, we must try to seize the process at the instant
of the production of C, and to detect — if we can, or as far as we
can — all that is indispensable for its production. In other words,
when our aim is not directly practical — like that of the " savage "
for instance : to compass a person's death in some way or other
— but rather speculative — like that of the coroner, for instance :
to discover how this person's death has been compassed — we must
obviously seek, not for all the alternative ways in which the person,
could have been killed, but for all the factors indispensable to the
way in which this particular person has been killed. So, too,
when we want to explain a kind of result, we must seek, not for
the various modes of producing it in different sets of circumstances,
but for that which is common to all the modes, and which, being
always "sufficient" and always "indispensable," will produce it
in any and every conceivable set of circumstances. For instance,
that "kind" of effect called "death" — that which is common to
all individal instances of death and in virtue of which we call each
of them a " death " — will be scientifically explained by us only
when we have succeeded in discovering what precise factor (or
group of factors) is present in every conceivable mode of pro
ducing " death," as being sufficient and indispensable for its pro
duction. A full scientific knowledge — were such attainable — of
the relation between a " natural " or " necessary " cause and its
effect, would thus show the relation to be reciprocal. One and

1 Empirical Logic, p. 71 (italics ours). 3 ibid., p. 53.

90 THE SCIENCE OF LOGIC

the same genus of effect (e.g. death) can have only one and the
same genus of cause (viz. that generic element which is common
to all species of causes of death, making them all alike destructive
of life) ; one and the same species of effect (e.g. death from small
pox) can have only one and the same species of cause (viz. the
microbe of smallpox) ; any one individual effect (e.g. the death of
Julius Caesar) can (in its individual totality) have had only one
individual (total) cause, viz. that to which it was actually due.1

Now, in the mathematical sciences we establish numerous
universal truths which are reciprocal.2 But is it always possible
to establish reciprocal causal relations in the inductive sciences?
On the contrary, it is rarely possible. Some logicians set it up
as an ideal at which the scientist must always aim. He is told
to commence his scientific investigations by working with the
popular concept of cause, which admits " plurality of causes," and
to try to approximate gradually towards the scientific concept
which excludes plurality. Dr. Mellone's expression of this theory
is clear and accurate. " In the absence of scientific knowledge of
the immediate cause, we have to bear in mind that different
combinations of circumstances may bring about the same event.
Practically we have to begin the investigation by examining those
different combinations of circumstances in which the event is
produced — considering them, at first, as so many different
' causes '. They are not the immediate cause ; but it is operative
in them."* We are to commence, therefore, with the various
distinct modes (" causes " in the popular sense) of producing a
certain kind of effect, and to finish by abstracting what is common
and essential in all of them (the " cause " in the stricter sense).

But this ideal is often unattainable, and, if attained, would be often com
paratively useless and uninstructive ; and this is so because " the phenomenon
under investigation is often highly complex, and subject to all sorts of varia
tion on the different occasions of its occurrence, through variations in the

1 Cf. JOSEPH, op cit., p. 65 : " Whenever science tries to find the cause not of
a particular event, such as the French Revolution (whose cause must be as unique
as that event itself is), but of an event of a kind, such as consumption, or com
mercial crises, it looks in the last resort for a commensurate cause. What is that
exact state or condition of the body, given which it must and without which it can
not be in a consumption ? What are those conditions in a commercial community,
given which there must and without which there cannot be a commercial crisis ? "
The same is true, of course, in regard to the cause of a " particular event " — except
that this is regarded as belonging to the domain of history, not of science, which
is " of the universal ".

3 Cf. JOSEPH, op. cit., pp. 443, supra, 212. 3 MIJLLONE, op. cit., p. 277.

CONCEPTS OF "REASON" AND "CAUSE" 91

objects or events contributing to its production ; not the whole nature of the
objects or events under whose influence it occurs is relevant to its occurrence,
but only certain particular properties or modes of action ; and it is possible
to formulate severally the principles of action involved, from which the joint
result may be seen to follow, where it would not be possible to assign to the
phenomenon any group of concrete objects or events as cause, about which we
could say not only that, given them the phenomenon must be given, but also
that, given the phenomenon, they must have been given too " *. . .

" For example, we may ask what is the cause of the monsoons — that is, of
the regular and periodic winds that blow steadily in certain regions for one
part of the year and for another in the opposite direction ? If we said that
they were due to periodic alterations in the distribution of atmospheric pressure,
it would not be very instructive ; for we really want to know what events
happening in those regions, produce these differences. Yet the events which
contribute to determine the deviation and direction of the monsoons are
numerous and variable. . . ." 2 And these numerous and variable events are
due to the variously combined influences and activities of sun and sea and
land and air and aqueous vapour— among other things. Now, in such a
case as this, to seek for the reciprocating or indispensable " cause " of the
monsoon would be futile. " To give the cause of monsoons, without deficiency
or superfluity, would mean that we must not mention the sun (because only the
heat of its rays is material), nor the sea (because only its fluidity and its power
of giving off vapour concern us, and a lake, if it was big enough, would do as
well), nor any other of the concrete things which act in the way required, but
only their requisite actions." 8 But no one would dream of giving the cause
of the monsoons without mentioning those various agencies ; and in giving
them " we shall have to include in our statement of the cause elements at
least theoretically superfluous ". Shall we, then, rest content with a bare
enumeration of these partly superfluous agencies ; simply stating, in explana
tion of the monsoons, that these are due to the combined influences of sun
and air and land and sea ? No ; something more than this is expected, even
though an exact statement of the " commensurate cause " is not expected.
There is a middle course, a third alternative, which is expected, and it is this :
that we " look for the principles in accordance with which [these] objects [or
agencies] act under certain circumstances ; then we can show that the mon
soon is only the complex result of the action of a number of objects under the
particular circumstances of the case, and in accordance with the principles of
action which our ' laws ' express " 4. In other words, " we alter the form of
our problem. Looking upon the phenomenon as the complex result of many
conditions, we attempt to determine not [merely] what assemblage of objects
or events will produce the result, nor [again, attempt to determine] on what
properties or events therein it depends [the reciprocating cause] ; but what
is the principle of action in \the~\ different objects or events, in virtue of
which some one particular condition necessary to the production of the
phenomenon is realized in them. For the reciprocating cause of a complex
phenomenon we substitute as the object of our search the principle in accord-

1 JOSEPH, op. cit., pp. 445, 446 (italics ours). 3 ibid., p. 444.

3 ibid., p. 445. 4 ibid, (italics ours).

92 THE SCIENCE OF LOGIC

ance with which a certain kind of object or event acts. Our problem is
better expressed as that of discovering laws of nature than causes" J

In explanation of the monsoons, for instance, we are expected " to point
out the difference in the power of the sun at any place produced by the
varying directness of its rays ; how the sea gives off vapour ; how vapour
absorbs part of the heat of the sun's rays ; how the heated water circulates
with the colder ; how the earth absorbs and retains the heat of the sun ; how
air is expanded by heat ; how the principle of atmospheric pressure acts under
conditions of different expansion ; and so forth. Then we can see that if a cer
tain combination of events occurs, a particular complex result must arise ; if the
sun travels from over the surface of the sea to over the interior of a continent,
we shall find monsoons ; for the difference between summer and winter
temperature will in the interior be very great, but on the sea, owing to the
way in which the moisture of the air absorbs part of the heat, and the currents
in the water carry away part, it is not so great ; hence as summer is ending,
the air inland will be hotter and have expanded more than out at sea, as
winter is ending, it will be colder and have contracted more ; so that at one
time the current of air sets inland in accordance with the laws of atmospheric
pressure, and at another time it sets shoreward ".a

Here we have an admirable example of the explanation of a complex
effect by stating the laws according to which the various contributing
agents act in such conjunctions as to bring about this effect. It is not the
" laws " or their combinations that produce the effect ; it is the various
" causes " or " agents " that produce the effect, by acting each according to
its own uniform " principle of action," that is, according to the " law " of its
nature (217). These "laws" are both descriptive and explanatory: de
scriptive of the modes of action of the causes, and explanatory of the effects by
showing how these latter are brought about by those causes (255).

JOSEPH, Logic, chaps. xix.,xxii. WELTON, op. cit. ii., pp. 1-60. VENN,
Empirical Logic, chaps, i., ii., iii. MERCIER, Logique, pp. 298-332. MEL-
LONE, op. cit., pp. 264 sqq. JOYCE, Logic, chaps, xv., xviii. MILL, Logic,

1 JOSEPH, op. cit., p. 444 (italics ours). *ibid., pp. 444-5.

CHAPTER IV.

PRESUPPOSITIONS OF INDUCTION: UNIFORMITY OF
NATURE.

223. INTERPRETATIONS OF THE PRINCIPLE OF UNIFORMITY
IN NATURE. — In the preceding chapter attention was called to
two principles presupposed by induction : " sufficient reason "
and "causality". There is another principle which it postulates
still more directly and explicitly, the Uniformity of Nature. The
aim of induction being to reach — as far as may be — general truths
or laws about certain domains of our experience, it does and must
assume in a special way that the agencies which it studies be uni
form in their modes of operation throughout space and time. Only
in so far forth as these agencies act regularly, uniformly, will our
generalizations about them be reliable. About what is variable,
unstable, capricious, we can make no certain or scientific general
statement.1 We can have science only of what is orderly and
amenable to law. Therefore, underlying the inductive process by
which we establish general laws of nature, there is the postulate
known as the uniformity of nature. It has been stated in many
alternative ways by logicians, philosophers, and scientists, the most
usual formula, perhaps, being this one : " The same physical causes,
acting in similar circumstances, produce similar results ".2 There
has also been much discussion about its precise import and rela
tion to induction, about the origin of our belief in it, and the
grounds on which we yield it our assent.

Before examining these questions, a word about the sphere of
application of the principle may not be out of place. Strictly

1c/. JOSEPH, op. cit., p. 374.

2 Compare the formula of Duns Scotus : " Whatever has resulted regularly and
constantly from the action of a non-free cause cannot be due to chance, but must be
connected with the nature of that cause, and will therefore always result from it "
(supra, 208). Other alternative statements are : " Nature is uniform in its mode of
action " ; " the future will resemble the past " ; " the unobserved will resemble the ob
served" ; " the unknown will resemble the known " (cf. VENN, op. cit., pp. 119 sqq.).

93

94 THE SCIENCE OF LOGIC

speaking, it applies only to the action of non-free or necessitating
causes; these we call "physical" or "natural" causes in the
present context, as distinct from the free, self-determining activity
of the human will. The action of the former produces physical
uniformity, that of the latter only uniformity in the wider sense
— moral uniformity. But it would be a mistake to imagine that
this looser and less reliable sort of uniformity, which characterizes
the phenomena dependent on human activity, is an insufficient
groundwork for scientific knowledge of these domains : the very
existence of the various social and economic sciences, their co
existence with human free-will, disproves any such assumption.1
About the generalizations of the latter sciences we can, of course,
have only moral certitude, not physical ; and it is to non-free
causes, and to the law of physical uniformity, that we must mainly
direct our attention here.

Is the law of uniformity, as understood to apply to the action
of non-free causes, an axiomatic, setf-evident, necessary, " analytic "
principle — like the principle of causality, for example, that " what
ever happens has a cause " ? Or is it rather a derived, " synthetic,"
mediately evident truth, to which we assent only on grounds of
experience ? Some have held the former, some the latter view.
As a matter of fact the principle can be, and has been, interpreted
in two ways. Understood as a hypothetical judgment, it is a self-
evident, axiomatic truth ; regarded as categorical, it is a truth of
experience.

The hypothetical judgment, " If, or whenever, or wherever,
the same physical (non-free) cause acts in similar circumstances
(and therefore unimpeded, not interfered with by other causes),
it will always produce the same sort of effect," — is an axiomatic,
analytic, self-evident judgment. For, as Father Joyce expresses
it, " the very concept of a natural agent, devoid of free-will, in
volves that, under the same circumstances, its action will be of
the same kind ".2 It is a judgment whose truth the mind grasps
directly and intuitively from an adequate understanding of the
notions involved in it: "physical, non-free cause," "repeated
action unimpeded," " similarity of effect ".

But the principle, thus stated, makes no categorical assertion

1 Cf. MAKER, Psychology, 4th edition, pp. 423-4. Mr. JOSEPH (op. cit., t . 375)
seems to identify man's free actions, with capricious, motiveless actions, and to regard
them as, therefore, " incalculable ". But this is not an accurate conception of the
" libertarian " view of the will. C/. MAKER, op. cit.t pp. 396 sqq.

9 Principles of Logic, p. 237.

UNIFORMITY OF NATURE 95

about any individual case. It " supposes the First Cause to preserve
the ordinary operation of natural laws".1 This supposition is expli
citly contained in the reference to "similar circumstances". A
case of interference by the First Cause would alter the circum
stances. Such a case would not come under the principle. As
stated, therefore, the principle is a metaphysically necessary
one. It is, moreover, self-evident to anyone who understands
the import of the concepts involved in it. These, however, are com
plex concepts, and to acquire them is a work of time and experi
ence ; for which reason we may admit that the principle, even
understood hypothetically, is, to use the words of Mill,2 " by no
means one of the earliest which any of us ... can have" reached.
It is a propositio per se nota in se (86). That is, it is an analytic, a
priori proposition, whose truth is grasped intuitively by the mind
as soon as the concepts involved in it are fully analysed and
juxtaposed in thought. But we may freely admit that it is not
a propositio per se nota quoad omnes, that it is not — like " two and
two are four " — immediately evident to everybody, because not
everybody has clear and definite notions about the nature of a
physical or non-free cause, its activity in similar conditions, and
uniformity of effect.

We need to become familiar with the ordinary operations of
nature in order to conceive the notion of natural cause, i.e. of a
cause which is not free to determine itself- — as the human will does
— to produce this, that, or the other effect : a cause which has one
definite, fixed line of action, one stable tendency which it endea
vours as it were to realize and satisfy by its action. But, as soon
as a person has formed, from his experience of the uniform re
currence of natural phenomena, the idea of a "physical or natural
cause or agent, acLing repeatedly in similar sets of circumstances" he
will see intuitively, by an analysis of that concept, and comparison
with the concept of "uniform production of the same effect" a
metaphysically necessary connexion between them.

The principle of uniformity, understood in this hypothetical or
formal sense, is, however, nothing more than a purely formal
generalization of an abstract judgment, which prescinds from the
actual existence or occurrence of any such entity as a "physical
or non-free cause ". It does not imply that there are such causes
in existence, nor that they act repeatedly in similar circumstances,

1 JOYCE, op. cit., p. 238. 2 Logic, III., xxi., 2.

96 THE SCIENCE OF LOGIC

but merely states that " If such causes do exist and act thus,
they will always produce the same classes of effects "

It may, perhaps, be objected that we could not have formed the
notion of "non-free causes " at all, unless there were such causes
in the world revealed to us by our senses. This, however, is
scarcely so. The data of our sense knowledge must, of course,
have presented such uniformity as suggested the idea of "non-
free " causes to us. But we might conceivably have been mis
taken in adopting that suggestion, and judging that the causes of
those phenomena are really non-free : just as those philosophers
who deny free-will maintain that we are really mistaken in con
cluding from the facts of our own internal experience that we have
free-will. However this may be, the hypothetical statement of the
principle of uniformity evades this question of fact in regard to
non-free causes. The categorical statement of the same principle,
however, implies and asserts the fact of their actual existence.

It is not, therefore, in the formal generalization of the abstract
principle — in the assertion that " If '(whenever ; wherever, as often
as) any physical cause acts in the same circumstances, it will pro
duce similar effects " — that the difficulty lies, but in its material
generalization, i.e., (a) in asserting that there are and have been and
will be such causes in existence, and (b] in proving that the various
cases which we allege to be actual instances illustrative of the
principle are indeed such.1

In order, for instance, to be able to apply the abstract principle
of uniformity in (a) establishing by induction the general law
that "an iron bar is lengthened by the application of heat," 2 and
in (ft) applying this law to any particular case, we must be able not
merely to assert the. formally general (hypothetical) principle that
" natural or non-free causes produce the same results if they act
repeatedly in similar circumstances," but we must be able further
more to assert categorically (a) that heat acting on iron is such a
cause, and will therefore always lengthen an iron bar, and (£) that
this particular case is really a case of an iron bar acted on by heat.

The general categorical assertion, that " the causes which are at
work in the physical universe are non-free, or fixed by nature in their
mode of action, and that therefore they always have acted'and always

lcf. MER«IER, Logique, p. 330.

2 We assume here, with Mill, whatever about the conventions of formal logic,
that all such physical laws and general truths, reached by experience, imply the exist
ence or occurrence of the things and events to which they refer (cf. 128).

UNIFORMITY OF NATURE 97

will act uniformly" goes distinctly farther than the hypothetical
principle that " if a cause is faced necessarily to one mode of action
it will act uniformly in similar circumstances". Yet those two
distinct and separate statements are sometimes identified, or rather
confounded, under the common designation of the " uniformity ot
nature ". And those who rightly distinguish between them
usually limit the latter title to the abstract, hypothetical principle,
describing the categorical assertion as belief1 " in the maintenance
of the present order of things in the universe ". Thus Dr. Mellone,
in his Introductory Text-Book of Logic? draws "an important dis
tinction between two meanings of the uniformity of nature: (i)
the uniformity of causation, (2) the maintenance of the present
order of things in the universe. Experience [he continues] shows
us that there are general 'laws' — i.e. kinds of orderly succes
sion in the outward course of events : such as appear in the suc
cession of day and night, summer and winter, seed-time and
harvest, life and death. The regular succession of events in a
thousand different ways accustoms us, from force of habit, to ex
pect things to happen in a regular order ; and we find that the
expectation is fulfilled. This constitutes an overwhelming pre
sumption in favour of the maintenance of the present arrangements
in nature ; but it does not show that derivations from this order
are impossible. An expectation, bred by experience and custom,
that events will occur in a certain way is not the same as a know
ledge that they must so occur ; and this knowledge is not in our
possession. We have no grounds for affirming that the sun must
rise to-morrow morning ; there is only an overwhelming presump
tion in favour of the expectation that it will. But the principle
of uniform causation tells us nothing as to the permanence of the
present ' choir of heaven and furniture of earth '. It only says
that the same cause will have the same effect ; and to this there
are no exceptions. The same cause may conceivably never act
again ; but this does not affect the truth of the principle that if
it did it would have the same effect ".

But, then, is the inductive process, by which we establish a
law of physical nature ("IfS is M it is P" : "Ifa bar of iron
be heated it will be elongated"}, an application merely of the

1 This " belief" extends to the past no less than to the future, to the distant as
well as to the near ; it is a conviction which has for its object the existence and opera
tion, throughout time and space, of natural or necessitating causes,

2 pp. 281-2.

VOL. II. 7

98 THE SCIENCE OF LOGIC

hypothetical "principle," or does it also involve the categorical
"belief"? The answer is that if the laws of physical nature are
anything more than statements of mere abstract possibilities ;
if they are taken to imply the actual existence and operation,
throughout space and time, of the agencies they refer to, then
the inductive process by which we reach them does undoubtedly
imply not only the hypothetical principle, but also the categorical
belief. And that physical laws are interpreted in this latter
sense, as informing us not about mere abstract possibilities, but
about concrete actualities, past, present, and future, there can be no
doubt. In reference to such a law, for example, as " Heating (M~}
an iron bar (S) causes its elongation (P] ". Dr. Mellone * says
that " the connexion between M and P is independent of time
and place. We can reason backwards to unobserved cases in
the past, and dip into the future and be sure that P will always
be produced by M".

But how sure can we be about this latter? No surer than
we can be that heat and iron (M and S} will continue to exist ;
for unless they continue to exist, the operation can never take
place. And what certitude have we that they will continue to
exist? The physical, hypothetical certitude which Dr. Mellone
describes as an " overwhelming presumption ". In fact, we can
not extend or apply a single physical law to a single future case
— or to a single past or distant case for that matter, if it lies out
side our actual experience — without assuming (a) that the causes
it refers to are "necessary," "natural," or "non-free" causes,
and (b] that they have acted, are acting, or will act, in the case
contemplated, without any obstacle or impediment from the inter
vention of other causes.

Similarly, Father Joyce'2 seems to take the "principle of
uniformity " as embodying not merely the abstract judgment
that "anon-free cause acts uniformly in similar circumstances,"
but also the judgment that " such causes do exist and act in the
universe," when he says that " in that principle we have the
guarantee that our universal judgment will be verified in fact.
Our judgment that A as such is the cause of a, would help us
but little, unless we further knew that in the real order the same
cause does actually always produce the same effect."

This being the sense in which Mill understood the principle, it

1 op. cit., p. 265. *op. cit., p. 219.

UNIFORMITY OF NATURE 99

is no wonder that he regarded it as synthetic, as reached by
experience, not as analytic and self-evident like the mere hypo
thetical statement of uniformity. If, therefore, the principle of
uniformity be understood to assert categorically our belief in the
actual existence and operation, throughout space and time, of
non-free causes, we have to determine (i) what are the ultimate
rational grounds on which we assent to this principle, and (2)
what are its relations to the processes of induction and deduction
respectively.

224. ULTIMATE RATIONAL GROUNDS OF OUR BELIEF IN
UNIFORMITY: THE SCHOLASTIC, EMPIRICIST, AND IDEALIST
VIEWS. — Firstly, as to the rational grounds of our assent to
the principle. We must bear in mind that it is a synthetic, or
a posteriori generalization from experience, about which we have
physical certitude.1 Our concept of physical or non-free cause
is not innate. We form it gradually from our acquaintance with
uniformity in the processes of physical nature. From our ex
perience of the uniform activities of the physical universe we
abstract the notion of a necessary or non-free cause, fixed in its
mode of action : just as from our internal experience of our
own activity, and from observation of the activities of men in
general, we abstract the notion of a free or self -deter mining cause,
not fixed to one mode of acting in similar circumstances. Hav
ing, then, defined for ourselves a non-free or physical cause as
" one which will always act the same way, by a necessity of
its nature or constitution, in similar circumstances," we deli
berately judge that the causes of which we have experience in
physical nature verify our definition : we judge that they will
always act the same way in similar circumstances, in the future as
in the past, provided something unwonted, extraordinary, unfore
seen, does not occur. Thus, while we quite recognize that at least
apparent exceptions to uniformity have occurred in the past, that
our knowledge of the forces of nature is limited, that some of
its phenomena " seem altogether capricious," 2 that unknown
agencies, not calculated by us, may have interfered, and may
again interfere, and surprise us by upsetting our expectations:
nevertheless, we consider it prudent and reasonable to base upon

1 C/. MAHER, Psychology (4th edition), p. 420: "The latter generalization [that
the ' laws of nature are constant '] is a contingent truth which we can easily con
ceive subject to exceptions ".

a MILL, op. clt.t III., iii., § 2.

zoo THE SCIENCE OF LOGIC

our actual experience of general uniformity, imperfect and pos
sibly interrupted though this may be, a firm belief or expectation
that the same regularity which has obtained within the limits of
our actual experience will obtain also outside these limits.

Thus, actual experience of uniformity may be regarded as
the proximate, psychical ground of our belief in uniformity beyond
this experience. But we must go further if we are to assign an
ultimate rational justification for this belief. If I am asked why
I believe that nature is uniform beyond the actual range of my
own personal sense experience, it will not suffice to answer :
" Because I have found it uniform within this range ". No doubt,
this is the true psychological account of the genesis of my ex
pectation that the uniformity will obtain beyond my experience ;
and, no doubt, I may quite prudently and reasonably act upon
this belief. I may go on investigating nature as a scientist,
observing, experimenting, conjecturing general truths or laws,
generalizing from experience, and in this way passing beyond
experience, even discovering and establishing laws of physical
nature : I may do all this without once pausing to inquire what
rational grounds I have at any time for going a single step
beyond my actual experience of nature and inferring anything
with any rational certitude about what is beyond this experience.
But what right have I to infer that because a thing has existed,
or an event happened, in a certain uniform way within my very
limited experience, it therefore does, or will, or must exist, or
happen, in the same way beyond ? What right had Leibniz to
think or say that " 'Tis all like here . . . The present is preg
nant with the future ; the future may be deciphered in the past.
. . . The distant is mirrored in the near"?1 The "leap" beyond
experience takes place in every single induction we make, because
we believe in the " uniformity of nature ". But what right have
we to believe in it? What view of nature will afford us a
rational justification of this belief?

Scholastic View. — Philosophers differ in assigning an ulti
mate rational ground for our belief in the uniformity of nature,
because they differ in their views about the ultimate nature of the
universe itself. The justification Scholastics offer — in common
with all who admit creation, and the dependence of all nature on

1 " C'est tout comme ici. . . . Le present est gros de 1'avenir ; le futur se pour-
rait lire dans le passe . . . l'e"loigne est exprim^ par le prochain." — apud VENN,
Empirical Logic, p. 81 ; cf. 124.

UNI FORM IT Y OF NA TURE i o i

the Providence of an All-wise Deity1 — is simple and intelligible.
By reasoning from effect to cause, by means of a posteriori argu
ments whereby we apply self-evident principles, like the principle
of causality, to the facts of sense experience, we establish with
certitude the existence of an All-powerful, All-wise, Supreme
Being, who has freely created the universe, freely conserves it in
existence, and freely concurs with the activity of all created
agencies ; who has manifestly ordered and arranged and designed
the universe, the " cosmos " as it is rightly called ; who has
evidently endowed the agencies of this visible universe with^Jra/
tendencies, in virtue of which they act uniformly unless whenever
or wherever He chooses to interfere (miraculously) with the
established physical order for some higher (moraF) end. Know
ing all this, we know that natural causes will continue to exist
and to act uniformly in accordance with His will and as long as
He wills. Knowing, too, that He is All-wise, we know and
believe that He will not interfere with the uniformity of physical
nature capriciously, so as to render our reliance on it uncertain.
Since He created its agencies "for man's use and benefit," this
Divine purpose forms a firm basis for our trust in their stability.
His occasional miraculous suspensions of its laws are for our
greater good, and cannot in any way weaken our belief in its
general uniformity (cf. 2 1 7).

Thus it is that our conception of physical nature as the work
of an All-wise Creator and Ruler, forms the ultimate rational
justification of that belief in the uniformity of nature, which is
partially embodied in the formulation and application of every
physical law. This, of course, does not mean that we must have
deliberately convinced ourselves of God's existence, creation, and
providence, before we can make a single inductive generalization
from actual experience in any department of natural research : we
may assume the uniformity of nature provisionally, and utilize
our postulate as scientists, without justifying to ourselves the use
we make of it. But if we want to justify this usage philosophically ;
we must, of course, put some rational interpretation on both nature
and thought — i.e. on our experience as a whole.

1 The Scottish school of philosophers are content to say that this belief is the
natural expression of an innate, instinctive law. There is no denying the natural
tendency to the belief; but to say that the latter must be " the effect of instinct,
not of reason," is hardly to explain it. The tendency to the belief should not be
called an "instinct"; for, although its exercise is spontaneous and unreflective,
still, on reflection, we can assign a rational basis for it.

102 THE SCIENCE OF LOGIC

The existence of God can be proved independently of the
assumption that nature is uniform in the sense in which this uni
formity has just been explained.1 Hence, the Scholastic justifica
tion of the postulate is free from all circular reasoning, in addition
to being intelligible and adequate. But perhaps this fallacy is
involved in applying belief in uniformity to individual inductive
generalizations before we have -explicitly assigned to this belief its
ultimate rational basis ? No, because every such generalization
is merely provisional : the assumption of uniformity invblved in
it awaits whatever rational justification we may be able to
supply for this assumption when we reflect upon it.

Empiricist View. — Mill was right, as we have seen above, in
saying that belief in the general uniformity of nature (in the
categorical sense) is " by no means one of the earliest " 2 of our
beliefs : it is not a mental assent which must precede every scien
tific induction we make : it is partially embodied in each, and
gradually extended over all nature.3 But he failed utterly to
assign any ground for rational, scientific certitude, whether about
this widest law of uniformity of nature, or about any minor
generalization reached by induction. He sought to show that
the minor generalizations we make without explicit advertence
or assent to the general uniformity of nature, can be only mere
enumerative inductions, i.e. more or less hazardous extensions of
observed uniformities to the region beyond our actual experience ;
that our belief in the general uniformity of nature is a gradual
summing up of these hazardous conclusions ; and that, neverthe
less, this summing-up process gives us the highest attainable scien
tific certitude about this law of uniformity, this widest of all
generalizations. The general uniformity of nature is, he teaches,
a generalization from a number of less general uniformities, them
selves reached by a " loose and uncertain mode of induction per
enumerationem simplicem ". The law of the uniformity of nature
" is itself an instance of induction, and by no means one of the
earliest which any of us, or which mankind in general, can have

1 The same observed and experienced uniformity which prompts us to act on the
assumption of its universality, also furnishes, of course, part of the data from which
the existence of God is demonstrated. But in using the data for this purpose we are
not assuming the principle of uniformity.

2 Logic, III., xxi., § 2.

3 Cf. infra, 225 ; VENN, op. cit., pp. 134 sqq. For the opposite view— that belief
in, or assumption of, general uniformity — is necessarily antecedent to any and every
inductive generalization, see JOSEPH, op. cit., pp. 386 sqq.

UNI FORM IT Y OF NA TURE 1 03

made. We arrive at this universal law by generalization from
many laws of inferior generality. . . . As, however, all rigorous
processes of induction presuppose the general uniformity, our
knowledge of the particular uniformities from which it was first
inferred was not, of course, derived from rigorous induction, but
from the loose and uncertain mode of induction/^ enumerationem
simplicem" *

And of this latter process he had already said : "It consists
in ascribing the character of general truths to all propositions
which are true in every instance that we happen to know of. ...
In science it carries us but a little way. We are forced to begin
with it ; we must often rely on it provisionally, in the absence
of means of more searching investigation." 2 There is here, ap
parently, no rational basis assigned, on which this " loose" process
can produce scientific certitude. Yet, it is by this process we
ascend to the " particular uniformities," and, by a second applica
tion of it, from these to the " general uniformity," on which
the validity of the whole inductive process is to be based. The
principle so obtained must necessarily be, as Professor Welton
expresses it, " untrustworthy in a twofold degree ; for it is an in
ference, uncertain in its very essence, from other inferences of the
same dubious character. . . . Mill's argument on this point is
indeed nothing but a petitio pn 'ncipii. We are, he says, ' to con
sider no minor generalization as proved except in so far as the
law of causation confirms it ' (III., xxi., § 3), and yet that law is to
be derived from those very same minor generalizations which it is
called upon to ' confirm'." 3

Mill is, of course, mistaken in thinking that we cannot make
a strict, scientific induction without hav'mg previously justified our
belief in the general uniformity of nature. We have pointed out
above that this is not necessary ; that we may accept the principle
provisionally and base our scientific inductions upon it. Mill,
however, thinks we can only make " enumerative " inductions ;
and upon these alone he endeavours to base our belief in that
general uniformity, which will then turn around and confirm
them. His attempt to avoid the charge of inconsistency in basing
the validity of the " rigorous " process upon the " loose and un
certain " process, reveals once more a rather naive petitio prindpii.
The difficulty he had to face was this : Enumerative induction,

1 Logic, III., xxi., § 2. 2 ibid., iii., § 2.

3 WELTON, Logic, ii., pp. 42, 43. C/~. JOSEPH, op. cit., pp. 388, 391.

104 THE SCIENCE OF LOGIC

i.e. generalizing from the mere counting of instances, is admittedly
a hazardous process and cannot give certitude. How, then, can
we be certain of the uniformity of nature, and through it, of
our scientific inductions, if uniformity itself is grounded on this
hazardous process of enumeration ? Mill commences his answer1
with this statement : " Now, the precariousness of the method of
simple enumeration is in an inverse ratio to the largeness of the
generalization ". Assuming this, he points out that the subject-
matter of the law of uniformity — which is the " largest " general
ization of all — is " so widely diffused that there is no time, no
place, and no combination of circumstances, but must afford an
example of its truth or of its falsity," and that it was "never
found otherwise than true ".2 From this he concludes that the
law of uniformity " takes its place among the most firmly estab
lished as well as the largest truths accessible to science ". This
is a plausible piece of reasoning until we advert to the fact that
its opening statement assumes what is to be proved. The reason
why we regard a wide enumerative induction as safer than a
narrow one, the reason why one which is found to range without
exception over an extensive region of time and space yields higher
certitude, is because we are made morally certain by it that the
special observed uniformity in question is not a casual but a
causal one, and because we ARE ALREADY CONVINCED, or ALREADY
ASSUME, that a CAUSAL uniformity will persist beyond and outside
our experience, in other words, THAT NATURE IS UNIFORM. Did
we not already believe in the uniformity of nature, all enumera
tive induction, whether wide or narrow, in fact all inference be
yond actual experience, would be equally hazardous. To assume
that we can thus differentiate between wide and narrow inductions,
in an attempt to prove that we can believe nature to be uniform,
is simply to beg the question at issue.

Mill's attempt, therefore, to assign a rational basis for belief in
the uniformity of nature breaks down. And hence he is unable
to justify the individual scientific inductions by which we establish
isolated laws of nature ; for in every one of these inductions there
is a partial application of the principle of uniformity ; every one
of them transcended the actual sense experience of the individual ;

1 Logic, III., xxi., § 3.

2 What about his previous recognition [III., iii., § 2] of phenomena, which " seem
altogether capricious," about the " course of nature" being " not only uniform" but
"also infinitely various"? Again, what about miracles? Or about the impossi
bility of inferring what must be, or even what will be, merely from what was or is ?

UNIFORMITY OF NATURE 105

every one of them " did most certainly outreach the boundaries
of observation as then and there obtained " ; l and in the Empiri
cist philosophy, which reduces all knowledge to sense experience,
there is nothing to justify a single step beyond the present data
of the individual's sense consciousness. This philosophy recog
nizes no channel of knowledge beyond the senses, and reduces all
nature, all reality, to a mere flow of conscious sensations in the
individual mind. The step, therefore, beyond what is actually
observed — in fact, the step beyond the contents of the present
transient moment of consciousness — is, for the phenomenist, at
best a presumption, a "hazard," a "leap,"2 a speculation, about
the validity of which we may have a more or less strong expecta
tion, hope, opinion, probability ; but not certitude proper : at least,
not a scientific or reasoned certitude, for which any sufficient rational
grounds can be assigned (cf. 2 1 9).

Idealist View. — In the sensist philosophy there is room for
knowledge of individual ^a^/ or phenomenon alone ; for law, neces
sity, the universal, there is no logical place. In the Scholastic
doctrine, that the universe is dependent on the free-will of an
All-wise Creator and Ruler, there is an intelligible place for
physical or conditional certitude about the nature, activities, and
laws of physical agencies, conceived as subject to the will and
wisdom of that Creator. The idealist philosophy errs in, the op
posite extreme from sensism by attributing to the processes of
external nature an absolute, metaphysical necessity to which
they can have no real claim. The advocates of this philosophy
— to which we have already called attention (cf. 215) — prefer to
speak of the unity of nature, rather than its uniformity. They
tell us that " the world must be conceived as a systematic totality,
with a thoroughgoing interrelation of parts . . . that nature is
a unity ... a system which remains identical with itself amidst
the unceasing changes of relations between its parts, and which,
by its own nature, necessitates and determines those changes ".3
And they assert this " unity " as a postulate or " presupposition,"
without which intelligible experience would be impossible.4

Now it is true, undoubtedly, that unless the world were a
harmonious system of interrelated elements, regular, uniform, con
sistent with itself throughout all its changes, we could not arrive

1 VENN, Empirical Logic, p. 131.

2 BAIN, Inductive Logic, book iii., chap, i., § i.

3 WELTON, Logic, ii., pp. 4, 5. 4 ibid.

io6 THE SCIENCE OF LOGIC

at a rational knowledge of it ; for knowing implies defining, ar
ranging, and classifying things ; and the validity of these processes
obviously depends on the condition that their objects have abiding,
permanent natures. Whatever is knowable, therefore, is reducible
to order within a system. But in this sense the unity implied in
reality is of course unity of order, unity by relation, not unity of
being or essence, as these philosophers would seem to imply. This
pantheistic postulate will not stand the test of critical analysis.
In the real world, as revealed to us through our senses, we detect
a unity of order, but not a unity of being ; we see in it manifold
evidences which justify us in inferring that it is created, conserved,
and ruled by some guiding intelligence distinct from it ; but we
do not by any means see in it only such logically necessary con
nexions and relations as would justify us in believing it to be a
mere manifestation or evolution of the activity of some immanent
intellect. We can prove that the " choir of heaven and furniture
of earth " are dependent on Divine providence, on the wisdom
and free-will of the Deity, and we can therefore be physically,
hypothetically certain of the generalizations we reach by means of
induction about the modes of existence and activity of agencies
created in time and space ; but absolute or metaphysical certitude
about these modes of existence and activity, the very nature of
these agencies, and the essential limitations of the human mind
itself, preclude us from ever reaching.

Modern logicians may, perhaps, be tempted to deprecate the introduction,
into a treatise on logic,1 of such metaphysical theses as that God has created
and conserves and governs the universe and concurs with its activities, and
that man is endowed with free-will, for the purpose of explaining the nature
and grounds of physical and moral certitude. But the fact is that these
latter cannot be satisfactorily explained, either in logic or outside it, with
out adopting some attitude or other as to the ultimate nature, origin, and mode
of existence, of this visible univei'se which furnishes the human mind with all
its data for knowledge. Metaphysical assumptions of some kind are inevit
able in logic, even although it is in metaphysics and not in logic that they
should be justified. If John Stuart Mill introduces into his logic, as he does,
the assumption of the empiricist or phenomenist philosophy, that all reality is
ultimately analysable into spontaneously associated sensations of the conscious
mind, and if Professors Bosanquet and Welton build their logical doctrine on
the idealist assumption of Hegel and Green, which identifies reality with
thought by declaring the former to be constituted by " thought-relations,"
Scholastics need not apologize for rejecting both the one and the other assump
tion as unsatisfactory and erroneous, for attributing a larger role to intellect

1 cf. JOYCE, Logic, pp. 237-8 ; RICKABV, First Principles, pp. 89, 93, 102.

UNIFORMITY OF NATURE 107

than the Empiricists, and a larger role to sense than the Idealists, for replacing
the Agnosticism of the former, and the Pantheism or Monism of the latter, by
the philosophy of Christian Theism, which teaches that the world was created
by an All-wise Deity, and is conserved and governed by His power and provi
dence.

Writers in sympathy with a spiritualist or idealist interpretation of experi
ence have furnished very destructive criticisms of Empiricism. But their own
substitutes are often far from satisfactory. We may instance the account of
uniformity given by Mr. Joseph.1 He deals with the principle as interpreted
in the categorical sense, i.e. as believed by us to be de facto applicable to the
universe revealed to us in sense experience. He shows clearly and conclu
sively that it cannot be established by induction in the manner propounded by
Mill.2 His own view is that uniformity is a postulate, an assumption which
must be made antecedently to all induction : " all induction assumes the
existence of universal connexions in nature ".;t He points out also, and rightly,
that belief in the uniformity of the causal relation really involves belief in its
necessary character, belief that it is a law* But he goes on to draw a dis
tinction between " conditional " and " unconditional " laws or principles. A
"conditional" principle he defines as one whose truth "depends upon con
ditions which are not stated in if";5 such a principle, therefore, may "admit
of exception " B when any of those unmentioned conditions are not verified.
An "unconditional" principle is, of course, one which is true absolutely
and unconditionally, one " that can have no exception ".7 The uniformity of
nature he apparently holds to be an unconditional principle or law, for he says
it " involves the truth, without exception or qualification, of all unconditional
laws ".s Let us see, then, how he attempts to show that it is unconditional.
For, if the principle of uniform causation is unconditional, it undoubtedly
"becomes . . . important to determine, if possible, when we have discovered
an unconditional law".9 He gives us two tests, one admittedly satisfactory ;
the other admittedly less so. Theyfrr/ is simply cogent self-evidence : "if a
principle is self-evident it must be unconditional ".10 Such truths, therefore, as
"two and two are four," "ex nihilo nihil fit" "a thing must be itself," etc.
are unconditional because self-evident. So, too, is the abstract, hypothetical
statement of uniformity — "if natural causes have fixed, stable modes of
acting . . . they will produce similar effects in similar circumstances " — " un
conditional " because it is " self-evident ". But is the categorical statement, that
"nature actually is and must be uniform," a self-evident proposition? It
certainly is not.11

I op. cit., c. xix. 2 pp. 387-389. 3 p. 371. 4 pp. 376 3qq.
5p. 381. «p. 386. 7p. 382. 8p. 381.

9 p. 382. 10 p. 386 ; cf. p. 384.

II We cannot claim the categorical principle to be self-evident unless we claim
that the application of our abstract, universal concepts (and of the evidently necessary
and universal abstract truths which the mind enunciates by comparing these con
cepts with one another) to the concrete data of our sense experience (for the inter
pretation of these latter), is an evidently valid process ; in other words, unless we
claim that the doctrine of Realism in regard to the significance of our intellectual
concepts is, in some form or other, an evidently true doctrine : an indefensible claim,
because some forms of realism are not true, and the true form is not evident. Yet,

io8 THE SCIENCE OF LOGIC

Let us therefore apply to it the second test, which is this : " if without
assuming [the principle] to be true, it is impossible to account for the facts of
our experience, we should have to suppose it unconditional ; though such im
possibility may be hard to establish "^ The law of uniform causation is
supposed to fulfil this test, to be the only principle on which we can " account
for the facts of our experience," and, therefore, to be unconditionally true.
And this supposed impossibility of otherwise accounting for "the facts of our
experience " is also alleged as the ultimate ground and justification of our
belief in the law : " With what right then do we assume it ? The answer to
this has been given in discussing what we mean by it. To deny it is to
resolve the universe into items that have no intelligible connexion ".2

This whole position calls for a few considerations. Firstly, to prove in
this indirect way that a principle must be true — because, namely, it is the
only one that will "account for the facts of our experience" — is a perfectly
legitimate procedure when the principle is not self-evident. It is a difficult
method, of course, to apply ; but, failing self-evidence, it is the only one ; nor
do we see why, having applied it carefully, " we should not be fully satisfied
with it,"3 as Mr. Joseph thinks we should not. Is he himself, then, not
fully satisfied with the only way in which the law of uniform causation in its
categorical or applied sense can be shown to be true ?

Secondly, if the law is established in this way, is it not based on facts, and
established by experience, as we have contended that it is ? * It is assumed

although Mr. Joseph nowhere states that the law of (uniform) causation (in the cate
gorical or applied sense) is self-evident, he does assert that our belief in it " rests . . .
on the perception that a thing must be itself. If it is the nature of one thing to produce
change in another, it will always produce that change in that other thing; just as, if
it is the nature of a triangle to be half the area of the rectangle on the same base
and between the same parallels, it will always be half that area" (op. cit., p. 390 n.).
But, manifestly, the parity between those two examples holds good only on an
assumption which is, to put it mildly, not self-evident : the assumption that the same
necessity which characterizes the relations between static, abstract thought- objects,
or possible essences, in the conceptual order — or a like necessity — also characterizes
the relations between the concrete sense phenomena that actually exist in the ever
changing conditions of space and time (cf. 219). Apparently, Mr. Joseph has failed
to distinguish between the self-evidence of the abstract law of uniformity within the
conceptual order, and the entirely different grounds on which the application of this
law to the concrete, actual domain of sense experience must be maintained as valid.
Jp. 382. a p. 390.

3 p. 382. The feeling that this method is not quite satisfactory seems to us to
reveal that attitude of mind which would restrict the terms " knowledge " and
"science" to self-evident truths, and conclusions derived from these by cogent
demonstrative reasoning.

4 We interpret Mr. Joseph's account of the principle, as given in his Logic,
pp. 380, 391, to propound the view that this principle is " unconditional " ; that we
know it to be " unconditional," because, although it is not self-evident, the facts
force us to admit it, because the denial of it would " resolve the universe into items
that have no intelligible connexion ". But this implies that the law is based on
experience, and reached a posteriori. Yet, elsewhere he seems to hold that the
principle is self-evident : cf. p. 390, n. (n. n, p. 107) ; also p. 401, where he writes:
" The law of the uniformity of nature itself, as we have seen, is not arrived at in
that way [i.e. a posteriori], since if we once doubt it, it is impossible to show that

UNI FORM IT Y OF NA TURE 1 09

of course, not prior to, but in and with, all our experience ; l but when we
seek rational grounds for our assumption of it, where can these be found but
in the facts, in our experience ? When a law is established by this pro
cedure, we must, of course, recognize that "had the facts been otherwise, we
need not have admitted the law ; and [that] we do not see, except on the
hypothesis that the law is true, why the facts might not have been other
wise ".2 This is the reason why Mr. Joseph regards such procedure as
unsatisfactory ; but if we believe in the law of uniform causation because it
is the only principle that will "account for the facts of our experience,"
surely we must be prepared to admit that "had the facts been otherwise we
need not have admitted the law " ; 3 and in this there can be nothing unsatis
factory. But if this is the way we justify our belief in the law, then, obviously,
that belief is not a prerequisite condition for experience, entirely prior to, and
independent of, experience, but is rather psychologically simultaneous with,
and philosophically grounded on, experience.

Thirdly, it must be carefully noted that the abstract, hypothetical law —
which alone is self-evident, being, in fact, reducible to the principle of
identity, as Mr. Joseph shows, and as we have already pointed out — does not
and cannot, of itself , "account for the facts of our experience". It belongs
to the conceptual or ideal order, the order of abstract objects of intellectual
thought ; whereas " the facts of our experience " belong to the phenomenal
order, i.e. is to the order of realities actually existing in space and time, and
subject to all the changeful conditions of such existence. But no purely
abstract, conceptual principle can, of itself, account for the actual existence or
permanence, in space and time, of the present " choir of heaven and furniture
of earth".4 It is the categorical principle alone — " Nature has been, is, and
will be, and must be, uniform "—that can give us any intelligible account of
the actual world of our experience, as distinct from a merely hypothetical
world constructed by our own thought from intellectual concepts. And
hence the supreme importance of determining in what sense nature must be
uniform, of "discussing what we mean by"5 this "must," and of assigning
a rational ground for our belief in this necessity, in the sense in which we
interpret it.

Fourthly, as already explained, we believe this "necessity," this "must,"
to be conditional, contingent, dependent on the Fiat of a Divine and All-wise

the facts are any more consistent with its falsity than with its truth ". The abstract
principle is, of course, self-evident, but the validity of its application to the actual
world of sense experience is not.

1 It is quite true that " if we once doubt" the truth of the principle as applied
to the actual universe, " it is impossible to show that the facts are any more con
sistent with its falsity than with its truth " (op. cit., p. 401), or, in fact, to reason at all
about events in space and time beyond actual experience ; but from this it does not
follow that assent to the principle must be antecedent to, and independent of, all
experience. The principle, even in its applied sense, is not reached by any process
of logical inference. None the less, it is based on experience. From experience we
abstract the concepts embodied in the principle. Experience suggests the abstract
principle as validly applicable to the real world ; we assume that it is so applicable ;
and further experience justifies the assumption.

2 JOSEPH, op. cit., p. 382. 3ibid. 4 C/. MELLONE, op. cit., p. 282.

5 JOSEPH, op. cit., p. 390.

no THE SCIENCE OF LOGIC

Greater and Ruler, whose existence and providence can be proved from " the
facts of our experience " : to us the principle means that " The course of
physical nature must be uniform if, and provided that, and in so far as, the
will of God makes it so ". If, then, we wish to formulate an ultimate, uncon
ditional, or absolutely necessary, law, for physical nature, or indeed for all
contingent reality, we shall find it in the simple statement that "The whole
course of contingent or created reality must be as God, the Necessary Being,
wills it to be ". If we accept J. S. Mill's definition of laws of nature in the
strict sense, as " the fewest and simplest assumptions, which being granted,
the whole existing order of nature would result " ; * the law we have just enun
ciated would be the really ultimate "law of nature," though this was very far
indeed from Mill's own thought. We have already referred to Mill's in
ability to transcend the " conditional," or to give any account of the nature of
that ultimate, outstanding condition on which "the present constitution of
things " 3 is dependent. Let us see whether Mr. Joseph is any more expli
cit in regard to the nature of this final and most important condition.

Understanding a law to be unconditional when its truth is not dependent
on any outstanding condition other than those explicitly stated in the formula
tion of the law,3 he goes on to inquire : " are there any unconditional laws
known to us?"4. He first refers to the mechanical view of the physical
universe, which purports to interpret and explain " all physical changes " as
"determined altogether according to physical laws," and to be all "purely
mechanical":5 according to which view these mechanical laws, while con
ditioning the existence and course of all physical nature, would be themselves
unconditional. He very rightly declines to accept this view on the ground
that it is " impossible to account on physical principles for the facts, of conscious
ness " 8 . . . " Thus to a physical theory of the world consciousness remains
unaccountable ; such a theory therefore cannot be complete or final ".7 He then
suggests in a mild way that " we are perhaps sometimes too hasty in supposing
that we see the necessary truth of physical principles ".8 Such a supposition
is, of course, not only too hasty, but also erroneous, seeing that such principles,
referring as they do to the order of concrete physical facts, cannot have the
purely abstract necessity of mathematical truths : " it might be said that in
the first law of motion it is self-evident indeed that a body will persist in its
state of rest or uniform rectilinear motion until something interferes with it,
but not that interference can come only from another body ; that the mathe
matical reasoning in physical science is necessary, but not the physical prin
ciples which supply the data to which mathematical reasoning is applied ;
and that the doctrine that a body can only be interfered with by another body
is one of these ".9 All this points to the conclusion that " the fundamental
physical laws are only conditionally true," 10 that is, dependent on conditions

1 Logic, III., iv., § i. * Logic, III., v., § 6: cf. supra, 219.

3 JOSEPH, op. cit., p. 381. 4p. 382. *ibid. 9ibid. 7p. 384. 8ibid.

9 p. 385 (italics are ours, except the last). The assertion that " a body can only
be interfered with by another body " is not really a physical "principle," nor can
physics even prove it to be true : what it is meant to convey is simply this, that
"physical science prescinds from all but material agencies " (Cf. MAKER, Psychology,
p. 518, n. 30),

"ibid.

UNIFORMITY OF NA TURE 1 1 1

which are not themselves physical, and whose nature, therefore, it is beyond the
scope of physical science as such to explain : " supposing that there are, if we
may so put it, spiritual conditions upon which the movements of bodies in the
last resort depend . . . then physical science at any rate cannot deal with those
conditions "-1 Of course it cannot, since it does not purport to deal with all
reality : but we expect from the physical scientist that he should not go on to
deny the existence of such conditions merely because they fall beyond his
scope and methods as a scientist : 2 he is doing a real service to his science by
recognizing its limitations. But physical science and philosophy are both
brought into disrepute by those who gratuitously deny the existence of ultra-
physical conditions and causes, who contend that mechanical laws are uncon
ditional, and that all existing reality can be explained by these laws, when, as
a matter of fact, such laws offer no ultimate explanation even of the material
universe. Mr. Joseph fails to note, however, that there is this still more funda
mental reason for rejecting the mechanical view : that it purports to explain
the actual, concrete existence and uniform course of nature, by the mere formu
lation of some one or some few mechanical laws. How could any abstract,
intellectual formula about atoms, mass, motion, energy, etc. — even were such
a formula self-evident — account for the actual existence and course of nature ?
An abstract law cannot account for existing facts, or for the uniformity or
necessity 3 of actual processes. Actual facts demand an actual cause, and so
does the mode— whether uniform, or necessary, or otherwise — in which they
happen. If, then, all physical nature is dependent on, and refers us to, an
ultra-physical or spiritual domain of reality, and if even the highest and
widest physical laws are not absolutely ultimate, but conditioned by the reality
or realities of this other domain, it is obviously the highest duty of the philo
sopher to determine the nature and influence of these conditions. But is it
not also the duty of the logician to take note of, and call attention to, all the
leading alternative ways in which these conditions have been, or may be, con
ceived by philosophers ? or at least not to convey the impression that these
alternatives are fewer than they really are ? Now, according to Mr. Joseph,
if we are dissatisfied with the " mechanical " alternative, " philosophy suggests

1 JOSEPH, op. cit., p. 385.

zcf. MAHER, Psychology, p. 420: "The student should always remember that
physical science simply assumes the law of uniform causation ; that its universality
is merely a postulate to be justified only in metaphysics ; and that the metaphysician,
who recognizes moral convictions to be not less real nor less weighty facts than
those of physical science, is bound to qualify, limit, or interpret the law when applied
to moral actions in accordance with his wider and more comprehensive view of ex
perience". C/. also pp. 517-24, especially p. 519, n. 32.

3 It is no ultimate explanation of this necessity to say that it is " mechanical ".
If all nature is merely one vast machine or mechanism, who made it ? The neces
sity we ascribe to the course of actual nature in time and space is not the necessity
we ascribe to abstract judgments about possible essences : it is not purely intellectual :
it is a manifestation of intelligence and will and power. The only immediate source
it can have is our experience of the order, regularity, uniformity of all nature, compel
ling us to interpret the latter as a cosmos, as the work of an Omnipotent Will directed
by Supreme Wisdom. The only necessity for which we can rationally account in
actual nature is that by which it pursues the course marked out for it by the Divine
Fiat. To say as a last word about the course of nature that it is "mechanical," is
no better than to ascribe it to mere chance, or to pronounce it an insoluble enigma.

1 1 2 THE SCIENCE OF LOGIC

that in the last resort, instead of explaining consciousness in terms of physical
law, we shall have to see in physical law a manifestation of intelligence. The
whole material order is an object of apprehension ; therein, however it stands
related to minds that apprehend it, it and they together form the complete
reality, or res completa ; and they cannot be understood except together ". '

As a final word on the problem, this is hardly satisfactory. At least, the
statement might be a little more explicit. In justification, presumably, of his
brevity, the author adds : " It is not our business to discuss here this central
metaphysical problem ". That is so ; but from what he does say, and leave
unsaid, about it, we are left in doubt whether or not he is really committing
himself to the philosophy of idealistic or spiritualistic monism. " The whole
material order," and " minds," " together form the complete reality, or res com
pleta" That sounds like monism. A few pages further on he writes : " If the
whole series of events in time can be regarded as an expression of the activity
of that which is in some way exempt from subjection to succession, then what
appears in time as future may have to be taken into account in giving a reason
for the present and the past, though of course the future cannot determine the
present in the same way as what precedes it does ".2 But this statement —
which apparently refers to the influence of final cause, or purpose, in the course
of events — is equally compatible with theism or with spiritualistic monism.
And we get no clue as to which alternative the author himself adopts ; he
merely adds : " The present chapter is perhaps already more than sufficiently
metaphysical ".

But there is a graver inconvenience in his treatment of the question : what
he has managed to say, and to leave unsaid, may seriously mislead the student.
When he chose to set over against the mechanical, materialist view of nature, the
Ideological, spiritualist view, he made mention of only one form of spiritualism,
the pantheistic or monistic form. Why has he passed over in silence the other
well-known alternative, the philosophy of theism ? Theism is at least a pos
sible alternative to monism. Therefore it claims a mention from the logician.
But, according to Mr. Joseph, if we reject mechanical materialism, " philosophy
suggests that in the last resort, instead of explaining consciousness in terms
of physical law, we shall have to see in a physical law a manifestation of in
telligence ".3 Philosophy does not suggest this as a " last resort ". And, even
if it did, the suggestion would be ambiguous : Of what intelligence are we to re
gard physical law as a manifestation ? our own individual intelligences ? or an
immanent cosmic intelligence — an anima mundi f an intelligence "with will,
or one without will ? an unconscious, or a self-conscious, intelligence ? And
what sort of manifestation ? — a manifestation of one reality, itself to itself, by
an inner process of self-evolution, so that the one reality is substance and pro
cess and law and cause and effect all at once ? These are all various forms
or phases of monism, which " philosophy," i.e. mature reflection on the facts
of experience, may suggest. But, besides all of them, philosophy has at all
times persistently suggested an alternative omitted by Mr. Joseph, the alter
native which we believe to be the true one, viz., that physical law is a
manifestation, to men's minds, of the intelligence and will of a Necessaiy,
Self-existent, Divine, All-perfect Being, really distinct from the finite, con
tingent, dependent, and conditioned universe of sense experience, the " world ''

1 JOSEPH, op. cit., p. 384. 2 p. 390, n. D p. 384 (italics ours).

UNIFORMITY OF NA TURE 1 1 3

which He has freely created, conserves, and rules, according to the eternal dic
tate of that wisdom whose work must needs be a cosmos. The explicit men
tion of theism, as at least a possible alternative to mechanical materialism and
monistic spiritualism, would have considerably enhanced the value of Mr.
Joseph's able treatment of the uniformity of causation.

We pointed out already, in connexion with the principle of sufficient
reason (215), as well as in the preceding paragraphs, that it is a mistake in
method to suppose that we must justify the particular view of nature as a
whole, or the particular interpretation of its uniformity, on which we base
our inductions and inferences, before we proceed to make any of those
inductions or inferences. It is one thing to set out in the investigation
or discovery of truth by making certain assumptions, and to justify these
assumptions in due course : it is another thing altogether to demand an
ultimate justification of them before we set out at all, and as a con
dition for setting out. The former procedure is rational, the latter de
mand is irrational. While, for instance, it is undoubtedly true that unless
reality were intelligible, knowledge would be impossible ; it does not fol
low that this truth must be explicitly assumed and placed as the necessary
foundation and starting-point of all search for truth ; just as we saw that it is
not necessary to assume a knowledge of the existence of an All-wise Ruler
of nature before believing anything else about nature. We must start
by assuming these principles of sufficient reason, causality, and unifor
mity : they are presuppositions of induction : it is by experience — in the
broadest sense — that we afterwards justify them.

There is an analogous assumption discussed in epistemology regarding
the capacity of the mind to discover truth : an intelligible reality and facul
ties capable of understanding it are necessary for an actual knowledge of
reality, but to prove beforehand that our faculties are capable does not seem
to be a necessary condition for arriving at such actual knowledge of reality.
A good stomach and wholesome food are necessary for a good digestion ;
but a knowledge that we have either the one or the other is by no means
necessary for the desired result. The sceptic has no right to prejudge the
question of the possibility of knowledge, or to decide it in the negative sense ;
but neither does it seem justifiable to prejudge it and decide it a priori in the
positive sense. It may not be decided a priori, but only by experience, by
testing our faculties, by letting them work and observing their mode of
operation. No doubt, it is the self-same faculty, which, by reflection, observes
and estimates the value of its own operations. But this involves us in no
circulus vitiosus ; for the philosopher's critical reflection on the spontaneous
workings of his own cognitive faculties does not purport to be a logical proof
of their soundness, but a psychological process by which he proceeds to
guarantee their soundness to himself, and to satisfy himself that they have
not been deluding him. And if the reflecting mind sees no reason to doubt
the validity of its own spontaneous assents, after a careful examination of
these, it is justified in rejecting scepticism as unreasonable. This larger
question, however, is not for logic, but for epistemology.

225. RELATION OF THE PRINCIPLE TO INDUCTION AND TO
DEDUCTION. — Passing now to the second question raised above
VOL. II. 8

114 THE SCIENCE OF LOGIC

(223, p. 99), we may inquire what is the precise role played by the
principle of uniformity in every process by which we establish
inductively a general physical law : what exactly is its relation
to induction? The principle is a standard according to which
we generalize, both formally and materially, every abstract rela
tion of cause and effect which we discover in the physical uni
verse ; it is a rule of the widest generality, the indefinite scope of
which we gradually realize by the application of it to wider and
wider generalizations in various departments of nature. If we
have determined, by the methods of inductive analysis, that a
certain kind or species of physical agency, A, is the physical
cause of a, we can forthwith generalize our discovery that " A as
such is the physical cause of a" by stating that " Whenever and
wherever A is operative, there will a be found " ; and in doing
this we are only making a special application of the wider prin
ciple of uniformity which tells us that "Whatever can be predi
cated of a physical cause or nature in the abstract (as causally
connected therewith) can be predicated of all instances of that
cause or nature ". It is not that the general law of uniformity is
reached first, and the narrower law (that "A will produce a")
deduced logically from it. In neither case — and indeed in no case
— is the discovery of a general law a ratiodnative process, a logical
inference (197, 212). Inference may have been involved in the
subsidiary processes by which we verify the abstract judgment
"A as such is the physical cause of a"; but the immediate
mental process by which the law is reached is a process of judg
ment (following on abstract conception), not a logical inference in
the strict sense of a conscious derivation of one judgment from
another, or others, which imply the former logically.1 But if in
duction is riot an inference, there can be no meaning in the
statement we meet so commonly in logical treatises, that the
principle of uniformity is the major premiss — whether immediate
or remote — of every induction? The principle does not help us to
reach the abstract -truth connecting cause and effect (" A as such is
the physical cause of a "). It is in generalizing the latter (to " All

1 Cf. JOYCE, op. cit., pp. 217, 227 ; though elsewhere he defines induction as the
" legitimate inference of universal laws from individual cases " (p. 215) : he uses the
word here, presumably in the wide sense of derivation, not in the sense of a
logically "inferential process" in which the principle of uniformity would be a
major premiss (p. 218). Cf. supra, 212.

SC/. Palaestra Logica, p. 130; MELLONE, op. cit., p. 384; MILL, Logic, III.,
in., § i.

UN I FOR MIT Y OF NA TURE 1 1 5

A's will produce a") that the principle finds a partial applica
tion ; just as in applying this generalized truth to particular cases
by the syllogism, the Aristotelean Dictum de omni is partially
applied. There is, therefore, a sense in which the law of unifor
mity bears a relation to the mental ascent from particular to
universal, analogous to that which the axiom of the Aristotelean
syllogism, the Dictum de omni, bears to the descent from universal
to particular (170, 191).

Every deductive syllogism in the first figure is a special or
narrower application of the Dictum. For instance, the syllogism
"Man is mortal, Socrates is a man, therefore Socrates is mortal "
may be thus expressed : " Mortality, which is predicated of the
class man, can be similarly predicated of Socrates, who belongs
to that class " ; from which it appears, too, that the Dictum cannot
be regarded as an ultimate major premiss of all syllogisms in
the first figure, but rather as a fundamental, standard syllogism
(?All M is P; S is M ; therefore S is P"} symbolizing that
type of mental process, and by its self-evidence justifying the
latter (I92).1

So, too, induction is a distinct mental process of ascent from
particular to universal ; and every such ascent is a narrower and
more special exercise of the fundamental, standard, typical in
duction, by which we reach the widest law of physical nature, viz.
that natural causes act uniformly — that whatever (a) has been dis
covered to be really due to a physical cause (A] in any observed
instance or instances, will be always and everywhere produced by
that cause. And, just as the Dictum de omni is not a principle
whose truth must be consciously grasped by the mind beforehand,
as a condition for reasoning validly by the syllogism, but is rather
a generalization of the syllogistic process, implicitly involved in
every syllogism and explicitly grasped only by a deliberate,
reflex analysis of this process itself, so the principle of the uni
formity of nature is not a truth which must be grasped as a
logical antecedent to justify the generalization made in each
separate induction, but is rather itself a wider induction partially
involved in every special induction, and explicitly grasped and
formulated in its fulness only when the mind comes to analyse
those special inductions afterwards.2

1 C/. VENN, op. cit., p. 126 : " When the Dictum was assigned as the ground of
the individual inference, all that we were doing was to generalize this latter ".

a Mr. JOSEPH (op. cit., pp. 407, 408) rightly rejects the view that uniformity of

8*

n6 THE SCIENCE OF LOGIC

It was not by supposing " belief in uniformity " to be " by
no means the earliest of our beliefs," but in supposing it to be
reached by a certain kind of " inference," while at the same time
supposing this kind of "inference" to depend for its validity on
an antecedent profession of this belief, that Mill fell into the
fallacy of petitio principii : just as we should fall into the fallacy
were we to suppose that our knowledge of the Dictum de omni is
an antecedent condition for the validity of the syllogism, and is
itself reached by a syllogism. Belief in the uniformity of nature
(in the categorical sense) is not a mental assent which must pre
cede every induction we make : it is partially embodied in each,
and is gradually extended by us to all nature.

In every scientific induction of a physical law, belief in the
uniformity of nature is, therefore, operative. For we embrace
the belief that the causes we are dealing with are necessitating
causes (i.e. causes invariably followed by the same effects), when,
in the first or abstractive stage of the process, we convince our
selves, from an observed case or cases, that "the nature A is
necessarily connected with the effect a ".l And in the second or
generalizing stage, in which we pass from this abstract judgment
to the universal judgment, " All A's will always and everywhere
produce a" we still more explicitly assent to what is a partial
application of the general principle that "in the real order the
same cause does always actually produce the same effect".2

But, if the principle of the uniformity of nature is thus shown
to be a general expression or summing up of the mental process
by which we pass from observed cases, through \\ieabstract, to the
universal judgment — front "Some (observed) J/'s are P," through
" M as such is P" to "All ATs are P" : is not the self-same
principle equally involved in the downward process by which we
pass deductively or syllogistically from the universal "All M's
are P " to its special applications in the conclusions " These or
those S's, which are (other, new, hitherto unobserved) M's, are

nature " is the ultimate major premiss of all inductions". He further admits that
" it is not, indeed, necessary, in a particular investigation, to assume this uniformity
to extend beyond the department of facts with which we are dealing"; but con
tends that it is, though only partially applied, nevertheless universally assumed, in
every particular induction (p. 407). It is not so assumed explicitly ; but when we
come to reflect on the grounds of our inductions we see that the universal principle
was implicit or latent in them : that otherwise we could not make our experience
intelligible : that our success in making experience intelligible through it justifies
our belief in it.

1 JOYCE, op. cit., p. 219. *ibid.

UNIFORMITY OF NA TURE 1 1 7

also P " ? Undoubtedly, the principle of uniformity is involved
in the application of the syllogism to any actual sphere of reality.
The Dictum de omni informs us that "Whatever can be predi
cated of a class can be predicated about any member of the
class ". But in order to make the predication about any new
instance of a class in any actual sphere, we must (a) identify the
instance as a member of that class, and (£) assume that all the
members have a stable, uniform nature, which constantly demands
the same predicates.^

When dealing with the merely formal aspect of the syllogism,
we regarded the terms of the latter as expressing abstract con
cepts of possible class-essences, apart from the question of their
verification or realization in any actual sphere of reality. We
supposed each abstract thought-object to be fixed, stable, un
changing. We had not, therefore, to raise the question whether
there is really a corresponding uniformity, regularity, stability, in
the actual spheres within which we suppose these concepts to
apply.

It is when we pass from the purely formal and hypothetical
processes of arranging and dividing abstract concepts logically
according to intension and extension, and then reasoning " con
sistently " from them, — to the material and. categorical processes of
classifying things, of verifying our definitions of the latter, and
reasoning " truly" or "demonstratively " about them, — that we feel
called upon to justify our belief in that real uniformity in things,
which is the objective ground and condition of our thinking,
judging, and reasoning rightly about them.2

Dr. Venn, in his Empirical Logic? asks the interesting ques
tion : How is it that an analysis of induction raises the question
as to the origin of our belief in the uniformity of nature, while
no corresponding difficulty is supposed to be felt in respect of
deduction ? He takes the example of a man bitten by a cobra.

1C/. JOSEPH, op. cit., p. 378 ; MELLONE, op. cit., p. 252 (referring to Ueberweg,
Logic, § 101) : " the worth of the syllogism as a form of knowledge depends on the
assumption that general laws of causation hold in nature, and may be known ".

2 " Geometrical proofs rest on the intuition of spatial relations, and algebraic
on the intuition of quantitative relations. . . . In fact, our belief in the uniformity of
space, and in the uniform formation of the numerical series, stands to mathematical
reasoning as our belief in the uniformity of nature stands to inductive. Deny them,
and in either case no general proposition remains possible any longer. Nay more,
no demonstration remains possible even about a particular case." — JOSEPH, Logic,
pp. 506, 507.

3 p. 124.

n8 THE SCIENCE OF LOGIC

We believe the man will die. We may assign our reason in
either of two ways : —

"Deductive: All men who are bitten die. The man XY
is bitten. Therefore XY will die.

" Inductive : The men A, B, C . . . were bitten and died.
The man XY has also been bitten. Therefore XY will die."

Ask him who gives the deductive answer why he considers
that the reason he assigns is a sufficient one : he will tell you that
it is so because " what holds good of a class holds good of every
member of that class ". Now ask a similar question of him who
gave the inductive answer : ask him why does he consider the
fact that " A, B, C . . . and all men who have been bitten died "
to be a sufficient reason for believing that XY will die : he will
tell you finally that he considers it to be a sufficient reason " be
cause nature is uniform ". Now, why is the man who gives the
deductive answer let alone at this point and not called on to
explain why he believes that " what holds good of a class holds
good of every member of that class," while the man who gives
the inductive answer is not let alone, but has to justify his belief
that " nature is uniform " ? The only reason for difference of
treatment would be because the deductive reasoner is not supposed
to be concerned with the application of his class-concepts to the
real world, but only with their consistency within the sphere of
abstract thought, in which they have been conceived as fixed,
static, unchanging : while the inductive reasoner is supposed to
be concerned with the real validity of those concepts, with their
application to the real world, and, therefore, with the existence of uni
formity in the real world itself.

But the moment a person attempts to apply a syllogism within
any domain of actual reality — in other words, to demonstrate or
prove anything as true — he is committing himself to a belief in
the " uniformity of nature " regarding certain classes of things
within that domain. Hence, those logicians who are inclined to
view their science as concerned exclusively with the consistency of
thought refuse to go behind such ultimate logical generalizations
as the Dictum de omni and the Uniformity of nature for the pur
pose of justifying these. Understanding by a logical ground or
reason for assent to a judgment, always some wider generalization
which includes the latter (198), they observe that there is no pos
sible wider generalization than either of the two in question ; and

UNIFORMITY OF NA TURE 1 1 9

they conclude that the justification of our assent to such principles
falls within the province of psychology or metaphysics, rather
than of logic.1

JOSEPH, Logic, chap, xix., pp. 407 sqq. VENN, Empirical Logic, chaps,
iv., v., and xv. JOYCE, Logic, chap. xv. MILL, Logic, III., iii., iv., v., and
xxi. MERCIER, Logique, pp. 326 sqq. MELLONE, Introd. Text-book of
Logic, pp. 1.^0 sqq. MAKER, Psychology, pp. 420, 517-24. WELTON, op.
cit., ii., pp. 1-30.

1 C/. VENN, op. cit., p. 128.

CHAPTER V.
HYPOTHESIS : ITS NATURE, FUNCTIONS, AND SOURCES.

226. FUNCTIONS OF SCIENTIFIC HYPOTHESIS.— We have seen
that the aim of science is to discover the causes and laws by
which we may explain the facts of our experience. Our know
ledge of these causes and laws is embodied in universal judgments,
and these universal judgments it is the function of induction to
establish. But we can neither discover nor verify a universal
judgment unless we are first led somehow or other to suspect or
suppose it to be true. Such suspicion or supposition we call an
hypothesis.

Not every supposition, however, is an hypothesis in the strict
or scientific sense of this term. For example, in order to help
our imagination in the study of phenomena due to gravity, we
suppose that if the total mass of a body were concentrated in a
mathematical point, called the centre of gravity of the body, that
point would manifest the same force and have the same weight
as the whole body. We imagine the earth as a mathematical
point. We conceive its total gravitation-force to be concentrated
in that point — its " centre of gravity ". We find it easier in this
way to measure that force, to bring home to ourselves the law by
which it acts on bodies on or near the earth's surface, than if we
tried to conceive the several particles of the earth's mass acting
each in its own place and independently of the others, on those
bodies. But we know, all the time, that the latter is really the
case, that our conception of " centre of gravity " has no fact for
its object, that the conception is from beginning to end a mere
fancy, a purely subjective conception having no other object than
an imagined possibility.1

Again, in order to help ourselves to conceive great distances
or magnitudes we often have recourse to mental images which
we call suppositions. To realize the distance of the moon from

1 C/. MERCIER, Logique, p. 339.

120

HYPOTHESIS 121

the earth we may suppose or imagine a cannon-ball travelling
at a velocity of five hundred yards per second and reaching the
moon after eight days : that image helps us to bring home to our
selves a distance so great that a mere statement of the number
of miles in it can hardly be pictured by us. But such a supposi
tion is not what we understand by a scientific hypothesis: it
belongs to the sphere of imagination exclusively, while a scientific
hypothesis is ^judgment bearing on our knowledge of reality. The
image of the cannon-ball gives us a clearer apprehension of some
thing we already knew ; an hypothesis aims at teaching us some
thing we did not know before.1 Here is a simple example of a
scientific hypothesis : The juice of the grape ferments : the origin
and nature of fermentation were at one time unknown : Pasteur
conjectured that it was due to germs that swarm on the grapes,
leaves, and stems, of the vine-tree. That was a scientific hy
pothesis.

An hypothesis , therefore, is an attempt at explanation : a pro
visional supposition made in order to explain scientifically some fact
or phenomenon.

The construction of hypotheses is not confined to the induc
tive sciences. The process described in connexion with deductive
reasoning, by Aristotle and his mediaeval commentators, as "tn-
ventio medii" " discovery of a middle term," i.e. of true and
proper premisses to prove a conclusion, is really identical with
what we nowadays call the conception or construction of an
hypothesis. But it is in the positive or inductive sciences that
hypothesis plays an all-important role. And in these sciences
we understand by it the conception or supposition of some cause
or law capable of explaining certain observed facts. Without
hypothesis we can make no progress in scientific investigation.
We cannot find the causes of phenomena without first suspecting
their existence and whereabouts. Our experiments will lead
nowhere unless made with the object of verifying some supposition.
To direct our investigations along certain lines towards the dis
covery of laws : such, in a word, is the function of hypothesis.

All hypotheses should have their origin in the observed facts
which we are attempting to explain (233, 234). But the actual
conception of hypotheses is amenable to no logical rules. It is just
here that the sagacity, genius, and originality, of the scientist and

1 Cf. MERCIER, Logique, p. 334.

122 THE SCIENCE OF LOGIC

inventor will have free scope (197). Wrong hypotheses will be
usually conceived before right ones. Kepler is said to have
conceived and disproved nineteen successively, before arriving at
the laws of planetary motion.1 It must not, however, be imagined
that hypotheses are useless unless they turn out to be true ; they
often admirably fulfil their function of directing investigation, and
do immense service to science, even though they be afterwards
disproved. Thus, in astronomy we have the famous example ot
the Ptolemaic or geocentric hypothesis, which gave place to the
Copernican or heliocentric hypothesis in the sixteenth century.

The conception of an hypothesis which is likely to prove
useful, and helpful to the progress of science, is usually possible
only to the well-trained mind that is stocked with information
about the matter under investigation, and is accordingly quick to
detect and utilize analogies. To such a mind, even the most
commonplace facts may suggest invaluable lines of speculation
and experiment — as the falling apple did for Newton, and the
dancing lid of the steaming kettle did for Watt. Whewell was
therefore right in emphasizing, as against Mill, the great import
ance of hypothesis, or as he called it, "colligation of facts by
means of an exact and appropriate conception," in the whole
inductive process.2 But there are various kinds of hypotheses;
and some are " more far-reaching in their effects than others ; for
some are much more general, and apply to a much larger
number and variety of facts. . . . Scientific hypotheses consist
for the most part not in the mere coupling in the mind, as cause
and effect, of two insulated phenomena (if the epithet may be
allowed) : but in the weaving of a large number of phenomena
into a coherent system by means of principles that fit the facts ".3
This brings us to the consideration of some of the principal types
of scientific hypothesis.

227. SCIENTIFIC VALUE OF VARIOUS KINDS OF HYPOTHESIS.
— We have described an hypothesis as a provisional explanation
of certain observed facts. Now, we know a fact scientifically
when we know all its causes, and the mode of its connexion with,
or dependence on, these causes. If we take any phenomenon, or
group of phenomena, involving within it a multiplicity of elements,
changes, motions, activities — for example, the motions of the

1 C/. WELTON, op. cit., ii., pp. 66, 86. JOSEPH, op. cit., pp. 435-6.
a Cf. WELTON, op. cit., pp. 48 sqq. JOSEPH, op. cit., p. 434.
3 JOSEPH, ibid., pp. 432, 433.

HYPOTHESIS 123

planets, or the phenomena of the refraction and reflexion of
light — we may conceive and verify hypotheses as to the exact
quantitative relations between those various elements and motions,
without for the time inquiring either into their origin or their
raison ctetre, their efficient or their final causes. We may, by
accurate observation and experiment, seek to arrive at an exact
quantitative expression of the various events and agencies which
make up the whole phenomenon. We may aim, in other words,
at weighing and measuring the facts, at describing them with
mathematical precision, at establishing formulae which will be
" descriptive statements of the exact character of the phenomena
to be explained, when their relations to other phenomena are
not in question " ; * at reaching expressions which will describe
concisely and accurately the quantitative side of those phenomena.
Now, the scientist's supposition or conjecture as to the exact
quantitative relation or ratio between some or all of the various
elements or motions in a given series of phenomena, has been
commonly called an Hypothesis of Law. And when such sup
position is verified, and formulated in clear and concise language,
it is what is commonly recognized in the physical sciences as a
Physical Law. A " law " of nature, in this sense of the term,2
tells us "how" a phenomenon takes place, i.e. in what exact
measure and proportion the various constituent agencies and
energies must be present and operative ; it is simply an exact
mathematical description of the measure in which a certain
phenomenon regularly occurs. Such, for example, are the " laws "
of refraction and reflexion of light ; or the " law " which states
that the strength of an electric current varies directly as the
electromotive force and inversely as the resistance of the circuit ;
or the "law" of gravitation, that any two bodies in the universe
tend to move towards each other with an acceleration that varies
directly as the product of their masses and inversely as the
square of their distance apart : " The business of physical
science," writes Mach, " is . . . the abstract quantitative expres
sion of facts. The rules which we form . . . [for this purpose]
... are the laws of nature." 3

But though this mathematical measurement of phenomena
gives us a clearer description of them, still it does not give us a

1 WELTON, Logic, vol. ii., p. 91.

"For another and deeper sense of this expression, see above, 217.

*apud WELTON, loc. cit.

i24 THE SCIENCE OF LOGIC

full insight into them, it does not explain them ; for explanation
reveals not merely how, or in what manner, an event happens, when
it does happen ; but also why it happens (its final cause), and
what makes it happen (its origin or efficient cause). And while,
as physical scientists, we may seek to establish " physical laws,"
in the sense of quantitative descriptions of the relations between the
various elements of a given regularly recurring phenomenon, we
cannot, as rational beings, rest content with such partial explana
tion, but are impelled by our nature to ask ourselves further
about the " whence " and the " wherefore " of the whole pheno
menon, and so to connect it with all its causes. We cannot help
asking those further questions, because the " sufficient reason "
of any phenomenon is not to be found in the isolated phenomenon
itself, but in the sum-total of all its causes. The Positivist school
of philosophers would, indeed, have science study " only the laws
of phenomena, and never the mode of production " * of these
phenomena by their causes. But science — or philosophy — will
insist on studying the latter. Man z£/z//and must seek the causes,
both efficient and final, as well as the mere description and
measure, of the phenomena surrounding him. And the hypotheses
he makes about the causes of any given phenomenon — as distinct
from those he makes with a view to arriving at a more exact
quantitative presentation and description of the constituent parts
of the phenomenon — have been called, in contradistinction to the
latter, Hypotheses of Cause.

For example, Newton's gravitation hypothesis was an
Hypothesis of Law in so far as it simply aimed at giving an
exact quantitative expression or description of the various relations
of mass, distance, and rate of motion, that make up the whole
complex group of phenomena presented to us in our experience
of falling bodies and of the motions of the moon and the planets :
and in so far as the conception of " gravitation " includes all
these phenomena in one common quantitative description, it has
been verified, and is now an established "theory "or "law".
That is to say, we now recognize as a verified and accurate de
scription of the manner and measure in which these motions of
matter occur throughout the universe, the statement that " the
acceleration with which any two distant bodies in the universe,
Mj and M2, tend to move towards each other through space,

1 WELTON, Logic, vol. ii., p. 91.

HYPOTHESIS 125

varies directly as the product of M; and M2, their masses, and
inversely as the square of their distance (D2) asunder —

But, beyond all this lies the question as to what is the de
termining cause of those motions. And as to this, we are indeed
free to assume that it is a certain natural property, an active
power or force (228), in the bodies themselves, in virtue of which
they determine or bring about these motions in this precise
manner and measure. But beyond the mere fact, which the
principle of causality forces us to admit, that there is in the
bodies which constitute the visible universe some adequate cause
of those motions, some force that produces them, we know as yet
practically nothing. What is the nature of that force? How
does it determine and bring about those motions whose magni
tude we can accurately estimate by an already verified law?
What sort is that influence? How is it exerted through space,
independently, as it would appear, of intervening bodies? We
describe it as " attraction," but what idea does this term convey
to our minds ? Thus, as to the nature of the cause in question,
as to what kind the force of gravity is, and how it acts, we are
still largely in the dark. Here, then, is a field for further
hypotheses, hypotheses of cause, whose purport will be to explain
the known fact of gravitation. Various hypotheses have been
framed at different times to connect this fact with the hypotheti
cal all-pervading ether, and with the fundamental constitution of
matter.1 So far, however, these are conjectures hazarded to help
our imagination in picturing the phenomenon to ourselves, rather
than possible explanations of it. Hypothesis, as we have de
fined it (226), is essentially explanatory : a supposition that does
not offer an explanation of phenomena, but merely aids us in
conceiving and describing them, would appear to fall outside our
definition. Every hypothesis of cause, i.e. every supposition of
some definite antecedent (or group of antecedents) as being the
real, actual cause of the phenomenon in question, is necessarily
explanatory : it offers — provisionally — an explanation of the
phenomenon. Hypotheses of law, on the other hand, in so far as
they merely describe with mathematical exactness the manner
in which phenomena occur, are rather descriptive than explanatory ;
but nevertheless, inasmuch as a correct quantitative estimate of

1 Cf. NYS, Cosmologie, p. 125. LESAGE, The Unseen Universe, § 140. PICTET,
&tudc critique du materialisme et du spiritualisme, p. 239.

126 THE SCIENCE OF LOGIC

those changes or activities suggests or reveals to us, at least
partially, the nature of their causes and of the laws according to
which these causes interact — for " operari sequitur esse" — and
inasmuch as hypotheses of law thus inevitably suggest hypotheses
of cause, the former as well as the latter have some claim to be
called hypotheses in the stricter sense, i.e. explanatory hypotheses.

Some hypotheses, whether they appear descriptive or ex
planatory, may be recognized from the beginning as having little
or no probability. We may know so little about some unfamiliar,
unexplored, complex, many-sided phenomena — such as those of
electricity, for example — as to be scarcely able to make any sup
position at all as to their real nature, laws, and causes. But
some provisional supposition as to the nature of the agent we call
electricity, is absolutely necessary if we want to collect, arrange,
describe, and discuss, in intelligible language, its various manifesta
tions, and their connexion with their supposed common cause.
And this supposition, moreover, if it is to be of any use in help
ing us towards an explanation of the phenomena, must be based
on some analogy with some known agent. If we make any sup
position at all, from which we can infer anything, about the un
known thing we call "electricity," we must suppose the latter to
be something resembling in some way or other some known natural
agent. Accordingly, the supposition was made by Franklin,
if only as a starting-point for investigation, and to see how it
would work — in other words, as a working hypothesis, — that
electricity was a fluid of some sort. This hypothesis, though
scarcely probable, and merely " better than none," the best per
haps in the circumstances, purported from the beginning to be
mainly descriptive, but was none the less, of its nature, explanatory
also, inasmuch as it supposed the real cause of the phenomena in
question to be some sort of fluid. That hypothesis was never
verified, and gradually lost ground, at least in its original form ;
though the " electron " hypothesis, which is closely analogous to
it, is now in turn taking the place of the two-fluid hypothesis.

In other cases, however, such working hypotheses may for a
long period grow steadily in probability according as they are
found capable of explaining a larger area of phenomena, as did the
Ptolemaic or geocentric hypotheses (in astronomy), with their
cycloids and epicycloids to account for the apparent motions of
the planets.1 So admirably did this group of hypotheses " ex-
1Cf. JOSEPH, op. cit., p. 435.

HYPOTHESIS 137

plain" the known phenomena, that it was pretty generally (and
erroneously) regarded, for centuries, as a fully verified or estab
lished system. But, as St. Thomas pointed out with his character
istically prudent reserve, some other hypothesis might perhaps
account after all equally well — or even better — for the apparent
motions of the heavenly bodies.1 And so after-events proved,
culminating in the substitution of the Copernican for the Ptolemaic
astronomy.

Or again, two conflicting hypotheses may appear to account
equally well for certain phenomena. These latter will be differ
ently described on either hypothesis. And both descriptions will
appear to be equally accurate. But evidently at least one of the
descriptions must be de facto inaccurate : the assumptions involved
in the very language used — based as this is on the supposition that
the phenomena are of such and such a nature, due to such and
such a cause, while they are quite otherwise in reality — such as
sumptions necessarily falsify the whole description.

We may conclude, then, that there is no fundamental differ
ence between working, descriptive, and explanatory hypotheses,
hypotheses of law, and hypotheses of cause, provided only and
always that they are suppositions which have for their objects the
REAL CAUSES of the observed phenomena, and the REAL LAWS accord
ing to which the changes wrought by those causes in the observed
phenomena actually take place.

228. NATURE AND VERIFICATION OF CAUSAL OR EXPLA
NATORY HYPOTHESES.— The first essential, then, of a scientific
hypothesis, is that it be a supposition of something real, equally
real with the phenomenon it is to explain. This at once disposes
of the class of suppositions referred to above (226), to which we
have recourse merely in order the better to realize some pheno
menon. But, furthermore, even when the object of our supposi
tion is not a mere fancied possibility, when we mean the cause or
law we are supposing, to be real, to be a fact, even then the ques
tion arises : Have we always or necessarily a scientific hypothesis, as
distinct from what some writers, for want of a better name, call
systematic or synthetic conceptions ? 2 What sort, in other words,

1 " Licet enim talibus suppositionibus factis apparentia salvarentur, non tamen op-
portet dicere has suppositiones esse veras, quia forte secundum aliquem alium modum,
nondum ab hominibus comprehensum, apparentia circa Stellas salvantur." — In Lib.
»i. De Ccelo et Mundo, 1. xvii.

•MERCIER, op. cit., p. 338.

128 THE SCIENCE OF LOGIC

must we suppose our cause to be, in order that our supposition of
its existence be a scientific hypothesis ?

The controversy as to what kind or concept of cause it is legiti
mate for us to employ in our hypotheses about the phenomena
of nature, is one of very long standing. No supposition of ours,
as to what is the cause of a phenomenon, will be of any use unless
it be verifiable. But what kind of cause must we suppose to be
operative, if our supposition is to be verifiable ? Newton insisted
that the object of our hypothesis must be a vera causa, a real
cause — meaning, thereby, to exclude arbitrary, fanciful, a priori
suppositions and prejudices, not suggested by facts of experience.
This, of course, is obviously right and proper. Must the cause,
however, be supposed to be itself a phenomenon of some sort, i.e.
something itself perceptible by the senses, so that the only valid
verification of such hypothesis would be actual discovery, by sense
perception, of the supposed cause, and actual observation of its
visible causal connexion with the effect ? Such a requirement is
rightly repudiated by scientists, though it is only such a sort of
cause that answers to Mill's definition.1 Followers of Mill's
phenomenist philosophy contend that it is a mere waste of time,
and a hindrance to real scientific progress, to refer the various
phenomena of mind, or of external nature, to corresponding
" faculties " or " powers " or " forces " in either domain. And
no doubt, such reference of individual effects, or classes of effects,
to corresponding efficient principles, whether these be called
" faculties " or " forces," would be calculated to retard further in
vestigation, if such reference were taken as an ultimate rational
explanation of those effects ; if, for instance, men were so foolish
as to think they had said the last word as to why opium induces
sleep by declaring opium to have a vis dormativa — to use the old
familiar example.

It is true that in the Renaissance period some of the decadent camp-followers
of the great mediaeval Scholastics left themselves open to this reproach by taking
refuge in such verbal explanations of natural phenomena.2 But up to quite

1 Logic, III., v., § 2. Cf. supra, p. 74, n. 3 ; infra, p. 131.

2C/. DE WULF, Scholasticism Old and New (2nd edition), pp. 147 sqq. ; His
tory of Medieval Philosophy, p. 503. It was not, however, the fault of those mediaeval
philosophers that the " forces " or " causes " in question were then, and are still for
the most part, " occult," i.e. such that we have no positive imagination of the mode
of their action. Modern scientists who are loudest in their ridicule of those " occult
forces "are themselves obliged to have recourse to " motions " and " masses " and
" ions" and " electrons " and " ids " and " biophors " and a whole host of such things,

HYPOTHESIS

129

recent times it was the fashion with modern philosophers and scientists, in their
boasted ignorance of mediaeval thought, to impute this and all manner of ab
surdities to Scholasticism generally, and with the inevitable result that the
ridicule they heaped upon their predecessors is now seen in the light of history
to recoil upon their own heads. The thirteenth-century Scholastics, no less
than their later critics, realized the importance of observation and experiment,
the necessity of noting analogies between phenomena, of endeavouring by ana
lysis of these analogies to reduce gradually, as far as possible, the number of
distinct " forces," or " powers " postulated for the explanation of phenomena.
They were never content to refer each separate phenomenon in nature to a
distinct and corresponding cause supposed to be capable of producing that effect
alone— to be sui generis, so to speak. They pushed investigation as far as the
conditions of their time permitted. And those who, in modern times, have in
herited the best traditions of Scholasticism, have always welcomed every careful
attempt of the positive and experimental sciences to unify our experience of
external nature by tracing large and varied and apparently unconnected fields
of phenomena to the operation of some one or some few common " agencies ".
They have nothing but approval for the methods whereby scientists have for
mulated and tested hypotheses for the exploration of hitherto unsuspected natural
" forces," or for the explanation of phenomena by referring these to already
known " causes," with which such phenomena were previously thought to have
no connexion. They themselves adopt these methods in physical science.
They are not content to say that the varied phenomena of external nature must
have causes, must be due to the operation — and co-operation — of nature's
forces and agencies. They endeavour to discover in what groups of pheno
menal antecedents the agencies productive of a given effect are operative.
They try to bring to light " the sum-total of the [phenomenal, perceptible] con
ditions, positive and negative taken together, the whole of the contingencies of
every description, which being realized the consequent [effect or phenomenon]
invariably follows " — which is Mill's own conception of the discovery of a
"cause".1 And it is only when the inductive methods fail for want of ana
logies on which to base hypotheses, i.e. in investigating the remoter causes of
wider fields of phenomena, and the Ultimate Cause of the whole phenomenal
universe, that they use the simple a posteriori argument to prove that such re
moter causes— and such Ultimate Cause— must exist, and to discover about
the nature of these just as much as the effects will warrant us in attributing
to the latter.

But Scholastics have held to the doctrine that while the senses stop at
phenomena, intellect or reason can discover, in these phenomena, "substances,"
" causes," " faculties," " forces," which constitute and permeate the world of
sense experience, and which reveal themselves to intellect by acting in and
through the phenomena of sense. And they have held to this doctrine in
obedience to such self-evident dictates of reason as that " every event must

just quite as occult, in their own hypotheses. " How could masses and motions that
must remain occult be anymore acceptable . . . than the occult powers of the ancient
Scholasticism ? " — DUHEM, L' Evolution de lamecaniqtie, p. 190. Cf. Dublin Review ,
April, 1906, pp. 332, 337, where Professor Windle suggests a comparison of some of
Weismann's hypotheses with the famous virtus dormativa.
1 Logic, iii., v., § 3.
VOL. II. 9

1 30 THE SCIENCE OF LOGIC

have a cause," " every change must be a change of some state," and " every
state must be a state of some subject or substance ". Of course, such principles
will not of themselves unlock the secrets of science by telling us whether this
and that event, or change, or state, have any underlying agencies, or causes,
or substances in common, or how many of the latter there are in the world of
sense experience altogether. Yet positivists and phenomenists appear to think
that something like this should be expected from those principles. For, not
rinding in the latter the key to any new positive information about nature, they
proclaim that " substance," " power," " force," " efficiency," " purpose," etc.
— in a word, all such objects of thought as lie beyond the ken of the senses —
are " occult " and " unknowable," and should therefore be discarded.1 But as
a matter of fact these objects are not " occult " to the intellect— of Positivists any
more than of Scholastics. The former, despite their disclaimer of agnosticism,
know just as much, or as little, about such objects of thought, as the latter : they
discourse about " substances " and " causes " and " forces " and " faculties " no
less than the latter : and we are all alike guided, in our ascent to such thought-
objects from the data of sense, by the scholastic principle that from the operations
of things we judge of their natures : operari sequitur esse ; qualis est operatio
talis est natura.

But positivists pretend to be able to " explain " the universe without calling
in the aid of any " hyperphysical " entity 2 — we shall see presently with what
effect, — and blame Scholastics for not discarding the " antiquated " metaphysics
of " substance " and " accident," of " faculty," " power," and " force," in the
philosophy of external nature. They have tried — unsuccessfully, of course —
to deliver human reason from the supposed bondage of theology and meta
physics, by eliminating from their system of thought all such " Scholastic "
notions. We m£y be pardoned if we hesitate to exchange the " antiquated "
system for the teaching of those later philosophers— who resolve all reality into
" states " or " phases " or " processes," while denying that there is any sub
stance or agent of which these are the states, phases, or processes ; or into a
transient " flow " of sensations in the individual's consciousness, while denying
that there is any permanent mind other than the said flow of sensations, or any
abiding, substantial ego, or individual, to experience and interpret these sensations,
and thus to remember past experience and to expect and anticipate future ex
perience. The fact is that this phenomenist philosophy has made itself unin
telligible by " divesting the human mind of its most fundamental conceptions " 3
— or, rather, by pretending to accomplish such a hopeless task : for it really
smuggles into its explanations, at every turn, under the mask of a new termin
ology of course, the very conceptions it pretends to dispense with.

In opposition to the traditional philosophy of those so-called
"occult" causes, Mill boldly proclaimed that he would deal only
with causes which were themselves " phenomena," i.e. entities
which would be in themselves perceptible by the senses : " I pre-

1 Cf. I. E. RECORD, April, 1910: " Some Current Phases of Physical Theories,"
p. 403 ; January, 19 10 : " The New Knowledge and its Limitations," p. 27.
3 Cf. I. E. RECORD, April, 1910, ibid.
3 WARD, Naturalism and Agnosticism, i., p. 65. Cf. I. E. RECORD, ibid., p. 400.

HYPOTHESIS 131

mise," he wrote, " that when ... I speak of the cause of any
phenomenon, I do not mean a cause which is not itself a pheno
menon ; I make no research into the ultimate or ontological cause
of anything".1 The trammels he thus sought to impose upon
human thought were soon deemed too irksome, not only by philo
sophers, but even by the scientists who professed a general sym
pathy with the positivist philosophy. It is, indeed, conceivable
that scientists might agree to confine their efforts exclusively to
the discovery of coexistences and sequences between phenomena,
and to eschew all thought and all mention of non-phenomenal or
imperceptible entities, even as mere aids to investigation.2 But of
course they have refused — and rightly — thus to debar themselves
from using their imagination at all events, in addition to their
senses. They have given a very wide interpretation indeed to the
term "phenomenon," if the "causes" which they contemplate
nowadays in their hypotheses are to be regarded as phenomena.
Not only are some of the objects of current scientific hypotheses
— i.e. some hypothetical causes of the phenomena of nature — not
perceptible themselves by the senses, but they are not even in any
true sense positively picturable by the imagination. We are very
far removed indeed from the " phenomenal antecedents " of Mill
when we are introduced into the domain of "ethers," "vortices,"
"corpuscles," "ions," and "electrons," by the physicist, or into
the domain of " ids " and " biophors " and " biotic energies " by
the physiologist. Indeed it is not so clear that scientists have not re
turned to the " occult " entities of the " antiquated " metaphysics,3
and merely rebaptized, in a more mechanical terminology, the
" materia prima " and "powers" and "efficiencies" and "vital
forces " of Aristotle and the Scholastics ! As a matter of fact, it
is now beginning to be recognized by scientists that all attempts
to explain nature, whether organic or inorganic, by collocations
and motions of material masses in space and time, i.e. by purely

1 Logic, 111., v., | 2.

3 C/. POINCARE, Science and Hypothesis, p. 223 : " The day will perhaps come
when physicists will no longer concern themselves with questions which are inacces
sible to positive methods, and will leave them to the metaphysicians. That day has
not come yet ; man does not so easily .resign himself to remaining for ever ignorant
of the causes of things."

3 See article, " Weismann and the Germ-Plasm Theory," in the Dublin Review,
April, 1906, where Professor Windle suggests the comparison of Weismann's hy
potheses with the "zns dormativa" and other such "virtutes occultae" of the
older philosophy. C/. also, What is Life ? by the same author (Sands & Co., 1908) ;
and I. E. RECORD, April, pp. 398 sqq.

9*

132 THE SCIENCE OF LOGIC

perceptible or picturable factors, and without the aid of purely con
ceptual or intelligible factors, such as force, power, efficiency, pur
pose and design, have proved futile; that concepts of hyperphysical
entities and influences, however " occult " to sense or imagination,
are indispensable for a rational explanation of nature's processes ;
in a word, that the cause or principle of action which may be the
object of a legitimate scientific hypothesis need not be itself a pheno
menon, directly perceptible by the senses.

It must, however, be such an agency, or group of agencies, that,
though not directly perceptible itself, it is perceptible in its effects :
it must be supposed to dwell in phenomena, to become operative
in certain combinations of phenomena, and to produce therein directly
perceptible effects. This indirect 'perceptibility of the supposed
causes, in their effects, is necessary and sufficient for the object of
a scientific hypothesis. In this way alone are "atoms," "elec
trons," " ions," " sub-atomic motions," " biophors," and all the
infinitesimally minute "causes " of modern scientific hypotheses,
perceptible or " phenomenal " : in their effects, in the phenomena
which they are supposed to actuate or constitute ; and in this
they differ in no way from the " materia prima" "forma sub-
stantialis" "qualities," "forces," "faculties," "natures," "pro
perties," etc., of Scholasticism: for these too are perceptible
indirectly, in their effects.

Properly speaking, all such explanatory factors of our experience are
" intelligible " or " noumenal," rather than " sensible " or " phenomenal ".
The need that impels us to look for an explanation of sense experience obliges
us to conjecture or suppose the real existence and operation of such — really
supra-sensible— agencies. The whole process of conceiving the latter, and
reasoning from such conceptions, is a process of the faculty which transcends
the faculties of sense — the intellect. It makes comparatively little difference
whether these conceptions, these hypothetical " causes," are more or less im
mersed in, and supported by, concrete imagination-pictures.1 The visible,

1 It might, perhaps, be argued that hypotheses having for their objects abstract
" powers," " forces," " natures," etc., in phenomena, cannot be so accurately verifi
able, nor, therefore, so fruitful to science, as hypotheses which contemplate only
such directly calculable factors as " atoms," " electrons," " undulations," etc. This
is scarcely true, for mathematical values may be assigned to the former as easily as
to the latter. It cannot be said that the British scientists have in any striking way
excelled the French in their contributions to science ; yet the former have been always
far more addicted than the latter to concrete, picturable, mechanical conceptions.
C/. DUHEM, Evolution de la mecanique (Paris, 1903, ch. xv.) ; Professor Windle's
article in the Dublin Review, already mentioned ; art. on " The Contrast of English
and French Concepts of Physical Theories," by the Rev. P. DE VREGILLK in the
Month, April, 1907, pp. 350 sqq. ; H. POINCARE'S Science and Hypothesis (Eng.

HYPOTHESIS 133

measurable phenomena, in which they are supposed to be operative, are
equally amenable to observation and experiment, whether the hypothetical
" causes " be conceived as " properties," " forces," " affinities," " qualities ; "
or as " atoms," " electrons " " vortices," " undulations," etc. Quantitative
values may be assigned to such factors, by whatever names we call the latter.
Since they are supposed to be factors operative in material phenomena, there
must be a quantitative aspect in their modits operandi ; only we must not forget
that this is not their sole aspect, and that we have not " explained " the facts
fully by " calculating " the measiirable aspects of these factors. Yet this is
likely to be forgotten by scientists who are influenced by the empirical philo
sophy. Their tendency naturally is to assume that " all perceptible facts are
measurable " 1 in terms of material masses and mechanical motions, and that
science can attain to nothing that is not thus measurable. But, for instance,
exhibitions of " talent, prudence or self-denial " 2 are perceptible facts. Yet,
surely, their " magnitude " cannot be measured by any mechanical standard.
The " attainment of precise mathematical law " is a proper ideal for those de
partments of research whose laws are capable of assuming " the form of pre
cise quantitative statement " ; 3 but to assume that all reality is thus quantita
tively measurable, and that exact measurement exhausts all we can know about
it, is utterly unjustifiable in point of method, as well as being erroneous in fact.
An unfortunate outcome of this tendency has been already instanced (201, 224,
cf. p. 141) in the hopeless attempts of some scientists and philosophers to ex
plain all the phenomena of the universe on the hypothesis that they are all
ultimately reducible to mechanical motions of atoms of matter, a supposition
which has absolutely nothing to recommend it but its excessive simplicity.4
Of course, the physical scientist as such may confine himself to the conception
and verification of hypotheses that are empirically verifiable, hypotheses about
the proximate, phenomenal antecedents of this or that series or group or order
of phenomena ; he may abstain from philosophizing, from seeking the ulti
mate causes of all physical phenomena : in which case he will have no occa
sion to " invoke the agency of beings whose existence cannot be empirically
verified," 5 i.e. beings like angels, spiritual souls, human free-will, God — for
whose modus operandi known physical agencies and laws furnish no analogy.
He may abstract from the influence of such agencies until he reaches the point
at which mere physical antecedents begin to appear insufficient or unsatisfac
tory for the explanation of his facts. Up to this point, being concerned with
proximate causes, he has no need to inquire into ultimate causes : hence, as a

tr.), ch. xii., pp. 213 sqq., and Introduction by Professor LARMOR, pp. xiv.-xvi. An
instructive illustration of the British frame of mind is to be found in a passage
from one of Lord Kelvin's lectures at the Johns Hopkins University (quoted by
DUHEM, op. cit., p. 194, from the author's Lectures on Molecular Dynamics, p. 132;
also by WARD, op. cit., i., p. 119, from Nature, vol. xxxi. (1885), p. 603 : " I never
satisfy myself till I can make a mechanical model of a thing. If I can make a
mechanical model I can understand it. As long as I cannot make a mechanical
model all the way through, I cannot understand. . . ." As to which Dr. Ward
pertinently asks: " Why must mechanism 'all the way through' be the one and
only means of intelligibility ? " (op. cit., p. 120).

1 WELTON, op. cit., ii., p. 160. 'ibid., p. 161. 3ibid.

4 Cf. WELTON, op. cit., ii., p. 209. 5 JOSEPH, op. cit., p. 429.

134 THE SCIENCE OF LOGIC

physical scientist, he may say with Bacon, " Deum semper excipimus " ; * for,
as Newman has somewhere said, science is a-theistic, or non-theistic, in the
sense that God does not come within its immediate scope. But all physical
investigations lead up sooner or later to a point at which physical, empirically
verifiable antecedents begin to appear unable to account for all the facts. If,
at this point, the scientist chooses to contend that physical antecedents — as,
for instance, atoms and motion — are still sufficient to account for everything,
he is indeed at liberty to propound this mechanical conception as an ultimate
philosophy of the universe — as Laplace appears to have done when he told
Napoleon that he had no need of the hypothesis of God in his Mecanique
Celeste ; a — but he cannot contend that physically verifiable hypotheses are alone
" legitimate," nor can he disallow hypotheses which postulate ultra-physical
causes, by the a priori assumption that such hypotheses are not " scientific ".
If no physical causes we can postulate are sufficient to explain the physical
universe as a whole, it is not only perfectly legitimate, it is even logically
necessary, and therefore "scientific," for us to postulate causes which are
ultra-physical. Such hypotheses cannot be described as " unscientific," or
" scientifically inadmissible," 3 for there a're causes other than physical or
phenomenal, and laws other than mechanical or mathematical, of which we
can, nevertheless, have scientific knowledge. No doubt, the terms " science "
and " scientific " are often narrowly used nowadays as synonymous with
the exact sciences of mathematics, abstract mechanics, and physics conceived
and treated mechanically ; 4 and sometimes with the mischievous insinuation
that in these departments alone is to be found certain knowledge ; but when
we speak of " the aim of science as such, and of the logical conditions
under which that aim can be realized," 5 it would be misleading to identify
science with physics, instead of understanding it in the philosophical sense
of all certain knowledge of things through their causes. Although, there
fore, when there is question of discovering the proximate causes of " a parti
cular natural event," our hypothesis "should be," as Mr. Joseph holds, "of
such a nature that observable facts, if we could find them, might prove
. . . it " ' by disproving all its rivals ; yet we cannot place this restriction on
the conception of certain wider and more fundamental explanatory theories
to which science leads, and to which we shall presently refer ; 7 nor does
Mr. Joseph appear to insist on such a restriction in these cases : 8 on the
contrary, in regard to such " postulates," or " fundamental assumptions," he
consents to " enlarging . . . the liberty of the mind " in a way we cannot
profess to understand, for he says " the fundamental assumptions of a science
may be metaphysically untenable, and we enlarge it [the " liberty of the
mind "] to extend to all which these assumptions cover, however it may be
ultimately impossible to think the facts in terms of them ".' If a scientist

1 De Principiis atque Originibus, ELLIS AND SPEDDING, iii., p. 80 ; — apud JOSEPH,
op. cit., p. 429.

2 Cf. JOSEPH, ibid. ; WARD, Naturalism and Agnosticism, i., pp. 3, 4, 45, 46,
64 ; POINCARE", op. cit., Introduction by Professor LARMOR, p. xiv.

3 JOSEPH, ibid.

4 Cf. WARD, op. cit., i., Lectures v., vi., and passim.

5 JOSEPH, ibid, (italics ours). *>ibid. 1 infra, p. 137.
*Cf. op. cit., pp. 468, 476-7; infra. 9ibid., p. 430, n. 2.

HYPOTHESIS 135

goes on constructing and testing hypotheses based on fundamental assump
tions which he knows to be metaphysically untenable, he must surely know
that, whatever practical utility they may possess as possible aids to experiment,
they cannot be true theories of reality, or ever form a constituent portion of
science proper, of truth, whether physical or metaphysical. The assumptions
Mr. Joseph has in mind are probably, among others, " the independent exist
ence of matter, the action of one independent thing on another, the produc
tion of a conscious state by a process in a physical organism " : * these he
regards as " unable to resist metaphysical criticism," 2 and as affording, there
fore, only a provisional validity to the scientific hypotheses and explanations
based upon them. No doubt, if such metaphysical theses are held as unproven
assumptions, the scientific theories based upon them will be only provisional.
For instance, the scientific theories based upon the hypothesis of an ether-
medium in space can be true only on the assumption that there is no actio in
distans in the actual physical universe. But it is one thing to accept any such
fundamental assumption provisionally, and proceed to build upon it, and an
other thing altogether to regard such an assumption as " metaphysically unten
able ". We take this latter expression as equivalent to rationally indefensible;
and, obviously, to build on such an assumption would be worse than illogical,
for it would be irrational. Mr. Joseph's difficulty, from the point of view
of metaphysics, against such assumptions of science as those referred to,
seems to be that they " are all unintelligible " 3. But this brings us again to
the question referred to in connexion with the principles of Sufficient Reason
and Uniformity of Nature : What is the criterion of intelligibility ? Is that
alone intelligible which is imaginable after mechanical analogies, and de-
scribable in terms of the purely quantitative concepts of mathematics and
dynamics ? and is it only such laws and principles that are to be recognized
as scientific ? 4 Such a restricted conception of the domain of the " intelligible "
and the " scientific " we regard as a good example of those metaphysical as
sumptions which are fairly open to serious criticism.

229. THE R6LE OF ANALOGY IN VERIFICATION : ULTIMATE
SYSTEMATIC CONCEPTIONS.— The " cause " which forms the object
of a scientific hypothesis need not, then, be itself a phenomenon.
Further, it need not be an agency which is already known as such
to be operative elsewhere in nature : otherwise no new natural
agency could be discovered by way of hypothesis. But it must
be conceived to bear some analogy or resemblance to some such
known agency. The reason of this requirement is not difficult
to find. It is only in so far as we conceive our supposed cause
to be analogous in its modus operandi to some known cause or
other, that we can infer anything as to the conduct of the former
in this or that particular set of circumstances. And it is only by
observing such operation — experimentally, if necessary and pos-

lop. cit., p. 469. *ibid. 'ibid.

4C/. WARD, op. cit., i., pp. 119, 120.

136 THE SCIENCE OF LOGIC

sible — in varied circumstances, and by seeing whether this tallies
with what we should expect, that we can hope to verify our hy
pothesis. The only means we have of going beyond the general
assertion we can make in virtue of the principle of causality — that
the phenomenon (C) has a determining cause — the only means of
discovering the latter, of detecting its whereabouts, and bringing it
to light, is by supposing it to be some definite cause of a certain
kind (say X], and then trying to verify this supposition by the
employment of some processes that may lead with certainty to X
as the only possible cause of the phenomenon in question, the only
possible element, amongst all the surroundings of the pheno
menon, which can be the determining cause of the latter. When
we have discovered that the supposed cause, X, is the only possible
cause of the phenomenon, then, and then only, can we infer, from
the reality of C, that the supposed cause, X, is its real cause ; for
X is an antecedent of which C is the consequent, and from the
reality of C we can infer the reality of X, only when the latter is
not merely the sufficient or necessitating, but also the only possible
cause of the former.

But it is obvious that we cannot bring any such independent
experimental processes to bear upon X, to determine if it be
real, unless we suppose it to be of a nature at least partially
known, i.e. to have some analogy with known causes, to be of
such a kind that we can deduce from it something else besides the
bare phenomenon for whose explanation it was postulated. If we
cannot draw any other inference from it except that ; if it is so
unique, so unknown to us otherwise, that all we can say about it
is that " it is a something which is the determining cause of this
phenomenon " ; if we cannot study it in varying sets of conditions,
and conceive what its effects would be, and how its influence
would be manifested therein, and see whether these inferences
tally with the phenomena that are observed to occur in these
conditions : if we cannot do all this, manifestly we cannot hope
to be able rigorously to verify our hypothesis ; for it is only by
doing all this that we can sift the surroundings of the pheno
menon and prove that the supposed cause, X, is the real one, by
proving that it is not only a sufficient (necessitating) cause, but
the only possible cause, that could determine or bring about the
phenomenon. Unless, for example, we supposed the so-called
luminiferous ether to resemble matter so far at least as to be sub
ject to the laws of motion, unless we supposed it to have some

HYPOTHESIS 137

analogy with the elastic medium, air, which propagates sound,
we could infer nothing at all about it in explanation of the pro
pagation of radiant heat and light. If it " were wholly different
from anything else known to us, we should in vain try to reason
about it".1

But now, granting all this ; granting that if the hypothesis is
to be verifiable in this sense, i.e. empirically, by being brought to
the test of facts, the supposed cause must have some analogy
with known causes ; the question at once arises : Is it always
possible to make an hypothesis of this kind ? Or must we not be
sometimes satisfied with supposing, as the real cause of the pheno
mena under observation, some cause for the conception of which
we can have no independent evidence, no analogy to aid us ; for
the real presence of which we have no independent evidence, i.e.
other than the actual phenomena under investigation ; and about
whose nature, therefore, we cannot hope to learn anything further
than what we can attribute to it as cause of these phenomena ? The
answer is, that certainly we must sometimes be satisfied with this
latter sort of supposition. In searching for the immediate causes
of the smaller sections of reality examined in the various special
sciences, analogies are more abundant. But according as we seek
the remoter and wider causes of more extended regions of reality,
our sources of analogy must of necessity become fewer and fewer,
and we are forced to fall back upon the supposition of causes about
whose nature we can get practically no other information than what
the study of the effect itself — the larger field of phenomena in ques
tion — will yield us. This is the case with all those wider and more
fundamental speculations, or " systematic conceptions," about the
ultimate nature and properties of the phenomenal universe, about
the constitution of matter, the cause of gravitation, the arrange
ment and motions of the heavenly bodies. Our hypothesis may
account sufficiently for all the facts that suggested it ; but who will
say that it is the only one that can account for them ? The most
we can say is, that of all the alternative hypotheses it is the one
that accounts best for the facts ; and this may give us moral
certitude that it is the right one, even though, strictly speaking,
we cannot pass from the affirmation of consequent to the affirma
tion of antecedent unless we know that the latter is the only
possible antecedent of the consequent in question.

1 JKVONS, Principles of Science, p. 512.

138 THE SCIENCE OF LOGIC

For centuries, the Ptolemaic system of astronomy was accepted as being
the only one that could account for the facts. It was only a man of the rare pene
tration of Aquinas who could point out that perhaps on some other hypothesis
these could be equally well explained : "forte secundum aliquem alium
modum nondum ab hominibus comprehensum apparentia circa Stellas sal-
vantur " ; 1 and the substitution of the Copernican system, three hundred years
afterwards, justified his suspicions. Probably no one at the present day would
venture to doubt the truth of the latter system. But there are in current
science several " systematic conceptions " of such a character that they can
scarcely ever be verified in the stricter sense of being shown to be the only
possible explanations of the facts. A few of these will help to illustrate how
such conceptions differ from strictly verifiable scientific hypotheses.

Lord Kelvin's theory that the ultimate atom of matter is a vortex-ring in a
perfect liquid, is rejected by Clifford as unscientific because " a perfect liquid is
not a known thing but a pure fiction ... a mere mathematical fiction " ; *
and, since we can deduce nothing from the absolutely unknown, the hypothesis
is unverifiable.

Laplace's hypothesis— that the solar system was at first a rotating nebula
from which the planets got detached, and from them in turn their satellites or
moons, all of which condensed and cooled down gradually by radiation, and
so solidified — is not verifiable either by observation or by experiment. It does
not bear upon the immediate, but upon the remote, far-distant origin of our
earth and solar system, at a time when the conditions of the natural forces at
work may have been very different from any with which we are at present
familiar. What hope, therefore, can we have of ever proving that these planets
could have developed in no other possible way ? It remains, therefore, a mere
hypothesis, and may have its function in science ; but it is not a scientific hypo
thesis in the strict sense, if by the latter we are to understand a supposition
whose truth can be rigorously established, to the exclusion of all alternatives,
by that experimental method of which Pasteur has so well said that it " leads
to absolute and unanswerable demonstration . . . and deceives none but
those who make a bad use of it ".3

The same remarks apply with equal force to the conception of an all-
pervading ether as a medium for the propagation of light, of radiant heat, of
electric and magnetic influence, etc. The existence of some medium is the
only alternative to actio in distans, the absolute impossibility of which is not
easily demonstrable ; and the nature of the supposed ether, the properties
with which it is endowed, are not by any means agreed upon by scientists.4
In those circumstances, no prudent scientist would venture to say that the ether
as he conceives it, and the modes of transmission of those various influences as

1 In Lib. II. de Cash et Mundo, lect. xvii. Cf. Summa Theol. ia, P. Q. 32, a,
i, ad 2. DE WULF, Scholasticism Old and New, p. 32.

2 CLIFFORD, Lectures and Essays, p. 169. — apud WELTON, op. cit., ii. pp. 74, 98.

3 MERCIER, op. cit., pp. 340-1.

*Cf. The " New Knowledge " and its Limitations, in the Irish Ecclesiastical
Record, January, 1910, pp. 23 sqq. — the fourth of a series of articles in which are
examined in some detail the implications of another of those " systematic concep
tions " — the electrical theory of matter. Cf. art. on The Philosophy of Energy, ibid.,
February, 1910, and Some Current Phases of Physical Theories, ibid., April, 1910.

HYPOTHESIS I39

he describes them, afford the only possible or conceivable explanation of those
phenomena.

Again, are vegetable and animal species fixed, or transformable ? Let a
naturalist suppose them to be transformable. He must proceed to experiment
on some cause supposed to be capable of effecting the transformation from
some one specific type to a different type, and so submit his supposition to the
control of facts. What might such a cause be ? A possible cause is sug
gested by the phenomena of artificial selection, and artificial cultivation or
rearing, which are found to be productive of new varieties and races. Darwin
observed those phenomena carefully and minutely, and then made the sup
position that there are at work in nature agencies analogous to those em
ployed by the artificial breeder, and capable of producing not merely new
varieties or races, but new species. Now, if there are really in nature some
such agencies, they can become the object of scientific hypotheses, and their
mode of action may be described— after the analogy of the intelligent artificial
selection, or intelligent sorting, of the breeder — as " natural selection ". But it
remains an open question whether the actual existence of such transforming
agencies in nature — if there are such — can ever be verified : and until their
existence and mode of operation are at least shown to be capable of verification,
the hypothesis will remain a mere systematic conception, an " idee directrice," ] a
methodological view of the world of living things, rather than a " scientific "
hypothesis.

Similarly, such an hypothesis as Weismann's germ-plasm theory to account
for the fact of heredity, can scarcely be regarded as a scientifically verifiable
hypothesis, involving, as it does, elements admittedly beyond the range of all
possible experience. Professor Windle, writing about it in the Dublin Review*
remarks that " the theory is a tolerably complex one to be built upon a system
of ' vital units ' which no one has ever seen or ever can demonstrate ".

Yet another instance of the same unsatisfactory class of conceptions is
that of Sir William Crookes, regarding the renovation of energy in the universe :
" that the heat radiations propagated outwards ... are transformed at the
confines of the universe into the primary — the essential— motion of chemical
atoms, which . . . gravitate inwards, and thus restore to the universe the
energy which would be lost to it through radiant heat." 3

On the other hand, a good example of a thoroughly scientific hypothesis,
afterwards experimentally verified beyond any possibility of doubt by the
" method of difference " (241), was Pasteur's supposition that the fermentation of
the grape was due to germs that settled on it, and not to mere chemical action.
He first extracted the juice from the interior of the grape without allowing it
to come into contact with the exterior covering, or with the air, sealed it her
metically in tubes, and found that it did not ferment. Again, in the month of
June— before the appearance of the coating of germ-cells, which begins in
July — he carefully surrounded certain grape-clusters with wadding, and so pro
tected them from the germs. The grapes of those bunches were pressed and
the juice obtained refused to ferment.

Equally convincing, perhaps, were the experiments of the same eminent

1 MERCIER, op. cit., p. 340, from which context the above example is taken.

2 April, 1906, p. 334 (italics ours).

3 apud GERARD, The Old Riddle and the Newest Answer, p. 26.

MO THE SCIENCE OF LOGIC

scientist, and of Professor Tyndall, in establishing the hypothesis of biogenesis,
and disproving that of abiogenesis or spontaneous generation. Yet, there are
scientists who still refuse to admit that the experiments of those two men finally
established the former, or disproved the latter hypothesis : a good illustration
of the possible differences of opinion as to the amount of verification that is
to be deemed adequate in any given case. " Every effort," writes Professor
Windle,1 " to prove the existence of spontaneous generation, has so far failed.
It is true, all this amounts to is that no experiment has ever yet succeeded in
showing that spontaneous generation takes place, and there are those who
urge that some experiment may yet turn out to be successful." The experi
ments of Professor Burke of Cambridge, upon gelatine acted on by radium,
do not seem to lend any probability to the hypothesis of spontaneous genera
tion. Weismann unscientifically regards the latter as the only possible hypo
thesis, though holding at the same time that the process will for ever escape
observation.

Finally, a brief comparison of the Atomic Theory (in chemistry) with the
Mechanical Conception of the Universe (in philosophy) will furnish an instructive
contrast between a strict scientific hypothesis and an unverifiable systematic
conception. The " atomic theory " in chemistry is an hypothesis which supposes
chemically simple bodies to be aggregates of particles indivisible by any known
chemical methods, and accordingly called atoms. This hypothesis is exceedingly
probable, if it is not indeed fully verified by the various arguments on which it
is based. One of these, for example, is drawn from the experimentally estab
lished Law of Multiple Proportions. For instance : nitrogen combines in
constant ratios by weight — 28 parts — with varying weights of oxygen, but
only on condition that these latter be always some multiple of a minimum
combining weight of oxygen — 16 parts. Thus N2, 28 parts by weight of
nitrogen, combines respectively with 16, 32, 48, 64, 80 parts by weight of
oxygen, to form five different oxides ; N2O, N.2O2, N^Oj, NaO4, N2OS.
Now, does not this remarkable fact or law suggest, as a possible — if not its only
possible — explanation, that the mass of oxygen represented by 16 is a fixed,
constant, chemically indivisible portion of matter, — an atom ? - Suppose 28
grammes of nitrogen and (say) 20 grammes of oxygen together submitted to the
chemical agencies capable of effecting a combination : why, if the mass of
oxygen were capable of indefinite division by those agencies, should 4 grammes
of oxygen invariably remain over ? Why should not that mass of 4 grammes
divide itself around on the 28 of nitrogen, seeing that these have an equally
strong affinity for all parts of the mass of oxygen ? But if we conceive the
28 grammes of nitrogen as containing a certain number of atoms — twice as
many as 16 grammes of oxygen contain — each pair of which nitrogen-atoms
unites, under the play of the chemical forces at work, with one atom of oxygen,
there will be evidently 4 grammes of atoms of oxygen left, each of which would
have to divide into four parts in order to give an additional share to each pair
of nitrogen-atoms. But the atom being, ex hypothesi, indivisible by the
chemical agencies at work, the 4 grammes of oxygen must remain unincorpor
ated into the compound.

Many scientists regard this hypothesis— that the chemically simple bodies
are made up of chemically indivisible particles, or atoms — as an established

1 Dublin Review, April, 1906, p. 340. * Nys, Cosmologie, p. 411.

HYPOTHESIS 141

theory. Recent researches into electrical phenomena, and into the properties of
radium, have, however, led scientists to suppose that there may be at work, in
nature, agencies other and more powerful than chemical forces, capable of dis
integrating, and indeed actually and constantly disintegrating, the chemical atoms
and molecules of all matter.

Quite different from this chemical atomic theory, though at first engrafted
on the latter, and advocated as an extension of the latter, is what we have
called the Atomic or Mechanical Conception of the Universe. While the
former hypothesis gives a view of matter which is most probably if not certainly
true as far as it goes, the latter is not only beyond the range of rigorous veri
fication, but may easily be shown to conflict with multitudes of facts, and to be
accordingly untenable. It would reduce all bodies, simple and compound, to
aggregations of homogeneous corpuscles infinites! mally smaller than the hydro
gen atom : it would endow those ultimate atoms with local motion in space,
and suppose them subject to the laws of mechanical motion alone : it would
then try to explain and account for all the phenomena of nature, all the forces
of nature, all the properties of bodies, animate and inanimate, even all the
phenomena of human life and mind, by the evolutions of those motions in
obedience to the principles of mechanics ! There is something peculiarly at
tractive — or seductive — about a conception that is so vast, so simple, so clearly
imaginable ; but, unfortunately for the mechanical conception, those attributes
are no test of truth.1 There is, indeed, in the human mind an innate craving
to simplify the complex, to reduce the manifold to unity ; but we must not
allow this craving to blind us to facts, or induce us to ignore the unexplained.
" There are more things in heaven and earth . . . than are dreamt of in " the
mechanical " philosophy " ! To weigh and measure phenomena exactly, is
not to know all about them. Nor, in our endeavour to explain some one aspect
of them, must we forget that there are others still unexplained.

230. VERIFICATION BY CUMULATIVE EVIDENCE.— It is clear,
then, that we must not expect the same sort of rigorous verifica
tion in every department of scientific and philosophic investigation.
In the special sciences, which seek the proximate causes of nar
rower fields of phenomena, we may hope to approach, if not to
realize, the ideal of establishing reciprocating causal relations
(221), by eliminating what is irrelevant — through the application
of the " experimental methods " to be explained in the next
chapter. But we must often be content to leave this elimination
incomplete, and so to bring to light only a non-reciprocating
cause.'2 Furthermore, there are multitudes of hypotheses in
science, in regard to which we can scarcely ever hope to be able
to assert that they are the only possible hypotheses that will

1 C/. WELTON, op. cit., ii., p. 209.

aC/. WELTON and MONAHAN, Intermediate Logic, chap, xxx., for distinction
bet%veen the Direct Development of Hypothesis by the " experimental methods," and
the Indirect Establishment of Hypotheses by inferences pointing to their superiority
as compared with other conceivable alternatives.

I42 THE SCIENCE OF LOGIC

explain the facts ; all we can say of some of them is that they
explain the facts more satisfactorily than any alternative hypo
theses so far suggested ; and if we find an hypothesis which was
conceived in explanation of one group of phenomena to be
capable of extension to many other cognate groups, and to explain
these satisfactorily also, such " consilience of inductions " may
make us morally certain that our hypothesis is the right one.

Our verification of such hypotheses will consist in our pointing to their
superior power of explaining facts. It is well to emphasize this point ; because,
firstly, it is with the validity of these wider and more general hypotheses that
philosophy, as distinct from the special sciences, is mainly concerned ; and
because, in the second place, the special sciences are full of them. As Mr.
Joseph rightly observes : " many at least of the most general and fundamental
of our scientific principles are accepted only because they explain the facts of
our experience better than any we can conceive in their stead ; they are there
fore, or were at the outset, hypotheses, used in explanation of facts, and proved
by their relative success in explaining them. We do not see why they are
true, but only why we must believe them to be true. They are established
inductively by the facts which they explain, and the failure of any rival hypo
thesis ; the facts are explained from them "-1 Now are we to regard such
hypotheses as proved or -verified, because they explain the facts " better than
any we can conceive in their stead " ? Mr. Joseph adds : " it is important to
realize that an hypothesis is not really proved by merely explaining the facts.
But many hypotheses are provisionally accepted, which are not proved, on the
ground that they explain the facts, and without the performance of what would
often be the impracticable task of showing that no other hypothesis could
equally well do so." 2 What kind and amount of credence, then, are we to
give to such hypotheses, the evidence for which is cumulative, though not
cogent ? This is an extremely delicate and difficult matter to determine ; and
all the more so because the hypotheses in question are usually of considerable
significance : they are the theories that shape men's convictions about the
ultimate causes and nature of the universe. Each such theory must be judged
on its merits ; and the responsibility of accepting or rejecting it, or holding it
provisionally, calls for the exercise of care, caution, and prudence.

231 .— « POSTULATES " AND THEIR JUSTIFICATION : " TRUTH "
OF VERIFIED HYPOTHESES. — There can be no reasonable doubt
that this cumulative evidence may become sufficient to warrant
an assent of moral certitude to such a theory. But men differ so
much in their mental outlook — on account of the different intel
lectual atmospheres, traditions, and beliefs, in which they have
lived and moved — that evidence which may satisfy one will be
deemed insufficient by another. Hence the conflicting philoso-

1 op. cit., pp. 476-7. Cf. MELLONE, op, cit., p. 332 : " It is this demonstration
that the consequences of a law do actually agree with facts, that forms for science
the verification of that law ".

9 ibid., p. 477n.

HYPOTHESIS 143

phies and divergent world-views that have at all times prevailed
among men. If we are to decide between these, to discern the
truth that is in them, and to eliminate the error, logic can merely
tell us that in this process we must be as unprejudiced, critical,
careful, and judicious as possible.1

A thoughtful analysis of the various fundamental judgments
which make up our general outlook on the inner nature and ulti
mate significance of the universe — whether these judgments be
called assumptions, postulates, axioms, principles, or beliefs
— may or may not have the effect of modifying some or all of
these latter ; but this effect it will undoubtedly have : it will show
us that in choosing between various alternative theories about the
remoter causes of things, in shaping our philosophical views
about the universe, we are all alike influenced more or less by
certain partly instinctive and implicit intellectual tendencies, which
are often not clearly realized in consciousness, and which, when
realized, are felt to be legitimate though they may not be capable
of logical justification by reference to any definite principles lying
beyond themselves. These tendencies or leanings have their
root in our " belief that the universe is rational," 2 and in our con
ception or " notion of what a rational universe should be ".3 This
conception, and this belief, Mr. Joseph considers to be " not
derived from experience " 4 inasmuch as they control our inter
pretation of experience. But it is not true that they are in our
possession prior to, and independently of, experience. Prior to
experience we have only our cognitive faculties — senses and
intellect. These alone we bring to the interpretation of experi
ence. It is sense experience, as interpreted by intellect, that
gives us our " notion of what a rational universe should be". If
that notion were prior to experience it should be the same in
all men ; but it is not : the agnostic, the monist, and the theist,
have different conceptions; and the conception which works
best, which proves most satisfactory, which fits in most harmoni
ously with human experience all round, is alone the true con
ception. Theism is the one which we believe to fulfil these
conditions.

3 Cf. WELTON and MONAHAN, op. cit., p. 398.

3 JOSEPH, op. cit., p. 469. » ibid.

4 ibid. The tendency to endow the mind with constitutive thought-principles
antecedent to all experience is very common among post-Kantian writers. It per
vades the otherwise excellent work of Professor Borden P. Bowne on the The Theory
of Thought and Knowledge (Harper Brothers, 1899).

144 THE SCIENCE OF LOGIC

Apart, however, from the question of the origin of such con
ceptions, there are undoubtedly in our minds the tendencies to
which we have referred. They have been crystallized in the
course of time by philosophers into maxims such as that known
as "Occam's1 razor": Entia non sunt multiplicanda praeter
necessitate™, — which may be interpreted as affirming " a presump
tion in favour of theories which require the smallest number of
ultimate principles,"2 for example, "in favour of the derivation
of the chemical element from some common source, or of the
reduction of the laws of gravitation, electricity, light and heat to
a common basis".3 It simply voices the innate yearning of the
human intellect to unify, as far as possible, the manifold of experi
ence. The same sort of prepossession is also expressed in the
maxims: "Simplex indicium veri" and " Natura non abundat
superftuis sed delectatur paucissimis ". In other words, we are
prompted to regard the simplicity of a conception or hypothesis
as an index of its truth. We give our preference to the simplest
of a number of equally probable alternative explanations, not
merely from the motive of practical convenience, but with a feel
ing that because the actual universe is rational the simplest theory
of things ought to be the true one.4

We can hardly say that the guiding principles embodied in
such maxims are " preconceived ideas " pure and simple. Rather,
they are gradually moulded in our minds by our progressive
understanding of the universe. But further reflection will teach
us that, if followed blindly and unquestioningly, they may mislead
us. It would be unwise to demand simplicity in hypotheses
merely on the ground that Nature always acts in the simplest way.
"Even so," writes M. Rabier,6 "to determine a priori what are
the simplest ways possible ', we should know what is the minimum
of complication necessary. And since we have no data to deter
mine the latter, it is quite useless to attempt an a priori solution
of the former. . . . The idea of the simplicity of nature's
methods, without its indispensable corrective, viz. a realization

1 Occam was one of the later mediaeval Scholastics. He lived in the first half of
the fourteenth century. C/. DE WULF, History of Medieval Philosophy, pp. 420-5.

a JOSEPH, of. cit., p. 470. 3ibid.

4 Hence, for instance, the ratio of the inverse square in the law of gravitation
is regarded as the true ratio, though some more complex ratio might yield results
deviating so slightly from those of the former as to escape detection in our actual
measurements and observations. C/. JOSEPH, ibid.

*Logique, p. 239.

HYPOTHESIS 145

of the inevitable requirements and difficulties of the facts, is the
parent of shallow minds."

But, when we have made full allowance for the complexity of
phenomena, and have to choose between theories all of which
appear to offer equally satisfactory explanations of the latter, we
should certainly choose the simplest theory. And the theist, at
all events, will find a sufficient rational ground for doing so, not
in any a priori postulate that the universe must be " rational" or
" intelligible," but in his own reasoned, a posteriori conviction
that the universe actually is the work of an All-wise God, governed
by His law, and reflecting His Intelligence.

Some philosophers, evidently influenced by the impossibility of securing
cogent logical proof 'of such ultimate hypotheses as we have been considering,
believe that no scientific hypothesis can be proved. For instance, we find it
contended that " a causal hypothesis is never proved in the strict sense of the
word. It is neither true nor false ; it is simply good or bad, useful or embar
rassing, as the case may be ".1 In confirmation of this view, the authority of
such well-known scientists as Que'telet and Ostwald is invoked ; the history of
innumerable hypotheses that have had their day and are long since exploded,
is also appealed to ; and, finally, attention is directed to the formal law of the
hypothetical syllogism : " Posito antecedente ponitur consequens ; at non e
converse. . . . We witness the reality only of the consequent, i.e. of the
phenomenon : we cannot thence conclude to the reality of the supposed ante
cedent. . . . Between the observed phenomena and the scientific hypothesis
there is a chasm that no reasoning can bridge. From the fact to the theory
there is a dialectic somersault that no logic can justify." 2

No doubt, logic will not justify the inference from consequent to antecedent
unless we are certain that the inferred antecedent is the only one possible.
Can we ever be certain of this ? Yes, whenever we can exclude all possible
alternatives. But how can we ever be certain that the excluded alternatives
are exhaustive of all the possibilities (213) ? No rules of logic will help us
here, except indeed the general directions it lays down for observation and
experiment ; but, by the proper conduct of these processes, we can often arrive
at physical certitude that our causal hypothesis is the right one because it is
the only possible one.

In regard, however, to those wider and more general hypotheses and con
ceptions which cannot be verified in this rigorous experimental manner, our
assent must be more or less provisional, although it may often prudently reach
that high degree of probability which is sometimes described as moral certitude.

232. THEISM AS A VERIFIABLE HYPOTHESIS. — Of course, as long as we
merely infer from actual phenomena the existence of an adequate cause, and
make no supposition or postulate whatever as to the nature of this cause,
beyond what the phenomena permit us to predicate about it, we are

xPere DE MUNNYNCK, O.P., in the Revue Neo-Scolastique, vol. vi., pp. 235
sqq.

VOL. IL 10

146 THE SCIENCE OF LOGIC

obviously not employing hypothesis at all, but simply the a posteriori argu
ment from effect to cause. Such arguments can undoubtedly reach real
causes ; and they are practically the only sort of inferences we can make when
we push back our investigations to those wider and ultimate regions of reality
where analogies for hypotheses fail us. And when, finally, we contemplate
the phenomenal universe as a whole, when we are brought face to face with
what Mill has called " the ultimate laws of nature (whatever they may be)," J
and " the co-existences between the ultimate properties of things— those
properties which are the causes of all phenomena, but are not themselves
caused by any phenomenon, and a cause for which could only be sought by
ascending to the origin of all things," 2 it is not by way of hypothesis and
verification, but by a posteriori reasoning from effect to cause, we proceed to
prove that the whole phenomenal universe, being contingent, not self-explain
ing, must have an originating First Cause, and that this Cause must be distinct
from all phenomena, self-existent, and, as regards perfection, adequate to the
production of all phenomenal reality ex nihilo — Creator, Conserver and Ruler
of the univeise.3 It is mainly, at all events, by a posteriori reasoning of this
kind that defenders of the philosophy of theism have traditionally established
its fundamental thesis : the existence of an All-wise, Omnipotent Deity, really
distinct from the phenomenal universe, which He has created, conserves in
being, and rules by His providence. Now, this a posteriori reasoning com
bines in its premisses certain principles (like that oi causality) which are claimed
by those who employ them to be necessary truths, validly applicable to every
conceivable sphere of reality ; and certain truths of experience which are like
wise claimed to be accurate interpretations of experience (224). But the
accuracy of those interpretations, and the validity of those principles, are
questioned by philosophers of other schools. Hegelian idealists deny the
accuracy of the realist interpretation of the data of sense experience ; Kantists
and phenomenists furthermore question the validity and necessity of the realist's
principles. Hence it is that the problem of establishing the truth of the
philosophy of theism may be regarded as a problem of proving this latter con
ception of the universe to be the true conception by showing that it offers for
all the facts of human experience an explanation vastly superior to those of
empirical phenomenism, Hegelian idealism, or any other alternative that can
be suggested ; that the explanation offered by theism is, in fact, the only satis
factory philosophy of human experience as a whole. This method has, indeed,
been already suggested by the comparison instituted in the preceding chapter
(224) between the three conceptions just mentioned. It is the method we
employ in establishing the realist interpretation of sense experience [that there
exists an external, material universe, really distinct from the percipient mind]
against such types of idealists as Berkeley, Hume, Mill, Bain, Spencer,

1 Logic, III., v., § 6, n. i. *ibid., xii., § 2.

8 But at this point phenomenists would have us abdicate the use of our reason :
asking us to believe that we cannot and must not ascend " to the origin of all things "
because such source of all phenomenal reality cannot be itself a "phenomenon".
Of course it cannot ; but is this any reason why we should doubt its reality ? The
things which " are not themselves caused by any phenomenon " must be caused by
something. And, since we can know about their cause whatever we are able to infer
from themselves, the contention of Agnosticism, that this cause is unknowable, must
be rejected as erroneous.

HYPOTHESIS 147

Huxley, as also Kant and his followers.1 " Briefly stated [writes Father
Rickaby], the whole proof of the present thesis will consist in showing that
the experienced facts of sensation are confessedly alike with our adversaries
and ourselves, and that only our way oj accounting for them is adequate." a
It will likewise be found that this same method is really, though perhaps only
implicitly, involved in the traditional lines of reasoning by which the philosophy
of theism has always been supported. And it is very desirable that in placing
this philosophy before the modern world, in comparing its claims to acceptance
with those of other current systems, its supporters should make more explicit
use of this method ; that is, that they should proceed explicitly by way of
hypothesis and -verification ; comparing their hypothesis with the facts of
human experience, and establishing it by showing its " relative success in ex
plaining them,"3 as compared with the relative failure of all competing
alternatives. This would involve no real change of method on the part of
Scholastic philosophers, who are the main upholders of theism ; but only
that they should develop more fully the analytical side of the Scholastic
method (202) by meeting, discussing, and removing the more recently formu
lated difficulties against the general principles which they utilize in the de
ductive, synthetic stage of their systematic reasonings.4

1 C/. RICKABY, First Principles of Knowledge, pp. 270-290.

2 ibid., p. 268 (italics ours). 3 JOSEPH, op. cit., p. 477.

4 This would remove even all apparent grounds for the really groundless re
proach of non-scholastic thinkers that " our arguments are too a priori . . . abstract
. . . technical " ; that our " principles are far from evident, and appear to be
gratuitously assumed," and so forth. See IRISH ECCLESIASTICAL RECORD, April,
1911, article on The Pragmatic Value of Theism, by LESLIE J. WALKER, S.J.
(pp. 338, 339). The article is an earnest plea for the wider use of the method re
ferred to in the text, for the defence of the philosophy of theism : because, on the one
hand, it would be understood and appreciated by modern thinkers whose " modes of
thought are almost all of one type," namely, that they " start with a hypothesis
which they proceed to verify by showing that its consequences harmonize with the
data of human experience " (p. 340) ; " nor," on the other hand, " would any of the
old arguments have to be given up, for all are essential to the completeness of the
methods. At most, traditional arguments would have to be stated in a somewhat
different form. Axioms and principles would not be asserted merely on the ground
of their self-evidence; but we should first of all formulate all principles and all
doctrines provisionally as ' hypotheses,' not of course in the sense that we should
lor a moment doubt their truth, any more than St. Thomas doubts the truth of God's
existence when he asks: An Deus sit? but merely as provisional positions shortly
to be proved. We should then proceed to verify our hypotheses ..." (pp. 352,
353). He applies the method himself in subsequent articles in the IRISH ECCLESI
ASTICAL RECORD (May, pp. 465-80). We are in no way detracting from the value
of this method by observing that it, too, must accept some " principles " or " axioms "
or "intuitions" on self-evidence alone, as starting points for rational interpreta
tion of experience, and reasoning therefrom ; for even though " the philosopher of
this twentieth century, having grown familiar with inductive or scientific methods
of proof, is no longer content with a priori reasoning from self-evident principles "
(p. 340), it is none the less true that "intuition is ... involved in [his own
* inductive '] process, and many statements are made [by himself] which cannot be
proved, but which are none the less axiomatic or evident " (ibid.). When is it law
ful, and when unlawful, to assume a judgment as a self-evident axiom (203) ? This
is a very grave question, which divides philosophers, and which logic is unable to
answer. Cf. infra, 275, A, c.

10*

148 THE SCIENCE OF LOGIC

233. SUMMARY OF LOGICAL REQUIREMENTS FOR A LEGITI
MATE HYPOTHESIS. — We may now briefly recapitulate the condi
tions required for a legitimate scientific hypothesis.

I . // must be based on preliminary observation of some fact or
groups of facts, be invented in order to explain them, and therefore
have for its object a real cause, a " vera causa ", This rule excludes
all subjective suppositions employed as aids to the imagination
(226). It also excludes all purely fanciful guesswork about causes.
Observed uniformities in facts must suggest hypotheses ; these must
not be constructed entirely from imagination ; they must have a
basis in accurate and unbiased observation of the facts ; they
must not be merely preconceived notions which we allow ourselves
to read into the facts. " The scientist," writes Claude Bernard,
"should have an hypothesis to verify; but he ought to make
sure that the facts on which it is based be accurately and imparti
ally observed. Hence he should be an observer no less than an
experimenter. As observer, he will simply and solely register
the phenomenon under observation. He will be, so to speak, a
photographer of phenomena : his observation will be a faithful re
presentation of nature, free from all prejudiced and preconceived
ideas. As observer, he will be passive, silent, receptive ; he will
listen to nature, and write under her dictation. Then, once he
has carefully observed the phenomenon, he will conceive an hypo
thesis and proceed to test it experimentally." * We must, there
fore, observe the facts without preconceived ideas ; that is, we
must observe before supposing, not vice versa. Simple as this
recommendation is in its formulation, it is by no means easy to
carry out in practice. Our initial observation and determination
of the phenomenon to be investigated must be impartial, not
biased by any preconceived views. Then, when we have conceived
our hypothesis, and proceed to test it by renewed observation and
experiment, we must resist all inclination to interpret the facts in
favour of it. We must be ever ready to modify or reject it.
Just as the wish can be father to the thought, so can attachment
to an hypothesis easily misguide and distort our reading of the
facts. It is difficult to guard against this undue influence while
we are conducting our observations and experiments for the
express purpose of testing our hypotheses. It is to secure impar
tiality in this testing process that Claude Bernard says to the

1 CLAUDE BERNARD, Introduction d Vitude de la midecine expirimentale, pp.
39-4°-

HYPOTHESIS 149

scientist : " On entering the laboratory leave your imagination
with your overcoat in the vestibule, but take it with you again
on your departure".1 That is to say: reflect on your experi
ments and observations, and conceive and test hypotheses about
them ; but never allow your hypotheses to influence your actual
reading of the facts when you are observing or experimenting.

2. // ought to be self -consistent, and free from conflict either with
established truths or undoubted facts. Truth cannot oppose truth.
Hence the demand for consistency, freedom from internal con
tradiction, intelligibility. This, as we have seen, is not to be
confounded with imaginability (228).

Again, the hypothesis must not contradict other established
truths or laws. Caution is needed, however, to make sure that
the contradiction is real, that it cannot be eliminated by any
possible restatement of such laws: for, sometimes an hypothesis
sheds a new light on an established law and leads to a more ac
curate or more extended formulation of the latter. Sometimes,
too, what is commonly believed to be an " established law " is in
reality a false and misleading theory,^, the Ptolemaic Astronomy.

In comparing our hypothesis with facts, the chief danger to
be avoided is a prejudiced interpretation or reading of the facts,
in favour of the hypothesis. If we find that facts are not in
accordance with our hypothesis, we must not say " so much the
worse for the facts," but rather " so much the worse for the
hypothesis ". On the other hand, however, we need not reject
our hypothesis until we are sure that it is really' incompatible
with the facts. And here we must take care that what we have
regarded as facts are not already mixed with half-unconscious
theories or interpretations which, in the light of our present hypo
thesis, we may now be able to eliminate from the mixture, and
so leave the residue of real fact compatible with our present hypo
thesis.2 Much, if not all, of what we commonly call " fact," is in
timately interwoven with what are really interpretations or theories ;
and some of these may have been false from the start. Mere
fact cannot be, interpreted fact must be, either true or false.
Hence we apply the name "fact" to what we believe to be a
truth, a true interpretation of fact (248). And in some of these
we may be mistaken, as people were when they regarded it as a
" fact " that the sun goes round the earth. When, therefore, we

1 CLAUDE BKRNARD, Introduction a Vetudc de la midecine experimental, p. 44.
3C/. JOSEPH, of>. cit., pp. 432-3.

ISO THE SCIENCE OF LOGIC

find " facts " discordant with our hypothesis, we must make sure
we have interpreted these facts rightly. Then we must see if
they can be made to fit in with our hypothesis by such correc
tion and modification of the latter as will incorporate in it factors
to account for those facts. Only when we fail to effect such a modi
fication of our hypothesis must the latter be rejected altogether.

3. It must be based on some analogy with known causes : it
must be capable of yielding exact deductive inferences : it must be
verifiable by the submission of those inferences to the control of ob
servation or experiment. These are three alternative statements
of one and the same requirement. We have seen already that it
may not be always possible to conceive an hypothesis which will
fulfil this condition: the degree in which an hypothesis does
lend itself to such verification is the measure of its " exact "
scientific character.

The combination of conditions I and 2 show how the func
tions of reason and sense alternate and aid each other in science.
Initial observations suggest an hypothesis. This in turn must be
verified : and to verify it the scientist must reason from it, and
submit his conclusions anew to the control of observation or ex
periment. " Thus," writes Claude Bernard, " the mind of the
scientist is placed between two observations, one which is for
him the starting-point of a reasoning process, the other its con
clusion." x

4. // is " verified" or " established" when it is shown to yield
not merely a sufficient explanation, but the only possible explanation,
of the facts it purports to account for (cf. 2 1 2). Our success in
showing this will vary with the nature of the facts and the scope
of the hypothesis. Sometimes the facts are subject to the con
trol of experiment, and the hypothesis is comparatively restricted
in its scope, so that we are able to eliminate and disprove all
conceivable alternatives, and thus attain to the ideal of a rigorous
verification. Again, the hypothesis, may be shown to be capable
of such extension, by consilience of inductions, that although we
may not hope to prove rigorously that it is the only possible ex
planation of the facts, yet we are able to show that it does
explain a vast field of fact, and does so more satisfactorily than
any suggested alternative : in which case we may give it a pro
visional assent amounting to moral certitude.2

lop. cit., ibid. — apud MERCIER, Logique, pp., 344-5.

3 It is often very difficult to distinguish, and there is often no practical distinc-

HYPOTHESIS 151

If, finally, in our inquiry into the ultimate cause and explana
tion of experience as a whole, the relation between the supposed
cause and this experience be such that we can argue a posteriori
from the latter to the existence and nature of the former — merely
in virtue of the principle of causality — then our reasoning may
reach certitude, provided we are able to show that the facts con
sist with no other interpretation. This we consider to be the
case in regard to the philosophy of theism as an explanation of
the whole field of human experience.

234. SOURCES OF SCIENTIFIC HYPOTHESES: ANALOGY.—
In a general way, it may be asserted that all hypotheses have
their origin in observation of facts and reflection on what we al
ready know about facts. We may, however, distinguish a few
of the more important immediate sources of hypotheses.

(i) Even reflection on the common class names and ordinary
generalizations embodied in the language we use, may raise prob
lems about the phenomena of experience, and suggest hypotheses
in explanation of them. All inquiry into the causes of things
presupposes, as its initial stage, the classification of similar things
on the basis of common attributes (63, 68), and the nomenclature
or system of class names or general terms concurrently embodied
in common language (69).* So that in the very language we use,
in the classifications embodied in it, and in the rough and ready
generalizations of ordinary life, we have to hand an abundance
of materials which suggest to the thoughtful mind new connexions
and relations, as hypotheses for verification. Observation will
often show the necessity of discarding or modifying customary
classifications, and of re-grouping things according to newly de
tected points of similarity or dissimilarity. But these processes
have their origin in the study and comparison of existing classes,
and in analysis of accepted generalizations. Thus, the relation
involved in an ordinary universal judgment — " All 5" is P" or
" If 5 is M it is P " — may, perhaps, be a reciprocal ration : and

tion, between an extremely high degree of probability and what is commonly called
certitude. And this is particularly true in the social and historical sciences. " Speak
ing strictly and in accordance with correct logical usage," writes M. Ernest Naville
(La Logique de I'Hypothese, p. 222), " the highest probability cannot become certi
tude. And yet it is an indisputable fact that there are crowds of hypotheses upon
which we have no hesitation in acting as if they were absolutely certain. Practice
is here in advance of theory, and does not follow quite the same law." The kind
and amount of evidence required for verification, and for a certain assent, are not
identical in all the sciences. They vary with the subject-matter.'
J Cf. JOSEPH, op. cil., pp. 413, 440.

15* THE SCIENCE OF LOGIC

the supposition that it is so is an hypothesis for verification.
Or we may put the matter in this way : Ordinary observation
discloses relations of uniform concomitance or sequence between
phenomena. In these uniformities science endeavours to detect
reciprocal causal relations (221). We know a phenomenon or
fact scientifically only when we know its connexion with, and its
dependence on, all that constitutes its one sufficient and indispens
able cause ; and when we place this cause and this fact in the
relation of antecedent and consequent, or of subject and predicate,
we know that the relation is not only universal but reciprocal ;
for example, not only that " all living organisms are mortal "
but that " all mortal things are living organisms ". But in order
to establish such a reciprocal relation we must have made explicit
the one essential ground of the consequent in question ; we must,
in other words, be certain that it can follow from this antecedent
and from no other. " If man is a living organism he is mortal ;
and if man is mortal he is a living organism " : because mortality
is a proprium of organic life, a property in the strict sense of
the word, " quod convenit omni, soli, semper, et ubique ". " If a
triangle is right-angled the middle point of the hypotenuse is
equidistant from the three vertices, and vice versa " : because
right-angled triangles alone are inscribable in semicircles. From
all this we see that the very observations which give rise to the
enunciation of universal relations — whether categorically, All S's
are P, or hypothetically, If S is M it is P — suggest the hypothesis
that these judgments may, perhaps, be in reality simply convertible,
although formally they can be converted only per accidens : into
Some Ps are S (which is equivalent to All Ps may be 5), and
IfS is P it may be M.

(2) We have already seen (217) that hypotheses may be sug
gested by Enumerative Induction. Even a single observed in
stance of a phenomenon may set one speculating or guessing as
to its cause. But the suggestion comes more easily when we
have observed a number of instances of the same coexistence or
sequence of two phenomena, particularly if this persists through
varying circumstances.1 The sole scientific value of enumerative
induction lies in its suggestion of an hypothesis as to the content
or nature of the instances examined. For example, the obser
vation of the facts that I + 3 = 22, I + 3 + 5 = 32, I + 3 + 5
7 =42, and so on, suggests the hypothesis of some necessary
1 As in the " method of agreement " (241).

HYPOTHESIS 153

equality — springing from the very nature of numbers — between
the sum the first n odd numbers and »2.

(3) More important still than enumerative induction, as a source
of hypotheses,— indeed by far the most fruitful source,— is Analogy.
Certain resemblances of an unexplained phenomenon to some
other already known and explained phenomenon, will suggest
the direction in which we ought to look for an explanation of
the former. Thus, Malus, accidentally observing, through a
double refracting prism, the light of the setting sun reflected from
the windows of the Luxembourg Palace, saw that the light dis
appeared at two opposite positions of the prism, like light pol
arized by passing through another prism ; and he argued by analogy
that this— and, apart, all reflected light— was likewise probably
polarized : an hypothesis which was speedily verified.

The term " analogy " is commonly understood nowadays to
mean a resemblance of any sort ; and by the "argument from
analogy " is understood an inference based on such resemblances.
Mill's description of it is simple and clear: "Two things re
semble each other in one or more respects ; a certain proposition
is true of one, therefore it is true of the other "* It is an argu
ment from partial resemblance between two phenomena (or
groups or series of phenomena) to some further point of resem
blance between them. A few simple examples will illustrate the
nature of this mode of inference.

(a) Cholera has been proved to be due to the action of a
certain known bacillus. Here is some other disease, which is
seen to present many symptoms similar to those of cholera.
Therefore, this disease also probably has its origin in the action
of some bacillus.

(b) The planet Mars revolves around the sun, has light and
heat from the sun, rotates on its axis, and appears to have
mountains and rivers — like the earth. Therefore, it may also be
the scene of vegetable and animal life.

(c) A is a man of certain character, disposition, opinions, etc.
(say xK) ; and he has acted in a particular way in certain circum
stances. B is also a man of the same character, etc. as A (say
xR} : x being the known common points, and R, Rl, the partially
differing and partially unknown residue in the case of each).
Therefore, B will probably act in the same way when placed in
similar circumstances.

1 Logic, III., xx., § 2.

154 THE SCIENCE OF LOGIC

(d] Rocks exposed to glacial action are seen to become
scored or striated.

Many rocks in this particular district are thus scored or
striated.

Therefore, this district has probably been the scene of glacial
action.

(e) In districts now exposed to glacial action we find perched
boulders.

In this district we also find perched boulders.

Therefore, etc. as in (d}.

(/) In districts now exposed to glacial action we find long
lines of accumulated stones and debris, which are called
" moraines ".

In this district we find such " moraines".

Therefore, etc. as in (d).

From those examples we see that the argument from analogy
naturally assumes the form of a syllogism in the second figure
with two affirmative premisses ; that, therefore, it does not/rav
the law suggested in the conclusion, but only makes the con
clusion more or \zss probable ; that this probability may, perhaps,
be a practically worthless and groundless suspicion ; — or that it
may amount to moral certitude : especially when, as in (d}, (e\
and (/), we have a number of independent analogical inferences
all pointing to the same conclusion.

The formal reason why we cannot derive a universal law
with certitude as conclusion from the premisses of such an argu
ment, is that it would involve the fallacy of undistributed middle.
Until we can convert our major premiss simply [from " All P is
M" to " All M is P"], and so construct a syllogism in the first
figure, we cannot be sure of our conclusion. We are not sure
in («) that the symptoms in which the particular disease agrees
with cholera can be due only to the action of a bacillus ; or in (b)
that the points in which Mars resembles the earth are sufficient
and indispensable for organic life ; or in (c] that the ground for A's
action is x, in which he agrees with B, rather than R, in which
he differs from B ;^ or in (d), (e), (/), that the scorings, perched
boulders, and " moraines " in question, might not possibly be ac
counted for otherwise than by glacial action. And the only way
we can become sure of these things (and so convert our major
premiss and prove our conclusion) is by a closer investigation of
1 C/. WELTON, op. cit., ii., pp. 71-3.

HYPOTHESIS 155

the phenomena. In other words, the material reason why we can
not regard the suggested law as certain, or verified, is because we
have not sufficiently analysed the facts. In each case, the points
of resemblance between the facts under observation and other
known facts, suggest that the causal law which accounts for those
points in the known facts may also account for them in the facts
now being examined. We are trying to extend a known law
to a new case. But this extension is an hypothesis which awaits
verification. The connexion of the two cases by a common law
is not verified by mere analogy as such. Analogy, as such, " sticks
in the particular instances," and gives only a more or less probable
conclusion.

There are good and bad arguments from analogy. The
probability of the conclusion may range indefinitely from zero
and practical certitude. On the one hand, the conclusion may
be far less probable than its contradictory, when, as in ($), the
points of resemblance seem to have little causal relation to
the conclusion inferred from them, and not to include such
essential conditions for this conclusion as the presence of oxygen
or air, and absence of extremes of temperature.1 Or, again, the
conclusion may be no more probable than its contradictory, when
conflicting analogies produce absolute doubt ; as, for example, in
the case of some lower form of living thing which may present
certain resemblances to animal life, and certain other equally
marked resemblances to vegetable life. Or, finally, it may
become evident that the resemblances are causally connected
with the inferred property, in which case the argument passes
beyond the stage of analogy, its premisses take the form of the
first figure of syllogism, and its conclusion becomes a certainly
established law. If some symptom common to cholera and the
other disease in example (a), above, could be shown to be due to
no other cause than the action of a bacillus, the conclusion would
become certain that the disease in question was due to such
action. In order, therefore, that an inference from resemblances
may lie within the limits of analogy, it must be probable, but
only probable, not certain, that the common characteristics are
causally connected with the conclusion based upon them.

235. WORTH OF ANALOGY : ITS FUNCTION IN VERIFICATION.
— How, then, are we to estimate the value or force of an argument
from analogy? On what will the probability of its conclusion
1 Cf. MELLONE, op. cit., p. 263.

156 THE SCIENCE OF LOGIC

depend? It will evidently depend on the degree of likelihood
there is that the common characteristics are in reality causally
connected with the conclusion that is based upon them. And
on what does this likelihood depend? According to Mill, it
varies in proportion to the amount of resemblance between the
two phenomena, i.e. to the number of independent points of
similarity as compared with the number of independent points
of difference, and with the total amount of known and unknown
elements in the two phenomena.1 But, not to speak of the
impossibility of " counting " the number of qualities assumed to
be "independent" of one another, this purely numerical test is
a very misleading one because it ignores the nature of the
characteristics, while it is precisely in their nature as active
properties, in their purpose or law? that their importance lies as
a basis or ground for inferring some further common bond of
law connecting the phenomena.

Two phenomena may resemble each other in quite a multitude
of respects which may furnish no real ground for inferring re
semblance in any additional property. Two boys may be of the
same age, height, strength, colour of eyes and hair, have similar
home surroundings, and attend the same school. Yet from these
resemblances we cannot infer with any degree of probability that
because one of them is very talented so must the other be likewise.
It is not by the number but by the importance of the points of
resemblance that • the strength of an analogy is to be estimated.
Now, their importance depends upon their nature as compared
with the nature of the additional property inferred in the con
clusion. "Importance" is a relative term. The points of
resemblance are " important " towards what is sought to be

1 Logic, III., xx., § 3. Cf. WELTON, op. cit., ii., p. 79. MELLONE, op. cit., p.
262. FOWLER, Inductive Logic, pp. 213-14.

2 In determining the significance or importance of characteristics in relation
to one another we are aided very materially by the consideration that the laws of
their nature are an expression of the purpose or design they are intended to serve
(217). "This is easily seen," writes Professor Welton, "when the cases with
which an inference is concerned are the purposive works of man. For example, by
analogy we conclude that certain flints found in the earth are remains of weapons,
because they bear marks of artificial shaping of such a kind as to adapt them to be
cutting or piercing instruments, and corresponding, moreover, to those of flint
weapons made and used by savages at the present day " (op. cit.t ii., p. 78). But
there is purpose in nature, organic and even inorganic (217), as well as in the works
of man. In botany and zoology many important laws have been brought to light
through analogies based on the connexion between the structure and development
of organs on the one hand, and the functions which it is assumed that they are intended
to discharge on the other. Cf. MELLONE, op. cit., p. 324.

HYPOTHESIS 157

inferred from them, just in so far as they are likely to be causally
connected with this latter. The points of difference, too, must be
noted; and these will be "important" as militating against the
analogy, and so weakening it, in so far as they appear to be of
such a kind as would be incompatible with the supposed causal
connexion. This supposition of a causal connexion has next to
be tested — by observation and, if possible, experiment — according
to methods set forth in the next chapter. Should these convince
us that the resemblances were merely accidental in regard to the
inferred characteristics, that the latter cannot really be affirmed
of the phenomenon under investigation, then the analogy of the
latter to the other phenomenon was bad and misleading from the
start. If, on the other hand, further analysis reveals some sort of
causal connexion which enables us either to verify our hypothesis,
or to modify it in some way, to alter its scope and restate it, and
to verify it in its altered condition, then the analogy will have
been so far good and useful and instructive.

We have referred to analogy as the application of known laws
to new sets of facts. Such attempts at extension usually lead
to restatements which give such laws a wider scope ; or to the
suggestion and verification of new hypotheses. These are the most
important functions of analogy in induction. We may illustrate
them by the following example, for which we are indebted to Dr.
Mellone's Text-book: —

" A conspicuous instance ... is seen in the early researches of Pasteur and
his friends into bacteriology, as described in the Life of Louis Pasteur by his
son-in-law. The old belief was that many contagious diseases were due to a
virus or poison introduced into the blood. Further research was undertaken
on the assumption that the cause of the diseases was something in the blood,
but not necessarily a virus. This was a suggestion by analogy with the
former belief, and it was experimentally proved by inoculating healthy
animals with a drop of the infected blood. Afterwards the presence of minute
animalculae, visible only by the microscope, was detected in the blood of
diseased animals ; but at first it was supposed that these minute organisms
could not produce such great effects. But subsequently Pasteur proved that
such a great effect as fermentation was caused by the growth of an invisible
vegetable organism ; hence analogy suggested that the animalculae whose
presence was detected in the infected blood, might after all be the true cause
of the diseases in question. This hypothesis, being experimentally verified,
was proved to be true by applications of the joint method \cf. 242]. The old
theory, that these diseases were caused by a virus introduced into the blood,
could only give a forced explanation of many known facts ; and it had to give
way to a new theory — harmonising all the facts. But the new theory was
originally suggested by analogy with the old ; and the speculations with

158 THE SCIENCE OF LOGIC

regard to the action of the virus which were based upon facts did not lose
their value ; they simply had to be revised by the aid of the new light shed
upon the question." l

" A pari" " a fortiori" and " a contrario " arguments, are all
arguments from analogy : " The planet Mars bears a close re
semblance to our earth, therefore, a pari, it is probably inhabited ".
" Work in the mines is hard on the health of male adults ; there
fore, a fortiori, it is injurious to women and children." " The
abuse of alcohol is a cause of national decay ; therefore, a con
trario, the suppression of that abuse will make for national
prosperity."

Inference by analogy is a very common form of reasoning, and
very liable to abuse ; the real significance of resemblances may
be misinterpreted : and the metaphorical use of language often
increases this danger. Some examples of inconclusive analogies
will be examined in the section on fallacies.2

The characteristic which we seek to prove of an observed
phenomenon, by analogy, may be known to belong to a single
other phenomenon, or to a whole class. More usually, perhaps, it
is something we suspect or know to be true of a whole class,
something embodied in a generalization or law, which law we
now seek to extend to the newly observed phenomenon. Or,
we may have in our minds only the two individual phenomena ;
but even here the inference — which Aristotle calls TrapaSeisffjia,
Example — is not made from particular to particular without the
aid of an implicit generalization. " The inference is the same,"
remarks Aristotle,3 "whether it be based on resemblance to one
case or to many " (193).

236. THE "ARGUMENT FROM EXAMPLE" IN ARISTOTLE.—
By the Argument from Example Aristotle meant an inference
from one individual phenomenon to another similar phenomenon
" by bringing the one under the same universal to which the
other is known to belong ".4 Manifestly, therefore, the Aristotelean
TrapdSeiyfAo, is what we now commonly call inference from
analogy. Comparing it with the inductive syllogism (207), he
describes it as " proving the major term of the middle by a term
resembling the minor" * This description he explains and justifies

lop. cit., p. 325. a C/. also JOSEPH, op. cit., pp. 494 sqq.

3 Anal. Prior., ii., 24 [21], (3).

* Anal. Prior., ii., 24 [26], (4) : Qa.vtp'bv oZcSri rb TrapaStiyfid tanv . . . us ptpoi
wpbs ntpes, orav &fi<j>u ftitv $ uwb ravr6, yvupi/ioy tf Odrfpor. Cf. sdsoRhet. i., 2, (15)-
(I?) I ii- 20.

• ibid.

HYPOTHESIS 159

by the following illustration : " The war between the Thebans
and Phocians was a war between neighbours, and was an evil ;
therefore war between the Thebans and Athenians, being a war
between neighbours, will also be an evil ". Here the major term
(" evil ") is " proved " of the middle term (" war between neigh
bours ") — that is to say, the implicit universal principle'^ " proved "
— by means of a term (" war between Thebans and Phocians ")
which resembles the minor term ("war between Thebans and
Athenians "). So that the whole process here consists in (a) an
enumerative induction based on the enumeration of a single in
stance ; and (£) the consequent application of the empirical
generalization thus reached, to a new case that is brought under
it, by a syllogism in the first figure : the conclusion of the latter
being only probable because its major premiss, the generalization,
is only probable. We may express the whole (as we may express
any argument from analogy) in a syllogism in the second figure
thus : " This disastrous war (between the Thebans and the
Phocians) was a war between neighbours (P is M} ; War between
Thebes and Athens will be a war between neighbours (S is M) ;
Therefore it will (probably) be disastrous (S is />)". If we
could cite additional instances of disastrous wars being wars
between neighbours, so much the better ; for it would strengthen
the supposition that " all wars between neighbours are disastrous ".
If, finally, we could verify this supposition and lay it down as an
established truth, we could substitute for the probable syllogism in
the second figure : " P is M ; S is M ; therefore 5 is P" a conclu
sive syllogism in the first figure " M is P ; S is M ; therefore .S"
is/"'.

Hence we can understand what has been said of the relation between
analogy and enumerative induction : " In the latter, because a number of
instances of a class x exhibit the attribute^, we infer that all x are^y ; in the
former, because two particulars a and b agree in certain respects x, we infer
that^y which is exhibited by a, will be exhibited by b also. In the latter, from
the limited extension of an attribute over a class, we infer its extension over
the whole class ; in the former, from a partial agreement between two in
dividuals in intension, we infer to a further agreement in intension. But the
one passes gradually into the other, for the former may be called the applica
tion to a particular case of a general principle inferred in the latter from a
larger number of instances than in the former. This is very plain in an
illustration which Aristotle gives of the ' example ' (his name for the argu
ment from analogy). A man might have inferred that Dionysius of Syracuse
designed to make himself tyrant, when he asked the people for a bodyguard ;
for Pisistratus of Athens asked for a bodyguard, and made himself tyrant

160 THE SCIENCE OF LOGIC

when he got it ; and likewise Theagenes at Megara. Both these fall under
the same general principle that a man who aims at a tyranny asks for a
bodyguard.1'1

237. ANALOGY AS UNDERSTOOD BY ARISTOTLE.— We have
just seen that what is nowadays called the argument from analogy
Aristotle called TrapdSeiy/jia. We have now to consider what he
understood by an argument from analogy. The term dvaXoyia
originally meant identity of relations. Four terms were said to
be analogous when the relation of the first to the second was the
same as that of the third to the fourth. Now if the relations are
identical, and if what is inferred from them depends on this
identity alone, the inference is cogent or necessary. And this is
pre-eminently the case in mathematics, where the terms, relations,
and inferences are purely quantitative. Here, then, the term
" analogy " meant equality of quantitative relations or ratios, " lo-6rij<f
\6yajv,"'2 and has been translated by the terms " proportio" "pro
portion ".3 If 2 : 4 : : 3 : 6, we can infer that because 2 is the
half of 4, 3 is the half of 6 ; and our reasoning is cogent, like any
other mathematical reasoning. But the name " dva\oyia" was
also applied to cases in which the terms, relations and inferences
were not quite, or not all, quantitative. Thus, ".r vibrations of
the air : 2 ^ vibrations : : a note : its octave," where the second
relation is not of the same order as the first ; or again, ";r vibra
tions of luminiferous ether : y vibrations : : the sensation of red :
the sensation of green," where again the second relation is quali
tative, not quantitative, but yet is so connected with the first
that it varies with, and can be known from, the latter; or again,
to quote Aristotle's example, intellect bears the same relation to
the soul as sight does to the body — i/oO? : tyvxij : : o-fris : <rw/ia,4
where there is no idea at all of number or quantity, but only of
nature or quality.

Now if what we infer from an identity of quantitative rela
tions does not depend exclusively on those relations, our inference
is not necessarily valid : I cannot validly infer that it will be twice
as expensive to send goods by rail from A to B as from C to D

1 "Rhet. a ii., 13576, 25-36. To make the inference to Dionysius necessary (of
course it is Dionysius I. who is meant), the principle would have to be, that a man
who asks for a bodyguard aims at a tyranny ; and that is really what the suspicious
citizen of Syracuse would have had in his mind." — JOSEPH, op. cit., pp. 500, 5or, n.

a ARISTOTLE, Fth. Nich., bk. v., 3 (8).

3 FOWLER, Inductive Logic, p. 210, n. 4 ; Deductive Logic, p. 71, n. 2. Cf. also
WKLTON, op. cit., ii., p. 75 ; JOSEPH, op. cit., pp. 492 sqq. *Eth. Nich., i., 6 (12).

HYPOTHESIS 161

because the former distance by rail is twice the latter. And
when we pass out of the domain of purely quantitative relations
it becomes difficult to know for certain (a) that the relations are
really identical, and (&) that what we infer from the identity de
pends on it alone. Our inference is based merely on similarity
of relations, and yields only a probable conclusion. This is the
sort of inference illustrated by Aristotle's example of the similar
relations of sight to body and intellect to soul. . It is a very
common form of inference. We may argue, for instance, that
because the relation of colony to mother-country is like that
of child to parent, the reciprocal rights and duties of the
former pair should be the same as those of the latter pair. Or
again, the colonies may be compared to the fruit that drops off
from the parent-tree when ripe.1 Obviously, inferences of this
kind may be of any degree of value — or of worthlessness. It is
such resemblances between things that give rise to the metaphori
cal use of language (e.g. " mother-country "). Metaphors are
simply analogies of this kind compressed into a single word or
phrase ; and metaphors are often misleading.

Between this " Aristotelean " analogy, and analogy in the
modern sense, there is no essential difference. In the former the
inference is based on similarity of relations, in the latter it is
based on similarity of qualities, properties, or characteristics of
any sort. The former may be symbolically stated : " a is related
to b as c is to d ; from the relation of a to £ such and such a
consequence follows, therefore it follows also from the relation of
cto d" ; the latter: "a resembles b in certain respects ;tr ; a ex
hibits the character y, therefore b will exhibit the character y
also".2 Similarity of relations must involve some similarity of
inherent attributes or qualities in the things related, and so it
was quite natural and inevitable that the term " analogy " should
be extended, as it has been, from the former to the latter.3

WALTON, Logic, ii., bk. v., chaps, iii. and iv. JOSEPH, Introd. to Logic,
chaps, xxi., xxii. and xxiii. ; pp. 492 sqq. MELLONE, op. cit., pp. 251-64,
317-40. MILL, Logic, III., v., xx. MERCIER, Logique, pp. 334-49-

XC/. JOSEPH, op. cit., p. 494. *ibid., p. 496. 3ibid., p. 498.

VOL. II. II

CHAPTER VI.

METHOD OF DISCOVERING CAUSAL LAWS BY ANALYSIS OF
FACTS : OBSERVATION AND EXPERIMENT.

238. OBSERVATION AND SELECTION : INITIAL PRECAU
TIONS. — It is the aim of induction to discover the causes of
phenomena, to verify as far as possible the laws according to
which we suppose these causes to act, and so to explain the phe
nomena by means of these laws and causes. We have examined,
so far, the general scope of the inductive method, the ways in
which a knowledge of laws and causes is suggested, and the logi
cal character of the procedure by which hypotheses are verified.
We have next to investigate, in some detail, the functions of ob
servation and experiment, with the more directly practical purpose
of bringing to light certain useful rules for the proper conduct and
application of these processes.

The events or occurrences of nature are complex and inter
related with one another. None of them stands apart in a state
of isolation. It is because they are so intimately interwoven that
we find it difficult to single out and mark off a " phenomenon "
for investigation, to analyse fully its surroundings, and to lay bare
those amongst them with which it is causally connected. Yet
we must do all this before we can say whether or not our sup
posed cause — the object of our hypothesis — is the real cause of
the phenomenon.

We observe an event occurring in certain circumstances or
surroundings. In our initial observation we have evidently to select
the phenomenon, and limit it or mark it off from its antecedent,
concomitant, and subsequent circumstances. We next want to
bring to light its cause, to find out the natural law according to
which it occurs. We therefore make some supposition or hy
pothesis as to the factor or group of factors with which it is
causally connected. * This, too, involves selection on our part. And
finally, we want to verify our hypothesis, i.e. to find out, if pos
sible, whether our supposed cause is the sufficient and indispens-

162

METHOD OF DISCOVERING CAUSAL LAWS 163

able cause of the phenomenon. Obviously, the only way to
reach certitude on this latter point is by instituting a careful and
detailed analysis of the whole phenomenon and its surroundings,
and so satisfying ourselves — by further and more searching ob
servation, under special and modified conditions if necessary —
that, amongst all the surroundings of the phenomenon, none have
a causal influence upon it except those supposed by us to have
such influence.

All observation of facts is selective. That is to say, what we
observe is largely determined by the nature and direction of the
interest we take in what comes under our notice. Our minds are
never purely passive, but are constantly interpreting the data of
sense experience, and reasoning more or less unconsciously from
those data. Hence arises an initial danger, that our observations
may be vitiated by bias. What we observe in any phenomenon
depends largely on our previous knowledge : the skilled engineer
" sees " more in the locomotive than the uneducated peasant,
though the latter may have sight, and all other senses, as sharp as
the former. Superior knowledge it is that renders observations
more fruitful. The well-stocked mind will perceive analogies
where the ordinary mind will not. The example of Malus, above
referred to, is a case in point. Yet this very psychological fact
exposes the observer to the danger of falling a victim to pre
conceived notions. We often think we see what we only imagine.

Again, the selection and isolation of the phenomenon to be
examined, and of the elements to be tested as its likely causes,
are more or less arbitrary processes, in the sense that they must
be determined and prosecuted by the individual himself: for their
proper and fruitful prosecution an extensive knowledge of the
matter in hand is the only guarantee. The investigator who is
not well acquainted with his subject will not be likely to detect all
the conditions that are operative, or to eliminate and disregard all
that are inoperative, in conducting his observations arid experi
ments. Against this, as against the danger of bias, logic can
furnish no safeguard. Both will be referred to at greater length
in connexion with Fallacies. There, also, we shall deal with yet
another mistake which may easily be made : the error of inferring
non-existence, whether of instances or of conditions, from mere non-
observation of the latter. It is only when these are of such a kind
that they could not have escaped observation had they existed,
that such inference is legitimate.

II *

1 64 THE SCIENCE OF LOGIC

239. EXPERIMENT : ITS RELATIONS TO OBSERVATION.—
Experiment is simply observation under special conditions brought
about by the observer himself, and modifying the object observed, ^^he
qualification introduced in the latter phrase is essential ; for if
the special conditions mentioned modify only the observer's
point of view, or his power or medium of observation, leaving the
object unchanged,, we do not speak of such an observation as an
experiment. Thus, "vivisection is experiment because the deter
minate conditions it produces enter as factors into the action of
the organism observed " ; while " common dissection is not ex
periment, though it introduces conditions in the way of separation
and demarcation as definite as anything can be,"1 because these
conditions merely prepare, without changing or forming part of,
the object under observation. So, also, we speak of observations
with the microscope, telescope, etc. The transition from pure
observation to definite experiment is, however, gradual ; they
differ in degree, not in kind. This is best illustrated in what have
been curiously called nature's experiments, or natural experiments.
In these the phenomena observed are altogether beyond our con
trol and, therefore, cannot be influenced by any activity of ours ;
but we take advantage of specially favourable circumstances, or
select a specially favourable medium or point of view, for our
observations : as when, for example, astronomers select special
times and places for their observations ; or meteorologists climb
high mountains, or ascend in balloons, to make climatic observa
tions ; or scientists lay long lines of wire, or erect magnetic stations,
or construct seismographs, for the purpose of observing and re
cording electric, magnetic, or seismic disturbances.

Experiment may, therefore, be rightly regarded as a special
kind or mode of observation : the latter being the genus, the
former a species. There is no real opposition between them,
although in observation the natural and passive aspects, in experi
ment the artificial and active aspects, predominate. The superior
value of the latter, as compared with the former, arises from the
fact that the common object of both — the acquiring of a full and
exact knowledge of all the operative conditions influencing the
phenomenon under investigation — can be attained only by calling
in the aid of experiment, and not by simple observation alone.
This will appear presently from an examination of the proper

^OSANQUET, Logic, vol. ii., p. 145.

METHOD OF DISCOVERING CAUSAL LAWS 165

function of experiment. At the same time it is important to bear
in mind that all experiment is subservient to, and terminates in,
observation. Moreover, in many departments of scientific re
search — as, for example, in ethics, zoology, geology, astronomy
— experiment is practically impossible, and accurate observation
must be relied on as our only and ultimate channel of experience.
240. THE FUNCTION OF EXPERIMENT; DIFFICULTIES OF
ANALYSIS. — When we remember that an hypothesis is verified by
endeavouring to show that it is sufficient and indispensable to ac
count for the facts (229), that the supposed cause is proved to be
the real cause by showing that no other cause is adequate, we
shall realize the necessity of analysing all the surroundings of the
phenomenon under investigation, of isolating the latter, of laying
aside all that is inoperative and unessential to its presence, in
order that we may be able gradually to bring to light its con
nexion with all the factors and conditions that really determine
its occurrence. This work of analysis — mental analysis in the
first place, and real analysis, separation, isolation of factors, as
far as this is feasible, in the second place — is really the most
difficult stage in scientific investigation. There may be causes
or influences at work, of whose existence we are totally
unaware : they may be part of the total proximate cause of the
phenomenon. And non-observation is no proof of non-existence.
On the other hand, certain circumstances which, in our experience,
have always accompanied the phenomenon, need not be in reality
causally connected with the latter : uniform coexistence or
sequence does not prove causal connexion. Hence our hypo
theses may at first include either too little or too much. The only
way to obviate these difficulties is by endeavouring to discover
fully and accurately ALL the circumstances accompanying the occur
rence of the phenomenon, so as to be able to eliminate the accidental
and retain the essential ones. It is for this purpose, for securing
a full knowledge of all the surroundings of a phenomenon, that
repeated observations — whether simple or experimental — are use
ful. If we could be certain, from the observation of a single
instance, that all the conditions we observed accompanying it, and
none others, were requisite for its production, we could straight
way formulate, and regard as established or verified, the natural
law connecting that phenomenon with its causes. But this is very
rarely, if ever, possible. Hence the need for observing a number
of instances.

1 66 THE SCIENCE OF LOGIC

Again, when we are sure that we have taken note of all the
circumstances that usually accompany a phenomenon, and set
ourselves to discriminate between those that are merely casual or
accidental, and those that are causal or essential, we soon advert
to the necessity of securing instances that differ from one another
in various respects. Instances that vary among themselves are
superior in value to instances that are practically similar to one
another, because the former enable us to eliminate as unessential
to the phenomenon the facts or circumstances which we noticed
to be absent in this, that, or the other, of the varied instances in
which the phenomenon occurred : the important principle under
lying this mode of elimination being that whatever circumstances
can be removed or eliminated without interfering with the happening
of a phenomenon are not causally connected with that phenomenon.
It is here that the superiority of experiment over simple obser
vation first becomes manifest. No doubt, in very numerous de
partments of research, nature presents us not only with similar
instances, but also with varied instances, of the occurrence of a
phenomenon. But it is when we can control the agencies of nature,
and modify them by experiment, that we can secure the most
fruitful variety of instances, the most fruitful combinations of
circumstances in which a phenomenon may or may not occur.
Experiment thus enables us actively to interrogate and cross-
question natural events, to analyse them more effectively, and to
disentangle more successfully the connexions which are casual
from those that are causal. The raw material furnished by nature,
in our sense experience, for scientific analysis and interpretation,
is for the most part chaotic and complex. The simple observer
has to take this material as he finds it ; the experimenter can
control and modify it, and determine for himself the special con
ditions under which his observation of it will take place.

The manner and order in which the experimenter is to handle
his materials and to operate upon them, must be left largely to
his own scientific knowledge, insight, and genius. His experi
ments will be guided by the hypotheses he has formed ; but, like
the actual formation of the latter, so, too, the actual procedure in
the former cannot be subjected to the guidance of any set of
mechanical rules. Logic can only analyse his procedure, and
point to some general principles of which that procedure is usually
an embodiment and application. Such is the principle under
lying the variation of instances in which a phenomenon occurs —

METHOD OF DISCOVERING CAUSAL LAWS 167

that whatever can be eliminated without interfering with a pheno
menon is not causally connected with the latter.

There is another principle of equal importance, at which we
arrive by the following simple consideration. No variety of
positive instances, i.e. instances in which the phenomenon occurs,
— no matter how great the number and variety — ought to satisfy
the investigator that he has successfully segregated all the es
sential conditions of the phenomenon from its accidental accom
paniments, if he can make an experiment whereby he will be able
to remove the supposed causal conditions from a positive instance,
in order to see whether by so doing he will thereby remove or
eliminate the phenomenon itself: thus changing the whole into a
negative instance, i.e. one in which the phenomenon does not occur.
For, if he can thus successfully change a positive into a negative
instance (or vice versa} by removing (or introducing) the supposed
cause, he will by this mode of elimination have secured greater
certitude about the accuracy of his hypothesis than any variety of
positive instances could give him. The principle underlying this
mode of elimination is that whatever cannot be removed or elimin
ated without interfering with a phenomenon is causally connected
with the latter.

In those two principles we use the terms " cause" and "causal
connexion " in the strictest sense, i.e. as reciprocating. They are
simple principles in theory, but often not easy to apply satisfac
torily in practice. This we shall see presently, from an examina
tion of the various experimental "methods," or "rules," or
" canons," which are merely so many ways of attempting to apply
the principles just formulated.

In the course of our observations, whether simple or experi
mental, an instance or instances may occur in which the effect is
absent though the supposed cause is present, or vice versa. Such
instances are called exceptions, or exceptional instances? If on care
ful examination these turn out to be not merely apparent but real
exceptions, they will, of course, oblige us either to modify our
hypothesis or to abandon it for a different one. For this reason
they are of the greatest importance in inductive research. One
single real exception to an hypothesis, i.e. to a supposed law, is
sufficient to disprove the latter as it actually stands.2 But, at the

1 The term " negative instance " is sometimes applied, in a restricted sense, to an
instance in which the phenomenon does not occur though the supposed cause is
present.

The legal aphorism, Exceptio probat regulam, is sometimes applied in a confus-

1 68 THE SCIENCE OF LOGIC

same time, the " exceptional " fact often suggests the direction in
which we ought so to modify our hypothesis that in its modified
form it will be compatible with the fact, which will then be no
longer an " exception ".

No logical rules can remove the difficulties inherent in the process of
analysis by which we seek to discover and prove the causal laws according to
which phenomena happen. When we have fixed upon a phenomenon (say/)
for investigation, we must mark off around it — by going backward in time and
outward in space (216) — a region or sphere (say S) of antecedent and con
comitant facts, among which we assume that we can find the total proximate
cause of the phenomenon. By this very limitation of our field of investigation we
have excluded the rest of the universe as presumably irrelevant to/. This initial
limitation of the sphere of intended analysis is essential in every inductive
process : for in no case can we hope to analyse the whole universe as a
system, of which our phenomenon,/, forms an integral portion.1 And so it is
quite possible to fall into the error of excluding from all consideration, from
the very start, some condition which may really be causally connected with
p. No logical canon will avail to guard against this danger. It can be
avoided successfully only by the investigator who has a sufficiently deep and
extensive knowledge of his whole department of inquiry to safeguard him
against thus excluding ab initio any really operative or essential factor.
Observation of a number of instances of the occurrence of the phenomenon
will, of course, be helpful here in enabling him so to circumscribe the field of
investigation, 5", that he will be sure it contains within it all that is sufficient
for the production of the phenomenon, /, — i.e. the sum-total of the influences
which, when present, will entail the occurrence of/. This limitation is speci
ally " liable to error when " — as Professor Welton observes 2 — " the pheno
mena are complex, and such error can only be detected by extremely careful
and varied experiments to determine whether any condition is operative which
had not been suspected and had therefore been [unconsciously] relegated to
the unanalysed " universe, as unessential to the phenomenon.

The next step, naturally, is the analysis of the whole sphere of investigation,

ing way to the process of proving inductive laws. In jurisprudence, the full statement
of the maxim is : Exceptio probat regulam pro casibus non exceptis. It simply means
that the existence of a case or group of cases known to have been specifically ex
empted or excepted, by the legislator, from the operation of a certain rule or law, is a
sufficient proof that the said rule or law exists and is binding in all similar cases not
specifically excepted. In induction, a merely apparent exception can scarcely be said
to " prove " the (hypothetical) rule or law, except in the negative sense of not disprov
ing it. And the only sense in which a real exception can be said to " prove " the
(hypothetical) rule or law is that, by securing the modification of a wrong hypo
thesis in the right direction, it contributes to the establishment or proof of the right
hypothesis.

1 Nor is this necessary in the special sciences, which seek the proximate causes
of things. But it is part of the function of philosophy to examine hypotheses which
are based on a consideration of the world of phenomena as a whole (229, 232).

*op. cit., ii. p. 120. He instances (from Jevons, Principles of Science, pp. 428-9)
the discovery, by Davy, of common salt in the air — its previously unsuspected
presence in the air having " caused great trouble" in connexion with electrolysis.

METHOD OF DISCOVERING CAUSAL LAWS 169

6', into separate elements or factors, a, &, c • . . . »/, #, 0, /, ?, r . . . , and
the supposition that some one factor or group of factors (say m) is the cause of
p. Here is where the difficulty increases ; and where some writers have left
themselves open to the charges of conveying false impressions as to the sim
plicity of the process by which the real cause is to be discovered, and of setting
up wrong ideals of this process. The difficulty lies in the fact that the breaking
up of any field of phenomena, coexisting in space or successive in time, into
separate entities, capable of being expressed and dealt with symbolically, as
a, b, c, etc., must be to a large extent a mental analysis, which cannot claim
to give us an adequate view of the complex reality as it actually is. It is only
abstract and incomplete aspects of the reality that can be so represented. No
doubt, it is only by such analysis that we can hope to detect causal connexions
between phenomena. But nature does not present its materials to us thus
analysed or broken up into separate factors. Its agencies act and interact ;
they often counteract and neutralize one another. Its influences cross and
recross and combine with one another in hidden and intricate ways. It is on
our making suggestive and fruitful analyses and syntheses of the materials
which constitute our sense-experience, that the progress of science depends.
When this work is done on the proper lines, the materials for induction are
prepared, and the rules laid down by Mill are easy and obvious ; but this
work of preparation is the most difficult stage in the whole inductive process.
And the rules in question rather suppose it to be done than help us to do it.
Mill made the mistake of practically overlooking this part of the process ; his
treatment of induction conveys the impression, the erroneous impression, that
nature furnishes us with prepared materials : with simple, isolated causes and
effects, which have only to be observed, enumerated, and expressed by separate
symbols (cf. 245).

The same is true of Bacon and Jevons (209, 210). Their treatment of
the subject ignores the difficulty of making a successful analysis of the field
of investigation into separate elements, about each of which we may next go on
to inquire whether or not it is the cause of the phenomenon, p. Into how
many alternatives are we to break up the field of investigation when we attempt
to state the problem in the form of a disjunctive proposition : " The cause of
p is either a, or £, or <r, . . . or /, or m, or «, or . . . " ? In other words, how
many hypotheses are we to make and test ? This is certainly not determined
for us by the way in which the data are given to us ; for they are not given
catalogued into elements. Nor is it possible to determine the number of
hypotheses, as Jevons suggests, by any merely formal counting of instances
and " calculation of mathematically possible combinations " J of elements
in those instances ; for even if the elements were in each instance really
distinct and independent of one another, as they certainly are not,
the number of instances would be an "unattainable infinite series,"2
and, hence, no certain conclusion could be obtained by such a method.

How, then, are we to proceed ? Are we, perhaps, to go on selecting
empirically and by haphazard, one after another, all the factors, a, b, c, d, . . .
which we can detect in the field of investigation, S, and test each separately,

1 WELTON, op. «'/., p. 59; cf. ibid., pp. 53-55; VENN, Empirical Logic, pp.
o.

2 WELTON, ibid., p. 59.

1 70 THE SCIENCE OF LOGIC

until we have sifted out the cause of p ? " Did we know all the conditions
present," writes Professor Welton, "and needed but to decide which were
operative and which were not, it would appear to be theoretically possible to
empirically determine this question by trying every possible combination of
both the presence and the absence of these conditions. Practically the enor
mous number of experiments involved would render this impossible ; and the
fact that conditions are not independent elements of reality would add another
difficulty. For the removal of one condition not infrequently affects the action
of those left behind, and similarly the addition of a new condition may cause
an alteration in the result which could not be produced by this condition by
itself but only through its union with others.".1 The latter difficulty would
multiply our experiments hopelessly if we proceeded in this empirical manner,
for we should have to test not only every separate element, but every possible
combination of the elements.

It is imperative, therefore, that our analysis be guided by an examination
of the nature of p and of S, an examination which will suggest some part of
S, say M, as sufficient for the occurrence of p : the residue of S, say fi,
remaining for the present unanalysed, as being presumably irrelevant to p,
We can next convince ourselves that m is sufficient for p by showing, if pos
sible, that wherever m occurs/) occurs, even in the absence of R. To prove this
we have to secure, if we can, the elimination of R; but it is quite possible
that in attempting this we may find that m is not sufficient for p, that some
part of R, say /, is also needed (leaving a residue R1 presumably irrelevant).
When we have thus determined what part of 5, say /m, is sufficient for the
occurrence of p, we have established the hypothetical " If 6" is Im it isp ". We
have next to see whether the reciprocal of this is also true, i.e. whether Im is
indispensable for the occurrence of p. That is, we have to verify, if possible,
the proposition " If S is p it is Im" or its equivalent (contrapositive), " If 5"
is not Im it is not/> ". It is much more difficult to prove that nothing in S —
or, for that matter, outside 5 — except /m, can produce^), than to prove merely
that Im is sufficient for p. It is attempted by endeavouring to secure nega
tive instances, i.e. instances of .S from which Im is removed, in order to see
if its removal will entail the disappearance of p. In other words, we endea
vour to find in 5" — or outside it, even — an instance of the occurrence of^> with
out the occurrence of Im. It is our failure to find^J anywhere without Im that
proves Im to be indispensable to/>. But here, too, it is possible that we may
find p occurring in the absence oflm, and accompanied only by R1 (or, indeed, by
R1 plus something outside S altogether). This will prove that what is indis
pensable to p is not really Im, but something which is to be found not only
in Im but in R^ (or in R1 plus something outside S). It proves, in other words,
that we had not sufficiently analysed Im, that Im contained the really indis
pensable cause of p (say x) and something irrelevant as -well ; and that this
x is to be found in R1 (or in R1 plus something outside S) as well as in Im.
Thus, it is only by a very careful, and possibly a very prolonged, observation,
whether simple or experimental, of negative instances, that we can finally bring
to light x as the reciprocating cause of p (leaving as an irrelevant residue /?").
And it will be seen how, in this process, our initial hypothesis (that m is the
cause of p) may have had to undergo many modifications and remouldings.

1 WELTON, op. cit. ii., p. 117.

METHOD OF DISCO VERING CA USAL LA WS 171

This outline of the experimental discovery and proof of a cause, contem
plates only a comparatively simple case. As a rule, the agencies operative in
nature are so complex, so interwoven, and so dependent on one another, that
the actual process of analysis cannot be adequately represented by any such
simple symbolism as we have been employing. The outline given will, how
ever, help us to realize that in every successful discovery and proof of a causal
relation " there is a comparison of the phenomenon \J>~\ both in the presence
[5* = x + A'2 + p~\ and in the absence \S = A52] of that particular condition \x\
we are investigating "-1 The observation of positive instances will help us to
include in the field of investigation, 6", all the really relevant operative influences
in regard to the phenomenon under investigation,// while the observation of
negative instances will help us to determine what part of 6" is indispensable to
the occurrence of the phenomenon, p. But in both sorts of instances there
are difficulties to be surmounted. Practically speaking, we can never com
pletely eliminate the " residue " from our positive instances ; we can never get
a positive instance of p without a residue A*, A*,1 or A12, accompanying the sup
posed m, Im, or x. And hence we have to make sure (i) that this residue
" includes nothing which is not known to be present, and whose influence, if it
existed, could be determined and allowed for " ; 2 and (2) that this residue, if
it cannot be totally eliminated, is at all events really irrelevant lop. We try
to make sure of these points — and so to convince ourselves that there is nothing
really operative unknown to us in the positive instances, besides the supposed
cause— by directing our attention to the residue, and analysing it in a series of
negative observations or experiments, i.e. instances in which the phenomenon,
p, does not occur. We remove, if possible, the supposed cause, leaving the
residue, in order to see if the phenomenon will disappear. Or, finding a case
in which both the latter and the supposed cause are absent, and the residue
alone present, we introduce, if possible, the supposed cause, to see whether the
phenomenon also will appear. This process of comparing positive with nega
tive instances is likely to bring to light operative influences of which we were
previously unaware, if there were really any such present in the unanalysed resi
due in the positive instances. It is by the negative instances that we prove
our supposed cause to be indispensable, and everything else irrelevant, to the
effect.

But this proof will be cogent only in so far as we are sure that in passing
from the positive to the negative instance, or vice versa, we have eliminated,
or introduced, nothing else but the supposed cause. And it is not easy to be
sure of this, on account of the complexity and interdependence of the causal
agencies that are operative in nature. In experimenting, our working prin
ciple should be, as far as possible, never to introduce or eliminate more than
one element at a time. If we vary more than one element at a time, we shall
not know to which of the elements, so varied, any resulting change is to be
attributed.

It will now be sufficiently clear that the conduct of analysis, by observation
and experiment, cannot be reduced to any set of mechanical rules or formulae.
The history of the inductive sciences, of the ways in which great scientific truths
have been de facto discovered and established, makes this fact still more evi
dent. A number of interesting and instructive examples are given by Professor

1 WELTON, op. cit., p. 118. a ibid., p. 121.

172 THE SCIENCE OF LOGIC

Welton l in a section which he concludes with these words : " Even such
an imperfect outline as the above makes abundantly manifest that induction
is by no means an easy process, or one that can be reduced to mechanical
rules ; that the procedure starts from and is guided throughout by hypotheses ;
that number of experiments is appealed to only as a guarantee that only known
conditions are operative ; that the procedure of perceptual analysis is to estab
lish a positive connexion, to purge this of exceptions and to limit and corro
borate it by negative instances ; and that one inductive enquiry gives rise to
others." 2

Many valuable and instructive examples will also be found in Mr. Joseph's
Introduction to Logic, especially in chapter xx.,3 where the author sets forth
a number to illustrate " the truth of the contention that inductive conclusions
are established disjunctively by the disproof of alternatives ".4 We have
already set forth this theory of the inductive process (212), and it now remains
to examine briefly the "experimental methods," or rules according to which
this process of eliminating alternatives may be conducted.

241. THE " RULES " OR " CANONS " OF INDUCTIVE ANALY
SIS; "METHODS" OF "AGREEMENT" AND "DIFFERENCE". — By
a study of the various plans of procedure actually adopted by
scientists in inductive research, logicians have been able to formu
late certain practical rules or canons of which an explicit knowledge
cannot fail to prove useful towards the discovery and proof of
causal laws.

Lord Bacon's tabulae praesentiae, tabulae absentiae, and tabulae
comparativae? represent a somewhat crude attempt at such formu
lation. Sir John Herschel's Preliminary Discourse on the Study
of Natural Philosophy marks an important step in the logical
analysis of scientific procedure, and it was from this work that
John Stuart Mill avowedly drew the four (or five) " methods "
that have been ever since inseparably associated with the latter's
name.6 Mill's formulation of them, however, is somewhat clumsy,
and is, besides, in many ways defective ; and, while altogether
overrating their value, he in part misunderstood their real scope
and significance. Those mistakes of his have been corrected by
subsequent logicians.7 Most of what these rules contain is implied
in what has been said in the previous section (240) concerning
analysis and experiment ; but what was there briefly outlined will
be better understood by formulating and illustrating the various

1op. cit. ii., pp. 122-41. "*ibid., pp. 140-1. Cf. infra, 245.

3 Cf. also chaps, xxii. and xxvi. 4 p. 408.

*Novum Organum, ii. passim, Cf. ADAM, La philosophic de Frangois Bacon
(Paris, 1890).

6 Cf, Inductive Logic, III., viii. and ix. ; JOSEPH, op. cit., p. 397, n. 2.

''Cf., for instance, the text-books ot WELTON, MELLONE and JOSEPH ; also Mr.
LAURIE'S articles in Mind (N.S., vol. ii., 1893).

METHOD OF DISCO VERING CA USAL LA WS 1 73

canons in question. They have been stated in a variety of ways,
nowhere, perhaps, more clearly than in Dr. Mellone's Introductory
Text-book of Logic,1 whose treatment of the subject we purpose
mainly to follow.

The first rule, which is called the METHOD OF AGREEMENT, or
of single agreement, he states in this wise : —

" WHEN OBSERVATION SHOWS THAT TWO EVENTS ACCOMPANY
ONE ANOTHER (EITHER SIMULTANEOUSLY OR IN SUCCESSION), IT
IS PROBABLE THAT THEY ARE CAUSALLY CONNECTED ; AND THE
PROBABILITY INCREASES WITH THE NUMBER AND VARIETY OF

THE INSTANCES."

This rule is based on the principle that whatever can be re
moved or eliminated without interfering with the phenomenon
is not causally connected with the latter ; and hence it is thus
briefly expressed by Mr. Joseph : 2 " Nothing is the cause of a
phenomenon in the absence of which it nevertheless occurs ". It
is a method of observation mainly, i.e. a rule to which we have
recourse when we cannot experiment. Its chief utility lies in the
fact that it suggests a causal connexion as an hypothesis for verifi
cation. What appears to be the sole invariable antecedent of a
phenomenon probably contains the " necessitating and indispens
able cause " of the latter ; though other things also may contain
this " necessitating and indispensable cause ". Hence, at best,
this rule merely suggests (without proving) that our " sole in
variable antecedent " is a cause (in the wider sense) of the phe
nomenon. And since it suggests (without proving) only a cause
in the wider sense, it does get us over the difficulty arising from
the fact that the same phenomenon can have a plurality of such
causes. Briefly, it fails to prove a reciprocating causal relation
because what we think to be the sole invariable antecedent (i)
may not be so de facto (since another may be invariably present
unknown to us) ; and therefore, possibly, (2} may not be relevant
to the phenomenon at all (since the latter may be in reality due
to the unknown antecedent) ; and (3) even though the observed
invariable antecedent is de facto the one which, when present,
necessitates the effect, it need not be indispensable to the latter ;
for it may merely contain this indispensable element plus some
thing irrelevant, while (for all we know) this indispensable ele
ment may be equally well supplied by each of the varying

Jchap. ix. ^op. cit., p. 403.

174 THE SCIENCE OF LOGIC

agencies actually observed, or by quite other agencies, and under
quite other conditions, than those under actual observation.

To take a simple illustration : " Suppose you mix three dif
ferent kinds of poison [B, C, D\ with water [A] and give it to
three people : they all die, but you cannot argue that the water
is the cause of death, though it is the only invariable antecedent ".*
You cannot even argue with certitude that the water is a cause of
death. And why ? Because you are not certain that it contains
the " necessitating and indispensable " cause of death : there may
be another "invariable antecedent" present in the three cases,
namely, something (say X} contained in, and common to, the
poisons, B, C, D , each of which therefore may be a cause ; while
the indispensable element, X, though not in A, is not eliminated
by the absence of C D, or of B D, or of B C, but is present and
operative in all three instances, A B, A C, and A D, first in B,
then in C, then in D. From all of which we see that the causal
hypothesis which this method can merely suggest, may con
ceivably be even a wrong hypothesis. Simple observation reveals
to us only what are causes in the wider sense ; and in the absence
of further analysis the method of agreement may possibly elimi
nate many such causes successively, leaving the indispensable factor
present every time, not in the observed " invariable" element, but
in one or other of the " varying" elements : " If heat, for instance,
is produced by friction, combustion, electricity, all these real causes
would be eliminated by this method, for they are points in which
the different instances of heat differ ".2 At best, then, this
method can merely suggest, as a more or less probable hypothesis
to be otherwise tested, the supposition that the observed invariable
antecedent is, or contains, the cause.

The rule was entitled by Mill the "method of agreement," because,
though the instances differ in details that are presumably irrelevant to the
phenomenon, they agree in the one presumably essential, and therefore im
portant, point. He formulated the rule in the following way : —

" If two or more instances of the phenomenon under investigation have
only one circumstance in common, the circumstance in which alone all the
instances agree, is the cause or effect of the given phenomenon."

He means, of course, "one circumstance in common" besides the pheno
menon itself, which is common to all the instances. " Two " instances would
give very little probability, for this depends on the number and variety of the
instances. Of course, z/we could be certain that the observed instances of
any phenomenon had really "only one circumstance in common" we could

1 Palaestra Logica, p. no, § 338. * MELLONE, of. cit., p. 297.

METHOD OF DISCOVERING CAUSAL LAWS 175

infer with certitude that this circumstance is a necessitating cause, though not
that it is the only possible (or indispensable) cause, of the phenomenon. But
the "if" here points to a condition that is practically never fulfilled in the
unanalysed data presented in our sense experience as the raw material for
induction.

The following is one of Mill's own illustrations of the method of agree
ment : " For example, let the effect be crystallization. We compare in
stances in which bodies are known to assume crystalline structure, but which
have no other point of agreement ; and we find them to have one, and as far
as we can observe, only one, antecedent in common : the deposition of a
solid matter from a liquid state, either a state of fusion or of solution. We
conclude, therefore, that the solidification of a substance from a liquid state is
an invariable antecedent of its crystallization."1

The second method is called the METHOD OF DIFFERENCE,
or of single difference. It is stated as follows by Dr.
Mellone : —

" WHEN THE ADDITION OF AN AGENT is FOLLOWED BY THE

APPEARANCE, OR ITS SUBTRACTION BY THE DISAPPEARANCE, OF
A CERTAIN EVENT, OTHER CIRCUMSTANCES REMAINING THE
SAME, THAT AGENT IS CAUSALLY CONNECTED WITH THE EVENT." 2
This rule is an application of the principle that whatever
cannot be eliminated without interfering with the phenomenon is
causally connected with the latter.3 We saw that the method of
agreement was a method mainly of observation, a method of dis
covering causal laws by suggesting these as hypotheses for verifica
tion. The present method is a method mainly of experiment, a
method of proving causal laws by the verification of hypotheses
already suggested. It compares a positive instance (in which the
phenomenon occurs) with a negative instance (in which the
phenomenon does not occur). It is only when we can produce
the positive and negative instances by experiment, as immediately
successive phases of the same general set of conditions and cir
cumstances, that the rule can be applied with any considerable
degree of success. And the reason is this : for the successful
application of the rule we must be sure that there is no other
difference between the two instances besides the presence of the sup
posed cause in the one and its absence in the other. But simple
observation can rarely, if ever, guarantee a certain conviction

1 Logic, III., viii., § i. 2oj>. cit., p. 300.

3 Mr. Joseph, emphasizing the fact that we are always led to the true cause in
directly, i.e. by eliminating what is not the cause, enunciates the present ground of
elimination in this way : " Nothing is the cause of a phenomenon in the presence
of which it nevertheless fails to occur,"— taking "cause," of course, as the strict,
reciprocating cause (op. cit,, p. 404).

176 THE SCIENCE OF LOGIC

that two instances offered by nature are of this sort. It is
only when we have thoroughly analysed all the surroundings of
the phenomenon, when we know all of them, when we can con
trol, modify, introduce, or remove, each of them separately, with
out disturbing the others, that we can be sure our two instances
have everything else in common, and differ only in the one essential
respect. This latter condition, we may remark, is why we call
this rule the " method of difference ".

In applying the rule experimentally it does not matter which
of the two instances, the positive or the negative, comes first in
order of time. Occasionally, we may find it more satisfactory —
or, rather, less unsatisfactory — to produce the two instances simul
taneously. " E.g. to try the effect of a certain manure on a
wheat crop, you would not try it one year and compare the
result with the year before, for the weather might be different.
You would take two fields exactly alike and try the manure in
one of them and not the other." *

For the most part, however, the instances are procured suc
cessively. The well-known coin and feather experiment will
afford a simple illustration. It is supposed that the greater
resistance of the air to the relatively larger volume of the lighter
sorts of bodies is the reason why these fall more slowly than
bodies of the heavier sort. This is the hypothesis for verifica
tion. To test it we contrive an experiment by means of the air-
pump. Before exhausting the receiver we take the coin and
feather and let them fall within the receiver : they fall in unequal
times (as they would outside the receiver) : the supposed cause
and the effect are both present, the resistance of the air and the
retardation of the fall of the feather. This is the positive in
stance. We next eliminate the supposed cause by exhausting
the receiver of air : we let the coin and feather fall in the ex
hausted receiver, and we observe that the effect has disappeared ;
the feather is not retarded, it falls as quickly as the coin. This
is the negative instance. Since, then, so far as we know, there
was no change in the circumstances of the falling coin and
feather, except the removal of the air, we conclude that the air
contained (among other things, assumed to be irrelevant) that
element (namely, resistance) which is the necessitating and only
possible cause of the phenomenon in the conditions of our experi-

1 Palaestra Logica, p. no, § 341. Cf. MELLONE, op. cit., p. 303 ; and JOSEPH,
op. cit., p. 519, for the limitations of such an experiment.

METHOD OF DISCOVERING CAUSAL LAWS 177

•ment, and in all similar sets of conditions. Further experiment is
hardly needed to convince us that it is the resistance of the
medium that necessitates the retardation : not necessarily atmo
spheric resistance, but the resistance of any other gases that
we might substitute for the atmosphere. Yet, strictly speaking,
the single experiment with the atmosphere assures us only that
the air is a cause of retardation in the fall of the feather.1 But
granted, now, that we have made, if necessary, such experiments
with other gaseous media, and convinced ourselves that in the
circumstances of those experiments, and therefore in all similar sets
of conditions, the resistance of a gaseous medium is the only possible
cause of the phenomenon, can we further infer, from such single
experiments, that this is the only possible cause of the phenome
non, absolutely and universally, i.e. in any and every conceivable
place, time, state or condition of things, in the universe ? No ; the
method of single difference does not by itself really guarantee
this further inference. What it brings to light as the "only
possible cause " may perhaps be not yet sufficiently analysed,
may perhaps contain " irrelevant matter " plus " the only possible
cause " ; so that this latter may perhaps be forthcoming else
where, in quite a different vehicle, other than that in which it was
embodied in any of our experiments. Hence the method of
single difference proves a cause ; but of itself it does not strictly
prove that this is the only possible cause. But the latter is the
only kind of cause that excludes plurality ; there may be a
plurality of causes of the former kind. Therefore, the present
method does not of itself completely exclude the uncertainty which
arises from the possibility of a plurality of causes . In other words,
the method of single difference does not of itself establish with
certitude a reciprocating causal relation.

Another illustration of the present rule and its limitations, is
afforded by experimental inquiry into the conditions for the pro
pagation of sound.2 It is supposed that the presence of some
elastic medium, such as air (or any other gas), between the ear and
the sounding body, is an indispensable condition for the propaga
tion of sound. This hypothesis is tested by ringing a bell in the

1 By substituting successively, for air, other gaseous media, having presumably
only RESISTING POWER in common, as a factor relevant to retardation of the feather,
and finding the retardation take place in every case, we satisfy ourselves, as far as we
can, by this application of the Method of Agreement, that it is resistance that causes
retardation.

2 Cf. JOSEPH, op. cit,, p. 442.

VOL. II. 12

1 78 THE SCIENCE OF LOGIC

receiver of an air-pump, first before exhausting, then after ex
hausting, the receiver. In the former (positive) instance the sound
is heard, in the latter (negative) instance it is not. From this
we conclude that the presence of air is a sufficient condition for
the propagation of sound ; not, however, that it is itself an indis
pensable condition, but only that it contains an indispensable
condition — supposed to be elasticity. This latter supposition
we may confirm by applying the method of agreement to a
number of positive instances, each containing a different elastic
medium. But even when this stage has been reached we cannot,
strictly speaking, be certain that elasticity is the only relevant
factor common to the media employed in the positive instances ;
nor, therefore, that it is a really indispensable factor in those
instances. Nor further, even were we convinced that elasticity
was one of the indispensable factors in the conditions of our experi
ments^ could we, strictly speaking, conclude that an elastic medium
is indispensable to the propagation of sound in any and every con
ceivable set of circumstances. For it might still be objected that
perhaps in some totally different set of circumstances a medium
with some other property instead of elasticity might be capable of
propagating sound. Such an alternative possibility we might be
disposed to regard as far-fetched ; but the only way of disproving
any such suggestion would be by obtaining a negative experiment
in which elasticity would be absent and the other supposed pro
perty present, arid in which sound would not be propagated. It will
be seen that the experiments throughout this example do not
purport to prove that elasticity is the only indispensable condition
of a sound-propagating medium, but only that it is an indispens
able condition. There might be elastic media which would not
propagate sound, owing to the absence of other indispensable con
ditions for such propagation. The hypothetical ether, supposed
to be the propagating medium of radiant heat, light, electric and
magnetic influences, may, perhaps, be incapable of transmitting
sound, even though it be elastic.

The method of difference has been stated in the following terms by Mill : —
" If an instance in which the phenomenon under investigation occurs, and
an instance in which it does not occur, have every circumstance in common
save one, that one occurring only in the former, the circumstance in which
alone the two instances differ, is the effect, or the cause, or an indispensable
part of the cause, of the phenomenon"1

1 Logic, III., viii., § 2.

METHOD OF DISCOVERING CAUSAL LAWS 179

Again he means, of course, " every circumstance in common save one," and
the circumstance of the successive presence and absence of the phenomenon
itself, which appears in one instance and not in the other. "It is scarcely
necessary," he adds, " to give examples of a logical process to which we
owe almost all the inductive conclusions we draw in early life. When a man
is shot through the heart, it is by this method we know that it was the gun
shot which killed him : for he was in the fulness of life immediately before, all
circumstances being the same except the wound." He regards the method of
difference as the experimental method, par excellence, as the only one by which
" we can ever, in the way of direct experience, arrive with certainty at causes."1
He also gives the following example : "If a bird is taken from a cage, and
instantly plunged into carbonic acid gas, the experimentalist may be fully as
sured (at all events after one or two repetitions) that no circumstance causing
suffocation had supervened in the interim, except the change from immersion
in the atmosphere to immersion in carbonic acid gas."

Mill is inclined to overrate the value of this method. He failed to see that
of itself it does not enable us to analyse the phenomena under investigation
sufficiently to reach the one necessitating and indispensable cause. We require
something better than the method of single difference to carry us beyond that
less perfect stage of science in which we must admit plurality of causes.

242. COMBINATION OF " AGREEMENT " AND " DIFFERENCE ".
— As long as our methods of analysis merely enable us to assert
that something is a cause of a certain kind of phenomenon, we
have to recognize that the latter may have other causes ; and it
may be reasonably objected that the one we allege to be operative
in any given instance is not the one that is really operative there.
We endeavour to remove this uncertainty by combining the
methods of agreement and difference. This may be done either
when we are obliged to have recourse to simple observation alone,
or when we can make use of experiment. In the former case it
may be well to call this combined method the DOUBLE METHOD OF
AGREEMENT ; and in the latter to call it the JOINT METHOD
OF DIFFERENCE AND AGREEMENT. The former title will em
phasize the fact that although there is an element of the method
of difference present — inasmuch as we have two sets of instances,
a positive set and a negative set — yet we have not the essentials
of the method of difference, since we have to rely on simple obser
vation which does not give us any pair of positive and negative
instances differing in one respect only ; while the method of agree
ment predominates inasmuch as it is applied to each set of instances
successively. The latter title will emphasize the fact that the
method of difference is applied experimentally to the matter in

1 *«<*., §3-
12 *

r8o THE SCIENCE OF LOGIC

hand, and that we seek to make good its limitations by experi
mental observation of a number of instances — especially of nega
tive instances — varying among themselves in accordance with the
method of agreement.

The DOUBLE METHOD OF AGREEMENT is stated thus by Dr.
Mellone1: "WHATEVER is PRESENT IN NUMEROUS OBSERVED

INSTANCES OF THE PRESENCE OF A PHENOMENON, AND ABSENT
IN NUMEROUS OBSERVED INSTANCES OF ITS ABSENCE, IS PROB
ABLY CONNECTED CAUSALLY WITH THE PHENOMENON".

The two sets of instances must, of course, be drawn from the
same field of investigation ; they must be in pan materia ; they
will, therefore, have a great deal in common (the more the better) ;
each negative instance will be so chosen as to resemble as much
as possible some positive instance ; if any such pair could be pro
cured with everything in common (save the supposed cause), we
should have the requisite data for the method of difference, and we
might not have recourse to the present method at all : it is pre
cisely because we cannot by simple observation procure two such
instances that we must, as the next best course, apply the present
method ; and in applying it we select positive instances which
vary as much as possible among themselves, and likewise nega
tive instances which, like the positive ones, vary as much as
possible among themselves. Of all these points we have a clear
and easy illustration in the following example : — 2

" A fever has broken out in a town ; what is the cause ?
The patients vary in age, general health, circumstances, etc., but
they are all supplied with milk from the same dairy. You sus
pect (by the method of agreement) that some taint in the milk has
caused the fever. Suppose the dairyman pleads the 'plurality
of causes ' ; viz. the possibility that some of the patients have got
the fever by direct infection, others from bad drains, others from
poor living, none from the milk. How would you answer him?
You would see whether those who did not drink the milk from
his dairy were also free from the fever. If you could say, ' here
are a number of people living under much the same circumstances
as the fever patients, some exposed to direct infection, some to
bad drains, some to semi-starvation, but none of them drink the
milk from your dairy and none of them have fever,' then the case
against the milk would be much strengthened ; because you could

lop. cit., p. 306.

2 Taken from the Palaestra Logica, p. in, § 346. Cf. infra, 245.

METHOD OF DISCO V BRING CA USAL LAWS 1 8 1

point to instances in which the other possible causes of the fever
had not produced it."

" You would not use this method if you could use Difference.
But you can neither, if any one drinks the milk and gets the
fever, be sure that the milk is the only new antecedent, nor find
two people exactly alike in everything likely to produce fever ex
cept that one has drunk the milk and the other has not."

When we attempt to trace causal connexions between the
phenomena which form the subject-matter of the social, politi
cal and economic sciences, we shall rarely find it feasible to apply
the method of difference simply ; we are obliged, therefore, to
have recourse to the double method of agreement, or to " con
comitant variations " (243), or " residues " (244).

Mill's formulation of this double method, which he called the indirect
method of difference, or, also, the joint method of agreement and difference, is
as follows : —

" If two or more instances in which the phenomenon occurs have only one
circumstance in common, while two or more instances in which it does not
occur have nothing in common save the absence of that circumstance ; the
circumstance in which alone the two sets of instances differ, is the effect, or
the cause, or an indispensable part of the cause, of the phenomenon"

This formula is vague, if not even misleading. Two instances in each
set would be rarely, if ever, sufficient. Very rarely can the positive in
stances have " only one circumstance in common," or the negative instances
" nothing in common save the absence of that circumstance ".

Among his examples of this method is the following : " It appears that
the instances in which much dew is deposited, which are very various, agree
in this, and, so far as we are able to observe, in this only, that they either
radiate heat rapidly or conduct it slowly : qualities between which there is no
other circumstance of agreement, than that by virtue of either, the body tends
to lose heat more rapidly from its surface than it can be restored from within.
The instances, on the contrary, in which no dew, or but a small quantity of it,
is formed, and which are also extremely various, agree (as far as we can observe)
in nothing except in not having this same property.1 We seem therefore to
have detected the characteristic difference between the substances on which
dew is produced and those on which it is not produced."2

Let us now see how the combination of difference and agree
ment is applied to data which we can control by experiment, in
accordance with what we have called the JOINT METHOD OF

1 i.e. in nothing that is considered likely to influence the presence or absence of
dew : for, surely, being in pari materia, concerned with the same group of phe
nomena, the instances must have several other positive (though presumably indif
ferent) circumstances in common, and must also agree in the absence of several other
presumably irrelevant circumstances.

8 Logic, III., ix., § 3.

1 82 THE SCIENCE OF LOGIC

DIFFERENCE AND AGREEMENT. This is really the method which
pushes experimental analysis to its farthest possible limits, and,
by doing so, enables us to eliminate by degrees the misgivings
that may still remain after we have applied the method of dif
ference. These misgivings arise, as we saw, from the fact that
the total cause, as determined by applications of the latter method,
may not after all be absolutely indispensable ; or, in other words,
that somewhere or somehow other agencies might conceivably be
substituted for it in whole or in part, and so produce the effect in
the total or partial absence of this cause. Now the only way of
allaying such suspicions is by conducting as many negative ex
periments as these suspicions demand, within what we consider to
be a reasonable sphere of investigation : experiments in each of
which our supposed cause is absent, and one or other of the con
ceivable alternatives present. Each such experiment, in which
the phenomenon is absent, negatives or disproves the suggested
alternative cause which has been introduced instead of the sup
posed real cause. This is, in reality, the method of analysis which
we have already outlined (240), and its connexion with the process
of verifying hypotheses by the disproof Q{ alternatives, as set forth
in a previous chapter (212), will be at once apparent ; for it simply
describes the manner in which that process of verification ought
to be conducted. The following is the canon in which Dr. Mel-
lone : embodies this method : —

" When one phenomenon has been shown to be THE CAUSE OF
ANOTHER UNDER GIVEN CONDITIONS, by the method of single dif
ference ; and when we fail to find or to construct any instance where
the one phenomenon occurs without the other : then it is probable
that the first is the ' UNCONDITIONALLY invariable antecedent' of
the second — i.e. that the latter can be produced in no other way than
by the former ; and the probability increases with the number and
variety of the negative instances all agreeing in the absence both of
the effect and its suspected cause. "

The phrase " unconditionally invariable antecedent " means the
" sufficient (or necessitating) and indispensable cause," or again,
the " reciprocating cause ". Dealing with the conditions for the
verification of an hypothesis, we saw that an hypothesis is rigor
ously verified when it has been shown to be the " only possible "
one that will account for the facts (229) ; and the question now oc-
currs : Does " only possible " mean " conceivable absolutely in the
1 op. dt., p. 309.

METHOD OF DISCOVERING CAUSAL LAWS 183

abstract," or rather, "the only one that the concrete facts of ex
perience warrant us in regarding as any way plausible or deserving
of serious consideration " ? And the latter alternative is, of course,
the true one. So, too, the practical question now arises : Over
what extent of field must we conduct our negative experiments,
or how many must we perform, or when should we be satisfied
that our supposed cause is really the only possible, or indispens
able, cause ? And the answer will be : when we have allayed
all reasonable fears that there may be other causes of the pheno
menon ; when we have examined and disproved all the alter
natives that we think really worthy of consideration. The decision
of this will obviously depend on the nature of the investigation,
and on the knowledge, insight, and prudence of the investigator.

An instructive illustration of the value of the joint method is that furnished
by investigations into the cause of fermentation.1 "When sugar is changed
into alcohol and carbonic acid in the ordinary alcoholic fermentation, the pro
cess is in some way related to the cells of the yeast plant. . . . For many
years these minute organisms received little or no attention ; but in 1838
Schwann, one of the founders of the cell theory, and Cagniard de la Tour,
demonstrated the vegetable nature of these yeast cells, and showed that they
grew and multiplied in saccharine solutions." The method of single agree
ment warranted the conclusion that they were probably a cause of fermenta
tion ; but not the conclusion that they were indispensable to fermentation.
Liebig contended that they merely formed " a substance which by purely
chemical action produces the chemical change called fermentation " — a sub
stance which might conceivably be produced otherwise than by the action of
living germs like the yeast cell. The hypothesis that such living germs cause
fermentation not in this indirect way, but by such direct and immediate action
that their presence is indispensable and has no possible substitute— this hypo
thesis had now to be tested. In other words, it had to be proved not only that
living germs cause fermentation, but also that nothing else can. Symbolizing
cause and effect by G and /% respectively, the two propositions " If G then f,"
and " If not G then not /%" had to be established. The first of these pro
positions offered no difficulty : it was accepted as sufficiently established for
the time by the method of single agreement. At all events, the onus of proving
that the presence of living germs in fermentable materials need not necessarily
cause fermentation, would have been rightly placed on the shoulders of any
one who would venture to put forward such a contention (cf. 207). But to
establish the second proposition a careful series of negative experiments had
to be conducted : the real difficulty in the case being to get negative instances
in which the complete absence of living germs would be assured beyond all
reasonable doubt. The following were some of the experiments : (i) " Gay-
Lussac showed that clean grapes or boiled grape juice, passed into the
Torricellian vacuum of a barometer-tube, remained free from fermentation for

1 Cf. MELLONE, op. cit., pp. 298-9, 310-11.

1 84 THE SCIENCE OF LOGIC

any length of time [' If not A (air) then not F'], but that if a single bubble
of air were admitted fermentation soon appeared ['If A then F']." This
careful experimental application of the method of single difference merely
proved that something in the air actually admitted, and therefore in all
similar air admitted in similar circumstances, causes fermentation. The sup
position that this " something " consists in living germs had yet to be proved
by negative experiments that would presumably rid the air of such germs.
(2) " Schwann repeated Gay-Lussac's experiment and showed that if the air
were admitted to the vacuum through a red-hot tube then fermentation did not
occur." This proved that the " something " could be destroyed by great heat,
and so went to strengthen the probability of the proposition " If not G, then
not F". (3) Still further probability was added by various experiments which
went to show that a " temperature of from 20° C. to 24° C. was most favour
able to " fermentation ; " while the process was stopped at freezing point
(o° C.) and again at 60° C. ; and boiling destroyed it". (4) "Afterwards
Helmholtz showed that oxygen produced by electrolysis in a sealed-up tube
containing a boiled fermentable fluid did not cause fermentation." Here
again, the probability of the proposition " If not G, then not F" is increased,
inasmuch as the pure oxygen so obtained differs from ordinary atmospheric air
in the absence of all extraneous organic impurities, living germs included.
(5) " Hoffmann showed that air filtered through cotton wool was incapable of
causing fermentation " — the air being presumably purified of all organic mat
ter, including living germs, by such filtering. Therefore, again, the proposi
tion " If not G, then not F" was corroborated. (6) Better than all the fore
going negative instances was the one secured by Helmholtz in the following
application of single difference, with its simultaneous positive and negative
instances : " He placed a sealed bladder full of grape juice in a vat of fer
menting juice, and found that the fluid in the bladder did not ferment. Thus
the cause of the fermentation could not pass through the bladder. If the
fermentation were excited, as Liebig held, by a separate substance formed by
the yeast cells, and presumably soluble, one would have expected it to pass
through the wall of the bladder ; but if the process were caused by the small
yeast cells, then one can see why fermentation was not excited, as the yeast
cells could not pass through the membrane." This experiment tended to
disprove the hypothesis of a soluble substance as the immediate cause of fer
mentation. It did not, however, prove Pasteur's view, that fermentation is not
a merely chemical process taking place outside the yeast-cells, but rather a
vital or physiological process which takes place within them and transforms the
assimilated sugar into alcohol and other products. So far as was yet known,
fermentation might be due to the chemical action of some insoluble product of
the vital functions of the yeast cell. Subsequent experiments did bring to
light a substance of this sort, namely zymase, to the action of which fermenta
tion seems to be immediately due : a substance which, however, can be
produced only by the vital functions of living cells.1

1 " In 1897 Buchner submitted yeast to great pressure, and isolated a nitrogenous
substance, enzymic in character, which he termed ' zymase '. This body is being
continually formed in the yeast cell, and decomposes the sugar which has diffused
into the cell. ... In this respect the plasma behaves in a similar manner towards

METHOD OF DISCOVERING CAUSAL LAWS 185

The following example1 will prove instructive as showing that the
method of difference often requires to be supplemented, and can be supple
mented, by the experimental examination of positive instances ; in other words,
by the experimental application of the method of agreement to a number
of positive instances ; the object being to determine what precise factor in
the ^previously observed "invariable antecedent" is really the factor that is
relevant or essential to the effect. As early as the thirteenth century Roger
Bacon had inferred, by the method of agreement, that the passage of light
through transparent globes, prisms, crystals, etc., was probably connected
causally with the production of " rainbow " colours. Four centuries later, Sir
Isaac Newton commenced his investigation of the phenomenon by an appli
cation of the method of difference. "A beam of the sun's light, admitted
through a small hole in an otherwise darkened room, produces on a screen a
circular image of the sun (negative instance). But on passing the beam
through a prism, the image becomes nearly five times as long as it is broad,
and is coloured from end to end by a succession of vivid tints (positive in
stance). Hence something in the glass is the cause of the colours [assuming
that no other factor was unconsciously introduced simultaneously with the
prism]." But what was the " something "? Was it (a) the particular size of
the prism ? (b) the particular quality of the glass ? (c) the particular position
in which the prism was held ? (d) the particular temperature of the glass ? (e)
the substance itself (glass) of the prism ? No. It was none of all these ; for
Newton proceeded to vary all these, to eliminate them successively in a
series of experiments, in all of which he retained what he himself suspected
to be the essential factor, viz. the prismatic shape of the various trans
parent media which he employed. The instances were all positive instances,
and the " prismatic shape " (of the medium) was common to all of them.
" He eliminated this [presumably in every instance] by placing on the
original prism a second one of exactly the same angle, but inverted, so that
together the two prisms formed a solid with parallel surfaces " ; thus securing
in each case a negative instance, and making each experiment an application
of the method of difference. He next conceived the hypothesis that white
light is really composed of various primary rays which are subject to refrac
tion in unequal degrees — from the red which is least, to the violet which is
most, refrangible. This hypothesis he verified by passing each colour of the
spectrum separately through a hole in the screen, and then through a second
prism : the latter refracting each of the rays in different degrees without
further decomposing any of them.

the sugars as does the living yeast cell. . . . According to Buchner the fermentative
activity of yeast-cell juice is not due to the presence of living yeast cells, or to the
action of living yeast protoplasm, but it is caused by a soluble enzyme. [But other
investigators brought to light certain facts which] cannot be explained by the theory
that it is a soluble enzyme which brings about the alcoholic fermentation of sugar.
The remarkable discoveries of Fischer and Buchner . . . reconcile Liebig's and
Pasteur's theories. Although the action of zymase may be regarded as mechanical,
this enzyme cannot be produced by any other than living protoplasm." — Encyclo
pedia Britannica, eleventh edit, vol. 10, p. 276.

1 From BADEN-POWELL'S History of Natural Philosophy, quoted by Dr.
MELLONE, op. cit., p. 301 ; cf. ibid., p. 298.

1 86 THE SCIENCE OF LOGIC

243. METHOD OF CONCOMITANT VARIATIONS. MEASURE
MENT. STATISTICS. — The methods we have examined so far are
often called qualitative methods, as distinct from the present and
the next following methods, which are often called quantitative.
The former enable us merely to discover the presence, and to
some extent the nature, quality, or kind, of the causes and effects
investigated ; the latter enable us to take advantage of exact
quantitative measurements, to calculate the extent and intensity
of the agencies with which we are dealing : an advantage which
has contributed enormously to the progress of the physical
sciences in modern times. These so-called quantitative methods
do not, however, differ in principle from the methods examined ;
they, too, are practical plans for eliminating supposed irrelevant
elements from the field of investigation.

The METHOD OF CONCOMITANT VARIATIONS, when applied
to phenomena which we can merely observe, may be regarded as
an improved application of the method of agreement ; when
applied to phenomena which we can control by experiment, it
may be considered as a special and more exact application of the
method of difference. Its canon is thus formulated by Mill : —

"WHATEVER PHENOMENON VARIES IN ANY MANNER WHEN
EVER ANOTHER PHENOMENON VARIES IN SOME PARTICULAR
MANNER, IS EITHER A CAUSE OR AN EFFECT OF THAT PHENO
MENON, OR IS CONNECTED WITH IT THROUGH SOME FACT OF
CAUSATION."

In somewhat simpler terms : If two phenomena always vary
together, other circumstances remaining the same or varying inde
pendently, there is probably a causal connexion between the two
phenomena}- Where we have to rely on simple observation, the
conclusion as to a causal connexion is only probable, because in
such cases we can rarely if ever be sure that all other circum
stances do remain the same, or vary independently. For the
same reason, simple observation cannot of itself assure us
whether the one phenomenon is the cause of the other, or
whether both are joint effects of a common cause. For instance,
though observation assures us that " the loudness of a clap of
thunder varies with the intensity of a flash of lightning," of itself

1 MELLONE, op. cit., p, 312. Mr. JOSEPH states it thus: " Nothing is the cause
of a phenomenon which varies when it is constant, or is constant when it varies,
or varies in no proportionate manner with it" (op. cit., p. 404). Cf. ibid., pp.
517-18, where the author points to the difficulty of applying the rule in the social
sciences, in which the discovery of reciprocating causes is practically impossible.

METHOD OF DISCO VERING CA USAL LAWS 187

it cannot assure us that "neither is the cause of the other, both
alike being effects of the electrical condition of the atmo
sphere".1 But when we can experiment we may succeed in
removing such sources of uncertainty.

The following examples will illustrate the experimental appli
cation of the method : (i) The first law of motion states that all
bodies in motion tend to remain moving with uniform velocity
in a straight line until acted on by some interfering force. How
was this law proved ? The method of difference could not be
applied, for it is impossible to procure a negative instance, i.e.
an instance with no interfering force and no retardation of uni
form rectilinear motion. It was well known that all moving
bodies are being constantly influenced by interfering forces of
such a kind that all of these cannot be totally eliminated, e.g.
gravity, friction, resistance of the atmosphere, etc. How, then,
verify the hypothesis that retardation of motion is always due to
such interfering influences ? Obviously, by trying to vary the
influence of these obstacles, to diminish it, for instance (since
total elimination is impossible), and then see whether, by doing
so, the phenomenon itself, the retardation of motion, would be
diminished proportionately. And this is what Borda did in his
experiments with the pendulum. The influence of gravity on
the oscillation of a pendulum had already been calculated. If
the first law of motion were true, an oscillating pendulum, unin-
terfered with by any other force than gravity, should remain
oscillating indefinitely. Friction at the point of suspension, and
atmospheric resistance, were the supposed causes of the retarda
tion. "The simple oscillation . . . which in ordinary circum
stances lasts but a few minutes, was prolonged in Borda's
experiments to nearly thirty hours, by diminishing as much as
possible the friction at the point of suspension, and by making
the body oscillate in a space exhausted as nearly as possible of
air." '2 The less of the supposed obstacles, the less retardation.
"There could, therefore, be no hesitation in assigning the whole
of the retardation of motion to the influence of the obstacles." 3
It was concluded, therefore, that in the absence of all interference
moving bodies would continue to move with uniform velocity in
a straight line. (2) Another simpler experimental example of
the method may be exhibited by projecting a body successively,
with the same initial velocity, along specially prepared surfaces

1 FOWLER, Inductive Logic, p. 177. 4 MILL, Logic, III., viii., § 7. :i ibid.

1 88 THE SCIENCE OF LOGIC

which vary in roughness, and measuring the rate at which in
crease of friction (the supposed cause) gradually retards the
motion.

From those examples it will be seen that the present method
is applicable to a class of experimental cases in which the method
of difference proper cannot be employed : viz. cases in which the
supposed causal agency or agencies are what are called " PER
MANENT CAUSES," i.e. of such a kind that they cannot be totally
eliminated from any experiment : friction, gravity, heat, electric
and magnetic influences, etc. Two instances in which the phe
nomenon is present in a greater and in a lesser degree may be
taken as representing the " positive " and the " negative " instance
respectively (the presence of a phenomenon in a lesser degree being
really the absence of a greater degree of that phenomenon) ; and
in this way the present method may be regarded as a modifica
tion of the method, of difference. It perfects the knowledge
obtained by the latter method, in so far as this knowledge bears
upon the quantitative proportion between cause and effect.

Numerous instruments for measuring are based upon the as
certained concomitant variations of certain natural causes and
effects. The thermometer, for instance, depends upon the con
comitant variation of heat and the expansion of mercury (or
certain substitutes, such as alcohol) in volume ; and the baro
meter on the concomitant variation of atmospheric weight or
pressure and the height of a column of mercury (or other fluids)
supported by that pressure.

While the method of concomitant variations is more exact
than the method of difference, by enabling us to measure the
quantitative proportion between cause and effect within the limits
of observation and experiment?- at the same time any inference that
the variation will continue at a regular rate beyond observed limits
is, for the most part, hazardous and unreliable : inasmuch as, under
changed conditions, other agencies may become operative.2
When the concomitant variations of physical phenomena can be
exactly measured within certain limits, and when we are sure that
all other circumstances are irrelevant, the variations may be such
as to enable us to conclude that the one phenomenon is the total
and indispensable cause of the other within these limits, and that
therefore it will continue such beyond these limits. Hence, al
though we can have no experience of perpetual rectilinear motion,

lCf. VENN, Empirical Logic, pp. 419-20. ''Cf. JOSEPH, op. cit., 463.

METHOD OF DISCOVERING CAUSAL LAWS 189

or of the total absence of impeding forces, which is its essential
condition, we nevertheless infer that, if this condition were ful
filled, the phenomenon would certainly take place. But where
the variations within our experience do not reveal in the one
phenomenon the total and indispensable cause of the other ;
where they do not assure us that in changed conditions no other
agencies could possibly interfere : then, of course, we cannot
infer an absolutely universal and reciprocating causal relation.
For instance, "though solids and liquids diminish in bulk as
heat is withdrawn, they do not diminish at such a rate as to
suggest that there is a temperature at which they would vanish
altogether".1 Again, in regard to gases, it is calculated that
"they diminish in bulk, when heat is withdrawn, at such a rate
that they would vanish altogether at a certain very low tempera
ture ('absolute zero'). But before reaching that point they
liquefy. . . . We must not assume [therefore, without proof]
that a variation will continue beyond observed limits. Water, to
which you communicate heat, up to a certain point only gets
hotter; when its temperature reaches 212° [F.] it boils."2

Applied experimentally, the method often enables us to
establish " laws " in the sense of exact quantitative statements of
the proportions in which certain factors are found to contribute
invariably to a complex total process or phenomenon within the
limits of a certain range of experience (227), without at the
same time enabling us to explain the nature of the causal relation
of those factors to one another, or to some other cause whether
known or unknown. A good example of this use of the method
is furnished by the experiments devised to determine the rate of
the acceleration due to the force of gravity at the earth's surface. 3

Let us now consider the method of concomitant variations
in its application to phenomena which we can merely observe,
without controlling experimentally. In the domain of physical
phenomena it is particularly applicable to what are called PERIODIC
CHANGES, i.e. certain regular changes of a phenomenon from a
greater to a lesser extent, or degree of intensity, and vice versa.
For instance, if we observe two neighbouring intermittent springs
acting at regular intervals, the one, say, of an hour, the other of
four hours, the latter discharging on each occasion about four
times as much water as the former ; we might infer that probably

1 Palaestra Logica, p. 118, § 361. *ibid.

3 Cf. FOWLER, op. cit., p. 194.

i go THE SCIENCE OF LOGIC

they came from chambers the one four times as large as the other,
each chamber being fed by the same stream. A better example
is that furnished by the daily, monthly, and yearly variations in
the motions of the tides. The cause of those tidal motions, with
their periodic variations, had long been unknown, although some
connexion of them with the moon had been suspected for centuries.
It was only, however, when Newton formulated the law of uni
versal gravitation, and when in the light of this law the combined
action of the sun and the moon upon the waters of the ocean be
gan to be studied, that scientists gradually discovered, in the re
lative positions and motions of the sun, moon, and earth, a set of
phenomena which varied concomitantly with the variations in the
tides, and which, by their variations, accounted satisfactorily for
the latter.

When we have to rely on observation alone, the degree of as
surance which the method gives us in any individual inquiry will
depend on the likelihood that no other unobserved influences are
relevant to the observed variations. In all such cases it may be
regarded as a modified application of the method of agreement
(single or double). The advantage it has over agreement is this :
it enables us to see that the supposed causally connected pheno
mena are not merely present in a variety of different instances,
but that they vary concomitantly in degree throughout these in
stances. This is better than observing merely the presence (or
the total absence) of such factors in a number of instances.

The method is used extensively, by way of observation, in
astronomy, in geology, and in the study of climatic phenomena.1
But its use in the biological, social, political, economic, and
commercial sciences, is perhaps still more extensive and import
ant.2 The extremely unreliable character of some of the infer
ences based upon it, is due to the fact that owing to the impossi
bility of sufficient analysis numerous influences really relevant to
the varying phenomena remain undetected. Numerous sets of
instances exhibiting concomitant variation of the degree of
development in " intelligence " with the weight of the brain — and
other sets exhibiting concomitant variation of the former with the
complexity of convolution in the latter — have been observed and

1 Cf. FOWLER, op. cit., pp. 182-87.

a It is not the employment of this method, but rather the extensive use of the
argument from analogy, in certain sciences, that has given currency to the descriptive
title " comparative," in reference to such sciences as e.g. " Comparative Philology,"
" Comparative Anatomy," " Comparative Psychology," etc.

METHOD OF DISCOVERING CAUSAL LAWS 191

tabulated by scientists, in their investigations of the animal king
dom, man included ; yet, for the reason just given, it would be rash
to hazard an inference that there is any necessary or causal con
nexion between these varying phenomena in the departments
from which the instances have been taken. But, on the other
hand, the data to which we can apply the method are often such
that it will yield highly probable, and even practically certain,
conclusions.

The following example, from Adam Smith's Wealth of Nations? illustrates
the combined use of Agreement and Concomitant Variations. The lowness
of money pi ices for goods in ancient times was regarded as due to the poverty
and barbarism of the ancient peoples. The author undertakes to prove that
low money prices are not caused by " poverty and barbarism," but may be
due to " the barrenness of the mines supplying the commercial world with gold
and silver " : (i) " China is a richer country than any part of Europe, yet the
value of the precious metals is higher there than anywhere in Europe,"
and the money prices therefore lower. Here we have " low money prices,"
without " poverty " ; therefore the latter cannot be the cause of the former.
No doubt, within the last four or five centuries Europe has grown more wealthy
and its money prices have risen : which may account for the impression that
low money prices indicate poverty. The increase in wealth has, however, no
real connexion with rise in money prices. (2) Increase of wealth is due to
" the fall of the feudal system and the growth of public security " : influences
present throughout Europe, except in Poland, where the feudal system still pre
vails (an. 1 793) and which is still poor. But low money prices cannot be due to
poverty, because in Poland, notwithstanding its poverty, " the money price of
corn (its most important single commodity) has risen " just as in the rest of
Europe. (3) In Spain and Portugal, which are also poor countries, money
prices have risen as in the richer countries during those centuries. Hence
poverty does not account for low money prices. (4) Money prices remained
low in ancient times because the output of gold and silver from the world's
mines was comparatively small, and these metals were therefore comparatively
more precious. But since the discovery of America mines have multiplied :
gold and silver have become more plentiful : the purchasing power of these
metals has diminished : money prices have therefore risen, especially in Spain
and Portugal, which, though poor countries, can command large supplies of
these metals from the mines of their American colonies at the cost of a com
paratively small expenditure of labour. Thus it was proved inductively that
low money prices are due, not to " poverty and barbarism " but to the com
parative " barrenness of the mines " and the consequent scarcity of the
precious metals. The same conclusions could be proved deductively from the
general principles that " a poor country cannot afford to give a comparatively
large supply of labour or any other commodity in exchange for a comparatively
small supply of gold or silver (i.e. a low money price)," and that " the
purchasing power of gold and silver depends on the amount of labour, energy,

1 Bk. i., chap, xi., vol. i., p. 365, 7th edit. 1793 ;—apud JOSEPH, op. cit.t p. 417.

192 THE SCIENCE OF LOGIC

expenditure of natural resources, with which these metals can be obtained, and
will therefore diminish (i.e. money prices will rise) according as mines become
numerous and fertile ".

In the sciences of observation, especially in the social, politi
cal, and economic sciences, the immediate data to which the present
method is most fruitfully applied are not merely isolated facts as
they come, more or less haphazard, under our notice. What is
true of all the methods (240) is true of the present one : the raw
materials of ordinary experience have to be prepared for its ap
plication. And here the preparation will consist in the careful
compilation of statistics.

We are said to compile statistics when we count or compute
the number of instances of the occurrence of a phenomenon — and
if possible, also, the measure or degree in which it occurs in each
instance — within any selected limits of time and space. Thus, if
we measure the rainfall of each of the counties of Ireland for each
month, or for each season, during a period of, say, five years, we
are preparing, arranging, tabulating, the results of our observations
in such a way as to enable us to suspect causal connexions,
which might otherwise have remained undetected, between rain
fall and other phenomena such as the succession of the seasons,
the distribution of land and water in the country, the prevalent
direction of the winds, the proximity of the ocean, the existence
of mountain ranges, etc. It is mainly by bringing to light the
existence of concomitant variations between phenomena, that
statistics thus suggest causal connexions, or help us to test con
nexions whose existence may have been already suspected.
Observations tabulated in this way enable us to compare the relative
frequency with which different phenomena occur, and often to
measure the relative amounts of these phenomena, within a given
range of time or space. Uniform concomitant variations, brought
to light in this way, suggest the existence of some law of causal
connexion between the phenomena so varying — and may even
convince us that the variations are not mere casual coincidences :
may, in other words, prove the existence of some causal law — without
at the same time enabling us to determine what is the total
cause of the variation, or what are the partial causes, or any of
them, in virtue of which the observed phenomena occur and vary
concomitantly as they do.

Suppose, for instance, that intemperance among the poorer
classes in a city is observed to vary concomitantly with the squalor

METHOD OF DISCO VERING CA USAL LA WS 1 93

and misery of the overcrowded tenement lodgings in which they
have their "homes": we may infer that such variation is not
merely accidental, that it is causal, that it reveals existence of some
law of causation ; but we may not safely infer that either pheno
menon is exclusively the «?#.$•£— whether partial or total — and
the other exclusively the effect; for there may be interaction:
each may be a partial cause of the other, and each, or both, may
be partly due to a combination of many other causes, such as de
fective early training, religious indifference, thriftlessness, absence
of opportunity for healthy recreation, high rents, unemployment,
excessive inducements to drink, insufficient control of the drink
traffic, etc. Again, suppose " that statistics show a close corre
spondence between a diminution in convictions for drunkenness
and an increase of money in saving-banks — whether in one town
in successive years, or in different towns at the same time ; — even
if other things do not remain the same, we should be justified in
concluding that both improvements, if not actually cause and
effect, depended on some common cause, improvement in wages
or education".1

244. METHOD OF RESIDUES. "CONJUNCTION OF CAUSES,"
AND " INTERMIXTURE OF EFFECTS ". — From all that has been said,
so far, about perceptual and experimental analysis, it will be evident
that in all cases we endeavour to make use of whatever knowledge
we already possess about the phenomena under investigation, and
about the whole department of facts to which they belong. Such
previous knowledge may help us in various ways — for instance,
by suggesting hypotheses to be tested, and the various grounds
of elimination to be applied successively in testing them. Now,
there is a special sort of consideration which will help further
analysis when we already know a great deal, comparatively speak
ing, about the nature and the exact measure of the causal agencies
and effects which make up the whole sphere of facts under ob
servation. It may, perhaps, for the sake of simplicity, be repre
sented in this way. If, in a whole complex process, abcdefgh, we
know already that the causal relations between abed and efgh,
between a and e, between b and /, between c and g, are all re
ciprocating causal relations ; then we can infer a similar relation
between d and h. Or, if h be absent from the whole complex
event — that is, if there be nothing in the event to account for d:
which, in all such cases, is described as a RESIDUAL PHENOMENON

1 Palaestra Logica, p. 113, § 353.
VOL. II. 13

I94 THE SCIENCE OF LOGIC

— we can infer that there must be, connected with the whole
event, something that causes d ; and we can then proceed to
search for this something in the surroundings of the event. No
doubt, our knowledge of a complex event is rarely so perfect as
this symbolism implies ; the latter represents rather an ideal. But
it expresses the sort of consideration embodied in the Method of
Residues. It shows us, too, that the analysis here effected is
mental rather than actual, and that deductive inference from our
previous knowledge is the predominant feature of this analysis.

We may now state the rule or canon which is the ground of
the analysis. It is formulated by Mill in this way : —

" SUBDUCT FROM ANY PHENOMENON SUCH PART AS is KNOWN

BY PREVIOUS INDUCTIONS TO BE THE EFFECT OF CERTAIN ANTE
CEDENTS, AND THE RESIDUE OF THE PHENOMENON IS THE EFFECT
OF THE REMAINING ANTECEDENTS."

It is stated more briefly, thus, by Mr. Joseph:1 "Nothing
is the cause of one phenomenon which is known to be the cause of a
different phenomenon." To suit cases where no antecedent is forth
coming, within the ambit of the complex event itself, for an un
explained residue, Dr. Mellone2 formulates the following rule,
which becomes, in such cases, a "finger-post to the unexplained" :
" When any part of a complex phenomenon is still unexplained by
the causes which have been assigned, a further cause for this re
mainder must be sought ".

The method can be applied both to experimental cases and
to cases of simple observation. As applied to the former it is a
quantitative method, its value depending on the degree of exact
ness with which we can make use of measurement. It is ex
tensively applied in this way to experiments in chemical analysis.
The following example, from Jevons' Elementary Lessons in Logic*
will illustrate the use of it. " Thus, the composition of water
is ascertained by taking a known weight of oxide of copper
[C], passing hydrogen [H] over it in a heated tube [T1] and con
densing the water [IV] produced in a tube [7^2J containing sul
phuric acid [in known weight, S]. If we subtract the original

lop. cit., p. 404. His formula emphasizes the fact that reciprocating causes
only are in contemplation. The author formulates (ibid, n.) other grounds of elimin
ation applicable to causes that are non-reciprocating either because they contain too
little (partial causes, sine qua conditions), or too much, for the effect. These are
eminently instructive, e.g. that from Hume's Treatise, etc., pt. III., xv. — " Where
several different objects produce the same effect, it must be by means of some quality,
which we discover to be common amongst them ".

»o/. cit., p. 3x5. 3P- 254.

METHOD OF DISCOVERING CAUSAL LAWS 195

weight of the condensing tube [T^ + S] from its final weight
[T"2 + S + W~\ we learn how much water is produced ; the quantity
of oxygen [O] in it is found by subtracting the final weight of the
oxide of copper \C ' - O] from its original weight [C]. If we then
subtract the weight of the oxygen [O] from that of the water [ W\
we learn the weight of the hydrogen [//] which we have combined
with the oxygen [O], When the experiment is very carefully
performed, as described in Dr. Roscoe's Lessons in Elementary
Chemistry (p. 38), we find that 88*89 parts by weight of oxygen
unite with n-ii parts by weight of hydrogen to form 100 parts
of water." Thus we have :

Total weight (initial stage) ^[T1 + C] + [72 + S]

(final stage) = [Tl + C - 0] + [T* + S + W]
Therefore the difference [ W - O] must represent the added hydro
gen [//]. That is to say, we know how to account for the total
weight at the initial stage ; we then add one single antecedent,
namely hydrogen ; therefore the excess of the final weight over
the initial weight must be due to the added hydrogen. From
this we can understand why the present method has been de
scribed as a peculiar application of the method of difference.

It will also enable us to understand why the method is ap
plicable only to a homogeneous intermixture of the effects of several
co-operating causes, or to some homogeneous aspect of these effects,
such as weight in the example given. Obviously, it is only when
several causes act at once, and when we have before u the
complex resulting effect of their co-operation, that the method
can be used at all. But we have to distinguish two ways in which
a number of causes may co-operate in the production of a total
effect. This latter may be either of the same kind as the effects
of the single causes acting separately would be ; or it may be of
a different kind from the single effects. In other words, any
''CONJUNCTION OF CAUSES,"/.*, joint action, simultaneous co
operation, of a number of causes, may be either a simple adding
together of these causes, a " COMPOSITION OF CAUSES," to pro
duce a " HOMOGENEOUS INTERMIXTURE OF EFFECTS" ; or it may
be a mutually modified co-operation of these causes, a " COM
BINATION OF CAUSES," to produce a " HETEROGENEOUS or
HETEROPATHIC INTERMIXTURE OF EFFECTS ". Chemical changes,
for instance, are heterogeneous or heteropathic effects of the combin
ing agencies which produce them. On the other hand, " if in
one experiment friction, combustion, compression, and electric

13*

196 THE SCIENCE OF LOGIC

action are all going on at once, each of these causes will produce
quantities of heat which will be added together . . . We may
call this a case of Iwmogeneous intermixture of effects. " * And it
is only to such cases the method of residues can be applied.
" There cannot be a simpler case . . . than ascertaining the
exact weight of any commodity in a cart, by weighing the cart
and load, and then subtracting the tare or weight of the cart
alone, which had been previously ascertained."2

The fact has been already emphasized, that it is impossible to regard
processes of causation as made up of discontinuous factors (240) ; but we
must, if we are to understand them, introduce discontinuity by the mental ab
straction involved in analysis. So, when we do isolate them mentally, we
must not forget that in the concrete actuality the factors are not independent of
one another. It is this mutual interdependence and interference of causes that
make inductive research so difficult. When causes " combine " to produce
" heteropathic " effects, experiment alone will enable us to detect the nature
of the separate influence of each, and the various kinds of effect each will pro
duce in combination with others. When causes co-operate by way of simple
" composition " to produce " homogeneous " effects, the action of any one
" may be (a) augmented, (b} diminished, (c} diverted, (e) wholly counteracted,
by that of another cause ; 3 and all these various kinds of interaction may
occur at the same time among the effects. Fowler observes truly that in every
case each cause produces its appropriate effect, even though it may have dis
appeared wholly or partly in the total result. . . . When the full conse
quences of a Law are thus affected (modified or neutralised) by other Laws,
it is called a tendency." A " tendency," therefore, is the action of a causal
i nfluence considered as impeded by an opposing causal influence.

The method of residues is employed extensively, by way of
experiment, " in making allowance for the errors or necessary
corrections in observations. Few thermometers are quite correct ;
but if we put a thermometer into melting snow, which has
exactly the temperature of o° Centigrade or 32° Fahr., we can
observe exactly how much ... we ought to add or subtract
from the readings of the thermometer to make them correct ".4
Here the discrepancy between the actual level of the mercury
and the point marked o° C., or 32° F., may be regarded as a
residual phenomenon, whose explanation is to be found in the
erroneous graduation of the instrument.

1 JEVONS, op. cit., p. 252. *ibid.t p. 253.

3 " Thus, for simple examples we may suppose a body (a) pulled by two forces in
exactly the same direction ; (b) pulled by two forces of different magnitudes in
exactly opposite directions; (c) pulled in one direction by one force, and by an
other force pulled in a direction at right angles to the former ; (rf) pulled by two
equal forces in exactly opposite directions, when no motion takes place ".— <MELLONE,
op. cit., p. 317, n.

4 JEVONS, op. cit., p. 253.

ME THOD OF DISCO V BRING CA VSAL LAWS 197

The use of the method of residues as a "finger-post to the un
explained" by the study of residual phenomena, has proved most
fruitful in scientific research, and deserves particular attention.
Applied in this way, it is obviously a method of discovery rather
than of proof, a source of hypotheses rather than a means of test
ing them. In sciences like astronomy and chemistry, where exact
calculations and measurements are extensively employed, very
remarkable discoveries have been made by the application of it.

" Almost all the greatest discoveries in astronomy," writes Sir
John Herschel,1 " have resulted from the consideration of residual
phenomena of a quantitative or numerical kind." The discovery
of the planet Neptune by Adams and Leverrier in 1846 is a
striking example. By calculating the effects of all known attrac
tions on the planet Uranus, the path of the latter in the heavens
was determined. This planet was actually found, however, to be
sometimes before and sometimes behind the place calculated for
it. It was concluded that the discrepancy, the " residual effect,"
must be due to the attractive influence of some unknown heavenly
body. The search for this latter resulted in the discovery of
a hitherto unknown planet — Neptune.

In the domain of chemistry, we may instance the discovery,
by Lord Rayleigh and Professor Ramsay, in 1894, of a chemical
element, which they called argon, present in the atmosphere in
very minute quantities. "The investigation started from the
detection of an unexplained residual phenomenon. Careful de
termination of density had shown that nitrogen obtained from
various chemical compounds is of a uniform density, but that
'atmospheric' nitrogen is about \ per cent, heavier".2 In ex
planation of this residual phenomenon numerous hypotheses were
advanced, and a long series of experiments culminated in the
discovery of the new chemical element.

245. SCOPE OF THE " METHODS ": USE OF SYMBOLS. — The
various modes of procedure that have been outlined under the
title of " methods," are simply applications of various grounds of
elimination, whereby we exclude irrelevant elements until the
causal connexion alone is left. They presuppose the dividing up
of our domain of inquiry into distinct factors, when mapping out
the field for possible hypotheses and forming the disjunctive judg
ment among the alternatives of which we hope to find the cause :
" x is caused by either a, or bt or c, or . . ., or m " (212). They

lapud MELLONE, op. cit., p. 316. 2C/. WELTON, op. cit., pp. 133-40.

198 THE SCIENCE OF LOGIC

then find, their application, one or other or all of them, in exclud
ing successively a, and b, and c , . . . until m alone is left : that is,
in establishing minor premisses for our alternative major, " The
cause of x is not a" " The cause of x is not b" etc., until we are
thus enabled indirectly to prove that " The cause of x is m ". In
proving each minor premiss, by the application of the " methods,"
there is deductive reasoning from the hypothesis that is being
tested. It is a mistake, therefore, to contrast the principles in
volved in these methods with the various principles or axioms of
deductive inference, by describing those as " material " and these
as " formal ". Nor can the rules for elimination be called " in
ductive " in the sense that they enable us to generalize directly
from the individual data of our experience, independently of hypo
thesis and deductive reasoning: for they do not enable us to general
ize in this way. It was Mill's mistake to think that they do ;
though he seems to have felt the difficulty of such a position :
for he admits the utility of hypothesis and deductive reasoning
in what he calls the "deductive method" j1 and although he re
stricts the application of the latter to the more complex sort of
phenomena, he is forced to admit that it is to this method " the
human mind is indebted for its most conspicuous triumphs in the
investigation of nature " 2. Indeed, even the simplest phenomena
of concrete nature are far too complex to admit of the direct appli
cation of any one of the "methods" to them. "The only true
function of the methods is, indeed, given by Mill himself when, in
speaking of cases in which there is an ' interference of causes with
one another,' he says : ' The instrument of Deduction alone is
adequate to unravel the complexities proceeding from this source ;
and the four methods have little more in their power than to
supply premises for, and a verification of, our deductions' (III., x.,

§3)"-3

Attention has already been called (240) to the fact that the
application of the so-called " inductive canons " supposes the
materials already analysed and prepared, " that limited groups
of antecedents and consequents, known to be causally connected,
have been separated out for the purpose of ' inductive ' inquiry,
whose task is only to obtain simple causal connexions by elimin
ating some of the elements still left. . . . Whewell is, indeed,
quite justified when he says : ' Upon these methods, the obvious

1 Logic, III., xi., § 93. Cf. supra, p. 45.

2 ibid. ; cf. WELTQN, op. cit., ii., pp. 59, 83. 3 WELTON, ibid., pp. 158-9,

METHOD OF DISCOVERING CAUSAL LAWS 199

thing to remark is, that they take for granted the very thing
which is most difficult to discover, the reduction of the phenomena
to formulae such as are here presented to us' (Phil, of Discovery,
P- 263)."!

The symbolizing of the methods by employing the letters of the alphabet
to represent the various elements that enter into a process of inductive analysis
has its advantages and its disadvantages. Its chief advantage is, perhaps,
that it helps us to realize more clearly what we are aiming at in each of the
methods. But, on the other hand, it is liable to create false impressions about
the nature of the analysis symbolized : the impression that the work of
analysis is simpler than it really is ; the impression, too, that the elements
with which we are dealing are distinct, isolated, independent, individual
entities, like the symbols themselves. The system of symbols employed by
Mill has an additional drawback : by employing corresponding capitals and
small letters for the antecedents and consequents, he conveys the impression
that nature presents us with corresponding connexions between the elements
of our experience ; whereas in reality these connexions have to be discovered
by ourselves. The following are his formulae for the various methods : —
Method of Agreement : —

ABC followed by a b c,
A D E „ „ ade,

.•. A and a are causally connected.
Method of Difference : —

ABC followed by a b c,
B C „ „ b c,
.-. A and a are causally connected.

Joint Method of Agreement and Differences. — Mill himself gives no
formula, but, following the lines of those just given, we arrive at some such
scheme as the following : —

A B C— a b c \

A D E — a d e \ positive instances ;
A F G— a fg >
B M N— b m n \

D O P — d o p \ negative instances ;
F Q R-/ q r J

.-. A and a are causally connected.
Method of Concomitant Variations : —
A1 B C— a1 b c,
A3 B C—a2 b c,
A3 B C— a3 b c,

.•. A and a are causally connected.
Method of Residues : —

A B C D is the known cause of a b c d
A „ „ „ a

B „ „ „ b

C „ „ „ c

.-. D and d are causally connected.

1 WELTON, ibid., pp. 148-9.

400 THE SCIENCE OF LOGIC

It would be superfluous to show how far this abstract symbolism falls
short of picturing the complexity of the concrete facts and processes it is
supposed to represent. Nor is it of sufficient importance to call for any ela
borate attempt at improvement. Logicians have, however, improved it in
various ways, while pointing out its many shortcomings.

The separation of the elements into antecedents and consequents has to
be effected by the investigator ; and he must bear in mind that the actual
influence of the cause is not prior in time to, but is simultaneous with, the
actual production of the effect. To illustrate these points, we may instance Dr.
Venn's manner of symbolizing the Joint Method : l —

" Surely what we want is something of the following kind. Let x be
some phenomenon in regard to which eleven antecedents, viz. A to K are to
be taken account of, and suppose that we have collected the following sets of
affirmative and negative instances : —

Affirmative Negative

ABCDE BCFG

ADEFG DEHI

AFGH I FG J K

A H I J K HIDE

" It is clear that A is the only element, of the given lot of eleven, which is
always present in the former set of instances, and the only one which is always
absent in the latter set. If we knew for certain that there could be only one cause,
then clearly A is that one. So much indeed is established by the affirmative
instances. What the negative instances do is to disprove one after another
of the alternative causes other than A. It might be that A was not a cause
at all, but that B, D, F, and H had respectively been at work in producing x
in the four cases in question. The negative instances disprove this, however ;
and since they take account of every one of the ten letters,— or cause symbols,
— B to K, and show that no one of these is operative, we are led to conclude
that A alone is the cause which we are seeking."

A theoretical knowledge of the method of inductive analysis,
by way of observation, experiment, and hypothesis, will help the
scientific investigator in his work ; but it will not determine for
him which, or how many, of the rules of elimination he must em
ploy in any given subject-matter, or in what order. This can be
determined only by his own insight, prudence, and knowledge of
the facts with which he is dealing. The progress of scientific dis
covery involves the use of all of them.

We may give here the following final example, which will illustrate the
combination of three of the " methods " to form a series of positive and negative
experiments for the purpose of verifying the hypothesis that life proceeds only
from life, and never appears by spontaneous generation : 2 Let us assume that
the reputed " spontaneous " production of minute living organisms is really due

1 Empirical Logic, pp. 430-1.

2 They are the experiments actually performed by Pasteur. Cf. JANET, Traite
de philosophie, n. 146. Paris, Delgrave, 1879.

METHOD OF DISCOVERING CAUSAL LAWS 201

to the presence of living germs held in suspension in the atmosphere ; that these
germs find in fermentible liquids, or in decomposing organic matter, suitable
media for multiplication. How are \ve to verify our hypothesis ?

1. We expose to the air a number of vessls all filled with such liquids, and
we find that wherever such germs can have access to them they ferment : the
supposed " spontaneous " generation takes place. Here we have the method
of agreement.

2. Next, we secure other vessels similarly filled and take care to seal them
hermetically in the purest atmosphere available,— upon the Alps, for example,
where there is little danger of encountering such germs. We lay the vessels
aside, and there they remain indefinitely without any sign of fermentation — evi
dently free from any living organism. Here we have negative instances which
agree in the absence of the supposed cause ; and which, together with the
positive instances in (i), illustrate the combination of agreement and difference.

3. We next expose to the air a variety of similarly filled vessels in a
variety of different localities where the atmosphere is tainted in different degrees
by the presence of such germs ; for example, in cellars where the air is cold
and still and all the germs probably settled, or far up on some high mountain
where the air is most likely free from organic impurities, or in the hot, tainted
atmosphere of a city where germs of all sorts abound, or in the moist shade of
trees or shrubs, in the summer months, when the air is known to swarm with
living microbes : we find the rapidity of fermentation, and the amount of living
organisms produced in the liquids, to be in proportion to the degree of impurity
of the atmosphere in each case. Here we have the Method of Concomitant
Variations. From which experiments we infer that life is caused in all cases
by the multiplication of some existing living thing, and, negatively, that non
living matter cannot give rise to life (cf. 229).

Living things, therefore, must be endowed with the natural property of
reproducing their kind upon the earth. The natural origin of a new living
organism is an already existing organism : Omne vivum ab ovo ; omnis cellula
ex cellula.

246. QUANTITATIVE DETERMINATION : MODES OF MEASURE
MENT. — Very little reflection will show that the progress of dis
covery in the physical sciences has been proportionate to the
degree in which exact measurement of phenomena has been found
to be feasable. * The sciences of physics and chemistry have passed
gradually from the study of qualities to the study of quantities :
their laws are now not regarded as exact until they are stated
quantitatively, or in mathematical formulae. But knowledge of
the quantitative aspect of things is not all knowledge of them ;
and, moreover, there are vast departments of facts whose quanti
tative aspect is of very minor importance to a scientific know
ledge of them. Hence, the attempt made in the last century
to reduce all the sciences to terms of mechanics (201, 217, 224,

1 Cf. L. POINCARE, The New Physics (International Scientific Series), chap. ii. ;
JOYCE, Principles of Logic, pp. 363 sqq. ; WELTON, op. cit., pp. 160-5, 182-7.

202 THE SCIENCE OF LOGIC

229) only brought discredit on a procedure that is perfectly
legitimate within proper bounds. What these bounds are, a
glance at the nature of measurement, and its units and standards,
will immediately disclose.

All measurement is observation — and something more. As
observation, it is inseparably connected with interpretation of the
data offered to us ; and interpretation, being judgment, is subject
to error. But measurement is more than observation ; it is com
parison of the observed fact with some other fact taken as standard
or unit. And this comparison is not merely mental ; it implies
direct application of the unit or standard to the measurable magni
tude, and sense-observation of the result of such application. The
accuracy of measurement, therefore, ultimately depends on the
acuteness of our powers of sense-perception. But these powers
are trustworthy only within a certain range ; and even within this
range they are not infallible. There are, for all the senses, what
are called minima sensibilia : objects so small that our senses are not
sufficiently delicate to become aware of any smaller. No doubt,
our powers of observation have been increased by such mechani
cal devices as the telescope and the microscope ; and our powers
of measuring, i.e. counting the application of a unit to a quantity,
are aided by such delicate instruments as the micrometer screw,
the electrometer, the bolometer,1 etc. But, even still, there is a
limit to the keenness of our sensibility ; so that every actual measure
ment is, normally speaking, only an approximation to the real state of
the facts. By accident, no doubt, a measurement may be just
accurate ; but, even when it is, we cannot be sure of this. So it
is no exaggeration to say, with Jevons,2 that " we may look upon
the existence of error in all measurements as the normal state of
things".

To fix upon certain fundamental and derived units for measur
ing various physical magnitudes, units of spatial extension (dis
tance, area, volume), of time, of mass, of velocity or rate of
motion, of acceleration, of mechanical energy, of temperature, of
electromotive force, of strength of electric current, etc. ; to devise
means of applying these units with a greater approximation to

1 " Langley's bolometer can detect a change of temperature of one hundred-
millionth of a degree C." JOYCE, op. cit., p. 364. So, too, in measuring mass,
" Metrology vouches for the hundredth of a milligramme in a kilogramme ; that is to
say, it estimates the hundred-millionth part of the magnitude studied ". — POINCARE,
op. cit., p. 33.

8 Principles of Science, p. 357.

METHOD OF DISCOVERING CAUSAL LAWS 203

accuracy ; and means of allowing for unavoidable deviations :
such are the main functions of what is nowadays really a distinct
science and art, known as Metrology}

It would be beyond the purpose of a treatise on general logic
to enter on the interesting but intricate questions involved in
determining the various units of measurement. It will be suffici
ent to observe here that all actual measurement is relative, i.e. it
is the perception of some magnitude, not absolutely, but as com
pared with the unit magnitude; that the unit magnitude itself
cannot, as such, be measured ; that for its constancy — on which
its accuracy as a unit depends — our only guarantee is our own
sense-perception, aided by whatever devices mechanical science
can offer us ; that these devices, though improving our powers
of perception, do not make the latter perfect ; while the devices
themselves may contain errors, or sources of error, peculiar to
themselves.

It is a problem of great practical importance, how to minim
ize the inaccuracies of measurement, and how best to make
allowance for the residual error which cannot be eliminated. The
needful degree of accuracy will, of course, depend on the nature
of the case under consideration. In building an iron bridge the
engineer must allow space for expansion due to heat ; else the
force of the expanding metal would burst the whole structure.
For this purpose, however, he does not need to determine the
coefficient of expansion of his materials with anything like the
precision and exactitude required by the maker of a naval
chronometer in regard to the compensation springs and balances
for this article. But, in all cases, it is the ideal of the scientist
to eliminate all error, as far as possible, from his calculations.
How, then, is he to deal with the various inaccuracies incidental
to measurement? In the first place, he must make allowance
for them as far as he is aware of their existence. In physical
experiments the possible sources of incorrect measurement are
manifold : variations of temperature, friction, atmospheric pres
sure, electrical or magnetic conditions ; defects in the measur
ing instruments, eg. through want of rigidity in the telescope,
through refraction in all optical instruments, through inaccurate
adjustment in chronometers, etc. Then, besides all these, there
are the sense-limitations of the individual observer, often involv
ing deviations l< in the same direction and to the same average

1 POINCARE, Op. Clt., p. 20.

204 THE SCIENCE OF LOGIC

amount"1 from the normal, and hence called the "personal
equation" or "personal error": e.g. "the inclination to record
the passage of a star across the wires of the telescope a little too
soon or a little too late. . . . The difference between the
judgment of observers at the Greenwich Observatory usually
varies from T^ to \ of a second, and remains pretty constant for
the same observers.'' 2 These various sources of inaccuracy can
be to some extent detected, and their disturbing influence elimin
ated by calculation. But when all this has been done, when all
possible precautions have been taken, it will still be found that
in the case of delicate measurements a series of equally reliable
trials, even when made by the same individual, will never yield
exactly, but only approximately, the same results : 3 thus showing
that, on account si unavoidable interfering influences, the observed
or registered magnitudes are only approximations to the true
magnitude.

Now it may be safely assumed, in the absence of any ground
for suspecting the contrary, that the various unknown sources
of discrepancy, in the results of such a series of measurements of
any magnitude, will tend to neutralize each other, as being
indifferent to excess or defect; that the true magnitude will,
therefore, lie somewhere between the greatest and the least
registered magnitudes ; that by taking the mean of all the
registered magnitudes we are approximating to the true mag
nitude ; and that this approximation will be closer the larger
the series of measurements which furnish this mean. From the
assumption that the sources of error yield excess and defect
indifferently in the individual measurements which make up the
series, the inference is unavoidable that the oscillations on each
side of the true magnitude will tend to balance each other in
the long run : so that the mean will tend in the long run to co
incide with the true magnitude.

There are two leading methods of determining the " mean " (of a number
of measurements) which is most likely to approximate most closely to the true
magnitude. The first of these— which is called the " METHOD OF MEANS "
— is applicable only when we are engaged in measuring some single magnitude,
such as the length of a line. It consists simply in taking the Arithmetical, or
the Geometrical, Mean of the actual measurements. Usually, the arithmetical

'JEVONS, Principles of Science, p. 347. yibid.

3 A result which shows a notable discrepancy from all the others of the series
should be rejected as being presumably vitiated by some extraordinary, though un
detected, error in the measurement.

METHOD OF DISCOVERING CAUSAL LAWS 205

mean is taken. " When, however, as happens in a few cases, some condition
is known to be operative which varies as the square of the distance, the
Geometrical Mean1 — i.e. \/o£ — gives the more accurate result. For ex
ample, if the true weight of an object is sought by weighing it successively in
the two scales of an imperfect balance, as gravity is an operative condition, the
true result will be the geometrical mean . . . though as, in small numbers,
this differs but little from the arithmetical mean, the latter is generally taken
as more easily calculated." a

The second method, called the " METHOD OF LEAST SQUARES," is applic
able when, as is usually the case, the magnitude we are measuring is com
pound, or, in other words, involves measurements of two or more separate
quantities one of which is some function of another. Our total measurement
will, in such cases, be a combination of two or more distinct series, such as
[Pj + P2 + P3 + P4 + • • • ] + [Qi + Q2 + 0.3 + Q4 + . . . ] + [R, + R, +
R3 -t- R4 +...], where P is perhaps some multiple of Q, and Q perhaps
some function, such as the square root, of R. Now, we cannot reduce these
three series to one, so as to take the arithmetical or geometrical mean of the
whole ; because there is already a parity between the errors of the three
series, and hence by squaring or otherwise altering the values of any single
series, for the purpose of reducing it to terms of another, we alter the value of
its errors as compared with those of the other series. We therefore have re
course to the Method of Least Squares, which rests upon this theorem : That
magnitude is most probably the true magnitude, which makes the sum of the
squares of the errors in the actual measurements the LEAST POSSIBLE. Such a
magnitude can always be discovered, from the actual values, by an algebraic
process. This method is really " an extension of the method of means, in that
it indicates the most probable mean in cases which involve a plurality of arith
metical means ".3 The property of having the sum of the squares of the
residual errors the least possible is always true of the arithmetical mean 4 ;
but it is also true of the mean magnitude of a compound series, a magnitude
which cannot be obtained by the simple process of finding the arithmetical
mean. The present method is, therefore, " the most general mode of finding
the true magnitude from a number of divergent measurements ; but when
these measurements involve one magnitude only, the simplest mode of applying
the method is to take the arithmetical mean ",5

247. " EMPIRICAL LAWS " AND THEIR EXPLANATION :
TRANSITION TO PART V. — In the present chapter an account
has been given of the analytical process by which we seek to
discover and establish laws by way of hypothesis ; and the con
ditions requisite for the latter were outlined in the last preceding

1 Rather than the Arithmetical Mean, iJL_. a WELTON op. cit., pp. 184-5.

3 ibid., p. 186.

4 For example, the sum of the squares on the residuals in the series 2, 5, 8 [(5 —
2)2 + (8 - 5)2 = 18] where the middie value is the arithmetical mean, is less than in
the series 2, 4, 8 [(4 - 2 )J + (8 - 4)* =* 20) where the intermediate value is not the
arithmetical mean. d WELTON, op. cit., p. 187.

206 THE SCIENCE OF LOGIC

chapter. We have seen, too, that all laws are embodied in general
judgments, and that induction is a process of generalization, based
on analysis of individual facts. We may distinguish, therefore,
between knowledge of particular " facts " and knowledge of the
" laws " reached by generalizing from these facts.

In regard to any individual fact, we may know simply that it
is so, or we may know further why it must be so (cur? and
quomodo ?). We know the latter if we know the causes which pro
duce the fact, and the laws according to which they produce it.
But the same is true of the laws themselves. If we conceive a
" law " simply as the generalization of a fact beyond the range of
experience, simply as a statement that a certain kind of fact did
and does and will happen, always and everywhere, in a uniform
manner in similar circumstances, in a word, simply as an asser
tion that some observed uniformity of fact holds good generally,
then, since "law" in this sense is merely a wider fact, we may
know of it too, in turn, either that it is so, or we may know also
why it is so.

Furthermore, confining our attention here to this concep
tion of a law, our knowledge that the law is so, i.e. that the fact
does happen uniformly beyond our experience as well as within
our experience — this knowledge may vary from a very slender
degree .of probability to physical certitude. Our confidence in
the universal truth of such a law, our belief in its reliability, will
vary with the degree in which analysis of the facts points to its
truth, (a] It may be a rough generalization from uncontradicted
experience, based upon mere enumeration of instances, without
any attempt at analysis, e.g. "All crows are black ". (&) It may
have been observed to hold good in varied instances, in accord
ance with the method of agreement, e.g. " All horned animals
are ruminants," " All ruminants are cloven-footed ". (c) It may
be a tentative extension of some known law to a new set of cases
by analogy, e.g. " All animals having their habitat in the Arctic
regions are, like the polar bear, white-coloured ". (cT) It may be
a supposed causal connexion, partially tested by the application of
one or more of the modes of analysis already described (240-4),
but not yet fully verified : an hypothesis in process of verification.
Of this latter we have had numerous examples. Now, generaliza
tions under any one of those various heads have this in common,
that they are all more or less probable ; but, since they are not cer
tain, they cannot be safely extended to cases that are not "adjacent,"

METHOD OF DISCOVERING CAUSAL LAWS 207

i.e. similar to the observed cases. We hesitate to apply them to
cases that differ considerably in their conditions from those we
have observed. Every such " law " or " generalization " is usually
called an " EMPIRICAL LAW," or an " EMPIRICAL GENERALIZA
TION ". By these expressions we mean some observed uniform
ity of connexion between phenomena, or of the mode in which a
phenomenon happens, which uniformity we expect to hold good
always and everywhere, though we do not understand it suffici
ently to be sure that it will hold good.

But suppose we have verified our hypothetical law by a
sufficient application of the various grounds of elimination em
bodied in the " methods " already set forth ; and that we are
therefore certain that our established causal connexion will de
facto hold good universally, that no other supposition would be
consistent with the facts of our experience : we may still be un
able to explain why such a connexion must hold good universally,
or, in other words, to connect the law in question with other laws,
and show how it is necessarily involved in, and derived from,
these. The phenomena connected by such a law " we see to be
connected, though how they are connected we know not," 1 be
cause we cannot explain the law that connects them. " They
are connected for us empirically, that is, in our experience ; " a
they are connected for us to some extent even " rationally, that is,
for our intelligence," 3 inasmuch as we have convinced ourselves
that the connexion is not merely a contingent connexion which
occurs within our experience, but that it is in some sense a
necessary connexion which must hold universally ; but we have
not &full intelligence, a full rational knowledge of the connexion,
so long as \*e are unable to see why the law connecting the
phenomena must be so. The law, though verified, is still for
us an isolated law, not connected "rationally," "logically,"
" scientifically," " philosophically," with any wider laws ; in other
words, not " scientifically explained ". Now, it is in accordance
with fairly common usage to describe also such verified but
unexplained laws as Empirical Laws, or Empirical Generalizations,
like the probable, unverified generalizations described in the pre
ceding paragraph.

It is evident, therefore, that laws may exist merely as empirical
laws for a long time before they are verified, and again for a long

1 JOYCE, op, cit., p. 369. »t6trf., p. 370. 3ibid.

208 THE SCIENCE OF LOGIC

time as verified before they are explained. When, at length, they
are explained by deriving them deductively from wider laws,
they are called DERIVATIVE LAWS, or SCIENTIFIC LAWS, simply.
Thus, it is a function of science to convert empirical laws into de
rivative scientific laws, by connecting them deductively with more
universal laws of causation.

But the "explanation" of these wider and more remote laws
of causation themselves is a matter of greater difficulty. We
have seen already in what a qualified sense we must understand
the sort of " verification " that can be attained when there is ques
tion of such laws (228-33). The law of universal gravitation, the
law of the conservation of energy, the first law of motion, the law
of biogenesis (" omnis cellula ex cellula vivente "), etc., are regarded
as " verified," merely because they explain facts more satisfactorily
than any conceivable alternative (230), and "on so wide a scale
that it is very unlikely that exceptions to them exist".1 Very
wide laws of this kind, " not yet explained" 2 themselves, but veri
fied by their extensive power of explaining both narrower laws
and individual facts, are called by scientists LAWS OF NATURE
simply, in contradistinction to the narrower or derivative laws 3
just referred to. But those wider laws too call for "explana
tion ".

The human mind is not satisfied to take these laws, whether wider or
narrower, as mere actual uniformities. Some logicians seem to identify laws
with facts ; 4 but law is something more than fact : fact is contingent, at least
all phenomenal or empirical fact ; 5 whereas law involves the idea of a neces
sity of some sort, the notion of what must be, rather than of what is. And
Mr. Joseph rightly says : " it must not be imagined that uniformity is the
fundamental element in the causal connexion, but necessity or law ".6 The
philosophical explanation of laws— that is, the sort of explanation ultimately
attainable by the human mind — leads, therefore, inevitably to inquiries into
the nature of the necessity attaching to "laws," "necessary truths,"
" principles," and "axioms " ; into the ideally perfect form of scientific know
ledge and scientific certitude ; into the ideal conditions for " scientific explana-

1 Palaestra Logica, p. 127, § 393. *ibid. 3 Cf. JOSEPH, op. cit., pp. 380-1.

4 The Empirical school of philosophers, of which Mill is a typical representative,
must consistently do so. Dr. Mellone, though dissenting from this attitude, says
" the truth is, to ' explain ' a fact, in science, comes in the last resort only to this,
that we show it to be part of a wider fact " (op. cit., p. 319). The scientist may, per
haps, be satisfied with this ; the inquiring human mind certainly is not : it wants to
know further whether, or how far, or in what sense, every fact that is must be so.

5 There is only one absolutely necessary fact, viz. the Necessary, Self existent
Being, God.— Cf. RICKABY, First Principles, p. 89.

8 op. cit., p. 376.

METHOD OF DISCOVERING CAUSAL LAWS 209

tion " and " demonstration ". Although such inquiries have been to some
extent anticipated in the various chapters of the present part of this volume,
they call for a little more explicit treatment.

From another point of view, we may regard the attainment of certitude or
certain knowledge as the goal of all scientific effort ; and we may regard it as
the practical aim of logic to prescribe the conditions for attaining to this ideal.
But, in the progress which the human mind may make towards this latter, it
may in some matters succeed in reaching certitude ; in others it may reach
only opinion or probability ; and in others again it may fail altogether by falling
into error. A consideration of these conditions, and their causes, will, there
fore, form the subject-matter of the remaining portion of our general inquiry.

WELTON, op. cit., bk. v., chaps, v., vi. and vii. JOSEPH, op. cit., chap, xx.,
xxii. and xxvi. MILL, Logic, III., chaps, vii.-x. MELLONE, op. cit. chap. ix.
VENN, Empirical Logic, chap. xvii. Palaestra Logica, part iii., chaps, iii.,
iv. and v. FOWLER, Inductive Logic, chap. iii. JOYCE, Logic, chaps, xx.
and xxiii.

VOL. II. 14

PART V.

THE ATTAINMENT OF SCIENCE AND CERTITUDE.

CHAPTER I.
SCIENCE AND DEMONSTRATION.

248. ELEMENTARY NOTIONS DEFINED : TRUTH, IGNOR
ANCE, ERROR, EVIDENCE, CERTITUDE, OPINION, PROBA
BILITY, DOUBT.— The terms "true," and "truth," are applied
to the things we know, to our knowledge of them, and to the
language in which we express this knowledge. Truth as applied
to things or reality, is called real or ontological truth. It is simply
the things, or reality, as revealed or manifested to some mind, and
thus related to that mind. It is identical with reality, and is the
proper object of metaphysics or ontology. The truth of lan
guage, called "truthfulness," or "veracity," is the conformity of
our language with our thought. It is ethical or moral in char
acter ; and the study of it belongs, therefore, to ethics or moral
philosophy. The truth of knowledge, called logical truth, is
the conformity of the mind judging about reality, or of the mind's
judgment about reality, with the reality to which the judgment
refers^ This knowledge and its truth are embodied in the mental
act of judgment.

The term " knowledge " expresses that relation of the mind
to its object (things or reality), of which everyone is conscious,
but which is so simple, fundamental, primordial, that it does not
admit of definition proper, though it may be psychologically

1 " Veritas intellectus est adaequatio rei et intellectus secundum quod intellectus
dicit esse quod est, vel non esse quod non est." — ST. THOMAS, Summa Contra
Gentes, i., q. 5. Cf. ST. THOMAS, In Met., iv., led. 8 : " Verumenim est cum dicitur
esse quod est vel non esse quod non est. Falsum autem est cum dicitur non esse
quod est aut esse quod non est" — which reproduces Aristotle's definition : " Tb /j.ty
yap \eyttv rb &«/ /*rj «!i/ai fj rb ^ by tlvai tyfvtios, rb Sf rb 6v tlvai Kai rb fj.^ t>v (ify flvai
a\i]dfst" Met. iii. 7, ed. Didot. Cf. MERCIER, Criteriologie, 5th edit. pp. 17-31 ;
SENTROUL, La verite et le progres du savoir, in the Revue neo-scolastique, May and
August, 1911.

210

SCIENCE AND DEMONSTRATION 211

analysed and described. By " knowledge simply " true know
ledge, or the possession of logical truth, is, of course, always meant.
The absence of such knowledge in a being capable of possessing it,
is called ignorance. Either the mind does not possess any ideas
at all about the matter in question, in which case it is absolutely
or totally ignorant, in a state of nescience regarding the thing ; or,
possessing some ideas about the thing, it does not know what is
the proper relation to establish between these, and is thus partially
ignorant, and in doubt.

The opposite of truth, or true knowledge, is error, or erroneous
belief. Error necessarily implies the possession of some
ideas about the object thought of, and is the disagreement of the
judgment which the mind has formed about the thing, and to
which it adheres, with the thing or reality in question.

When the mind adheres firmly to a judgment which it knows
to be true, it is said to have certitude. Certitude is, therefore, the
fixed or firm assent or adherence of the mind to a truth, without any
prudent fear of error. It can be had about immediately evident
judgments, or about those that are mediately evident, i.e. known
by reasoning. The name Science is applied specially to know
ledge of which we have mediate certitude ; we are said rather to
have Intelligence (" Intelligentia ") or Intellectual Intuition of im
mediate, abstract first principles, and Sense Intuition of the im
mediate, concrete facts of sense: we "see" these rather than
"learn" them. Mediate certitude presupposes, and rests ulti
mately on, certitude that is immediate.

Properly, therefore, certitude is a state of the mind, the quality
of our mental assent to a judgment which we have formed, which
is true, and which we know to be true. The object to which the
mind assents in forming such a judgment is, as already explained
(78, 80), the reality itself, seen and grasped by the mind through
the relation established between the two aspects of that reality,
represented by subject and predicate. The reality itself, thus
looked at as the object of a true and certain mental judgment,
is usually called a certainty, or an objective certainty (in addition
to its still more common name, a truth) ; while the mental state
is described as the state of certitude}-

When or how can we be certain that our judgment, our knowledge, is
true ? — that we possess the truth ? When, on reflection, we find that the
evidence — which is the cause or motive of our firm or certain assent — is fully

1 C/. CLARKE, Logic, p. 426; NEWMAN, Grammar of Assent, pp. 195-6.

212 THE SCIENCE OF LOGIC

sufficient to guarantee such assent. And what is this objective evidence that
calls forth our assent ? It is, in ultimate analysis, simply the objective re
lation between two aspects of the same reality, between subject and predi
cate, shining in clearly upon the mind, and grasped by the mind in forming
the judgment, in interpreting the reality through this mental act. It is, there
fore, simply the manifestation of reality to the mind. In other words, it is
the real or ontological truth ; it is Being, apprehended by the mind as its
natural, proper object : " Objectum Intellectus est Ens " is the Scholastic
formula which sums up this whole doctrine on the criterion of truth and the
motive of certitude.

The state of certitude, alone, excludes all prudent fear of error.
When the judgment connects two simple, abstract concepts, whose
comprehension is perfectly clear, the relation of subject to pre
dicate is seen to be absolutely necessary and immutable, so that the
object of our thought could not possibly be otherwise without
a contradiction in thought. With regard to such self-evident
judgments — "per se nota non solum in se sed quoad nos et omnes " *
there can be no possibility of error. Our assent is compelled ; the
evidence is cogent.

But when we pass to concepts that are more complex, and judg
ments arising out of them, the evidence for such judgments is
usually not so clear ; the relations are not so manifest ; they need
not compel our assent : we realize that, absolutely speaking, error
is possible in their regard ; and hence we are free to withhold
assent if we choose, though at the same time we may see the
evidence to be such that it leaves no ground or reason for a
prudent fear of error.

Similarly, of the judgments which we form on the immediate
testimony of our senses, and by which we interpret the facts of
immediate sense experience, many are so evidently true that, al
though we might conceive ourselves to have been mistaken in
regard to them, there is no prudent ground for any fear that we
are mistaken. Again, the same is true, in its measure, of judg
ments for the truth of which we rely on the testimony of our
fellow-men. In all such cases, where prudent fear of error is ex
cluded, and where the judgment to which we assent is actually true,
we have certitude.

When such fear is not wholly excluded by the grounds or
reasons we have for our assent, the judgment is described as
"probable " : our attitude towards it is called " opinion " : 2 the mind

1 ZIGLIARA, Logica, (41), v.

2 Or, also, "belief," in one of the many meanings of this term.

SCIENCE AND DEMONSTRATION 213

here inclines towards one of two contradictory judgments as true,
but not so strongly as to exclude a prudent fear that it may be
false and the other true. The one to which it inclines is said to
be "probably" true. It will be equally probable with its contra
dictory, or more probable, or less probable, than the latter, accord
ing as the reasons for it are equal to, or less, or greater than, the
reasons for the latter. Here our assent is not fixed or stable ; it
is provisional. Opinion, therefore, is the provisional assent of the
mind to one of two contradictory judgments, with more or less fear
of error. When the fear is so trifling as to be practically negli
gible, our assent is commonly described as moral certitude.
When, on the other hand, our fear of error in assenting to a judg
ment is exceedingly great, our assent is called a mere suspicion,
rather than an opinion.

When the mind is balanced, hesitating, wavering between two
contradictory judgments, without adhering to either of them, it is
said to be in " doubt," or " suspense " : it suspends or reserves its
assent. Doubt, therefore, is the state of the mind suspending its
assent for fear of error. It is said to be a negative doubt if there
are no reasons on either side, positive if there are equal reasons
on both sides. Deliberate doubt always implies a judgment or
judgments about the weight of the evidence for and against ; to
gether with the absence of any judgment about the main matter
under consideration.

The chief attitudes of the mind towards a truth, are, therefore,
certitude, opinion, suspicion, and doubt ; the latter indicating the
entire absence or suspense of assent.

But our estimate of the grounds of our assent may possibly be erroneous :
we may be deceived into assenting with more or less firmness to a false judg
ment : and, hence, we can conceive degrees of assent varying indefinitely from
that of certitude or absolute adherence to the true judgment, to that of the
strongest adherence to its false contradictory. These two extreme states
of mind are, of course, contraries. The latter state — firm assent to an erron
eous judgment — has no special name other than that of error, a term which
primarily means the disagreement of the judgment with reality. Conversely,
the term truth is sometimes used to signify the subjective mental state of cer
tain assent to a true judgment, rather than the conformity of the latter with
objective reality. In these subjective meanings of the terms, truth is the
contrary of error. For, regarded subjectively, simply as states of the mind,
the state of ignotance — implying, as it does, either the absence of all ideas
(ignorance, simply), or the absence of assent to any judgment about the
matter (doubt)— is intermediate between the state of assent to a true judgment,
and that of assent to an erroneous one about the same subject-matter.

2i4 THE SCIENCE OF LOGIC

But, regarded in their proper, objective sense, as characteristics of the
judgment, i.e. of the relation between the mind and its object, logical truth
and error imply contradictorily opposite relations of the mind to its object :
that of positive conformity with the latter, and that of positive discrepancy or
divergence from it. Granted some definite relation or other of the mind to
the thing, or, in other words, some judgment about the thing, the opposition
between these two kinds of relation is contradictory opposition : the relation
is either one of agreement or one of disagreement ; there is no mean. Every
judgment has a contradictory ; and of a pair of contradictories one must be
true and the other must be false. We cannot have, as a mean between them,
a judgment which is partly true and partly false.

This last statement seems at first sight entirely opposed to our ordinary
habits of thought and expression. Are we not constantly describing state
ments we hear, as " more or less true," as containing " a certain amount of
truth," or " a grain of truth and a large measure of error " ? Are we not
constantly distinguishing truth from error in the judgments formed and ex
pressed in every department of experience ? That is undoubtedly so ; but
what, in reality, does it prove ? Merely that such statements are ambiguous,
are open to a variety of interpretations, express or imply or suggest not one
simple judgment, but many ; and that, while some of these latter are true,
some also are erroneous.

249. THREE KINDS OF CERTITUDE : METAPHYSICAL, PHYSI
CAL, AND MORAL. — Our assent to any judgment as true may be
influenced, and often is, no doubt, largely influenced, by motives
of a non-intellectual character, by our likes or dislikes, by our
character and beliefs, by our feelings and emotions. Of these
logic cannot take account, except indirectly : its main concern is
with the intellectual motives ', the rational grounds or reasons, of our
assents. Assent is an intellectual act, and no assent can be
rational without sufficient rational grounds. Moreover, it is our
reason that must ultimately decide what weight of influence we
may prudently and reasonably allow to non-intellectual motives
in determining our assent in any given case. Logic, then, is con
cerned with the intellectual grounds of certitude, and these are all
included in the term "evidence".

Now, broadly speaking, we may distinguish three great sources
of evidence, and three corresponding kinds of certitude.1 (a)
Analysis and comparison of abstract ideas — involving some judg
ments that are immediately evident, and others mediately evident,
inferred from the former — are processes which yield metaphysical
certitude, (b) The testimony of our senses — involving judgments
about the immediate data of our sense experience, and general

1Cf. TOOHEY, The Three kinds of Certitude, in the Irish Theological Quarterly,
vol. iv., n. 15, pp. 254 sqq. (July, 1909).

SCIENCE AND DEMONSTRATION 215

judgments established by induction about the facts of sense — is
a source of physical certitude, (c] The testimony of our fellow-
men is, under certain conditions, a source of moral certitude. But
evidence from all three sources combines and coalesces in the
production of the greater part of the certain knowledge which is
actually possessed by men generally.

The main characteristic of pure metaphysical certitude is this,
that it is for the most part 1 confined to truths of the abstract
order, to judgments about possible essences or objects of thought,
judgments which abstract from the question of the existence or
non-existence, occurrence or non-occurrence, of these objects in
the sphere of actual reality. In other words, it concerns judg
ments, whether affirmative or negative, in materia necessaria (85-8) ;
or again, judgments which affirm a necessary identity or a necessary
incompatibility between the objective concepts compared ; that is
to say, judgments which have been described as apodeictic (89-90).
And all such judgments, dealing as they do with the necessary
implications of concepts, are the intellectual expressions of taws,
and are, therefore, universal judgments — at least potentially uni
versal.2 All the truths of pure mathematics are of this order.'
The evidence is intrinsic to the truths themselves ; and it is
cogent, whether it be immediate evidence of axioms, or mediate
evidence of conclusions deduced logically from such axioms.

Physical certitude is, first of all, the certitude we may have
about the actual existence or occurrence of concrete facts of our
own individual sense experience. These all occur in time and
space. For present facts of actual sense experience we rely on
the testimony of our senses ; for certitude about past facts of our
own individual experience we must rely on memory. But,

1 Except where the concept of the subject involves in it the concept of actual
existence. " We have an example of existence being involved in the idea when we
mentally or orally affirm ' I exist '. I cannot even think ' I ' without implicitly
affirming that I exist ; the very fact of saying to myself ' I ' is an acknowledgment
that I exist, for I cannot think ' I ' without existing and being conscious of my
existence. Hence to say ' I do not exist ' is to be involved in a concrete contradic
tion, just as to say ' Two and two do not make four ' is to be involved in an abstract
contradiction ; it is to deny in the predicate what is implicitly affirmed in the
subject. . . . Hence it is that we are each of us metaphysically certain of our own
existence, and the causal proof of the Being of a God which is based upon our
personal existence leads to metaphysical certitude that God exists." — TOOHEY, ibid.,
pp. 255-6.

2 Their actual extension may include only a single subject, as, for example,
when such judgments are formed about the thinking subject himself, or about God,
the Necessary Being.

216 THE SCIENCE OP LOGIC

secondly, what about facts that fall outside our own individual
experience, whether these be past, or present, or future ? Apart
from the moral certitude we may have of the occurrence of any
such facts on the extrinsic evidence of human testimony or au
thority, can we have physical certitude about them ? Obviously,
they do not present their own intrinsic evidence to us immedi
ately ; but they may do so mediately, i.e. by way of some known
and proved connexions between them and certain other facts
which we have ourselves experienced directly and immediately.
We may be certain, for instance, that, besides the bars of iron
we ourselves have seen being elongated by heat, other bars of
iron have been, or are being, or will be, likewise elongated by
heat, provided that in such cases, past, present, or future, certain
conditions be fulfilled. But, note that our certitude here is about
the conditional occurrence of these other instances : we are certain
that they have occurred, or do, or will occur, not absolutely, but
contingently on the fulfilment of certain conditions — such for
instance as the actual existence of other bars of iron and other
sources of heat, the repetition in them of the physical conditions
involved in the law that " heat elongates iron bars," the uni
formity of the action of physical causes, the absence of interfering
causes (224). Our certitude of their occurrence asyfo/j, involves,
and is based upon, our certitude of the universal prevalence and
validity of laws within the domain of these facts. Law is the
rational connecting link between experienced facts and unex
perienced facts. Hence, our certitude about such unexperienced
facts is not precisely certitude that they did, or do, or will occur;
but, rather, that they must occur. It is a mediate, inferential
certitude, based on prior certitude regarding the laws. Now, of
the laws on which these inferences are based, some, no doubt,
are absolutely and self-evidently necessary, such as the principle
of causality ; but others are inductively established laws, the
necessity of which we have seen to be, in ultimate analysis, not
an. absolute, unconditional necessity, but rather a conditional
necessity, contingent on the will of the Supreme Being who rules
the whole created universe (224). This kind of certitude, which
we thus obtain by induction from experienced facts, regarding
the conditional prevalence of laws, and the conditional occurrence
of unexperienced facts inferred from the latter, is likewise com
monly recognized and described as physical certitude.

Moral certitude is the certitude of belief based upon authority ;

SCIENCE AND DEMONSTRATION 217

and, in this sense, it may be had either for individual facts or for
general laws. The certitude of historical knowledge is of this
kind. But there is a sort of certitude, also called " moral," which
is based upon intrinsic evidence. It is the certitude we have
concerning (a) the generalizations we form, from our own ex
perience, about the conduct and activities of free agents ; and (b]
concerning the individual facts, phenomena, or instances, to
which we apply these generalizations. Such generalizations we
call " moral universals," liable to exceptions ; and their applica
tion to individual cases we know to be more or less precarious.
Such is the certitude we have, for instance, about the truth of
these judgments : " Men are naturally truthful," and, therefore,
" A.B., who has no inducement or temptation to deceive me, is
telling me the truth " ; " Parents naturally love their children,"
and, therefore, " A.B. and CD., whom I know to be good people,
love their children " ; " Men respect and protect the lives of their
fellow-men," and, therefore, " My food at dinner to-day will not
be poisoned ". Finally, we may have, whether for facts or for
laws, such a weight of cumulative evidence of various kinds as
will warrant that very high degree of probability which is com
monly called " practical " or " moral " certitude.

250. NECESSARY TRUTH OF METAPHYSICAL LAWS; CON
TINGENT TRUTH OF PHYSICAL LAWS AND FACTS.— There is
an inclination among modern philosophers and scientists not to
recognize as a "scientific law" any general formula or statement
to which we can conceive an exception. We should, they think, so
formulate our laws, by finding out accurately, and expressing
hypothetically, all the conditions for the truth of these, that they
may admit of no exception as stated. But when we pass from
the abstract world of mathematics, and from the first principles
of thought and being in logic and in metaphysics, where the mind
abstracts from the concrete reality and marks out clearly for itself
the grounds for its judgments ; l when we come to complex and
concrete reality as revealed in the physical world through sensa
tion, and try to grasp the laws according to which phenomena
take place, it is not so easy to apprehend all the causes and
conditions of their appearance, and so to embody these in our
formulae that the latter will be true by an absolute necessity of
thought? Of course, if such care be taken, our judgments in all

1 Cf. WELTON, Logic, ii., p. 202 ; MELLONE, Introductory Text-book of Logic,
pp. 265-70.

a WELTON, ibid., p. 205.

2i8 THE SCIENCE OF LOGIC

departments of human knowledge will be of the same inviolable
necessity, but they will be almost 1 all abstract and hypothetical.
If we make provision for all possible conditions, including the
Divine Will, and also human free-will, for physical and moral
facts, then our universal judgments in these departments will be
as necessarily true as our metaphysical judgments. The pro
positions, " If the natural causes of the planetary movements con
tinue to exist and to act as heretofore, uninterfered with by a higher
Power, the sun will rise to-morrow," and " If the inhabitants of
the town A are exactly of the same mind and character as those
of the town B, they will make an equally gallant defence when
attacked " — are as necessarily true as " If a triangle be inscribed in
a semicircle, it will be right-angled ". 2 All three alike are em
bodiments of the principle of identity in this way : " If a given
cause or reason be sufficient to produce or account for a given
fact or truth, it will produce or account for this absolutely, con
tinually, universally". And in so far as they embody this
principle they share in its absolute necessity.

But, then, they are only hypothetical as regards the verification
of their antecedents (223), and in the first two judgments this
verification involves more than it is given to man to fathom in
regard to any future cases of them : for they deal, not with ab
stract, possible objects of thought, but with concrete, actual things
and events. Our assurance about the categorical proposition
that " The sun will rise to-morrow " is not absolute or necessary,
but contingent on our certitude that the causes of the planetary
motions will continue to exist and to act unimpeded as in the
past ; and since all this is dependent on the free will of the
Creator, our certitude about it cannot be absolute.3 In the second
case, similarly, our ignorance as to any future fulfilment of the
antecedent is increased by the intervention of the free will of man.
Hence it is that our knowledge of the continued occurrence or
recurrence of concrete, existing phenomena, whether physical or
moral, is hypothetical and contingent: the permanence of the
grounds on which they are based is hidden from us. I am not
compelled, therefore, to assent to the categorical proposition that
" The sun will rise to-morrow ". To have cogent evidence either
for or against it would imply on my part a certain knowledge of
the Divine Will. From which it follows that man can never

> Cf. p. 215, n. i. a Cf. JOSEPH, op. cit.t pp. 507-8.

3 Cf. JOYCE, Logic, p. 237.

SCIENCE AND DEMONSTRATION 219

analyse the conditions or antecedents of a concrete, actual fact or
phenomenon, sufficiently to be compelled by the evidence to pro
nounce categorically that it will recur.

Truths for which we have necessary or cogent evidence —
" necessary " or " metaphysical " truths — are all abstract : they
formulate relations between aspects of reality apart from their
existence or happening. * Even when categorical in expression, as
e.g. "Triangles inscribed in semicircles are right-angled," they
are conditional in thought (134-5) as regards the actuality of their
antecedents. The logical necessity of these relations between
subject and predicate is the necessity by which any abstract
object of thought is identical with itself, with all that the mind
apprehends in it. It is a necessity that pertains to the abstract
essences of things. So long, therefore, as we deal with purely
abstract judgments, such as those of mathematics, we can analyse
the grounds for the abstract relations we establish, and can see
these to be cogent Such truths are called "necessary," because
they express essentially or intellectually necessary relations be
tween abstract objects of thought. But when we deal with general
izations about concrete, existing things, beyond actual sense ex
perience, our analysis must always leave an unknown and uncertain
residue, that, namely, which is the ground for the persistence —
through the changing conditions of time and space — of the
elements about which we are thinking. For truths, therefore,
which imply the actual existence, beyond experience, of the
elements of reality to which they refer, the ground or evidence
can never be cogent, can never necessitate our assent. These are
called, and rightly called, "contingent" truths, because they make
such mental assertions about things as will hold good only if
those things persist in the concrete existence and activity with
which we know them to have been endowed within our experi
ence.

Of course, if we express this assumption about their persistence, in formu
lating " a general judgment concerning natural phenomena " a — that is, a
judgment affirming their universal repetition throughout all time and space
whenever and wherever all the conditions of our hypothesis are verified, — we

1 They are " altogether independent of any physical process. In some cases we
see that certain concepts, statically considered, stand in a relation of identity (or
difference) under pain of a contradiction in terms. ... In other cases a causal
relation is involved in the very nature of the abstract concept, apart from any dynamic
efficiency."— JOYCE, op. cit., pp. 238-9. C/., however, p. 215, n. i.

3 WELTON, ibid., p. 205.

220 THE SCIENCE OF LOGIC

are, eo ipso, making our law as abstract, hypothetical, and necessary as any
law of mathematics ; and we can say of it, when thus formulated, " that if it is
once true, it is always true, and that so far as it is true it is necessary in that
system of reality " l : for all conceivable reality is subject to the laws of thought,
and, therefore, to the principle of identity.

In this sense— and it may be well to call attention to it here — every judg
ment, even the particular, elementary interpretation of a sense experience,
such as " It rains," is necessarily and universally true : in the sense that if true
at all it is always and everywhere true (80). If it rained at a particular time
and place, it is true throughout all time and space that it did rain then and
there. The laws of thought are thus involved in all intellectual judgments,
and it is just because they are that all truth — all true judgments — can be de
scribed in a real, admissible, and intelligible sense, as " necessary ". This
necessity is purely logical, i.e. it belongs to the mental act of judgment, and
virtually amounts to this, that if the judgment is true it cannot be otherwise
than true.

Such necessity supposes and is dependent on a mental analysis and com
parison of certain elements or aspects of reality. It is not, therefore, a merely
subjective, psychical necessity ; for the mind may abstain altogether from analys
ing the elements of reality in question, or pronouncing any judgment upon
them. There is no necessity about the actual occurrence or existence of such
a mental process : it need never have taken place. But, granting that the
process of analysis has taken place, it will lay bare the grounds for the judg
ment formulated. If this be about abstract objects of thought the objective
grounds will be, or may be, cogent ; if it be an attempt to affirm a general law
about the actual happening of phenomena, the grounds for a categorical state
ment will not be cogent, for, to use the words of Green, " any proposition
about a natural phenomenon is true of it only under conditions of which we
do not know all, while a proposition about a geometrical figure ... is true
of it under conditions which we completely know ".a

The general propositions in which natural or physical laws are formu
lated do not usually express, but rather abstract from, the one all-im
portant condition on which their absolute truth depends, the positive Will
of the Creator ; and hence we speak of their necessity and universality— or
their necessary and universal truth, which we call " physical "—as being not
" absolute " but " hypothetical," " contingent," i.e. dependent on the Free
Will of the Creator. 3 To the ordinary formulae, therefore, which express the
" laws " of " Physical Nature " we can conceive exceptions. The Author of
Nature can derogate from them, i.e. He can so alter or interfere with the
conditions of the -existence and activity of created agencies that our formula,
which did not count on such interference, may be, in a particular case, inapplic
able. If we formulated our law so as to include, and take account of, such
interference, the law thus hypotherically formulated could not be disturbed by
such intervention. This is why logical, metaphysical, and mathematical laws
or truths are unchangeable : because they deal with hypothetical relations
which obtain, by a necessity of thought, between abstract objects that are

1 WELTON, op. cit., p. 205. C/. supra, p. 218.

* Phil. Works, vol. il, pp. 349-50, apud WELTON, I.e. (italics ours).

1 C/. JOYCE, Logic, p. 237.

SCIENCE AND DEMONSTRATION 221

considered apart from all actual existence of the concrete things in which they
are realized (206).

The general truths of physical science, on the other hand, and of the
sciences which deal with phenomena dependent on the free activity of man,
are not inviolable in their necessity, or absolutely all-embracing in their
universality. They are, nevertheless, truths to which we can give a certain,
i.e. a steady, firm assent, because we know that the Divine interference with
natural agencies, being controlled by Divine Wisdom, will not be arbitrary or
capricious ; and that although men are free, and thus masters of their own
acts, they act, as a rule, not capriciously, but in accordance with their common
nature, as men. Hence we have grounds for " generalizations " or " laws "
that are physically or morally universal, and for assenting to these laws, and
to their applications, with physical or moral certitude.

We can be certain that physical laws are necessarily true in this hypo
thetical sense, i.e. that they must hold good contingently on the Divine Will
and Wisdom ; and that no other necessity attaches to themselves or their
applications besides the consequent necessity of obeying the Divine Fiat (219).
It is in vain that scientist or philosopher, agnostic or monist, endeavours to
attach an absolute or essential necessity to the domain of contingent existential
fact. Physical laws have only a hypothetical necessity ; and this necessity
receives a rational explanation only in the philosophy of theism which re
cognizes the universe as a contingent reality, freely created, conserved, and
governed, by the Power and Wisdom of a Necessary Being. The absolute,
logical necessity, claimed for physical laws by the philosophy of monistic
idealism, has no ground in common sense or everyday experience, and remains
enshrouded in a mist of mystery (224).1 The world of sense experience furnishes
adequate grounds for proving the existence of a Necessary Intelligence and
Will, distinct from itself. The monism of Hegel and his followers interprets
this same world as the purely intellectual manifestation of a necessary, self-
existent mind or idea. In its exclusive attachment to the conceptually abstract,
universal^ and necessary relations, established by our intellects between the
objects of our thought-processes, monism loses sight of the other great aspect
of reality — its phenomenal aspect, reality as revealed to our senses. But in
the light of sense experience we are forced to believe that what actually exists
is not abstract but concrete, not universal but individual (6), not unique but
manifold. Of these things or realities our intellects can gain true, though
inadequate, knowledge by the system of universal thought-relations which it

xThis applies equally to the "mechanical" necessity ascribed by Empiricists
to the processes and laws of nature. It is no ultimate explanation of this necessity
to say that it is " mechanical ". If all nature is merely one vast machine or
mechanism, who made it ? The necessity we ascribe to the course of actual nature
in time and space is not the necessity we ascribe to abstract judgments about
possible essences : it is not purely intellectual. The only immediate source it can
have is our experience of the order, regularity, uniformity of all nature, compelling
us to interpret the latter as a Cosmos, as the work of an Omnipotent Will directed
by Supreme Wisdom. The only necessity for which we can rationally account in
actual nature is that by which it pursues the course marked out for it by the Divine
Fiat. To say as a last word about the course of nature that it is " mechanical," is
scarcely any better than to ascribe it to mere chance, or to pronounce it an insoluble
enigma.

222 THE SCIENCE OF LOGIC

establishes between abstract aspects of these things, and whereby it interprets
the latter. No doubt, in formulating such relations our intellects are guided
by certain absolutely immutable and necessary principles called laws of
thought ; we cannot think reality except according to these laws. But these
laws themselves — the principles of identity, contradiction, etc. — called
"formal " because they are standards to which all valid thought must con
form—are not mere innate, subjective, empty intellectual grooves, themselves
devoid of material content, mere forms with which thought clothes or invests
all its material ; they too are material and have content, because they too are
formed by the intellect operating on the data of sense experience. It is only
the intellectual faculty of acquiring them that is innate and prior to all in
dividual experience.

These abstract relations, grasped by intellectual thought, continue to grow
in complexity under the reasoning power of the mind, and the more complex
of them are explained by referring them to the less complex from which they
were deduced ; the less complex are a causa cognoscendi as regards the more
complex. But we must not forget that this is all in the order of abstract
thought, or imagine that concrete reality is also a system in which the
simpler element is the causa essendi of the more complex. To conceive the
real world as nothing else than a system of logically reasoned, abstract
relations, regarded or thought of as objective, is either to ignore the evidence
of our senses altogether and regard concrete sense-phenomena as unreal, or
else to impose upon the physical world revealed in the data of sense experience,
as the only laws that govern it, certain relations that are considered as a
subjective product of pure thought independent of sense experience, and which
are on that account regarded as of absolute necessity — that is, whose violation
would be unthinkable. This is simply to ignore the concrete for the abstract,
and to reduce reality to a subjective creation of the mind. It gives a fictitious
sort of objectivity to that " mental construction " which it calls " the world "
or " reality," and is calculated to convey an erroneous impression about the
" necessity " of the laws that govern the physical universe. To conceive the
latter as a closed system of activities every fact or phenomenon in which will
be " explained " by establishing between it and the whole certain relations of
an absolutely immutable character, and to regard nothing as " scientifically
known " or " explained " except in so far as it can be shown to be subject to
such absolutely necessary relations, is to impose gratuitously a metaphysical
or absolute necessity on the activities of physical nature, to accept a one-sided,
abstract, unreal conception of the universe, to narrow " scientific " knowledge
arbitrarily to the domain of pure abstraction, and to regard the totality of
things in the concrete as scientifically unknowable.

No doubt, if we had an ideally perfect scientific knowledge of any pheno
menon or fact, we should know that " it could not possibly be other than " 1 God
sees and wills it to be. But no human mind ever has known, or ever can know,
any concrete fact or phenomenon in that way. It can know thus only the abstract
relations which itself discerns in phenomena. It can know, too, that the things

1 Cf. ARISTOTLE, Anal. Post., i., 2 ; WELTON, Logic, ii., p. 188 ; cf. supra, 224,
p. 98. The only actual reality that " could not possibly be other than it is," is the
Self-existent Reality of the Necessary Being. And the nature of that Being cannot
be known directly or intuitively by the human mind.

SCIENCE AND DEMONSTRATION 223

from which it abstracted the data for these relations exist in conformity with
these relations, granted that as a fact they exist : but that such things must
exist by any necessity arising from thinking them in the abstract, is utterly un
warranted and untrue. The reality of the phenomena revealed to us in sense
experience as constituting the physical universe does not contain or show forth
any absolute necessity for its existence as a concrete system ; though it gives
rise to a hypothetical necessity in the relations by which we conceive it in the
abstract. The intellect derives from sense experience, by the process of ab
straction, the (abstract) elements which it compares. From the fact that those
elements are apprehended by the intellect in the abstract — free from their
conditions of concrete existence in time and space as phenomena of sense
experience, — the relations between them, logical, mathematical, and metaphysi
cal, are. likewise apprehended as fixed, static, unchangeable. But, while we
can understand that those necessary and universal relations apply to reality
as thought of in the abstract by the intellect, that is, to the elements abstracted
from sense experience, we must also remember that the intellect can discern,
between those same elements as given in sense experience, other relations —
not logical, or metaphysical, or mathematical, but physical— relations that
are not necessary in the sense that any modification of them would be un
thinkable, but which are stable, nevertheless, and permanent, in the hypo
thesis and in the measure that certain influences, to which their concrete exist
ence in time and space is subject, will not interfere with these relations.

There is no need to dwell any longer here on the erroneous conceptualism
of Hegelian idealists regarding the relations between thought and reality,
between abstract and concrete, between the object of the intellect and the ob
ject of sense. Nor is it necessary to do more than merely indicate that the
only satisfactory way of grasping and reconciling the terms of those relations
is to be fourd in the Scholastic doctrine of Moderate Realism : The object of
the intellect, while it is apprehended formally as abstract and universal only
by the intellect, is nevertheless really and fundamentally present and inherent
in the concrete object of sense : " Universale est formaliter in mente et
fundamentaliter in re " : " The universal exists formally as such only in the
intellect but it has a foundation in the thing (of sense experience) ",J

251. ARISTOTLE'S IDEAL OF " SCIENTIFIC " KNOWLEDGE. —
We have frequently referred already to discussions as to the nature
and grounds of the "necessity" attaching to scientific truths or
laws, and to the distinction between abstract, necessary truth and
concrete, contingent fact (cf. 220, 223). Those inquiries natur
ally lead up to the question : What, then, is the ideally perfect
form to which our knowledge, our interpretation of universal ex
perience, aims, or should aim, at attaining? This problem
involves an analysis of many fundamental logical concepts —
especially those of Deduction, Induction, Demonstration, Explanation,
and Science — and may, indeed, be regarded as the " most difficult

1 Cf. JOYCE, Principles of Logic, pp. 132-6, supra, pp. 107-8.

224 THE SCIENCE OF LOGIC

of logical questions".1 Apart from the deeper philosophical as
pects of the problem, which belong rather to epistemology, there
is the purely logical aspect which arises from its bearings upon
logical method. And here, perhaps the principal difficulty in
treating it arises from the fact that the theory as to what con
stitutes the perfect form of knowledge or science has been worked
out from two distinct standpoints. Aristotle's conception of
science is built up from the standpoint of deduction, and worked
out in connexion with his doctrine on scientific Demonstration.
The modern conception of science is closely allied with induction,
and is set forth under the theory of Scientific Explanation.
These two views of the ideal of science are not mutually op
posed, but, when rightly understood, rather supplement each
other. We shall outline each of them successively, and endeavour
to compare them.

About the reasoning processes which enter into all scientific
research, three distinct questions might be asked : (i) Are our
conclusions validly derived from our premisses ? (2) What sort
ought our premisses to be, if our knowledge is to be the most
perfect attainable? (3) By what sort of processes do we reach,
and establish or justify, the premisses we actually make use of?
Aristotle's three treatises on inference — the Prior Analytics, the
Posterior Analytics, and the Topics — are devoted to these three
questions respectively. The first examines the formal validity
of inference ; the second and third examine ,the conditions for its
truth. We argue sometimes from abstract, self-evident, necessary
principles ; sometimes from generalizations — reached through ob
servation, induction, or authority — not certain and necessary like
the former principles, but only contingent and probable. In
the Topics Aristotle dealt with these less perfect sources of
knowledge by " analysing and formulating the actual procedure
of his contemporaries ; he did not, upon the whole, go ahead of
the science, the disputation, the rhetoric and the pleadings of his
day ".2 Roughly speaking, he covered the ground that would be
covered nowadays by the logic of induction and probability. The
knowledge which he conceived to be the ideal of perfect know
ledge was that derived by the syllogistic, synthetic method of
reasoning from necessary axioms like those of mathematics ; and
in the Posterior Analytics he inquired into the nature of demon-

1 JOSEPH, op. dt., pp. 343, 349, 487. 2 ibid., p. 348.

SCIENCE AND DEMONSTRATION 225

strative premisses and the conditions of the demonstrative syllogism
which is productive of the highest form of knowledge — Science.

Not all knowledge that is certain is scientific in Aristotle's
sense of this term. Science he describes as knowledge of a thing
through its cause ; and an adequate knowledge of the cause, he
adds, will enable us to see that the thing cannot be otherwise than
it is. i

Science, then, in the strict Aristotelean meaning of the term,
is apparently confined to a knowledge of things " that cannot be
otherwise," z.£. of abstract, metaphysically necessary truths, truths
that are in materia necessaria, that may not be denied without
violating some law of thought or involving some contradiction.2
In ordinary modern usage, the term science includes our certain
knowledge of another vast body of truths, endowed with
a necessity of an inferior kind, not absolute but hypothetical,
contingent, physical. In a still wider sense, it embraces our
knowledge of moral, social, historical truths, etc., whose necessity
is based on the stability of the laws that govern human inter
course : truths about which we have moral certitude.

252. NATURE AND CONDITIONS OF DEMONSTRATION. —
Observing, in the next place, that we get science by Demonstra
tion, Aristotle describes the latter as a syllogism that engenders
science ; 3 and he then proceeds to lay down the conditions for a
cogent demonstrative, or apodeictic, syllogism : science, or demon
strated knowledge, must be inferred " from premisses that are true,
ultimate, immediate, better known than, prior to, and causes of,
the conclusion ; from premisses that are the proper principles of
the demonstrated truth : for without such the syllogism will nof
be demonstrative, or productive of science".4

In the first place the premisses must be true ; for, " though
formally a true conclusion may be got from false premisses, the
error still infects the mind, and will lead to a false conclusion

8« oMfittf tKaffrov air\ias . . . '6rav t4\v r' alriav olia/j.fvOa yiyviaffKtiv
8t' tjv rb irpaynd iffnv, 8rt fKtivov alria fffn, Kal /xij 4i>$exf<T0ai TOUT' a\\<as «xetl/ — Anal.
Post., i., cap. ii., i. In the term " cause " Aristotle here includes the four great classes
of cause, formal and material, efficient and final. — Cf. Anal. Post., ii., cap. x. [xi.], i.

2 Cf. DE MARIA, Logica (and edition), pp. 258, 259, 269 ; ZIGLIARA, Logica, (41).

3 Qafifv 5e Kal Si' &7ro5ei£ ews flStvai. 'Airo'Seifu' Sf \tyo> ffi/AAi-yiffjubi/ tiriaTT]noviM&v.
ibid., i., cap. ii., 3, 4.

4 Ei Tolvvv 4ffT\ rb liriffTaaOai olov t8f/j.fv, avdyitr) Kal T^V OTroSei/cTi/c^J' 4iriffTr)/jiri>>
^{ a.\T)f)G>v T' elvai KO.\ irptaruif Kal d/xetrcoi/ Kal yvupifMtartpeai/ Kal irporepuv Kal alriwv rov
(TVfj.irfpdff/j.aTOs • OVTU yap tffovrai Kal al apx<*l oiKtiai rov SfiKvv/jievov. 2v\\oytar/*bs fi.fi>
yap tffrai Kal avfv TOVTCOV, diro'Seifis 5' OVK ?crrai • ov yap irorfiffft iiriariinriv, ibid., 5, 6.

VOL. II. 15

226 THE SCIENCE OF LOGIC

somewhere ".l The mind which sees the true conclusion only as
in the false premisses, and zs following from these, can be scarcely
said to possess "truth," or " conformity with reality" : unless, in
deed, when it drops the false premisses and assents to the con
clusion absolutely ; and even then it cannot have certitude about
the truth of the conclusion, any more than it could about the
truth of thefatse premisses from which it inferred them. Besides,
the aim of demonstration is to derive a true conclusion from true
premisses — the natural source of such a conclusion.

Secondly, demonstration must rest ultimately on first truths or
principles, i.e. truths which are not themselves demonstrable, but
immediately evident or self-evident. Such principles are called
axioms. The concepts embodied in them are so simple that the
relations expressed between these concepts are immediately appre
hended by the intellect, without recourse to any simpler concepts
as middle terms. Were the mind incapable of assenting with
absolute certitude to such indemonstrable, self-evident truths, no
certitude and no science would be possible. For either the pre
misses by which a scientific conclusion is established are immedi
ately evident, or their truth has been established by antecedent
premisses; about which latter the same question arises. But
such a series of conclusions and premisses cannot stretch back
indefinitely, for if it did the certainty of any one link could never
be established. And if the series is finite, some of its members
must be first and indemonstrable. These, moreover, must be
self-evident ; if they were not, no conclusions from them could
be evident, or therefore certain or scientific. Such self-evident
axioms are found involved in all the special sciences.2 They are
called first principles: 3 not in an absolute sense, but relatively to
the conclusions they generate in the science that employs them.

Each science has its own first principles — "generating"
principles as they are called. But then, also, human knowledge
can be unified. Sciences of a lesser scope are subordinate to
those of a wider scope, and borrow their initial notions and
principles from the latter.4 And hence the notions that are
"absolutely first" are those investigated in the science which

1 JOSEPH, op. cit., p. 342 n. Cf. supra, 148.

2 Some sciences may take as their principles truths established as conclusions
in other sciences.

3 A principle is that by which a thing exists or comes into existence (ontological
principle) ; or comes into our knowledge (logical principle).

4 Cf. JOSEPH, of. cit., p. 359, n. 2.

SCIENCE AND DEMONSTRATION 227

Aristotle and the Scholastics call Philosophia Prima, first philo
sophy, or general metaphysics. Such, for example, are the notions of
thing, being, essence, existence, negation, distinction, change, potenti
ality, actuality, accident, substance, cause, etc. These notions can
not be defined, properly speaking ; though they may be explained,
and the mind thus aided to distinguish and compare them. The
self-evident judgments which formulate mental relations based
upon them are, in the stricter sense, "first principles " ; and in
the strictest sense of all we describe as "first" those best
known principles of contradiction, identity, and excluded middle,
which, in the domain of logic, are seen to be regulative laws to
which all demonstrative reasoning and all consistent thinking
must conform, rather than principles which — like those of the
special sciences — enter themselves as premisses into our reason
ing processes.

Thirdly, the premisses must give the cause of the conclusion.
Not only ought the knowledge of the premisses to produce the know
ledge of the conclusion in our minds, in our " logical " order — that
is true of all reasoning, — but the premisses, to be strictly demon
strative, ought to reveal to us the real, ontological cause of what
is announced in the conclusion: understanding "cause" in the
comprehensive sense in which it includes the formal, material, and
final causes, as well as the efficient cause. While Aristotle rightly
emphasized the importance of formal and final causes in science,
modern logicians lay stress on the role of the efficient cause (216-
18). The Aristotelean doctrine on causal demonstration is very
clearly expressed by Dr. Mellone as follows : —

" Consider the premise ' if anything is M it is P '. Regarded as a logical
proposition, in the formal sense, it states that the antecedent is the reason of
the consequent : looked at in reference to the real world, it states that M is the
cause of P ; it implies that we have discovered a law of causation in Nature,
and M is the cause in question. Now when the syllogism is changed from the
hypothetical to the categorical form, M becomes the middle term : —

Hypothetical Categorical

If Anything is M it is />, All M is P,

S is M; S is M;

.-.Sis P. .:S\s P.

Hence Aristotle says TO /ieV yap alnov TO pto-ov (An. Post., II., ii., 2) :
' the middle term expresses the cause '. We may therefore say with Ueber-
weg (Logic, § 101) : the worth of the syllogism as a form of knowledge depends
on the assumption that general laws of causation hold in nature, and may be
known ; and that syllogism has the greatest scientific value in which the
mediating concept (the middle term), by which we know the truth of the

IS*

228 THE SCIENCE OF LOGIC

conclusion, expresses the real cause of the fact stated in the conclusion. This
is essentially the Aristotelian doctrine." l

Fourthly, the premisses must be really prior to the conclusion,
inasmuch as the middle term of a demonstration is the "cause,"
and this is naturally prior to its effect. When there is question
of a physical efficient cause, which produces its effect by means
of motion or physical change, the cause must precede the effect
in time, because motion, being successive, involves duration?
But it is not essential to a real or ontological principle that it
be prior in time to what proceeds from it. For instance, the
formal and material causes, which are the real, intrinsic, consti
tutive principles of any material being, need not necessarily exist
prior to the being that is constituted by their union : the human
soul may, at one and the same instant of time, be created and
united with the material principle to form the human individual :
but each principle is prior logically* and naturally — " prius ratione
et natura " : \6ytp r) tyva-et irporepov — to that which is constituted
by their union.

Fifthly, the premisses must be better known, or, rather, more
knowable or intelligible, than the conclusion. The aim of all in
ference is to lead us from the better known to the less known or
to the unknown. But demonstration leads us from the real prin
ciple or cause to that which proceeds therefrom ; and how can
the former be more "known "or "knowable" than the latter?
Aristotle explains how this is to be understood, by his famous
distinction between the order of nature or reality and the order
of our experience : "Prior and more knowable" he writes,4 " may
be understood in two distinct ways : in nature and in our experi
ence. What are prior and more familiar_/0r us are what lie nearest
to sense- perception ; whereas what are prior and more intelligible
simply are the things which lie more remote from sense. Now

1 MELLONE, op. cit.t p. 252 ; cf. ibid., pp. 258-9.

2 Cf. ST. THOMAS, Quaestiones Disputatae : De Potentia, xiii.

3 The " logical " order referred to here is not the order in which our minds
acquire knowledge, the order of experience ; it is rather the order in which we under
stand things to be related in the real, or natural, or ontological order. Cf. infra,
pp. 229, 231-2.

4 TlpSrfpa 8' iffrl *ol yv<apifj.untpci 8jx&>J ' ov -yip ra.vr'bv irp6r(pov rfj <p<u<rfi icaJ irpbs
Tinas irp6Ttpov, oiiSf yixopi/juaTtpov KaJ rifuv yi><apin<S>Ttpov. Atya> 5« vpbs fipas fiti/ icpArepa
KCU yvupifitarepa ra tyyvrfpov rfjr aiffdfio'teas, awAccs Si irpdrepa /ca! yvaopifjuartpa. rek
iroppanepw. "Effrt 8e iroppondrw /j.fv ret Ka06\ov nd\iffra, tyyvrdrw 8« T«k Kaff ^Kaffra •
Kol ayrf/ceiTou TOUT' dAA.yjA.otJ. — Anal. Post., i., cap. ii., 10. Cf. JOSEPH, op. cit., pp.
354 sqq. ; WELTON, op. cit., ii., p. 33 ; MERCIER, Logique, pp. 287-90.

SCIENCE AND DEMONSTRATION 229

what are most remote are mainly universals, while what are nearest
are singulars : things mutually opposed to one another." This
distinction between the order of our experience and that of reality
is an important one. Acquaintance with " particular " facts of
sense experience is the beginning of all our knowledge ; while its
ultimate goal is an intellectual understanding of the " universal " or
common natures, the unifying specific types, or forms, or essences
(e'So?), which are the source of their uniform activities, which
reveal to us the laws of their nature, and form the ground of all
our universal or scientific judgments concerning them, including,
of course, the consequent scientific (demonstrative or explanatory)
understanding of the (contingent) particulars as embodying these
(necessary) universals. When we have reached this understanding
of the " kind " or " species," we have the key to all scientific
knowledge of the individuals in which the " kind " or " species "
is embodied. But how do we reach such knowledge of the uni
versal type ?

Having in mind such an abstract science as geometry, Aris
totle answered, and rightly, that we get our definitions, which are
the mental expression of this knowledge, by abstracting concepts
from sense-data, comparing those concepts, and seeing intuitively
self-evident relations arise between the latter.1 Sense experience
is necessary, no doubt, in order to furnish us with the concepts
of the common natures or essences, but these latter are not them
selves empirical facts ; they are not sensible, but intelligible ; they
are apprehended in the sense-data by intellectual abstraction and
intuition ; and what is true of those abstract objects of intellectual
thought is necessarily and universally true of the concrete par
ticulars which embody them ; while there is, besides, in each
particular, empirical fact, much that is contingent, and, therefore,
scientifically unknowable.2 Thus, according to Aristotle, "all
science is of the necessary and universal " ; while, at the same time,
science gives us genuine knowledge about the particular pheno
mena of our sense experience, inasmuch as these latter are em
bodiments or realizations of universal natures or essences.

253. RESTRICTED SCOPE OF ARISTOTELEAN " SCIENCE ".—The explana
tion just outlined is quite satisfactory in its application to abstract metaphysics
and mathematics : the ultimate laws conceived by the mind in thinking about
real being — laws of thought, as they are called— and also the fundamental

1 Cf. JOSEPH, op. cit., p. 355 ; WINDELBAND, History of Philosophy, pp. 136-43.

2 WlNDELBAND, ibid., p. 143.

230 THE SCIENCE OF LOGIC

principles of magnitude and multitude in geometry and mathematics, are reached
in the way indicated by Aristotle. But have we the same sort of unerring intel
lectual insight into " the essence of gold or of an elephant or of a tortoise " l as
we have, say, into the essence and definition of a triangle ? Aristotle seems to
have regarded it as impossible for the human mind to attain to " absolutely ne
cessary " truths about the essences of the multitudinous phenomena that form
the subject-matter of the special sciences ; and in his Topics he has indicated
various means of reaching and testing those less perfect and less reliable
generalizations with which, in the absence of "absolutely necessary " truths,
the human mind must rest content.

He was right in recognizing that we cannot have the same " absolutely
necessary " truth about concrete existing facts or phenomena as we have about
abstract, possible essences ; for the actual realizations of these latter are con
tingent, not necessary. I see that " two and two must be four " because it is
intrinsically and absolutely self-evident, and no conceivable sort of experience
could contradict it ; I see that " heat must elongate iron " because actual ex
perience forces me to believe that heat and iron are de facto so constituted.
Aristotle recognized only truths of the former class as principles of demonstra
tion and science in the stricter sense ; and these we accept " because our
intellect assures us of their truth " a. In a somewhat wider sense, however,
he admits " science " of that which, though not " absolutely necessary," never
theless holds good " always, under certain conditions," or " for the most part ".*
This is the domain of those sciences whose laws are established by induction.
Now, it has been thought that Aristotle claimed we should have the same sort
of intellectual assurance for these " laws " as we have for abstract, self-evi
dent axioms, before the former can be recognized as principles of demonstra
tive science. He seems to Mr. Joseph to demand the " ipse dixit of an incom
municable intuition ... as a means whereby we are to establish the most
important of all judgments, the general propositions on which the sciences
rest ".4 But Aristotle could hardly have failed to see that we have no such
intuition of what are now commonly known as inductive laws.5 It was on that

1 JOSEPH, op. cit., p. 356. * ibid., p. 357.

3C/. WINDELBAND, op. cit., p. 143. 4 ibid.

6 Such laws differ manifestly from geometrical axioms in this, that they are not,
like the latter, seen to be true by an absolute, intrinsic necessity arising out of the
very nature of reality as conceived in the abstract by the intellect ; and Aristotle surely
knew this to be true of all laws established merely by induction, of all generalizations
from experience. The evidence for the truth of these lies in our experience of con
tingent fact : they are seen to be true by a necessity which is contingent and hypo
thetical. Empirical fact forces us to assent to them as true. Such facts might
conceivably have been otherwise ; but, being what they are, the only intelligible in
terpretation we can put upon them involves our acceptance of the inductively
established law as being true de facto. If we are asked why do we believe such a
law to be true, we answer that facts force us to believe it. If we are asked further
why is it true, or why are the facts (which force us to believe it) such as they are,
we cannot answer that the law must be true, or that the facts must be so, by an
absolute, inviolable necessity of their very nature, in the same way as "two and two
must be four " by an absolute necessity arising from the nature of numbers con
ceived in the abstract. We can only answer that the facts are so, and that conse
quently the law is true, because the Creator of the actual universe has made the
universe so, and not otherwise. Cf. 224, 255.

SCIENCE AND DEMONSTRATION 231

account he excluded them from the domain of demonstrative science proper ;
thereby, perhaps, unduly narrowing the scope of " scientific " knowledge. For
doing so, we may, in the words of Mr. Joseph, " say this much in his favour.
Such an intellectual apprehension of the necessary truth of the principles
from which demonstration is to start forms part of our ideal of knowledge ; ]
doubtless it seldom enough forms part of the actuality. But Aristotle
idealized ; he spoke of what, as he conceived, science in the fullest sense
of the term involved, and forgot to state, or failed to see that the sciences
did not realize it."

There seems, however, to be a more serious deficiency in this Aristotelean
conception of science. We can understand well enough by means of it how
a body of abstract truths like those of mathematics — truths about a system of
possible, ideal essences — may be derived from ideally necessary axioms and
principles, of the widest extension and the simplest or poorest comprehension.
But does it enable us to understand how the existing things and concrete facts
of the whole actual universe, ourselves included, are derived from, and depend
ent on, their real causes ? It does not : a chain of abstract demonstrative
reasoning in geometry is hardly an adequate representation of the form in
which the human mind possesses a synthetic or philosophical knowledge of the
actual universe. In the former the " first principles " are abstract and self-
evident, and the mediating concepts or middle terms, which are the " causes "
of the successive conclusions, are poorer in their comprehension or fulness of
meaning than these latter ; whereas in a synthetic knowledge of the concrete,
actual universe, the existence of a First Principle or First Cause, on which all
else depends, is not self-evident, but must be proved a posteriori by the principle
of causality ; and, furthermore, the First Cause, and all created subordinate causes
which serve as middle terms in our synthetic explanation of actual facts, must
be richer in comprehension than these latter, inasmuch as they must contain in
themselves all the perfections of the latter ; and, finally, the laws according to
which these causes act in the production of the actual course of nature, or
order of the universe, must be established by induction. No doubt, Aristotle
realized the force of a posteriori proof, and utilized it to establish the existence,
wisdom, and perfection, of an immovable Prime Mover of the universe.2 No
doubt, also, he propounded the doctrine of moderate realism, which alone makes
scientific knowledge of concrete facts possible— the doctrine that the reality
revealed to the intellect in abstract thought is embodied in the concrete data of
sense.3 But his theory of demonstrative science, which sets forth the connexion
of self-evident abstract principles with their conclusions as a representation of the

114 With this proviso," the author adds, "that for perfect knowledge all the
parts of truth ought to seem mutually to involve each other. In mathematics, where
alone we seem to achieve this insight into the necessity of the relations between the
parts of a systematic body of truth, we find our theorems reciprocally demonstrable ;
and if twice two could be three, the whole system of numerical relations would be
revolutionized . . ." (p. 358, n.). A system of truths reciprocally demonstrable in
this way, may, perhaps, be allowed to be the ideal of a science of abstract, possible
essences. But it certainly has never been proved to be our ideal of human science (in
the sense of certain knowledge) of the concrete, existing things that make up the
actual universe.

2C/. DE WULF, History of Medieval Philosophy, pp. 39-41.

3 ibid., p. 37 ; WINDELBAND, History of Philosophy, p. 139.

232 THE SCIENCE OF LOGIC

real order, appears to be too narrow and one-sided ; nor does he show clearly
how it is to be connected with our inductive and a posteriori reasoning from the
facts of experience, so as to help us in building up a synthetic world-view, or
philosophy of the universe as a whole. He was right in holding that our
scientific knowledge of any individual fact could never surpass what is deducible
from the specific type embodied in it, or reach to the individual, accidental,
determinations of the fact ((rv/x£€j3»7Kora). But he is not clear as to how we
reach the necessary and universal judgments which give us knowledge about
real essences, outside the domain of the purely abstract sciences. If he de
manded for them the " ipse dixit of an incommunicable intuition " * he demanded
what people generally will say is not forthcoming. He does seem to have held
that such principles are not reached by any process of inductive generalization,
or a posteriori reasoning from experience. And yet, outside the limited domain
of abstract mathematics and metaphysics, where we have self-evident intuitions
of possible essences, the only means we have of discovering and establishing
scientific truths, i.e. necessary and universal truths, about the actual world, are
induction and a posteriori reasoning.

254. PRINCIPAL KINDS OF PROOF.— (a) Causal or " A priori"
Proof; Proof of Fact or " A posteriori" Proof ; "A Simultaneo"
Proof. Besides strict Causal Demonstration, by which we know
anything scientifically through a knowledge of all its causes, and
of the way in which it is produced by its causes (aTroSe^t? BIOTI :
demonstratio propter quid : proof which shows the causes of any
thing),2 there is a sort of demonstration called Proof of Fact.
(a7ro8et£i? art or el ecrri : demonstratio quia), which gives us certi
tude that a thing is so, without explaining to us why it is so.
It falls naturally into a syllogism in the first figure, and differs
from the demonstrative syllogism proper only in this, that it has
for middle term not a "cause" — which is prior to the conclusion
in the real order, fyvcrei, or \6yy -rrporepov — but some " effect "
or otherwise connected fact which, though not really prior to the
conclusion, is prior to it in our experience (yfiiv Trporepov), and
is for us a sure evidence (rex^piov3) of the truth of the conclu
sion. Thus, when we argue from an effect that the supposed
cause is such or such, our argument will be cogent if we know
that no other cause could account for the effect in question. This
is often possible, as, for instance, in the diagnosis of a disease by
studying the patient's symptoms. So, also, when, in virtue of the
principle of causality, we argue from the existence of an effect to
the existence of an adequate cause, we are making valid use of

1 JOSEPH, op. cit., p. 357.

2 Cf. Anal. Post., ii.f cap. x. [xi.], i, where Aristotle enumerates the four causes.

3 Rhet., i., c. ii., 16, 17. Aristotle mentions this proof in connexion with the
Enthyweme. Cf. JOSEPH, op. cit., p. 323 n. ; supra, 234-5.

SCIENCE AND DEMONSTRATION 233

this " proof of fact ". Such are the proofs by which Aristotle and
the Schoolmen have argued from the existence of motion, causa
tion, and contingent being, to the existence of an immovable
Prime Mover, a First Cause, a Necessary Being, distinct from the
universe.

Strict or causal demonstration is also commonly known as
"a priori proof" ; while " proof of fact " is known as " a posteriori
proof". Causal proof is called " a priori" because it proceeds
from what is naturally or really prior, to that which is naturally
or really posterior. And since the effect is naturally or really
posterior to the cause, an argument which proceeds from effect to
cause is called " a posteriori".

When the middle term is really neither prior nor posterior to
the conclusion, when the passage of inference is from one of two
concomitant connected facts, or abstract aspects of reality, to the
other, the argument is called an " a simultaneo argument ". The
great historic example of this is the argument by which St.
Anselm (1033-1 [09) sought to prove the existence of God from
the notion we have of His infinite perfection. In the domain of
induction, a part arguments, arguments from Example, and from
Analogy, are in a certain sense "a simultaneo"; while in the
domain of deduction, proofs that are based upon reciprocal pro
perties and relations (spatial or numerical) might also be regarded
as "<2 simultaneo" (258).

(b} Indirect Proof 'or Reductio ad Imposstbile.1 The forms of
proof already examined prove the truth of their conclusions
directly. Where this cannot be done, it may be possible to show
indirectly that a judgment is true, by showing that if it were false
and its contradictory true, something impossible, absurd, or self-
contradictory would follow. This method of establishing a truth
by disproving its contradictory, is, obviously less satisfactory and
less scientific than direct proof; for it does not give the mind
any insight into the positive, intrinsic causes or reasons why the
established proposition is really true. Nevertheless, it is of great
importance as a path to certain knowledge, and it is used ex
tensively in every department of research. It is, as we saw, the
sort of consideration underlying inferences in the second figure
of syllogism (169). We have seen, too, that laws are discovered
and verified inductively by disproving alternatives through the

1 tis rb aSvvarov iirayuiyf), — Cf. Anal. Prior., i., c. xxiii. [xliv.], 2 ; supra 169. For
a different use of the term cnrayuyji cf. Anal. Prior., ii., c. xxvii. [xxv.j.

234 THE SCIENCE OF LOGIC

application of arguments in the second figure of syllogism (209,
212). Hence, it is by this process of indirect proof we know
that inductively verified laws are de facto true, even though we
may not be able to explain the latter, or show why they are true

(247).

In dialectical discussions, when one of the disputants makes use (provision
ally, and without necessarily assenting to them himself) of premisses admitted
by the other, in order to disprove the latter's main contention, the former is
said to be arguing " ad hominem " or making use of the " argumentum ad
hominem ". This latter expression is, however, also used, in quite a different
sense, to designate a special form of the fallacy known as Ignoratio Elenchi
(275, A, a).

(c) Pure, Empiric, and Mixed Demonstration. This is a divi
sion of direct or ostensive proof, and is based upon the nature of
the judgments which are employed as premisses. Pure demon
stration is that into which none but metaphysically necessary
judgments enter (85-90, 198). It is exemplified in abstract
metaphysics and mathematics. Empiric demonstration is that
in which the premisses are synthetic judgments, truths of fact,
inductively established generalizations, as in the physical sciences.
Such demonstrations must, of course, conform to the a priori and
absolutely necessary laws of thought ; and each step or syllogism
must contain at least one universal premiss, endowed with some
degree of necessity ; but these need not be analytic or metaphysic
ally necessary propositions (198).

Mixed demonstration is that which contains both pure or
abstract, and empirical or concrete premisses. The major states
some metaphysically necessary principle ; the minor asserts an
empirical application of it ; and the conclusion infers some con
sequence categorically. Such, for example, is the line of proof by
which the existence of God, as the uncaused First Cause, is estab
lished : A series of efficient causes, directly subordinate to one
another in their activity, cannot exist without an independent and
uncaused First Cause. But we see in the world concrete ex
amples of the existence of such series. Therefore an independent
First Cause exists, namely God.

This is, perhaps, the most important of all forms of proof. By
means of it we can apply the rational principles of abstract thought,
the great necessary truths of the ideal or conceptual order, to the
concrete facts and data of our sense experience. And it is only
by such a process of proof we can infer from " the things that

SCIENCE AND DEMONSTRATION 235

are made " l the supreme truth of God's existence, which is the
goal of all philosophy. Mixed proof, in this application of it,
whereby we ascend from the knowledge of effects to the knowledge
that there must exist a cause adequate to account for them, is
obviously a posteriori. It is not to be confounded with ordinary
scientific induction, which gives us physical certitude about the laws
of created causes (229-33); for, based as it is on the principle of
causality and the immediate data of consciousness (249), it gives
us metaphysical certitude of the existence of a First Cause.

(d] Circular or Regressive Demonstration. — Reason ascends
(by induction, or by a posteriori demonstration) from effect to
cause, and then descends again to explain the former by the
latter. Its movement is first analytic, then synthetic (202). It
thus completes a sort of circle or regress, returning in a certain
sense to its starting-point. Such a complete process is called
circular or regressive reasoning. This is the natural path of valid
thought in the discovery and proof of truth. Hence it must not
be confounded with the fallacy known as the vicious circle (the
circulus vitiosus or petitio principii). The latter is an attempt to
prove a premiss by means of the conclusion which that very pre
miss is employed to establish2 (198). But regressive demonstra
tion sets out inductively from some fact or phenomenon, whose
existence is certain, though its nature or cause is only vaguely con
jectured as an hypothesis ; and it returns from that nature or cause
to the existing fact, only when it has established the former, and
reached such a knowledge of it as explains the fact or phenomenon
in question.

255. DEMONSTRATION AND SCIENTIFIC EXPLANATION.
" POPULAR EXPLANATION ".—What strict Aristotelean demon
stration is to the deductive sciences, that scientific explanation is
to the inductive sciences. We are said rather to demonstrate a
"truth" and to explain a "fact," but the difference is only a
verbal one. A " truth " is a judgment that is in conformity with
some reality which it purports to interpret ; the judgment itself
is the logical truth, the reality is the ontological truth. The reality
itself has various names: "being," "thing," "event," "fact,"
" phenomenon ". The judgment which asserts that a thing " is "

1 Rom. i. 20.

2 The premisses of a valid demonstration must be known otherwise than through
a knowledge of the conclusion itself; they must be known from an independent
source.

236 THE SCIENCE OF LOGIC

or " exists," that a fact " takes place," that an event " happens,"
is said indiscriminately to assert a " truth " or a " fact ". The ex
pressions " That is zfact" and "That is true" are synonymous.
Now, to give a causal demonstration (a demonstratio propter quid —
Siori) of the truth of such an assertion is evidently the same as to
explain fully why and wherefore the thing or event or phenomenon
exists or takes place as it does — to " show " or " demonstrate " it,
in and through its connexions with all its causes.

Nevertheless, the term "demonstration" seems by preference
to be applied to the process by which we connect abstract truths
with their first principles; and "explanation" to the process by
which we connect the concrete existence and happening of things
and events with their causes, and so come to understand the modes
in which, or the laws according to which, they are produced by
those causes. We may know that the three angles of a triangle
are equal to two right angles without knowing why ; and we may
know that ice begins to form on the surface of a pond and not at
the bottom, without knowing why. To answer the first "why " is
to demonstrate a theorem in geometry ; to answer the second is
to explain a phenomenon in physics. To demonstrate truths is
simply to show their connexion with simpler truths which we
already understand, and ultimately with first principles : to show
how they are involved in the latter, to harmonize and fit them in
with that part of our knowledge to which they are logically or
rationally akin. To explain facts is simply to show why they
happen, how they occur, how they are connected with their causes,
what these causes are, and what are the laws according to which
they bring those facts about. We demonstrate consequent by
antecedent until we reach first principles ; we explain effects by
causes until we reach remote causes, and, ultimately, the One, Un
created First Cause.

It is in this discovery of causes, and of the laws to which
their activities conform, that scientific explanation essentially
consists. We " explain " a fact or phenomenon when we show
it to be an instance of the application of some law. But this
" law " itself may be only a general statement of the uniform
occurrence of the fact in certain definite circumstances (247) ;
and if so, the " law " itself needs explanation, suggesting as it does
a distinct " why ? " of its own. And so we try to explain the law
itself in turn. This we do either (i) by showing that it expresses
the combined application, simultaneous or successive, of certain

SCIENCE AND DEMONSTRATION 237

other already known laws.1 For instance, the law that de
scribes the path of a projectile as a parabola expresses the com
bined effects of the initial motion and of gravitation, acting
simultaneously. The law that rocks and mountains are disinte
grated by frost succeeding rain, is an expression of the joint
effect of causes acting successively, each according to already
known laws of its own. Or (2) we may be able to connect the
law in question with other known laws showing them to be all
special applications of some wider and more general law. Thus,
the law of gravitation connected and " explained " the laws of
falling bodies and the laws of the revolving planets. We have
already met numerous other examples of explanation ; and when
dealing with hypothesis and causation we discussed the nature
of the limitations within which phenomena can be " explained ".
It is sometimes stated that Aristotle's conception of science
is entirely different from the modern conception. But — apart
from the fact that inductively established laws and their appli
cations, which are nowadays universally regarded as " scientific,"
would not be so regarded by Aristotle — the difference really lies
only in the terminology. He conceived science, after the manner
of geometry, as starting from the definition, which reveals the
essence of the "kind," and demonstrating the properties deriv
able from the latter. His theory of the specific type or form,
as embodied in the individuals and forming their essence,
was copiously illustrated by examples drawn from the domain of
biology. But it is not so easy to distinguish the attributes that
are essential to an organic type from the properties of the latter,
as it is to distinguish between the essence or definition of a
triangle and its properties. And the same difficulty prevails in
all the sciences which deal with concrete, actually existing things.
Hence, in these sciences, " for definition such as we have it in
geometry, we must substitute classification ; and for the demon
stration of properties, the discovery of laws. A classification
attempts to establish types ; it selects some particular character
istics as determining the type of any species. ... It will be the
description of the type, drawn up on such principles as these,
that will serve for definition ".2 Obviously, there is no change
of ideal in substituting classification for definition ; our aim in
classification is to reach definitions of real kinds of things. So,

1 C/. MELLONE, op. tit., pp. 328 sqq. ; JOSEPH, op. cit., pp. 474 sqq.

2 JOSEPH, op. cit., p. 89. Cf. supra, 47, 66.

238 THE SCIENCE OF LOGIC

too, the " discovery of laws" according to which natural agencies
co-operate in maintaining the order of nature, is, eo ipso, the
" demonstration of properties " which characterize those agencies.
Mr. Joseph points to what is rather a contrast of terminology than
a conflict of views when he says l " Science seeks to-day to
establish for the most part what are called ' laws of nature ' ;
and these are generally answers rather to the question ' Under
what conditions do such and such a change take place ? ' than
to the question ' What is the definition of such and such a sub
ject ? ' or ' What are its essential attributes ? ' " He seems to
think that the contrast lies in the different manner of putting the
problems : " though it is possible to bring many scientific in
vestigations to-day under one or other of the types of question
which Aristotle says we inquire into, yet looking to his examples,
one must confess that (as is natural) he puts the problems of
science to himself in a very different manner from that in which
scientific men put them now ".2 But the difference lies rather
in the nature and scope of the problems themselves: the pro
gress of discovery since the days of Aristotle has inevitably given
rise to scientific problems of which he could not have had even
a suspicion. And Mr. Joseph admits that it is " more in respect
of the problems to be answered than of the logical character of
the reasoning by which we must prove our answers to them, that
Aristotle's views (as represented in the Topics} are antiquated".3

It will serve to bring out more clearly the nature of scientific
explanation, if we contrast it briefly with the process of Illustra
tion, which sometimes gets the name of " Popular Explanation ".
While the former enables us to understand things by what is
naturally prior to them, the latter helps us to take in and realize
new facts by what is prior in our experience to these latter. All
progress in knowledge must be from the better known to the less
known : ignotum per ignotius is not an aid to knowledge, but an
impediment.

Since, however, explanatory principles are more remote from
experience than familiar facts, we often have to try to take in

1 op. cit., pp. 358-9.

a ibid., p. 359, n. i. He refers to Anal. Post., ii., c. i. i : rk ^rovfj.fvd ianv laa. rbv
aptGnbv 8crairep &ri<TT<£/uefla. frjToC/i«»' 5i rtrrapa, rb Sri, rb $i6ri, fl <t<TTt, rl fffrtv.
From the context these four would appear to be two alternative ways of asking (i)
whether a thing is, and (2) why it is. In other words, it distinguishes two kinds of
proof, namely, proof of fact, and causal proof or strict demonstration. Cf. 254.

3 ibid.

SCIENCE AND DEMONSTRATION 239

some strange fact, or new generalization, before we understand
the principles which really explain it. And we are enabled to
take it in if it is described for us in terms of some already known,
familiar facts. Such descriptions, by means of rough analogies
and illustrations, are very extensively employed in all attempts
at popularizing the truths of science, and bringing them somehow
or other within the mental horizon of the man in the street or the
youthful learner. And such descriptions are sometimes called
individual, or subjective, or popular "explanations," because they
are addressed to individual minds that are not yet capable of
understanding the real explanation of the matters so described.

To borrow an example quoted by Professor Welton from Clifford's Lectures
and Essays : J "It is [a popular] explanation of the moon's motion to say that
she is a falling body, only she is going so fast and is so far off that she falls
quite round to the other side of the earth, instead of hitting it ; and so goes on
for ever ". This does not give us the why or wherefore of the fact : it is not a
scientific explanation : We cannot understand the moon's motion scientifically
until we are able to refer it to the laws of motion and gravitation. " But it is
no [popular] explanation to say that a body falls because of gravitation. That
means that the motion of the body may be resolved into a motion of every one
of its particles towards every one of the particles of the earth, with an accelera
tion inversely as the square of the distance between them. But this attraction
of two particles must always, I think, be less familiar than the original falling
body, however early the children of the future begin to read their Newton."
Therefore the latter explanation is not "popular" ; but it is "scientific" ; it
is an explanation by principles and causes and laws which are in themselves
prior to the concrete facts (priora in se, natura sua], though not more familiar
to us (priora et notiora quoad nos}.

256. LIMITATIONS OF SCIENTIFIC EXPLANATION. — If we regard scientific
explanation as the process of bringing particular facts under inductively
established laws, and of unifying these separate, isolated laws by bringing them
in turn under still wider and remoter inductive generalizations, then there arises
this peculiar difficulty : that we are explaining particular facts and narrower laws
by an appeal to wider ultimate laws which do not themselves admit of a similar
explanation. We saw something analogous in examining demonstration : it
also rests ultimately on principles that are themselves indemonstrable. But
then, these latter are self-evident, whereas the widest generalizations of induc
tion are not self-evident ; and hence Aristotle would not recognize the knowledge
based on these as " scientific " in the strict sense. But such knowledge is now
universally regarded as scientific ; and rightly so, for these ultimate inductive
laws have sufficient evidence of their truth in the facts of experience. They are
not intrinsically and immediately evident like the axioms of geometry, but they
are believed to be true because we see that they alone are compatible with the
facts of experience, or, at all events, that they furnish us with the most satis
factory explanation we can find for the facts of experience (221, 230). We

Jpp. 102-3, apud WELTON, op. cit., ii., p. 190.

240 THE SCIENCE OF LOGIC

see intuitively that the abstract principles of logic, metaphysics, and mathematics
must be true absolutely, because reality as conceived in the abstract by the
intellect, or, in other words, the abstract, possible essences of things, are seen
by the intellect to involve necessarily the truth of those principles. We do not
see in this intuitive manner that our widest inductive generalizations — such as the
law of gravitation, or the uniformity of nature — are true in this same absolute
sense ; for they are not. But we see that they are, de facto, hypothetically and
contingently true, because our sense experience of concrete, contingent facts
forces us to admit their truth, and would not be explicable, or intelligible, or
rational, on any other hypothesis.1 We see why we must believe them to be
true, namely, because the facts of our experience are what they are. But it
may be said that this knowledge is not explanatory : that it does not show us
why the laws in question must be true. And this may be admitted ; for no
contingent, hypothetical laws, however wide, can offer an ultimate explanation
of concrete facts. Laws are but the expression of the modus agendi, the
manner of acting, of causes or combinations of causes. And we shall not have
fully explained any concrete fact in the universe until we know why the agencies
of nature act according to those widest laws — why, for example, matter gravitates,
or why life comes only from life, or why natural causes act uniformly.

" We may point to facts," writes Mr. Joseph,2 " from which it follows that
we must believe a proposition ; but we do not thereby explain the proposition,
It is the thing believed, and not our believing, which must be shown to follow,
if we are to say that we are finding an explanation." But " the thing believed "
is the proposition. And unless the proposition itself were seen by us to follow
from our previous interpretations of experience, neither would our belief in it
follow from these. We give our assent to the existential propositions em
bodying the facts, because we have the testimony of our senses that the facts
are so. And we give our assent to the laws because we see that the facts
involve these latter. The next question, about both facts and laws, is, Why are
they so ? Or, to apply the same question to one great assent underlying all
inductive inference : We believe that physical agencies are uniform in their
activities because they are uniform, but why are they uniform ? Philosophers
differ in their answers to this ultimate question because they differ in their
views as to the nature of reality as a whole. The sufficient reason which
satisfies all theists, why this and all facts are so — the one which they consider
the only true reason — is that the Will of God has made them so. In reaching

1 Mr. Joseph says of logical principles that " every explanation must be
consistent with them but they will not themselves explain anything " (op. cit., p. 466).
But if the principles of abstract (geometrical) magnitude and number " explain " or
"demonstrate" the abstract conclusions derived from them in geometry and
mathematics, so do the principles of pure thought and being " explain " or " demon
strate " the abstract conclusions of logic and metaphysics. But by " Explanation "
he understands here proximate or " scientific " explanation, as opposed to ultimate or
"philosophical " explanation ; for he says : " In all explanations, our premisses are
1 special ' or ' proper ' or scientific principles " (ibid.) ; though he goes on to raise
distinctly ultimate or philosophical questions in discussing " Explanation ". In ac
cordance with our view of logic, as concerned not merely with " scientific " but also
with " philosophical " thought (202) we take the term " Explanation " in its fuller and
deeper sense.

2 op. cit., p. 466, n. i.

SCIENCE AND DEMONSTRATION 241

this position we do not rely on induction alone ; we reach a stage at which
we must substitute the simple a posteriori argument from effect to cause.
This we do when we pass from the special sciences, which deal with the
proximate causes of limited groups of phenomena, and the proximate principles
of special departments of knowledge, into philosophy, which aims at offering
an ultimate explanation of all truths and of all things — as far as the human
mind can attain to such, — by tracing all truths and all things to the One Divine
Being who is the First Principle of all truth and the First Cause of all created
reality (232).

257. AN ERRONEOUS VIEW OF EXPLANATION. — In contrast with this
theistic view of Explanation— as a knowledge of things through their causes,
terminating ultimately in the recognition of a Supreme First Cause, the Deity,
on Whom the universe of sense depends — we have the Hegelian, Idealistic
view of Explanation as the knowledge of things through their relations to other
things, terminating in the conviction that all are parts of one systematic, self-
existent, self-explaining whole.1

Writers of this school identify " reality " with " thought," and endeavour
to show that " things " are " sets of unalterable relations " established or con
stituted by " mind ". The effect of this attitude on their logic is to extend the
necessary and universal relations which we institute between our abstract con
cepts, to what we call the concrete world of phenomena : in other words, to
assume or postulate that the world of our experience is governed by the same
necessary laws as govern our necessary judgments (215, 224). To suppose, thus,
that everything which actually exists or happens does so by the same necessity
by which whatever happens has a cause, by which a thing is what it is, by
which two and two are four, etc., is to confound the actual with the possible,
the existent with the merely thinkable, the physical or moral necessity which
governs those things and occurrences that are dependent on the Divine Will
and on human free will with the logical and metaphysical necessity which
characterizes the relations established by our thought between abstract, possible
essences. Hence these authors set up the strict Aristotelean concept of science
— the knowledge by which we know that a thing " cannot be otherwise than
it is " — as the ideal of all science, even of physical and moral phenomena ;
whereas it really applies only to those sciences which yield metaphysically
necessary judgments about abstract objects of thought considered by the mind
in a " possible " state, i.e. as apart from actual existence and free from all
change. Professor Welton, for example, lays down as a " postulate of know
ledge " in regard to the actual world, that we must assume its " every detail,
even the smallest, as so determined by conditions that, under the circumstances,
it could not possibly be other than it is. That the given is necessary is an
assumption without which it .would be helpless to attempt to explain it, for all
explanation resolves itself into ascertaining the exact conditions by which the
given is determined. When the conditions of every detail of a phenomenon
are so fully and exactly known that not only a phenomenon of this general
character, but just this very phenomenon, with exactly these details, and
each in exactly this amount, must follow from those conditions and from
those only, then that phenomenon is fully explained. Doubtless, in the vast

1 WELTON, Logic, ii., ch. vii., § 159 ; cf. JOYCE, Principles of Logic, pp. 248-
5i, 338-

VOL. II. 1 6

242 THE SCIENCE OF LOGIC

majority of cases such thoroughness ... is not attained. . . . But the ideal
of explanation is the same : it is thorough in so far as the given can be shown
to be the necessary consequence of certain definite and necessary conditions.'1'1 l
The " necessity " referred to here is that which characterizes science in
the strict Aristotelean sense, whereby we are said to know a thing scientifically
when we know that it " cannot possibly be other than it is ". To demand
such " necessity " as a hall-mark of all scientific explanation is tantamount to
a declaration that we can have no scientific knowledge of the concrete, actual,
existing world at all, but only of the abstract, possible objects of thought con
ceived by our own intellects.

Father Joyce, in his Principles of Logic? contrasts this [Idealistic] account
of explanation, as that of the part by the whole of an organism, with the
Scholastic [Theistic] account, as that of effect by cause in an organization. Of
course, the Idealist conception of the universe as one in nature or being
(Monism, Pantheism}, and not merely one in order (a " Cosmos " distinct
from the Infinite Being who created it ; Dualism, Theism), and of individual
" things " and " events " as not really distinct from one another, but as made
up of groups of " relations " conceived by that one Mind, which is the world
— such a conception is entirely erroneous.3 But its evil effect on the doctrines
of " Explanation," " Demonstration," and " Science " is to narrow these con
cepts unduly by setting up for them too exacting and even impossible ideals,
rather than, as Father Joyce states, to make them purely provisional and involve
them in an endless regress. Even in the Scholastic view of explanation there
is a true sense in Mr. Bosanquet's remark that " nothing can be known
rightly, without knowing all else rightly " ; 4 for, all research into the ultimate
reason of logical first principles and other axiomatic truths leads us ultimately
to the Divine Intellect ; and all research into the ultimate causes of existing
things leads us ultimately to the Divine Will ; and we take it that Divine
Wisdom has so planned the created cosmos, and interrelated its parts, that the
whole might be understood in the part, and the part in the whole, if these
were known "rightly," i.e. comprehensively; but to know them thus would
be to see into the Fiat of the Divine Will, which is proper to God alone : the
only " must " the only " necessity " there can be in actual things and events,
past, present, future, is that they must be as God freely wills them to be (224).
Since the immediate causes of any individual phenomenon depend on
remote ones, and these on remoter ones still ; and since in this way no indi
vidual phenomenon in nature is isolated, but each is bound up with the others :
zfull and complete knowledge of any one would necessitate a like knowledge
of all nature. If, therefore, the latter were regarded, according to the Mon
istic view, as a closed system subject to absolute logical necessity or determinism,
and if we were certain of the truth of this view — as we are of its falsity,— we
could entertain hopes of a complete and perfect knowledge of all reality ; and
our knowledge of physical causation would be an absolutely certain knowledge
of an absolutely necessary relation between phenomena. Few, however, have
the hardihood to put forward such a claim. " As the universe is a systematic

1 op. cit., vol. ii., pp. 188-9 (italics ours). 2pp. 338-9.

3 A trenchant and destructive analysis of these Neo-Hegelian views will be
found in Professor Veitch's Knowing and Being (Blackwood, 1889).

4 Logic, p. 393, apud JOYCE, ibid.

SCIENCE AND DEMONSTRATION 243

whole, ' writes Professor Welton, "[the totality of the conditions of any
concrete phenomenon] is, in its primary meaning, that whole system. In this
sense an ultimate analysis is obviously impossible. . . . " '

If, however, the whole physical universe and all its activities be regarded
as contingent, and dependent on the free creating and conserving influence of
a Supreme, Self-existent, Necessary Being, distinct from this universe, then,
obviously, our certitude about these activities and their laws cannot be necessary,
absolute, metaphysical, but only contingent, conditional, physical.

Mr. Joseph 2 seems to think that all our scientific knowledge rests ulti
mately on certain assumptions, or "maxims," or "anticipations," — such as our
" notion of what a rational universe should be," and our " belief that the
universe is rational," and our belief in the " uniformity of nature," — which
are neither self-evident nor capable of deductive explanation on the one hand,
nor "derived from experience" on the other (231). If our assent to such
fundamental truths, no matter by what name we call them, is thus in no way
rationally explicable or justifiable, the science that is based upon them ceases
to be rational too, inasmuch as its foundations are insoluble enigmas. But the
human mind has never acquiesced in any such ultimate avowal of its own
impotence. It claims — and it is right in claiming, for it really possesses — the
power to justify its assent to these foundations of science, by connecting them
rationally with the truth of God's existence. And this truth it undoubtedly
derives " from experience " — that is, from experience as revealed to the senses
and interpreted by reason. For all facts, including the existence of God, the
First Fact, experience, in this full sense, is our ultimate court of appeal.

So, too, the truth of the uniformity of nature (224) is not independent
of experience in the same way as mathematical axioms are ; though this seems
to be the way in which Mr. Joseph regards it.3 Not only do we derive from
experience the concepts involved in it, as indeed he admits,4 but the truth
itself, referring, as it does, not to the abstract, conceptual order merely, but to
the concrete, existing order of things, is grounded in, and confirmed by, ex
perience. Not that we can ever positively call it into doubt : to do so would
be as fatal as to doubt seriously the capacity of the mind to attain to truth :
it is one of those principles the truth of which we must postulate or assume
provisionally from the start : an assumption which experience justifies after
wards, by illustrating the success of these principles rather than by any formal
demonstration of them.

258. DISCOVERY AND PROOF OF TRUTH BY INDUCTION AND BY
DEDUCTION.— The question is sometimes asked whether logic ought to con
cern itself with laying down canons for the discovery of truth as well as for the
proof of truth (210). There can be no doubt that it ought. And as a
matter of fact it always does ; nor is this surprising when we remember that
although " discovery " naturally precedes " proof " or explanation, yet we can
scarcely be said to have " discovered " a truth fully, i.e. to have mastered it
mentally and made it our own, until we have connected it rationally with the
rest of our knowledge, and seen its relations to kindred truths, and their bearing
upon one another — in a word, until we have " explained " or " proved " it
scientifically.

lop. cit., ii., p. 119. *op. cit., p. 469.

3 Cf. op. cit., pp. 506, 510, 511. * ibid., p. 511.

16 *

244 THE SCIENCE OF LOGIC

We have already compared deduction and induction as methods, or lines
of direction, according to which progress in knowledge may be made (213).
Let us now compare them briefly from the standpoint of their material contents,
inquiring how truth is discovered and proved in each.

The problem of discovering and proving a general truth or law by induction
may be stated in this way : Given that in a particular case (or cases), S, is
observed to be connected with P, find whether and why " All S's are P," or,
discover and prove that '•'•All S's are P ". And the problem should be re
garded as fully solved only when we can assert that " All .S's will be and must
be P, because, or provided that, or as long as (a) they will be M, and (b} M
will be P ; and in no other conditions or circumstances ". This solution sup
poses that in M we have reached the ground or reason which not only neces
sitates the connexion between 6" and P, but which alone can necessitate this
connexion — on the assumption that the course of nature is not miraculously
interfered with. It supposes that we are able to overcome and remove all
indefiniteness from the conditions, to eliminate "plurality of antecedents (140)
or causes" (221) by discovering among all the possible groups (each of which
was regarded as a distinct and separate " antecedent "), the one necessitating
and indispensable factor which was common to, and operative in, all of them,
and in virtue of which all of them necessitated, though no one of them was in
dispensable to, the given consequent.

Let us see, in the next place, how the problem of discovering and proving
a truth, whether general or particular, by deduction, may be stated. What
exactly is the nature of the mental process by which truths are discovered and
proved " deductively," — in geometry, for example ? It would certainly be an
inadequate and misleading statement of the deductive method to represent
the problem of deduction as : " Given a certain antecedent, or certain pre
misses, find the consequent or conclusion." In discussing the nature and
characteristics of inference (197, 198) we saw that the real difficulty of dis
covering and proving new truths deductively lay rather in discovering proper
antecedents— fresh and fruitful combinations of old truths for the formation of
new sets of premisses, — than in the comparatively simple task of detecting
the new consequent or conclusion in the newly formed premisses, and formally
inferring it therefrom. If the general inductive problem might be stated :
" Given one of the multitudinous facts of sense experience, which make up the
physical universe, discover the causes and laws by which it happens," the
general deductive problem might be stated : " Given a knowledge of certain,
necessary, self-evident principles, discover all the truths involved in them ".

" Deduction and Induction," writes Dr. Mellone,1 " are not two different
and independent kinds of reasoning. The real process of thinking is the same in
ooth — i.e. to find a place for some fact as a detail within a system \cf. 212,
213]. In the case of syllogistic deductive reasoning our 'system ' is partly
known beforehand, in the form of a general law under which the fact or detail
is brought. We start, having in our hands the common thread which unites
the various facts. But in Inductive reasoning we have to find the common
thread. We [a] start with certain kinds of facts which occur together in our
experience. We \b~\ assume that there is some principle which unites them ;
and our object is to read out of these particular details the general law of

1 op. cit., p. 383.

SCIENCE AND DEMONSTRATION 245

their connection, and \c\ if possible, to explain this connection by further con
necting it with other laws : and this is to connect facts and laws into a
systematic whole."

With some qualifications, this presents the case correctly. We may admit
that in both induction and deduction the common aim is to systematize ; but
it is more. We must know the contents of the system before arranging them ;
the mental process of advancing in knowledge, whether inductively or deduc
tively, involves discovery as well as proof. We start, in deduction, with the
knowledge of a number of general laws, but without a knowledge — or even a
suspicion, at first — of any of the consequents that may be evolved out of them,
and made to serve in turn as proximate antecedents for further consequents.
We have " in our hands " not any common thread which we see or know to
be the means of uniting further truths or facts, but rather with a whole tangled
skein of endless threads, growing into and out of one another, and leading out
ward and onward we know not where. The complicated details involved in
them it is the duty of the deductive scientist to bring to light ; and he does
this by obtaining successive intuitions of new relations in the domain of
abstract thought which he has under consideration— for example, by intuitions
of spatial or quantitative relations in the study of geometry or algebra.1

The first step in the discovery of a new truth, " S is /*," by deduction,
seems to be (a) the observation of some case or cases in which de facto " 5 is
P" or (V) the occurrence, to our minds reflecting on known truths, of some
such connexions (between these latter) as suggest to us the possibility that
" S as such is P ". It might, for example, have been (a) the actual measure
ment of a few instances that first led to the surmise that "The right-angled
triangle as such has always and necessarily the square on its hypotenuse
equal in area to the sum of the squares on its sides ". Or (b\ the theorem
might have first suggested itself to a geometrician from some speculations of
his, some mental connexions he established by pondering on the concepts and
truths he already possessed about triangles, squares, etc. In either case the
process, so far, would seem to correspond to the inductive scientist's initial
observation of certain facts, leading him to suspect, and to conceive as an
hypothesis, the truth of the judgment " S as such is P ". Neither the deduc
tive nor the inductive investigator may ever have experienced a single actual
case of S being P : but only some other truths or facts relative to S and P,
which might have suggested that there is perhaps a necessary or causal con
nexion between the latter.

Of course, if the deductive inquirer, in his meditations, actually hits upon
some notion (M), which reveals to him a necessary connexion between S and
P, he simultaneously discovers and proves this latter connexion. As soon as
he realizes simultaneously in consciousness the truth of the two judgments,
that " M as such is P " and " S as such is M," he instantly discovers, and
simultaneously demonstrates (nay, discovers by demonstrating, by explaining
its how and why} that " 5" as such is P " (197, 198). In such a case, the con
ception of the new truth as an hypothesis is simultaneous with its verification
as a truth, and with its demonstration through its " causes ".

Similarly, were the inductive inquirer to discover, among observed facts
relating to S and P, some agency (M) whose operation he now realized to be

1 Cf, JOSEPH, op. cit., p. 505.

246 THE SCIENCE OF LOGIC

such as would, in the circumstances, necessitate S being P, he would, eo ipso^
have both discovered and proved S to be P, even though he had never yet
witnessed a single actual case of S being P. Such a mode, however, of
simultaneous discovery and proof, is rare in the inductive sciences, though it
represents, perhaps, what more usually takes place in direct, progressive, de
ductive lines of demonstrative inference (187, 188).

However, it does not always happen, even in deduction, that the investi
gator thus simultaneously suspects, verifies, and demonstrates or explains, a
new truth. Let us, therefore, pursue the case in which the geometrician, for
instance, after finding by measurement that the square on the hypotenuse of
a given right-angled triangle was equal in area to the sum of the squares on
the sides, supposes this to be always and necessarily true of all right-angled
triangles, without yet knowing either that it is, or why it is, true. He sets
about verifying and proving his supposition — not by carefully measuring a
number of other right-angled triangles, but rather by reflecting that if the
general proposition is true there must be a discoverable reason why it is true,
a reason which will demonstrate its truth. Hence he proceeds to seek for
something (Af) in the nature of S and P — of the squares on the hypotenuse
and sides of a right-angled triangle — in virtue of which S and P necessarily in
volve each other. This M he must discover by reflection on what he already
knows about triangles, squares, etc., by analysing and comparing his notions,
by making mental experiments, as it were, with a view to eliminating from all
the judgments which he finds crowding in upon his mind around " 5" is /*,"
those that are unessential to the latter, until he succeeds in explaining or
demonstrating to himself that " S is P " by connecting it through the medium
of M with truths he has already established for certain, and so, ultimately,
with first principles.

Thus, here too, as before, he verifies the new judgment " S is P," or dis
covers that it is always true de facto, by demons trating it, by showing it to be
necessarily involved in already known and proved truths. In induction, on the
other hand, a general law is often discovered and verified long before it can be
explained (247). Apart from this point, however, there is a certain analogy be
tween the process just outlined and the experimental testing and verification of
an hypothesis in induction. Both are illustrations of what the Schoolmen called
" inventio medii" the process of finding a " middle term " of proof (167, 197).
In induction, having observed 6" to be de facto connected with P in some case
or cases, our task is to find out whether the connexion is a necessary, causal
connexion, or only an accidental, contingent one ; and we prove that it is causal
by showing (if we can) that something essential to S, namely M, is necessarily
or causally connected with P. But how do we satisfy ourselves here that the
M which connects S with P is itself necessarily connected with P ? In other
words, how do we know that our premisses (especially our major premiss, " M
is P ") are necessarily and universally true ? Not as in the deductive sciences,
by showing our premisses to be either intrinsically self-evident principles or else
derived by demonstration from such principles, but, as we saw in dealing with
the verification of hypotheses (229-33) by convincing ourselves, through obser
vation and experiment, that nothing else but the truth of those premisses is
compatible with the conclusion which we know to be true as a fact. In other
words, we have to convince ourselves, by inductive investigation, that those pre-

SCIENCE AND DEMONSTRATION 247

misses alone account for the conclusion. It may be that we do not yet under
stand why they must be true, not having so far found an " explanation " or
" proof" of them, but the facts revealed in the conclusion force us to believe
that they are de facto true ; and that they alone are true compatibly with these
facts. The establishing of such reciprocal relations between " cause " and
" effect," between " antecedent " and consequent," is an ideal at which induc
tion aims (212).

The attainment of this ideal involves a higher degree of precision in these
latter concepts and terms than they possess in ordinary thought and language.
Hence, while the canons of formal inference, following the wider usage which is
consistent with plurality of " causes," or " reasons," or " antecedents," forbids
us to infer the antecedent from the consequent, induction aims at reaching such
an exact knowledge of the causal or rational relation, and its terms, as will
make the relation reciprocal, and so enable us to infer from consequent to ante
cedent as well as from antecedent to consequent (221). We have seen already
that induction does not often realize this ideal of knowledge ; but at all events,
starting from facts as consequents, it establishes the truth of causal laws as ante
cedents, by this kind of consideration : that these antecedents are true because
they account satisfactorily for their consequents, and are the only ones that
account for them so far as observation and experiment can inform us. And
inductive science has no other and no better " explanation " to offer for its ulti
mate generalizations than the superior success of these latter in accounting for
the facts of our experience (230) : " Many explanations are put forward," says
Mr. Joseph,1 " which do not appeal only to principles already known, but have it
as their avowed object to prove one or more of the principles which they employ.
Explanation then figures as an instrument of induction ; and J. S. Mill spoke
accordingly of a 'deductive method of induction,' and rightly attributed great
scientific importance to the process which he called by that name. No better
instance . . . can be given than the familiar instance of the . . . theory of
gravitation . . . [which Newton] proved for the first time by his use of it in
explanation."

We have now to note that deductive science does not rely on any con
sideration of this kind for the proof of its antecedents : it does not prove its
antecedents by showing that they alone can account for the consequents in
ferred from them. It proves them by deriving them from self-evident first
principles. And as a matter of fact the antecedents so proved are, perhaps for
the most part, not the only antecedents from which the consequents actually
inferred can be derived. In the demonstrative proofs by which conclusions
are derived from first principles in the deductive sciences, the antecedents are
regarded as sufficient grounds, but not necessarily as the only or indispensable
grounds, of the consequents (213). This is noteworthy — that in order to estab
lish a conclusion deductively by a " causal " demonstration (252), it is required
indeed that the middle term give some " cause " which will necessitate the
conclusion, but not that it give the only or indispensable " cause " of the latter.
In other words, a causal proof is recognized as a strict demonstration even
although it does not give the only possible cause of the conclusion : for one
and the same conclusion there may be a plurality of antecedents, a plurality
of distinct lines of demonstration, each connecting the conclusion in some
lop. cit., p. 477.

248 THE SCIENCE OF LOGIC

special way of its own with first principles. Each of these antecedents gives
a " cause " of the conclusion, i.e. something which is nearer to first principles,
and more evident, than the conclusion itself; or, at least, something which
helps us to understand why the conclusion is true, by showing forth some
intrinsic connexion of the latter with the whole system of reality to which it
belongs. In proportion to the depth and clearness of our insight into this
system, we shall be able to see the mental, rational relations that obtain among
those antecedents themselves, and between these and their antecedents and
consequents. When these relations are reciprocal, the antecedent cannot be
said to give a " cause " of the consequent (254, a). "Still," writes Mr.
Joseph,1 " the reasoning is deductive, since our premisses display to us the
rational necessity of the conclusion, and do not leave it resting on a mere
necessity of inference " ; that is, on the necessity of an inference which is
" based on an appeal to facts which might conceivably have been otherwise ".2

In the mathematical sciences, where we deal with conclusions arising from
self-evident intuitions of Quantity (" magnitude " and " multitude "), truths are
often reciprocally related, so that the distinction between antecedent and con
sequent practically vanishes. Not only can we, having demonstrated a truth,
A, from first principles, use it in turn to demonstrate another truth, C, but
we can embrace the alternative of demonstrating C from first principles and
then using it to demonstrate A. If we know two such propositions to be re
ciprocals, i.e. such that the truth of either involves the truth of the other,
and if, further, we know one of them to be true, we can prove the truth of
the other by showing that the latter as antecedent proves the truth of the
former as consequent.

" Thus in proving a theorem, or solving a problem which is supposed to
be set before us, we take the result provisionally for granted as a starting-
point, and say ; If this be true then would that, and if that be true so would
some other ; and so on, until we come to some already recognized truth.
The fact of being led back to this point establishes the conclusion ".3 The
process might be symbolized thus : " If Z then F, if Fthen X, . . . if Z? then
A ; but A ; therefore Z ". The validity of this inference depends on the
assumption that the truth of the consequent involves that of the antecedent :
an assumption not guaranteed in ordinary thought, of which alone the formal
canons of inference take cognizance. It is, however, often admissible in mathe
matics " where most of our propositions are of the nature of equations, rather
than ordinary predications," * and are, therefore, reciprocal and simply con
vertible.

259. MORAL CERTITUDE IN THE " HUMAN " SCIENCES.— In
the foregoing sections (249-58) we have been considering the
sources, conditions, and limitations of those sorts of " scientific "
knowledge about which we can have metaphysical or physical
certitude. But there is also a sort of knowledge which is rightly
called " scientific," about which we have moral certitude. Among
the many more or less closely allied meanings of" moral certitude,"
we may distinguish these three : (i) firm or certain assent to

lop. cit. p. 505, n. 2. *ibid., p, 410, n. i.

3 VENN, Empirical Logic, p. 369. * ibid, p., 370.

SCIENCE AND DEMONSTRATION 249

general truths (and their applications) concerning the facts or
phenomena exhibited in the conduct of men, considered as free
moral and social agents ; (2) firm belief based on the authority
of human testimony concerning matters of fact beyond the range
of personal sense experience ; (3) a very high degree of opinion,
practically amounting to a firm or certain assent, based on cumu
lative evidence. With this latter we shall deal in the following
chapter.

Understood in the first sense, moral certitude is a genuinely firm
or certain assent to general truths established by induction. It is
the sort of certitude that prevails in regard to the subject-matter
of the ethical, social, political, and economic sciences. The laws
established in these sciences are based upon the undeniable exist
ence of uniform tendencies implanted in human nature. These
propensities are variously described as " moral " laws ; " moral,"
or "human," or "rational," or "social" "instincts"; "natural
bias"; "inclinations of free agents," etc.1 They are quite com
patible with the existence of free-will. They are only conditionally
necessary, i.e. their applications to particular cases hold good only
on the condition that in those cases man will not run counter to
the dictates of his rational nature — as he may do, and is free to do,
absolutely speaking. But this foreseen contingency does not
diminish the firmness of our assent to these " moral " laws, any
more than* the foreseen contingency of a miracle interferes with
our assent to " physical " laws. Nor is there any reason why the
mere absolute possibility that a man may act " unnaturally,"
" abnormally," " unreasonably" in a particular case, should destroy
our moral certitude that he will not do so, by producing in our
minds a " prudent fear " that he will ; just as the bare, absolute
possibility of a miracle does not destroy our physical certitude
about particular applications of physical laws. Provided we see
no special reason to expect something abnormal in a particular
case, we are certain that the law will apply. "When we assert
that certitude shuts out all doubt and obviates all danger of a mis
take, we have reference to well-founded, prudent, rational doubts,
and to the danger of error truly such ; and not to unfounded,
foolish, irrational misgivings, and merely fantastic, imaginary perils.
These latter are to be scouted and disregarded, and hence cannot
destroy our firm adherence to the truth. As regards danger of
error in particular [cases] . . . danger signifies exposure to
1 C/. ROTHER, S.J., Certitude (St. Louis, 1911), pp. 12-17, 4O-7<x

250 THE SCIENCE OF LOGIC

imminent or threatening evil ; and, I think, it will be conceded by
all that no risk is run, no chances are taken, if in reliance on the
physical laws and moral instincts, I rest assured, for instance, that
the solid oaken boards of my room, on which I am standing, will
not be suddenly turned into thin air, but will continue to support
me ; or that a gay young student, who whilst boating with some
of his friends has fallen overboard, will not refuse to grasp the oar
held out to him." l

260. BELIEF ON AUTHORITY.— The moral certitude which we
possess about truths of fact on the testimony of our fellow-men,2
is based upon two of the " moral laws " referred to in the previous
section, namely, (i) that men can attain to a certain knowledge of
the facts of their experience, and (2) that men are naturally truth
ful in communicating such information to their fellow-men. In
order to give a certain assent to any statement or proposition on the
motive of authority, we must be sure that this authority is endowed
with two qualifications : (i) knowledge (" sdentia "), and (2) truth
fulness (" veracitas"*) : that our authority is not deceived, and is not
deceiving us. Manifestly, there is often very large room for the
exercise of prudence, discretion, and judicious discrimination, in
convincing ourselves of the presence of these two necessary con
ditions. And hence the practical impossibility of drawing any
sharp line of demarcation between the evidence that will produce
the firm assent of strict moral certitude, and the evidence which will
guarantee only that very high* degree of probability which is com
monly described as " practical " certitude, or " moral" certitude in
the wider sense of this expression (233, 249).

The knowledge which is based upon human testimony as to
matters of fact is often described as " belief," in contradistinction
to " science ". There are undoubtedly grounds for the distinction.
The motive for the assent which is called " belief" is extrinsic
evidence : the testimony of a witness is somethiug extrinsic to the
truth to which he testifies ; whereas the motive for " scientific "
assent is intrinsic evidence : it is something that is understood or
seen in the truth or fact itself. Again, science is universally
understood to be a knowledge primarily of general truths or laws,
and of facts only as embodying and exemplifying these ; whereas

1 ROTHER, op. cit., pp. 48, 49 ; cf. ibid., pp. 52-54.

"Assent to truth on Divine Authority is called Supernatural Faith. Before
assenting to a truth revealed by God we must be certain (a) that God exists, and (b)
that He has revealed the truth in question. These previous assents are called
pn-ambula fidei, preliminaries of faith.

SCIENCE AND DEMONSTRATION 251

belief on authority is primarily and mainly an assent to individual
truths of fact, irrespective of the laws embodied in these latter.
But from those points of difference it must not be inferred that
" scientific " knowledge, simply as such, is either more certain or
more important than knowledge of facts on human authority.
It would be a serious mistake to think that it is. From the
general standpoint of philosophy, that is, from the standpoint of
man's general outlook on the world and life, and on his own
nature, destiny, and place in the universe, there are individual
historical facts that are incomparably more momentous than whole
bodies of " scientific " knowledge. The great group of facts com
prised in the establishment of the Christian religion nearly two
thousand years ago, is bound up with truths of greater import to
men than, for instance, all the laws of the science of mechanics.
" Scientific " knowledge is not, therefore, merely as such, more
important than the knowledge known as " belief". Neither is it
always and necessarily superior to the latter from the point of view
of certitude, or firmness of assent. The character of the mental
state, as revealed in consciousness, is undoubtedly not the same
when I assent to the truth that " The three angles of a triangle are
equal to two right angles" as when I believe that " The Liffey is
not flowing backwards to-day," or that " Great Britain is an
island " ; but my assent is " firm " or " certain " in all three cases.

Human testimony can never, of course, be an ultimate motive
of certain assent. Such assent, given on the authority of such
testimony, must be always preceded by two other assents — to
the two judgments, " My informant is not deceived," and " He is
not deceiving me ". Now, if we assent to these judgments, or
either of them, on the authority of some other testimony, the
same two conditions have to be verified in regard to this latter
testimony. Hence, under pain of being involved in an endless
regress, we must ultimately have intrinsic evidence for the presence
of the two requisite qualifications in some testimony of the series.

Furthermore, in matters of science, where the truth can be
ascertained by rational investigation into the intrinsic evidence,
the right and proper certitude to seek is scientific certitude. But
the authority of a teacher or master is not a motive that can
produce certitude of this kind. It is an extrinsic motive, which
can produce certitude of belief ; and hence we cannot appeal to it
in scientific research. In science, where our aim is to reach scientific
certitude, such an appeal is the weakest of all arguments. This

252 THE SCIENCE OF LOGIC

has been the uniform teaching of Scholastic philosophers at all
times.1 They have taught that human authority in matters of
science is only a " confirming criterion " of truth and certitude.
And it is a commonplace truth of experience that when an
individual investigator brings to light some new conclusion by
a long line of laborious and sustained reasoning, the fact that
other investigators have reached the same conclusion, and assent
to it as true, corroborates his own findings and strengthens his
belief that his reasoning has been sound and logical.

But because Scholastic philosophers, being for the most part Catholics,
have always taught that God has revealed to man truths of supreme import
ance, and has established on earth an institution endowed with infallible au
thority to teach those truths ; and because, too, they have rightly insisted on
the undeniable fact that men can and do reasonably hold, with a certitude that
is based not upon intrinsic evidence ; but on the authority of their fellow -men,
the vastly preponderating bulk of their certain knowledge : Scholastic philo
sophy has been wrongly and unjustifiably accused of opposing the progress of
science by setting up human authority in the place of man's natural reason 2
(201). It is only ignorance of the real teachings both of Scholastic philosophy
and of Catholic theology that could have originated and perpetuated such
charges. Even the uneducated Catholic knows that faith in revealed truth —
or, indeed, in any truth that is believed on authority— ought to be reasonable,
that blind faith is unnatural to a reasoning being and derogatory to the dignity
of his nature, that his faith would be irrational were he not convinced with
certitude that the channel, through which he has received what he believes,
is a reliable one.

Scientific certitude is, of course, desirable, about matters which can be
known scientifically. But even about these how infinitesimally few there are,
comparatively speaking, who are in possession of really scientific certitude !
It is not scientifically certain assents, but beliefs based on authority, that shape
the conduct of men's lives. The multitudes of mankind are influenced and
led by the authority of the few ; and no less in the twentieth than in the
fifteenth, or tenth, or fifth, centuries. The masses may transfer their allegiance
from leader to leader, but they will ever be led by some authority or other —
as those are, nowadays, who proclaim in the name of modern science that
reason is at last emancipated from the shackles of authority and will henceforth
bow in reverence to science alone ! s

1 " Locus ab auctoritate quae fundatur super ratione humana est infirmissi-
mus." — ST. THOMAS, Summa Theologica, I., Q. I., art. viii., ad 2.

2 For an account of a recent attempt to revive those calumnies, cf. art. " Philo
sophy and Sectarianism in Belfast University " in the Irish Theological Quarterly,
October 1910 (reprinted, Dublin 1910) ; The Value of Scholastic Philosophy (Report
of Privy Council Investigation. Dublin : Catholic Truth Society, 1910) ; O'KEEFFE,
art. Scholastic Philosophy, in the Irish Ecclesiastical Record, April, 1911. For a
fuller treatment of the real attitude of Scholastic philosophy towards authority at
all times, we may refer the reader to De Wulf, Scholasticism Old and New (2nd
edit. 1910), pp. 53-75, 190-200: History of Medieval Philosophy, pp. 109-113, 173-
177, 206-212, 348-358, 403-406, 501-505.

3 Mr. Balfour shows very clearly, in his Foundations of Belief (P. III., ch. 11.)

SCIENCE AND DEMONSTRATION 253

261. HISTORICAL SCIENCE AND CERTITUDE: ITS CRITERIA
AND SOURCES. — The writing of history has for its aim to give us
a faithful, vivid, and instructive picture of the past ; and this is
an art rather than a science. But it presupposes the accurate
determination of past events, the detection of the combined
agencies that culminated in those events, and the discovery and
illustration of the human forces, instincts, tendencies or " laws"
— social, racial, religious, political, economic, etc. — according to
which those various agencies have co-operated. Now all this
belongs to historical research, which is obviously a science, as being
concerned with the elucidation of such laws. And when the
historian seeks to synthesize these laws, to explain them de
ductively by connecting them with the more fundamental motives,
impulses, and instincts of man as a social being, he is labouring in
that domain which has been rightly called the philosophy of history.

In the work of historical research, the investigator is assisted
by a body of practical canons or rules of method, the formulation
and study of which constitute the methodology of his science.
The part of logic which deals with general rules of method (Part
IV. of the present treatise), applicable to all branches of investi
gation, might be described as "general methodology"; the
supplementary canons arising from the special application of
these to the particular subject-matter of any individual science,
form the " special methodology " of that science. Since it is the
tendency of logic nowadays to expound the general rules of
method with somewhat too exclusive reference to the physical
sciences (201), a bare outline, at least, of the principal rules or
canons employed in arriving at truth on human testimony, cannot
be considered out of place here.1

what a preponderating share of our assents is due to authority, and how very little
is the ripe fruit of personal reflection. Not merely the prescriptions of domestic or
civil or religious authority, but the current ideas of the age and country in which we
live, the ever-changing phases of " public opinion," the popular worship of some
hero of the hour, or some fashionable theory : all these influences envelop us in
a sort of " psychological climate " or " atmosphere," which moulds and colours our
beliefs and convictions, and which none of us can possibly escape.

1 For fuller treatment of the subject (under the Scholastic title " De arte critica ")
cf. ZIGLIARA, Log-tea, (60), (61) ; HICKEY, Summula Philosophiae Scholasticae,
i., pp. 257-75 (Editio altera, 1911); RICKABY, First Principles of Knowledge,
pp. 377-90. Among writers who deal ex professo with historical criticism, the fol
lowing may be consulted : DE SMEDT, Principles de la critique historique (Lidge,
1883) ; IDEM, Introductio generalis ad historian ecclesiasticam critice tractandam
(Ghent, 1876) ; LANGLOIS and SEIGNOBOS, Introduction aux etudes historiques (3rd
edit. Paris, 1905) ; FREEMAN, The Methods of Historical Studies (London, 1886) ;
DELEHAYE, Les legendes hagiographiques (2nd edit. Paris, 1906 ; English tr. also

254 THE SCIENCE OF LOGIC

Criteria of human testimony. By testimony (testimonium)
we mean the sensible or visible manifestation — oral, written, or
otherwise — of one's knowledge to others. If the knowledge com
municated be doctrinal or scientific, its communication constitutes
what is called the teaching office (" magisterium "), and the com
municator is called a teacher or master (" doctor'1 or " magister"} ;
if it is knowledge of fact, its communication may be called
narration (" narratio "), and he who communicates it a witness or
narrator (" testis," " narrator"}.

The authority (" auctoritas ") of the person or persons com
municating the knowledge, is, of course, the value of their
testimony as a motive for assenting to what they teach or narrate.
The firmness of our intellectual assent or belief should be in
proportion to the ascertained value of the testimony ; if it is in
excess of this, it is not belief but credulity. Our assent may, there
fore, vary from mere opinion or probability in some cases, or
practical certitude in others, to strict moral certitude, which latter
may sometimes be as firm in its own order as physical or meta
physical certitude in theirs.

Quite a number of the practical rules laid down for testing
the knowledge and truthfulness of the source of our information
are obvious dictates of plain common sense. For example, in
regard to the knowledge possessed by our witnesses or narrators,
(a) we prefer, ceteris paribus, the testimony of an eye-witness to
that of one who testifies on hearsay ; (fr) that of a contemporary
(with the facts) to that of a subsequent writer, (c) that of a
number of independent (or, better still, mutually hostile)
witnesses, to that of interdependent or co-operating witnesses in
fluenced by the same point of view. Furthermore, we must (d)
ascertain from every available source, and take into account,
the attitude of the narrator in regard to the events narrated, and
everything that bears upon his powers of observation : whether
he ia prudent and painstaking, or credulous, or imaginative ;
whether he is influenced by unconscious prejudice or attachment
to a special " point of view," or by an apologetic purpose. It
is extremely important, if extremely difficult, to distinguish
between the facts narrated and the personal views, or theories, or

published) ; IDEM, Hagiography (art. in the Catholic Encyclopedia, Vol. VII.) ;
KIRSCH, History (ibid, with authorities there referred to) ; CAUCHIE, Introduction a
Vhistoire ecclesiastique (Louvain) ; O'MAHONY, The Alleged Epoch in Historical
Criticism at the Close of the Seventeenth Century, in the Record of the Maynooth
Union, 1911.

SCIENCE AND DEMONSTRATION 255

hypotheses, with which the writer colours his presentation of the
facts : these are liable to be distorted in the presentation — par
ticularly in " books which treat of comparative mythology, com
parative religion, the origin of social institutions, and such
matters, in which documents are scarce and obscure, or written
in a language ill-understood, while inferences are often more
marked by ingenuity than conclusiveness " l. Finally, to mention
one other point out of many, (e) we must be influenced by the
nature of the facts narrated, in determining whether the writer or
witness may not have been deceived : strange, unusual, unexpected,
wonderful (alleged) events, will naturally require to have been
submitted to closer and more careful scrutiny than ordinary facts,
before they can reasonably claim our assent. Here, the character,
education, and beliefs of the witnesses, the age and circumstances
in which they lived, the object with which they wrote, the amount
of imaginative embellishment with which it was understood in
their time that narratives of events might be clothed, their general
conception of what constituted " history," are all considerations
of paramount importance. They are called for chiefly, of course,
in the domain of religious history, and are concerned mainly
with the miraculous.

That miracles are possible, this is not the place to prove. We have rather
merely to point out that it is a flagrant -violation of logical method to dismiss
all narratives of the miraculous from human history as untrue and incredible
on the ground that " miracles are impossible," as long as the latter contention
remains unproven. To assert a priori, as something self-evident, that " miracles
are impossible," is an excellent example of the fallacy known as undue as
sumption of axioms (275, A, c). There has prevailed for the past few centuries
a rather superficial rationalism which cannot, or will not, see that its gratuitous
rejection of the miraculous involves it in this fallacy. Granting that miracles
are possible, the reality of any individual alleged miraculous fact must stand or
fall with the evidence adduced for or against it. Modern research in the domain
of historical criticism has established many invaluable canons for the better ap
preciation and understanding of miracle-narratives in ancient and mediaeval
religious literature : canons which enable us to appraise more accurately the
historical worth of what is contained in such documents, and to understand
better their scope and import. It is all-important, for instance, to realize that
exact fidelity to objective fact, exclusive of all apologetic purpose, and rigorous
verification of sources, in the writing of history or biography, are comparatively
modern requirements, which were not demanded in ancient times, or in the
Middle Ages, and need not, therefore, be expected in the writings that have
come down to us from those periods.2

Next, in regard to the truthfulness of our authorities, we
1 RICKABY, op. cit., p. 382. *ibid.t pp. 383-5.

256 THE SCIENCE OF LOGIC

have to consider, for instance, (a) whether these were consciously
prejudiced by apologetic purpose, or personal views or motives,
to such a degree that they may have misstated or misrepresented
the facts ; (£) whether the facts and circumstances were such that
the writers could have deceived their contemporaries and posterity
had they tried to do so ; (c) whether the character of the writers,
as known from all available sources, was truthful and upright, or
dishonest and unreliable.

It will be plain that some considerations render testimony
suspect without enabling us to trace its unreliability definitely
to the ignorance, or definitely to the untruthfulness, of its source.
Such, for instance, is the inference we may sometimes be forced
to draw from the silence of all other witnesses in regard to an
alleged fact recorded by one or a few, — the argumentum ex
silentio, as it is called. When can we argue that some allegation
of fact is untrue, because, though the alleged fact is vouched for
by one or a few writers, it is not mentioned by any other contem
porary writer? Manifestly, not always; but only when the
alleged fact is such that had it really happened it would certainly
not have been left unrecorded by all other writers of the time.
But of this it is for the most part very difficult to be sure. There
are many instances in which such " arguments from silence,"
after being held for ages as conclusive, have been themselves
discredited by subsequent authentication of the supposed dis
credited facts. This should make us cautious and moderate in
the use of such inference.1

Sources of historical science. The human records or remains
from which we derive our knowledge of the past, may be divided
conveniently into three great classes : (a} monuments of every
kind ; (&) documents written or printed ; (c) oral tradition. By
monuments we understand works of art constructed to commem
orate an event — coins, statues, columns, temples, etc. Their
significance and value, as evidences of historical facts, belong to
the science of archeology.

Written or printed documents are our most valuable source of
information about the past. The interpretation of ancient
written documents (manuscripts] belongs to the science and art
of palceography. Before an ancient book or manuscript can be
used as a reliable source, we must be sure that it is authentic or
genuine. This implies (i) that it really comes from the author

J RlCKABY, Op. (it., pp. 386-7.

SCIENCE AND DEMONSTRATION 257

to whom it is ascribed, or belongs to the epoch and country to
which it is assigned ; (2) that it has not been interpolated or cor
rupted by the interference of other hands. The proper ascription
of a document is ascertained partly by external, and partly by
internal evidence. Evidence of authorship, or of time or place
of composition, is said to be external when derived from sources
other than the document itself. The chief external evidence in
most cases will be found in what tradition, oral or written, has
handed down in each case. If tradition, whether oral or
written, ascribes the composition of a work to a certain author,
time, or place, and if there is no special reason to doubt the reliability
of its source, we can be morally certain that the tradition is cor
rect : for the simple reason that men are naturally truthful —
" nemo gratis mendax" — and that human testimony under due
conditions is a sufficient criterion of truth. If, for instance, we
find all contemporary and immediately subsequent writers, who
refer to a work, ascribe it to a certain author, this may in itself
suffice to settle the question. But, on the other hand, it may
perhaps merely create an initial presumption in favour of the
alleged authorship, and form a basis for further critical inquiry.
This is true especially of all works that come down to us from
the centuries prior to the invention of printing — which dates from
the end of the fifteenth century. The origins of all traditions as to
authorship, previous to this latter date, call for careful scrutiny ;
for in those earlier ages it was comparatively easy to give cur
rency to writings by falsely representing them as the works of
eminent authorities ; and this facility was largely availed of.

Where external evidence is doubtful or conflicting, or where
there is no such evidence at all, the internal evidence, derived
from the work itself, may prove to be very valuable. Internal
evidence must, of course, be very conclusive before it can upset a
strong, uniform, and apparently well-grounded tradition as to
authorship ; but as a matter of fact it has exploded many such
traditions ; and it is constantly furnishing conclusive settlements
to disputed questions regarding the provenance of documents.
Internal evidence is of various kinds : (a) a comparison of the
style of the work in question with that of other works known for
certain to come from the supposed author, will be of more or
less assistance in determining authorship ; (£) references, in the
document, to events the dates of which are known, will help to
fix the date of composition (the possibility and the fact of prophecy,
VOL. II. 17

258 THE SCIENCE OF LOGIC

in religious literature, being dealt with as in the case of miracles) ;
(V) the consistency or inconsistency of the contents of the document
with other certain works of the supposed author will also help to
decide ; and, in regard to manuscripts, (d] the form of the hand
writing, modes of contraction, formation of the letters, etc., will
often enable us to fix with sufficient accuracy the century, or
country, or both, in which the manuscript was written.

By the integrity of a document we mean its fidelity in re
presenting what the author actually wrote. This connotes absence
of all later interpolations in the case of original manuscripts;
and, furthermore, freedom from copyists' errors in the case of
copies. Where the original written text is in existence, and
known for certain to be such, it is, of course, the best evidence of
what the author wished to express. But where, as in the case
of all ancient works, we have only copies, and comparatively
late copies, these invariably differ more or less among themselves.
In all such cases, we aim at re-constituting the original text, or
getting as near as possible to the latter, by collating all the best
and oldest extant manuscript copies. This is only one of the wide
fields of investigation that form the domain of historical criticism.
We have set down oral tradition in the third place as a source
of historical or moral certitude. About the first beginnings of
human institutions we have only oral traditions to rely on.
When the art of writing was invented, these began to be com
mitted to documents ; and, many centuries later, were embodied
in printed literature. Authentic documents can only testify to
the existence of an oral tradition down to the date of composition
of such documents ; and it is with the value of the oral tradition
itself we are concerned here. Now, oral tradition can be a suffi
cient motive for moral certitude. It is only, of course, in regard
to facts of very great moment to some nation, or section of the
human race, or to the race as a whole, that we actually have
uninterrupted oral tradition. Again, such tradition can assure
us only about the substance of such facts, not about minor details ;
in regard to these latter, oral tradition naturally and inevitably
fluctuates : the very nature of this mode of narrating and trans
mitting knowledge from generation to generation involves
imperfections and limitations of this kind. Furthermore, even
in regard to the substance of the fact transmitted, the tradition
must be not only continuous, reaching back to the fact itself, but
also widespread (in a country, or continent, or throughout the

SCIENCE AND DEMONSTRATION 259

world, as the case may be), and uniform or self-consistent (while
it may vary, even to inconsistency, about details). Our evidence
that a tradition has been continuous, that it reaches back to the
fact itself, will be sometimes mainly negative : lying in our in
ability to trace its origin to any subsequent source. But for
the continuity and genuine origin of many traditions we can
have valuable positive evidence : the existence of written docu
ments, or of monuments, whether national, popular, tribal,
military, or religious, testifying to the continuity of the tradition
back to the time of the fact which it enshrines. The most
reliable evidences to the origin and continuity of any form of
social custom, or religious belief, are, of course, those that come from
documents and monuments that have been brought into existence
by the people, or institution, or society, conforming to such
custom, or professing such form of belief. There are, perhaps, no
oral traditions more strongly confirmed and corroborated by such
evidences than those of the Catholic Church. We can sometimes
prove that a given belief really had its origin at a certain time,
and in certain facts, by proving that such belief could not have
originated in a spurious tradition of later origin, or, in other
words, that such a tradition could not have arisen in such a
deceptive manner. This form of proof is known as the argument
from prescription.

The proof that oral tradition can produce moral certitude is
based upon the principle that men are naturally truthful, and
upon the fact that in certain cases it is morally impossible that
ignorance or deception could have intervened. The cases
in point are those of remarkable public facts of great moment
to whole peoples or nations, or to the human race as a whole.
To admit that men generally could either be mistaken themselves,
or mislead all their contemporaries and all posterity in regard to
such facts, would amount to a practical denial that man is
capable of attaining to any truth.

ROTHER, Certitude: a Study in Philosophy. RICKEY, Summula
Philosophiae Scholasticae, vol. i., pp. 143-70. TOOHEY, The Three Kinds
of Certitude, Irish Theol. Quarterly, July, 1909. RICKABY, First Principles,
pt. i., chaps, iii., iv. and v. ; pt. ii., chaps, vii. and viii. WELTON, op. tit., ii.,
bk. v., chap. vii. JOYCE, Principles of Logic, pp. 132-6. JOSEPH, op. tit.,
chaps, xvii., xxiii., xxv. MERCIER, Logique, pp. 286-93 ; Criteriologie
Gen'erale (5me edit.), pp. 5-35. MELLONE, op. tit., pp. 252, 258-9, 326-32,
382 sqq. WINDELBAND, History of Philosophy (Eng. tr.), pp. 132-54. DE
WULF, History of Medieval Philosophy, pp. 39 sqq.

17*

CHAPTER II.
OPINION AND PROBABILITY.

262. NATURE OF PROBABILITY : CUMULATIVE EVIDENCE :
" PRACTICAL " CERTITUDE. — When the evidence, whether mediate
or immediate, on which our assent to a judgment is based, ex
cludes all prudent fear of error, our assent is firm ; and this firmness
of assent is termed certitude (248). When a normally constituted
mind would not deem the evidence sufficient to exclude all such
fear from its assent, the latter is called opinion. The intellectual
motives, or reasons, which produce such assent, are described as
" probable evidence ". In the presence of such evidence we can
not be sure that our judgment is true, that it represents, even
partially, the reality as it is ; but we can recognize in the judg
ment a certain degree of verisimilitude : that it is more or less
like the truth, or likely to be true ; or, again, a certain degree of
probability : that the judgment is more or less probable, i.e. capable
of being proved, established, demonstrated, later on ; and we will
therefore give — or at least ought to give — to such a judgment a
degree of assent proportionate to the weight of the evidence.
While, therefore, opinion is the subjective mental assent, we may
define the probability or verisimilitude of a judgment as the degree
of likelihood, estimated from the evidence in favour of the truth of the
judgment, that the latter is really true.

Probability, therefore, is not the " approach " or " approxima
tion " of a judgment to truth, to conformity of the mind with
reality, in the sense that the Judgment itself is more or less true, but
only in the sense that the evidence pointing to its truth is more or
less strong.1 The judgment itself, as a mental unit, a mental pro
duct, giving one representation of the reality, must be either true or
false all the time : it cannot be more or less ; either the mind in
assenting to the judgment is in conformity with reality or it is not.
There are not, properly speaking, any grades or degrees of con-

1 Cf. ZIGLIARA, Logica, (42) ; supra, 248.
260

OPINION AND PROBABILITY 261

formity : conformity is not divisible. When, therefore, a judgment
or proposition is spoken of as " more or less true," we must bear
in mind the correct meaning of such language : that there is in
the judgment a true sense and a false one, that these can be dis
tinguished or separated, that this part is true and that false, and
that the original composite judgment, in which the unanalysed,
or insufficiently analysed, concepts and judgments were united
into one mental relation between subject and predicate, wasfatse,
taken as a whole, putting the mind that formulated it out of har
mony with reality (248).

Opinion, therefore, is the result of objective evidence which
is not grasped or comprehended subjectively with sufficient clear
ness to guarantee a certain assent. If objective evidence, which is
really sufficient for moral certitude, is grasped with sufficient
clearness, but is undervalued, underestimated by the mind that
receives it, it will not actually exclude the fear of error from such
a mind, though it would from a normal mind. The subjective
element is thus seen to be a factor in determining those varying
grades of assent ; but logic deals only with the objective element,
and its effect upon the normal mind, leaving the study of the sub
jective factors to psychology.

Neither can logic furnish any calculus for determining the
precise degree of mental assent proportionate to a given weight
of probable reasons. Mental assent is a vital, conscious act,
entirely beyond the scope of measurement in terms of any
mechanical or quantitative units. It is the objective factors,
which constitute the "probable evidence," that are alone in any
way amenable to what has been called the " Logic of Chance " or
the " Logic of Probability " (264). The degree of assent with which
the individual will respond to probable evidence, and allow the
latter to influence his actions and shape his conduct, is a matter of
personal prudence and discretion.

Probable evidence, as we saw, may vary in strength from the
extremely vague and doubtful indications that give rise to a mere
suspicion, to the very solid and substantial motives that produce
the sort of assent described in common language as " moral
certitude ." Hence, as there are degrees in the positive firmness
of a certain assent, so there are also degrees in that of a probable
one. The question may therefore be asked : Can opinion pass
gradually into certitude, a probable judgment into a judgment
certainly true, a probability into a certainty? Or, the question

262 THE SCIENCE OF LOGIC

may be put in this way : If we are to understand by cumulative
evidence, one form of which is circumstantial evidence, a more
or less considerable collection of reasons or motives, all of which
point towards the truth of the judgment, and each of which, taken
by itself, would only create a suspicion of that truth, can such a
cumulation of reasons ever produce certitude? It is a matter of
experience that they often do produce an assent which excludes
all prudent fear of error, and which falls, therefore, within the
definition of certitude. Such assents are commonly described as
morally certain.1 They constitute the vast majority of the assents
upon which man's ordinary activity in life is based. Nor is
there any reason why we should deny to them the quality of
certitude. No doubt, the evidence for them is not of that cogent
character which excludes even the abstract possibility of error, as
it is in the case of metaphysical certitude. But it can exclude all
prudent fear of error : so that in the concrete circumstances it is
morally impossible that we should be deceived. And if we find
ourselves in this state of mind, after having exercised all due care
and caution in weighing and analysing the evidence, we have certitude.
It has to be remembered, however, that in applying the
" moral laws" or "generalizations" already mentioned — such, for
instance, as that " man is naturally truthful " — to individual cases,
our assent must be for the most part qualified by some measure
of reserve. It will be a " practical " certitude : an assent upon
which a prudent man would act But this means, after all, that
the assent is in practice equivalent to a certain assent, though it
is not really a certain assent. For, even in the concrete circum
stances we may be deceived. If, for instance, it is an assent on
the authority of a fellow-man, it may happen that, notwithstand
ing his well-known prudence and care in observing facts, he was
in some unaccountable way deceived just on this occasion. Or,
even though his veracity may be above suspicion, he may have
had some interest, unknown to us, in deceiving us just this once,
and may have succumbed to the temptation. " The unexpected
happened " ; and in our surprise we begin to see that our " prac
tical " certitude was not certitude at all. Similarly, a jury reaches
" practical certitude," on strong circumstantial evidence, that the
prisoner in the dock committed the murder of which he stands
accused. On this practical certitude the prisoner is condemned
to death : and all who have carefully followed the evidence agree
1 Cf. CLARKE, Logic, pp. 426-428.

OPINION AND PROBABILITY 263

with the verdict. Yet cases have occasionally occurred in which
it was afterwards proved beyond all shadow of doubt that the con
demned man was innocent of the crime. What do such facts
prove? That the human mind is incapable of attaining to genuine
certitude ? No ; but only that it is not infallible in the weighing
and testing of evidence; that even when men have exercised
what is commonly considered to be sufficient care, caution, and
prudence, they may embrace what is erroneous. And such oc
casional failures will teach prudent men to be still more cautious
in deciding grave issues on " practical " certitude.

263. PROBABLE ARGUMENTS : THE ARISTOTELEAN ENTHY-
MEME. — Among the many kinds of judgments which call for a
probable assent, the following are the more important classes :
(i) some of our interpretations of the immediate data of our sense
experience ; (2) some judgments — whether universal, singular, or
particular — based on the motive of human testimony ; (3) induc
tive generalizations from sense-experience, by way of enumerative
induction, analogy, or unverified hypothesis ; (4) conclusions de
rived by deductive inference from probable premisses ; (5) to which
may be added judgments reached by the application of the calculus
of probability (266-8).

These various sources of probability do not reveal any new
forms of inference. When probability is reached by inference, the
obstacles to a certain assent lie not in the form but in the matter
of the inferential process. With many of those sources of prob
ability, as, for instance, those of the third class just mentioned, we
are already familiar. Indeed, the main sphere of probability is to
be found in induction. Before reaching a certain, scientific know
ledge of the inductively established general law, we have to pass
through many stages where our knowledge of it amounts to a
greater or smaller probability. All those various steps we have
already examined : the rough empirical generalizations from enu
merative induction, the arguments from example and analogy,
suggestions of more or less probable hypotheses, and, finally,
the processes of analysis, and the methods of experiment, by
which we seek to verify those probabilities and transfer them
into the sphere of certainties.

Judgments derived from the first source mentioned above do
not seem at first sight to involve any inference at all. But sense
experience is, as a matter of fact, invariably accompanied not only
by judgment or interpretation, but also by inference (238). This

264 THE SCIENCE OF LOGIC

inference is always practically unconscious, but it may be made ex
plicit in a syllogism of the second figure. Thus, if in the shadows
of the evening I see an object indistinctly looming into the field
of vision, I may think or judge immediately : " That is a horse ".
But the mental process is really this : —

" A horse presents such and such appearances ;

" This object presents those same appearances ;

" Therefore this object is a horse."

And it is manifest that this process will produce certitude only
where I can be sure that " Whatever presents those appearances
is a horse " ; in other words, where I can convert the major pre
miss simply, and so replace the formally invalid syllogism of the
second figure by a valid " proof of fact " in the first figure. If I
cannot do this, the " inference of perception," as it is sometimes
called, will only produce probability. It is clearly of the same
form as the argument from analogy, and falls under the class of
argument known as the Aristotelean enthymeme, with which we
shall deal presently.

The second source of probability mentioned above is human
testimony. When we cannot secure sufficient evidence, as to the
knowledge and trustworthiness of our authority, to produce moral
certitude, we must rest content with a probable assent to what
ever we accept on such authority : even though the natural yearn
ing of the mind is for a certain knowledge of the truth. Certitude
is not always attainable ; people often have to be content with
that high degree of probability which amounts to practical certi
tude. Hence it has been said that " Probability is the guide of
life " : The farmer sows his fields, the manufacturer erects his
machinery, the merchant opens his business, the soldier goes to
battle, young people marry, and statesmen legislate. Under the
influence of what determining motives ? What has the future to
offer them ? Hopes of success ; Probabilities}-

As a fourth source of probability we have set down deductive
inference from premisses which are not all certain. If any one
premiss of an inference be only probable, the conclusion cannot
be more than probable : it must follow the weaker premiss. A
probable argument may be defined as an argument whose premisses

1 " Tola praesens vita per probabilitatem maxime ducitur. Relationes omnes
hominum in familia et in republica viventium, probabilitate fundantur. Qui scribit,
qui navigat, qui militat, qui uxorem ducit, et qui leges condit, nonnisi intuitu proba-
bilis eventus operatur." — LEPIDI, Elementa Philosophiae Christianae, i., p. 318.

OPINION AND PROBABILITY 265

do not warrant a certain, but only a probable, conclusion. This may
happen in two ways : (a) either because the premisses contain a
judgment which is only probably true ; or (fr) because, though
the premisses are all true, they do not necessarily involve, but
only suggest, or point to, the truth of the conclusion we may
seek to derive from them.

(a) The former class of argument was described by Aristotle
as a syllogism from probabilities : <7tA.Xo7ioyi09 e'£ elxormv — the
eiVo? being one of those rough generalizations or " moral uni-
versals " commonly accepted as " practical " certainties. Where
we have a number of such probable syllogisms depending on one
another, in the form of a sorites (188), and leading up to a conclu
sion, we have what is called " chain evidence ". And as a chain
cannot be any stronger than its weakest link, the probability of
the conclusion in such a case cannot be greater than that of the
weakest premiss. It is usually considerably less ; for, since each
probable premiss inherits, besides its own innate weakness, that
of all its antecedents, the conclusion must inherit the combined
weakness of them all.1

Care should be taken to distinguish chain evidence from cir
cumstantial evidence; in the latter the various probable signs
are independent of one another, and their combination, therefore,
forms a cumulation or addition of probabilities which may pos
sibly be so strong as to issue in moral certitude.

(b) The second kind of probable argument is that in which
the premisses, though true, do not necessarily involve the conclu
sion sought to be derived from them. This is what Aristotle
described as the syllogism from signs, or symptoms, or indications :
a-v\\oyt,a-fio<f e'£ a-rjfieiojv. And to both arguments — the syllogism
from probabilities, and the syllogism from signs — he gave the title
of Enthymeme. The Enthymeme, therefore, in Aristotle's meaning
of the latter term — the " Aristotelean " enthymeme, as it is now

1 " For instance, a man is accused of murder. There is very strong evidence that
a man just like the prisoner was in the company of the murdered man on the night
when the murder was committed. It is almost certain that the man who was known
to be in his company did the deed. There is, moreover, a strong presumption against
the theory urged by the counsel for the defence, that the deceased made an unpro
voked attack on his companion on the night in question and met his death from him
in self-defence. But it does not follow that the accused should be convicted of mur
der. For if the probability of the three circumstances pointing to guilt is three to
one, the balance of probability is nevertheless rather against than in favour of their
being all of them true, and this means that it is more likely that the accused was
innocent than that he was guilty." — CLARKE, Logic, p. 430.

266 THE SCIENCE OF LOGIC

called — is an argument from likelihoods or signs : a-v\\ojiarfio<j e£
€iKora)v % ffrjpdwv. He defines it in the Prior Analytics, and often
recurs to it in the Rhetoric, calling it here the " Rhetorical syllo
gism" z for the obvious reason that it does not convince by pro
ducing scientific certitude, but only persuades, and is therefore
extensively used by the public speaker whose object is to win the
adherence of his audience.

The <rr)/j,€iov is some particular fact which is regarded as prob
able evidence either of some other particular fact, or of the truth
of some general assertion.

For example : —

" Ambitious men are liberal ;

" Pittacus is ambitious ;

" Therefore Pittacus is liberal."

Here the ambition of Pittacus is regarded as a sign of his liberality
— one particular fact as the sign of another. If the general prin
ciple " Ambitious men are liberal " were certainly true, ambition
would be no longer merely ^probable sign — cnj^eLov — of liberality ;
it would be a certain evidence — Tetc/jt^piov — 2 of the latter ; and the
syllogism would become a valid proof of fact, producing certitude ;
though it would not be a demonstration, or produce scientific cer
titude. An example of a conclusive argument from a reK^piov
would be : —

" All such combinations of symptoms mean consumption ;

" Here we have such a combination ;

" Therefore this is a case of consumption." 3

Where, as in the former syllogism, the general principle invoked
in the premisses is an et'/eo?, the syllogism may also be rightly
regarded as an argument from a general likelihood or probability.

The enthymemes just given are in the first figure. Here are
some examples of the enthymeme in the second figure, which also
argues from one particular fact to another as signified by the
former : —

" Ambitious men are liberal ;

" Pittacus is liberal ;

" Therefore Pittacus is ambitious."

1 Anal. Prior., II., xxvii. ; Rhet., I., i. and ii. Cf. JOSEPH, op. cit., p. 323 n. ;
KEYNES, Formal Logic, p. 322 ; MELLONE, op. cit., pp. 253-8 ; JOYCE, op. cit.,
p. 253 ; CLARKE, Logic, pp. 356, 429.

2 Rhet., I., ii. » MELLONE op. cit., p. 258.

OPINION AND PROBABILITY 267

Or, again : —

" Murderers flee from the scene of the crime ;
"A. B. flees from the scene of the crime ;
" Therefore A. B. may be the murderer ; " l

— where flight is regarded as a sign of guilt. This by itself is
a very weak argument; but it may help to form a "coil" of
circumstantial evidence. For example, suppose that A. B.'s house
is searched, and that his clothes are found to be bloodstained, we
may add this item to the evidence : —

" The murderer's clothes must have been bloodstained in the

struggle of which there are unmistakable evidences ;
" A. B.'s clothes are bloodstained ;
" Therefore A. B. is probably the murderer."

Suppose, further, that we can argue thus : —

" The murderer's boots made these fresh foot-marks ;
"A. B.'s boots fit exactly into these foot-marks ;
" Therefore A. B. is probably the murderer."

Those three "circumstances" together have considerable weight.
Now suppose there is observed something very singular about the
foot-marks — some altogether peculiar arrangement of the nail-
marks, for example, — and that the nails of A. B.'s boots are found
to reproduce exactly this arrangement : we at once feel the enor
mous force of such a circumstance. We conclude that A. B.'s
boots were worn by the murderer, for no other boots could, in the
circumstances, have produced the foot-marks in question : —

" The boots worn by the murderer produced these foot-marks ;
" The boots that produced these foot-marks are A. B.'s boots ;
"Therefore the boots worn by the murderer were A. B.'s
boots."

And A.B. alone was seen to flee from the scene of the crime ;
and his clothes are blood-stained. Such is a simple example of
circumstantial evidence.

It is clear that all arguments from analogy and example fall
into the form of enthymemes in the second figure (234).

Where a particular fact is alleged as a sign or indication of the
truth of some general principle the enthymeme falls naturally into
the third figure. For example : —

1 MELLONE, op. cit., p. 258.

268 THE SCIENCE OF LOGIC

11 Socrates was just ;

" Socrates was wise ;

" Therefore the wise are just."

Here, Socrates may be regarded as an indication or illustration —
a a-Tjfteiov — of the connexion between wisdom and justice. The
" inductive syllogism," which suggests a universal law from an
enumeration of instances (207), is an enthymeme of this kind.

The " probable syllogism " was called an " enthymeme " by Aristotle be
cause it proceeds from what is found by reflection ((vdv^ais ; eVtfi^eicr&u)
to be a general likelihood, or a symptom of the inferred conclusion. And he
called the same kind of argument a " rhetorical syllogism " because orators,
whose function it is to persuade rather than to convince, have frequent recourse
to it. The enthymeme in the modern sense of this term, might also be called
a " rhetorical syllogism," inasmuch as it is not customary in ordinary discourse,
and outside formal disputation, to give expression to all the constituent judg
ments in a process of reasoning. It is not clear why the term enthymeme came
to be applied to a syllogism with a suppressed premiss or conclusion. Possibly
owing to a misinterpretation of Aristotle, Anal., Prior., II. xxvii. — where he
says : " If one premiss is stated we have only an [argument from an] indica
tion ; if the other is also stated, we have a syllogism 'V He does not mean
here to suggest that the syllogism so stated is not an enthymeme ; for it is an
enthymeme in Aristotle's sense whether one or both premisses are expressed.
In another passage — Rhet., I., ii., § 13 — he observes that if one premiss of an
enthymeme be such that it is easily supplied by the hearer, there is no need to
state it expressly.s Those passages may account for the modern use of the
term.

264. ESTIMATION OF PROBABILITY : THE CONCEPT OF
"CHANCE". — \Ve have already remarked that it is quite impos
sible to measure the degree of our subjective, mental assent to a
probable judgment, by any mathematical calculus. It is, how
ever, sometimes possible to apply such a calculus to the objective
factors themselves which point to the truth, or to the falsity, of a
judgment. This method of dealing with the data for probable
judgments may be considered here as a distinct source of these
latter (263).

There are innumerable phenomena around us which happen
we know not how or why. We are unable, by induction or other
wise, to discover their causes. We do not know the laws according
to which they happen. Hence we have no scientific knowledge,

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OPINION AND PROBABILITY 269

and no certitude, as to how, when, where, or in what circumstances,
they will recur in the future, or have occurred in the past So
far as we know, they occur "irregularly": they just "happen"
or "chance " to occur. Hence we speak of the "chances" for or
against the occurrence of some such event at a given time and
place, or in a given set of circumstances ; and we endeavour to
calculate those "chances," for and against its happening, and so
to "estimate its probability ". Special treatises have been written
on the nature and rules of this logical calculus of probability or
chance l ; but in a general treatise on logic a brief statement of
the leading principles and their applications will be sufficient.
The first important concept that calls for examination in this
connexion is the concept of chance.

Chance is not the negation of causality : nothing is casual in
the sense of being causeless. Every event, everything that happens
or begins to be, has a cause. There is a causal connexion be
tween any two events either of which has any positive influence
on the production or happening of the other. Induction aims at
discovering causal connexions. But there are phenomena, con
nected in time and space, which have no such obvious causal
influence on one another. Their concurrence in time or space is
a "coincidence," a "chance" concurrence. In seeking for the
causes of a given phenomenon we meet several of its concomitant
circumstances, and recognize these to be " irrelevant ". Their
presence or absence has no influence on the phenomenon ; the con
nexion between them and it is not causal but casual — a " chance "
connexion.2

For example, a person speaks of having " chanced " or
" happened " to meet a particular old friend from the country,
at a certain street corner in town, at a particular moment when
he was just in the act of posting a letter to that friend. It was
a " remarkable coincidence," and " unexpected occurrence ".
Each part of the total phenomenon had its causes, but neither had
any influence in bringing about the other, nor can we see in the
causes of either part anything that would of its nature have any
influence in determining the coincidence, in time or space, of the
other part. Thus, the coincidence of phenomena not connected
as cause and effect, or of various " indifferent " or " irrelevant "

1 C/. VENN, Logic of Chance ; BOUDON, Le calcul des probability ; BERTRAND,
Calcul des probabilites ; MANSION, Sur la portee objective du calcul des probabilites.
9 C/. VENN, Logic of Chance, p. 245.

a?o THE SCIENCE OF LOGIC

elements of the same complex phenomenon, we regard as " due to
chance," because they are unexplainable, unaccountable, irre
ducible to law, by any effort of ours.

Similarly, there are phenomena whose recurrence is so irregular,
arbitrary, uncertain, devoid of any element of uniformity, that we
can entertain no hope of tracing the laws according to which their
determining causes combine to bring them about. Thus, a homo
geneous, cubic die has each of its faces marked with a different
number of spots, up to six. In a dozen throws, the three and the
five have turned up three times each, the two and the four twice each,
the one and the six only once each : no correspondence of the order
in which the figures appear, with the arithmetical series, one to six,
or with any other known principle or law : no correspondence
with the order of results in any other dozen of throws. So,
too, the trump in a deal at cards "chances " or "happens " to be
the ace of hearts, or the king of diamonds, etc. Such phenomena
we describe as matters of " chance ".

Of course, when we say that a definite occurrence of that sort
is the result of "chance," we do not mean to deny that the actual
result was fully and perfectly determined by the whole combina
tion of causes that brought it about ; we merely mean that we
are unable to see how those causes necessarily determined or
brought about the actual occurrence. We fail to see anything
either in the die or in our casting of it, in the cards or in our
shuffling of them, in the coin or in our tossing of it, to necessitate
the turning of the six rather than of the one, of the ace of hearts
rather than of any other card of the pack, of the " head " rather
than of the "tail " of the coin. So far as we know the nature of
all the antecedents in such cases, we see absolutely nothing in the
dice or the cards or the coins, or in our manipulation of them,
to bring about any one result out of a large number of equally
possible alternatives, rather than any other. And yet the fact that
this result happened, and not any other, is an all-sufficient proof
that there were at work influences which determined the occur
rence of it rather than of any other. But all we know about the
antecedents is that they must cause some alternative ; and because
we do not know which, we say that it "chanced" to occur.
Thus, "chance " is a name for our ignorance.

So, also, the fact that some one particular phenomenon, or part
of a phenomenon, accompanies or coincides with some other in
time and space throughout our experience — this fact too must

OPINION AND PROBABILITY 271

have its sufficient reason, even though we may fail to see it. We
can see no connexion between the causes of each. But we are
forced to think that if our minds were able to analyse fully, and
to trace back clearly to their sources, each set of causes, we should
necessarily find between them some connexion capable of account
ing for the coincidence. In other words, a mind which under
stood all things, all reality, all causes, fully and adequately, would
see not only the reasons and causes of the isolated elements them
selves, but also of the interrelations and connexions of concomi
tance or sequence between all those elements ; and would see how
all those causes conspired, each according to its nature, and to the
law of its own activity, to produce each of the individual events
that appear to our limited intelligences so irregular, so devoid of
order, so incapable of being known scientifically, or reduced to taw.1

We are forced to those conclusions on the ground that every
event has a cause ; that the real world is knowable, intelligible,
rational, or, in other words, that it offers an ultimate sufficient
reason, in explanation of every element and of every coincidence
of elements, to a mind capable of comprehending it. It is easy
to understand, therefore, that for an Omniscient Intelligence there
can be no such thing as chance : the sufficient reason of every
event is fully discerned by such an intelligence in the totality of
its causes. But such perfect knowledge is for us an unattainable
ideal, on account of the limitations of our minds confronted with
the complexity of the real world. Not to speak of the self-deter
mining activity of the human will, or of the conscious causality of
the animal kingdom, or of vital activities in the organic world,
even physical causes in the inorganic kingdom are so complex and
hidden in their combinations that we can never hope to attain to
such a knowledge of them as will enable us to dispense with the
concept of " chance " (267).

But even though for an Omniscient Intelligence there can be
no such thing as chance, and even though the concept has its
origin in the finiteness of our minds, yet it cannot be regarded
as a purely subjective concept ; for the ignorance whence it springs
has a very real and objective foundation in the complexity and
vastness of that world which the finite human mind is ever trying
to understand.

Mr. Welton, understanding by " cause " the " sum-total of the determining
conditions," gives the following account of the concept of chance.2 " When in
1 VENN, of. cil., ibid. * Logic, vol. ii., p. 165.

272 THE SCIENCE OP LOGIC

any particular case we do not know what conditions are operative, we cannot
tell, on the one hand, what result will appear, nor, on the other, can we say
positively what conditions have produced a certain given event. In such cases
we are accustomed to speak of the occurrence as due to chance. But our whole
conception of the unity of nature forbids the idea that any element of reality
can be really casual. [The turning of any particular face, for example, is casual
relatively to the die itself, in the sense that the die itself contributes nothing to
wards this particular result ; and casual relatively to the whole concrete cast
of the die, in the sense that we do not know what combination of antecedents
brings about the result in the concrete case ; but not, of course, in the sense
that the result has no determining antecedents ; it must have them, by the prin
ciple of causality. Hence the author continues :] Every detail is, in the strictest
sense, necessary, and determined absolutely by conditions — all is causal, nothing
casual [for ' casual ' here means, equivalently, ' causeless ']. Were our know
ledge complete, then, the idea of chance would disappear ; it is due solely to
the imperfection of that knowledge. This imperfection is, of course, greater
in some cases than in others ; it may affect the event as a whole, or it may
only affect some particular aspect of it. But, even with imperfect knowledge,
we are often called upon to come to a decision or to act. The question then
arises as to what we ought rationally to expect."

265. CONDITIONS FOR THE MATHEMATICAL ESTIMATION
OF PROBABILITY. — We have now seen that "chance " or " coinci
dence " connotes simply the possession of imperfect or incomplete
knowledge about the antecedents or causes of a phenomenon.
This is the first condition for the application of a calculus of
probability to the data of our experience : a knowledge sufficient
to assure us, for example, that a phenomenon must happen in
some one or other of a definite number of alternative ways, but
insufficient to assure us in which of these ways it will happen.
We know, for instance, that in any single throw of a die the
laws of gravity, inertia, motion, elasticity, action and reaction, the
antecedent position of the die and of the box, the intensity, direc
tion, and duration of each rattle, and innumerable other unknown
and inappreciable influences — all conspire together for the pro
duction of the actual result of this particular throw. But we are
conscious, on the other hand, that the combination of factors de
termining this particular result, rather than any other, surpasses
our comprehension. x We know the general set of antecedents which
gives rise to some particular result out of a number of possible
alternative results. We recognize that while many of them are

1 Cf. WBLTON, op. cit., p. 167 : " For example, if a penny is tossed it will fall
with either head or tail uppermost. Now, which will be uppermost in any particular
throw will be exactly determined by such conditions as the position of the coin at
starting, how it is grasped in the fingers, the force and direction of the twist, etc.
But what special form these conditions will take we are totally ignorant. ..."

OPINION AND PROBABILITY 273

an inseparable portion of the experience, or even exert a positive
causal influence on the general result — the die itself and its natural
properties, for example, — yet they contribute precisely in the same
way to every possible alternative result, and are therefore rightly
called " indifferent " causes of any one result in particular. We
know, too, that in each particular experience there are some ante
cedents whose combination determines this particular result rather
than any other. But we do not know what these are, or, at least,
how exactly they will combine. And it is our ignorance on this
point that allows and obliges us to estimate the " chances " or
" probabilities " which the indifferent antecedents have of being
united in a given case with a given concrete result out of many
possible alternative ones. In throwing dice, for example, we
know that the die itself — so long as it is not " loaded " for the
purpose of giving it a " natural inclination " to fall on some
particular face — is equally indifferent to each of the six faces.
Furthermore, we are unable either to control, or estimate, or re
duce to any law, the actual combination of the numerous influences
that determine a particular result — forces which emanate with
varying intensity from the thrower at each successive throw, and
forces which, like gravity, operate independently of him.1

There is a second condition to which our data must conform,
before we can apply to them any definite rules for the estimation
of probability. The same general set of conditions and ante
cedents must be present and operative throughout the whole
region of time and space from which these data are drawn. An

1 " Take such a simple example as that of dropping a Stone to the ground. We
say, in accordance with the common expression of the causal relation, that if the
stone be dropped again just as it was before, it will fall on the same spot. True ; and
for most practical purposes the thing can be done readily enough ; but if perfect
quantitative accuracy were required we should soon find that we had undertaken a
troublesome task. The stone must be held in exactly the same position as before,
for the friction of the air influences its fall ; it must be dropped from exactly the same
height and over the same spot on the floor ; the atmospheric currents, nay the very
temperature of the air, must remain unchanged ; and so on indefinitely with further
demands, as quickly as those already formulated were assumed to be satisfied."

" If it be urged that all this is merely useless subtlety the retort is simple, and, I
think, conclusive, viz. that many millions of pounds have changed hands in accord
ance with these conditions of things. It is simply because we cannot do the same
thing over again, or calculate how far we shall fall short of doing so, even when our
instrument in hand is purposely made of as accurate a shape as possible, that the
roulette and the die can be employed for gambling purposes. So impossible is it
found to be to spin a top twice with the same velocity, or to discharge a cube twice
from the same position, that the fanatics of the gaming table never dream of pre
dicting results from this side, but put their trust in appeals to statistics and other
such considerations." — VENN, Empirical Logic, pp. 65, 66 ; cf. ibid., pp. 100, 105.
VOL. II. 18

274 THE SCIENCE OF LOGIC

unknown alteration in those influences would upset our calcula
tions. For example, were the uniform shape of a die, or the
uniform density of its texture, to alter imperceptibly, the equality
of alternatives which is essential to the calculation of probability
would be destroyed. It is, in fact, by determining experimentally
whether some one alternative occurs more frequently than it
should occur if the chances were equal, that we detect the exist
ence of a " bias " which may lead to the discovery of some causal
connexion or law (267). l In throwing dice, for instance, the five
may be found to turn up 97 times out of 600 trials, and 1003
times out of 6000 ; from which it is concluded a posteriori that
the probability in favour of the turning of five lies between ^V^
and !£$§ — or is about £. The experiment — so far as it goes,
for it cannot be carried on indefinitely — verifies the supposition
that the sum-total of the influences at work was indifferent, and
hence made as often for any one as for any other alternative.
It is only, therefore, when we have the agencies under our own
control, and can experiment with them, that we can secure with
absolute certainty the constant prevalence of the same set of con
ditions. This is secured in all ordinary " games of pure chance ".
Before inquiring how far it can be assumed to prevail in natural
phenomena (268), we will examine the application of the calculus
of probability to data that are assumed to fulfil the two conditions
just set forth. We may observe here, however, that when the
requisite conditions are present, the estimate can be made for past
events as well as for future ones. The theory applies independently
of time. No doubt, its usual application is to games of chance,
dealing with a future event. But when some one, we do not
know which, out of a certain definite number of equally possible
alternatives has happened, we can apply the theory to determine
what degree of probability there is that such a definite alternative
has happened.

"Thus, for example, it is extremely improbable that a hand at whist
should consist entirely of trumps. Yet the probability of this is no less than
that of any other one definite hand. It is its interesting character which draws
special attention to it, and causes us to recognize how enormous are the odds
against it. This we do not recognize in the case of other hands. If, then, a
person told us he had held a hand of thirteen trumps the previous evening we
should probably feel more hesitation in believing him than if he told us he had
held a hand consisting of certain definitely named cards. Yet the antecedent
improbability would be no greater in the one case than in the other. Were

1 Cf. JOYCE, op. cit., p. 372 ; VENN, Logic of Chance, pp. 78-82.

OPINION AND PROBABILITY 275

the person, however, to claim that he had, previously to playing, written down
the contents of a certain hand, and that he had been actually dealt that hand,
we should probably hesitate to receive his statement just as much as if he told
us he had been dealt thirteen trumps ; for the previous defining of the hand
would have made the odds against it as apparent as in the other case. When
we hesitate to believe the statement of such coincidences it is because we feel
that the odds against the occurrence were antecedently very great, and we
balance that with the odds in favour of the credibility of the witness. If we do
not doubt his credibility we receive his statement in spite of its antecedent im
probability, for to assume that the extremely improbable is impossible is to fall
into a dangerous fallacy." 1

The data for probable knowledge furnish us with some certain
knowledge ; without some certitude there could be no probability.
What we are certain of in regard to such data may be expressed
in the form of a disjunctive proposition : e.g. " The result of
throwing a die will be to turn up either the one, or the two, or
the three, or the four, or the five, or the six " ; or symbolically,
" A is either X-^ or X^ or X3 ... or X£ — where A represents a
particular throw, and Xlt X2, etc., the possible alternative results.
We do not know whether the result of the throw A will be X± or
not ; whether the definite judgment " A is X± will prove true.
But it may be true ; we are entitled to entertain some degree of
rational expectation that it will be true ; and the question now is
whether we have any means of measuring the likelihood, the
rational expectation we may entertain, of its truth. The mathe
matical calculus of probability places such a means at our dis
posal. It aims at expressing probability by means of fractions.

When the chances for and against an event are equal, we are
left in absolute doubt about its happening ; the probability is then
expressed by the fraction •£. When the chances are all for and
none against, the fraction has grown to unity, and the probability
becomes a certainty that the event will happen, or has happened.
When the chances are none for and all against, the fraction has
decreased to zero, and represents certainty against the event.
But those are limits towards which the chances may tend in
definitely without ever absolutely reaching them. The event is
said to be "probable" or "improbable" according as the fraction
is greater t>r less than £. Close approximation to the positive
and negative limits — to unity or to zero — are spoken of as
"moral certainties" and "bare possibilities" respectively.

We have now to examine briefly, in their logical aspect, the

1 WELTON, op. cit., pp. 169-70, 178-80. C/. BORDEN P. BOWNE, Theory of
Thought and Knowledge, pp. 187-8.

18 *

276 THE SCIENCE OF LOGIC

mathematical principles laid down for the estimation of prob
ability, considering those processes of estimation as modes of
reasoning from various combinations of disjunctive judgments.

266. RULES FOR ESTIMATING PROBABILITY. — (i) Simple
events. The probability of a simple event is expressed by a
fraction whose numerator is the number of favourable alternatives,
and denominator the total number of alternatives.

Thus, if A can occur, or has occurred, in any of n different ways, their
sum, A, will represent certainty (for we know A will occur, or has occurred),
and is best expressed by unity. The probability of any particular case out of
the n is, therefore, i/«. Out of «, the total number of alternatives, (n- i) are
against, and i for, the occurrence of any given alternative. As there are six
faces to a die, one only of which is marked 4, and the others differently, the
chance of turning some of the others, besides the 4, is (n— i) or five times
greater than the chance of turning the 4 ; i.e. the probability for the 4 is i/»,
or i, the probability against it («- i)/», or $, Again, as there are fifty-two
cards in a pack, but each particular value or number is present in four
different ways, the probability in favour of drawing some particular value will
be /j, and the probability against it $f, as there are four chances in favour of
any particular value and forty-eight against. If there be a question of draw
ing some particular card, e.g. the ace of hearts, the probability is only ^.

(2) Compound events. If an event is compound, i.e. made up
of a number of simple events connected together, these latter will
be (a) either independent, or (£) dependent on one another ; hence,
two cases arise.

(a) Compound of independent events. The probability of an
event composed of a number of independent simple events, whether
simultaneous or successive, is the product of the probabilities of
the latter taken separately.

Suppose, for example, A and B to be two urns, A containing two white
balls and one black, say w^ -a>, and bv and B likewise containing two white
balls and one black, say a/,, «/4 and £a : what is the probability of drawing
(simultaneously or successively, it matters not) a black ball from each ? The
draw from A may be represented by the proposition, " If S is A it is either
o/i or a/2 or b\ " ; that from B by the proposition, " If S is B it is either vu3 or
o/4 or <V'. Now, if we combine both experiments, we find that the total
number of possible ways of drawing two balls is 3 x 3, as any one of the three
possible draws from A may combine with any one of the three possible
draws from B. The double draw will be expressed by the proposition : "If 5"
is AB it is either a/t 0/3, or TV. a/4, or w1 b^ ; or w\ ws, or w% a/4, or o>2 £, ; or
bl it/-.,, or bi o/4, or &l b* " : from which we see that the probability of a double
black is £, i.e. the product of the two simple probabilities i x i. We see,
likewise, that the probability of drawing two whites is |, or J x $, a further
verification of the principle. " Lastly, as the probability of white is in each
case !, and that of black is I, so [| x J = ] f is the probability both that the

OPINION AND PROBABILITY 277

drawings will give first white and then black, and that they will yield first
black and then white ; this is shown to be true by the fact that the final pro
position yields two cases in which white is followed by black, and two cases
in which black is followed by white." 1

Similarly, if the first urn contains 3 white and 4 black, and the second
4 white and 5 black balls, the number of possible ways of drawing two balls
is 7 x 9 = 63, the number of ways of drawing two whites 3x4=12, and of
drawing two blacks 4 x 5 = 20 ; consequently the probability of drawing
two whites is H and of drawing two blacks f#.

It will be seen that there is no difference in principle or theory between
this sort of compound, and the simple event itself, the disjunctive proposition
expressing the former being a combination of the alternatives of each inde
pendent simple event.

(£) Compound of dependent events. If two simple events are
so connected that the occurrence of the first affects the probability
of the occurrence of the second, the probability of the compound
event will be the product of the probability of the first with the
probability of the second as affected by the first,

For example, what is the probability of drawing two white balls in suc
cession, without replacing the first drawn, from an urn containing two white
balls and one black one? If a black is drawn first the estimate is rendered
impossible. The probability of drawing a white first is f . If it is drawn, the
constitution of the urn for the second draw is modified by the first draw.
There are now only two balls, one white and one black, in the urn ; and the
probability of drawing the white is $. The two draws may be represented by
the two propositions : —

A is either w} or «/, or b\
B is either TV* or b^

Where b.^ is the same ball as bv and o/2 the white ball that remains after vt^ or
o/a has been extracted. Those two propositions combined will give six alter
natives, of which two are pairs of whites : " AB is either a/, a/3, or a/i £2, or
TV?, -a/;J, or wa bi, or ^-0/3, or 6\ b^ " ; from which we see the probability of
drawing two whites is |, or the first simple probability multiplied by the second
as affected by the occurrence of the first, i.e., \ x \.

The same result may be stated in this way : The probability of drawing a
white first, and consequently of the second draw taking place at all, is \. In
the hypothesis that it does take place, the probability of drawing the white
again is \. Therefore the probability of drawing two whites is \ x \ = \.

(3) Total probability of events which may happen in a plurality
of ways. When the same simple event may occur in many inde
pendent groups of conditions, its total probability is the sum of
the probabilities that the various conditions will be verified.

For example, what is the probability of turning a " head " in one or other
of two consecutive throws of a penny, or (which is the same) in one throw of two

1 W ELTON, op. cit., p. 173, whose treatment is largely followed in the present
section.

a?8 THE SCIENCE OF LOGIC

pennies? The total number of possible combinations of head and tail in either hypo
thesis is 4 : h\h.a h^ /,^2, /,/2 ; and out of these four alternatives, three yield a
head. The probability is therefore \. Now this is the sum of the two separate
simple probabilities. For, if we toss one coin twice the chance of getting a head
the first time is \ ; the chance of the second toss taking place at all is contingent
on the failure of the first, i.e. is \ ; and the chance of its securing a head if it do
take place is \. Therefore the total chance from the second toss is \. Con
sequently the total chance by both tosses is \ + * = £ . If we toss two coins,
A and B, simultaneously, the chance of A turning a head is i, and the event of
its failure being combined with the heading of B (/^2) is \ ; or that of heading
B I, and of combining its failure with the success of A \ ; in either case the
total probability of securing a head is 4 + \ = |. Or again : What is the prob
ability that a throw of two dice, A and B, will yield any given number be
tween 2 and 12, say 7 ? There are 36 alternatives in a throw. The desired
number, 7, can be obtained in six different ways, viz. when A and B are re
spectively I and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and i. Now the prob
ability of the occurrence of any individual alternative of these she is •& ; and
as any one of them will yield the desired result, 7, the probability of the occur
rence of the latter is the sum of these six probabilities, or 3°ff= i .

267. INVERSE PROBABILITY : BERNOULLI'S THEOREM :
ELIMINATION OF CHANCE.— So far, the problems examined have
been all of the same general character, namely : Given the con
ditions capable of realizing indifferently any one of a known num
ber of possible alternative events, what is the probability that a
particular alternative, a, will occur ? This is called direct or a
priori probability. The inverse problem is the following : Given
that a certain event has happened, to which of a number of pos
sible alternative causes is it most probably due ? The event here
in question always yields some data for an indirect or a posteriori
probability, and is, of course, always an actual application or
realization of some a priori probability. The determination of
this a priori or antecedent probability will give a probable know
ledge of the actual causes from which the phenomenon or event
has followed. Thus, for example, an urn is known to contain
three balls, but their colour is unknown. We are asked to deter
mine their colour by repeatedly drawing one and returning it.
We draw a white : it gives us no reason to conclude anything
about the colour of the others. But if we next draw a black we
thereby know that the contents of the box may be either w w b
or w b b ; but that these two do not exhaust all the alternatives,
another possible one being w b x, where x may be another colour.
If, however, we continue to draw only blacks and whites, the
probability against x being some third colour (say red) rapidly
decreases. For if a red ball were there, the probability against

OPINION AND PROBABILITY 279

its being drawn the first time would be §, the second time | x |,
. . . the eighth time (f)8, or less than \\. If, therefore, it has not
appeared in eight draws, the probability that there is no such ball
in the urn is over 24 to I, — which would generally be regarded
as practical certitude.

Again, suppose it known that the three balls are either black or white, or
a combination of black and white in an unknown ratio. This gives four pos
sible alternative contents before the drawings commence, w w w, w w t>, w b 6,
b b b ; from which we gather that the probability in favour of a particular con
tent of the urn is \. Now if a white ball be drawn first, it excludes the possi
bility of b b b. As the remaining three alternatives show six possible ways of
drawing a white ball, the probability in favour of drawing any individual white
ball is \. Therefore the probability that the white actually drawn was from
ivivw, is £ or i, that it was from wwb, \ or ^, that it was from w b l>, I. That
is how the probabilities stand at the end of the first drawing. If, however, a
second drawing brings forth a black ball, w w u> is excluded, and the alterna
tives wwb and w b b are regarded as equally probable. But if a third drawing
gives a white, it makes the probability of wwb twice as great as that of tub b,
and its absolute probability therefore |. For, assuming wwbio be real, the
probability of securing the result actually attained, i.e. of drawing a white, a
black, and a white, is I x \ x | = 7*T ; whereas the total probability of such a
combination from zy £ £ is J x -5 x J = ^y, or half as great as the former.

The problem of estimating inverse probability — of determin
ing to which of a number of possible alternative antecedents, or
groups of antecedents, a given event or series of events is due —
is identical with the problem of determining the true magnitude
of a phenomenon by a series of approximate measurements (246,
268) ; for that problem might be stated thus : " Given a series of
registered approximate measurements of a magnitude, what is
most probably the true magnitude that has yielded those measure
ments "?

When it is said that the probability of heading a coin is •£, or
of turning up a definite face in casting a die, £, does this imply any
further certitude in regard to our data, beyond that already re
ferred to (265) — the certitude that some face of the coin, or of the
die, will turn up at each throw ? It does not, about any individual
throw ; but it does imply further certitude about the nature of the
average of an indefinite number of throws : granted that all the
alternatives are and remain equally probable, we are certain that
in an indefinite number of throws the coin would be headed on an
average every second throw, or a definite face of the die turned
on an average every sixth throw. In other words, we are certain
that the a priori probability is £ in one case, and \ in the other.

28o THE SCIENCE OF LOGIC

Although we cannot be sure that the result of any particular
throw will be a head, or a six, we can be sure that if we kept
on throwing indefinitely, the heads obtained would be •£, or the
sixes ^, of the whole series of trials. The reason for such certitude
about the results of a hypothetical indefinite series of experiences
is a negative one : because, namely, any other result would be un
accountable, would be an effect without a cause. But in any definite
series of experiences we are prepared to find that the actual results
may deviate somewhat from what the apriori probability points to —
from i or \ in the cases just mentioned. We are justified, how
ever, in expecting further, that (i) the greater the total number
of experiences the more closely will the actual results approximate
to the a priori probability; though (2) in a larger number of ex
periences we are prepared to find that the deviation from the a
priori probability is in itself greater than in a smaller number of
experiences. In other words, as the series of trials extends, the
absolute magnitude of the possible deviations will also increase ;
but its relative magnitude, its proportion to the total number of
trials, will decrease : so that the actual results tend progressively
towards the realization of the antecedent probability.

Within what limits, in any given series of experiences, should
the actual results fluctuate around the antecedent probability ? What
is the largest deviation that we should expect, in a given set of
trials, from a known or assumed antecedent probability? If we
could solve this problem, we could in some degree eliminate
chance, and conclude that the excessive deviation must be due to the
operation of some cause (264). " If we are able to say," writes Fr.
Joyce,1 " that in a definite number of trials, certain limits will not
be overstepped, and if it is discovered that the result is totally at
variance with our mathematical estimate, then it becomes clear that
we were mistaken in our view as to the nature of the case. . . .
A loaded die gives, it is true, very irregular results. Were it not
so, it would be detected at once, and so defeat its own purpose.
But there comes a point at which, after a certain number of trials,
the mathematician is able to say that the appearances of the six
exceed the limits of mere chance, and that the very act of throw
ing must tend to turn that face uppermost."

A noted mathematician, James Bernouilli (1650-1705), devoted
many years to the study of this whole question of deviations from

1 op. dt. P. 378-

OPINION AND PROBABILITY 281

a priori probability.1 According to his researches, if, for instance,
the antecedent probability of an event is f " the odds are 1000 to
I that in 25,500 trials the event shall occur not more than 1 5,841
times, and not less than 14,819, — that is, that the deviation from
15,300, the ideally probable number, shall not exceed -^ of the
number of trials".2 Or, again, if from an urn containing white
arid black balls in the proportion of two white to one black, we
were to draw 90,000 times, returning each ball after drawing it,
the number of blacks drawn should be between 29,400 and 30,600,
showing a deviation of not more than 600, that is ?%%$?;> °r TTTT>
from s> which is the antecedent probability. Were we, how
ever, to increase the number of draws 100 times (to 9,000,000),
the deviation should increase only ten times, i.e. to 6000, the
number of blacks drawn lying between 2,994,000 and 3,006,000
— which would be a deviation of only J^TT frorn the antecedent
probability.

We see, then, that as the number of experiences is multiplied,
the absolute magnitude of the fluctuations also increases, but
the amount of their difference from the antecedent probability
diminishes.3 The first of those two facts enables us to foretell
the certain ruin, in the long run, of any one who continues to play
at a fair or equal game of chance. Suppose, for example, that
two persons, A and S, play at tossing pennies one at a time, each
player putting a penny stake on each toss, A betting for head,
and B for tail, throughout. While A is very wealthy, however, B
has only a shilling. The latter will be financially " ruined " when
the number of heads exceeds the number of tails by twelve. Now
the probability that this will take place within a certain number
of throws can be calculated, and will be found to increase steadily
and to tend ever towards certainty according as the total number
of throws increases. From the second part of the theorem —
that the actual results tend progressively to approximate towards
the antecedent probability — we infer that the greater the number
of experiences the greater will be the value of the results in point-

1 Cf. CROFTON, art. on " Probability " in the Encyclopaedia Britannica ;
BAUDOT, art. on " Probability " in the Nouveau Dictionnnire des Sciences.

'JOYCE, ibid., p. 377.

3 " Le theor£me de Bernoulli; revient a ceci : ' Si on fait un nombre inde"finiment
croissant d'6preuves, 1'^cart est infiniment petit par rapport au nombre des e"preuves '.
II faut bien remarquer quec'est 1'e'cart relatif qui tend vers ze"ro, l'e"cart absolu devient
au contraire de plus en plus grand. "—BAUDOT, Probabilite ; apud JOYCE, ibid., p.
377. "• a.

282 THE SCIENCE OF LOGIC

ing with ever increasing probability to the actual alternative ante
cedent, or combination of antecedents, from which those results
actually followed ; the greater, too, will be their value in re
vealing to us the real nature of the supposed alternatives, and
in thus " eliminating chance ".

268. APPLICATION OF THE CALCULUS OF PROBABILITY TO
NATURAL AND SOCIAL PHENOMENA.— The mathematical estima
tion of probability is best illustrated in games of chance, where it
is applied to specially prepared materials. Can we utilize it to
estimate probability in regard to the occurrence, or recurrence, of
complex natural and social phenomena, the causes of which we
know either not at all or only imperfectly? Attempts have been
made in various directions to apply it to such data — with, how
ever, no remarkable degree of success. As a matter of fact, the
degree of rational expectation we may entertain about the future
recurrence of any natural phenomena which we have repeatedly
observed occurring in the past, but are unable as yet to refer to
its causes, — such probability we never think of basing on the con
siderations that apply to an artificial game of chance, or of
measuring by means of the calculus outlined above. Rather,
in such cases, our first endeavour is to detect uniformities of
coexistence or sequence even among phenomena which appear
at first sight irregular and unconnected ; and we do so by com
piling statistics, and seeking for hitherto unobserved concomitant
variations (243, 249). Research in this direction often leads to
the discovery of causes.

Suppose, however, that we are in the presence of a phenomenon
which sometimes happens and sometimes does not happen in
circumstances of the same general character : we may set ourselves
the task of discovering whether or not this set of circumstances
as a whole, so far as we know it, is " indifferent " to the occur
rence or non-occurrence of the event in question. We are face
to face with a result recurring irregularly in certain condi
tions. We want to find out, if possible, whether it is causally,
or only casually, connected with those conditions. For this pur
pose we see whether or how far we can " eliminate chance" by
applying the rule for calculating inverse probability (267). But
there are two considerations which reveal the difficulty of such a
procedure. One is that we may possibly know very little about
even the general set of antecedents to whose combination the
event, when it does occur, is really due. The other is that this

OPINION AND PROBABILITY 283

general set of antecedents, whatever it is, may be gradually chang
ing in character, without our knowledge (265). Especially in
regard to social or partly social phenomena — the frequency of
various crimes ; the rate of births, marriages, and deaths ; politi
cal or economic crises, etc. — our uncertainty as to the permanence
of their causes and conditions must always render our probable
estimates about the future very precarious. Yet this seems to be
the only direction in which we can reasonably utilize the calculus :
that is, for the purpose of discovering whether or not certain
given conditions have only an " indifferent " or " casual " con
nexion with an event, or whether, on the contrary, we can elimi
nate chance by detecting a " bias," or, in other words, a causal
connexion, between the event and some of those conditions.

Curious attempts have been made, however, by various logicians, to de
termine mathematically our probability as to the future recurrence of an event,
by an appeal to the number of times we have observed the event to have
occurred in the past. Thus, according to Professor Welton, following Lotze,1
the occurrence of an event once may be taken as one reason for expecting its
recurrence. Apart from that, the chances for and against its recurrence would
be equal. There are, therefore, two reasons altogether for expecting its recur
rence and one against expecting it ; so that the probability of its recurring is
§. Generalizing from this, we see that if an event has occurred m times, the
two possibilities of its recurring or not, once again, make the total number of
alternatives m + 2, of which m + i are favourable. The probability of re
currence is therefore Evidently, then, uncontradicted experience

m + 2

should give rise rapidly to a very high probability, which would continue to
grow with continued experience. That the sun has risen daily for 5000 years
would make the probability VHHli that it will rise to-morrow. " It will be
seen," he continues, " that this calculation of probability is the true basis of
induction by simple enumeration. The formula shows that with wide and un
contradicted experience the probability that an empirical law which summarizes
that experience will hold good in one more case is very high. But it also
shows that extension of it beyond the realm of actual experience becomes
increasingly uncertain with increase in the width of that extension. For, if the
formula is written to show the probability that an event which has occurred m

times will happen n 'times more, it becomes m + — for m + 2 in the

(m + n + i)

original formula = m + i + i, where i is the number of new cases, i.e. n—
which obviously decreases in value as n is increased. Again, another modifi
cation of it shows how the actual experience of the failure of the event, weakens
the probability of its recurrence. For if an event has occurred m times and
failed to occur « times under circumstances where it might have been expected
to happen, then there are already m + n cases ; the possibilities that it may or

1 LOTZE, Logic, § 282 (5)— apud WELTON, op. cit., ii., pp. 180-82. Cf. VENN,
Logic of Chance, pp. 196 sqq. ; 358 sqq.

284 THE SCIENCE OF LOGIC

may not occur again add ^ more, and thus, the probability for its recurrence is

(m ^ l' , which decreases as n increases. In this case, the extension to 4>

(m + n + 2)

more cases becomes still more hazardous, as its formula is i!Li_£] — >

(m + n + p + i)
— decreasing as p increases.

Now, plausible as all this may appear, it can be shown to lead to very

questionable conclusions. The mathematical formula -pLLIL rightly ex
presses the probability of drawing a white ball next time from a bag contain
ing " any number, we know not what, of balls each of which is white or black," l
after we have drawn a white ball m times successively. But in applying the
formula to determine the probability of the recurrence of any natural pheno
menon we are assuming " that the universe may be likened to such a bag " ; •
an assumption which is at the very least so groundless that we need not be
surprised if it leads to some fantastic conclusions.

Again, it is only by experience we can discover whether or how far the
degree of our rational expectation of the recurrence of natural events is in ac
cordance with such a formula ; 3 and even in so far as we do detect some such
accordance, we feel that our probability is not really based on, or measured by,
the formula : in applying the formula to our data " we only give the appearance
of logic to a conclusion we have otherwise gained. Without consulting experi
ence as to the application of the law, and thus making it superfluous, we should
be met by Venn's objection. It has rained for three days ; I have given three
false alarms of fire ; I have fed my chickens three times with strychnine.
What is the probability for the fourth case ? By the rule it is. four-fifths that
it will rain the fourth day, that the neighbours will respond to the next alarm,
and that my chickens will die the next time." 4

These conclusions are a sufficient rtductio ad absurdum of all attempts to

employ any such " rule of succession " as that contained in the formula -

(m + 2)

for the purpose of determining the probability of the recurrence of a
natural event. As a matter of fact, whereas in some cases the repeated oc
currence of an event in the past does make its future recurrence more probable,
in other cases it has the opposite effect (as in giving false alarms), and in others,
again, it has simply no effect : the past facts tell us nothing about the proba
bility of the next occurrence (as in fair games of chance). 8 Hence the original
assumption, that repeated occurrences always increase the probability of re
currence, is illegitimate.

We pass next to another doubtful application of the calculus, namely, to
the domain of human testimony. Professor Welton says 8 that " the theory of
probability is applicable to the credibility of testimony as well as to the pre
diction of a future occurrence ". But, just as in the latter case, so in the former,
we have to make arbitrary or hazardous assumptions which render such appli
cations of the theory practically worthless. " Suppose," he writes, in intro
ducing an example,7 " that two witnesses, the probability of whose accuracy

1 VENN, op. cit., p. 197. *ibid. s ibid.

* BOWNE, Theory of Thought and Knowledge, p. 190.

•VENN, op. cit., pp. 358, 363. *of>. «'/., ii., p. 169. 7 ibid, p. 180,

OPINION AND PROBABILITY 285

is \ and f respectively, agree in affirming the occurrence of an event . . . whose
antecedent probability is \ . . ." But the whole practical difficulty — the
practical impossibility, it may be called — lies precisely in fixing, with any pre
tension to mathematical accuracy, the degree of probability as to their accur
acy in such cases. Of course, if that could be done, the value of their combined
testimony would be £ x \ = T\ that the event occurred, and i x 4 = 7V that
it did not occur : the odds are 6 to I in its favour, and its probability is £.
But how can the accuracy of their testimony be so estimated ? Is it because
they have been found to tell the truth three out of four times, and two out of
three times, respectively ? But then their carefulness and competence (scientia),
no less than their truthfulness (veracitas), must be taken into account. And,
furthermore, the general conditions are so variable, the fluctuations to which
human character is subject under the influence of strong motives and temp
tations are so great and so uncertain, as to render the whole calculation
practically worthless (cf. 260, 261).

To take another instance from the social sciences : A judge delivers a
wrong sentence once in ten times on an average ; can he be compared, as
Condorcet and Poisson have compared him, to an urn containing nine white
balls and one black one ? The comparison is scarcely less inaccurate than
uncomplimentary. Bertrand's criticism is unanswerable : " The urn is as passive
and indifferent to the influences playing upon it as the balls ; and the general
set of conditions remains ever and always the same throughout the repeated
drawings. But the judges listen to the evidence, and consult with one another
about it ; they hear the same facts, and each bases his sentence, whether it be
wrong or right, upon those same facts. And just as one has his reasons for
judging rightly, so has the other his reasons for judging in the opposite sense.
It is not that he has put his hand, as it were, into the urn of his own mind,
and drawn forth by chance an erroneous sentence. No ; the influences that
lead up to that sentence are of quite a different order from those that deter
mine the drawing of a ball from an urn. He has believed a false witness, or
distrusted an honest one, owing to some unfortunate combination of circum
stances ; or he has been unduly influenced by the pleading of a clever advo
cate ; or he has perhaps been prejudiced by self-interest or some other
consideration. The very same objective evidence has elicited just the opposite
sentence from his two colleagues ; so that the probability of their pronouncing
all three the same sentence is not at all to be compared with the probability
of drawing three balls of the same colour by three independent draws." 1

269. FUNCTIONS OF STATISTICS AND AVERAGES: THEIR
RIGHT AND WRONG INTERPRETATIONS.2— In the presence of such
complex social phenomena as we have referred to already, or of
complex natural phenomena like those relating to climate, for
example, — where unknown causes are interfering, through un
discovered laws, with those already known, — the compilation of
statistics and averages will enable us to lay down highly probable,
or morally certain, judgments, not about the happening of an

1 J. BERTRAND, Calcul des probability, p. 236.
2C/. MBRCIER, Logique, pp. 349-51, 361-70.

286 THE SCIENCE OF LOGIC

individual event at a definite point of space and time, or about
the happening of a whole class of such events, but about the
happening of a more or less definite proportion of events of a
certain class within more or less definite limits of space and time.
Suppose, for instance, it has been observed to have rained on an
average three days in the week during the past twenty years in
a certain district. We may be morally certain that if the
general climatic conditions of the district continue unchanged
we shall have the same average in the future.

But, furthermore, knowing as we do that these results were
the outcome of numerous natural causes interacting according to
undiscovered laws, we have no reason to doubt that closer and
more prolonged and detailed scrutiny of all the climatic condi
tions of that district, and of other districts, may gradually enable-
us to bring to light these laws, or some of them. Of course, no
induction has yet brought to light the laws that have deter
mined the given condensation of vapour and consequent rainfall ;
nor has any probable hypothesis as yet suggested what these
laws may be. The phenomenon itself is so complex, the ante
cedent and concomitant conditions of such condensations of
vapour in the atmosphere as lead to rain, are so manifold, their
action and interaction so intimate and elusive, that it has been
impossible, so far, to determine the exact influence of each
elementary factor, and to formulate the law of their combined
activities.1 Provisionally, therefore, we have recourse to statistics :
we catalogue the greatest possible number of instances, note their
frequency and their coincidences with other occurrences, in the
hope of discovering some clue to a causal connexion (243). We
measure the rainfall during the different seasons of the year, per
week, per day, per hour, etc., noting the altitude and other geo
graphical conditions, the direction of the winds, etc. We draw
up tables of all those various coincidences in the hope that sooner
or later we may be able to eliminate the irrelevant circumstances,
to trace the recurrence of the phenomenon to its natural causes,
and bring to light the laws of their activity.

Or, again, the ratio of male to female births has been in
vestigated, for over 200,000,000 children. For nearly two cen
turies the numbers of each sex born have been found to be
practically equal — without any exception whatever of time or

1 Cf. example (of monsoons) quoted above, 222, from Mr. JOSEPH'S Logic, pp.
444-5-

OPINION AND PROBABILITY 287

country. Yet, not quite equal : the male births have been found
to exceed the female in the ratio of between 104 and 108 males
to 100 females. Now those remarkable facts, — that the numbers
of births of each sex are practically equal, that there is a slight
preponderance in the number of male births, and that this is
found to hold good of every race, north and south, east and west,
in town and country, among rich and poor alike, — those facts are
surely due to the operation of some undiscovered laws of nature.
For such a constant persistence of this remarkable ratio, there
must be a sufficient reason in the nature of the antecedents them
selves of those births, even though we have not the slightest
suspicion as to what the natural properties may be to whose
operation, in the antecedents, those uniformities are due.

All we can do in such cases is to note and observe carefully
all the circumstances that we may suspect of having any possible
influence in determining the nature of the recurring phenomenon.
If, going a step further, we try to investigate the concurrence of
those circumstances, their variation, the isolated influence of each,
we are entering on the employment of the " inductive methods".
As soon as some observer detects, amongst all those chaotic
surroundings, certain elements which he supposes to be the con
stant, necessary antecedents of the phenomenon in question, he
makes a scientific hypothesis. The verification of this hypo
thesis will be the work of induction proper.

By statistics, therefore, we make a simple enumeration of the
phenomena to be explained, we reach rough, empirical general
izations, which suggest hypotheses that may be later on erected
into natural laws for the explanation of those phenomena. From
statistics we often, therefore, obtain suggestions or indications of
the laws underlying complex phenomena, and whose existence
had been hitherto unsuspected.

The value of statistics must not, however, be overestimated.
When we are investigating the nature and causes of things and
events in the natural and social sciences, we are face to face with
facts. In statistics about those events we are brought face to
face with syntheses. The statistician must regard his figures as a
sort of symbol, whose character and significance are more or less
enigmatic; and he must diligently seek out all the probable
causes of the facts he has symbolized before him, with a view to
their scientific explanation.1

1 C/. LIESSE, La statistique, p. 49.

288 THE SCIENCE OF LOGIC

Take the case of mortality statistics. A series of deaths is
not a phenomenon of precisely the same sort as the drawing of
a series of cards from a pack. Each particular death — the death
of this particular person at this particular time and place — is
the necessary outcome of certain (partially known and partially
unknown) natural causes, operating detrimentally in his organism ;
or it may be the inevitable result of a complex concurrence of
natural causes culminating in a fatal accident. The drawing of
this particular card from the pack is likewise determined by the
concurrence of a number of unknown natural causes. The dif
ference is not in the individual cases : it lies in this, that while
the general set of antecedents does not vary in the case of draw
ing a series of cards, it may vary considerably in a series of
deaths. The number of deaths per year in any country depends
on many and variable factors ; and, consequently, the average
number of deaths during any period of years furnish a very
uncertain' basis for conjecturing the average number during
another period of the same duration. In Belgium, for example,
the average age of the inhabitants in 1829 was 31 years 5
months; in 1856, 38 years I month; in 1890, 45 years I
month.1

Tables of mortality form part of the basis on which the
business of life insurance companies is conducted. Yet those
tables are recognized as only rough approximations to any real
constancy : the actuaries take care to revise and readjust their
tables frequently, in order to keep them in agreement with the
actual facts.

There is still more reason for caution in making any attempt
to explain phenomena of the psychological, moral, or social orders
by statistics and averages, or to erect such statistical uniformities
into laws? During the last century great hopes were aroused of
reading the secrets of moral and social phenomena by the appli
cation of statistics to their domain. In his Essai de physique
sociale, published in 1839, Qu6telet proposed to himself to study,
by their consequences, " the natural causes, whether favourable
or unfavourable, that influence the development of man". The
initiative of this able Belgian scholar opened up the way to a
number of highly interesting but extremely delicate researches.
He himself brought his observations to bear on the age at which

1 MANSION, op. eit., p. 32. JC/. WELTON, op. cit., ii., p. 198.

OPINION AND PROBABILITY 289

people marry. Those observations extended over the years 1 841-
1865. For example, during the years 1841 to 1 846, the number
of men who got married in the towns of Belgium between the
ages of twenty-five and thirty, were, respectively, 2681, 2658,
2698, 2698. l Again, the statistics of crimes showed the same
marked constancy. " There is an annual tax [of human beings]
which we pay with frightful regularity to the prisons, convict
settlements, and scaffolds." 2 " It is well known," writes Pro
fessor Welton,3 " that the number of persons who commit certain
crimes, who are born, or who die, in the course of a year bears
a remarkably uniform proportion to the total number of the in
habitants of any given country; there is, as we say, a pretty
constant average preserved in many of the phenomena of social
life. For example, something over seventy people out of every
million commit suicide every year in England and Wales, whilst
in Saxony the proportion is about five times as great as this, and
in Ireland only about one-third as large. And these numbers
are found to remain very uniform from year to year. Moreover,
the averages are found to vary with great regularity according to
the months of the year, being highest in June, falling regularly
to December, and then gradually rising again ; and this occurs
year after year. Further, the proportion who commit suicide at
different ages remains fairly constant."

Now what does this constancy of averages point to? To a
" ' law ' which must of necessity be fulfilled " ? 4 No, but simply
" to the fact that social and material conditions remain compara
tively unchanged for mankind in general. But it is an error to
assume that such a statistical uniformity proves anything beyond
its own existence. . . . With regard to the future we can only
judge that the same numbers will be found to hold, if the same
general conditions remain. . . . But this is mere tautology, for it
simply says, If the past be exactly repeated it will be exactly re
peated. The very question is whether all the conditions — known
and unknown — will remain unchanged. . . . But uniformity in
averages . . . involves no necessity for its own continuance. No
doubt every element of reality is strictly determined in all its de
tails by its conditions — given exactly those conditions, that result
is necessary. But this necessity is concealed by the average,
which neglects all the particular characteristics of the individual

1 QUETELET, Systeme sociale, p. 68. *ibid.

3 WELTON, op. cit., p. 198. ^ibid., 198-9.

VOL. II. 19

290 THE SCIENCE OF LOGIC

instances. Necessity is only found when conditions are exactly
determined, and ex hypothesi that is just what is not done in the
case of an average. As Sigwart says: 'Such uniformities of
numbers and averages are primarily mere descriptions of facts,
which need explanation as much as the uniformity of the alterna
tion between day and night ; and the explanation can be found
only where the actual conditions . . . are forthcoming. But
these are the concrete conditions of the particular instances
counted, they are not directly causes of the numbers ; it is only
the nature of the concrete causes which can show it to be neces
sary for the effects to appear in certain numbers and numerical
relations' (Logic, Eng. trans., vol. ii., p. 490)." l

Inferences from statistics about natural and social phenomena
can never, therefore, be more than probable approximations—
not laws. Those phenomena result from the combination of
numerous unknown or partly unknown causes ; and we have
no guarantee that these will persist unchanged. No doubt, if the
future faithfully resemble the past, the tabulated averages will recur.
But who knows accurately what has been the past? Or what
guarantee have we for thinking that the future will be a repeti
tion of it ? Furthermore, we will have observed fluctuations of
more or less importance in the number and order of the past
events, and we must take warning from them not to expect any
greater regularity in the future.

Careful and conscientious scientists, like Quetelet, recognize in what a
transferred sense the word " law " is applicable to the moral world. He pro
tested against the accusation that according to his theory every year should
necessarily produce its crop of crimes in the same number and order, and with
the same invariable distribution of each class of crime over the same regions.
He objected to the word " invariable," and never used it himself in his
writings. On the contrary, he had written expressly : " The laws relating to
the condition of the social body are not necessarily invariable : they can change
with the nature of the causes that give rise to them ".a

But hasty and unreflecting people have pushed to absurd extremes the
idea of seeking in statistics an explanation of the whole vast group of pheno
mena which constitute the subject-matter of the social, political, and economic
sciences, to erect statistical averages and uniformities into laws, and to estab
lish a new science which was to be a sort of social mathematics. It was
obviously under the influence of such preoccupations as these that Buckle
wrote paragraphs like the following : " In a given state of society a certain
number of persons must put an end to their own life. This is the general
law, and the special question as to who shall commit the crime depends of course

1 WELTON, op. cit., p. 199. *op. cit., p. 15.

OPINION AND PROBABILITY 291

upon special laws ; which, however, in their total action, must obey the large
social law to which they are all subordinate. And the power of the larger law
is so irresistible, that neither love of life nor fear of another world can avail
anything towards even checking its operation ".'

It is only by a complete misconception of the significance of averages
that any such " must" or any such rigorously necessary " /««/," can be thus
read into them. An average is not to be regarded as a secret something which
determines events. This blunder is often made in social statistics. After
finding a certain average in human affairs, we conclude that some secret fate
is at work. By the aid of a little rhetoric we easily persuade ourselves that an
event is fully accounted for when " the law of averages " demands it. " There
may be an average in birth and death and crime, but after all, the average is
not responsible for any of them. It takes something more potent than an
average to produce typhoid fever or to crack a safe." "

That there is a certain regularity in those social phenomena which result
from man's free activity is undeniable. But the regularity is periodical rather
than constant ; nor is there any exact law governing the duration of the phases
or periods. Tabulated returns have been made out, showing the periodical
recurrence of economic crises in France, England, and the United States,
from the beginning of the century to 1882. The practical coincidence of the
dates in those tables clearly indicates similarity of causes and solidarity of
their activity and effects. But if the fact of periodicity is certain, the apparition
of such commercial crises, and the intervals between them, are variable ele
ments. This variability is the outcome of causes so complex that it is quite
impossible to attempt to formulate any sort of a periodic law.3

"The free action of human beings," writes M. Bertrand,4 "as also the
action of animals — in spite of what Descartes has said of them — bring into
the domain of causality an element inaccessible to the calculus."

The justice of this remark must be apparent to any impartial student of
natural and social phenomena. We have already referred to the futility of any
attempt to reduce all reality to a system subject to purely mechanical laws. A
cosmic system made up of " indifferent " atoms and local motion, capable of
exact mathematical measurement, and invariable in the sum-total of its elements

lHist. of Civilization, vol. i., p. 25, apud WELTON, op. cit., p. 199.

2 BOWNE, op. cit.t p. 188.

3 The table of cases from 1800 to 1882 is as follows : —

France. England. United States.

1804 1803 1803

1810 1810 1810

1814-1815 1815 1814

1818 1818 1818

1825 1825 1826

1830 1830

1836-1839 1836-1839 1837-1839

1847 1847 1848

1857 1857 1857

1864 1864-1866

1873 1873

1882 1882 1882

4 op. cit., Preface, p. xlix,

19*

292 THE SCIENCE OF LOGIC

and their possible combinations, would furnish an excellent theatre for the
play of " chance ". And any isolated and limited portion of it would illustrate
the theory of probability as admirably as a game of chance. The ancient
Greeks conceived the world as formed by a chance arrangement of atoms — a
concursus fortuitus atomorum. Many moderns clothe the same crude con
ception in a more scientific and pretentious terminology. Such a mechanical
conception of the universe is only a prejudice. Even in the inorganic world
there is a great deal more than mere mechanics. " As Mach puts it ; ' Purely
mechanical phenomena do not exist . . . [They] are abstractions made, either
intentionally or from necessity, for facilitating our comprehension of things.
The same thing is true of the other classes of physical phenomena. . . . The
view that makes mechanics the basis of the remaining branches of physics, and
explains all physical phenomena by mechanical ideas, is in our judgment a
prejudice . . . The mechanical theory of nature ... is an artificial concep
tion.' " * And, just as mechanics is inseparable from the physics of the inor
ganic world, so is the latter inseparable from, and inevitably influenced by, the
activities of the organic world — animal sensation and appetition, human know
ledge and volition : " Processes, thus, that in appearance are purely mechani
cal, are, in addition to their evident mechanical features, always physiological.
. . . The science of mechanics does not comprise the foundations, no, nor even
a part of the world, but only an aspect of it." a

Besides the laws, therefore, which govern the processes of the inorganic
world, there are likewise laws which govern the conscious activities of the brute
creation, and laws that govern the free activities of man. But the mode of
causality is not the same in these three orders. It is not the same kind of law
that connects cause and effect in each. If we describe as a mechanical
necessity the connexion of cause and effect in a steam engine, we must find
another adjective for the necessity, or the law, by which a dog obeys (or disobeys)
his master ; for sensation and appetite make the dog something more than
a machine, and introduce an " indeterminate " element, an element of " uncer
tainty," into our calculations. And we must find yet another conception of
law for the free, self-determining activity of the human will, and for the general
uniformity that prevails in human conduct, notwithstanding the " mechanically "
disconcerting, but very real, factor of human freedom.

We have already shown (223) that the constancy actually observed in
social phenomena is not incompatible with human freedom. We may add
here the following eloquent passage from Quetelet, which will, perhaps, be
found as suggestive and instructive as it is interesting : "Amongst the facts dis
closed in my book, the one which has given rise to most alarm is the constancy
of crime from year to year. By a comparison of numbers, I believed I had data
for inferring, as a natural consequence, that in a given country, under the
same conditions and influences, we might expect a repetition of the same facts,
a reproduction of the same crimes and the same condemnations. But how
was this received ? A crowd of timid people raised the cry of fatalism ! " The
facts, nevertheless, were undeniable ; the whole thing was to interpret, to
understand them. " Now what do the facts teach us ? This, simply, — that
in any given State, subject to the influence of the same causes, the effects will

1 MACH, Principles of Mechanics, pp. 495-6 ; apud WELTON, op. cit., ii., p. 209.
*MACH, ibid., p. 507, apud WELTON, ibid.

OPINION AND PROBABILITY 293

not differ appreciably ; they will oscillate more or less about some mean.
Now, mark well what I have said : subject to the influence of the same causes ;
so 'that, therefore, if those causes change, the effects will be likewise modi
fied. But, since the laws and principles of religion and morality are the
source of the influences in question, I cherish not only the hope, but — what you
perhaps do not — the deepest conviction even, that society can be reformed
and ameliorated."

" But, you ask, what becomes of free will ? In presence of the facts I am
not concerned to debate this much-discussed question, but yet I cannot pass
it over in silence, for the simple reason that it seems to me to involve in itself
one of the most admirable laws in all creation, a law of conservation which
furnishes a new proof of the wisdom of the Creator, a proof, the existence of
which you, with your cramped conceptions on the moral organization of man,
have been unable even to suspect. To avoid the reproach of denying free
will entirely, must we go to the opposite extreme and allow it an absolutely
indefinite scope ? Or, in that event, what would have become of the whole
race centuries ago, — with all the mad follies that have entered the minds of
men, and all those evil inclinations that have— even as things are— desolated
society ? Scourges have come and gone, but man and his faculties remain
unchanged, at least so far as our observation serves us. And why ? Because
the self-same finger that has traced its confines for the ocean has likewise set
their limits to man's turbulent passions, and the self-same voice has com
manded both : thus far you shall go but no farther. When we have to make
up our minds about the simplest matter, do we not find ourselves under the
influence of our habits, and our needs, and our social conditions and relations,
and of a whole crowd of conflicting motives which drag us to the one side
and to the other ? Nay, so strong are those influences that we have no hesi
tation in predicting, even about people whom we know but slightly, or not at
all, what decision they are going to take. Why those innumerable forecasts
and guesses you are making every day of your life, if you are not convinced
beforehand in each particular case that the influence of inherited character
and motives, etc., and not free will itself, will determine the issue ? Looking
out on the world a priori you give this free will the very widest latitude ; but,
when you pass from theory to practice, and talk of what is going on perpet
ually around you, you flatly contradict your a priori self by making your pre
dictions about individuals ! Yes, about individuals, in whom motives, etc.,
can oscillate to such a degree that it would be against all the principles of the
theory of probabilities to take them as data for the calculus, or to base even
the slightest inductions upon them." l

WELTON, Logic, ii., pp. 165-80. CLARKE, Logic, pp. 356-424 sqq.
ZIGLIARA, Summa Philosophica, i. (42). MELLONE, op. cit., pp. 251-61.
JOSEPH, Logic, pp. 323. KEYNES, Formal Logic, p. 367. VENN, Logic of
Chance, passim. JOYCE, Logic, pt. ii., chap, xxiii. BORDEN P. BOWNE,
Theory of Thought and Knowledge, pp. 178 sqq. MERCIER, Logique, pp.
350-70. GREISE, La Statistique, QuETELET, Sy steme sociale. Cf. works
mentioned, p. 269, n.

1 QU£TELET, Etudes sur Vhomme, pp. ii, 12. For Qu£telet's attitude towards
free will, cf. LOTTIN, Le libre arbitre et les lots sociologiques, in the Revue Nio-scol-
astique, November, 1911 ; QUETELBT, Statisticien et sociologue (Louvain, 1912).

CHAPTER III.
ERROR AND FALLACIES.

270. LOGICAL TREATMENT OF ERROR AND ITS SOURCES.—
Certitude, probability or opinion, doubt, and error — such are the
various states of mind we experience in our search for truth.
It is the function of logic, as a practical science, to guard us
against the last of these states, and to enable us, as far as may be,
to reach the first. Hence, it analyses our processes of judging,
reasoning, generalizing, and demonstrating, with a view to dis
cover, and to familiarize us with, the laws and conditions of correct
or accurate thought. And we shall be made all the more capable
of conforming our own thinking processes to those laws, if we
conclude the treatment of our subject by a special study of the
more common sources of error, the ways in which we are most
likely to fail in the application of logical principles. We shall
have a better grasp of the ways in which we ought to think, when
we have contrasted these with the ways in which we ought not to
think. Not, indeed, that the knowledge of these latter will be an
infallible safeguard against error. Nevertheless, it will certainly
be helpful to us, — " Forewarned, forearmed ". If, for instance,
the conclusion of an invalid argument happens to be true, and to
be known by us as true, this very knowledge might throw us off
our guard and lead us to accepting the argument as valid : it
would be less likely to do so were we familiar with the various
ways in which deception may creep into an argument. Or, again,
if we know the conclusion to be false we know that there must
be something wrong with the argument ; but, without a know
ledge of the rules of reasoning, and their possible violations, we
may be unable to discover what it is precisely that is wrong, es
pecially if the premisses seem true : we may know there is a flaw
somewhere, without being able to see through it, to explain it, to
lay bare the source of it. No doubt, in the course of our work,
we have already pointed out, by way of contrast, in illustration

294

ERKOR AND FALLACIES

295

of the various canons and conditions of correct thinking, the
more common violations of the latter. But that was only in
passing ; and the whole subject of Fallacies demands for itself a
separate and more explicit treatment.

A systematic classification, however, of the ways in which the
human mind can fall into error, seems to be, from the nature of
the case, practically if not absolutely impossible ; for error con
forms to no laws. Of course it breaks laws, the laws that would,
if observed, conduct to truth ; and hence we may attempt to
classify the heads or sources of error according to the laws or
canons violated by the mind in reaching the error. This is the
plan adopted by Professor Welton.1 It suffers, in common with
other classifications, from this drawback, that the same individual
example of an error, arrived at through a certain process of thought,
may be referred to different heads or types of fallacy, may be
traced to the violation of different logical principles. This diffi
culty, of referring concrete cases to their proper headings, is present
in every scheme — whether of attempted classification, or of mere
enumeration of the various types of fallacy. Apart from this
difficulty, however, of referring individual instances to a type, it
would seem practically impossible to give an entirely exhaustive
catalogue of the types themselves, the kinds of fallacious thought-
processes in which the mind may become involved ; because
there are possible sources of error peculiar to every new depart
ment into which we may carry our search after truth. We must,
then, only endeavour to notice at least all the more important and
common forms of deception incident to such investigation.

With the special sources of error involved in the subject-matter of this
or that particular science it is not, of course, the function of logic to deal,
but only with common sources. Still, this must not be pressed too far. We
have already followed the workings of reason a certain distance into various
kinds of subject-matter, into the matter of induction, into that of deduction, into
the reasoning process known as the Aristotelean syllogism, and into certain
analogous forms of mediate reasoning (192) ; and we have seen that every
where, even in the mental act of judgment, the form assumed by our thought-
process depends to a certain extent upon the matter thought about (10, 81).
Hence there will be certain sources of error— certain misconceptions, mistakes,
and ambiguities — peculiar to the investigation of this or that particular subject-
matter. The reason of this is — partly, at least— because the different kinds of
subject-matter call forth different types or forms of reasoning, in accordance
with certain axioms that involve conceptions or intuitions of certain systems of
relations —such as those of space, time, or quantitative proportion — on which

1 op. cit., ii., bk. vii.

*g6 THE SCIENCE OF LOGIC

this or that special form of reasoning is based. In so far as such initial
conceptions and the reasoning processes dependent on them are, of them
selves and apart from their particular subject-matter, liable to be misappre
hended or misapplied, they call for notice in a general treatment of logic. If,
for instance, I argue that because " a is half of d, and c is half of 6, therefore
c is half of a" it is, no doubt, " only a perception of the nature of quantity that
reveals . . . the invalidity of the . . . argument " j1 but this does not remove
the fallacy from the jurisdiction of logic, for it is a function of logic to determine
what is, and what is not, an axiom or self-evident truth, whatever be the subject-
matter in question. The assumption that " things which bear the same quan
titative relation to the same thing bear this same relation to one another," is a
misconception of the truth that such things " bear a relation of equality to one
another ". It is as much the duty of logic to expose this " undue assumption
of axioms " as, for instance, to expose the fallacy of arguing that " because all
the angles of a triangle are equal to two right angles, and A B C is an angle
of a triangle, therefore it is equal to two right angles " — a fallacy which may
similarly be resolved into the misconception of an axiom, -viz. the Dictum de
omni.

271.— ERROR AND FALLACY.— The forms or types of mis
leading thought-processes examined in logic are usually compre
hended under the general title of Fallacies, But this term has
considerable elasticity of meaning : it has been used in all shades
of meaning, from the widest sense of " any erroneous judgment or
belief," to the narrowest sense of " the violation of some formal
rule of inference ".

The former usage is too wide. It is not the false judgment or
belief itself we should call a fallacy, but rather the causes or
sources to which the presence of that error in the mind is due.
That something or other, in the origin or progress of the thought-
process, which deceived the mind into assenting to a false judg
ment — that is the fallacy proper. Where the error is reached
through a process of inference, it may be due either to the
assumption, at some point in the process, of a false premiss, or to
the acceptance of a formally inconclusive inference as valid. To
restrict the meaning of the termfaHacy to the latter class of cases,
is as inconvenient as to restrict the term logic to an exposition of
the formal laws of inference, thus making it a science of mere
consistency. This usage is too narrow. Besides, the distinction
between accepting a false premiss and an inconclusive argument
is not fundamental. The mind, which, for one reason or another,
accepts a formally invalid inference as valid, is by that very fact
assenting to a false proposition as true : for the formal force of an

1 JOSEPH, op. cit., p. 530.

ERROR AND FALLACIES 297

inference can always be expressed in a hypothetical judgment show
ing forth the necessary dependence of consequent on antecedent :
and that judgment, stated in general terms, is the axiom or canon
of the form of inference in question. Hence, to accept a formally
invalid inference as valid, is to mistake for an evident axiom
or canon some judgment that is neither evident nor true. In
fact, every logical fallacy may be analysed into the acceptance by
the mind of some false judgment as true.1

When tacit assent to an implied false judgment, whether this
be a canon or a premiss,2 leads to further error, we shall call such
false assumption a fallacy ; as also the assumption of a false pre
miss at any stage in a reasoning process : provided always there
is a semblance of validity or truth about the judgment so accepted.
This latter condition is essential to a fallacy. Only by being
deceived can the mind be led into error ; and it can be deceived
only because error can assume for it the semblance of truth.
When, therefore, a judgment is manifestly false, an argument
plainly inconclusive, some rule or canon of correct thinking openly
violated, there is no fallacy, because there is no deception. An
argument which openly violates some formal rule of infer
ence is sometimes called a paralogism, or, also, a case of " non
sequitur ".

We have said that a false judgment, simply as such, cannot
properly be called a fallacy, that the latter is to be sought rather
in the grounds and motives which induced us to assent to the false
judgment as true. We can, however, distinguish between the logical
grounds or reasons, and the psychological motives, for our assent
to a judgment (198, 225). The logical grounds are designated by
the general title of evidence (248) : they appeal directly to the
intellect, and are its proper object. The evidence for any proposed
judgment is either mediate or immediate. If we assent to a judg-

1 This is illustrated by Mr. JOSEPH in connexion with the fallacy "post hoc,
Propter hoc" : " Nor is it peculiar to this fallacy," he writes (op. cit., pp. 554-5),
" that it can be expressed as a false principle. Equivocation proceeds on the false
principle that a word is always used with the same meaning : Accident on the prin
ciple that whatever is predicated of a thing may be predicated of its attribute, and
vice versa : Secundum Quid on the principle that what is true with certain qualifica
tions is also true without them. And the fact that these different types of fallacious
inference severally depend on a false, or misleading, principle, is what was meant by
calling them loci of fallacy."

2 When " the falsity of the premiss can only be ascertained empirically," Mr.
JOSEPH (ibid., 532) will not call its assumption a fallacy. This usage would exclude
such inductive fallacies as non-observation or mal-observation. We prefer to extend
the term to " any false assumption used as a premiss " (ibid., 535).

298 THE SCIENCE OF LOGIC

ment on account of its known connexion with some other already
known judgment or judgments, it is called a conclusion, and its
evidence is mediate. If, on the contrary, we assent to it on its
own account, because of the direct appeal it makes to our intellect
as true, it is called a principle, or a j^-evident, or immediately
evident, truth.

It needs but little experience of life, however, to convince us
that men differ widely in the judgments they accept as self-
evident ; and this is, in part at least, because men's assents are
influenced not by intellectual evidence alone, but also by non-
intellectual motives. Their estimate of the evidence is partly
dependent on their character and dispositions, their mental habits
and training, their likes and dislikes, their will, passions, emotions,
etc. (231). These are psychological influences, of which logic can take
no direct notice. But when there is question of assent to judgments
on immediate evidence, of estimating this latter, and discriminating
between real and apparent evidence, it is not easy to divide
the misleading influences at work into psychological and logical.
Against influences supposed to belong to the former class — passion,
prejudice, party-spirit, precipitancy, etc., logic can merely give
a general warning (203). Only when the source or cause of the
deception is a violation of some logical principle, can logic deal more
effectually with it. Of the source of the deception, the victim of
a fallacy is, of course, always and necessarily unconscious : the
mind aware of its deception would be no longer deceived. But
when deliberate reflection on our thought-processes brings into
consciousness the causes which have misled us, these will always
appear to have been either inadvertent and indeliberate violations
of some of the laws and principles of correct thought, propounded
in logic, or else to have been misleading influences of a more subtle
and subjective kind, springing from character, prejudice, mental
training, etc. The former alone we shall call Logical Fallacies.

We may, therefore, define a Logical Fallacy as a violation of
some logical principle, calculated to lead to error by reason of its
apparent validity.

272. SOME ATTEMPTED " CLASSIFICATIONS" OF FALLACIES.
" FORMAL " AND " MATERIAL " FALLACIES. — (a} The line of
thought we have just followed suggests a classification of fallacies
made by John Stuart Mill : a " catalogue of the varieties of ap
parent evidence which are not real evidence ".*

1 Logic, V., i., § i.

ERROR AND FALLACIES 299

Assents to false judgments on immediate " apparent " evidence,
he calls fallacies of simple inspection. If the evidence is mediate,
we may have fallacies of inference. These he subdivides into
fallacies of confusion, in which there is " an indistinct, indefinite,
and fluctuating conception of what the evidence is " ; * and falla
cies due to " a false estimate of the probative force of known
evidence".2 The latter may be incident either to deduction or to
induction ; and in each case it may be due either to the assumption
of false premisses, or to a miscalculation of the probative force of
true ones. The assumption of false premisses in deduction he
identifies with fallacies of simple inspection ; wrong estimates
of the probative force of deductive arguments he calls fallacies of
ratiocination. The two corresponding types of fallacy in induc
tion he calls respectively fallacies of observation and fallacies of
generalization. Thus we reach five main classes, some of which
are made to yield a number of sub-classes. The following scheme
will show forth the various members of the division : —

Fallacies.

(1) Of simple inspection ; Of inference ;

I

I I

(2) Of confusion ; Of miscalculation of force of evidence.

|

Of deduction. Of induction.

I I

( I ) Assumption of false premisses ; (4) Fallacies of observation ;

(3) Fallacies of ratiocination ; (5) Fallacies of generalization.

This classification is based upon an intelligible principle, but
it is not exhaustive as it stands ; its headings are very general,
and we shall find a more convenient plan of treatment than to
try to work these out in detail.

(b) Bacon's classification of the sources of error, or obstacles to the
right "interpretation of nature" is not without interest. He calls them
" Idola " — phantoms which mislead the mind in the processes which sub
serve induction, just as "sophistical reasonings" mislead in ordinary argu
mentation? He reduces them to four great classes; (i) "Idola Tribus"

1 Logic, V., vii., § i. 2 ibid. s Nov. Org., i., Aph. xl.-lxviii.

300 THE SCIENCE OF LOGIC

or Phantoms of the Tribe: tendencies inherent in human nature itself, ex
posing men to the danger of interpreting falsely the impressions made upon
their senses; (2) " Idola Species" or Phantoms of the Cave: sources of
error peculiar to the individual, owing to his personal idiosyncrasies and
mental habits ; (3) "Idola Fort," or Phantoms of the Market Place : decep
tions due to the limitations of language, which is the medium of intercourse
and exchange of ideas among men; (4) '•'•Idola Theatri," or Phantoms of
the Theatre : false theories and teachings that have gained currency and are
accepted unquestioningly because they happen to be the fashion of the time.

(c) Of far greater importance than the classifications of Mill
or Bacon is Aristotle's enumeration : not, perhaps, because of any
exceptional intrinsic merit, but because it has furnished logic with
a universally recognized nomenclature of the more important fal
lacies, and has never been entirely superseded. Aristotle dealt
with fallacies in the last book of his Organon, under the title
of Sophistical Refutations, Sophistici Elenchi, Trepl a-ofaariKfov
€\eyxwv. He wrote at a time when public oral discussions and
disputations were of the highest educational, social, and political
importance, when great issues were decided by the masses on
hearing conflicting views championed by special pleaders, when
skill in rhetoric, or the art of persuading by plausible reasons,
was eagerly ambitioned by public men, and profitably taught by
those influential educators of the Athenian youth, the sophists.
It was with a view to exposing the various dialectical deceits and
devices for misleading, which were currently used in those public
debates, that Aristotle wrote the Trepl ao$i<rruc&v eXej^wv. Those
" sophistical arguments," or " sophisms," as he called them, were
connected in his mind with the intention to deceive or mislead : *
it was indeed the sophists' own avowed exclusive concern for
dialectical victory, irrespective of truth and right, that eventu
ally brought their name and methods and arguments into disre
pute. Aristotle's " sophisms," therefore, all regard inference, and
inference conducted by way of oral disputation. Hence his list
is not exhaustive ; and, such as it is, it contains many fallacies,
arising from the use of language, which are nowadays likely to be
regarded as trifling ; though they must have given some trouble
at a time when so much depended upon the general impression
produced by public dialectical encounters, for which we have, per-

1 Kant applies the term Sophism to a fallacy used for the purpose of deceiving
another, and Paralogism to a fallacy which deceives the person who uses it. This
ground of distinction is psychological, not logical. The logical nature of a fallacy
is independent of the intention of the party using it.

ERROR AND FALLACIES 301

haps, no parallel in modern times, beyond an occasional brilliant
display of cross-examination in our law courts.

Aristotle divides fallacies into two groups : (i) So<f>la-fj.aTa
Trapa Trjv \el~iv, sophismata "in dictione" fallacies due to ambig
uity in language ; and (2) Sofaa-para e£<u T??<? Xe^e&j?, sophismata
"extra dictionem" fallacies from sources other than ambiguity of
language. This division is, of course, exhaustive because dicho-
tomous ; but there is no positive bond between the various
members of the second or negative class. In the latter he enume
rates seven species, in the former six. They are as follows : —

(A) Sophismata in dictione : —

(1) Equivocatio^ equivocation, Trapa rrjv o^mw^Lav — due to
ambiguity in a single term (ovo^ia).

(2) Amphibolia, amphiboly (or amphibology),1 Trapa rqv
an$i$o\iav — due to ambiguity in the construction of a sentence
or phrase (XOYO?).

(3) Compositio (or sensus compositus\ composition, Trapa rrjv
crvvBeo-iv — due to taking together what ought to be kept separate.

(4) Divisio (or sensus divisus), division, Trapa ryv Siaipea-iv —
due to separating what ought to be kept together.

(5) Accentus, accent, Trapa rrjv Trpoa-wSiav — due to confusion
of meanings differentiated by diversity of accent or quantity.

(6) Figura dictionis, figure of speech, Trapa TO a"xfi/j.a rr)<;
A,e£ea><? — due to misinterpretation of the force of a verbal inflexion.

(.5) Sophismata extra dictionem : —

(1) Accidens, accident, Trapa TO o-vpfteftrj/tos — equating subject
with attribute.

(2) A dicto simpliciter ad dictum secundum quid, and its con
verse, a dicto secundum quid ad dictum simpliciter (no English name
for this ; called briefly Secundum Quid), Trapa TO a-rrXw? 17 Try
\eyear0ai, teal //.^ Kvpi&s — ignoring the limitations or special con
ditions under which a statement is true or false.

(3) Ignoratio elenchi, arguing beside the point, Trapa rrjv rov
eXe7%ou ayvotav — mistaking the matter in debate.

(4) Petitio principii, begging the question, Trapa TO eV apxfi
\afjLftdveiv — assuming in some form or other the proposition to
be proved.

" The Greek word is a a/t(/>i/3oAio, which is said to be an airrfrrj irapo rbv \6yov,
as distinct from <J/xa>j/y/u'a, when the ambiguity is in an w0/ua (Soph., El. vii. 1693, 22).
Hence arose the compound a/j.<t>i&o\o\oyta, which became corrupted into amphibology,
as tlSu\o\arpfia became corrupted into idolatry," — JOSEPH, op. cit., p, 539, n. 2.

30» THE SCIENCE OF LOGIC

($) Non causa pro causa, false cause, Trapa TO p>rj atriov to? ainov
— supposing a conclusion to follow from a premiss which is really
irrelevant.

(6) Consequents, consequent, irapa TO eTropevov — assuming that
a hypothetical proposition is always and necessarily reciprocal.

(7) Plures interrogationes, many questions, Trapa TO ra ovo
€pa)T-qp,aTa ev Troieiv — asking a question in such a form that a
single answer involves more than one admission.

(d) Aristotle's distinction between fallacies in dictione and
fallacies extra dictionem is not the same as Whately's division into
logical, and non-logical or material. By " logical " fallacies
Whately meant those in which "the conclusion does not follow"
from the premisses ; by " material," those in which the " conclusion
does follow " from the premisses. In the former class, the defect
of proof lies either in a manifest violation of some of the formal
laws of the syllogism — quaternio terminorum, undistributed middle,
illicit major, illicit minor, negative premisses, etc., defects which
remain even when symbols are substituted for the terms and
concepts, and which Aristotle would not regard as sophisms owing
to the transparency of the mistake ; — or the defect lies in a simi
lar violation masked in ambiguous language. The transparent
defects Whately called purely logical, the cloaked defects semi-
logical fallacies. The latter he regarded as all alike reducible to
ambiguous middle term, including in this class all Aristotle's
sophisms except the ignoratio elenchi, the petitio principii, and the
non causa pro causa. These three he included in his " material "
fallacies, by which he understood mistakes due to assuming false
or unproven premisses, or premisses which prove the wrong con
clusion. Whately's main distinction — between formally incon
clusive arguments, and other sources of error — is sound and in
telligible. But his nomenclature is objectionable. It is due to
his narrow, nominalistic view of the scope of logic. All fallacies
are logical, inasmuch as they are violations of logical principles or
canons. Then, although most of Aristotle's sophismata, included
in Whately's class of " semi-logical " fallacies, do in fact usually
lead to formally invalid syllogisms through ambiguous middle
terms, yet this is not clear in regard to some ; and they certainly
may lead to error otherwise as well. Hence the attempt to
group them under such a head is unsatisfactory. Finally, on his
own view of the scope of logic, Whately should not have dealt
at all with what he called " non-logical " or " material " fallacies.

ERROR AND FALLACIES 303

The distinction between a " formal " fallacy and a " material "
fallacy is not fixed or clear — any more than that between " formal "
and "material" logic. But at all events in a reasoning process,
we can distinguish between the narrower " formal " or " consis
tency " aspect, which is independent of the truth of the premisses
and the meaning of the terms used, and the " material " or
"truth" aspect. Now, the formal validity of an inference, in
this narrow sense, being independent of the subject-matter, i.e.
of the meaning of the concepts and terms employed, it is only
when the invalidity persists with the symbols, i.e. when some of
the formal laws of reasoning are violated, that the fallacy is a
formal one. If the fallacy lies in the language, i.e. in the meaning of
the terms employed, in ambiguities of meaning, then its source is
in the subject-matter, in the things for which the terms stand, and
the fallacy is a material fallacy. An ambiguous middle term in
a syllogism is, therefore, in this sense a material fallacy : when its
two distinct meanings are explicitly substituted for it by two dis
tinct terms, we have immediately the formal fallacy of quaternio
terminorum. In this meaning of the expression " material
fallacy," all Aristotle's sophismata in dictione are, when they enter
into an inference, material fallacies ; while some of his fallacies
extra dictionem are formal in the sense that they can be repre
sented in symbols ; so that it is a mistake to confound Aristotle's
two lists with Whately's semi-logical and material fallacies,
respectively : a mistake into which Jevons seems to have fallen.1

(e) There is, finally, Professor Welton's classification, which we
purpose to follow : the classification according to the logical prin
ciples violated.

273. FALLACIES INCIDENT TO CONCEPTION.— We shall first
consider the fallacies incident to conception (Part I.) — to the pro
cesses of forming concepts, of expressing these in terms, of secur
ing clearness and distinctness in thought and language by
definition and division, by analysis and comparison of the various
logical characteristics of concept and term. Violations of the
rules of logical definition and division lead to faulty conceptions,
and thence to erroneous judgments and reasonings. Indeed, most
of the fallacies incident to conception may be regarded as due
to faulty definition. They include many of Aristotle's sophis
mata in dictione.

(a) EQUIVOCATION.— The use of the same word in different

1 Elementary Lessons in Logic, xx. and xxi.

304 THE SCIENCE OF LOGIC

senses is the simplest and commonest form of ambiguity in
language. It is due to vagueness of conception, resulting from
want of accurate definition. Any of three terms of a syllogism
may be ambiguous : most usually it is " ambiguous middle " we
meet: in which case the syllogism really contains four terms.
Many of the stock examples of this fallacy, found in handbooks
of logic, are trifling ; its most debased and trivial form being the
pun. But equivocation is really a fertile source of very serious
and elusive errors. In the course of any sustained argument,
after the manner of the sorites, it may easily lurk unsuspected, owing
to the almost imperceptible differences in the varying shades of
meaning which may attach to the same term in different con
texts. Language is not a perfect instrument of thought. It
needs but little reflection on the elasticity of meaning discern
ible in such terms as " idea," " cause," " law," " nature,"
"government," "liberty," "money," "free-trade," "socialism,"
" home rule," etc. — to enable one to realize what an amount of
error may be traced to this fallacy as its source. The following
few examples will be sufficient for illustration : " Finis rei est
illius perfectio ; mors est finis vitae ; ergo mors est perfectio
vitae ". " What is rare is dear ; a horse for a penny is rare ; there
fore a horse for a penny is dear." "Criminal actions are punish
able by law ; prosecutions for theft are criminal actions ; therefore
prosecutions for theft are punishable by law."

(£) The fallacy of the CONCEPT WITH INCOMPATIBLE ATTRI
BUTES arises from a vague, unreflecting, careless way of thinking,
which can be remedied only by the deliberate analysis demanded
by the process of logical definition. To speak, for instance, of an
" indivisible portion of matter " is just as self-contradictory as to
speak of a " square circle "; while an ultimate analysis of some
of our concepts is so difficult that philosophers have at all times
disagreed as to whether or not certain combinations of them
—•such, for instance, as "infinite quantity" — are self-contradic
tory.

(<:) COMPOSITIO and Divisio, or the fallacies of confounding
the sensus compositus with the sensus divisus. Composition is the
fallacy of combining what ought to be kept separate; division
is the converse fallacy, of separating what ought to be kept com
bined. Aristotle seems to have had in view here the unlawful
combination or separation merely of words or phrases. " Three
and four are odd arid even ; three and four are seven ; therefore

ERROR AND FALLACIES 305

seven is odd and even " (composition). " Seven and five are equal
to eight and four ; therefore seven is equal to five, and eight to
four " (division). " ' Is it possible for a man who is walking not
to walk ? ' ( Yes.' ' Then it is possible for a man to walk with
out walking'" (composition). "'Though you are not now
walking, you can walk?' 'Yes.' 'But if you can thus do a
thing when- you are not doing it, you can desire a thing when
you are not desiring it ' " (composition : it is only the capacity
to desire, not the actual desire, that can coexist with the state of
actually not desiring}.

Of course, the illicit combination or separation of words, as
in the cases just given, involves an illicit combination or separa
tion, in our thought, of the objects denoted. But sometimes the
fallacious mental process is not reproduced in the language. Con
founding the distributive with the collective use of terms is, perhaps,
the way in which the fallacy is most usually committed. The
showman who announced that children of both sexes would be ad
mitted free, and then proceeded to charge both for boys and girls,
— on the plea that none were " children of both sexes," — com
bined in thought the sexes which the language he used did not
necessarily separate, but which were naturally assumed by all
to be taken as separate. "All the angles of a triangle are
equal to two right angles ; A B C is an angle of a triangle ; there
fore it is equal to two right angles " (division). Such instances
might also be classified as special cases of equivocation, seeing
that they turn on the employment of an ambiguous term in
different senses.

The spendthrift who thinks that, because he can prudently
spend the portion A, or the portion B, or the portion C ... of
his revenue, he can therefore prudently spend A, and B, and C
. . ., is guilty of the fallacy of composition ; the miser who argues
that, because he cannot prudently subscribe to charities A, and
B, and C, and D . . ., he cannot prudently subscribe to any of
them, is guilty of the converse fallacy, of division. The person
who argues that protective tariffs would benefit all the industries
of a country because it can be shown that such tariffs benefit this
or that special industry, is guilty of the fallacy of composition.
The person who argues that because a knowledge of this, that,
and the other science, benefits the community, therefore every
citizen should be taught all the sciences in the schools, is guilty
of the same fallacy. " 'Does one grain of corn make a heap?'

VOL. II. 20

306 THE SCIENCE OF LOGIC

'No.' 'Do two?' 'No.' . . . 'Do two million?'" This ex
ample gave the name sorites to this class of fallacy among the
Greek sophists. Exactly similar is the example called the calvus :
'"Does pulling one hair from a man's head make him bald?'
'No.' 'Does pulling two?'" etc. They may be regarded as
examples of the fallacy of composition. Here is an instructive
example of the fallacy of composition, from John Stuart Mill's
work on Utilitarianism : J " No reason can be given why the
general happiness is desirable, except that each person, as far as
he believes it to be attainable, desires his own happiness. This,
however, being a fact, we have not only all the proof the case
admits of, but all which it is possible to require, that happiness
is a good : that each person's happiness is a good to that person,
and the general happiness, therefore, a good to the aggregate of
all persons ". Apart from all the ambiguities (in the terms
" good," " desirable," " happiness ") which make the reasoning
in this passage worthless, it is also vitiated by the fallacy of
arguing that because A desires his own happiness (or what is
" good " to himself*), and B his own, and C his own . . . there
fore A desires the happiness of (or what is " good " to) B, C, D
. . . (as well as his own), and similarly B, and similarly C . . . ;
and that therefore the general happiness is desired by all, and is
therefore a " good " to all.

(d] ACCENTUS.— By the fallacy of accent (or prosody} Aristotle
meant the mistake of using a wrong tonic accent, or stress of
the voice, in pronouncing the written Greek word : the written
language had, in his time, no signs to mark the differences of stress
and breathing in speech. The same mistake can arise in Latin
from giving a wrong quantity in pronouncing the written word :
" Omne malum est fugiendum ; pomum est malum ; ergo fugien-
dum ". It was distinguished from equivocation, perhaps because
words differently pronounced, though spelled the same way, are
scarcely the same word ; and the ambiguity was regarded as con
fined to written language. It is nowadays generally understood
to embrace all ambiguities of meaning which turn on change of
emphasis in speech: the commandment "Thou shalt not bear
false witness against thy neighbour " may be made to bear dif
ferent meanings according to the word emphasized. De Morgan
would regard as an instance of this fallacy the introduction (with
out notice), into a quotation, of italics not in the original, or the

1 P- 53.

ERROR AND FALLACIES 307

omission of italics that were in the original, or any similar at
tempt to convey more or less than the context guaranteed in the
original.

0) By the fallacy of FlGURA DlCTIONIS, Figure of Speech, Aris
totle designated the erroneous supposition that the same inflexions,
or roots, or other modifications of grammatical form in words, al
ways imply similar kinds or modifications of meaning : that "poeta
is feminine because Latin words of that form are usually feminine " ;
that " a man who walks on the whole day tramples on the whole
day " ; that " important is a negative notion because impotent
is negative " ; that when a person " is resolved " to do a certain
thing he does not act freely but is passive, because when he " is
beaten " or when he " is flattered " he is passive ; that a wooden
" image " is unreal because what is " imaginary " is unreal ; that
paronyms like "artist," "artisan," and "artful" must have simi
lar meanings (confounding etymology with connotation). J. S.
Mill gives as an instance " the popular error that strong drink must
be a cause of strength " — which, if it were true, would be equally,
if not eo ipso, true of strong poison ! But Mill has himself fallen
a victim to the fallacy in a passage in his Utilitarianism,1- which
has since become classical in this connexion : " The only proof
capable of being given that an object is visible is that people
actually see it. The only proof that a sound is audible is because
people hear it : and so of the other sources of our experience.
In like manner, I apprehend, the sole evidence it is possible to
produce that anything is desirable, is that people do actually
desire it." The force of this argument rests upon the assumption
that the termination -able .in " desirable " has the same sort of
meaning as the termination -ible in " visible " and " audible " ; but
this assumption is false, for though " visible " and " audible "
mean " what can be " seen and heard, " desirable " in the context
means what ought to be desired, not merely " what can be desired " ;
and, therefore, since Mill's argument only proves that what people
actually desire can be desired, while purporting to prove that what
they do desire is desirable in the real sense of the word, i.e. ought
to be desired, the argument is also an excellent example of the
fallacy of ignoratio elenchi (275, A, a). This example, therefore,
also illustrates the fact that the same individual argument may
be referred to different types of fallacy. Thefigura dictionis it
self may be regarded as a special sort of false analogy (275, £t b).

1 p- 53-

20*

3o8 THE SCIENCE OF LOGIC

274. FALLACIES INCIDENT TO JUDGMENT AND IMMEDIATE
INFERENCE (Part II.).1

(a) THE SELF-CONTRADICTORY JUDGMENT.— Many of the
fallacies incident to judgment have their source in vagueness of
conception, so that the difference between them and those already
enumerated is not fundamental. We may commence with the
self-contradictory judgment. The mind cannot, of course, con
sciously accept what it sees to be a contradiction ; but here, as
in the case of the self-contradictory concept, it accepts what is
really contradictory just because it does not think clearly. Fol
lowing the tendency to make general assertions where only
particular assertions are justified, we may be betrayed into the
self-contradictory statement that "every rule has exceptions".
By laying down this as universally true we thereby claim that it
has no exceptions : therefore some rules have no exceptions :
hence our statement contradicts itself. Much ingenuity has been
expended in showing that the old sophism of the Liar (A/revSo/z.ei'o?)
does not really disprove the universal applicability of the law of
contradiction.2 " Epimenides, the Cretan, says that all Cretans
are always liars." On the hypothesis that this assertion of his is
true, he too must be lying when he makes the assertion, i.e. the
assertion itself must be false on the very hypothesis on which it
is true. The statement from his mouth contradicts itself. The
essential characteristic of an assertion or proposition is its claim
to be true. If we assume that the proposition " All Cretans
always lie" is objectively true, it is a contradiction to suppose at
the same time that Epimenides can assert this proposition.

(£) AMPHIBOLY is the fallacy arising from ambiguity in the
structure of a sentence. As equivocation is ambiguity in terms,
so amphiboly is ambiguity in propositions. Latin is much ex
posed to this fallacy in the construction of the accusative with
the infinitive : " Aio te Eacida, Romanes vincere posse " is the
well-known reply of the oracle of Apollo to Pyrrhus; "TO /3ou-
\€<rdai \afteiv fie rov<f 7roXe/uov<? " is one of Aristotle's examples ;
the witch's prophecy in Shakespeare's Henry VI., "The duke
yet lives that Henry shall depose," is yet another example.

This form of ambiguity may easily arise in English from care-

1 The fallacies incident to mediate inference (Part III.) have been sufficiently
considered in connexion with the rules of the syllogism and the various laws and
canons of hypothetical and disjunctive reasoning.

* Cf. KEYNES, Formal Logic, fourth edit., pp. 457 sqq.

ERROR AND FALLACIES 309

lessness about the proper sequence of words in constructing the
sentence. Here are a few instances : " How much are twice
four and seven ? " (It may be fifteen, or twenty-two.) " I accom
plished my business and returned the day after." " Lost a valu
able umbrella belonging to a gentleman with a curiously carved
head." " Lord Salisbury will reply to Mr. Gladstone's recent
speech at the Guildhall." " Wolsey left at his death many build
ings which he had commenced in an unfinished state."

(<r) The fallacies A DICTO SECUNDUM QUID AD DICTUM SIM-
PLICITER, and A DICTO SIMPLICITER AD DICTUM SECUNDUM QUID,
have this in common, that they confound what is true absolutely
with what is true only under certain restrictions and limitations.
The former consists essentially in arguing from a statement which
is true with certain limitations or qualifications, as if it were true
absolutely, always, and apart from those qualifications. Aristotle
illustrates it by examples which are apparent violations of the
principle of contradiction, e.g. " arguing that an object which is
partly white and partly black is both white and not white ". This
is confounding " white in a certain respect " (secundum quid, irrf)
with " white absolutely " (simpliciter, aTrXw?). Similarly, to
argue that " we should never give alms, because giving alms to
professional tramps promotes idleness," is to commit this fallacy.
So, also, the argument that "because alcoholic drinks are per
nicious they should be forbidden," would be regarded as an in
stance of the fallacy by those who hold the alleged premiss to be
true only secundum quid, i.e. of immoderate quantities. Some
instances of this fallacy might be classified under the head of
illicit generalization (275, B, c) : they are attempts to extend a
statement beyond the special circumstances in which it is true.

A similar fallacy is committed by arguing from one special
case to another special case, regardless of circumstances which
invalidate the inference. It might be described as the fallacy
a dicto secundum unum aliquid ad dictum secundum aliquid aliud ;
it is really a sort of false analogy (275, B, #). " He who takes life
in sport is cruel ; therefore he who eats flesh encourages cruelty."
The story is told in the Decameron of the servant who brought
to table a stork minus one of the legs. To his master's inquiry
about the other leg he replied that storks have only one leg each.
Master and servant settled the dispute by adjourning after dinner
to a field where a number of storks were standing each on one
leg. When the master shouted they put down each its other leg

310 THE SCIENCE OF LOGIC

and flew away. " But," replied the servant, " if you had shouted
to the stork at dinner he would have shown his other leg too."

The fallacy a dicto simpliciter ad dictum secundum quid is
generally regarded as the converse of the one just explained.
It consists essentially in the assumption that what holds true
normally, as a general rule, will be true always, and without quali
fication, of any individual case or cases, irrespective of special
circumstances that may alter these cases. Here " simpliciter "
means "generally speaking ". The "moral " universal, admitting
of exceptions, is misinterpreted as a strict, necessary universal,
and applied to the exceptions. It is forgotten that " circum
stances alter cases ". Some special case is wrongly regarded as an
instance of a principle, when the case in question is not really an
instance, owing to the presence in it of special conditions not
contemplated by the principle. It is the illicit application of a
general rule to a special case which does not fall under the rule.
The fallacy, therefore, occurs in the process which is the special
function of the syllogism : the application of general principles to
particular cases. And it can be committed by misinterpreting
either the scope of the principle or the nature of the case. " The
employment of labour is beneficial to the community, therefore it
will benefit the community to find some occupation or other, no
matter how useless, for unemployed workmen." "Water boils at
1 00° centigrade ; therefore it will cook an egg in a few minutes
at the top of Mont Blanc." " It is unjust to interfere with a
man's private property ; therefore State interference with land
tenure, by compulsory sale or otherwise, is unjust." " Thou shalt
not kill ; therefore war is never lawful ; or the killing of animals
for human food." "What you bought yesterday you ate to
day ; you bought raw meat yesterday ; therefore you ate raw
meat to-day." "This piece of raw meat," remarks De Morgan
in his Logic,1 " has remained uncooked, as fresh as ever, a pro
digious time. It was raw when Reisch mentioned it in the Mar
garita Philosophica in 1496 ; and Dr. Whately found it in just
the same state in 1826." What is predicated about the subject
in the major premiss is true of that subject " simpliciter" but not
of that subject "secundum quid" i.e. in its state of rawness.

The fallacy a dicto simpliciter ad dictum secundum quid is
commonly identified nowadays with the fallacy of the accident,
and the fallacy a dicto secundum quid ad dictum simpliciter is
1 p. 251.

ERROR AND FALLACIES 311

described as the " converse fallacy of the accident ". The examples,
too, by which the fallacy of the accident is usually illustrated,
fail to distinguish the latter from the fallacy we have just been
considering.1

(d) ACCIDENS. The precise nature of this fallacy — "-rra/oa
TO o-vv/3e@r)K6s," "per accidens " — has not been clearly determined.
It appears to be the mistake of assuming that whatever is pre-
dicable of a subject is also predicable of its "accidents," i.e. of
attributes that are not commensurate with that subject ; or, con
versely, that the "accidents" of a given predicate are also, and
equally with the latter, predicable of its subject. Here are some
of the examples and solutions offered by Aristotle. " 'Do you
know Corsicus?' 'Yes.' ' Do you know the man approaching
you with his face muffled?' 'No.' 'But he is Corsicus, and
you said you knew him.'" To be "a man approaching with
his face muffled," is an accident of Corsicus ; and it does not
follow that because Corsicus is known, this accidental state of him
is known. " Six is a few ; and thirty-six is six times six ; there
fore thirty-six is a few." But it is accidental to thirty-six to be
regarded as a few groups ; hence though " fewness " may be pre
dicated about an accidental condition of thirty-six it cannot be
predicated of thirty-six itself. " To call you an animal is to speak
the truth ; to call you an ass is to call you an animal ; therefore
to call you an ass is to speak the truth." The fallacy here lies
in the minor premiss, in the assumption that if " animal " can
be predicated about a given subject, " ass," which is an accident
of this predicate, can likewise be predicated of it. (The species-
notion is always an accidens of the genus-notion : the fundamen-
tum divisionis must be an accidens of the genus : some animals are
asses, but an animal need not necessarily be an ass). Sometimes,
of course, a subject (or predicate) and one of its accidents may
be de facto commensurate. In such cases the fallacy does not
occur: we know from the subject-matter that the subject (or pre
dicate) may be validly replaced by its commensurate accident.
For instance, although the fallacy is committed in arguing that
all plane rectilinear figures have the sums of their interior angles
equal to two right angles, because this latter is true of all plane
triangles ; yet the fallacy is avoided in arguing that because all
right-angled triangles have the square on the hypotenuse equal

1 Cf. JOSEPH, op. cit., p. 547 ; WELTON, op. cit., ii., p. 256 ; Palaestra Logica,
p. 86.

3i2 THE SCIENCE OF LOGIC

to the sum of the squares on the remaining sides, the same
is true of all triangles inscribable in semi-circles : for in this case
we know that the acddens " inscribable in a semi-circle " is com
mensurate with the subject " right-angled triangle " ; that what we
can predicate of the former we may predicate of the latter ; that
the proposition, " right-angled triangles are inscribable in semi
circles," being a reciprocal proposition, is simply convertible. Wher
ever the fallacy occurs it will be found to lie in the assumption
that some proposition is simply convertible, which is really con
vertible only per accidens. Hence the name of the fallacy. Take
the inference : " This dog is yours ; this dog is a terrier ; there
fore this terrier is yours " ; — evidently a valid inference. But is
there not illicit process of the minor term ? Apparently there
is ; and apparently the conclusion should be " a terrier (or some
terrier) is yours " ; but really the minor premiss contains the
information " this dog is this terrier " — which justifies the defi
nite conclusion.

We have seen that the fallacy a dicto simpliciter ad dictum
secundum quid is committed when we attach the predicate of a
genus to some subject which is not really contained in, or subordin
ate to, that genus. We now see that the fallacy of the accident
is committed by unlawfully equating a genus and its subordinate
notions (species or individuals), either as subjects of the same
predicate (" All men are rational ; all angels are rational ; there
fore all men are angels ") ; or as predicates of the same subject
(" All men are rational ; all men are bipeds ; therefore, all bipeds
are rational ").

(e) CONSEQUENS. The fallacy of the consequent is the mis
take of inferring the truth of the antecedent from the truth of
the consequent, or the falsity of the consequent from the falsity
of the antecedent, of a hypothetical proposition.1 It is therefore
illicit conversion, or contraposition, or inversion, based on the
erroneous supposition that the hypothetical judgment is al
ways reciprocal. " If a religion can elevate the soul it will sur
vive persecution ; therefore if a religion survives persecution it
must elevate the soul ; and if it does not elevate the soul it will
not survive persecution." " This man has no visible means of
support ; therefore he is a professional thief." There is an ob-

1 Another mistake is that of interpreting the antecedent of a hypothetical as
necessarily giving a causa essendi of the consequent : it need only give a ratio cog-
no$cendi, a symptom, or effect, of the latter.

ERROR AND FALLACIES 313

vious analogy between the simple conversion of the categorical
"A " proposition in the fallacy of the accident, and the attempt to
argue from consequent to antecedent in the hypothetical pro
position. The establishment of laws of nature in the form of
reciprocal hypotheticals is an ideal at which science aims ; and
when we know from the subject-matter that a given hypothetical
is reciprocal we can derive from it the inferences just mentioned ;
but, apart from such knowledge, the mere form of the hypotheti
cal does not guarantee them. The fallacy is committed in in
ductive research when an hypothesis is regarded as proved by the
mere fact that it explains the very phenomenon to account for
which it was invented : it falls into the form " If A then C ; but
C ; therefore A " : an inference which is formally invalid, inasmuch
as it ignores the possibility of a plurality of antecedents or causes.
Two very common and dangerous forms of the fallacy of the
consequent are the assumptions (a) that we refute or disprove a
thesis by showing that the arguments alleged in support of it are
unsound (whether by reason of false premisses or of formal in
validity) ; (£) that the arguments in support of a thesis are neces
sarily sound (both materially and formally) because the thesis itself
is true (148). In regard to (a), we must remember that the only
way to disprove or refute a thesis is by positively proving its contra
dictory. Suppose that two premisses, A and £, are advanced
in proof of a conclusion, C. He who advances the argument
asserts two things (i) " If A and B, then C" (the formal validity
of his syllogism), and (2) " A and B are both true " (its material
validity). Now, evidently, if we merely show that his argument
is formally invalid (" If A and B, not necessarily C "), or that
his premisses are not true ("Not both A and B"\ we do not
thereby establish the proposition "Not C": except, indeed, the
combination of (i) and (2) are known to furnish the only possible
ground of C. Similarly, in regard to (#), we have to bear in mind
that a true conclusion is often defended by false or inconclusive
reasons — a good cause is i often supported (and injured) by bad
arguments. A true conclusion does not guarantee the formal
validity of any argument that may be alleged as proving it ; nor,
when the argument is formally valid, does the true conclusion
guarantee the truth of the alleged premisses : unless these be the
only ones from which the conclusion in question can follow ; and
this latter is not guaranteed in any particular case by the mere
formal validity of the argument.

3 14 THE SCIENCE OF LOGIC

(/) PLURES INTERROGATIONES. The fallacy of many ques
tions consists in so putting a question that a single answer will
involve more than one admission. In its simplest form it com
bines many questions into one, and insists on a categorical " Yes "
or " No " for answer : " Is he a socialist and a conspirator ? Yes
or No ? " More frequently, the question is single, but is based upon
a certain admission which it wrongly assumes as already made :
" Have you given up your intemperate habits? " The traditional
example, " Have you cast your horns ? " gives the fallacy the
name of cornutus. Such traps must be met by a distinction
between the various parts of the question (" Distinguo "), or by
a denial of the assumed admission (" Nego suppositum"}. The
fallacy is rather frequently committed by giving reasons and argu
ments in explanation of some supposed fact which is not really a
fact at all. It is open to question whether, for example, it is not
committed by those who endeavour to show how protective tariffs
encourage the industries of a country ; or how communication is
effected with the souls of the dead ; or how dowsers detect subter
ranean springs.

The policy of " tacking," in the American Legislature, is
a sort of practical application of this fallacy. " The President
of the United States can veto bills, and does veto them freely ;
but he can only veto a bill as a whole. It is therefore not
uncommon for the Legislature to tack on to a bill which the
President feels bound to let pass a clause containing a measure
to which it is known that he objects ; so that if he assents, he
allows what he disapproves of, and if he dissents, he disallows
what he approves." l

On analysis, this fallacy will be found to involve misinter
pretation of an alternative or disjunctive judgment. The alternatives
enumerated or suggested are tacitly and erroneously assumed to be
exhaustive, when they are really not so. The alternatives that a
person " either has or has not " given up his intemperate habits,
is apparently exhaustive, but is not really so, for the desitive pro
position is not simple, but compound (95). " Is he a socialist
and a conspirator ? Yes or No ? " implies that the alternatives " He
is both or he is neither " are exhaustive. We have, in other
words, a wrong application of the principle of excluded middle.
The disjunctive premiss of a dilemma should enumerate all the
alternatives permitted by the subject-matter ; and failure to secure
1 JOSEPH, op. cit., p. 557.

ERROR AND FALLACIES 315

this complete enumeration is the most common source of the in
conclusive dilemma (185).

A cognate fallacy is that of supposing that the alternatives
enumerated in the alternative judgment are always mutually ex
clusive (145).

275. FALLACIES INCIDENT TO METHOD (Part IV.)- — We may
perhaps conveniently divide these into two main classes : (A)
Fallacies incident to deduction or proof ; and (R) Fallacies incident
to induction or discovery.

(A] Fallacies incident to deduction or proof: —

(a) IGNORATIO ELENCHI is the fallacy of proving the wrong
conclusion. By an eX^y^o? Aristotle meant an argument by
which a disputant established the contradictory of his opponent's
conclusion, thereby refuting the latter ; and the disputant com
mitted this fallacy if he proved anything other than the exact
contradictory of his opponent's thesis — if, in other words, he mis
took the proposition he had to establish. The fallacy is nowa
days understood to include all cases of " arguing beside the
point," " proving the wrong conclusion," " missing the point at
issue " — whether deliberately and with intent to deceive, or not.
The argument used in such cases may be perfectly valid ; but it
is not to the point, and herein lies the fallacy. To argue that a
particular branch of study — for example, the study of the Irish
language — -should not be included in the curriculum of our schools,
on the plea that it will never earn " bread and butter " for nine-
tenths of those who study it, would be a typical instance of the
fallacy. Even though the study of Irish might be useless as a
means of earning a livelihood, it might be highly desirable on
other grounds. Again, to point out a disadvantage or difficulty
against some practical proposal — some social reform, for instance
— is not to prove it impracticable or undesirable : for this it
would be necessary to prove that the difficulties or disadvantages
against it outweigh the advantages of carrying the proposal into
effect Or, again, to show up the weakness of an adversary's
arguments is not to prove his contention unsound : such an as
sumption, involving the fallacy of the consequent^ would be also
ignoratio elenchi.

This fallacy, of confusing the point at issue in some way or
other, is of most frequent occurrence in every domain of argu
mentation. Pleadings at law, political debates in parliament or
on the platform, newspaper controversies on questions of public

316 THE SCIENCE OF LOGIC

interest, discussions in books and periodicals, whether on theology,
philosophy, science, art, literature, etc. — furnish an unfailing sup
ply of examples. It is a favourite device with those who have to
support a weak cause. The attorney for a defendant is said to
have handed the barrister his brief marked " No case ; abuse the
plaintiff's attorney ". Discussions on topics of great and urgent
practical importance — religious, ethical, social, political, educa
tional, administrative, etc. — naturally stir up deep and strong per
sonal feeling ; and hence they tend to stray from a calm, impartial
consideration of the merits of the question, and to confuse the
issues by irrelevant personalities and recriminations. Such dis
plays offend not merely against the requirements of courtesy and
good taste, but also against the canons of logic, as being instances
of fallacious reasoning — of ignoratio elenchi. They will be duly
discounted by those who can recognize them for what they really
are : substitutes for real argument, betrayals of weakness or defeat.
The writer or speaker who is clearly conscious of holding a
well-reasoned position can afford to be calm, courteous, patient,
provided he is addressing intelligent people ; but if he wants to
carry the crowd against the demagogue, he cannot afford to despise
the power of rhetoric, or to dispense with the art of oratory.

There are many minor forms of the fallacy. The argumentum
ad baculum is an appeal to physical force. The argumentum ad
populum, or " appeal to the gallery," for the purpose of exciting
the feelings, or arousing the passions, of the crowd, is the favourite
device of the mob-orator. The argumentum ad ignorantiam is
the fallacious reasoning that is made to pass muster owing to the
ignorance of those to whom it is addressed. The argumen
tum ad verecundiam is an appeal to the people's veneration for
authority, in matters that should be decided by reason, and on
their own merits. The appeal ad misericordiam is any argument
to show that a person deserves pity, when proof of his innocence is
demanded. Socrates refused to have recourse to it, though urged
by his friends to do so, when condemned to death by his judges.

The argumentum adhominem, or " tu quoque" style of argument,
is a fairly common form of the ignoratio elenchi ; it includes such
practices as personal abuse, recrimination, charges of inconsistency,
etc. If the personal character of one party is relevant to the
trustworthiness of his allegations, it will not, of course, be ignoratio
elenchi on the part of the other party to impeach the former's
veracity. In cross-examination, a counsel can lawfully shake the

ERROR AND FALLACIES 317

credibility of a hostile witness by showing that the latter has a
criminal record, and that his evidence is unreliable. Sometimes,
too, we may be quite satisfied to show that, whatever about our
own position, that of our adversary at all events is unsustainable,
being inconsistent with the latter s own principles or admissions.
This is refuting him " out of his own mouth," from his own ad
missions in theory or in practice, and without committing ourselves
to the truth of such admissions (254, &). Thus, Christ silenced
those who blamed Him for curing on the sabbath by asking them
which of them, if his ox or his ass had fallen into a ditch, would
not pull it out on the sabbath.

(6} PETITIO PRINCIPH, or " begging the question? is the fallacy
of assuming as a premiss, in some form or other, either the very
proposition to be proved, or a proposition which can be proved
only by means of the latter. It is, therefore, a fallacy incident to
demonstration, proof, scientific explanation. The student will be
familiar with it already, from what has been said on the Nature
of Inference (195-6) and on the Uniformity of Nature (224); but
it can be so hidden and harmful that it calls for special analysis.
The title of the fallacy recalls the language of the dialectical
disputation (205), in which the disputant sought his premisses, for
the refutation of his adversary, among the latter's admissions. If
he endeavoured to get his adversary to admit the very point in dis
pute, or used this as a premiss against the latter, or used some
other proposition which he could establish only by means of such
an admission, his refutation would be sophistical : he would have
" begged the question " ; he would have assumed as a premiss1 a
proposition which he could not legitimately assume for his pur
pose.

Aristotle distinguishes five ways in which the fallacy can
occur: (i) by assuming the very proposition itself to be proved,
usually under cover of synonyms ; (2) by assuming, for the proof
of a particular proposition, a universal principle which cannot be
itself established except through a knowledge of that particular ; (3)

1 The universal propositions accepted as starting-points of disputation were
called by the Scholastics principia (cf. WELTON, op. cit., ii., p. 283). These were
either self-evident axioms, or demonstrable and universally admitted truths. The
fallacy of assuming as a principle something which is not such, is dealt with below
as "Undue Assumption of Axioms". It is not quite the same as "begging the
question," i.e. assuming either the conclusion to be proved, or some proposition
which can be proved only by means of this conclusion : this would be better called
Petitio Quaesiti, or Petitio Quastionis; but the traditional name, Petitio Principii, is
too well established to be disturbed by any alteration of usage.

3i 8 THE SCIENCE OF LOGIC

by assuming a particular to prove the universal which involves it ;
(4) by assuming successively, in parts, the proposition to be
proved ; (5) by assuming, without independent proof j a proposition
which is the reciprocal of the proposition to be proved. This
last is too simple to need notice. It is arguing, for instance, that
Cork is south of Dublin because Dublin is north of Cork. The
fourth mode is merely a variety of the first. Aristotle instances
the attempt to prove " that the art of healing is knowledge of what
is wholesome and unwholesome " by assuming it successively to be
a knowledge of each. The third mode is really the inductive
fallacy of supposing that enumerative induction establishes a uni
versal truth (207). We have, therefore, to consider the first two
modes, which are the really important ones.

(i) The very proposition to be proved is rarely assumed as a
premiss, except under cover of some circumlocution. As simpler
examples we may take the following : " The House of Lords is
out of date because an upper chamber in England is an anachron
ism ". " The bill before the house is well calculated to elevate
the character of education in the country, for the general standard
of instruction in all the schools will be raised by it."

De Morgan, in his Budget of Paradoxes (p. 327), gives an interesting
example, from an attempt at squaring the circle, by a Mr. James Smith, in a
work entitled Nut to Crack. Smith attempted to prove that the ratio of circum
ference to diameter is 3$, by assuming that it is so, and showing that every other
ratio is, on this hypothesis^ absurd : " I think you will not dare to dispute my
right to this hypothesis, when I can prove by means of it that every other value
of IT will lead to the grossest absurdities ; unless indeed you are disposed to
dispute the right of Euclid to adopt a false line hypothetical ly, for the purpose
of a reductio ad absurdum demonstration in pure geometry ". He thus con
founds his own fallacious procedure with Euclid's process of indirect proof.
He argues that " if 3! be the right ratio, then all other ratios will be wrong ;
but they will be wrong, on the hypothesis ; therefore the hypothesis is right " ;
whereas he should have shown, independently of his hypothesis, that they will
be all wrong. He argues that " If A is true, B will be false ; but B will be
false if A is true ; therefore A is true" — instead of arguing " If A is true, B
will be false, but B is false, therefore (since B includes all suppositions other
than A} A is true." In the reductio ad absurdum Euclid argues that " If A
is false B will be true ; but B is false ; therefore A is true." " Euclid assumes
what he wants to disprove, and shows that his assumption leads to absurdity,
and so upsets itself. Mr. Smith assumes what he wants to prove, and shows
that his assumption makes other propositions lead to absurdity. This is
enough for all who can reason." (De Morgan, ibid.).

The example just given suggests a method of procedure which is an exceed
ingly seductive form of the fallacy, a method which apparently entraps honest
reasoners themselves just as frequently as it is knowingly used by dishonest

ERROR AND FALLACIES 319

reasoners with intent to deceive. Some theory is put forward as a thesis to be
established— the extreme evolution hypothesis, for instance, including abio-
genesis ; or the theory of transformation of species by " natural selection " ; or
the view that all religious belief originated in a primitive feeling of fear which per
sonified the forces of nature ; or the doctrine that the known universe is purely
mechanical, belief in free-will and in purpose or design in nature being an
illusion of the mind ; or the agnostic attitude that miracles, revelation, the
supernatural, are all alike impossible. . . . The advocate describes and ex
pounds his theory ; interprets relevant facts in the light of it ; gets his reader
around gradually to look at these provisionally from his own point of view ;
shows as plausibly as possible how the facts may be seen to fit in with his
theory, or to corroborate it ; insists on reading the facts through the theory, on
describing — and, so, colouring — these in terms of the theory ; substitutes, as far
as may be, for the facts themselves, the interpretations he has given them from
the theory ; then ventures to show how what he calls the facts (thus coloured,
interpreted, manipulated, as they have been) are inconsistent with any other
view, and will admit of no other explanation than his own ; and so insinuates
the conclusion that the theory advocated is the tiue one. The serious student
of religious, philosophical, and scientific literature, who happens to have culti
vated the faculty of thinking logically for himself, and of testing what he is asked
to accept, will be amazed at the facility and frequency with which writers
deceive themselves, or their readers, or both, with pages, or chapters, or even
volumes, of such solemn question-begging argumentation. It is not that such
writers naively believe, or make believe, that an hypothesis must be true merely
because it can give a plausible explanation of the facts. Rather they try to per
suade themselves and their readers to look at the facts only through the coloured
glass of the hypothesis, and, by such means, to believe that there is no other way
in which the facts can be intelligibly apprehended or explained. The^/z/20
principii is committed by gratuitously interpreting all the facts only in the light
of the preconceived theory. The whole process may also be regarded as an
illustration of the fallacy of the consequent : arguing from the truth of the
consequent to the truth of the antecedent.

When the fallacy of petitio principii is committed in a single
step of inference, it is called the hysteronproteron (vcrrepov irporepov).
It is usually concealed by the use of synonyms. Sometimes the
judgment, expressed in abstract terms, is given as a reason for itself
in concrete terms : " Opium induces sleep because it has a soporific
quality ". Sometimes the fallacy is committed by a single " ques
tion-begging epithet" — generally either laudatory or condemna
tory: as when, to prove that some new measure ought to be re
sisted, we call it an innovation, or contend that it would call
into question an irrevocable law. The hysteron proteron may be
expressed symbolically by the syllogism, " M is P ; S is M ; . '. S
is P" where M is a synonym for S, or for P : the syllogism would
then read "S isP; S is S ; .-. S is P" or " P is P ; S is P ; .: S
is P" ; .thus showing one premiss as a tautology and the other as

320 THE SCIENCE OF LOGIC

identical with the conclusion. "Whatever has a soporific quality
induces sleep" is a tautology ; " opium has a soporific quality " is
the same as the conclusion to be proved : " Opium produces
sleep ".

When the conclusion is separated by more than a single step
of inference from the assumption, the fallacy is called the circulus
in demonstrando, circulus vitiosus, or arguing in a circle. Thus,
if we were to prove the immortality of the soul from its simplicity
(as Plato does in the Phaedo], and then prove its simplicity from
its immortality (as he does in the Republic], we should be arguing
in a circle. It may be expressed thus : " M is Pt S is M, .'. S is
P ; and M is P because 5 is P and M is S."

(2) The second, and perhaps more common, form of petitio
principii, consists not in assuming the very conclusion itself to
be proved, but in assuming, without independent proof , some wider
principle which involves the latter, arid which could not have been
proved or established otherwise than through a prior knowledge of
the latter. To this head we may refer all cases wherein the as
sumed proposition, whether wider than the conclusion or not,
is such that it could not have been known or established other
wise than through a prior assumption of the truth of the con
clusion.

We have already dealt with Mill's contention that all syllogism
commits this form of petitio principii (195-6). We saw there, how
ever/that the fallacy is really committed only when a premiss is
assumed which could not be established otherwise than through
a knowledge of the conclusion ; that this is usually the case when
the premiss in question is a mere collective proposition ; but that
genuine universal premisses can be known with certitude inde
pendently of any knowledge of instances to which they are
applicable, arid otherwise than by enumeration of these in
stances.

A few examples will suffice here to illustrate this form of the
fallacy. Galileo accuses Aristotle of having committed it in the
following argument : " The nature of heavy things is to tend
towards the centre of the universe, and of light things to fly from
it ; experience proves that heavy things tend towards the
centre of the earth, and that light things fly from it ; therefore
the centre of the earth is the centre of the universe ". Spencer,
in his work on Education, after distinguishing two values in any
branch of study — value for knowledge imparted, and value as a

ERROR AND FALLACIES 321

mental training, — proceeded to argue that the branches he had
shown to have the first value must have the second value like
wise : on the ground that it " would be utterly contrary to the
beautiful economy of nature, if one kind of culture were needed
for the gaining of information and another kind were needed
as a mental gymnastic ".l This is simply assuming as universally
true what he wanted to prove of the cases he examined. Here
are a few briefer instances : " The imposition of legacy duties is
justifiable, because all property passing by will ought to be
taxed" ; " His cruelty may be inferred from his cowardice, for
all cowards are cruel " ; "A table of logarithms must be entertain
ing, for all books are so ".

If our assent to the principle of the Uniformity of Nature were based
upon simple enumerative induction, and if at the same time all induction de
pended for its validity on a prior belief in the Uniformity of Nature, we
should never be able rationally to justify this belief, or, consequently, to put
our trust in any single inductive generalization (apart altogether from this other
damaging fact, that enumerative induction can never beget scientific certitude).
Yet Mill contends that the petitio principii, apparently involved in this attitude,
is only apparent, not real. Unfortunately, it is real. And when Mill attempts
to show that the position is free from the fallacy, so far from succeeding, the
attempt only involves him in the fallacy afresh. His line of argument has
been examined already (224), but the matter is of such importance that a
reference to it in the present context will not be superfluous.

According to Mill, the principle of the Uniformity of Nature is the
" ultimate major premise of all induction " ; communicating its reliability to
all inductions ; without which none would be valid ; which, therefore, we
must hold for certain, antecedently to all inductions that are scientific, that give
certitude. How, then, do we come to give a certain assent to this principle ?
on what grounds ? by what process ? We reach it, Mill answers, through a
vast induction per enumerationem simplicem, by which we accumulate and
generalize "many laws of inferior generality," each of which was reached by
a like process of generalizing from enumerated instances 2. But how can we
make an induction per enumerationem simplicem, before we are sure of the
principle, if all induction presupposes certitude about the principle ? And,
anyhow, is not enumerative induction so admittedly weak that of itself it can
never carry us beyond an empirical generalization, to the certitude we need
for the principle of uniformity as a .basis for scientifically certain physical laws ?
Mill replies that most enumerative inductions do presuppose the principle
established ; that, therefore, this process does not and cannot in ordinary
cases establish a law ; but he attempts to show that the enumerative induction
by whic^ we reach the principle in question is different from all other lesser
enumerative inductions, and does give us certitude about the principle. And
here is how he proceeds : The wider the field of experience over which we
generalize by enumerative induction, the safer this process becomes ( a state-

1apud WELTON, op. cit., ii., p. 284. 2 Cf. WELTON, op. cit., ii., pp. 42, 43.

VOL. II. 21

322 THE SCIENCE OF LOGIC

ment which is true only on the assumption that natural causes act uni
formly) : so that when the domain of generalization embraces all experience,
as it does in the case of this principle, enumerative induction can beget certitude,
and " the distinction between empirical laws and laws of nature vanishes "
(Logic, III., xxi., § 3). But how does he prove, without assuming uniformity in
nature, the assertion that the safeness of the generalization grows with the
extent of its domain f His only attempt at proof is the observation that the
wider the field of experience on which a generalization is based the more likely
we are to meet with adverse instances, if any such occurred. But this already
supposes belief in uniformity, for why should we attempt at all to generalize
beyond experience did we not believe in uniformity ? Granted this belief, an
adverse instance would convince us that our supposed causal connexion was
not really causal, because not uniform ; but without such belief an adverse
instance would be really devoid of all significance for us. Granted the uni
formity of nature, the wider our actual uncontradicted experience of a given
sequence, the more likely it is to be a causal sequence ; but if we have yet
to prove that natural causes must act regularly, not capriciously and chaotically,
how can any such experience of itself guarantee any generalization, even a
single step beyond itself ? Or what can be the use of comparing all actual
experience in time and space, no matter how extensive, with all possible ex
perience, in the hope of concluding directly from the former to the latter ? Yet
this is what Mill does : " If we suppose, then, the subject-matter of any
generalisation to be so widely diffused that there is no time, no place, and no
combination of circumstances [within or beyond actual experience] but must
afford an example either of its truth or of its falsity, and if it be never found
[within actual experience] otherwise than true, its truth cannot be contingent
on any collocations, unless such as exist at all times and places [even outside
actual experience] " (ibid.) In other words, the domain of experience to
which the principle refers is so wide, being all possible experience, that every
time and place must afford an instance either of its truth or of its falsity ;
but it has been found to be true at all times and in all places within actual ex
perience ; therefore it is true of all times and places beyond our experience !
The premisses give no right to any such conclusion.

0) UNDUE ASSUMPTION OF AXIOMS. All proof presupposes,
and proceeds ultimately from, self-evident truths, called principles
or axioms : some of which are " common " principles, of universal
application, while others are "proper" to the subject-matter of
this or that special science (252). Now axioms are indemon
strable ; their evidence is immediate, i.e. embodied in themselves ;
so that their truth must be apprehended by an act of intellectual
intuition or vision. The theory of all this is easy enough. Noth
ing could be more reasonable, or more necessary, than the demand
of logic, that truths which are really axioms ought to be ad
mitted by all to be such, and that, conversely, no judgment
which is not really an axiom should be accepted or allowed to
pass current as such. The violation of this latter demand involves

ERROR AND FALLACIES 323

the fallacy under consideration ; but the violation of the former
demand involves a corresponding fallacy, which might be called
Undue Rejection of Axioms. The same considerations apply to
both mistakes ; and when we set them down as logical fallacies
we assume, of course, that the intellect, the faculty which appre
hends truth and estimates evidence, is essentially similar in all
normal human beings; that it is similarly affected in all by the
same kind and degree of evidence ; that it is, therefore, similarly
impelled in all to assent to really self-evident truths. In a word,
we assume that a knowable reality forms the object of human
science, and that all normally constituted minds behave in the
same way towards this reality. This assumption, itself, is not,
perhaps, an axiomatic truth, but is rather one of those postulates
or assumptions which are indispensable to all research, and
which are justified only by actual human experience. The only
" proof" of the contention that man can discover some truths
with certitude, lies in the fact that he has discovered some ; and
to doubt man's capacity in this regard would be to paralyse the
mind, and so destroy completely the path to any truth what
soever.

But, granting that man can discover truth, and, consequently,
that some truths are really self-evident to all normal minds, the
question as to which truths are really axioms, and which are
not, is a grave and momentous question. While no one has
ever seriously doubted the self-evident character of the funda
mental laws of thought, and of certain abstract1 principles of
mathematics and metaphysics, there has always existed an
abundance of controversy as to the ultimate significance of such
abstract truths of the ideal order, when applied to the concrete data
of sense experience for the purpose of obtaining a rational inter
pretation of the universe in which we live (224, 229-32).

The settlement of these controversies, the elimination of errors as to which
judgments are self-evident axioms, which are only postulates justifiable by
experience, which are even unjustifiable, erroneous, or misleading, assumptions
— all this belongs to epistemology, and not to logic ; though, in our treat
ment of Induction, Demonstration, and Scientific Explanation, we have been
afforded opportunities of glancing at some of the conflicting philosophies in
which the discussion of these problems has issued. That view of the universe,
which is embodied in materialism, materialistic monism, phenomenism,
sensism, positivism, agnosticism, apparently accepts, as an indisputable truth
or axiom, the false and unjustifiable assumption that whatever transcends the
scope and range of our sense faculties is unreal, worthless, and inadmissible.

21 *

324 THE SCIENCE OF LOGIC

In denying the existence, or at least the cognoscibility, of suprasensible reality
in any mode or form, it is making an unjustifiable application of the maxim :
Entia non sunt multiplicanda praeter necessitate™. (231). At the opposite
extreme lies the philosophy of idealist or spiritualist monism, which regards
even the material universe as a mere manifestation or expression of the thought-
activity of One Immanent Spirit or Mind : a view which appears to accept as
axiomatic this other false and misleading assumption, that whatever is real is
intelligible in terms of abstract thought, and that whatever cannot be totally
included in this ideal domain is illusory and unreal.

Prepossessions in favour of certain broad, general views or
theories about things, dispose us to exaggerate the evidence for
these views, or to set down as evidence what is really not evidence
at all. And, by dint of refusing to see things otherwise than in
the light of these theories, we may gradually persuade ourselves
that the latter are self-evident, axiomatic. Thus it is that
questionable postulates are wrongly allowed to assume the rank
of axioms in the minds of those who entertain them. It is not
so much because of formal fallacies in our conscious reasoning
processes that profound philosophical errors are so prevalent.
These are due rather to an unquestioning and uncritical ac
ceptance of doctrines, beliefs, and opinions, which happen to
appear plausible to us on account of our own individual mental
development, and of the special intellectual atmosphere in which
we have been trained from our earliest days : phantoms of the
cave, of the theatre, and of the market place.

For the human mind, the domain of really self-evident axioms
is very limited ; and they are all abstract. But there is a larger
domain of what may be called concrete truths of" common sense,"
in reference to which all individual minds are not equally receptive.
Education ; intellectual, moral, and religious training ; mental
companionship with books and teachers ; character, habit, and
disposition ; likes and dislikes ; passions and prejudices ; — all
these are agencies of enormous influence in moulding the individual
mind for the right or wrong discernment of evidence : for the
reception or rejection of important truths of the concrete order,
truths that have a direct bearing on life and conduct, and which,
though not strictly axiomatic in the sense of mathematical prin
ciples, nor on the other hand capable of strict and cogent demon
stration, are nevertheless such that the normal mind, unimpeded
by any one-sided bias, will unhesitatingly assent to them, and will
act with entire reasonableness in doing so. Against these sources
of deviation from the healthy, normal state of mind, logic has no

ERROR AND FALLACIES 325

infallible safeguard to offer. It can merely emphasize the im
portance of these influences, point them out to us for our con
sideration, and call our attention to the undeniable fact that
though the faculty for discerning truth is of the same nature in all
men, nevertheless different men are so differently disposed in
mental habits and equipment that what appears self-evident to
one may well appear not only inevident, but utterly untrue, to
another.

While it would be wrong to say that the " normal mind " is itself an ab
straction, never to be met in real life, it must be admitted that there is great
variety in the attitudes of different minds, face to face with the same real uni
verse, and that in our actual experience of life we meet many strange mixtures of
scepticism and credulity. But from the historical fact that philosophers in
every age have propounded conflicting and irreconcilable solutions of the most
momentous problems concerning man and the universe, it would be a mistake
to conclude — as some have concluded — that truth on these grave matters is un
attainable, and that therefore the inquiring human mind is fated t6 move, how
ever reluctantly, towards the dark, final bourne of doubt and agnosticism. For
we have a right to conclude merely that the human mind is both finite and
fallible, that there is no royal road to knowledge, that truth must be sought
after, that the more precious the truth, the more diligent must be the search,
that it is only by a cautious, painstaking, perseverfng application of the mind,
deception and error can be avoided. The historical study of the workings of
human thought upon philosophical problems, its gropings and findings, its gains
and losses, its advances and aberrations, cannot fail to convince the unprejudiced
student that man is capable of attaining to sufficient truth about his own origin,
nature, and destiny, and his proper place in the universe, to guide his life aright,
if he only has the will to do so. It will, no doubt, convince him at the same
time that the work of discovering truth, and living up to it, is noble and elevat
ing, if difficult and sometimes even arduous. He will be surprised at first to
discover that so many great minds have greatly erred in regard to the funda
mental truths of human life. But, according as he realizes the complexity of
the problems they had to face, the conflicting evidences they had to weigh, the
traditional beliefs or disbeliefs in which they were trained, and all the objective
sources of error that surrounded them, his surprise will gradually diminish.
And it will be likely to disappear altogether if he fixes his" attention on the
subjective sources of error by which even great minds may be disturbed and led
astray. These phantoms of the tribe need only to be mentioned, to make us
realize something of their dangerous influence.

On the part of the intellect, sloth is a source of much error : it is the cause
of undue haste in the search for truth. Doubt is an irksome state of mind ;
suspense is unpleasant ; while assent brings rest. Assent is the goal to which
inquiry is the path. But the path is through a land of pitfalls and will-o'-the-
wisps ; and the passage to a right assent is often laborious. Hence the temp
tation to move along hastily and without due care, to stifle misgivings, and to
cut short the search by resting in assent to some position the truth of which is
not really guaranteed by the evidences our inquiry may have brought to light.

326 THE SCIENCE OF LOGIC

This is a violation of that canon of method which counsels us to proceed
step by step in the discovery of truth (203). '

Another obstacle to the attainment of truth, one that is rooted in the will
rather than the intellect, is the prejudice created by the habit of a long-standing
and cherished belief. " Prout unusquisque affectus est ita judicat," says the
author of the Imitation of Christ : the wish is father to the thought. There
lurks no small danger to the cause of truth in the fear of having our habitual
mental attitude in any way disturbed, of being unceremoniously robbed of what
we have always complacently accepted for the truth. It is decidedly unpleasant
to have cherished beliefs rudely exploded. Habit is tyrannical, as St. Thomas
well observes ; 2 and requires not a little courage to break with it. Hence
our eagerness to accept whatever falls in with the habits we have formed, and
to give it an unhesitating welcome. " We like to hear people talk of all things
in the way we have been accustomed to think of them and to hear them talked
about." :t

Yet another source of failure is the absence of a disinterested love for the
truth. A well-known French psychologist, M. Henri Joly, has some suggestive
remarks on this subject : " Very often," he writes, " we do not find the truth
because we do not seek it. . . . For we do not seek the truth when we give to
the investigation of facts and questions a mere superficial, half-hearted attention ;
when pride prompts us to imagine that by a simple glance we can see well and
see all ; when we are too impatient for the gratification of an idle curiosity ;
when a hasty half-truth pleases us better than a full truth brought to light labori
ously ; when we stubbornly cling to an hypothesis for the sole reason that we
have invented it ; when we obstinately adhere to an opinion simply because we
committed ourselves to it in the beginning and are unwilling now to acknow
ledge our error ; when, finally, our estimate of things is influenced less by what
they are in themselves than by the way they affect our interests, our passions,
our sympathies, our prejudices, our likes and dislikes ".

" But why do we not seek the truth f Because we do not love it suffici
ently. \ do not mean that we positively love its opposite, which is error ; but
that we are not ready to dare all, and to sacrifice all, for the sake of truth. In
the field of science we pitch our camps and form our parties ; we bring to all
our discussions a. party spirit if we are disciples, the spirit of personal vanity
if we speak for ourselves. We prefer new and striking hypotheses to truths

1 Cf. ST. THOMAS, Summa TheoL, ii. ii., Q. 53, a. 3.

2" Ea quae sunt consueta, libentius audiuntur et facilius recipiuntur. Dignum
enim videtur nobis, ut ita dicatur de quocunque, sicut consuevimus audire. Et si quae
dicantur nobis praeter ea quae consuevimus audire, non videntur similia in veritate
his quae consuevimus audire. Sed videntur nobis minus nota et magis extranea a
ratione propter hoc quod sunt inconsueta. Illud enim quod est consuetum, est nobis
magis notum. Cujus ratio est, quia consuetude vertitur in naturam ; unde et habitus
ex consuetudine generatur, qui iuclinat per modum naturae. Ex hoc autem quod
aliquis habet talem naturam vel talem habitum, habet proportionem determinatam
ad hoc vel illud. Requiritur autem ad quamlibet cognitionem determinata proportio
cognoscentis ad cognoscibile. Et ideo sec undum diversitatem naturarum et habituum
accidet diversitas circa cognitionem. . . . Sic igitur quia consuetude causal habitum
consimilem naturae, contingit quod ea quae sunt consueta sint notiora." — ST.
THOMAS, In II. Met., Lect. 5.

» ibid.

ERROR AND FALLACIES 327

already old. Above all, we want to make a name ; and so our zeal for the truth
is gradually replaced by anxiety to embrace up-to-date opinions, or to attract
attention by the fearlessness of our views and the brilliancy of our writings.
We criticize our adversaries and are glad if we can make them contradict them
selves ; we controvert their arguments and build up elaborate demonstrations
of oar own : and we take greater delight in all this than in the discovery and
possession of the truth. But in all this we are showing a greater love for our
own views, for our own selves and interests, than for truth : and, as St. Augustine
well says, he that does not love the truth will not find it : ' Sapientia et veritas
nisi totis animi viribus concupiscatur, nullo modo inveniri poterit '." *

He who has a disinterested love for truth will prize it more highly than
originality. "A great man," says M. Emile Boutroux,2 " will not aim at being
novel or original, but at finding out the truth." He will discuss, but in order
to prepare the way for the truth, not to assert his own superiority : according
to the admirable sentence of St. Ignatius, Rationes modeste afferantur eo
animo ut suus veritati sit locus, non ut in ea re superiores inveniantur.

When such a one sets himself to examine a system of philosophy he will
try to get at the author's point of view, and to enter into the latter's thoughts ;
he will not engage in a mere search for weak points, with the unworthy idea that
the more he disparages others the more renown he will win for himself. Instead
of revelling in an author's apparent inconsistencies, he will examine the latter's
views with a ready impartiality, and try to reconcile them, remembering that
every error contains a soul of truth of which it is a perversion or exaggeration.
Such criticism will be invaluable to himself, as a test whereby to control his
own personal convictions.

At the same time, there is the opposite extreme to be avoided : impartiality
is not indifference. He is no lover of truth who admits indiscriminately all sorts
of opinions, who affects to regard them from a superior height with a conde
scending sort of sceptical curiosity, as if they had all the same value for the in
dividual and the same significance for society. Whether the indifference of the
dilettante springs from pride or from sloth, it is a betrayal of truth and a crime
against reason. Love of truth is hatred of error. We cannot embrace the
former without condemning the latter. An easy toleration of all sorts of con
flicting opinions in regard to religion and philosophy, is not unfrequently re
garded in our own day as the hall-mark of enlightenment and broadmindedness,
whereas it is in truth a mark of mental imbecility, or intellectual indolence.

(d] NON CAUSA PRO CAUSA, OR " FALSE CAUSE". By causa
(ainov) Aristotle here meant not a cause in the ordinary sense
of causa essendi, but a reason, a causa cognoscendi. The fallacy
consists in assigning as a reason for some conclusion a pro
position which is really irrelevant to that conclusion. Aristotle
contemplated especially cases in which this occurred in the

1 H. JOLY, Nouveau cours de Philosophic. Logique, pp. 312-13. For instructive
views on the same subject, cf. BALMES, Art d'arriver au vrai, chap, xxii ; OLLE LAP-
RUNE, De la certitude morale ; La philosophic et le temps present ; Les sources de
la paix intellectuelle.

*£tudes d'histoire et de la philosophic, p. 8.

328 THE SCIENCE OF LOGIC

reductio ad impossibile, or indirect proof (169, 254, <£). In this pro
cess we disprove a thesis by showing that the assumption of its
truth would lead to absurdities ; or we prove a thesis by showing
that the assumption of its falsity would lead to absurdities. Now,
the fallacy under consideration is committed if the absurdities do
in reality follow not from the assumption made, but from some
extraneous and irrelevant proposition which we have foisted into
our argument. The absurd conclusion is wrdngly sought to be
fathered upon the initial assumption. Hence Aristotle calls the
fallacy also " Non per hoc" " Non propter hoc" which is the
answer by which the fallacy ought to be met : " Your conclusion
is indeed absurd (or impossible), not, however, because of your
assumption about my thesis, but quite independently of it ".
The following instance is from Father Joyce's Logic (p. 281):
" Thus, if we suppose the sophist's opponent to have affirmed that
the death penalty for murder is just, the sophist might argue as
follows : ' The position leads to an absurdity : for granting that
the death penalty for murder is just, and that punishment is to
be held just in so far as it is efficacious as a deterrent, then it
follows that it would be equally just to inflict the death-penalty
for pocket-picking'. Here the original statement has nothing
to do with the conclusion obtained. This follows from the
principle that the justice of a punishment is measured by its
efficacy as a deterrent, — a principle which is in no way connected
with the statement that the death penalty for murder is just."

Aristotle includes under the head of this fallacy all cases in
which a conclusion is drawn from premisses which are quite
irrelevant to it, and which, for want of any better classification
we describe as cases of " No n Sequitur " : " arguments so foolish
and inconsequent, that they cannot even be said to simulate
cogency; these cannot be positively characterized, but must be
lumped together by the mere negative mark of inconclu-

siveness

As the fallacy of non causa pro causa, in Aristotle's sense,
was peculiar to dialectical disputations, and is of comparatively
rare occurrence nowadays, its name has been transferred pretty
commonly to the inductive fallacy of mistaking for the cause of an
event something that is not really the cause, the fallacy of Post
(or cum} hoc, ergo propter hoc (infra, B. c}. This mistake, of con
founding temporal sequence or coexistence of facts with causality,
1 JOSEPH, op. cit., p. 529.

ERROR AND FALLACIES 3*9

is not quite the same as confounding a temporal sequence or co
existence of judgments in the mind with the logical consequence
of conclusion from premisses. But little ambiguity can arise
from giving the name of false cause to the inductive fallacy in
question. And this mistake of confounding mere sequence or
coexistence with causality or consequence is one of the many
modes of the fallacy of Illicit generalization which will be ex
amined presently.

(B} Fallacies incident to induction or discovery :a —

(a) In induction we pass from observation of particular facts,
through analogy, and hypothesis, to the discovery and verification
of general laws. Here, then, the first possible source of error
will be IMPERFECT OBSERVATION, and the fallacy may be either
negative or positive in character.

(i) NON-OBSERVATION is the fallacy of overlooking something
that ought to have been observed. The function of observation is
to select and isolate the facts from which we hope to bring to
light some causal law (238). Hence we may either fail to
notice instances pertinent to the kind of fact we are investigating,
or fail to notice influences that are really operative in the in
stances actually observed.

Prejudice in favour of some preconceived theory is the most
potent cause of neglect to observe pertinent instances. The
process and product of our observation are profoundly influenced
by the unconscious interference and intermixture of our previous
knowledge and beliefs. " The opponents of Copernicus argued
that the earth did not move, because if it did, a stone let fall
from the top of a high tower would not reach the ground at the
foot of the tower, but at a little distance, from it, in a contrary
direction to the earth's course ; in the same manner (they said)
as, if a ball is let fall from the mast-head when the ship is in full
sail, it does not fall exactly at the foot of the mast, but nearer
to the stern of the vessel. The Copernicans would have silenced
these objectors at once if they had tried dropping a ball from
the mast-head, since they would have found that it does fall
exactly at the foot, as the theory requires : but no ; they
admitted the spurious fact and struggled vainly to make out a
difference between the two cases ".2 The opponents of the new

1 Cf. WELTON, op. cit., ii., pp. 261-77, whose treatment is here closely
followed.

a MILL, Logic, V., iv. § 3.

330 THE SCIENCE OF LOGIC

theory neglected to secure and examine an experimental instance,
because they assumed that if examined it would corroborate the
old one ; the Copernicans were not sufficiently scientific to
question this ; while the inferences of both parties alike reveal to
us how comparatively elementary was the scientific knowledge
that prevailed in those days about the laws of motion.

It is important in the next place to note, and to guard
against, the natural tendency to neglect NEGATIVE instances. Strik
ing instances of a coexistence or sequence impress us, drawing
off our attention from the cases in which the coexistence or se
quence has not occurred ; and so we are tempted to see a causal
connexion in what may be merely casual. Remembering the
few instances in which our dreams have been " fulfilled," and
ignoring the far more numerous instances in which they have
not, we are tempted to think that dreams are really prophetic.
It has been already pointed out (238) that non-observation,
whether of instances or of operative influences, does not prove
their non-existence.

Non-observation of operative influences is one of the greatest
dangers to induction. The accuracy of our hypotheses and
generalizations depends upon the success with which we isolate
our phenomena, eliminating only what is unessential, and taking
into account all that is essential, to their occurrence. It was
commonly believed in the seventeenth century that a wound
could be healed by the application of a certain salve or powder
to the instrument that caused the wound, the latter being kept
clean and cool during the process of healing. The cure was
attributed to the "sympathetic" influence of the salve, rather
than to the unobserved recuperative forces of the patient's con
stitution when left to act in favourable conditions. As De
Morgan well remarks,1 "If we remember the dreadful notions
upon drugs which prevailed, both as to quantity and quality, we
shall readily see that any way of not dressing the wound would
have been useful ". This form of fallacy is particularly prevalent
and difficult to avoid in exploring the causes of complex social,
economic, political, and religious phenomena.

(2) MAL-OBSERVATION is the wrong interpretation of what
falls immediately under sense perception. It is due to the mis
leading interference of unconscious inference arising from habitual
beliefs, prejudices, and mental tendencies. Many people believe

1 Budget of Paradoxes, p. 66 ; apud WELTON, op. cit., ii., p. 264.

ERROR AMD FALLACIES 331

they have seen ghosts when they have really seen tombstones
or stray donkeys. It requires some reflection to realize what a
vast amount of inference is inseparably bound up in sense per
ception. The success of conjuring, ventriloquism, etc., is based
on our partial incapacity to separate, from what we actually see
or hear, our own misleading inferences, and our habitual associa
tions of ideas. In all such cases of error, it is in the interpretation
the mistake is committed, not in the perception itself: the sense-
impression is always what it ought to be in the circumstances.
So it is when, looking from a train which is stationary at another
which is passing close by, we imagine that the latter is at rest
and our own train in motion. So, too, we imagine that we
see the sun moving around the earth, and the stars revolving
around the pole, when it is really the diurnal revolution of the
earth on its axis that causes those appearances. Our only safe
guard against mal-observation is a lively advertence to its ever-
present dangers, together with the fullest knowledge we can
acquire on the subject-matter under investigation.

(£) FALSE ANALOGY.— We have seen that analogy is a fertile
source of scientific hypothesis (234). An analogy or resemblance
which is only apparent, not real, is called a false analogy. The
points of similarity are not due to the operation of some common
cause. Hence, an hypothesis based on such an analogy will be
misleading, and must be abandoned ; and this often happens in
scientific research. Or, again, the observed analogy may indeed
be real, but may have been assumed by the inquirer to be more,
or less, extensive than it really is ; he may misinterpret it and
extend its scope unduly in one direction, or fail to apprehend
its real application in another direction. An analogy whose
scope and weight are thus wrongly estimated, may be called an
imperfect analogy ; the hypothesis based upon it will need to
be remoulded before it can be verified, and so transformed into
a law. This, too, frequently occurs in science: indeed it may
be regarded as the usual procedure in inductive research. Non-
observation of operative influences is the most frequent cause of
imperfection in our analogies.

It is a common mistake to miss the point of an analogy, that
is, to misinterpret its real significance, to base upon it an infer
ence, conclusion, or hypothesis, other than that to which it really
points. If the just man shows skill in regard to the possession
of property, it does not follow (as the Platonic Socrates humor-

33* THE SCIENCE OF LOGIC

ously argues in the Republic) that because the thief also displays
skill in this direction the just man must be a thief. The
metaphorical use of language is an unfailing source of such
sophisms. The relations of the mother-country to its colonies, of
the head, or heart, of the body to the metropolis of a country, of
the governor of a state to the pilot of a ship, of the political
community or society to the individual organism — are all cases
in point (234). Within due limits they may yield legitimate infer
ences ; but they become fallacious if the analogy be pressed too
far. In all cases, differences must be noted and weighed no less
than resemblances. Finally, it must be remembered that mere
analogy as such never amounts to proof ".

(c) ILLICIT GENERALIZATION. The tendency to generalize
from insufficient data, is perhaps the principal pitfall of the un
scientific mind. The "man in the street" is fond of making
" sweeping statements ". The general assertion is always simple
and brief. It brings a feeling of rest and satisfaction ; and so,
the plain man is inclined to take refuge in it — prematurely. But
the failing is not peculiar to him. The many causes which
account for undue haste in assenting to conclusions — impatience
or indolence in the laborious work of inductive research, the
habit of a priori reasoning, the influence of prejudice, conscious
and unconscious, insufficient knowledge and equipment for accu
rate investigation, etc. — all these are constantly working mischief
in every domain of science.

The great leaders of science are, indeed, seldom betrayed into
going beyond their premisses. Hazardous, sensational prophecies
in the name of science, have no attraction for their prudent and
well-trained minds. But the smaller and narrower type of mind
is itself misled, and misleads others. The work of popularizing
science, i.e. true science, of spreading truth among the masses, is
unquestionably a most praiseworthy work. But there are many
half-educated camp-followers of science, who, actuated by less
laudable motives, are constantly popularizing travesties of science ;
who misrepresent its conclusions ; who palm off false and im
probable hypotheses on unsuspecting people as established
truths ; who are attracted less by what is true than by what is
sensational ; who are influenced less by the scientific spirit of
impartial inquiry than by their own likes and dislikes ; to whom
the laborious search after truth is a less congenial task than that
of attacking whatever is opposed to their own preconceived

ERROR AND FALLACIES 333

notions. In this dissemination of error, the fallacy of illicit
generalization plays a large part. The wildest guesses, the
merest speculations of the scientist, are proclaimed as established
truths of science ; and verified laws are extended beyond their
rightful domain. This fallacious procedure has special reference
to the formation and verification of scientific hypotheses^ and to
the establishment of scientific truths or laws. It may assume a
variety of forms.

In the process of verifying an hypothesis, and so setting it up,
and yielding our assent to it, as a general principle or law, we
sometimes succumb to the temptation of ignoring extreme cases,
which, if taken into account, would necessitate a modification and
restatement of our general conclusion. " The application of the
extreme case is very often the only test by which an ambiguous
assumption [or generalization] can be dealt with. . . . Where any
thing is asserted which is true with exceptions, there is often great
difficulty in forcing the assertor to attempt to lay down a canon
by which to distinguish the rule from the exception? Yet everything
depends upon this, " for the question will always be whether the
example belongs to the rule or the exception ". But " when
one case is brought forward which is certainly an exception, the
assertor will, in nine cases out of ten, refuse to see why it is
brought forward. He will treat it as a fallacious argument
against the rule, instead of admitting that it is a good reason why he
should define the method of distinguishing the exceptions" * Such
an attitude is, of course, in flagrant antagonism to the method
by which hypotheses can be accurately moulded into scientific
laws (234, 240). A scientific law should be so stated as to ad
mit of no "exceptions" other than those for which the state
ment of it makes express provision : " A rule may have exceptions,
it is said ; but this is hardly a correct statement. A rule with
exceptions is no rule, unless the exceptions be definite and deter-
minable : in which case the exceptions are exclusions by another
rule." *

The fallacy to which empirical generalizations (247) are
most exposed, is that of wrongly interpreting their scope and im
port : of mistaking them for established universal laws, and so
extending them to cases which they do not, or at least may not,

1 DE MORQAN, Formal Logic, pp. 270-1 ; apud WELTON, op. cit., p. 271 (italics
ours).

8 ibid., p. 272.

334 THE SCIENCE OF LOGIC

really cover. Mere observation of an uninterrupted uniformity
can never of itself transform the latter into a law ; only scientific
inductive analysis can achieve this result. To generalize from
mere observed uniformity of sequence is to confound sequence with
consequence, and so to run the risk of setting down as causal a. con
nexion which may be merely casual : the fallacy already referred
to as post hoc, ergo propter hoc.

The conclusion of a merely enumerative induction can never
be safely extended to instances that differ notably in their cir
cumstances from those actually observed. In the social sciences,
politics, and economics, most generalizations are only rough and
empirical ; it would therefore be a mistake to extend " such a
generalization founded upon a survey of the social conditions of
any one country at any particular time to other times and other
peoples".1 This might also be brought under the head of false
analogy. The latter fallacy, and indeed many other of the forms
of fallacy already examined, involve illicit generalization : which
is thus a rather extensive locus of fallacies.

It may be also regarded as involved in uncritical and indis-
criminating appeals to men of supposed great authority in matters
of human science: the fallacy lying in the assumption that because
such men have won great fame by their writings or researches in
certain departments of investigation they must therefore be
authorities in every domain. Such procedure is certainly a vio
lation of scientific method ; but it might be classified as a sort
of undue assumption of axioms, or of positions not sufficiently
proved, as well as under illicit generalization. " A striking ex
ample of this fallacy," writes Professor Welton, " is found in the in
tellectual idolatry with which the Schoolmen regarded Aristotle."
But this is less than historical justice to the Schoolmen : it is really
true only of the mediaeval Averroistic commentators of Aristotle.2
Nor need we go to the Middle Ages for examples of such
idolatry : the cult of Kant, of Hegel, of Darwin, in modern times,
would furnish fairly apt illustrations of undue deference to the
authority of an individual.

It has been already observed that the whole inductive process
is, in the main, a process of generalization : so that all fallacies
incident to induction are likely to involve illicit generalization in
some shape or form. All the difficulties of the process of in-

1 WELTON, op. cit., p. 273.

3DE WULF, History of Medieval Philosophy, pp. 228, sqq., 379, sqq.

ERROR AND FALLACIES 335

ductive analysis and generalization have been pointed out already
in the course of the various chapters devoted to an examination
of the process. It will therefore be sufficient here to recall very
briefly a few of the principal ones.

In establishing a general causal law there is always the pos
sibility of not having included all the really operative influences,
or of having included some that are not really operative ; and
in applying the law there is the danger that we may fail to de
tect the presence of counteracting conditions. Intermixture of
causes in the concrete world of physical and social phenomena
makes the application of laws to actual facts a matter of ex
treme delicacy. In the process of applying laws to new facts,
for the purpose of explaining these latter, we are constantly being
brought face to face with all sorts of anomalies and exceptions.
These always demand further analysis : which will determine
whether they are apparent or real exceptions, whether they are
due to the interfering influence of other known causes, or prove
to us that the statement of our law is too wide, or too narrow, and
so needs further adjustment and rectification. Thus, the work
of applying laws invariably contributes to a more accurate and
definite conception of the latter. " For example, to state that
the boiling-point of a liquid depends on the temperature would
be to omit the equally essential condition of atmospheric pres
sure. Thus, to say that water boils at 100° C. is wrong; it
boils at that temperature under the pressure of one atmosphere ;
i.e., the normal atmospheric pressure at the sea-level. Up a
mountain the boiling-point is different.1

Needless to say, the exact formulation of scientific laws, and
of the conditions under which they are applicable in the con
crete, is a matter of much greater complexity, as also of
much greater moment, in the human sciences, than in the
physical sciences. There, the facts are not amenable to quanti
tative measurement. Operative influences which take the form
of human motive^ of action are more elusive than mechanical,
physical, chemical, or physiological energies. Facts of mind and
facts of matter do not belong to the same order ; nor can the
evidence, on which the scientific knowledge of such facts is based,
be expected to conform to the same order of critical canons and
requirements in both cases. And this obvious consideration is

1 WELTON, op. cit., p. 275.

336 THE SCIENCE OF LOGIC

sometimes neglected in attempts to set up the same sort of ideal
for all departments of science (203).

Finally, it is not always easy to determine, whether in the
physical or in the human sciences, what are the determining or
causal factors, and what the determined elements or effects, in
the complex phenomena actually before us ; and the difficulty is
increased by the undoubtedly common fact of interaction, the
fact that the elements are often, by their mutual interaction in
the reality, partly causes and partly effects (243). As an
illustration of the difficulty of discriminating between cause and
effect, we are informed " that meteorologists are not agreed
whether the copious and sudden downfalls of rain which usually
attend thunder-storms are the cause or the effect of the electric
discharge. The common opinion is that they are the effect,
but Sir John Herschel held that they were the cause."1 And,
as illustrating the interaction between cause and effect, a thought
ful and suggestive passage from Sir G. C. Lewis's Methods of
Observation and Reasoning in Politics 2 will be amply sufficient :
"Thus," he writes, "habits of industry may produce wealth,
whilst the acquisition of wealth may promote industry ; again,
habits of study may sharpen the understanding, and the in
creased acuteness of the understanding may afterwards increase
the appetite for study. . . . The general intelligence and good
sense of the people may promote its good government, and the
goodness of the government may, in its turn, increase the in
telligence of the people, and contribute to the formation of sound
opinions among them. Drunkenness is in general the conse
quence of a low degree of intelligence, as may be observed both
among savages and in civilized countries. But, in return, a habit of
drunkenness prevents the cultivation of intellect, and strengthens
the cause out of which it grows. As Plato remarks, education
improves nature, and nature facilitates education. National
character, again, is both effect and cause : it reacts on the circum
stances from which it arises. The national peculiarities of a
people, its race, physical structure, climate, territory, etc., form
originally a certain character, which tends to create certain in
stitutions, political and domestic, in harmony with that character.
These institutions strengthen, perpetuate, and reproduce the
character out of which they grew, and so on in succession, each

1 WELTON, op. cit., pp. 275-6. a vol. i., p. 375 ; apud WELTON, op. cit., p. 276.

ERROR AND FALLACIES 337

new effect becoming in turn a new cause. Thus, a brave,
energetic, restless nation, exposed to attack from neighbours,
organizes military institutions : these institutions promote and
maintain a warlike spirit : this warlike spirit again assists the
development of the military organization, and it is further pro
moted by territorial conquests and success in war, which may be
its result — each successive effect thus adding to the cause out of
which it sprung."

WELTON, Logic, II., bk. vii. JOSEPH, Logic, chap, xxvii. JOYCE, Logic,
pt. i., chap. xvii. MILL, Logic, bk. v. MELLONE, Introd. Text-book of
Logic, chap. x. MERCIER, Logique, pp. 245-68. JEVONS, Elementary
Lessons in Logic, xx., xxi. ; Palaestra Logica, chap. x. BOWNE, Theory of
Thought and Knowledge, pt. ii., chap. xi. KEYNES, Formal Logic, pp. 457
sqq.

VOL. II. 22

QUESTIONS.
PART IV.

CHAP. I. — How do we come to assent to the premisses used in deductive
reasoning ? Distinguish three classes of general truths in reference to
reasoning. How far should logic deal with the methods of investigation to
be observed in the special sciences ? Illustrate historically the influence of the
sciences on logic. Indicate some other departments of human research
which claim from logic equal recognition with physics. Define Logical
Method, Analysis, Synthesis. On what basis are sciences classified as
deductive or inductive? "There is one and only one scientific method":
State the general rules of method. Explain the use of analysis and synthesis
in teaching. Describe the " Scholastic Methods of Exposition and Debate ".
What are the advantages and the defects of a purely Scholastic training ?

CHAP. II. — How do we ascend from particular facts to metaphysically
necessary principles ? Give the widest meaning of the word Induction, and
its Greek equivalent. What is ^propositio per se nota — in se — quoad nos —
quoad aliquos — quoad omnes ? Distinguish between the " induction " of
"necessary" truths in mathematics, and "physical" induction. Distinguish
between enumerative and scientific induction ; between " complete " and
"incomplete," "formal" and "material". Give examples of the so-called
"inductive syllogism" which concludes by complete enumeration. State
and explain Aristotle's definition of it. What are its drawbacks? When
complete, is it scientific ? What relation does it bear to the ordinary (deduc
tive) syllogism? Will incomplete enumeration, as such, demonstrate the
general law (" M is P ") f Why ? What efficacy did Aristotle attribute to it ?
What useful purpose does it serve ? Show that Aristotle and the Scholastic
philosophers of the Middle Ages were acquainted with scientific induction.
Account for the widespread error on this point. What name did the
Scholastics, after Aristotle, give to scientific induction ? On what principle
did Scotus base generalization from particulars? Why did the Scholastics
not make any progress in physical induction? Explain the teachings of (i)
Roger Bacon ; (2) Francis Bacon ; (3) Newton ; (4) Whewell ; (5) J. S. Mill ;
(6) Jevons— on induction. Explain, and illustrate by an example, the various
steps in the inductive process. Compare deduction with induction (i) as
methods ; (2) as inferential processes. Would you describe any form or
forms of reasoning as specially characteristic of induction ? How do you
understand the description of induction as an " inverse process " ?

CHAP. III.— Should \og\cformulate the rational principles which form
the grounds of our ascent from facts to laws ? Should it jitstify those prin
ciples ? Mention some of the more important notions involved in physical
induction. Formulate the " Principle of Sufficient Reason ". Has it a real

338

QUESTIONS 339

as well as a logical application ? Is the ultimate reason of logical principles
itself real? Describe (a) the Phenomenist, (b) the Hegelian, views of
Reality. Is the Causa Essendi always also the Causa Cognoscenti?
What is the Scholastic view about Reality ? State the " Principle of
Causality ". Define " Cause ". Distinguish it from " Condition ". Explain
the Aristotelean fourfold division of " Cause ". What class of cause is
mainly sought in physical induction ? Show, by an example, how each of the
four causes is sought by induction. Do inanimate causes act " for ends " ?
Is there evidence of plan, purpose, design, in the action of physical causes ?
Define " Essence" and "Nature". Explain the use, and various meanings,
of the word " Law," in induction. Contrast the " teleological " with the
" mechanical " conception of the universe. Can the latter be explained with
out recourse to " final," " formal," and " material " causes ? Where are the
two latter properly sought? Is the view that an event is produced by
" efficient " causes incompatible with the view that it is due to " final " causes ?
Give the traditional definition of "Efficient Cause". Distinguish various
kinds of efficient cause. Are all efficient causes "necessary" causes?
What notion have modern writers substituted for that of " efficiency " ? Are
all causes, of which we can have knowledge, necessarily perceptible by our
senses ? Give an account of the empirical view of efficient causality. What
did Mill mean by " invariable antecedent " ? By " unconditional " ? By
" necessary " ? Is " necessity " " invariability " ? Is it " unconditionalness " ?
Can we, according to Mill, really know an antecedent to be " unconditionally
invariable " ? Give Mill's three statements of the meaning of " Cause ".
What did he mean by " unconditional " antecedent ? Must the " cause "
have disappeared, or can it have disappeared, before the " effect " appears ?
Explain " Cessante causa cessat effectus ". How are cause and effect con
nected ? Explain " Actio et Passio sunt idem numero Motus", Is this
" tnotus " identical with the agens, or the patiens f or the two latter with each
other ? May all physical efficient causality be resolved into local motion, or
change of spatial relations ? Can one event have many " partial " causes
combining to form one " total cause " ? Can the same kind of event have
different total causes ? Why does the popular mind so conceive a " necessary
cause " that, although the latter can have only one effect, yet this one effect
may have several different " necessary causes " ? Which of the two — cause
or effect — is conceived by the popular mind in the more abstract state ? Does
the scientist make the concept of " cause " more abstract, or less abstract,
than it is in the popular mind ? Is plurality of causes consistent with the
scientific concept of total cause ? What do you understand by the immediate
(total) cause ? by the determining cause ? In order to " explain " an effect
by its causes, how far back along the converging chains of efficient causality
must the scientist go ? How near to the effect must he come ?

CHAP. IV. — State the " Principle of the Uniformity of Nature ". To
what class of causes does it mainly refer ? Distinguish between two different
senses in which it may be interpreted. Understood hypothetically, is it
analytic, a priori, metaphysically necessary, self-evident ? Do propositions
which express ordinary physical laws imply the existence or occurrence of
the facts and phenomena to which they refer ? State the principle of uni
formity categorically. Is our belief in this uniformity physically, or meta-

22 *

340 THE SCIENCE OF LOGIC

physically, certain ? Is this belief involved in induction ? Is it a synthetic,
or an analytic, judgment ? What right have we to infer general uniformity
from observed partial uniformity ? Does the validity of induction presuppose
belief in the existence of God? Does it rest ultimately on this belief? Is
the (categorial) principle of uniformity reached by induction. Must it be
reached antecedently to the establishing of any narrower law of nature ?
How does Mill account for our belief in the uniformity of nature ? Are the
inductions by which we establish special laws of nature, enumerative ? Is
" belief in uniformity " a " presupposition " of " rigorous induction " ? Ac
count for Mill's failure to derive scientific certitude from induction. What
kind of " unity " is discernible in the physical universe ? In order to reach
certitude by means of induction, must we postulate that the universe is in
telligible ? that physical phenomena are connected by metaphysical rela
tions ? What sort of certitude do we reach by induction, and why ? Is the
principle of uniformity the "major premiss" of the inductive process? Is
the latter an inference at all ? Compare the function of the principle of uni
formity in induction, with the function of the Dictum de omni et nullo in
deduction. Is belief in uniformity involved in the use of deduction ? Why
are the grounds of this belief not discussed in the logic of deduction ?

CHAP. V. — What is the function of hypothesis? Is every supposition in
science an hypothesis ? Must an hypothesis be true in order to be useful ?
Describe the various kinds of hypothesis distinguished by logicians, and
compare them with one another. In an hypothesis of cause, must the sup
posed cause be itself a phenomenon? Must it be at least picturable by the
imagination ? How far, or in what sense, must it be capable of detection ?
What are so-called " occult " causes ? Are any hypotheses admissible in
philosophy though not admissible in science, or vice versa? Explain the
rote of analogy in suggesting and verifying hypotheses. Are all legitimate
hypotheses capable of rigorous verification ? In what does this latter con
sist ? Can hypotheses be verified by cumulative evidence ? What do you
understand by " Consilience of Inductions," and " Extension of Hypotheses " ?
Discuss the significance of simplicity in an hypothesis. Why do philosophers
differ as to what the ultimate systematic conception really is, which would
best explain the totality of human experience ? Indicate briefly the condi
tions for a legitimate scientific hypothesis. Besides analogy, indicate some
other sources of hypotheses. Explain and illustrate the argument from
analogy. How is the force of such an argument to be tested ? How are
such arguments formally expressed ? Expound and illustrate the teaching of
Aristotle on Example and Analogy.

CHAP. VI. — Show that all observation involves selection, judgment, and
inference. Compare experiment with observation. What is the aim of per
ceptual analysis in induction ? Give an outline of the process of experimen
tal analysis of facts, indicating the causes of its complexity and difficulty.
Explain the significance of "exceptions," and the reason for repetition of
instances. What is to guide us in marking off the field for observation and
experiment ? What two principles of elimination underlie all applications of
the analytic process ? Enumerate the various ways in which the process can
be conducted. Does logic enable us to determine which of these "methods "
we are to apply in a given inductive inquiry ? Formulate and illustrate each

QUESTIONS 341

of the methods. Compare "agreement" with "difference". Explain and
illustrate two ways in which these may be combined. Is the joint method
of difference and agreement the strongest of all the methods ? Distinguish
between qualitative and quantitative methods. Compare the method of con
comitant variations with the methods of agreement and difference. To what
classes of phenomena is the former specially applicable ? What are its
limitations ? How is it subserved by statistics ? Compare the method of
residues with the methods of agreement and difference. What are its
characteristics ? What are the various ways in which causes or effects may
be conjoined ? What is the common aim of all the " methods " ? Can they
be adequately expressed by any system of symbols ? Explain the nature of
measurement and its influence on the progress of science. "All measurement
is relative and only approximate " ? What are the sources of inaccuracy ?
By what means is this latter minimized ? Distinguish between verification
and explanation, between fact and law, between empirical laws, derivative
laws, and laws of nature.

PART V.

CHAP. I.— Enumerate and define the various elementary notions sub
sidiary to the treatment of science and certitude. Describe and compare the
three kinds of certitude. Compare metaphysical with physical laws ; neces
sary with contingent truths ; categorical with hypothetical necessity ; know
ledge of possible essences with knowledge of actual facts. What is our
justification for applying abstract metaphysical principles to the interpretation
of the world of concrete fact ? From what standpoint did Aristotle obtain his
conception of the ideally perfect form of human knowledge ? From what
standpoint is the modern conception formed ? Are these two views in neces
sary conflict ? Explain, according to Aristotle, the nature and requirements
of scientific demonstration. Explain " The middle term expresses the cause ".
Discuss the distinction between what is <f)v<rfi or Xdyo> Trporepov, and what
is Trpos rjfias iTpvrfpov. How, according to Aristotle, do we reach the former ?
Do deductive applications of inductively established laws yield "science " in
the Aristotelean sense of this term ? Compare demonstration with scientific
explanation. How do we "explain " a fact, a law or uniform series of facts?
Distinguish between " popular " and " scientific " explanation. Have actual
facts or events the same kind of necessary connexion with other facts or
events as a conclusion in geometry has with its premisses ? What is the
difference ? Are the latter dependent on the Divine Will, and the former on
the Divine Intellect only? What is the only ultimate explanation of all
actual facts ? Contrast the Hegelian with the Theistic view of explanation.
Should logic teach us how to "discover " truths, as well as how to "prove "
truths already discovered ? Compare discovery and proof by induction, with
discovery and proof by deduction. Does the middle term of a demonstra
tive syllogism give the " only possible " cause of the conclusion ? Compare
the ultimate principles of deductive demonstration with the ultimate explana
tory laws reached by induction. Assign three meanings to the expression,
"moral certitude". Can certitude be based on "moral," "human," "ra
tional," propensities ? Do any of these underlie belief that is based on
human authority ? On what conditions does the latter warrant certitude ?

342 THE SCIENCE OF LOGIC

Compare "belief" with "science". Can human testimony be an ultimate
motive for certain assent ? State some rules of historical criticism for ascer
taining (a) the knowledge, (b) the veracity, of human testimony. Classify
the chief sources of historical information. How are the authenticity and
integrity of documents ascertained ? Discuss the value, and the limitations,
of oral traditions ; of the argumentum ex silentio ; of the argument from
prescription.

CHAP. II. — Define opinion and probability. Are there grades or degrees
of truth, or of probability, in our judgments ? Are there degrees of firmness
in our opinions or assents ? Can opinion ever pass into certitude by the aid
of cumulative evidence ? Distinguish between various kinds of probable
judgments. What is a " Probable Syllogism " ? What is chain evidence ?
How does it differ from circumstantial evidence ? Are probable arguments
from authority of much practical utility? Define the Aristotelean Enthy-
meme. How does it differ from the Modern Enthymeme? What did
Aristotle understand by oTj/mW, Tttpypiov, and €i\or, respectively ? Give
examples of Aristotelean Enthymemes in the first, second, and third figures,
respectively. Distinguish between " causal " and " casual ". What is a
" chance coincidence," or a " chance recurrence " ? Are there " coincidences "
or " coexistences " that are ultimately unexplainable ? When is a pheno
menon said to be " due to chance " ? Would the possession of perfect know
ledge eliminate the concept of chance ? What is the object of this concept ?
Indicate two essential conditions for the application of the theory of proba
bility to any group of phenomena. Explain the formulae : " If S is A it is X,"
and "5 is either A^XV A.2X2, A3X3, ..." Does the theory apply equally
to past and to future events ? State and illustrate the rules for estimating
the probability of (a) simple events ; (6} compound independent events ; (c)
compound dependent events ; (d) the total probability of an event that may
happen in various ways. What is " inverse probability " ? How is it applied
in measuring magnitudes? in eliminating chance? Explain Bernouillfs
Theorem. How may the calculus be applied to natural and social pheno
mena ? What are the obstacles to its application ? Can it measure our
probability as to the recurrence of a natural event ? or the credibility of human
testimony? How do statistics subserve inductive inquiry? Discuss the
connexion between " statistical uniformities " and " laws," between free will
and the regularity of social phenomena.

CHAP. III. — Discuss the possibility of classifying the modes, or the
sources, of human error. Distinguish between error and fallacy. Define
fallacy, sophism, paralogism. Describe the classifications of Mill, Bacon, Aris
totle, and Jevons, respectively. Discuss the division of fallacies into formal
or logical, semi-logical, and material. Are fallacies in dictione formal or
material ? Explain and exemplify each of the fallacies incident to conception ;
to judgment. Compare the fallacy of Secundum Quid with that of Accidens.
Illustrate the various forms of (a) Ignoratio Elenchi ; (b} Petitio Prindpii.
Distinguish between axioms and postulates. Why do men differ so much in
their views upon the great questions of religion and philosophy ? What are
the subjective, and what the objective, obstacles to the attainment of truth ?
Explain the fallacy incident to indirect proof. What fallacies are to be
avoided in (a) observation, (&) analogy, (<r) generalization ?

INDEX.

Abscissio infiniti, i., 345.
Absolute terms, i., 70.
Abstract terms, i., 57-63.
Abstraction, i., 4, 205 ; ii., 14, 24-6.
Accent, fallacy, of, ii., 301, 306-7.
Accident, fallacy of, it., 297, 301, 310-12.

— predicable, i., 77, 86-8.
Accidental judgments, i., 170-80.
Actio et passio, etc., ii., 81.

— category of, i., 141, 147-8 ; and
cause, ii., 81-2.

ADAM, ii., 172.
ADAMS, ii., 197.
Added determinants, inference by, i.,

246.

A Dicto, etc., fallacy of, ii., 301, 309-11.
Adjacent cases, ii., 206-7.
Adversative propositions, i., 271.
Aequipollentta, i., 232, 312.
Affinity, i., 130.

Affirmation and negation, i., 202-3.
Agnosticism, ii., 59-61, 79, 107, 130, 146,

222.

Agreement, method of, ii., 173-5 ; com
bination with difference, 179-85.

ALBERT THE GREAT, ii., 21, 33.

ALDRICH, i., 326, 352.

Alternative judgments and propositions,
i., 280-91 ; fallacies of, ii., 314-15.

— subjects, i., 281 ; predicates, i., 281.

— syllogisms ; pure, i., 362 ; mixed,
363-5-

— terms, i., 198.

Ambiguity in language, i., 44, 189, 192,
307-8.

Ambiguous middle, i., 307.

Amphiboly, fallacy of, ii., 301, 308-9.

Ampliative propositions, i., 170-80.

Analogical use of terms, i., 43-4; predi
cation, 149.

Analogy, i., 393 ; its function in induc
tion, ii., 135-42, 150, 153-5 ; force of,
156-8 ; and enumerative induction, 159.

Analysis, i., 5 ; in definition, 91 ; in judg
ment, 157-8, 174; in method, ii., 9-10;
in teaching, 14-16 ; in induction, 32,
36 ; experimental, 165 sqq.

Analytic method, i., 378 ; ii., 7 ; analytico-
synthetic, 9.

— chains of reasoning, i., 377, 383-4.

— definition, i., 91-2.

Analytic propositions, i., 170-80, 404-5;

"l.i 94-
ANSELM, ST., ii., 233.
Antecedent, v. consequent, and ground.
Antepraedicamenta, i., 136.
Antilogism, i., 324, 340-1.
Apodeictic judgments, i., 181-5 > "•> 215
Appetitus natiiralis, it., 66.
Apprehension, simple and complex, i.,

2, 6.
Approximation, methods of, ii., 204-5 !

and probability, 279.
Argument, regressive, ii., 45.
Argumentum a fortiori, i., 388; it., 158.

— a contrario, ii., 158.

— apart, ii., 158.

— a posteriori, ii., 53, 108, 129, 146, 151
232-3-

— a priori, ii., 53, 232-3.

— a simultaneo, ii., 233.

— ex praescriptione, ii., 259.
silentio, ii., 256.

— ad hominem, ii., 234, 316-7.
bacitlum, ii., 316.

— tnisericordiam, ii., 316.

— — iguorantiam, ii., 316.
Aristotelean enthymeme.

— sorites, i., 379-84.

ARISTOTLE, on moderate realism, i., 9;
ii., 231 ; logical treatises, i., 40 ; predic-
ables, i., 73 ; ii., 80 ; categories, i., 136-
42,1147-9 ; on judgment, 154 ; on denial,
204; on conversion, 236; ii., 80; on
def. of syllogism, i., 292-3 ; Dictum de
omni et nullo, 300-4 ; on indirect re
duction, 339 ; on ficdfffts, 349 ; on in
direct moods of the first figure, 350 ; on
hypothetical arguments, 366; on
method, ii., 10, 16-17 ; influence on
mediaeval thought, 19; on induction,
24; on inductive syllogism, 28, 31-2,
158 ; on ascent to the universal, 30-4,
229-32 ; on scientific induction
(fHirfipia), 32-4 ; on causes, 62, 64 ; on
purpose in nature, 67; on Trapd$eiyfi.a
(" example "), 158-9 ; on probable know
ledge, 224 ; on analogy, 160-1 ; on truth
210 ; on enthymeme, 265-8 ; on de
monstration, 223-9 ; kind of, 232-5 ; on
science, 223-5, 230-2, 237-9, 242; on
fallacies, ii., 300-2 ; analysis of, 303-29.

343

344

7 HE SCIENCE OF LOGIC

Art, distinguished from Science, i., 14-16.
Artificial classifications, i., 122-31.
Assent, ii., 210-14.

— and inference, i., 297.

Assertoric propositions, i., 180-5 255,
257, 284, 289, 290.

Association of ideas, i., 3, 51.

Assumption of axioms and postulates,
ii., 13-14, 60, 106-7, 109, in, 113, 135,
143-5, 147, 243, 255, 298, 322-7.

Atomism, chemical, ii., 140-7.

— mechanical, v. mechanical view of
universe.

Attributive terms, i., 60.

— view of predication, i., 207-8 ; reverse
of, 208.

Augmentative judgments, i., 170-80.
AUGUSTINE, ST., i., 142 ; ii., 10, 19, 327.
Authenticity of manuscripts, ii., 257.
Authority, ii., 249 ; in science, 251-2, 334 ;
in history, 254.

— divine, ii., 250.

Averages, ii., 279-82 ; functions of, 285-7 '.

and "law," 289-93.
AVERROES, i., 350.
Axioms, of mediate inference, i., 299-301 ;

ii., 50 ; in philosophy, ii., 10, 13 ; 117,

142-5, 243.

BACON, FRANCIS, Lord Verulam, ii., 37-
4*. 5i, 53, 56, 134, 169, i?2, 299-300.

BACON, ROGER, ii., 21, 37, 185.

BAIN, i., 10, 232 ; ii., 105, 146.

BALFOUR, ii., 252-3.

Ballot-box theory of nature, ii., 38, 43.

BALMES, ii., 327.

Barbara, Celarent, etc., history of, i., 326,
352.

BAUDOT, ii., 281.

BAYNES, i., 213.

Begging the Question, v. Petitio Principii.

Belief, and science, ii., 97, 250-2; and
opinion, 212 ; and authority, 216-7,
250-3 ; in uniformity of nature, grounds
of, ii., 99-"3-

Beliefs, v. assumption of axioms.

BENTHAM, i., 124.

BERKELEY, ii., 146.

BERNARD, Cl., ii., 148-50.

BERNOULLI'S theorem, ii., 280-2.

BERTRAND, ii., 269, 285, 291.

Bias, ii., 6, 148, 163, 254, 273-4, 3*9-

324-

Bifid division, v. dichotomy.
BORDA'S experiments, ii., 187.
BOSANQUET, i., ii ; on judgment, 161 ;

on reciprocal judgment, 276, 288 ; ii.,

45, 106, 242.
BOUDON, ii., 269.
BOUTROUX, ii., 327.
BOWEN, i., 214, 232.
BOWNE, B. P., ii., 275, 284, 291.
BRADLEY, i., ii ; on judgment, 160-1, 174.

BUCKLE, ii., 290-1.
BURKE, ii., 140.

CAJETAN, Cardinal, i., 17^.

Calculus of probability, ii., 268-81 ; appli
cations of, 282-5.

Calvus, fallacy of, i., 379 ; ii., 306.

Casual and causal connexions in nature,
ii., 166, 322.

Categorematic words, i., 34, 36.

Categorical judgment, nature of, i., 154-
64.

— propositions, relation to conditionals,
i., 269-70 ; to hypotheticals, 273 ; to dis
junctives, 288-9.

— and hypothetical statement of laws in
induction, ii., 58-60, 93-100, 217-23.

Categories, in logic and in metaphysics,
i., 135-6 ; and predicables, 138 ; Aris
totle's enumerated, 141-2; and lan
guage, 142-5 ; and reality, 145-6 ;
Kantian, 150-1 ; compared with Aris
totle's, 152-3.

CAUCHIE, ii., 254.

Causa essendi, and causa cognoscendi, i.,
345, 349 ; ii., 222, 327.

Causal demonstration, ii., 232-3.

— hypotheses, ii., 122-7.

Causality, i., 148 ; principle of, ii., 61 ; and
uniformity of nature, 71-5 ; sensist view
of, 70-80 ; and space and time, 80-4 ;
and chance, 268-72.

Cause and condition, ii., 62-3.
• — reason or ground, ii., 61, 85, 227,
231-2.

Causes, definitions and divisions of, ii.,
62-6, 180 ; necessitating and indispen
sable, 84 ; non -reciprocating, 85-92 ;
" plurality " of, i., 275 ; ii., 84-92, 167,
244, 247-8 ; free or self-determining,
94-5 ; conjunction of, 195-6 ; interaction
of, 335-7-

Certainty, n., 211, 263.

Certitude, ii., 211; and prudence, 212;
three kinds of, 214-17, 235 ; in the
" human " sciences, 248-59 ; and prob
ability, 260-3.

Cessante causa, etc., ii., 81.

Chains of reasoning, i., 377-84 ; ii., 265.

Chance, logic of, ii., 261 ; concept of,
268-72 ; elimination of, 280-3 ; estima
tion of, 276-8, 282-3 ; and mechanical
view of nature, 291-3.

Change, i., 148; and causation, ii., 81-2.

— of relation, i., 269.
CICERO, i., 379.

Circulus in definiendo, i., 109.

— in demonstrando, ii., 320.
Circumstantial evidence, i., 394-5 ', »•»

262, 265, 267.

Class compartments, i., 117, 217, 250-3
261.

— inclusion view of judgment, i., 210-16.

INDEX

345

Class name, i., 193.

Classification, i., 121-31 ; and hypothesis,
i., 131 ; ii., 151 ; of widest concepts, i.,
135 ; and disjunctive judgments, i.,
286, 289.

CLARKE, on species infimcz, i., 80-1 ; on
pradicamenta, 137 ; on singular pro
positions, 192 ; on dilemma, 375 ; on
fallacies of method, ii., 12 ; on method
of teaching, 15-16, 211 ; on " chain "
evidence, 265.

CLIFFORD, ii., 138, 239.

Co-division, i., 113.

Coexistences and sequences, ii., 68.

Cognate genus, i., 78.

— species, i., 78.

Collective judgments, i., 189, 300-1, 402-
4 408, 412 ; ii., 27-32, 48, 320.

— terms, i., 46, 189 ; ii., 305.
Colligation of facts, ii., 42, 122.
Combination of causes, ii., 195-6.
Common sense, truths of, ii., 324-5.
" Comparative " sciences, ii., 190.
Compartmental view of judgment, v. class

compartments.

Complementary terms, 66, «. i.
Complex conception, inference by, i., 247.

— concepts and terms, i., 37, 198, 284-5,
290.

— dilemmas, i., 367-9.

— propositions, i., 169, 197-8, 283-4.
Composition and division, fallacies of, i.,

47, 226 ; ii., 301, 304-6.

— of causes and effects, ii., 85, 195-6.
Compound propositions, i., 169, 197-8 ;

opposition of, 223 ; 265 ; and complex,

284-5.
Comprehension of concepts and terms, i.,

49, 63, 172.
Comprehensive view of predication, i.,

209-10.

Conceivability, sphere of, i., 250.
Concepts, i., 17, 37 ; divisions of, 42-71 ;

specific, 76 ; and imagination images

in science, ii., 131-2, 149; fallacies

incident to, ii., 303-7.
Conceptualism, i., 10.
Conceptualist view of logic, i., 20, 26.
Conceptus objectivus, i., 37 «.
Conclusion, its relation to premisses, i.,

295-7. 3i4» 316-7, 401 ; "., 225-6, 294-5,

3J3-
Conclusions, logical grounds and ultimate

sources of, i., 410-12.
Concomitant variations, method of, ii.,

185-93 ; and agreement, 190 ; limita
tions of, 191, 201 ; and statistics, 192-3,

282.

Concrete terms, i., 57-63.
Condition and cause, ii., 62-3 ; totality of

conditions, ii., 70-80.
Conditional propositions, distinguished

from hypothetical, i,, 265-6; and cate-

goricals, 269-70 ; existential import of,

269-70 ; modality of, 270.
Conditional syllogisms, pure, i., 356-8

mixed, 358-61.
CONDORCET, ii., 285.
Confusion, fallacies of, ii., 299.
Conjunction of causes, ii., 85, 195-6.
Conjunctive propositions, i., 280, 282.

— terms, i., 198.

Connotation, i., 48-52 ; and denotation,
56 ; and definition, 93, 104 ; objectivity
of, 175-

Connotative view of predication, i., 208-9.

Consequens, fallacy of, i., 272-3, 279, 297 ;
ii., 312-13, 319.

Consequent, and antecedent in deduction
and induction, ii., 53-5.

Consequentia, or consequence in reason
ing, i., 295-6, conseqence and sequence,

^ ii., 165.

Consilience of inductions, ii., 42, 142.

Consistency, logic of, i., 20, 22, 253 ; ii.,
118 ; and truth, i., 19, 22 ; ii., 118.

Constructive definition, i., 106-7.

— dilemma, i., 367-8.

— hypothetical syllogism, i., 359.

— method, ii., 7.

Content of concepts, i., 48-50.
Contingent judgments and propositions,
i., 170-80, 200-2 ; ii., 99, 218-19.

— being, ii., 61, 221.

— modality, i., 181.

— necessity and law, i., 176 ; ii., 218-19.
Continuity, of cause and effect, ii., 81-2,

196.

Contradiction, in judgments and proposi
tions, i., 221-4.

— in terms, i., 64-8.

— principle of, i., 24, 222, 224.
Contraposition, i., 241-3 ; and induction,

243 ; ii., 152, 170.

Contrary judgments and propositions
i., 224-5.

— terms, i., 68-9.
Contraversion, i., 232.
Conventional element in language, i.,

35 ; in connotation, i., 50-2.
Conventional intension, i., 49.
Converse relation, inference by, i., 247.
Conversion of propositions, i., 232-41 ; by

negation, 241.

Conversio syllogistni, i., 337.
Copernican astronomy, ii., 122, 127, 329.
Copula, logical, i., 154, 165, 202, 249,

386-7, 391.

Copulative propositions, i., 280, 282.
Correlative terms, i., 70.
Criteria of truth, i., 28-9, 161; ii., 4,

107-8, 2ii-i2, 250-2.
Criteriology, i., 28-9, 147 ; ii., 4.
CROFTON, ii., 281.
CROOKES, Sir W., ii., 139.
Cross-division, i., 118.

346

THE SCIENCE OF LOGIC

Cumulative evidence, i., 394-5 ; ii., 141-2,
217, 249, 262.

DARWIN, ii., 139, 334.

DAVY, ii., 168.

Deductio ad impossibile, v. reductio.

Deduction, and induction, ii., 8, 9, 48-55,
117-19, 243-8 (cf. inference and method).

Deductive inference, i., 391-2, 412 ; de
finitions of, ii., 51 ; in mathematics, ii.,
25, 243-8.

Definite singular propositions, i., 193.

— numerical propositions, i., 197.
Definition, its functions, i., 89-91 ; ii., 2 ;

formation of, i., 91-5 ; fixity of, 95-6 ;
limits of, 96-7 ; ii., 237 ; nominal and
real, i., 99-106, 134, 252; existential
import of, 101-2, 407; private, 106;
genetic, 106-7 I physical, 107 ; rules of,
108-11; as involving fallacy in infer
ence, 405-6 ; not arbitrarily invented in
mathematics, ii., 25-6, 230, 237.

DELEHAYE, ii., 253.

DELORME, ii., 37.

Demonstration, i., 333-4, 345 ; ii., 52-3,
108, 142 ; and explanation, 224, 235-9 '»
conditions of, 225-0 ; kinds of, 232-5 ;
and verification, 245-8.

DE MORGAN, i., 39, 232, 307, 313, 314,
316, 389 ; ii., 306, 310, 318, 320, 333.

DE MUNNYNCK, ii., 145.

Denial, nature and ground of, i., 203-6.

Denotation, i., 52-64.

DE QUINCEY, i., 103.

Derivative laws, ii., 208.

DESCARTES, i., 149 ; ii., 10, 291.

Description, i., 107.

Descriptive hypotheses, ii., 123-5.

Design, v. purpose.

Desitive propositions, i., 200.

DE SMEDT, ii., 253.

Destructive dilemma, i., 367-8.

— hypothetical syllogism, i., 359.
Determination, and negation, i., 204-6.

— of moods of syllogism, i., 320-4, 327-
3i-

Determinative clauses, i., 157, 198.

Determining cause, ii., 64.

Development, conception of, ii., 10.

DE WULF, i., 93, 318; ii., 10, 17, 19, 128,
138, 144, 231, 252, 334.

Diagnosis, i., 125, 345.

Diagnostic definition, i., 133.

Diagrams, Euler's, i., 211-12, 236, 310.

Dialectic, ii., 52.

Dichotomy, i., 115-7.

Dictum de omni et nullo, i., 209, 300-4 ;
and rules of syllogism, 305-6 ; and first
figure, 344, 386, 389 ; its real and con
ceptual import, 390, ii., 27 ; and uni
formity of nature, 115-9.

— de dive no, i., 346.
Didactic method, ii., 7, 14-16.

Difference, method of, ii., 175-9; com
bination with agreement, 179-85.

Differentia, predicable of, i., 77, 81-2.

Dilemma, i., 367-75 ; formal and material
validity of, 370-3.

DIOGENES of Laerte, i., 40.

Direct determination of valid moods of
syllogism, i., 329-31.

— reduction of syllogisms, i., 335-9.
Discourse, universe of, i., 54, 65, 161, 249-

52, 255.
Discovery, and instruction or exposition,

ii., 14, 15 ; and proof, 42-3 ; deductive

and inductive, 243-8.
Discretive propositions, i., 271.
Discursive reasoning, i., 18, 295, 297.
Disjunctive propositions, i., 280-91 ; in

calculus of probability, ii., 275-82.

— syllogisms, pure, i., 362 ; mixed, 363-
5 ; in induction, ii., 39, 50-2, 142, 172,
182.

Disputationcs quodlibetales, ii., 17.

Distinctive explanation, i., 107.

Distribution of terms in propositions, i.,
186-8 ; intensive, 202, 209 ; of conse
quent in hypotheticals, i., 270-1, 279,
357-

Distributive use of terms, i., 47 ; ii., 305.

Divisio, fallacy of, i., 47, 226 ; ii., 301,
304-6.

Division, logical, functions of, i., 112-13 I
nature of, 113-4; formal and material,
115-7 I rules of, 118-21 ; and definition,
113; and disjunctive judgments, 286,
289.

Divisions of logic, i., 17-19; ii., 2-7.

Documents, historical, ii., 256-8.

Double method of agreement, ii., 179-81.

Doubt, ii., 213.

— and modality, i., 184-5; '" "if" judg
ments, 267-9.

Dualism, v. monism, theism.
DUHEM, ii., 129, 132.

Education, and method, ii., 14.

Eductions, i., 229-46 ; table of, 245 ;
material, 245-7; and existential import,
256-8 ; from conditionals, 272-3 ; from
hypotheticals, 278-9 ; from alternatives
or disjunctives, 290-1 ; and rule of
quality in syllogism, 311-12.

Effect and cause, ii., 63 ; as correlative,
80-1 ; not identical, 82.

Effects, intermixture of, ii., 195-6.

Efficient cause, ii., 62-5 ; traditional and
empirical concepts of, 70-80 ; kinds of,
71 ; efficiency not necessity, 73-4 ; and
space relations, 83.

ttWf, ii., 265.

r«0€(m, i., 349, 354.

Elements of syllogism, i., 294-7.

Elimination, in inductive analysis, i., 275 ;
ii., 38, 50, 52, 55, 165-72, 244 ; in de-

INDEX

347

duction, ii., 244-8 ; of errors in measure
ment, ii., 203-5 ; in mediate inference,
i., 296-7.

Empiric demonstration, It., 234.

Empirical generalizations or laws, ii., 205-

9, 333-4-

— judgments, i., 170-80.
Empiricism, ii., 59-61, 75 sqq. ; and uni
formity of nature, 102-5.

Ens rationis, i., 31, 72.

— reale, i., 30, 31.
Enthymeme, Aristotelean, ii., 265-8.

— modern, i., 376-7.

Enumeration of instances, i., 347-8, 402 ;
ii., 27-32.

Enumerative induction, ii., 27-32, 39, 43,
48, 102-4, 152, 159 ; and theory of
chance, 283-4 ; and pctitio principii,
318, 321-2; and generalization, 334.

— judgments, i., 190, 300, 402-4 ; ii.,
27-32.

Epicheirema, i., 378, 383-4.
Epistemology, i., 28-9; ii., 113, 323.
Episyllogism, i., 377.
Episyllogistic chains of reasoning, i., 377-

83-
Equational view of judgment, i., 216-18,

234-

Equivalence of propositions, :., 231-2, 312.
Equivocal terms, i., 43-4.
Equivocation, fallacy of, ii., 297, 301,

3°3-4-

Error, ii., 211, 213; and fallacy, 296-8;
sources of, 325-7.

Essence, notion of, i., 75-6; zndproprium,
83-4, 175-7 I »M 237 ; nominal and real,
i., 76, 84; and substance, 141; and
nature, ii., 67.

Essential judgments, i., 170-80.

Ethical truth, ii., 210.

Etymology, and connotation, i., 64.

EUCLID, i., 242 ; ii., ii, 31, 318.

EULER, i., 2ii-i2, 236, 310.

Evidence, circumstantial, i., 394-5 ; ii., 262,
267 ; " chain " evidence, 265 ; histori
cal, ii., 5-6, 217; nature of, 211-14;
sources of, 214-17 ; extrinsic and in
trinsic, 216, 250 ; mediate and immedi
ate, 226-7, 297-8 ; external and internal,
257-8 ; probable, 261 ; estimation of,
ii., 59, 213, 299, 325-7.

Evolution, and classification, i., 130-1 ; as
a standpoint, ii., 10.

Example, argument from, ii., 158-60.

Exceptio probat regulam, ii., 167-8.

Exceptions, significance of, ii., 167 ; to
necessary truths, and to physical laws
217-23 ; and rule, ii., 308, 333.

Exceptive propositions, i., 200, 241.

Excluded middle, principle of, i., 24-5
203, 222, 224, 226, 231-2.

Exclusive figure of syllogism, i., 344 ; in
induction, ii., 39-40.

Exclusive propositions, i., 199-200, 241.
;emplification, i., 97-9, 103.

Existence, implication of, in definitions,
i., 101-2, 252; in categorical judgments,
248-62 ; in conditionals, 269-70 ; ii.,
96 ; logical meaning of " exist," i.,
251.

existential formulation of judgment, i.,
164, 234, 261.

— propositions, i., 164, 217-8, 221, 251.
experience and proof, ii., 53, 97, 108-9 ;

and interpretative principles, ii., 142-5,

243-
Ixpcrientia (tfiirftpta, = induction), ii., 33-

4-
experiment, and observation, ii., 164-5 ;

" natural," 164 ; functions of, 165

sqq.; practical canon of, 171.
experimental analysis, difficulties of, ii.,

168-72 ; principles of, 166-7.

— methods, ii., 42, 172-201.
^explanation, distinctive, i., 107.

— scientific, ii., 50, 52, 53, 89, 142 ; and
verification, 207-8, 239-40, 245-8 ; and
demonstration, 224, 235-9 '< limits of,
239-41 ; in deduction and in induction,
243-8.

— popular, ii., 238-9.

— ultimate or philosophical, ii., 59-61,
128 ; and verification, 142, 208-9, 239-
43, 245-8 ; and statistics, 291.

Explanatory hypotheses, ii., 124-5.
Explicative clauses, i., 198.

— propositions, i., 170-80.
Exponible propositions, i., 198-200, 215.
Expositio or t/cOetris, i., 349, 354.
Exposition, method of, ii., 14-16; scho
lastic method of, 16-22.

Extension, of terms, i., 48-57 ; in pro
positions, 186-8 ; in syllogisms, 293,
301-4.

— of hypotheses, v. hypotheses and con
silience of inductions.

— of laws, ii., 206-7.

Extensive view of predication, i., 210-16.

definition, i., 97-9.
" Extreme case," function of, ii., 333.
Extremes of syllogism, i., 294-5.

Fact, and theory, ii., 60, 149-50 ; and
truth, 235-6 ; and law, 206, 223, 236-9.

— necessary, i., 180 ; ii., 208, 222.
Faculties, mental, i., 1-8.

Fallacies and logic, ii., 294-6; and error,
296-8 ; classifications of, 295, 298-303 ;
formal and material, 302-3.

False analogy, ii., 307, 309, 331-2, 334.

— cause, ii., 327-9.

Feeling, Mill's category of, i., 150.
Figure of speech, ii., 301, 307-8.
Figures of syllogism, i., 319-31 ; char
acteristics of each, 343-55.
Final causes, ii., 59, 62, 64, 65-70, na.

348

THE SCIENCE OF LOGIC

"Finger-post to the unexplained," ii.,

914, 197.
First figure of syllogism, special rules of,

i., 321 ; characteristics of, 343-4.

— and second intentions of the mind,
i-i 32, 72.

FORBES, i., 317 (v. Palaestra Logica).

Force of concepts, i., 48.

Form and matter, of thought, i., 20-3,

146, 150, 152, 264-5, 285 ; ii., 295-6 ;

of judgment, i., 162-4 I °f syllogism,

i., 294-7.
Formal cause, ii., 62, 64, 65, 83.

— contradictories, i., 65-7.

— division, i., 115-7.

— hypothetical, i., 274.

— logic, i., 19-23, 162, 264-5; ii., 296,
302-3.

— propositions, i., 172-3.

— validity of inference, i., 295-7.

— fallacies, ii., 296-7, 302-3.

" Forms," Bacon on, ii., 38-40.
Formulation of judgment, schemes of,

i., 164-6 ; for " if" judgments, 265-7.
Four terms, fallacy of, i., 307.
Fourfold scheme of propositions, i., 186-

8.
Fourth figure of syllogism, special rules

of, i., 323-4 ; critical analysis of, 350-

FOWLER, i., 232, 375 ; ii., 156, 160, 187,

189.

FREEMAN, ii., 253.
Free will and causality, ii., 71, 74.

— and uniformity ot nature, ii., 94, 218.

— and science, ii., 94, 217, 249.

— and social statistics, ii., 289-93.
Fundamental syllogisms, i., 326-7.
Fundamentum divisionis, i., 112, 113, 115-

6, 119; ii., 311.

— relationis, i., 70.

GALEN, i., 350-1.

Galenian Figure, i., 319.

General judgments and propositions, two

kinds of, i., 190-2 (cf. collective, enume-

rativc).

— terms, i., 44-6.

Generalization in language, i., 44, 50, 96.

— formal and material, i., 409 ; ii., 40, 47,
95-6, 114-19, 216-17 ; two ideals of, ii.,
40, 41 ; fallacies of, ii., 299, 309, 332-7.

Generalizations, empirical, ii., 206-9.
Generic differentia, i., 82.

— judgments, i., 191, 201, 403.

— pfopria, i., 82-3.
Genetic definition, i., 106-7.

Genus, predicable of, i., 77 ; kinds of, 78.
" Geometrical " induction, ii., 25.

— inferences, v. mathematical.
GEORGIUS SCHOLARIUS (GENNADIUS), i.,

318.
GERARD, ii., 139.

Gesture " language," i., 34.

Goclenian sorites, i., 379-84.

Grammar, i., 34, 142-5.

Grammatical analysis, i., 35-6, 142, 155

GREEN, T. H., i., ii ; ii., 106, 220.

GROTE, on Aristotle's categories, i., 143-4.

Grounds or reasons, logical, i., 386 ; and
ultimate sources of knowledge i., 410-
12 ; ii., 297 ; ground and consequent,
ii., 54-5 ; and cause, ii., 61, 85.

— logical, proximate, and ultimate, ii.,
99-100, 118-19.

Growth of language, i., 44.

Habit, as quality, i., 141 ; as category, i.,
142, 148.

HABRICH, ii., 14.

HAMILTON, Sir W., i., 20 ; on definition,
100-1 ; on categories, 149 ; on com
prehensive view of predication, 210 ; on
extensive view, and quantification of
predicate, 210-16, 332 ; his postulate,
212 ; on dilemma, 375.

HEGEL and Hegelianism, i., ii, 153; ii.,
60-1, 69-70, 83, 105-6, 146, 221-3, 241-3,
324, 334-

HERSCHEL, Sir J., ii., 172, 197.

Heteropathic effects, ii., 195-6.

HICKEY, i., 318, 332 ; ii., 253.

HIRD, i., 317 (v. Palaestra Logica).

Historical propositions, i., 195, 234.

— evidence, ii., 5-6, 217.
History and Science, ii., 5-6, 253-9.
HOBBES, i., 10, 43.

HOBHOUSE, on formal science, i., 163.

HOLMAN, i., 307.

Homogeneous effects, ii., 195-6.

Horns of dilemma, i., 371.

HUME, i., 10, 395 ; ii., 59, 75-6, 146, 194.

HUXLEY, ii., 21, 147.

Hyperphysical entities in science, ii.,

132-5-

Hypothesis, and classification, i., 130-1 ;
ii., 151 ; and particular judgments, i.,
195 ; and enumerative induction, ii.,
32, 152 ; nature and functions of, 120-
2 ; verification of, 50, 128, 135-42, 146-
7, 150, 207, 319, 333 ; in deduction,
244-8 ; kinds of, 122-7 '< conditions for,
148-51 ; sources of, 151-5 ; extension
of, 142, 155, 157-8, 206.

Hypothetical judgments and propositions,
and categorical, i., 263-4 ; and con
ditional, 265-6 ; ii., 94 ; modality of, i.,
273, 277-8 ; eductions from, 278-9 ;
and disjunctives, 289 ; fallacies incident
to, ii., 312-3.

— necessity of metaphysical laws, ii.,
217-23.

— sorites, i., 380-1.

— syllogisms, pure, i., 356-8; mixed,!.,
358-61.

Hysteron proleron, ii., 319.

INDEX

349

Idealism, v. HHGEL and Phenomenism.
Identity, and diversity, i., 24, 308; syl
logistic axioms of, 229, 386.

— and similarity, ii., 160-1 ; 218, 220.

— principle of, i., 23-4, 236.

" /do/a," Lord Bacon's, ii., 37-8, 299-300,

324-5-
" If" j

judgments and propositions, i., 263-

79-

Ignava ratio, i., 374.
Ignorance, ii., 211, 213.
Ignoratio Elenchi, ii., 301, 315-17.
Illative sense, ii., 22.
Illicit process, in inference, i., 309-10 ; in

hypothetical^, 361.

— generalization, fallacies of, ii., 309,
329, 332-7.

Illustrative proof or explanation, ii., 31-2,
238-9.

Immediate inference, i., 229-47 > an^ exis
tential import, 256-8 ; and mediate,
292-3, 385 ; and hypothetical syllogism,
361-2 ; fallacies of, ii., 308-15.

Immutability of truth, i., 161-2 ; ii., 220.

" Imperfect " figures of syllogism, i.,

335-

— induction, u., 27.
Impersonal judgments, i., 155, 164.
Implication of existence, in propositions,

i., 164, 195, 217, 221, 235, 248-62 ; in
definitions, 101-2, 407.

— of terms, i., 48 sqq.

Implications and import, of propositions,

i., 164-6, 199, 229, 234, 396.
Import, existential, v, implication of ex

istence.
Important characters, in classification, i.,

127-31 ; in analogy, ii., 156-8.
Impossible modal judgments, i., 180-5.
Inaccuracy, in measurement, ii., 202-5.
Inceptive propositions, i., 200.
Incompatible attributes, fallacy of, ii.,

304 ; terms, i., 64, 69 ; judgments, 205-6.
Incomplete induction, v. imperfect, and

enumerative.
Indefinite propositions, i., 194-5 5 singu

lars, 193, 200.

— terms, v. infinite.

Indesignate propositions, i., 200-2, 270.
Indirect moods of syllogism, i., 323, 350-5.

— proof, i., 339 ; ii., 233-4, 3*8, 328.

— reduction, i., 339-43.
Indispensable cause or condition, ii., 64, 84.
Individual substances, i., 75, 139 ; pro

parties and accidents, 82-8.
Individuation, i., 86, 140.
Induction, aim of, ii., 23, 235 ; as an in

verse process, ii., 54-5.

— and contraposition, i., 243.

— and deduction, ii., 8, 48-55, 117-19,
243-8.

— and inference, i., 408, 411 ; ii., 24,
48-53, 109, 114.

induction, and probability, ii., 43, 206-9,
212-14.

— enumerative, ii., 27-32, 39, 40, 43, 48,
102-4, 152, 159 ; and theory of chance,
283-4.

fallacies, incident to, ii., 329-37.

— grounds of, ii., 44, 56 sqq.

— imperfect and perfect, ii., 27.

— presuppositions of, ii., 55 sqq.

— scientific, ii., 32-7, 40, 44.

— steps of, ii., 41-2, 44, 47, 49.

— views of, ii., 24, 32-45.

Inductive inference, i., 408, 411 ; ii., 24

— method, ii., 8, 13.

— methods, Mill's, ii., 172-200.

— syllogism, i., 347 ; ii., 27-32 ; as
illustrative " proof," 31-2 ; 267-8.

Inference, nature of, i., 6, 78, 229, 231,
385-92, 397-401-

— and verbal change, i., 166, 212, 231.

— by added determinants, i., 246.
by complex conception, i., 247.

— by converse relation, i., 247.

— from particulars, i., 313.

— immediate, i., 229, 292-3, 385.

— inductive and deductive compared, ii.,

51-3-

— in " if" judgments, i., 267-9.

— mediate, i., 292-3, 385-92; summary
of teaching on, 412-14.

— paradox of, i., 396-401.

Infima species, i., 79-81, 97, 122, 129 ; ii.,

139-

Infinitation, i., 232.
Infinite judgments, i., 202.

— terms, i., 66, 232.

Inseparable 'dccidens, i., 87 ; and pro-

prium, 175-7, 200-2.
Integration, i., 214.
Integrity of documents, ii., 258.
Intellect and sense in science, ii., 128-35,

ISO-
Intension of concepts and terms, i., 48-

57; kinds of, 49, 398; and extension,

55-7 < m propositions, 207-8 ; in syllo

gisms, 293, 301-4 ; and possibility of

inference, 398.

Intentio universalitatis, i., 8, 390.
Intentions, first and second, i., 32, 72,

148, 390.

Interaction, v. cause.
Interference of causes, ii., 169, 171.
Intermixture of effects, ii., 195-6.
Interpretation, i., 5, 160 ; of meaning in

judgment, 207 sqq.
Intuition of universal truths, 5., 407 ; ii.,

24-6, 211, 229, 232, 247-8.
Inventio medii, i., 332 ; ii., 55, 121, 246.
Inventive method, ii., 7.
Inverse probability, ii., 278-82.

— processes, ii., 54-5.
Inversion, i., 243-5.

35°

THE SCIENCE OF LOGIC

Irony, Socratic, ii., 15.

Irrelevant elements, elimination of, i.,

276 ; ii., 165-72, 269.
IRVINE, i., 307.
" Isolated " laws, ii., 207.

JANET, ii., 200.

JEVONS, i., 39, 232, 244, 375 ; ii., 37, 43,
55. 137. 168, 169, 194-6, 202, 204, 303.

JOANNES A S. THOMA, i., 14, n. 2.

JOHN XXL, Pope, i., 317, 352.

JOHNSON, i., 323.

Joint method of difference and agreement,
ii., 181-3.

JOLY, M. HKNRI, ii., 326-7.

JOSEPH, on form and matter of thought,
i., 21, 163, 264-5; ii., 296; on exten
sion and denotation, i., 57 ; on pro
perties, 85 ; on principle of individua-
tion, 86, 140 ; on definition, 92 ; on
basis of division, 119; on the cate
gories, 147 ; on predication per accidens,
156 ; on verbal and real judgments, 171 ;
on modality, 181, 185 ; on quantity
of judgment, 191 ; on particular pro
positions, 194-5 : on negation, 205 ; on
immediate inferences, 232, 234-5, 237>
239-40 ; on existential import of copula,
249 ; on hypothetical judgment, 264 ;
on disjunctive judgments, 285, 287-8 ;
on definition of syllogism, 293, 366, 391-
2 ; on the Dictum de muni, 300, 303-4 ;
on undistributed middle, 309 ; on figures
of syllogism, 344-55 ; on simple dilem
mas, 369, 375 ; on deductive, inductive,
and mathematical inferences, 391-2,
411; ii., 31, 40, 47, 49-53, 117, 142,
172, 231, 247, 248 ; on subsumption in
syllogism, i., 406; on elimination in
induction, ii., 38, 50, 52 ; on mechanical
view of reality, 69 ', on efficient and
necessary causality and free will, 73-
5 ; on scope and ideal of science, 75,
108, 224, 229-32, 237-8 ; on meta
physical assumptions, 134-5, I43"5»
243 ; on concepts of cause, 80, 88, 90-
2, 208 ; on grounds of belief in unifor
mity of nature, 102, 107-13, 115-16,
243 ; on function of hypothesis, 122 ;
on analogy, 158-60; on experimental
methods, 173, 175, 186, 191, 194 ; on
inductive explanation, 247 ; on fallacies ;
297, 301, 311, 328.

JOYCE, on necessary judgments, i., 176 ;
on traditional rules of syllogism, 317;
on mnemonic lines, 352 ; on logical and
real principles in inference, 389-90 ; on
circumstantial evidence, 394-5 ; on in
duction not an inference, 408 ; ii., 114 ;
on inductive syllogism, ii., 27, 31 ; on
scholastic view of induction, 33 ; on
uniformity of nature, 94, 98, 116; on
measurement, 202 ; on explanation,

242-3 ; of laws, 207 ; on metaphysical
truths, 219; on chance, 274, 280; on
fallacies, 328.

Judgment (v. propositions), i., 17, 18 ;
Kant's divisions of, 151 ; process of,
154-8 ; objective truth of, 158-62 ; de
finitions of, 161 ; problems on import
of, 167-8 ; classifications of, 168-70 ;
necessary and contingent, with syn
onyms, 170-80 ; 201-2 ; ii., 217-23 ; ob
jectivity of necessary judgments, i., 174-
9 ; modality of, 180-5, 261 ; quantity of
categorical, 188-98 ; affirmative and
negative, 202-6; opposition in cate
gorical judgments, 219 sqq. ; existen
tial import of, 248-62 ; hypothetical and
conditional, 263-79; disjunctive and
alternative, 280-6 ; inference from " par
ticulars," 386, 392-5 ; fallacies incident
to, ii., 308-15.

KANT, i., 10, 20 ; on the categories,
146, 150-3 ; on analytic and synthetic
judgments, 177-80 ; on modality, 183-5 '•>
on first figure of syllogism, 334 ; on
realism, ii., 146-7; on fallacies, 300;

334-

KELVIN, Lord, ii., 133, 138.

KEPLER, ii., 122.

Key, analytical, i., 125.

KEYNES, Dr., on laws of thought, i., 27 ;
ii., 308 ; on meaning and implication,
i., 50, 165-6, 234 ; on denotation, 55 ;
on negative terms, 66 ; on definition,
94. 95. 99 > on simple, complex and
compound judgments and terms, 169
198-9, 283-4 ; on verbal and real
propositions, 172 ; on modality, 183 ;
on denial, 203-6; on quantification of
predicate, 212-16, 332 ; on equational
reading of propositions, 217-18 ; on
contraposition, 242 ; on universe of
discourse, 55, 249; on existential im
port, 249-262 ; on conditional and hy
pothetical propositions, 267, 270, 274,
276-8 ; on alternative and disjunctive
propositions, 283 ; on eductions and
rules of syllogism, 312; on simplifica
tion of rules of syllogism, 315-17 ; on
fourth figure of syllogism, 324 ; on
existential import in syllogism, 331-2;
on antilogism, 340-1 ; on first figure,
344 ; on second figure, 345 ; on third
figure, 349 ; on " disjunctive " syllog
isms, 365 ; on dilemmas, 375 ; on sorites,
382-3 ; on non-syllogistic inferences,
387 ; on petitio principii in inference,
404-5.

Kinds, natural, i., 129; ii., 139.

KIRSCH, ii., 254.

LAMBERT, i., 344.

LANGLOIS and SEIGNOBOS, ii., 253.

INDEX

35*

Language, ambiguities of, i., 44, 189, 192,
283 ; ii., 301 sqq.

— and categories, i., 142-5.

— and existential import, i., 258-60.

— and thought, i., 35.

— definition of, i., 34.

— functions of, i., 34-7.

— generalization t»nd specialization of,
i., 44, 50, 96.

— of animals, i., 34.

— of gesture, i., 34.
LAPLACE, ii., 134, 138.
LARMOR, ii., 133, 134.
LAURIE, H., ii., 172.

Law, meanings of, ii., 68-70, 123, 124.

— and cause, 91-2, 240-1 ; hypotheses of,
123-5.

— and fact, 206, 208, 216, 223, 236-9.

— and property, ii., 237-8.

— and statistical uniformity, 288-93.

— of parsimony, i., 197; ii., 85.
Laws, derivative, ii., 208.

— descriptive and explanatory, ii., 69,
92, 189.

— empirical, n., 206-9.

— explanation of, ii., 237-43.

— fallacies in establishing, ii., 334-7.

— necessary character of, v. necessity,
and truth.

— of nature, ii., 98, no, 123, 208 ; ex
ceptions to, 220.

— of thought, i., 23-28 ; and syllogism,
298-9 ; not purely formal, ii., 222.

Lazy argument, i., 374.

Least squares, method of, ii., 205.

LEIBNIZ, i., 27, 178 ; ii., 21, 100.

LEO XIII., Pope, ii., 21.

LEPIDI, ii., 264.

LESAGE, ii., 125.

LEVERRIER, ii., 197.

LEWIS, Sir G. C., ii., 336-7.

" Liar," fallacy of, ii., 308.

LIESSE, ii., 287.

Limitation, conversion by, i., 236.

Limitative judgments, i., 202.

Limiting clauses, i., 157, 198.

Linea praedicamentalis, i., 78.

LOCKE, i., 10, 103, 149, 395 ; ii., 75.

Logica critica, i., 29.

— dialectica, i., 29.

— docens, i., 16, 38 «.

— utens, i., 16, 38 n.

Logic, and allied sciences, i., 30-41.

— applied, ii., i, 117-19.

— as science and art, i., 13-16.

— critical, i., 28-9.

— definitions of, i., 38.

— divisions of, i., 17-19.

— formal and material, i., 19-23, 28-9,
162-4, 253 ; ii., 117-19. 296, 302-3.

— formal object of, i., 14.

— history of, i., 40-7 ; ii., 2-7.

— natural and artificial, i., 12, 13, 38.

Logic of "chance," or "probability," ii.,
261.

— of relatives, i., 247, 391.

— real, i., 28-9.

— scope of, i., 12; ii., 2-7, 294-6.

— sources of, i., 39-41.

— subject-matter of, i., 14, 16-19.

— uses of, i., 38-9; ii., 294.

Logical concetvability, or possibility, i.,
249-50, 264.

— equations, i., 216-18, 234.

— truth, ii., 210-11.

— whole and part, i., 114.
LOTTIN, ii., 293.

LOTZE, on negative terms, i., 67 ; on
dilemma, 375 ; on chance, ii., 283.

MACH, ii., 123, 292.

Magnitude, v. measurement, and quanti
tative.

MAHER, i., 161, 409; ii., 16, 25, 94, 99,
no, in.

Major premiss, i., 295, 367.

— term, i., 294, 351-2.

illicit process of, i., 309.

Mai-observation, ii., 163, 330-1.
MALUS, ii., 153, 163.

MANSEL, i., 20 ; on categories, 142, 152-3,

264, 352, 375-
MANSION, ii., 269.
Manuscripts, value of, ii., 256-8.
Many questions, fallacy of, i., 379 ; ii.,

302, 314-15.
Many-worded terms, i., 37, 197-8, 259,

283-4.
Material and formal, in logic, v. formal

and logic.

— cause, ii., 62, 65, 83.

— division, i., 115.

— fallacies, ii., 302-3.

— obversion, i., 232.
Mathematical axioms, and logical, i.,

299, 391 J "•. 24°-

— calculus of probabilities, ii., 275-85.

— inferences, i., 392 ; ii., 25, 51, 53, 117,
244-8.

induction, ii., 25.

— science, ii., 25, 54-5, 229-30, 244-8.

— truths, i., 179-80; ii., 220-1.
Matter, of judgment and proposition, i.,

262-4.

— of inference and syllogism, i., 294-7.
Mean, v. averages.

Meaning in terms, two kinds of, i., 48, 50.

— and implications, of propositions, i.,
164-6, 199, 229, 234, 396.

Means, method of, ii., 204-5.
Measurement, ii., 186, 188 ; nature, units,

and limits of, 202-4 ; methods of, 204-5 ;

and probability, 279 ; sphere of, 335-6.
Mechanical view of the universe, ii., 6, 59-

60, 68-9, 75, 110-13, 130-5, 140-1, 221,

291-3.

352

THE SCIENCE OF LOGIC

Mechanical conceptions in science, ii.,

I32-3-

Mediate axioms, of syllogism, i., 299-301,
324.

— inference, i., 292-3 ; and categorical
syllogisms, 385-92 ; and hypothetical
syllogisms, 361-2 ; from particulars,
392-5 ; remote and proximate materials
of, 409-10.

MELLONE, Dr. S. H., on denial, i., 204 ;
on collective premisses in syllogism,
402 ; ii. 9 ; on geometrical definitions,
ii., 25 ; on scholastic view of induction,
33 ; on uniformity of nature, 72-3, 97-
8, 114, 117 ; on cause and effect, 81-2 ;
on efficiency and necessity, 73 ; on
plurality of causes, 86-7, 90 ; on verifi
cation of hypothesis, 142 ; on analogy,
155, 157 ; on experimental methods,
173-86, 194; on intermixture of effects,
196 ; on residual phenomena, 197 ; on
fact and law, 208 ; on demonstration,
227-8 ; on deduction and induction,
244-5 ; on enthymeme, 266-7.

Membra dividentia, i., 112.

Memory, and physical certitude, ii., 215.

Metaphor, i., 43-4 ; ii., 161, 332.

Metaphysical certitude, ii., 106 ; nature
and source of, 214-15; of God's exist
ence, 235.

— necessity, i., 170-80; as abstract i and
hypothetical, ii., 217-23.

— analysis, i., 93, 114.

— laws or principles, ii., 106, 217-23.

— judgments and propositions, i., 170-80.
Metaphysics, and logic, i., 30-3, 135,

145-7, 252; ii., 106 sqq. ; 111-13, 130.

Metathesis, i., 336.

Method, i., 19, 378; ii., 1-22; didactic
and inventive, 7 ; analytico-synthetic,
9; of teaching, 14-16; scholastic, 16-
22 ; deductive and inductive, 48-9 ; in
physical science, mediaeval and
modern, 128-35 ; of perceptual induc
tive analysis, 165-72 ; fallacies incident
to, 315-37; experimental "methods,"
172-200 ; scope of, 197-201 ; methods
of measurement, 204-5.

Methodology, ii., i, 13-14, 253.

MERCIER, Cardinal, i., 91, 101, 145; on
the Dictum de omni, 301-3, 318; on
necessary judgment as premiss of in
ference, 405 ; on discovery by inference,
409 ; on method, ii., 10 ; 16, 21 ; ex
amples of inductive process, 45-7, 56-
7 ; on uniformity of nature, 96 ; on
hypothesis, 120-1, 127, 138,139, 150;
on truth, 210 ; on demonstration, 228 ;
on statistics, 285 sqq.

Metrology, ii., 203.

MICHAEL PSELLUS, i., 318.

Middle Ages, and method, ii., 4, 10 ; and
induction, 35-7 ; and history, 255.

Middle term, i., 294-5 ; undistributed, 308-
9, 317; finding middle terms, 332-4;
ii., 53-4, 244-8; and "cause," 227-8,
247-8.

MILL, J. S., i., 10 ; on definition, 101 ;
on classification, 127 ; on categories,
149-50 ; on connotative reading of
judgments, 209; on immediate infer
ence, 234 ; on existential import, 258 ;
Nota notae, 303-4 ; on inference from
particulars, 393-7 ; on the syllogism as
a petitio principii, 401-4 ; ii., 30, 39 ;
on induction, 42-3, 122; on "deduc
tive," method in induction, 45, 198,
247 ; sensism, 59, 74, 79, 104-5 ; on
" cause," 76-80, 128-31 ; on plurality
of causes, 86 ; on uniformity of nature,
98-9, 102-5, IIO> IIO"» 321-22; on laws
of nature, 146 ; on analogy, 153, 156 ;
on experimental methods, 169, 172-
200 ; classification of fallacies, 298-9,
306, 307.

Minima sensibilia, ii., 202.

Minor premiss, i., 295, 367.

— term, i., 294, 351-2.

illicit process of, i., 309.

Miracles and method, ii., 255.
Mixed demonstration, ii., 233-5.

— syllogisms, i., 297-8 ; hypothetical,
358-62 ; not immediate inferences, 361-
2 ; in induction, ii., 49-50 ; disjunctive,
i., 363-6 ; in induction, ii., 39, 50-2.

Mnemonic lines for moods of syllogism,
i., 326, 336 ; older forms of, 352.

Modal judgments and propositions, i.,
180-5, 227, 261, 284, 289, 290.

Modality, objective, i., 180-3 I subjective,

183-5-

Modi dicendi, per se and per accidens, i.,
171-4.

Modus, in proposition, i., 180-1 ; in syllo
gism, 320, 359-60, 364-5.

MONAHAN, ii., 141, 143.

Monism, ii., 60, 105-7, II2> 22I'3» 242 !
323-4-

Monuments, ii., 256.

Moods, of syllogism, i., 320-31; and ex
istential import, 331-2 ; indirect moods,
351 ; of hypothetical syllogism, 357-
60 ; of disjunctive syllogism, 364-5 ;
of dilemma, 370.

Moral certitude, ii., 150-1 ; nature and
source of, 215, 217, 221, 248-50, 259,
262.

— laws, ii., 249-50.

— necessity, i., 183, 404-5.

— obligation, necessity of, ii., 78.

— universals, i., 201 ; ii., 217, 262, 265,
310.

Motio, motus, actio et passio, n., 81-2.
MULLER, Max, on categories and speech

»-, 144-5-
Multiple quantification, i., 197.

INDEX

353

Name, i., 37 ; proper, 46, 96.
Named moods of syllogism, i., 325.
Natural classification, i., 122-31.

— experiments, ii., 164.

— judgments and propositions, i., 156,
323, 352.

— kinds, i., 129; ii., 139.

— sciences, ii., 68.

— selection, ii., 139.

Nature, laws of, ii., 98, no, 123, 208;
exceptions to, 220.

— meanings of, i., 75 ; ii., 66-7.
NAVILLE, Ernst, ii., 151.

Necessary character of truth, i., 161-2,
179-80 ; ii., 220-3.

— fact, i., 182 ; ii., 208, 222, 231, 233.

— judgments and propositions, i., 170-
80, 200-2, 209, 225 ; ii., 23-4, 215, 217-
23-

— modals, i., 181-3.

— ( = necessitating) causes, ii., 64, 71,
84-92.

Necessity, kinds of, i., 176, 183, 404-5,
414; ii., 23, 78, 292; conditional, of
physical laws, ii., 110-13, 216, 219,
230, 242-3 ; of metaphysical laws, 217-
23, 229-30.

— and efficiency, 11., 73-4 ; and uncon-
ditionalness, 77-80.

— explanations of, ii., 60, 75-80, 109-10.
Negation, and affirmation, i., 202-3.
Negative definitions, i., 108, no-n.

— hypothetical, i., 270, 276-9, 357.

— instances, ii., 167, 170 ; function of,
171 ; non-observation of, 330.

— judgments and propositions, i., 202-6.

— premisses, i., 310-12.

— terms, i., 65-7, 202-6, 231-2.
Neo-Platonism, ii., 10.

NEWMAN, Cardinal, i., 39, 163-4, 17&> 394 '>

ii., 22, 134, 211.
NEWTON, ii., 41, 50, 122, 124, 128, 185

190,247.

Nomenclature, i., 131-2.
Nominal definitions, and real, i., 99-104,

105-6, 134, 252 ; ii., 74.

— essences, i., 76, 84.
Nominalism, i., 10.
Nominalist view of logic, i., 20.

Non causa pro causa, fallacy of, ii., 302,

327-9-

Non-connotative terms, i., 62-4.
Non-denotative terms, i., 61.
Non-observation, fallacies of, ii., 163, 165,

329-30.
" Non per hoc " ; " non propter hoc" ii.,

328.

" Non sequitur" ii., 328.
" Normal mind " and axioms, ii., 325.
Nota notae., i., 209, 303-4.
Notions, transcendental, i., 149.
Numerically definite propositions, i., 197
Nvs, ii., 125, 140.

VOL. II. 23

Objective, and subjective elements in
truth, i., 177-80 ; ii., 220-3 ; in laws of
thought, i., 25-7 ; ii., 222.
views of modality, i., 180-5.

— extension, i., 55.

— intension, i., 49.

— reference of judgment, i., 160-2; 203-
4, 248-52, 264.

Observation, and experiment, ii., 164-5 ;
repeated observation, 165, 168.

— errors in, ii., 196 ; and measurement,
202-5 ; and inference, 263-4, 331-

— fallacies of, ii., 299, 329-31.
Obversion, i., 230-2.
OCCAM, ii., 144.
Occasionalism, ii., 74.

Occult" forces and motions, it., 128-32.

O'KEEFFE, ii., 252.

OLLE LAPRUNE, ii., 327.

O'MAHONY, ii,, 254.

Ontological truth, ii., 58, 210, 212, 235.

Opinion, ii., 213 (cf. probability , belief).

Opposition of judgments and propositions,
i., 219-28 ; and existential import, 256-
7 ; of conditionals, 270-2 ; of hypo-
theticals, 276-8 ; of disjunctives, 290.

— of terms, i., 64-9.

— of truth and error, ii., 213-4.

— square of, i., 220.

Oral tradition, ii., 256, 258-9.
Organon, Aristotle's, i., 40.
Origin and sources of hypotheses, i., 195 ;
ii., 32, 151-5.

of logic, i., 38-41.

Original moods of syllogism, i., 324-6.
Ostensive reduction, i., 335-9.
OSTWALD, ii., 145.

Palaeography, ii., 256.

Palaestra logica, cited, ii., 174, 176,

180-1, 189, 193, 208, 311.
Pantheism, ii., 61, 106-7, 242.
Paradox of inference, i., 396-401.
Paralogism, ii., 297, 300.
Paronyms, ii., 307.
Parsimony, law of, i., 197 ; ii., 85.
Part, logical, i., 114.
Partial contrapositive, i., 241.
Particular judgments and propositions,

i., 194-5 ; inference from, 313, 1386,

392-5-

Partitive conversion, i., 236.
PASCAL, ii., 22.

Passio, category of, i., 142, 147-8.
PASTEUR, ii., 121, 138, 139, 157, 200.
Pedagogics, ii., 14.
Pejorem sequitur, etc., i., 318.
Per accidens conversion, i., 236-7.

— predication, i., 156, 172.
Percept, i., 3.

Perfect figure of syllogism, {.,300, 319,

335-

— induction, 11., 27.

354

THE SCIENCE OF LOGIC

Periodic changes, ii., 189-90.
Permanent causes, ii., 188.
Permutation, i., 232.
Per se predication, i., 170-4.
" Personal equation," ii., 204.
Petitio Principii, fallacy of, ii., 235, 301,
317-22.

— and syllogism, i., 401-7 ; and grounds
of belief in uniformity of nature, ii.,
103-5, Il6> 321-2.

PETRUS HISPANUS, i., 317, 318, 352.
Phantasm, i., 3-4.
Phantoms, Bacon's, v. idola.
Phenomenism, ii., 59-60, 130, 146, 322-4.
Phenomenon, and cause, ii., 76-80, 128-

31-
Philology, on thought and speech, i.,

144-5.
Philosophy, i., 19, 135 ; and method, ii.,

10 (v. sciences).

— errors in, ii., 325-6.

Physical certitude, ii., 98-100, 106 ; nature
and source of, 215-6, 221.

— causes, ii., 64, 71.

— division, i., 107, 114.

— judgments and propositions, i., 170-80.

— law and necessity, ii., 78, 100-13,
123-4, 221-3.

— sciences, rise of, ii., 4-5 ; scope of,
26, 62-3, 74, 75, 110-13, 124, 131, 133 ;
and method, 49, 63, 68.

PIAT, ii., 15.

PICTET, ii., 125.

Place, category of, i., 142.

PLATO, i., 9, ro, ii, 92 ; ii., 19, 20, 336.

Plurality of causes, i., 275 ; ii., 84-92,

187, 244, 247-8.

Plurative propositions, i., 195-6.
Plvres interrogcitiones, fallacy of, i., 379 ;

ii., 3I4-5-
POINCARE, H., ii., 131, 133, 134.

— L., ii., 201, 202, 203.
POISSON, ii., 285.
Polylemma, i., 367.
Polysyllogism, i., 377-8.
Ponendo tollens, modus, i., 364-5.
Ponens, modus, i., 359.
POKPHYRY, i., 72, 85.
Porphyry's tree, i., 78-9, 116.
Positive instances, function of, ii., 171.

— terms, i., 65-7.
Positivism, ii., 15, 59, 124, 130.
Possible propositions, i., 184.
Possibility, sphere of logical, i., 249-50;

and actual reality, 264.
Postpracdicamenta, i., 136.
" Post hoc ergo propter hoc" ii., 328-9,

334-
Postulates, ii., 10, 23,60, 106-7, IO9. ZI1J

justification of, 142-5.
Posture, category of, i., 142, 144.
Practical certitude, ii., 262 (cf. moral

certitude}.

Practical science, i., 15.

Praedicabilia, i., 72.

Praedicamenta, i., 7, 136 (v. categories).

PRANTL, i., 39, 136, 318.

Predicables, Aristotle's and Porphyry's,
i., 72-3 ; classification of, 73-6 ; defini
tions of, 76-7 ; and categories, 138 ; as
relations, ibid.

Predicamental line, i., 78.

Predicate, i., 154-5 ; distinction from sub
ject, 156-8 ; distribution of, 187 ; quanti
fication of, 202-16, 332.

Predication, views of, i., 207 sqq., predi
cative view of, 207-8, 301, 302-4.

Premisses, i., 292 ; discovery and proof,
of. 375 ; ii-, i, 2, 23-4 ; deductive and
inductive, 246-7.

Prescription, argument from, ii., 259.

Primae intentiones mentis, i., 32, 73.

Principle, i., 8 ; logical and real, 135 ; in
syllogism, 295.

Principles, of demonstration, ii., 226;
of thought, i., 23-8 ; and being, 135 ;
ii., 226 ; " regulative," ii., 13, 143-5,
227 ; conditional and unconditional, ii.,
107-13.

Prius natura, and prins nobis, ii., ii, 16,
65, 227-9, 231-2.

Private definition, i., 106.

Privative conception, inference by, i.,
232.

— terms, i., 69.

Probability, i. 19 ; and modality, 183-5 ;
ii., 5, 151 ; in analogy, 153-61 ; in in
duction or generalization, 206-9 ; 212-
14, 263 ; nature of, 260-3 ; sources of,
263 ; calculation of, 262-85 ; inverse,
278-82.

Probable arguments, ii., 263-8.

Problematic judgments, i., 180-5, 347>
358.

Progressive chains of reasoning, i., 377-

83-

Proof, v. demonstration and explanation.

Proper names, i., 46 ; and connotation,
63, 96.

Property, i., 77, 82-6 ; and necessary
judgments, i., 171-80; physical, 176;
ii., 45-7, 125, 237.

" Proportio," ii., 160.

Propositio infinita, i. 202.

Propositions (v. judgment), primi, secun-
dii et tertii adjacentis, i., 155 ; struc
ture of, 154-8-; natural and inordinate,
156 ; formulation of, 164-6 ; simple,
complex and compound, 169, 197-200 ;
necessary and contingent, 170-80 ; pro-
positio per se nota, and per aliud nota,
170 ; ii., 24 ; modal, ii., 180-5, 227 ;
form of, 186 ; universal and particu
lar, 188-98 ; collective, 189 ; singular,
192-3,227; plurative, 195-6; exponible,
198-200 ; indesignate, 200-2 ; views on

INDEX

355

import of, 207-18 ; opposition of cate-
goricals, 219-28, 290 ; eductions from,
229-46 ; existential import of, 248-62 ;
hypothetical and conditional, 265-79 ;
disjunctive and alternative, 280-91 ; in
ference from " particulars," 386, 392-5.

Proprium (v. property), predicable of,
i., 77 ; ii., 152 ; and essence, i., 83-4 ;
kinds of, 82-3 ; and necessary judg
ments, 171-80 ; and accidens, 175-7.

Prosody, fallacy of, ii., 306.

Prosyllogism, i., 377.

irpdrfpov <f>vff(i, and IT. Tjfuv, v. prius, etc.

Proximo, species, i., 78.

Proximate cause, ii., 63-4.

— matter of syllogism, i., 294.

Proximum genus, i., 78.

PSELLUS, i., 318.

Psychology, and logic, i., 33, 412.

Ptolemaic astronomy,
149. 329

i., 122, 126, 138,

Pure, empiric, and mixed demonstrations,
ii., 234-5.

— categorical syllogisms, i., 297-8 ; hypo
thetical, 356-8 ; disjunctive (alterna
tive), 362.

— propositions, i., 170.
Purely formal division, i., 117.

— logic, i., 20-2, 162, 264-5.
Purpose, in classification, i., 123-31.

— in analogy, ii., 156.

— in nature, ii., 59, 62, 66-70, 112.

«' Quadruped " logical, i., 307.
Qualitative analysis, ii., 165 sqq.
Quality, category of, i., 141 ; and relation,
ii., 161.

— of categorical propositions, i., 202-6;
of conditionals, 270 ; of hypotheticals,
277.

Quando, category of, i., 142.
Quantification of predicate, i., 212-16;

and syllogism, 332.
Quantitative and qualitative methods, ii.,

186.

— aspect of facts, ii., 123, 132-5, 141,
160-1, 201, 335.

— determination, ii., 201-5.
Quantity, category of, i., 141.

— of categorical propositions, i., 186 sqq. ;

National propositions, i., 170-80.
iaw materials of thought, i., 3, 17 n. 2.
IAY, i., 232.

^AYLEIGH, Lord, ii., 197.
Real and logical accidents, i., 86-8, 138.

— definition, i., 99-104.

— essences, i., 76, 84.

— propositions, i., 170-80.

Realism, extreme and moderate, i., 9, 10 ;

Ontologistic and Platonic, 10 ; truth

of realism not self-evident, ii., 107-8 ;

moderate realism and experience, 221-3.
Reality, and thought, i., 42-3, 249-52 ; ii.,

58 ; possible and actual, i., 264.

— and principle of sufficient (reason, ii.,
58-64, «3-

— as object of logic and of metaphysics,
i-, 30-33-

— Empiricist view of, v. Empiricism.

— Hegelian-idealist view of, v. Hegel.

— Scholastic, Theistic view of, v. Theism.
Xealm of denotation, i., 52-4, 248-52.
Reason, v. ground.

— Principle of sufficient, i., 27 ; and
syllogism, 359 ; and reality, ii., 58-61
"3-

Reasoning, v. inference.
Rebutting dilemmas, i., 371-3.
Reciprocal propositions, i., 237 ; as the

ideal of science, 274-5, 296, 360-1 ; ii.,

85-92, 151-2, 231, 247-8, 312.

— and non-reciprocal causes, ii., 84-92,
167.

Reductio ad absurdum, i., 337, 339-43,

346, 353-4 5 »»., 233-4, 328.
Reduction of syllogisms, i., 335-44 ; of

hypothetical and disjunctive to cate-

of conditionals, 270 ; of hypotheticals

227.

Quaternio terminorum, i., 307, 317.
Question, in syllogism, i., 293, 295.
QUETELET, ii., 145, 288, 289, 290, 292-3
Quodlibeta, ii., 17.

RABIER, i., 303 ; ii., 144.

Ramean tree, i., 78.

RAMSAY, ii., 197.

RAMUS, i., 78.

Ratiocinatio, Ratiocinium, i., 18, 292.

Ratiocination, fallacies of, ii., 299.

orical, 365-6 ; of dilemmas, 370-3.

gone;
eferen

377,

Referential hypotheticals, i., 274.
Refutation, ways of, i., 223, 225, 295.
Regressive chains of reasoning,

383-4-

— demonstration, ii., 45, 235.
REINSTADLER, i., 318.
REISCH, ii., 310.
Relation, category of, i., 141, 148; and

ratio, ii., 160-1.
Relative terms, i., 70.
Relatives, logic of, i., 247, 391.
Remote matter of syllogism, i., 294.
Remotive propositions, i., 280, 282.

Renaissance, influence on logical method,

ii., 4) 10, 36, 128-9.
Repugnant propositions, i., 205-6; terms,

i., 69.
Resemblance, in classification, i., 128-31 ;

in analogy, ii., 156-8.
Residual phenomena, ii., 193, 197.
Residues, method of, ii., 193-7.
Rhetoric, i., 34.
Rhetorical syllogism, ii., 268.
RICHARD, P., ii., 20, 22.
RICKABY, ii., 106, 147, 208, 253, 255.
2 *

356

THE SCIENCE OF LOGIC

ROBERTS, W. J., ii., 64.

ROGER BACON, ii., 21, 37, 185.

ROTHER, ii., 249-50.

Rule, and exception, ii., 167, 217-23.

SATOLLI, i., 101.

Scepticism and dogmatism, ii., 113.

Schemes of judgments and propositions,

i., 164-6.
Scholastic debates, ii., 16-19.

— metaphysics, ii., 128-31, 228.

— method, ii., 4 ; appraised, 19-22.

— teaching methods, ii., 16-19.

— terminology, ii., 17-19, 317.

— philosophy, and method, ii., 10, 19,
in, 128-35.

— view of science, v. science.

of causes, ii., 62, 64, 78.

of demonstration, ii., 225 sqq.

Scholastics, on categories, i., 146 ; on

necessary judgments, 170-83 ; on ex
istential import, 252-4, 256 ; on rules
of syllogism, 312, 318; on " inventio
medii," 332-4; on method, ii., 4, 16-19,
128-35; on induction, 33-7; on truth,
58-9 ; on purpose in nature, 67-70 ; on
basis of necessary causation, 78 ; on
plurality of causes, 86; on belief in
uniformity of nature, 100-2 ; on demon
stration, 233 ; on authority in science,
252
Science, and art, i., 15.

— and belief, ii., 97, 250-2.

— free will, and necessary causation, ii.,
72, 94, 217.

Sciences, special, and philosophical, ii.,
3-7, 101, in, 124, 131, 133-4, 142, 168,
208, 226-7, 240-1.

— speculative and practical, i., 15.

— deductive and inductive, ii., 4-5, 7-9,
235, 243-8.

— historical, ii., 253-9.

— human, ii., 6, 248-9.

Scientific knowledge, ideal of, ii., 23, 108,
134, 208, 223-32.

— nomenclature, i., 131-2.

— terminology, i., 132-4.
Scope of concepts, i., 48.

— of logic, i., 19-23.

Scottish philosophers, on uniformity of

nature, ii., 101.

SCOTUS, DUNS, ii., 21, 33, 35-7, 93.
Second figure of syllogism, rules of, i.,

322 ; characteristics of, 344-6.
Secundae intentiones mentis, i., 32, 72,

390-

Secundum quid, fallacy of, ii., 309-11.
Selection, in sense perception, ii., 162-3.
Self-contradictory concepts, ii., 304 ;

judgments, 308.
fft}ft,tlov, ii., 266-7.
Sensation and thought, i., 2-4.
Sensism, ii., 59, 79, 104-5, 130, 323-4-

Sensus communis, i., 3.

SENTROUL, ii., 210.

Separable accidents, i., 86-8, 201-2.

Sequence and consequence, ii., 165, 328-9,

334-

— causality, ii., 80-4.
SEXTUS EMPIRICUS, i., 303, 401.
SHYRESWOOD, W. of, i., 352.
Sign, i., 35.

SIGWART, i., 66, 185, 206, 350; ii., 45, 290.
Silence, argument from, ii., 256.
Simple, complex, and compound judg
ments, i., 169, 197-200, 283-4.

— and complex terms, i., 198, 290.

— apprehension, i., 2, 17.

— inspection, fallacies of, ii., 299.

— contraposition, i., 241.

— conversion, i., 231-40.

— dilemmas, i., 367-8.

" Simplex indicium veri," ii., 144-5.
Singular concepts, i., 63, 394.

— judgments and propositions, i., 192-3,
227, 239. ,

— terms, i., 45-6.

Situs, category of, i., 142, 144.
SMITH'S " Nut to crack," ii., 318.
SOCRATES, i., 92; ii., 15, 331.
Sophisms, ii., 300-1.
Sorites, i., 378-84 ; ii., 265, 304.

— fallacy of, i., 379 ; ii., 306.
Space and causality, ii., 83.

I SPALDING, i., 232.

! Specialization in language, i., 44, 50, 96.
Species, predicable of, i., 76-7.

— fixed infima, i., 79-81, 97, 130; ii.,
139-

— and genus, in logic and in biology, i.,
80, 130.

I Specific and individual essences, i., 75-6.

— differentia, i., 79-82.

— proprium, i., 82-4.
Specification, of terms in judgment, i.,

213-16.

Speculative science, i., 15.
Speech, parts of, and logical terms, i.,

35 ; and categories, 143.
SPENCER, H., ii., 14, 146, 320-1.
Sphere of application in concepts, i., 52-

4. 248-52.

— of reference in judgments, i., 160-2,
203-4, 248-52.

— of inductive analysis, limitation of, ii.,
168, 182-3.

SPINOZA, i., 149 ; ii., 10.

Square of opposition, i., 220.

Standards of measurement, ii., 202.

Statistics, ii., 5 ; and concomitant varia
tions, 192-3, 282; uses of, 285-7; and
induction, 287; interpretation of, 287-93.

STOCK, St. G., i., 226, 232, 375.

STOICS, on categories, i., 149 ; on sorites,
379-

Strength of analogies, ii., 156-8.

INDEX

357

Strengthened syllogisms, i., 326-7.
Subaltern moods of syllogism, i., 325.

— opposition, i., 220-1.
Subcontrary opposition, i., 226-7.
Subdivision, i., 113.

Subject, grammatical, logical, and ultim
ate, of propositions, i., 155, 161, 248-9
264.

Subjective intension, i., 49, 63.

— view of modality, i., 183-5.
Substance, category of, i., 139, 141, 143 ;

and attribute, 366, 386-7 ; in induction

ii., 83, 129.

Substances, first and second, i., 75, 139.
Substantial terms, i., 46-7.
Sufficient reason, v. reason.

— (= necessitating) cause, ii., 64, 71
79, 168, 244.

Suggestion and implication, i., 51, 63,
258 ; and inference, 394 ; in teaching,
ii., 15.

— of hypotheses, ii., 151-5.
Summa Theologica, ii., 17.
Summum genus, i., 78, 96, 127.
Suppositio,\., 48.

— materialis, i., 37.

Suprasensible not unknowable, ii., 59-60.

Suprema genera rerum, i., 137.

Suspicion, ii., 213.

Syllogism, syllogisms, etymology and de
finitions of, i., 293, 385-92 ; matter and
form of, 294-7 ; formal validity ex
pressed as a hypothetical proposition,
296 ; pure and mixed, 297-8 ; and laws
of thought, 298-9 ; mediate axioms of,
299-304 ; general canons of, 305-18 ;
figures and moods of, 319-331 ; and
existential import, 331-2 ; and quanti
fication of predicate, 332; reduction
of, 335-44 ; figures compared, 344-55 ;
mixed, 356-75 ; and mediate inference,
385-92 ; characteristics of syllogistic
reasoning, 385-6 ; and deductive infer
ence, 391-2, 412 ; ii., 51-3 ; and fallacy
of petitio principii, i., 401-7 ; and uni
formity of nature, ii., 115-19 ; probable
syllogism, ii., 159, 263-8 ; rhetorical,
ii., 268 ; demonstrative, ii., 225-9.

Syllogistic reasoning, v. syllogism, and
inference.

Symbolic logic, i., 117.

Symbols, use of, i., 23 ; for experimental
methods, ii., 199-200.

Syncategorematic words, i., 34, 36.

Synonyms, i., 172.

Synthesis, in definition, i., 91 ; in judg
ment, i., 157-8, 171 ; in method, ii.,
9-10 ; and analysis in teaching, ii.,
14-16.

Synthetic method, i., 378 ; ii., 7-10.

— chains of reasoning, i., 377-83.

— judgments and propositions, i., 170-80 ;
ii., 94 ; synthetic a priori, i., 179.

Systematic conceptions, ii., 127, 137-42,
145, 319.

Tabula, Lord Bacon's, ii., 172.

Tautology, i., 272, 276.

Teaching, methods of, ii., 14-22.

TfKfj.'ftptov, ii., 232, 266.

Teleology and mechanicism in philosophy

of nature, v. mechanical, and purpose.
Tendency, defined, ii., 196.
Terminology, scientific, i., 132-4.
Terms, definition of, i., 37 ; divisions of,

42-71.

— ambiguous, i., 44, 189.

— distribution of, in proposition, i., 186-8.

— relation to concepts and to things, i.,
42-3, too.

— simple and complex, single-worded and
many-worded, i., 37, 197-8, 259, 283-5,
290.

Testimony, qualities of, ii., 250 ; not
ultimate, 251 ; criteria of, 254-6 ; and
probability, 264 ; and calculus of proba
bility, 284-5.

Tests of truth, v. criteria.

Tetralemma, i., 367.

Theism, philosophy of, ii., 61, 78 ; and
uniformity of nature, 100-2, 106-7,
109-10, 112-13, r43» as a verifiable
hypothesis, 145-7 ; 230-2, 234-6, 240-3.

THEOPHRASTUS, i., 351.

Theory and fact, ii., 60, 149-50.

— and hypothesis, ii., 124.

— of knowledge, i., 28-9.
Thesis, in syllogism, i., 292.

Third figure of syllogism, special rules
of, i., 322-3 ; characteristics of, 346-50.

THOMAS AQUINAS, ST., i., 13, 15, 32, 43,
141, 148, 173, 394 ; ii. 3, 12, 17, 21, 29,
33-4. 47. 67, 82, 127, 138, 147, 210,
228, 252, 326.

THOMSON, Archbishop, i., 20, 212, 375.

Thought and language, i., 35.

— and sensation, i., 2-4.

— and things, i., 42-3, 249-52.

— form and matter of, i., 20-3, 146, 150,
152.

— laws of, v. Laws of Thought.
Time, category of, i., 142-4, 150; and

causation, ii., 80-4, 228.

— of predication and in predication, i.,
161-2.

Tollendo ponens, modus, i., 364 ; in in
duction, ii., 39.
Tollens, modus, i., 359.
TOOHEY, ii., 214-5.
Total cause, ii., 63-5.
Totum divisum, i., 112.

— logicum, i., 114.

— metaphysicum, i., 114.
Traditional logic, i., 29 ; and existential

mport, 252-4, 256; 272.

— scheme of propositions, i., 186-8.

THE SCIENCE OF LOGIC

Transcendental notions, i., 149.

Transversion, i.. 269.

Tree of Porphyry, i., 78-9.

Tres modi sciendi, i., 90 ; ii., 2.

Truth, and judgment, i., 158-62; ob
jective character of, i., 160-2, 179-80 ;
ii., 220-3 ; in hypothetical judgments,
i., 263-4; ii., 217-23; in alternative
judgments, i., 290, 371 ; definition and
kinds of truth, ii., 210, 213, 235 ; truth
indivisible, 214, 260-1 ; attainable,
325-7 ; necessity of, v. necessity.

" Tu quoque" ii., 316.

TYNDALL, ii., 140.

Type, definition by, i., 97-9.

Types, organic and inorganic, i., 129.

Ubi, category of, 142.

UEBERWEG, on nominal definition, i., 100-
i ; on dilemma, 375 ; on regressive
reasoning, ii., 9 ; on induction, 34 ; on
application of syllogism, 117, 227.

Ultimate sources of inferred conclusions,
i., 410-12, 414.

Unconditional principles in science and
philosophy, ii., 107-13.

Undistributed middle, i., 308.

Undue assumption of axioms (cf. assump
tion), ii., 255, 317, 322-7, 334.

— rejection of axioms, ii., 323.
Uniformity of nature, principle of, as

categorical, ii., 96-9, 109; as hypo
thetical, 94-6, 109.

— grounds of belief in, 99-113, 116,
320-22.

— recognized by Scholastics, ii., 35-7,
67, 93-

— relation to deduction and syllogism,
ii., 116-19; to induction, 114-16.

— and causality, ii., 71-2.

— and possibility of science, ii., 73-4,
93-4-

— sphere of application of, ii., 94.
Unitary terms, i., 46.

Units of measurement, ii., 202.
Unity of nature, ii., 105-6.
Universal concepts, formation of, i., 4-8,
63; direct and reflex, 138.

— grammar, i., 34.

— judgment in reasoning, immediate, i.,
231-2, 236 ; syllogistic, 313-5 ; mediate,
392-5 ; errors on its function, 395 sqq.,
403 ; apprehension and application of,
407-12 ; ii., 216-17, 262-3.

— judgments and propositions, categori
cal, i., 188-98.

Universality, grades of, in judgment, i.,
188-92, 201-2 ; 404-6 ; ii., 23, 215-17.

Universals, controversies on significance
of, i., 8-n ; ii., 107-8, 221-3.

Universe, ultimate views of, v. Hegel,
mechanical, scholastic, theism,

— of discourse, i., 54, 65, 161, 249-52, 255.

Univocal terms, i., 43-4; predication
149.

Validity of inference, formal and material
i., 294-7, 3I4~I7» 40* » 'n dilemmas,
370-3.

— of thought, i., 19-23.
VEITCH, i., 39, 174 ; ii., 242.

VENN, Dr. J., on denotation, i., 55 ; on
definition, 90, 102 ; on classification
125, 129, 130 ; on existential import,
259; on "if" judgments, 267 - 70 ; on
alternative judgments, 281 ; on dis
covery by inference, 400, 408 ; on in
duction and inference, 411-12 ; on
enumerative treatment of induction, ii.,
43; on inverse processes, 55, 248; on
causes, 62 ; on plurality of causes, 87-
9 ; on uniformity of nature, 93, 100,
105, 117-19; on experimental analysis,
169 ; on symbolic notation of experi
mental methods, 200 ; on chance, 269,
271, 273, 283-4.

Vera causa, ii., 128.

Verbal disputes, ;., 103-5.

— division, i., 114.

— propositions, i., 170-80.

— transformations, and inference, i., 166,
212, 231, 239, 396.

Verification, v. hypothesis.

Vicious circle, i., 401 ; ii. , 113, 235,320.

" Vires occultae" v. occult.

Vis cogitativa, i., 394.

VREOILLE, Pere de, ii., 132.

WALKER, L. J., ii., 147.

WARD, ii., 130, 131, 133, 134, 135.

WATT, ii., 122.

Weakened conclusions, i., 325.

Weaker premiss, i., 317-8 ; ii., 264-5.

WEISMANN, ii., 129, 131, 139, 140.

WELTON, Prof. J., on principle of suffi
cient reason, and reality, i., 27 ; ii., 59-
60 ; onproprium, i., 83 ; on definition, i.,
go, 93, 98-9, 102, no; on division, i.,
117, 127-8; on categories, 137-8, 144;
on subject and predicate, 156-7 ; on
grounds of negation, 205-6 ; on quantifi
cation of predicate, 213-16 ; on material
inferences, 247 ; on conditional judg
ments, 271 ; on disjunctive judgments,
286, 288-9 ! on direct determination of
valid moods of syllogism, 329-31 ; on
second figure, 345 ; on pure hypotheti
cal syllogisms, 357-8 ; on pure disjunc
tive syllogisms, 362 ; on dilemmas, 375 ;
on non-syllogistic mediate inferences,
391 ; on regressive reasoning, ii., 8-9 ;
on method of teaching, 15, 16 ; on in
ductive syllogism, 29 ; on scholastic
view of induction, 33 ; on induction as
an inverse process, 55 ; on mechanical
view of reality, 69, 133, 141 ; on efficient

INDEX

359

causality, 73, 83 ; on cause and effect
as identical, 82 ; on plurality of causes,
86-7 ; on " uniformity " and " unity " of
nature, 103, 105-6; on hypothesis, 123,
141 ; on analogy, 154, 156 ; on ex
perimental analysis, 168-72, 198 ; on
methods of measurement, 204-5 ! on
necessary truth, 217-23 ; on explana
tion, 239, 241-3 ; on chance, 271-2,
274-5, 277-85 ; on averages, 289-93 5
on fallacies, 303, 311, 317, 320-1, 329-37.

WHATELY, Archbishop, i., 20, 375 ; ii.,
302-3, 310.

" When," category of, i., 142.

" Where,'' category of, i., 142.

WHEWELL, on terminology, i., 133-4 1 on
induction, ii., 42, 122 ; on experimental
methods, 198-9.

Whole, logical and metaphysical, i., 114.

WILLIAM OF SHYRESWOOD, i., 352.

WILLMANN, ii., 14.

WlNDELBAND, ii., 229-31.
WlNDLE, ii., 129, 131, 139, 140.

Words, classification of, in grammar and

in logic, i., 34.
Working hypothesis, ii., 126-7.

ZENO, i., 369, 371, 375.
ZIGLIARA, i., 81, 318, 332, 342 ; ii., 2, 19,
86, 212, 253, 260.

BC
71'
.06