Six essays on the Platonic theory of knowledge : as expounded in the later dialogues and reviewed by Aristotle

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SIX ESSAYS

ON

THE PLATONIC THEORY OF
KNOWLEDGE

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UG,r

Zlf\ SIX ESSAYS

ON

THE PLATONIC THEORY OF
KNOWLEDGE

as expounded in the later dialogues and
reviewed by Aristotle

by
MARIE V. WILLIAMS

late Marion Kennedy Student of Newnham College

Cambridge :

at the University Press

1908

Camtmtige :

PRINTED BY JOHN CLAY, M.A.
AT THE UNIVERSITY PRESS.

PREFACE

rilHE following essays, written during my tenure of a
-*- studentship at Newnham College, Cambridge, were
the outcome of a genuine interest in the Platonic
controversy, and of a desire to satisfy myself, by
independent study, regarding the doctrines that the
later dialogues seem to teach. In a subject that has
for so long been the source of disagreements one can
scarcely hope to produce a work that will commend
itself to every critic, or to bridge in any degree the
chasm that already yawns between the two leading
schools of interpretation ; and I must own frankly, at
once, that I belong to the school that sees in the later
work of Plato a fuller development and elaboration of
the ideal scheme which was at first but vaguely sketched.
It is not the spirit of controversy, however, but the hope
for a better understanding of this position on the part
of other controversialists, that has led me to publish
these papers. In preparing them I have not neglected
to make myself acquainted with the position taken by
other schools; but that I am chiefly indebted to the
Platonic scholars of Cambridge cannot be denied.

\

VI PREFACE

A word perhaps should be said in regard to the
order in which the Platonic dialogues are here taken.
I have assumed throughout — and I believe there is now
almost general agreement on this point — that the six
dialogues with which I chiefly deal, viz., the Parmenides,
Theaetetus, Sophist, Politicus, Philebus and Timaeus, are
posterior to the Republic and the Phaedo, and that,
whatever be the order in which they are to be ranked,
they belong, roughly speaking, to the same period of
Plato's thought. The special order in which they are
grouped here was particularly suited to the form of my
essays, being based mainly on affinity in subject-matter;
and any re-arrangement of the first four would not
materially affect any of the conclusions I have reached.
The Philebus and the Timaeus, however, I cannot help
regarding for many reasons as posterior to the other
four, and I believe that this, too, will be conceded by
the majority of scholars. For my own part, I would go
further and make the Timaeus the latest of them all,
though I do not think that this particular article of faith
is absolutely essential for the acceptance of the results
of my essays. The Philebus and the Timaeus have so
much in common that they must have belonged to
practically the same period of Plato's life ; and the
obscurity of the former might plausibly be assigned
either to the initial vagueness of a fresh development
in Plato's philosophy, or to the contraction due to
recapitulation.

PREFACE Vll

I have derived the greatest benefit from Professor
Jackson's articles in the "Journal of Philology", and from
Mr Archer-Hind's edition of the Timaeus. I have read,
too, with great interest various articles by Professor
Shorey in the " American Journal of Philology", and
others by Mr A. E. Taylor in "Mind". I have profited
also from Carlill's lately-published edition of the
Theaetetus and Philebus.

My grateful thanks are due to Mr R. D. Archer-
Hind for much kind help and criticism, and also to
Dr Budge of the British Museum for various suggestions
regarding the subject-matter of Essay V. I must also
acknowledge my obligations to Miss Alice Gardner, of
Newnham College, and Miss M. E. Thomson, of King's
College, Aberdeen, for their help at the proof-correcting
stage. Finally, I must thank the officials of the
University Press for their courteous assistance in the
details of publication.

M. V. W.

ISLEWORTH,

January Zlst, 1908.

CONTENTS

ESSAY PAGE

I. The Search for Knowledge ... 1

II. The Analogy of the Arts and its Ap-

plication in the Politicus and Philebus 24

III. The World-process of the Timceus . 44

IV. The Ideas as 9Api0[ioi .... 67

V. The Pythagorean 'ApiOp-ol and their Re-

lation to the Platonic Ideas . . 88

VI. The Aristotelian Critique of the Ideas

and Numbers of Plato . . . 109

ESSAY I.

THE SEARCH FOR KNOWLEDGE.

The desire for knowledge, so Aristotle1 tells us, is
implanted by nature in all men, but the intensity of
the desire varies in different ages, and in different
types of men, and in the same men at different stages
of their lives. Plato, we know, found in it a motive
power that never ceased, throughout a long life, to urge
him on to intellectual labour and achievement, but even
in his history one may detect times of crisis, in which
the fervour of a glorious hope, or a dogged pertinacity
in research, shows that he is grappling with the problem
in its vastness.

It is in the Phaedo and the Republic, first of all,
that he makes a systematic attempt to formulate a
scheme of knowledge. In the former, disappointed by
his study of Anaxagoras, he determines to make use of
the indirect method of \6yot, if thereby he may attain
to metaphysical verity. In the latter his scheme is
complete, his plans are laid, and already he beholds in
anticipation the ISea rdyaOov, which is exalted above
both knowledge and being, and is the goal of every

1 Met. A. i. 1.
w. 1

2 THE SEARCH FOR KNOWLEDGE

human effort. The last chapters of Book vi reveal the
philosopher's aspiration visualised and glorified, and we
cannot doubt that he has actual and definite hope of
attaining to the truth he is pursuing along the lines
which he there indicates. Yet the dialectical method
of the Republic is not of a kind to satisfy either pupils
or master; it is obscured by excess of light : the flights
of imagination have reached a height to which sober
intellect cannot climb. It is imperative, therefore, that
the process of ascent from the assumption of etSr] to the
attainment of the ap%?) dwirodero^ should be described
in language of scientific precision, and a still /uLa/cporepa
7T€pio8os must be undertaken before knowledge is
attainable. It is with some of the sign-posts that mark
off this more circuitous route that the present papers
propose to deal.

It would be as well to have in mind at the outset
the leading features of the metaphysical and dialectical
scheme of the Republic, and of its complementary
dialogue, the Phaedo, which belongs to the same stage
of Platonic thought, and may perhaps have been written
somewhat earlier.

In the first place we are definitely informed1 that,
quite apart from the world of sensible things, which,
being subject to the Heracleitean flux, can never be
objects of knowledge, there are certain perfect and
immutable forms, eiSij avrd /cad* avrd. The exact signi-
ficance of the phrase avrd /cad' avrd is not easy of
determination, but in the light of Aristotle's2 evidence
it seems plain that the efty are transcendental unities,

1 Rep. 476 a ; 596 a ; Phaedo 100 b seq.

2 Met. A. 987b 7.

THE SEARCH FOR KNOWLEDGE 3

exalted in some vague and mysterious way above the
world of sensible phenomena by reason of their utter
perfection and immobility. The ideas, then, are avra
Ka6" avra chiefly in virtue of the sharp contrast
drawn between them and material things, for that they
had some connexion with one another, and with the
idea of Good, is an inevitable consequence of the
dialectical scheme propounded in Book VI.

Further, we are told that the things of sense,
through fjL€0€%i<; in ecSrj, become possessed of certain
characteristics, and are called by certain names and
described in certain terms, an attempt thereby being
made to explain the possibility of predication1. Every
predicate corresponds to an immutable idea, in which
the particular of which it is predicated participates.
Here again one is unable to render a satisfactory
account of the word fjueOegis. The qualification, 077-77 Srj
teal 07r&>? 7rpoa<yevofjLevr), introduced at Phaedo 100 D,
certainly shows that the method was but hazily con-
ceived in the mind of Plato himself, and that the
import of the word is mainly metaphorical, like that of
the kindred term /jLLfjLTjcris, which occurs more frequently,
though not exclusively, in the later dialogues2. By
the very vagueness of its statement the doctrine was
assuredly exposed to the literal interpretation which
is ridiculed in the Parmenides, but that this inter-
pretation was Plato's deliberate meaning in the Phaedo
and the Republic we have no justification for saying.

Such then is the nature of the elhrj which form the
ground- work of the dialectical process of Republic VI,

1 See Ar. Met. A. 987b 9, 10.

2 Cf. Rep. x. 597 seq.

1—2

4 THE SEARCH FOR KNOWLEDGE

a process which, in contradistinction to the inferior
system of Sidvota, leads directly from the assumption
of hypotheses to a first cause of all, and is in no way
dependent upon the things of sense. Whereas Stdvoia
proceeds from the assumption of hypotheses to a con-
clusion, dialectic proceeds upwards from hypothesis to
hypothesis, until the idea of Good, upon which all
other ideas depend, is in sight. Once the IBea rdyadov
is reached, the hypotheses through which it is attained
become realities ; they are no longer ideas hypothetically
asserted but actively realised. The ideas which are
thus hypothetically assumed are illustrated chiefly by
the universals of mathematics, and one may conclude
that it was chiefly through ideas of this nature that
Plato thought of rising to a knowledge of the Good;
but, on the analogy of the converse process of \6<yoc
mentioned at Phaedo 101 D, and from the fact that £wa,
<f>vT€VTa, etc., are at 510 B, 511 A said to serve as
el/coves in the lower vorfcris, one would conclude that
other universal hypotheses too, such as the assumption
of an avro to %wov, are conceived of as contributing
some share to the realisation of the Good. As to the
function of Xojol, it would appear that a X070? or
definition is the mental or verbal counterpart of the
elSos whose existence is asserted, and that the \6yot
play an important part in the dialectical process. The
first step is to postulate an elSo?, the next to define it,
then, in virtue of the knowledge thus gained, an elSo?
of a yet higher order is postulated until the ISea
rdyaOov is reached. When the ISea rdya6ov has been
defined and grasped, we have not only true knowledge
but true being, for in the idea of Good knowledge and

THE SEARCH FOR KNOWLEDGE O

being coincide, and the mere fact of attaining to it has
proved that our \6yoi were correct representatives of
the ideal reality. Thence, as Plato says, the dialectician
may descend with confidence in the line of the ecS?],
verifying all the assumptions that he originally made ;
the vTToQeaeis have now become apxai m virtue of their
connexion with the apxh avvTroOero^.

The system of knowledge, then, as delineated in the
Republic, is at best a sketch. It is shadowy and inde-
finite, and proclaims itself a product of immature
thought. It shows no comprehension of the essential
differences in general predicates, no consciousness that
some have a relative, others a substantive, significance.
In short, the scheme must not only be re-stated, but
re-thought, before any satisfactory advance can be made ;
and before it can be re-stated, or even re-thought, the
whole subject of predication and thought must be
thoroughly analysed, investigated, and systematised.
To this preliminary task Plato addresses himself es-
pecially in the Parmenides, Theaetetus, Sophist and
Politicus; the greater task of re-thinking and re-
stating his earlier scheme belongs chiefly, though not
exclusively, to the Philebus and Timaeus. I now pro-
pose to deal with some of the most striking contributions
of the Parmenides, Theaetetus and Sophist to the
logical problem, reserving for further treatment the
constructive results of the Politicus, Philebus and
Timaeus.

The first half of the Parmenides consists mainly of
an account of the ideal theory of the Phaedo and Re-
public, followed by a systematic criticism of the theory
as it was stated in those dialogues. First of all we

6 THE SEARCH FOR KNOWLEDGE

remark that the young Socrates, who is introduced as
the exponent of the theory, and of its importance in the
problem of predication, displays considerable aversion
to assuming ideas to correspond to every predicate ;
also that there seems to be a tendency to draw dis-
tinctions within the ideal world, and to class certain
ideas together, instead of collecting them under the
heterogeneous category that Republic 596 A implies.
Here ideas of qualities, of ethical notions, of natural
species, of meaner objects, are enumerated separately,
as if it were unconsciously felt that they are essentially
distinct from one another. Socrates, though assenting
cheerfully to the assumption of ideas of qualities and
of ethical notions, seems less convinced of the existence
of ideas of natural kinds, and his whole soul revolts
from the thought of ideas of such things as hair, mud,
dirt : Parmenides, however, rebukes him, on the ground
that such a feeling is unworthy of the true philosopher.
" You are young, Socrates," he says, <: and when philo-
sophy has got a firmer hold of you, you will not despise
even the meanest things " — a remark which should be
borne in mind as indicating in general the line of
development which the young Socrates, and Plato,
whom he represents, may be expected to take.

The destructive criticism that follows is well known
to every reader of Plato. If the particular participates
in the idea, it must participate either in the whole or a
part ; if in the whole, the idea is not one but many ; if
in the part, the idea becomes divided, and is many.
Hence the idea is either not a unity, or else particulars
cannot participate in it. Furthermore, if every plurality
of particulars called by the same name has an idea

THE SEARCH FOR KNOWLEDGE 7

corresponding to it, the idea will be indefinitely
multiplied, for the idea when added to the first group
constitutes another group, for which another idea must
be postulated, and so on ad infinitum. These two argu-
ments, it must be noted, are aimed, not so much at the
existence of ideas, as against the statements regarding
their nature which were made in the Phaedo and Re-
public. It is not the existence of ideas, but their
supposed actual immanence in particulars, and their
intimate connexion with predication, that is chiefly
attacked — a conclusion which is confirmed by the
further steps of the controversy.

Socrates, to extricate himself from these difficulties,
suggests that the fatal consequences might not follow
if the idea were conceived of as a voij/jlcl existing only
in ^ifvyai. Parmenides, however, points out that every
vorijxa must be supposed to have an object, and that
this would only give us the old idea back again,
remarking further that such a conception of the idea in
no way justifies an inherent connexion between ideas
and phenomena. To this Socrates replies, as if by
sudden inspiration, that perhaps the connexion is
not /jb€0e^c<;, after all, but the ideas are to be thought
of as irapahei^fxara earcora iv rfj (f>va€t, also that
particulars partake of ideas in virtue of resemblance
and nothing else. But even this brilliant suggestion is
of no avail so long as he holds that the predication of
likeness involves the existence of an idea, bv reason of
which the particulars resemble each other and the idea.
The infinite regress meets us still, and we have made
no progress.

But, says Parmenides, the greatest difficulty of all

8 THE SEARCH FOR KNOWLEDGE

is yet to come. If ideas are to be avrd tcad' avrd,
separately existent apart from particulars, then they
are altogether remote from the sphere of human
thought and action, and cannot possibly serve as ob-
jects of human knowledge: if they have relations, they
are related to one another only, and have no intercourse
with the things of sense which are said to resemble
them. Yet, without a belief in their existence, what
hope is there of attaining to truth ? There must be
eternal fixities somewhere on which the mind can rest,
and before Socrates can hope to attack so great a
dilemma as this his intellect must be trained and dis-
ciplined by the severest logical method.

We have seen, then, that the first portion of the
Parmenides expresses considerable dissatisfaction with
the earlier statement of the ideal theory, and at the
same time throws out various suggestions with a view
to its amendment. Whither all this self-criticism is
tending has not yet become clear, but the main results
may be summarised as follows. In general, we note a
pronounced hesitation in admitting elhrj avrd kcl6"
avrd of every predicate, coupled with a tendency to
distinguish between different classes of elhrj ; secondly,
we have an assurance from Parmenides that there will
come a time when Socrates will not disdain the lowliest
things of nature. In particular, it is shown that the
inseparable connexion of ideas with the possibility of
predication cannot be reconciled with any view of the
nature of the ideas (and we may therefore suppose that
Plato henceforward dispenses with that connexion) ;
secondly, that the doctrine of immanence, if understood
literally, is inconsistent with the nature of the idea,

THE SEARCH FOR KNOWLEDGE \)

whether it be transcendentally existent, or a vorjfjLa in
the human mind, whereas the expression fxi^rjai^, pro-
vided there be no necessity to postulate an idea for
every predicate, is perhaps less open to objection ;
thirdly, that the eZSo? avro /ca0' avro can never be
merely a vorj^xa in the human mind, for a vorj/ia implies
an object, an existent something beyond itself, and this
is only the old idea back again ; fourthly, that the ideas,
although they have been completely severed from the
world of time and space, are yet indispensable in the
search for truth, since man must always have beyond
him a goal on which his eyes may rest. Without some
eternal fixity the art of dialectic must perish.

The exact relation borne by the hypotheses of the
Parmenides to the former half of the dialogue has
always been matter of dispute. Ostensibly, of course,
they furnish an exercise in logical discipline, and the
method employed is similar to the propaedeutic exercise
of hiavoia in the Republic. That some intimate con-
nexion, however, exists between the subject-matter of
the two parts must be the conclusion of all who take
Plato seriously. It will be remembered that, at the
very beginning of the dialogue, Socrates, relying on the
theory of predication that is stated in the Republic,
joined issue with Zeno, and saw no difficulty in attribu-
ting contrary predicates to concrete things, but that
on the other hand he did think it impossible that
contrary attributes should pertain to the transcen-
dental ideas which informed particulars, and gave them
their existence. Such being the state of mind of
Socrates at the outset, it would seem reasonable to
look for some solution of his original difficulty in the

10 THE SEARCH FOR KNOWLEDGE

discussion of the eight hypotheses; also, inasmuch
as his explanation of contrary predication as connected
with ideas has completely broken down, one would
expect some light to be thrown on the circumstances
of contrary predication. By a brief enumeration of the
salient points in the eight hypotheses, I hope to show
not only that these expectations are realised, but that
considerable progress is made towards the solution of
the great dilemma concerning the ideas with which
the first part closed.

In the discussion of the first and fourth hypotheses,
which stipulate the existence of to ev, when bv implies
self-identity and nothing more, we find it impossible to
predicate anything either of to ev or of TaWa, and
where predication is impossible, knowledge is a fortiori
impossible. On the other hand, from the reasoning of
Hypotheses VI and Vlii, we conclude that if to ev is
supposed to be utterly non-existent, it is equally certain
that neither predication nor knowledge is possible,
whether of ev itself or of TaWa. If, however, ev be
conceived of as existing, not merely in self-identity,
but in relation to TaWa, all manner of predication may
take place both in regard to ev and to TaWa, and
knowledge of both ev and TaWa becomes possible
(Hyp. II and in).

Now it is of course obvious that the ev of Hypotheses
I and iv has an immediate reference to the ev of the
Eleatic Zeno, and that the inconsistencies arising from
his peculiar position are here conspicuously exposed.
We are, accordingly, led to infer that to ev throughout
the hypotheses refers in the first instance to the one
supreme reality, whether it be conceived according to

THE SEARCH FOR KNOWLEDGE 11

the Eleatic or the Platonic scheme. The main result
of the six hypotheses mentioned will then be this.
The supreme reality, if it is to be known, must have
relations with every form of reality, and must have a
connexion with all inferior existences. In short, the
supreme idea, the ISea rdyaOov, or whatever else it may
be termed, is known only in conjunction with other
ideas, and with the infinite flux of sense. Conversely,
the flux of sense and the other ideas are to be known
only in so far as they are related to the one supreme
unity. And if a subordinate idea be for the moment
regarded as eV, as a unity apart from the supreme idea,
it too is to be known only as it enters into combination
with the infinite many.

Hypotheses v and vn add to our information con-
cerning this supreme unity. From Hypothesis v we
learn that to ev may have a negative determination
applied to it, and yet be capable of being known, and of
bearing descriptive epithets. Here we have of course
a foretaste of the justification of to fjurj bv in the Sophist ;
it is implied that negative may be as true and as
valuable as positive predicates. Hypothesis vn points
to a distinction between opinion and knowledge.
Assertion of some sort is shown to be possible even
where the existence of an all-embracing unity is denied,
inasmuch as the plurality of things may be gathered
together in aggregates (oy/coi), each of which, possessing
an apparent unity, enters into apparent relationships
with itself and other things. Being mere aggregates,
however, they have no organic coherence and fall to
pieces when analysed.

Such is the main outcome of the discussion of the

12 THE SEARCH FOR KNOWLEDGE

eight hypotheses, but a closer inspection reveals direct
reference to the other problems that are before Plato's
mind. In the first place, avro to ev at 129 C was
taken as an example of an elSos avro kclO* avro, and
Socrates there expressed great curiosity to know
whether the idea ev could be shown to be iroWd, and
whether in general ideas themselves, in contradistinc-
tion to particulars, are capable of diverse predicates,
i.e. of communion with one another. The results of
the hypotheses are an ample proof that such predication
is possible, and that kolvcovlcl of some sort must exist :
avro to eV, to be known, must be capable of receiving
all manner of predication, and of entering into all
kinds of relation. But for the final discussion of
this KOivcovia we must look to the later Sophist and
Timaeus.

Meantime has any light been thrown on the theory
of predication itself? In a very significant passage at
143 D, E, it is carefully shown that as soon as any
notion, however simple, comes before the mind for
analysis, number is at once generated, and the mind is
forced to count. The notion of number, then, appears
to be a necessity of the mind's action. This principle
applies not only to number, but to all predicates of a
similar kind, as the whole exposition proves. However
slight may be the notion under examination, however
restricted and confined, the mind in passing judgment
is forced to predicate and to make use of a number
of common terms such as like, unlike, same, other,
which express the various relations that one thing
bears to another. Hence, though no dogmatic teach-
ing about predication is to be found, it is taken

THE SEARCH FOR KNOWLEDGE 13

for granted from first to last that predication is a sine
qua non of logical analysis, and that no transcendental
explanation need be assumed.

The latter half of the Parmenides, then, has made
a considerable contribution towards the solution of the
problems of the first half. Predication, without which
knowledge cannot possibly advance, is shown to be a
natural activity of the intellect, and the use of predicates
of number, likeness and difference, equality and in-
equality, etc., is indispensable to the consideration of
any subject whatsoever. Moreover, the ideas and the
supreme idea, if they are to be not merely existent, but
objects of knowledge, must have a real and lasting
relation with one another and with the world of
sense. Conversely, the world of sense, in so far as it
may be known, must be regarded as entering into
relation with the supreme unity and its determina-
tions.

Passing on to the Theaetetus, we are confronted
with another attempt to solve the problem of knowledge.
The Parmenides, after first demonstrating the impossi-
bility of regarding ecSn avra /ca6' avra as objects of
knowledge, so long as they retain the characteristics
ascribed to them in the Phaedo and the Republic,
proceeds to delineate the necessary character of ecSr] if
they are to be not merely ovra but iiriar^rd. The
Theaetetus, falling back on the general question " What
is knowledge ?," leads by a process of exhaustion to the
same conclusion as the Parmenides. Whereas in the
Parmenides Plato was content to investigate and
partially to reconstruct his own view of knowledge, he
is now determined to deal no less faithfully with the

0

14 THE SEARCH FOR KNOWLEDGE

theories of others, that he may be the more certain of
his own system. Hence, in this dialogue and in the
Sophist, we not only see Socrates endeavouring to test
the mental productions of Theaetetus, but Plato himself
examining the soundness of his predecessors in philo-
sophy, resolved to discard the dross and retain the gold
tried in the furnace of his dialectic.

Theaetetus' first thesis makes €7rcarr]fi7) identical
with aiadrjat^, and in the lengthy conversation that
follows we have an estimate of the value attached by
Plato to the perpetual flux of sense. By^a combination
of Protagorean with Heracleitean principles1 he evolves
a theory of sensation by which the fact of sensation
depends entirely on the juxtaposition of object and
subject; to alaOrjTov and to aio-6avb\xe.vov are each a
movement that is generated by the contact. Thus
neither the sensation of whiteness nor the colour white
has any existence in itself; they are simply the
product of the object as irotovv and the subject as
iraayov. As a result, the sensation of whiteness is
supposed to reside in the eye, and the colour white is
projected outwards by the mind and made to inhere in
the object.

This explanation of sensation, which cannot be
assigned to any contemporary, and would therefore
appear to be that of Plato himself, clearly attributes no
permanent reality to the /civr)o-€is of perceiving or o|^
being perceived : they are yeveaet^ that come into being
and again depart, varying in character, not only with
different subjects, but with the same subject under
different circumstances. We conclude, therefore, that

1 Theaet. 182 a, b.

THE SEARCH FOR KNOWLEDGE 15

hot and cold, hard and soft, wet and dry, white and
black, and the like, have no absolute existence; they
count for nothing in the search for reality ; they are but
the momentary product of the interaction of subject
and object. Since they have no existence except in the
consciousness of the percipient, and vary indefinitely
with different persons, and with the same person at
different times, they have no fixed value, and cannot be
objects of knowledge. This argument, besides being of
supreme weight for the refutation of Theaetetus' first
thesis, is of great importance as indicating the tendency
of Plato's thought ; the character of sensible qualities
as secondary products of the activity of mind is main-
tained throughout the later dialogues, and finds
expression in the Laws1. Moreover, it would be
superfluous, in the light of this exposition, to wonder
"wKetlTer Plato still has recourse to an immanent idea to
make a particular thing white or hot or sweet, as the
language of the Phaedo and the Republic would indicate.
Such qualities now possess neither fixity nor reality ;
that reality of a kind must appertain to the itolovv and
irdaxov which generate them is proved by the later
Sophist, and marks an important step in Plato's develop-
ment.

The interest of the argument next centres round/^/
Theaetetus' second thesis, viz., eiriaTrjfiT] is to 6p6a
8ol~d%€Lv. Socrates has discovered that the fact of
perception is not concerned with sense merely, but that
the soul avrrj 8l avTrjs compares the data of sensation
and passes judgment upon them, assigning or denying
to them certain tcoiva, or general predicates. These

1 Laws 897 a.

\

16 THE SEARCH FOR KNOWLEDGE

fcoiva, oixoloVj avofioiov, ev, 7r\f)0osy etc., carry our
thoughts back to the Parmenides, where we had a
practical demonstration of the fact that certain general
predicates are necessary parts of the soul's machinery.
The general aim of this portion of the dialogue, then, is
to show that true opinion, or the process of apprehending
correctly certain kolvcl of relation, does not constitute
knowledge. After a long digression on the nature of
false opinion, in which the solution of the Sophist,
though not directly stated, is nevertheless implied, and in
which ho^a^eiv is shown to apply not merely to sensibles
but to mental abstractions as well, the main thesis is
summarily disposed of by a reference to the rhetorical
art. A man may conceivably pass a true judgment
without having any clear grasp or realisation of the
matter at issue. True opinion may be a factor in
knowledge, but we have not yet seized upon the vital
constituent.

An attempt is immediately made to supply the
deficiency by the addition of a X0709, i.e., some verbal
expression of the content of true opinion. Various
interpretations of the word X6709 are then mentioned ;
X0709 may mean (a) the mere verbal utterance, or
(6) the enumeration of elements, in which the Cynics
and Socrates supposed knowledge to consist, or (c) the
definition by characteristic difference, Plato's own accep-
tation of the term. Each of these processes in turn is
proved to be insufficient to explain the fact of knowledge ;
they all presuppose the existence of something else
which is known and is the object of knowledge, whereas
they are merely subsidiary to its attainment.

We are, therefore, forced to the conclusion that no

THE SEARCH FOR KNOWLEDGE 17

theory of knowledge in which the existence of ideas is
"not assumed can hope to pass the test of criticism.
Mere sensation, as Heracleitean and Protagorean
doctrine alike demonstrate, can never furnish a
standard. The process of Sogd&tv, or apprehension of
relations, may be useful enough, but it is not the sum-
total of knowledge. Even the scientific expression of
such judgments does not bring us any nearer the goal.
Our only hope is to discover as quickly as may be the
nature of those elZrj for which we have long been
seeking. .

In the Sophist there are four subjects that demand
our attention — the method of SocdpeaLs, the problem of
/jlt) 6v, the fjiijiara yevrj, and the definition of ovcria as
r) tov iroLelv r) irdcryeiv Svvcl/jlis. All of these, with the
exception of the last, are concerned with the method
rather than the object of knowledge, and hence we look
to the Sophist for enlightenment on the processes of
thought and predication rather than for an exposition
of the ideas. The method of StaLpeais, proceeding by
subdivision and classification, was first described vaguely
in a much earlier dialogue, the Phaedms, and there it
was impressed upon us that the essential of good
hialpecris1 is to divide /car ap6pa y irefyvice feat /jltj
eTTL^xetpeiv Karayvvvat fiepos /JLTjSev. The same rule is
enforced in the hiaipeai^ of the Sophist, as well as in
the similar process in the Politicus. The mind, in virtue
of its innate power of distinguishing ravrov, Odrepov,
o/jlolov, avofjiotov and the other kolvcl, starts from the
observation of one common element, and then, proceed-
ing by hiaipeais icard jjuepr], seizes on the characteristic

1 Phaedrus 265 B.
w. 2

18 THE SEARCH FOR KNOWLEDGE

difference of the object to be defined. All definition
must be preceded by Siaipeats, and since definition is
the verbal expression of a truth which is known, it
follows that hiaipeGLs will be an important adjunct to
the process of knowledge in general.

The method of hiaipea^, when applied to the
Sophist, leads to a consideration of the problem of
fir) ov, and finally to the whole question of predication.
In the course of a long argument, containing criticisms
of the Eleatic and various other schools, it is proved
that bv and fir) bv may not merely denote Being and
Not-Being in the absolute sense, but may signify the
positive and negative determinations respectively of
the thing to which they are applied. "Ov, in short, is
copulative as well as substantive, and in the former
sense both bv and fir) bv may be applied to the same
thing ; fir) bv is simply Odrepov, a category that inheres
in all existence.

Closely connected with the subject of fir] bv is the
analysis of the five fieycara <yevrj, in which are included
the final analysis and solution of the problem of pre-
dication, to which there have been continual references
in the Parmenides and Theaetetus. He that would
deny the possibility of predication subverts every
attempt to form a theory of the universe, and hence
the possibility of predication must be accepted as a
necessary, axiomatic truth. But, if there is to be
predication, we must concede a certain /cotvcovla or
power of communicability in predicates, since the
same thing is capable of receiving various attributes
and of entering into various and even contradictory
relations. The five great yevrj or categories of ov,

THE SEARCH FOR KNOWLEDGE 19

ravrov, ddrepov, ardac^, /civtjctls are then distinguished,
and it is shown that ov, ravrov and ddrepov universally,
and ardai^ and /clvtjgls generally, are found to inhere
together in the same thing, and hence may be said
to have communication one with another. But al-
though these categories are termed eiS?) and are said
to KOivcovelv the one with the other — the requirement
made in the Parmenides for the ideal world no less
than the sensible- — there is no indication whatever
that ravrov, Odrepov, etc., are the transcendental ideas
which are to be the goal of knowledge ; they are
instruments merely which are to aid in the search.
When we come to the Timaeus1, indeed, we find them
definitely classified, not as ideas, but as methods of the
soul's activity.

The conception of falsity, too, is illuminated in the
sections that follow. Thought, opinion, and imagina-
tion are all sometimes false, but this falsity consists
not in the assertion of not-being or nothing, but in
the attribution of things that are not as though they
were.

By far the most significant teaching of the Sophist
is to be found at p. 247 E, and the sections that follow.
The materialists,, who believe in nothing that they
cannot seize with their hands, are confronted with the
elSoov <j>l\ot, who place ovaia and yevecris at opposite
poles, and deny that there can be any communication
between them. These latter are, of course, the supporters
of the theory of ideas as originally formulated in the
Phaedo and Republic, and Plato, now bent on reconciling
the two conflicting modes of thought, seeks some con-

1 Tim, 35 a seq.

2—2

20 THE SEARCH FOR KNOWLEDGE

ception of ovaia which may bridge the gulf that yawns
between the ideal and material worlds. Recalling the
doctrine of sensation which he had put forward in the
Theaetetus, he offers a novel definition of ovaia, viz.,
i) rod irotelv rj irdayeiv 7Tpo? to a/JbiKporarop hvvafiLS.
Ylotelv and iraayjciv are, of course, manifested in various
forms, and refer both to the physical activity and
passivity of sense, and to the psychical ycyvooa/cetp
and ryt<yvcoaK€a6at. It is to be noted, however, that
whereas the mind or soul in sensation is iraaypv, in the
region of knowledge it is itoiovv, and the object of its
knowledge, ovaia, is rcaayov. But the main argument
centres in the fact that subject and object are equally in
movement, and are therefore equally real forms of ovaia,
A further step is taken at p. 249. Anything that
is 6vtu>s ov must surely, says Plato, possess, not merely
movement, but vov$, £corj, and yjrvxv as well. The
statement is, of course, an echo of that theory of soul as
being the first and only source of movement which was
formulated first in the earlier Phaedrus 1 and remained
to the end the permanent basis of Plato's philosophy 2.
The important result in the present instance, however,
is the inevitable inference that not merely rj tyvxh V
yiyvojafcei, but to yiyvcoa/cofjuevov, whatever it be, is akin
to vov<$ and ^corj and -v^f%^, and must therefore be a
form or manifestation of soul. Even the objects of sense,
despised though they be because of the Heracleitean
flux, may now serve a purpose in the progress of know-
ledge. Since they too, in some mysterious way, are
TTotovvTa, no less than yfrvxr/, there must be a reality of
some sort underlying them ; and we have been assured
1 Phaedrus 245 c. 2 Laics 896 seq.

THE SEARCH FOR KNOWLEDGE 21

that the highest reality of all is to be found in the nature
of mind and soul.

But though activity, life, soul, mind are inseparable
from the ovtws ov, we must be careful, says Plato, not
to refuse it also the attributes of permanency and
stability. If these were lacking, truly our newly-found
reality would be little better than the peovra of sense,
and make us despair once more of attaining to know-
ledge. Reality, it is true, is possessed of activity and
life, but that life and activity are manifested under
permanent conditions and according to eternal, immu-
table modes (/cara ravra /cat ojctclvtcos teal irepl to
avro). Hence neither motion nor rest is the exclusive
attribute of the 6Wg>? ov.

To sum up the results of our investigation, we have,
first of all, justified predication on the ground of
necessity, and have vindicated the right of the soul to
pass judgment on any data supplied to her without the
mediation of any exalted and mysterious existences
called ideas. Next, in regard to the ideas, it was found
at the beginning of the Parmenides that so long as the
idea possesses the characteristics ascribed to it in the
Phaedo and Republic, knowledge must be forever be-
yond jour .reach, and yet that unless the existence of an
idea of some sort be assumed, knowledge must remain
equally impossible. The Theaetetus corroborated this
by showing successively that neither sensations, nor
those common forms of predication which are essential
to the activity of thought, nor yet the scientific expres-
sion of thought by definition, connotative or denotative,
can in themselves constitute knowledge ; they are the
instruments, not the objects, of knowledge. We are,

'22 THE SEARCH FOR KNOWLEDGE

therefore, obliged to postulate ideas, and there is not
wanting a hope that their true nature will finally be
revealed, considerable illumination having already been
gained from the Parmenides and the Sophist For the
ideas of the older time are being divided up into classes.
The predicates bv and ixrj 6V, 6/jlolov and avofjuotov, and
the like, are found to be fxeytara yevrj, forms of thought,
essential modes of the soul's activity, and, though they
may retain the old title of etSrjy they are very different
in kind from the eiSy avra kcl6' avra of the Phaedo,
nor do they carry the significant attributes of the latter.
Sensible qualities, being simply yeveaeus, have no fixity
at all, and cannot assume the importance even of the
/jbeytcrra yevr]. Ethical conceptions of ayadov, kclkov,
and the like, are in the ordinary way obtained chiefly
through a diligent comparison of past and future1, and
are relative to circumstance ; on the other hand, there
is a reference to avrrj StKatocrvpr], avrr) dSt/cia at
Theaetetus 175 C. It is, therefore, uncertain for the
present whether there are still to be ideas of moral
notions or even of natural species, though in regard to
these last we have been told that the meaner things of
nature have an equal claim to respect with the greater.
Under these circumstances it can hardly be denied
that the ideal doctrine of the Republic, in which there
was an idea for every predication, did not stand for any
eternal and unassailable truth even in Plato's own mind.
One may almost say, in the words of Jowett 2, that the
earliest ideas were only a " semi-mythical form in which
he attempts to realise abstractions," and they certainly

1 Theaet. 186 a, b.

2 Introd. to Cratylus, p. 623.

THE SEARCH FOR KNOWLEDGE 23

were to a large extent " replaced by a rational theory
of psychology." Plato, however, is bent on retaining the
machinery and terminology of the ideal theory; the
assumption of these eternal existences is still indis-
pensable, if he is to explain the universe at all. With
the aid of the ideas he kept the Sophists and Cynics at
bay while he deliberated about his answer to their most
pressing question, viz., " What is Predication ? " ; and
the ideas must still be his stimulus and inspiration if
he is yet to satisfy them on the deeper subjects of
Knowledge and Being.

For the present, therefore, we are assured that the
ideas still exist, though they are fewer in number than
heretofore. Furthermore, reality, both as knowing and
as known, as acting and as being acted upon, has been
declared to be of the nature of mind, and it is in the
light of these two general observations that we shall
now proceed to interpret the ontology of the dialogues
that follow.

ESSAY II.

THE ANALOGY OF THE ARTS AND ITS APPLICATION
IN THE POLITIC US AND PH1LEBUS.

A favourite and effective device of Plato, when
intent on the elucidation of ethical and metaphysical
truth, is to introduce one or other of the constructive
or imitative arts to serve as an illustration. In the
earlier dialogues simile and application are alike simple :
the statesman is the pilot of the state, the philosopher
is the doctor of souls, and so on. But as Plato's powers
matured, and his aims grew more ambitious, he began
to make a more elaborate and significant use of this
instrument. At the beginning of Republic x, for instance,
the constructive art of the carpenter and the imitative
art of the painter serve to illuminate the nature of
the ideas, and the kind of relation borne by them to
the world of sense. The 6e6$, who is parallel to the
carpenter, makes the ideal bed, which is one and
imperishable ; the re/crcov, taking the ideal bed as his
7rapdS€cyfjia or model, constructs a material bed ; while
the painter, with only the material bed as his model,
makes an image which is in the third degree removed
from ideal truth. The immediate purpose of this, of
course, is to degrade mimetic art considerably, and to

THE ANALOGY OF THE ARTS 25

place it far below constructive art in the scale of truth ;
incidentally, however, Plato has shown how valuable
an ally the arts may become in the exposition of the
ideas. This, coupled with the intimation we had in
the Parmenides that the ideas might be TrapaSeiryfiara
iarcora ev rrj (frvcrei, and that ixi\xr)<Ji<$, rather than
fjLe6e%L$, should describe the relation borne to them by
<yiyv6/jL€va, would reasonably lead us to expect a more
extensive use of this metaphor in the dialogues we are
now considering. As a matter of fact, Plato in the
Politicus and the Philebus is very largely dependent on
constructive art for the adequate expression of his
doctrine. In the present paper, therefore, I propose
to examine the application of this analogy in these
dialogues, hoping that in the sequel some further light
may have been thrown on the nature of the ideas, and
consequently on the system of knowledge which is the
goal of our endeavours.

The first object for our consideration will be a
remarkable passage in the Politicus, in which Plato
gives utterance to his high estimation of an art which
has already come prominently forward in the Protagoras1
--the art of measurement. At 283 B, Socrates, in order
co show his respondent that their digression on the art
of weaving was not too lengthy, declares that the whole
nature of excess and defect must be made clear. In
the first place, he says, measurement of excess and
defect is of two kinds, the first being that which deals
with relative size and merely compares one object
writh another, the other that which judges things
according to their approximation to a perpiov, a

1 Protag. 356 d.

26 THE ANALOGY OF THE ARTS AND ITS

mean, a fixed standard. The latter is by far the
more important ; in fact, it is the principle upon which
all yeveo-Ls, all production, is based, and without it the
arts could not exist. Every artist strives to attain a
standard, and in so far as he falls short of this standard,
is his work faulty and bad. Excess and defect are real
evils, and to guard against them is the first necessity
of art.

Now it is plain that the usual connotation of perpiov
and of fjL€Tpr)TL/cf/ has been considerably extended in
this exposition. At the outset, to /juerpcov would seem
to signify a unit or norm of measurement, in reference
to which things relatively great or small may be
accurately measured. But this simple meaning is soon
superseded, for at 284 A seq. we learn that the arts
make use of to /meTpiov, not as a norm or unit of
measurement, but as an ideal, a standard, by the
attainment of which alone things dyaOa and fcdXd are
produced. Hence fxeTp^Tifcr], in this new Platonic
sense, is not merely an art of measurement, but an art
which compares the productions of Te^xyv1 with to
irpkirov teal to 8eov. It is a critical science, which
passes judgment on aicevacrTd in virtue of a fixtd
standard, with which it is acquainted. At the same
time it is to be noticed that the connexion of fjbeTpijTLKrj
with spatial and mathematical measure is apparently
maintained throughout, inasmuch as it is described at
the final summing-up2 as including oiroaai rkyyai tov
dptdfjiov Kal /jLTj/crj Kal j3a6rf teal ttXcittj 7rpo? to fieTptov
teal to nrpeirov Kal top tcaipov fieTpovcri. In short, to
fieTptov, in relation to the arts, is an ideal standard,
1 284 e. 2 284 e.

APPLICATION IN THE POLITIGUS AND PH1LEBUS 27

consisting of certain fixed mathematical combinations,
or proportions, to which the products of the arts should
approximate.

Such being clearly the significance of to fierpcov in
the arts, our next step will be to determine its value
when employed in the demonstration of metaphysical
truth. At 284 D Socrates expresses his conviction
that, at some future time, this notion of to fierptov will
be called into requisition Trpcs rrjv irepl avro ravpcftes
airohet^iv. We therefore expect to hear more of it,
and our expectation is fully realised in the Philebus.

At 16 B, c, of the Philebus there occurs a remarkable
reference to the process of hialpeaLs, of which Socrates
remarks1, ?;? iyco ipaarrjs el fit, del. This method has
been responsible for every great discovery of the arts,
and it is based on the principle that ev and 7ro\\a are
to be found everywhere, and that irepas and anreipov,
limit and infinity, are inherent in the very nature of
things. It is, therefore, the duty of the dialectician to
posit one elSos for every infinity of particulars, and not
to rest satisfied until he has discovered the definite
number (oVocra) of species that are to be inserted
between.

This general reference to irepa^ and airetpov, as
representing in the abstract that which can be accu-
rately estimated and defined, as contrasted with that
which defies determination and classification, prepares
us for the more abstruse discussion of these notions at
23 c seq. At this point of the dialogue Socrates has
proved that to dvOpcoirivov dyaOov (the discovery of
which is the sole aim of the treatise), is to be identified
1 Cf. Phaedrus 266 b.

28 THE ANALOGY OF THE ARTS AND ITS

with neither of the two claimants, vovs and rjhovrj, in
separation, but that it must consist in a fii/cro? ySto?,
which is the compound of both. It is at the same time
maintained by Socrates that the ingredient in this
Ijluctos /3to? which makes it ayaObv is more akin to
vovs than to rjSovrj, and that, if this can be proved, the
life of reason must be awarded the second prize. With
a view to demonstrating this superiority of vovs over
7]Sov7], he proposes to examine both, and to place them,
according to their merits, in one or other of four classes,
within which, he says, irdvra rd vvv ovtcl iv to5 ttclvti
are contained.

Now the classification here referred to, in which the
notions of irepas and dirupov reappear, is primarily a
dissection, as it were, of the universe based on meta-
physical principles. Such is the immediate inference
one draws from the impressive manner in which the
subject is introduced (top 8eov eXe^yofjuev irov to fjuev
aireipov Sell; at tcop ovtcov, to Se vrepa?), and from the
fact that the first intimation of the division into direipov
and ivepa^ came as a suggestion regarding the solution
of those inconsistencies which marred the theory of
ideas. Moreover, the divisions themselves accord most
easily with this interpretation. It is not the first time
that the notions diretpov and Trepan have been conjoined
in a metaphysical analysis of reality. In the second
and third hypotheses of the Parmenides, where a
similar classification is evolved, there is an undoubted
reference to metaphysical theory2. There we find ev
representing the supreme ideal unity, and TaKka the
world of phenomena, also the adjectives ireirepaafjiiva
1 15 a, b. 2 Parm, 144 e; 158 d.

APPLICATION IN THE P0L1TICUS AND PHILEBUS 29

and airetpa applied as essential characteristics to raXka.
These four correspond in inverse order to the airetpov,
rrepa^, /jliktov and atria of the Philebus. Our conclu-
sion is reinforced again by the fact that the fourth
and greatest class, the atria rr)s /u£efc>9, is proclaimed
to be vovs, which governs both universe and individual,
since our examination of the Sophist1 has proved
indisputably that vovs is henceforward to have the
pre-eminence in Plato's explanation of the universe.

Since the classification then appears to rest on a
metaphysical basis, one would expect to find the meta-
physical principle faithfully adhered to throughout.
Plato's avowed object in this dialogue, however, is not
metaphysical but practical ; he wishes to arrive at a
logical determination-of the avQpunrivov <z<ya06v. Hence
the metaphysical classification throughout the argument
is made subservient to practical considerations, and it
is apparently appropriated simply in order that some
unique authority, as it were, may support Socrates
in his estimate of the three different lives. This
peculiarity, combined with the generally confused
and fragmentary state of the dialogue, makes it ex-
tremely difficult to arrive with certainty at the original
significance of the four yivrj. The ybiicrbv 761/09, which
should properly include only the unions of metaphysical
aireupa and irepara, is made to contain the /U/CT09 /3io<;,
a union of an aireipov, r/Sovtj, not with irepas, but with
an airia (vovs) ; rjbovrj2, too, is classed at one time under
ro airetpov, at another under ro pmcrov ; and at 26 A, B,
oopa, which, in so far as it denotes a certain atmospheric
state, is surely to be ranked with ^ei^oov and ttvI^o^ in
1 Soph. 249 a seq. 2 27 e ; 31 a, b, c.

30 THE ANALOGY OF THE ARTS AND ITS

a table of metaphysical valuations, is separated from
them on the fanciful ground that good things cannot
be classed with arreipa, which are evil. It is clear that
the same principle of classification is not maintained
throughout. Plato has, in fact, for the purposes of
the dialogue, turned a set of metaphysical distinctions
into a loose, popular classification ; and, since our aim
is to arrive at his metaphysical teaching, we must
endeavour to describe the four yevrj as they appear
when divested of those inconsistencies which are
peculiar to the dialogue.

It must, first of all, be noted that the whole
classification here is based upon the analogy of the
constructive arts. The universe is regarded as a living
/coo-fxos, a whole compounded of body and soul, and
containing within it all inferior bodies and souls.
Within this icoo-fios is going on continually a process
of fjbl^i<; or yeveats (the very word used for artistic
production in the Politicus), and all the four kinds of
ovra of which to irav consists are, in one capacity or
another, involved in this yeveais. Now it was shown
in the Politicus that the first essential of every art is a
fierpiov, or ideal standard, in accordance with which
the particular product is fashioned. Besides this,
however; we know that there is needed first, v\r), or
to TrpooToyeves KTrj^a of Politicus 288 E, e£ wv koX ev
ol? SrjfjLLovpyovGLV oiroaat twv re^vcov vvv etprjvrat ;
secondly, the opyava crvvairca of Politicus 287 D ; and
thirdly, the artist or SrjfjLLovpyos himself. Of these to
IxeTpiov undoubtedly corresponds to irepas in the
Philebus, inasmuch as it is definitely identified with it
at 24 c and 66 A, and is moreover described as being

APPLICATION IN THE P0LIT1CUS AND PHILEBUS 31

the cause of fjuerptorrj^ and av/jt^erpia1 in its fit/crd.
The artist's vXtj is to be correlated with the avreipov,
into which to ire pas is said to enter, thereby producing
a fiiKTov compounded of both2. The whole language
of the passage implies that irepas is applied to diretpov
as form to material. That the alria is parallel to the
871/jLLovpyos follows obviously from its description3 as to
ttoiovv and to iravra tcl ytyvofieva Brjfxtovpyovv. As
to the opyava avvalria, some doubt may at present
exist as to their identification, but we cannot go far
wrong in connecting them, provisionally at least, with
the Trepas, which, in company with to diretpov, is called
to SovXevov eh yeveatv atria*. A more complete ana-
lysis of all these conceptions must now be attempted.

Beginning then with the class of vXr), what is the
essential nature of to arreipov, and what things are
included in it ? Socrates tells us that it is the class of
to /jtaXXov real tjttov, and that the quality of indefmite-
ness is inherent in it. Its nature is such as to forbid
any application of rkXos or iroaov ; as soon as any such
notion is connected with it, it loses its characteristic
and ceases to be what it is (avrco TereXevrrjicaTov).
The class is made up of Oepfiorepov /cal yjrv^poTepop,
%r)poTepov Kal vyporepov, TrXeov /cat eXarrov, Qclttov
Kal /3paSvT€pov, fjtel^ov /cat afit/cporepov, and the like,
of everything, in fact, that admits of to acf)68pa /cat to
rjpe/jta. To rjSv /cal to Xvirrjpov, therefore, would come
under the same category5 — a fact which is explicitly
acknowledged by Socrates quite apart from any reference
to the quantitative hedonism of Philebus. At 31 B, it is

1 64 e ; 65. 2 24 c, d. 3 26 e ; 27 b. 4 27 a.

5 28 a; 31 a; 41 d.

32 THE ANALOGY OF THE ARTS AND ITS

true, there is a temporary lapse of consistency, and he
speaks of it as a yuicTov, but there, as in other places,
the metaphysical interest has been superseded, and
Socrates is looking at pleasure and pain as concrete
facts, and is seeking to define them on a popular basis.

Now this talk of hotter and colder, drier and wetter,
with the accompanying statement of their indefmiteness
and of the impossibility of applying to them any fixed
character, takes our minds back to the earlier part of
the Theaetetus, where all the qualities dependent on
sensation came in for a vigorous examination. As
a result, we found that all these qualities, being due to
a /clvrjcTLs between subject and object, had no existence
except in the consciousness of the percipient. They
were subjective phenomena, varying indefinitely with
different subjects and therefore possessing no fixed
value. Their apparent externality, too, was due to the
percipient subject alone, which projected outside itself
a something1 which could not have come into being apart
from itself. To aireipov, then, is the class of hotter and
colder, of subjective affections, which vary indefinitely
and have no claim on real existence. The comparative
form in which they are expressed serves to stamp them
with the mark of unceasing variableness, and one feels
inclined, with Natorp2, to see in them a striking re-
semblance to the oy/cot, of the Parmenides 3, which bear
relation to one another only, and of which the least
part, as well as the greatest, is branded as infinity.

Sensible qualities, then, in general, serve as vkr) in

1 Theaet. 156 e seq.

2 Natorp, Plato's Ideenlehre (Leipzig 1903).

3 Parm, 164, 165.

APPLICATION IN THE POLITIGUS AND PHILEBUS 33

the production of the fit/era of the universe. But
there are not wanting certain signs which show that
a far more subtle conception is, at any rate, at the back
of Plato's mind, even though it may not as yet have
taken definite shape. At 24 D we hear of rj rod fxaXKov
fcal tjttov eh pa, into which to iroaov and to pieTpuov
are supposed to enter, and which evidently is that
which affords a place, a home, for these ciiretpa, such
as they are. Now it is, of course, impossible to con-
ceive of anything as subject to infinite fluctuation, like
the airetpa, without at the same time allowing to
it extension of some kind, in which the fluctuations
may take place; we should remember, moreover, that
to fxel^ov teal o-fii/cpoTepov1 is one of the airetpa, and the
eSpa of an ajretpov of this sort would be very definitely
extension, and nothing else. Hence the eSpa must
inevitably be identified with extension, the home of
fluctuation and Becoming, although the slight use
made of it at this juncture forbids us to lay any great
stress on the conception at present. The final analysis
of extension does not concern Plato in the Philebus,
and he may or may not have intended to make it the
nre^TTTov yevos which is mentioned so casually at 23 D.
The vXtj, then, of the world-process is in the
Philebus made to consist of sensible qualities, with
a slight but unmistakeable reference to a eSpa, in
which the qualities reside, and which is the inevitable
condition of the yeveaus of the jjulktcl. In fact, there
would seem to be here a distinct use of the two functions
of vXrj which are mentioned at Politicus 288 D (e£ &v
koX iv oh Srj/jbLovpyovatv al Teyyai).

J25 c.
w. 3

34 THE ANALOGY OF THE ARTS AND ITS

We now come to the class of irepas, and here
a difficulty awaits us, although it would at first sight
seem quite easy to identify it with to /juerpiov of the
Politicus. Here, as elsewhere in the dialogue, Plato
does not seem to have one clear conception in mind
throughout. The class as a whole is styled to ire pas,
or the limit. But as early as 24 c we hear of two
sorts of ire pas, called respectively to ttogov and to
fierptov, the very names of which indicate a difference
in kind. Our knowledge of the Politicus naturally
makes us think of to fieTptov as an ideal standard,
dependent indeed upon mathematical determinations,
but only in the sense that a law is dependent upon the
material in which it finds expression. That the same
signification attaches to it here would seem to follow
from its equation with to KaLpiov and rj al'Sios (frvo-cs
at 66 A. As for iroaov, it would appear to signify
quantity, or magnitude, and nothing further.

This distinction within to irepas is immediately borne
out by the special mention1 of to ire pas e^ov, that which
contains or possesses limit, and rj tov irepaTos yevva2, the
offspring of limit, which are evidently identical with
each other and with to iroaov. The examples which
Plato cites, to laov, to harXaaiov, /cal Trap 6 tl irep av
rrpos apiOfjidv dpiOfxos rj /jueTpov fj irpbs fxeTpov, are all
mathematical determinations, just the relations that
are essential to the expression of a mathematical
proportion or law, such as the p,€Tpiov of the Politicus
was found to be.

We cannot, therefore, go far wrong in dividing to
Trepas into two classes, to [xeTpcov and to iroaov, the first
1 24 a. 2 25 d.

APPLICATION IN THE P0LIT1CUS AND PHILEBUS 35

representing the ideal law which governs the production
of fjbc/crd, the second the mathematical magnitudes and
relations through which it works. This conclusion finds
special confirmation in the language of a succeeding
passage, for at 26 D the whole process of plfys is described
as a " generation into existence out of numerical
relations established with the agency of limit" (yeveats
eh ovcriav itc rcov jxera rod Treparos direipyacrpbevoyv
lierpoiv). The perpiov of the artist, then, is parallel
to the fjuerpiov that governs the yeveo-cs of the universe,
and which is an immaterial law, finding best expression
in a later sentence of the dialogue 1 : k6o~plo$ tis
daoouaTOS ap^cov koXoos ipyjrv^ov aoo/jLaros ; and the
opyava awaiTta are surely nothing else than the iroad,
the Treparos yevva, which are the indispensable instru-
ments through which the pbirptov operates.

The class of pluctcl should not detain us long, for
they are a multitude in number 2, and the most easily
identified of all. They cover the whole realm of concrete
existence, and include every discoverable species of the
natural world. Unfortunately, however, Plato has here
signally failed in clearness of thought and language,
and at this juncture of the argument he seems to be
governed entirely by the practical considerations of the
dialogue, leaving out of sight the metaphysical principle
on which the division is primarily based. Since the
Iilktos ^to?, upon which the whole argument bears, is
not a natural fitrcrov, but an imaginary conception, it
is only pLucra of this kind that he chooses to cite as
examples, things which are patera, not in a meta-
physical, but in a figurative, sense. Acting thus on
1 64 b. 2 26 c.

a— 2

36 THE ANALOGY OF THE ARTS AND ITS

the popular belief that all evil is airetpov, all good
Treirepaa/jievov, he mentions vyteia, /cdWos and la^vs
as typical members of the mixed class ; whereas the
whole trend of the argument is to show that these
words signify, not jjuktcl themselves, but attributes
which attach to them when they are faithful copies of
to fierpiov. They are the scientific terms applied by
the mind in its capacity of critic, and are therefore to
be classed with vovs as a part of its machinery. As
for /jiovorcfCT], it is obviously out of place among the
/jbtfcra here. Movcri/crj is a constructive art, and it is
constructive art that supplies the analogy upon which
this whole classification of the physical universe is
based; nothing could be more unreasonable than to
introduce a simile as part of its application. We are
satisfied, therefore, that fiL/crd, in strictness, represent
natural substances and nothing more.

With regard to the alrta, which corresponds to the
Srj/jLLovpybs of the arts, we are told in indisputable
language 1 that it is vovs and nothing else. But what
aspect of vovs ? At this crisis of the argument Socrates
declares in most impressive language that the universe,
so far from being ruled by blind force, is controlled by
a universal vovs and ao^ia, and that this universal z/ov?
is the source of our inferior intelligences, just as surely
as our bodies are derived from its body. Clearly then
the cause of the universe is inseparably connected
with the universal vovs, but not, I may remark, with
the universal vovs regarded as separate from the uni-
verse ; the vov$ of 30 a seq. is not only present in all
things, but is distributed especially into the finite

1 Phil. 30 c.

APPLICATION IN THE POLITICUS AND PHILEBUS 37

souls of men. The dvOpwinvo^ vovs is bound up with
the universal vovs, and shares with it the function of
atria, just as in the Sophist1 divine and human vovs
alike are centres of activity.

In other passages, of course, where the alria rrjs
/u£ew? is not in question, we find the divine vov$
regarded as something apart from the universe, as
pure intellectual activity2, that which represents the
most divine life of all. But this aXrjOivos ko\ Oetos
vov$ suffers neither pleasure nor pain, and is liable to
none of those affections which limit the capacities of
men. Its entire separation from the influences of body
raises it above all participation in the physical universe.
The divine reason in this aspect, therefore, cannot be
the universal 1/0O9 distributing itself into finite intelli-
gences, nor can it be regarded as mingling airetpa
(subjective phenomena) with iroad (mathematical re-
lations peculiar to the human intellect) in order to
produce material things. The Oelos vovs, considered
as pure intellect in continual activity, is single and
separate ; but, in its character of alria tt}? /u^eo)?, it
must be regarded as multiform, and as acting through
the subordinate intelligences of which it is the source.

Our analysis of Plato's four yevr) thus results in
a view of the universe, and of the material things of
which it is composed, as a generation and as a mixture
of certain ingredients brought about by a definite agent.
Material things are compounds of sensible qualities and
mathematical determinations, fused together by the
universal vovs, regarded as acting plurally through
the inferior minds into which it is subdivided, and

1 Soph. 248 e. 2 22 c.

38 THE ANALOGY OF THE ARTS AND ITS

as copying an immaterial ideal law which expresses
itself in the mathematical relations aforesaid. Here
truly is an explanation of phenomenal existence which
in subtlety and power far transcends the older theory,
in which we were told, indeed, of an infinite world of
ideas, but which threw no light whatever on the
function or modus operandi of those ideas.

Some doubt has existed as to whether the doctrine
of the Philebus admits of ideas at all, and the four
yivT] have been regarded as a by-product of Plato's
thought. A careful consideration of the class of irepas,
however, combined with the knowledge that the im-
perative necessity of revising the ideal theory x was in
Plato's mind as he wrote, leads us to the conclusion
that in the Trepan he had at last arrived at a conception
of the ideas which his critics were powerless to assail.
To this it has been frequently objected that the
difficulty of 15 B, viz., that the idea exists both apart
from, and immanent in, particulars, is not thereby
removed. Such an objection, however, does not ap-
pear to take account of the division of to Trepas into
to fieTptov and to ttogov, of which to /leTptov alone
represents the idea, to iroaov the instrument of its
operation. Transcendence and immanence are still its
characteristics, but the new explanation of its nature
practically reconciles the two. The law of proportion
which governs the production of a pllktov is certainly
something other than the pmcTov itself, removed from
it as far as the ideal is removed from the material, but
it is also in a sense immanent in the pllktov, since it
gives to the latter its characteristics, and is itself

1 15 B.

APPLICATION IN THE POLITIGUS AND PHILEBUS 39

illustrated therein in virtue of its representatives, the
iroaa. Such then is the character of the idea as
portrayed in the Philebus ; it is a law of mathe-
matical proportion which governs the generation of
phenomenal things, that is, not merely a scientific
generalisation attained through observation and experi-
ment, but rather an eternal necessity inherent in the
very nature of a thing and expressing its peculiar
reality. Further light on this notion, however, must be
reserved till we come to the examination of the Timaeus.

An important question remains. Of what things
are there ideas of this sort, and where is the line to be
drawn ? To this the exposition of the yevrj seems to
provide a clear answer. There are ideas of all finer a,
and the fitKra of the material universe are surely
every species of natural substance, whether animate
or inanimate, organic or inorganic. The mere fact
that sensible qualities, mathematical relations, mind
and all its activities in art and science, are to be found
outside the class of fierptov serves to rule them out of
the list of ideas ; and of these the first two classes were
already, in the Theaetetus, Parmenides, and Sophist,
banished from the realm of the ideas.

A few words should be said in regard to two classes
of existences which are not included in those mentioned
above. The first of these, cnc^vaaTa, of which, like every- -
thing else, there were ideas * in the time of the Republic,
seems since then to have declined in importance. In
the critique of the Parmenides2 Socrates apparently
does not think it worth while even to mention them,
and the same applies to Philebus 15 A. They have, it
1 See Crat. 389 a. 2 Parm. 130 c.

40 THE ANALOGY OF THE ARTS AND ITS

is true, served a purpose, and no slight one, in affording
a striking analogy, which Plato has used with effect in
both the Philebus and the Timaeus, for the elucidation of
the ideal doctrine. It is, however, quite incredible
that Plato should have included them in the fxt/cra of
the universe, which are subject to the fierpiov imposed
by universal vovs. If they are to be placed in tne
yevr] at all, it must be as an appendage to the class of
vovs, which, as we gather from 66 B, includes iTriarrjfjLat
and re^vac of all sorts, and, presumably, their products
also.

The other class of existences referred to, that of to
vyietvov, to dya06v, to koKov, etc., is of far greater
importance, and certainly of greater philosophical
significance, since they have served as typical examples
of ideal reality from the time of the Symposium onwards1.
They are not, however, natural fiiKTa, and, consequently,
it is impossible, from the point of view of the Philebus,
to attribute to them a fxeTpcov in the same sense in
which it applies to the others. In order to determine
their essential nature, we must examine for a moment
the conception of Good as revealed at the close of the
dialogue. At 64 A there is thrown out a hint to the
effect that by an analysis of a special jjluctov, viz., the
/MtcTos /3/o?, we may hope to learn tl ttotc ev T6 dvOpcoiray
teal tS ttclvtl 7T6(pvK6v dyaOov zeal Tuva iSeav clvttjv
elvai 7tot€ /jbavTevTeov. Then follow immediately the
three criteria by which a thing is judged to be good
or the reverse. These criteria, in contradistinction to
the popular requirements of Tekeiov, l/cavov, aipeTov,
have a metaphysical bearing, and are, first of all,
1 Cf. Theaet. 175 c ; Phil. 15 a ; 62 a.

APPLICATION IN THE POLITICUS AND PHILEBUS 41

aXrjdeta, secondly, /jberptorr]^, and thirdly, av/JL/Jb€Tpia.
Now it is obvious from the confused arrangement of
the passage that these three notions are employed
loosely, and that they are in reality closely akin to one
another, being different aspects of the same thing.
'AXrjdeia, in Plato's strict usage, always implies corre-
spondence with an ideal reality, and that this is its
application here seems to follow from the fact that the
principle of valuation is no longer popular, but meta-
physical. MerpLOTrjs, if we are to keep to the new
sense of fxerpcov established in the Politicus and the
Philebus, will mean the quality of being /juerpiov, or
of conforming to to /jLerpcov, i.e., the ideal standard;
whereas crv^ixerpla, the condition of a whole when its
parts are duly proportioned, will represent the material
aspect of /jLETpcoTTj^1, since it is conformity with the
ixerpiov that makes the particular ingredients percept-
ibly symmetrical. It is, accordingly, clear that there
is in reality only one criterion of the good. The most
general term for it is akrjOeta, which signifies approxi-
mation to the ideal. The expression most characteristic
of the Philebus is fjuerpLorr]?, since it implies the special
interpretation of the ideal which the Philebus presents.
Finally, /jLerpLorr)? reveals itself in the concrete par-
ticular as av^fjuerpia, or harmonious relation of parts,
and is, in this aspect, the cause of kclWos. The test
of goodness, then, in the material universe at least, is
approximation to the fjuirpiov, and this test, says Plato,
holds whatever be the (jllktov under consideration.
Hence to ayaOdv and to /cdWos, when applied to the
jxiKTa of the universe, are no longer suprasensual
realities ; they are rather part of the machinery of a

1 See 25 e.

42 THE ANALOGY OF THE ARTS AND ITS

particular science, a science of per pr)T tier), whose func-
tion it is to compare things, not with one another, but
with the absolute fierpiov which is the law of their
existence. In the Politicus we became acquainted
with a science of art-criticism, which looked upon all
divergence from the standard as an evil, which must in
all cases be avoided ; and now we find that there is a
still higher ixerpr^TtKr}, a science of ideal aesthetics,
whose business it is to judge the yiyvofieva of the world
in the light of the absolute idea. But the Good and
the Beautiful are not ideas, which inhere in fiitcrd, and
thereby make them materially good and beautiful ;
they are simply terms of relation, a part of the
machinery which every art must have, and they are to
be ranked, not with the ideas, but with the Te%z/<z£,
which are an appendage to vovs. In the region of
ethics, indeed, we have yet to show that Plato was to
the end faithful to his belief in a supreme avro dyaOov
or its equivalent : in the Timaeus we are presented
with his final standard of moral goodness. But, in
everything that concerns the physical excellence of
ycyvofieva, he is now content to point to the fxerpcov of
each thing as the supreme test of its value.

We have, therefore, in succession excluded from
the ideal world sensible qualities, relations, objects of
iTTLo-TrjixaL and T€%vai, aKevaard, and also the terms
good and beautiful and their opposites ; and the word
eZSo? or Ihea is henceforward to be applied especially
to the organic types of nature, and all species of natural
substances.

But what steps must be taken in order to discover
these fjuerpca ? If Plato means them to take' the place
of the old iheat as objects of knowledge, how are they

APPLICATION IN THE POLITICVS AND PHILEBUS 43

to become known to us ? Surely in the way which
Plato himself has indicated. At a very early stage1 of
the dialogue Socrates brings up the eternal question of
the One and the Many, and Protarchus, with youthful
ardour, is anxious to attack it then and there in its
most subtle form, viz., in its application to the theory
of ideas. The only way, says Socrates, to unravel the
mystery of the One and the Many in any form is to
make use of the old method of hiaipea^, which he had
employed many a time in his search for truth, in the
region of politics and ethics no less than in metaphysics.
Limit and unlimitedness are present everywhere, not
only in the physical universe, but in the realm of know-
ledge too : the very method of definition is founded on
a recognition of the two principles. Whatever then it
be that we seek to know, let us posit one genus for it,
and then in the light of this genus resolve the indefinity
of the individual representatives into a definite number
of species, among which the object of our search will be
found. The true nature of /juerpta is accordingly to be
discovered by the use of this supremely efficient instru-
ment ; careful analysis of the indefinity of particulars
will reveal the nature of the species, as well as of
the genus. The fxerpcov of either is the eternal law of
proportion which governs it, and it cannot but reveal
itself to him who makes search with diligence. Of so
much we are for the present assured : but for a com-
prehensive view of the whole scheme of knowledge and
of its detailed dependence upon the theory of ideal
Being, we must look to the Timaeus, which now awaits
our consideration.

1 14 c seq.

ESSAY III.

THE WOKLD-PEOCESS OF THE TIMAEUS.

In our consideration of the Philebus we were called
upon to regard the world as the result of a process or
generation analogous to that which is concerned with
production in the arts. The universe, we were told, is
a ycyvo/jievov, a product brought into being by the
agency of vovs, which combines sensible qualities with
mathematical relations, and makes them conform to
certain fierpta, or eternal laws of formation. In the
myth of the Timaeus we find this doctrine not merely
reiterated, but extended and developed in the greatest
detail, and with a far more elaborate use of the symbol-
ism with which we are already acquainted. The whole
cosmos, with all its various interrelated parts, in all its
activities both great and small, is spread out before us
in one of the most magnificent allegories that the world
has ever seen. Abstract conceptions, which in the
Sophist were presented to us in logical simplicity, are
here displayed in the picturesque dress of personifica-
tion ; the universe is represented as being constructed
after a material fashion out of the immaterial elements
into which Plato has analysed it in thought. Our
present object is to make a general estimate of the
purport of the myth, reserving for separate treatment

THE WORLD-PROCESS OF THE TIMAEUS 45

its bearing upon Plato's final statement regarding the
nature of knowledge.

A brief resume of the story till the end of c. xvi1,
which marks a definite break in the exposition, is the
first essential. First of all, says Plato, it behoves us to
draw a distinction between that which is and that
which becomes, between to ov ael, yeveauv S* ov/c eyov,
and to yiyvo/jLevov fiev aei, ov he ovheiroTe : the first
is apprehended by reason alone, the second is the
object of opinion and irrational sensation. To which
of these does the universe belong ? Surely, since it
is visible and tangible, and generally apprehensible by
Soga and alaOrjcrts, to that which is ytyvo/juevov and not
ov. But the peculiarity of the phenomenal is that it
always has an aWla, hence one must be found for the
universe. Moreover, a thing can only be fair when the
Srj/juovpyds who fashions it takes the ideal as his model ;
that the universe is fair no one can dispute; it is
icaXkio-Tos tcov yeyovoTcov. Therefore, whatever be its
cause, the ideal must be the model upon which it is
built.

Now, in order that the universe might be koXov, its
ah La, or, to adopt the language of " production," artificer
produced in it harmony and measure, and also, seeing
that of sensible things that which possesses vovs is
always superior to that which has it not, he placed vovs
in yfrvxv and yfrv^v in crco^a, since apart from tyvxv
Z/0O9 cannot inhere in anything. As for the TrapdSety/jLa,
in imitation of which the world was fashioned, it is a
£cbov, the all-embracing vorjTov %coov, containing in
itself all other vorjTa £<ba, to koWlcttov twv voovfjLevcov.

1 Tim. 47 e.

46 THE WORLD-PROCESS OF THE TIMAEUS

As for the crcoyua of the cosmos, it is composed of
the whole sum of fire, air, earth and water. These four
ingredients are essential, since, although two only, fire
and earth, are requisite for visibility and tangibility,
two others must be added as means in order to make
the resultant body a perfect unity. This body is a
perfect whole made up of perfect parts; and, seeing
that it includes within itself all animals, it possesses
that shape which comprehends all other shapes, viz.,
the spherical. It has no need of organs, but revolves
upon its own axis in a uniform circular motion, the
motion most typical of the action of vovs and $po-

V7]CTL<;.

But, although we have spoken of tyvxv as being
placed within body, we do not therefore imply that
(Tcofia is older or of greater importance than yfrv^V
which inheres in it. The truth is rather to be expressed
in this way : ^v^V rules over aco^a, and penetrates it
through and through. It is composed of three ingre-
dients ; the aixepLo-TOs and del Kara ravrd eyovva
ovo-lci, and that which, being divided in material bodies,
is ycyvofjievov, ov 8e ovheirorey are mingled with a third
form of ovaia which is, like them, compounded of
ravrbv and Odrepov1. These three forms of ovaia the
artificer welded together into a unity, hard though it
was to mingle Odrepov with ravrov. Further, he
divided the mixture thus formed into portions corre-
sponding to the intervals of the diatonic scale; after
which, the whole of soul being divided into two halves,

1 This rendering of the sentence beginning rrjs djuepiarov (35 a)
has the authority, among ancient commentators, of Proclos and
Plutarch (7repi rrjs iv TifAaiip xf/vxoyovias, c. 25).

THE WORLD-PROCESS OF THE T1MAEUS 47

he laid them across one another in the shape of the
letter X, and formed of them two intersecting circles.
The one of these, which revolved to the right by way
of the side, he called the circle of ravrov, that which
revolved to the left diagonally, the circle of Odrepov.
To the circle of ravrbv he not only gave supremacy
over the circle of Odrepov, but he left it single and
undivided, whereas the circle of Odrepov was cleft into
seven concentric circles corresponding to the orbits of
the seven planets.

Next, in order to make the k6o-\ios resemble still
more its eternal TrapaSeiy/jua, he produced within it an
everlasting image of eternity, which has been named
time, and for the measurement of which he fashioned
the planets which revolve in the seven orbits of Odrepov.
All these, together with the fixed stars, are living
deities, spherical in shape, composed chiefly of fire, bat
whereas the fixed stars follow the motion of the Same
only, which is most like to the activity of reason, the
planets are endowed with the motions of Same and
Other both.

The universe, however, was not yet complete, for as
many varieties of ISeat as vovs beholds in the avrb
%coov, so many the artificer thought should be contained
in the oparov £ooov ; and of these there are, besides the
Oelov yevos of stars, three inferior classes, viz., the tribes
which inhabit the air, the water, and the earth. With
a view to the making of these, he called together the
race of heavenly stars, and, addressing them as Oeol
Oewv, showed how ro irav could not be truly irav until
there were placed within it the inferior animals also ;
yet he himself could not make these, for they would

48 THE WORLD-PROCESS OF THE TIMAEUS

thus become the equal of the deities themselves, whose
bodies had been rendered indissoluble by his own will.
Consequently to the stars he assigned the duty of
moulding for the vorjrd £coa such bodies as were
appropriate for them, as well as the task of providing
them with sustenance, and of receiving them again at
death. But, before he committed to the deities the
immortal principle of the £coa, he took such portion of
the three ingredients as was left over from the former
mixture, and, having compounded it in less perfect
proportions, he divided the whole into individual souls
equal in number to the fixed stars. These souls, being
placed each in one of the stars as in a chariot, were
then shown the nature of the universe and its inevitable
laws : how that they should each be planted in one of
the planets, and that it was given to them to choose
how they would live; if they lived in righteousness,
they should hereafter return to their kindred star and
be happy, but if otherwise, they must pass in graduated
stages first into the form of a woman, and thereafter
into the forms of beasts in due order, according to their
manner of life. Then the planetary gods, obeying the
command of their father, made mortal bodies of the
four elements they found in the universe, and these
bodies they made so far as possible in the image of
the cosmic and starry bodies, placing the circles of
ravrov and Odrepov within the spherical body called
the head. At birth the soul of the creatures thus
made was overcome with disorder and tumult, owing to
the disturbances caused by the influx of nourishment
and the impact of external sensations. The circle of
the Same was impeded and the circle of the Other

THE WORLD-PROCESS OF THE TIMAEUS 49

distorted, so that neither Reason nor Sensation func-
tioned correctly. In time, however, the commotion
abated and the motions of the Same and Other resumed
their proper course ; then might such a soul, if it used
its opportunities aright, attain to the excellence of
knowledge and intellectual liberty.

All the rest of the body, hands, feet, and sense-
organs, were given merely to minister to the comfort
of the head, which was its divinest part. Sight and
hearing, and all our senses, were bestowed for this one
purpose, that, through observing the orbits of heavenly
beings, we might be enabled to order aright the
revolution of reason in our own souls, and pursue divine
philosophy, the greatest gift of God to men.

So much will suffice for an examination of the main
principles of the myth ; the detailed physical exposition
that follows may well claim our attention in a separate
paper. First of all a word or two must be said as to
the claims of this story to be considered as an allegory
at all. Such a view of it is assuredly no novelty, for it
apparently prevailed in the Platonic school from the
time of Aristotle onwards. The latter refers distinctly
to such an interpretation in de Caelo1 ; Plutarch, too,
though maintaining a literal interpretation himself2, is
obviously conscious that the opposite view was the
favourite among his contemporaries. Aristotle, in de
Caelo, pours contempt upon those who compare the
simile of creation in time to a diagram, in explanation
of which tense-forms are used, not to indicate time-
relation, but merely with a view to clearness in expo-

1 Ar. de Caelo i. 10,

2 Plutarch, ire pi ttjs ev Ti/xcuc^ \pvxoyovias.

W. i

50 THE WORLD-PROCESS OF THE TIMAEUS

sition. The cases, he says, are not parallel, for all the
separate parts of a diagram can co-exist, whereas dragla
and rages, which in the Timaeus are made to follow
one another, can never co-exist. Simplicius1, however,
replied that the dragia represents, not a separate force,
but an ever-present tendency which makes itself felt
even in the midst of rages. There is, in fact, nothing
in the Timaeus myth that can be regarded as existing
in separation from anything else ; all the solitary forces
there at work are abstractions, separated by sheer
reason from the environment of which they are a vital
part, and without which they themselves could not exist.
A literal interpretation, indeed, would raise endless
difficulties; the whole phraseology and arrangement
seem to militate against it. We are met from the
beginning with conceptions such as ovaia, ravrov,
Odrepov, which take us right back to the logical
analysis of the Sophist, and which we cannot possibly
regard as material things. Again, the story never
proceeds uninterruptedly to a conclusion. Instead of
a narrator who sees clearly before his mind's eye
a definite series of events, we have here, as it were,
a photographer, who is continually presenting us with
the same scene taken from different points of view.
Thus, in the beginning2, the body of the universe is
presumably fashioned out of the four elements, whose
existence is pre-supposed ; later at 53 B, however,
these elements themselves are represented as being
shaped by the 0e6<; elheai re kcl\ aptOfjuols. Could this
possibly be part of a story which depends on time-
sequence for its intelligibility ? Similar instances are
1 Simplicius, commentary on this passage. 2 31 b.

THE WORLD-PROCESS OF THE TIMAEUS 51

to be found at 29 a and 30 A, where to yeyovos and
to oparbv are introduced before any yeveat^ has taken
place, and at 34 B and c, where we are told in
almost the same breath that ^v^t) is created within
body (as if body were prior), and also that awfjua is in
no sense to be counted prior to yfrvxt], Plato here, in
fact, tells us plainly that he does not intend his words
to be taken literally. Finally, of course, there is the
insuperable difficulty, emphasised by Proclos, of ex-
plaining how time can be conceived of as being created
as one of a series of creations all of which take place
in time.

We may, then, I think, take it for granted that the
myth of the Timaeus does not profess to describe any
actual yevecns of the world in time ; and we shall be
content to interpret yeveacs in the same sense as Plato
himself, at 28 B, c, interprets it : that is, to irav is to
be regarded as a yiyvo^evov, not because it has in any
sense been produced at any special period, but because
it belongs to the class of things, which, being objects
of 86 £a and ataOrjai^, are ever in flux and opposed to
that which is truly 6v. In this sense only Plato
affirms that 6 ovpavo? yeyovev, and the problem he sets
before himself in the Timaeus is two-fold : first, who
or what is the air La of this continual yeveais, and
secondly, what is the irapaZeiy^a in imitation of which
it is framed, what is the eternal reality in virtue of
which alone it retains such existence as it has ? Our
present object, then, will be to elicit from the poetical
phraseology of the myth the result of Plato's deliberations
on these two points.

In the beginning of his exposition Plato told us

4—2

52 THE WORLD-PROCESS OF THE TIMAEUS

that it would be hard to describe the atria of the
universe in any hard and fast language. He was
content for the present simply to assume its existence
and to call it the hrjfuovpyos, the creator of all visible
things. As the story proceeds, however, it is clear that
the air la may be regarded in two lights : it may be,
first of all, the cause of motion, or of the actual yeveais
of phenomena, and, secondly, the final cause, the ideal
" good " which is the end and aim of this yeveais. The
former aspect is unfolded in those passages 1 which re-
present the SrjfMovpyos as the actual cause of becoming,
and the communicator of motion to the bodily universe.
The atria as final cause is depicted chiefly in the de-
scriptions2 of the yeveais of soul, where the Srjfjiiovpyd^
is actuated by a beneficent purpose, and is practically
identical with the idea of good, and especially at 41 A,
where he supplies the soul-principle for the inferior
animals, but declines to have any share in the creation
of their bodies, or of the evil which they must necessarily
encounter. The atria here is obviously no movent
cause, but, to quote Plato's own words, rwv vorjroov del
re ovrtov apiarov, the highest of ideal existences. He is
voijaei fxera \6yov 7repi\rj7rrbv3 and /nerd vov Karafyaves*
He is, in short, to be identified with the supreme
irapdheiyfxa itself.

In his character as the originator of motion the
Srjfjiiovpycx; of the Timaeus would appear to be scarcely
different from the t|tu%j) rov koct/jiov, which is consistently
represented as having the cause of motion in herself
(36 e), and as being the primary cause of motion in all
other things (46 e). Plato is still true to his belief of

1 28 c ; 34 a. 2 29 e ; 37 a. 3 28 a.

THE WORLD-PROCESS OF THE TIMAEUS 53

the Phaedo, and more elaborate declaration in the
Philebus, that a divine vov$, an all-governing reason, is
the cause of all that is phenomenal. In words that
remind one most strongly of the Phaedo he affirms that
there are two kinds of causes, primary and secondary,
and whereas the latter embraces all manner of physical
processes, which most men regard as true causes, the
former sort is invisible, the direct activity of mind
and soul; and he that loves reason and knowledge
must seek the rational cause first, and the secondary
causes which transmit, but do not create motion, only
for the sake of the primary. We understand, therefore,
that mind and soul are the cause of the activity of the
universe no less than of human action and production ;
we must postulate a universal mind and soul to govern
the infinite movement of the world. Everything that
Plato regards as necessary for the completion of the
universe is summed up at 47 E as ra Sea vov heh-qixtovp-
<yr)fi€va.

This view not only endorses the statement of the
Philebus already referred to, but is re-affirmed by the
well-known passage in the Laws, in which ^rvx7l l> the
avTOKivrjTos, is represented as the source of all the
yeveens of the world. It has in itself the power of
moving, not only itself, but other things as well ; all its
primary motions of fiovXTjais, fiovXevais, Soga, and the
like, are reflected in the corporeal movements to which
they give rise. In the 6elov yevo? of the stars "^v^r) as
dpxh KLvtjaeays is seen in its greatest perfection, for in
them vov? is least subject to the seductions of sense,
and their physical motions betoken the supreme regu-
1 Laws 896 d, e. Cf. Phaedrus 245 c.

o4 THE WORLD-PROCESS OF THE TIMAEUS

larity and precision of the soul-movements which they
reflect.

There remains the larger question of the atria as
the final cause of the universe. Having satisfied our-
selves that the movent cause is to be found in a universal
yfrvxVi we have still to seek its Trapahetyixa, the idea
or end for which it came into being. But before we
undertake this new quest, it would be as well to have
in mind the main features of this universe as Plato
has sketched it1. It is a single, all-comprehensive
animal, possessed of vov<s and yfrvxv as well as body,
and containing all visible creatures that exist. Its
body comprehends all fire, air, water and earth2, so
that nothing is left behind with which another aclofia
might be formed. It is o\ov ig oXcov airdvrcov,
possessing no organs of sense, and therefore destitute of
sensations except in so far as it may be said to have
them through its various parts. Its shape is spherical,
for the animal that contains within itself all possible
animals should surely have that form which may be
filled with all possible shapes, and its only motion is
a revolution upon its own axis — that physical motion
which approaches nearest to the pure activity of mind3.
As regards its soul, one cannot be far wrong in
ascribing to it, though in purer and more perfect pro-
portions, a structure similar to that which one perceives
in the -^v^ai of individual men. Wvxv is a compound,
formed of the ovaia which is afxepiarQ^ and ever
changeless, and the ovaia which is ytyvofjievov and
divided in visible bodies, mingled with a third ingre-
dient, Essence, which, like them, is a mixture of two

1 30 b. 2 32 d seq. 3 Cf. Laivs 898 a.

THE WORLD-PROCESS OF THE T1MAEUS 55

things, ravrbv and Odrepov, and which, together with
these last, corresponds to one of the leading categories
of the Sophist, which are employed by the human mind
whenever she passes judgment on, or attains to know-
ledge of, anything whatsoever. A question arises here
as to Plato's exact meaning in saying that yjrv^r) is a com-
pound of this sort, and that the changeless and changing
world, together with Essence, are composed of these two
ingredients, ravrbv and Odrepov. The answer is surely
to be found at 37 A, B. There we find it clearly stated
that yjrv)(r}, whenever she comes in contact with any-
thing, whether it belongs to the class of the d/juepcarov,
or that of the fiepiarov, being affected in her entire sub-
stance, tells that wherewith the thing is same, and that
wherefrom it is different. Hence we understand that
the function of yfrvxv> whether it be that of cosmos or
individual, is to declare the relation of Same and Other
in regard to everything that comes under her operation,
whether it belong to the permanent and intelligible
sphere, or that of the sensible and ever-changing.
^v%rj thus has the intelligible and sensible as ingre-
dients because she deals with both alike, and these are
mingled with Essence, i.e., with Same and Other, inas-
much as these last are the leading predicates which she
necessarily employs in all her functioning. The whole
realm of ideas, moreover, and the sensible world of flux
likewise, are composed of Same and Other, inasmuch as
the mind is eternally decomposing them, different though
they be in kind, into these same two elements. In
fact, all existent things, so far as they are known,
may be said to consist of these ingredients.

This doctrine is not one that need surprise us here ;

56 THE WORLD-PROCESS OF THE TIMAEUS

it was stated before in a less explicit form in the
Sophist1. There, it will be remembered, the knowing
subject is said to have Koii'fovia with to yiyvofievov by
means of ataBrjat^, and with to ovtms ov by means of
yjrv^j, bid Xoyta/jiov ; here we have the theory of tyvxn
as a compound of the intelligible and the sensible. Also
the categories ovaia, tclvtov, Odrepov and the like, are
found to have kolvoovlcl with one another in virtue of
their inherence in the same thing when analysed by
the same mind. Putting these two statements to-
gether, we arrive at the doctrine of the Timaeus. The
knowing subject, or, to borrow the language of the
Timaeus, the soul, in virtue of her /cotvcovla with
the objects both of €irtaT7]fjL7] and atadrjat^, imparts
to both the attributes Same, Other and the like,
which are the universal predicates indispensable to
her activity, so that they may be said to consist of
these attributes. Hence the categories too, being
found in the same objects, have koivcdvlcl with one
another; and — a fact which is more important in the
light of one of the duoplai of the Parmenides — the
ideal world itself, consisting, in virtue of the Koivwvia
of ^vyj), of tclvtov, Odrepov and the rest, is capable of
receiving contrary attributes no less than the pheno-
menal : this, however, is no longer due to the /cotvcovia
of incompatible ideal entities, but to the necessary
functioning of the mind, which, by participating in its
object, makes the object participate in all manner of
contradictory categories. Ideal and material worlds,
then, so far as they are known, may be said to consist of
Same and Other.

1 Sophist 248 a.

THE WORLD-PROCESS OF THE TIMAEUS 57

But ^frvxVy besides possessing Same and Other, and
thereby Essence, as primary ingredients of her nature,
has in addition the two motions, Same and Other,
which apply respectively to the faculties of reason and
sensation, inasmuch as reason is concerned with that
which is Kara ravrd e%oi>, sensation with that which is
continually Odrepov, ytyvo/mevov zeal diroWvfjievov (28 A).
They are made to revolve after the fashion of the
spheres of the fixed stars and planets, simply because
Plato regards all physical motions as the counterpart of
the noetic activity of vovs. Each of these circles, further,
consists itself of Same and Other, for they are the
essential modes of all activities of soul. Here we are
in a position to realise even more perfectly why Plato
should from the outset make the afxepcarov, which is
votjtov, and the fjueptarov, which is the object of
sensation, ingredients in the formation of soul ; soul
partakes of the nature of both of these in virtue of her
apprehension of both. One is reminded of the defini-
tion of ovaia which was introduced in the Sophist to
satisfy Idealists and Materialists at once — fj hvvafjLis
rov iroielv rj irdayeiv. Applied by the idealists, this
definition included both ovaia and tyvx/j ; applied by
the materialists, it included both to alo-Orjrov and to
alaOavofjbevov. Hence ^f%^, in any case, was to be
counted ovaia, inasmuch as it operated in both spheres.
Plato, therefore, is still maintaining his compromise
between materialism and idealism. Aware of the
merits on both sides, he will not reject either utterly,
and his conception of soul as the comprehensive essence,
through which ideas and phenomena alike are appre-
hended, and as the eternal cause to which phenomena

58 THE WORLD-PROCESS OF THE TIMAEUS

owe their being, preserves the sovereignty of the ideal
world, while accounting for the apparent reality of
material things.

Besides functioning as reason and sensation and
operating through Same and Other, the soul is repre-
sented as being composed of mathematical ratios,
corresponding to the intervals of the diatonic scale.
This of course signifies simply that the apprehension of
harmony, too, is one of the striking modes of its
operation. Soul, then, is Hot itself a harmony, as
Simmias tried to hold in the Phaedo, but it has
within it the power of grasping and understanding
musical relations in virtue of number and proportion,
which are indispensable modes of its activity.

In his account of ^rvxh Plato has been enabled to
lay down certain definite principles and to come to
some definite conclusions. Concerning the body of the
cosmos and its component parts, however, he cannot
attain to certitude in any degree. It is ordained that
everything which is visible shall be in eternal flux ;
consequently everything that goes to make up the
materia] universe is subject to incessant variation of
form. Not only do organisms suffer daily change
within themselves, but they themselves in their
entirety are forever passing away and being replaced
by others, with the exception indeed of the stars, the
heavenly bodies, who stand highest in the realm of
creation, and in a peculiar way represent the universe
itself, for they are its leading constituents, and from
them is derived the substance of the smaller constituents.
This, I think, is all that is meant by the creation by the
0€ol 0€cov of mortal bodies. The individual souls of

THE WORLD-PROCESS OF THE TIMAEUS 59

men, animals, and all lower existences, receive their
bodily form from the planets, who are the firstborn of
the #eo9, or rather, the highest phenomenal existences
in the universe. The fixed stars have already been
called into requisition to act as the 6xv/jLaTa °f the
souls while they listen to the Artificer's harangue
regarding the laws of the universe; and just as this
detail has a metaphorical significance merely, so the
creative function of the planets means simply that all
lower creatures derive then* substance from the heavenly
bodies. Plato's language seems to me to admit of no
other interpretation. The Brjfjbcovpyo^ himself is the
cause of the creation and differentiation of the souls ;
what the Oeol do is simply to provide material for the
bodies, to nourish the bodies when made, and to
receive them again at death. Nothing can be gained
by attempting to extract an unnecessary complexity in
Plato's metaphysics from the picturesque scene in which
the Srj/jiiovpyos, calling together the 6eol 6ewv, entrusts
to them the making of the bodies of inferior creatures.
But, to resume our account of the flux, part of the law
of change is that the inferior souls, which are parts of
the great soul, take upon them the nature of man, and
thereafter that of woman and the lower animals,
according to the merit or demerit of their successive
lives. The possession of body and sensation is an
unceasing source of temptation, and when a man is
mastered by the lower impulses of his soul, it is
ordained that his soul shall pass first into the body of
a woman, and, if even then he fails to repent of the
error of his way, into the form of some beast suited
to his particular nature. Only through following the

60 THE WORLD-PROCESS OF THE TIMAEUS

dictates of reason can he hope to escape, and rising
beyond the trammels of the body, return to his first
and best estate (rrplv ttj tclvtov /cal opboiov irepcoSo) rfj
iv avroj ^vveTTiaTrofievo^ top ito\vv o^Xov /cal varepov
irpoa^vvra i/c Trvpos /cal vSaros /cal depos /cal 7*79,
@opv/3(o8r] /cat aXoyov ovra, Xoya) /cpaTr}aa<$ e/9 to rrjs
irpooTTj's ical dpicrTTis ac^i/coLTo elSo? e£eo)9. 42 D).

We have now reached a point where we may pause

to consider the nature of the idea or 7rapaB6Lyfia}

which, Plato says, the Srj/juovpyds had in view in the

production of a universe such as we have described-

That universe, fair though it be, is not calculated to

inspire the philosopher with satisfaction, for it is fated

to undergo incessant change, and the inferior souls

within it, by reason of their connexion with body, are

ever subject to misfortune. The world of sense is

unreal (28 a) : it is an eternal illusion : it has in it

nothing akin to reason or thought (46 d) : it only exists

in so far as it is seen or handled (31 b). Hence only

when a man's soul is free from sin, and thereby casts

off the incubus of body, will the illusion of sense cease

to have a meaning for him1; then his reason will work

in harmony with that of the All. How then are we to

describe the ideal permanency to which the Brj/uLovpyos

looked beyond all the flux of sense? It is to twv voov/xe-

vcov koWkjtov /cal /caTa iravra Tekeov2. But it is before

all else a £doov, an eternal and perfect animal, which

contains within itself all other vorjTa fwa that are.

Now a %S)ov, as Plato indicates time and again, is a

complex being possessing faculties both bodily and

mental ; but if a %wov is to be votjtov merely, if it is to

1 42 d. 2 30 d.

THE WORLD-PROCESS OF THE TIM A E US 61

be placed in the category of the changeless and eternal,
it must assuredly, on Platonic principles, divest itself of
everything that is perceptible, of all those attributes
which cling to it in virtue of its bodily nature. As a
result of this process it becomes not even ^rvxv (since
y{rvxv, too, in this dialogue, is concerned in part with
bodily functions), but vovs pure and simple. As the
Kebes of the Phaedo puts it : o\<p teal iravrl o/jLocorepov
earl tyvxh T(P ^€i gmtclvtcos eyovTt /uaWov rj tco fir)1.

The supreme irapdhei'yixa of the universe, then, being
a %ooov and a votjtov t^wov, is vovs, a perfect universal
vovs; and the ideas of the subordinate creatures are
only fiopia /caO" ev real Kara yevrj of the avro o
€<tti %ooov2. At 39 E Plato says: "As many kinds as
mind perceives to exist in the avro £ooov, so many did
the Srj/jLiovpyos think fit that the visible world should
contain, and of these there are in the main four kinds,
first, the heavenly deities, and after them the tribes
that inhabit the air, the water, and the earth." This
statement translated into ordinary language means
that only the animal creation, the various tribes that
inhabit the four elements, merit ideal counterparts and
a share in the avro £gW, the consummation of all
existence. Now this restriction of ideas to the various
species of animals carries our thoughts at once to the
transmigration theory, and the fact that within all
these tribes, from man downwards, there is a constant
struggle between higher and lower impulses, with the
result that the individual soul is continually being
reincarnated in a higher or a lower form. The animals
for whom ideas are reserved are exactly those who come
1 Phaedo 79 e. 2 30 c.

1)2 THE WORLD-PROCESS OF THE TIMAEU&

within the range of transmigration, the tribes of air,
earth and sea, each of which, according to Plato,
represents the souls of mortal men which have
degenerated through the taint of sin. It is true, of
course, that the heavenly deities, who are immeasur-
ably removed from human frailty and the need of
transmigration alike, are also mentioned ; but Plato has
so often emphasised their pre-eminence, and their close
connexion with the All itself, that one is not surprised
to find them at the head of the ideas here. They
assuredly will have their counterpart in the ideal
sphere, for they of all material things are the most
perfect imitators of Reason. The members of the
vegetable kingdom, on the other hand, which at first
sight would not seem to enter into the scheme of
transmigration, have no place in the list of ideas as
here given. Plato, however, acknowledged them to be
feoa of a kind, and he must inevitably in drawing up a
complete list of ideas have included them both in his
system of transmigration and of ideas. Empedocles,
his predecessor in the transmigration-doctrine, not only
made plants participate in the process of metempsychosis,
but affirmed that he himself had been a ddfjuvos.

It would appear, therefore, that the scheme of ideas
as here propounded has its basis in ethics. The tribes of
the air, earth, and sea are assigned a share in the avro
%(bov because they are degenerate forms of the im-
mortal principle of soul, which when it is conceived
as functioning in perfect purity and unity, like the
d\r]0ivd<; /cat Oelos vom of Philebus 22 c, is the ideal
%(hov itself. It is only the body, and the sensations
and lusts that attend upon it, that keep the individual

THE WORLD-PROCESS OF THE TIMAEUS 63

^rvxh from functioning in harmony with that of the
All ; they inflict upon it harder and harder penalties
in proportion to its weakness, and prevent the reali-
sation of that ideal universe, an all-embracing mind,
working in unison with itself as one whole, perfect and
undivided. The beasts of the field, then, the fowls of
the air, and the fish of the sea, have each in their kind
a share in the ideal ^ov, for they represent a portion
of the universal soul, which is ever constant, though
subject to the adverse power of sin : and the eternal
prototype of each is simply a specific or generic deter-
mination, as the case may be, of the universal vovs, which
is the supreme idea and irapaSeiy/jia, the ultimate goal
of all human endeavour. In other words, Plato here
indicates that the ideas, which have for so long been
the cardinal principle of his ontology, are in the last
analysis special modes of regarding a universal vovs,
for the realisation of which every soul, albeit uncon-
sciously, strives, the final end and purpose of that
everlasting process of which the world-soul is the cause
— the world-soul itself conceived in its highest phase
and measured by its highest achievement. Thus the
idea of star is simply one aspect of the universal vovs,
which must be considered as providing the type for
the soul-activity of the stars, and of every soul through-
out the whole range of living genera and species, and
also, secondarily and indirectly, as being the cause of
everything that is icakbv in the visible world. Even
in the Sophist Plato repudiated the thought that to
TravTeXws ov1 could be devoid of £corj; and these
€L$r] are confined to £ooa alone. No room for in-

1 Sophist 249 a.

64 THE WORLD-PROCESS OF THE T1MAEUS

animate objects can possibly be made in the four-
fold classification of 40 A without forcing the language
beyond measure. The position which Plato assigns to
inanimate substances, such as the four elements, and
the nature of the ideas of these, will be defined when
we come to our examination of the physical portion of
the Timaeus.

Priority in time in the myth stands, as we have
shown above, for priority in ideal importance, and
when Plato speaks of a man, after many transmigrations
and much conflict with bodily passion, attaining to his
first and best nature, we may be sure that the first and
best nature is that which is ideally and eternally first,
though not in time. Hence the journey by which the
soul is freed from bodily hindrance, and learns to
function in harmony with the great soul of the uni-
verse, is not strictly a " return " in time, but the much-
wished-for and well-nigh unrealisable ideal of the
philosopher. If every soul were to attain to its first
estate, then the supreme idea would be perfectly
represented in time, and Plato is not without hope
that some souls at least may pass beyond the reach of
bodily hindrance and evil 1. The soul of him who is free
from bodily ills will be given a place on its kindred
star and learn the nature of the universe as it truly is,
like the souls of those who, in the Phaedrus, viewed
the ideas in the supracelestial region. For Plato's
deos is not a God, who literally creates, in the
beginning, a universe that is altogether fair and good,
and souls whom no spot of imperfection has yet
touched; it is the eternal idea, for which the whole
1 42 c, d ; 44 c ; 90 d.

THE WORLD-PROCESS OF THE TIMAEUS 65

creation yearns, and strives through many imperfections
to reach, and towards which every achievement of the
intellect, every victory gained by soul over body, is an
advance.

To sum up the metaphysical significance of the
world-process which we have been reviewing, Plato
seems in the first portion of the Timaeus to have
enunciated in a poetical form the leading features of
his latest view of the universe. From the first he felt
sure that there was some permanent principle or
principles underlying variable phenomena. He has
made diligent search for it, and, as his declarations
in the Phaedo, Philebus, and Sophist would lead us to
expect, he has found it in soul and mind. Reason is
the highest and best thing of which the human being
has experience, hence to nothing less than reason can
he attribute the perfection and ultimate reality of
everything he sees. Even physical motion is but the
material counterpart of noetic activity ; and time, which
measures all physical motion and change, is but the
image of eternity, throughout which the activity of
supreme z/ou? endures.

And Reason has two aspects ; it is both atria and
rrapdhetyfjia, of which the latter is prior in logical and
ideal importance. The source of existence is in its
highest phase the source of good, as the teaching of
the Republic leads us to expect. To the universal soul
man owes his very existence, and he must forever seek
and emulate it in its divine and ideal form, if he is
to gain a happy life. When every soul in the universe
has become attuned to the harmony of the universal
z/ou?, and has cast off all that burden of earth and fire

w. 5

66 THE WORLD-PROCESS OF THE TIMAEUS

and water, which clung to it in virtue of the faculties
of sense, then, and not till then, will come the perfect
representation in time of the supreme idea of the uni-
verse, and the various ideas of animal life of which it is
composed. And, if ever the individual intellect is thus
exalted, it shall know and realise for the first time true
beauty and justice and knowledge, that aspect of the
ideal world that impressed itself first on Plato's mind1.
Those eternal essences, which were the load-star of his
early ambitions, have now found a resting-place worthy
of their exalted rank. We saw that one of the chief
results of the Parmenides was the conviction that the
ideas and the supreme idea, if they are to be not merely
existent, but objects of knowledge, must have real and
lasting connexion with one another as well as with the
flux of sense. Here, then, in the Timaeus, we find
this condition fulfilled ; the ideas stand to the supreme
idea in the most intimate of relations: they are aspects
of the perfect and all-sufficient vovs, which is brought
into vital contact with the souls of all the generic and
specific forms of life.

Finally, may we not say that Plato has in this
dialogue amply satisfied the criteria furnished by the
criticism of the Parmenides and Sophist ? The supreme
eV, if it is to be known, must exist not in self-identity
merely, but in relation to the many too. Further, in
the Sophist it was found that it must possess Kivr^at^,
Zoorj, vovs and yjrvxv- We are now assured that the
Oecos j'ovs is the supreme eV, that it has life and
activity, and that only in so far as they imitate it
successfully can the individual souls be said to possess
reality at all.

1 Cf. Phaedo 114 c.

ESSAY IV.

THE IDEAS AS 'AptdfioL

The portion of the Timaeus with which we must
now deal forms a contrast in many respects to the
former half, which we have just left. The object of the
earlier chapters was not so much to describe to us the
cosmos in its material aspect, as to unveil to us its ideal
prototype, and to take us to the very source of all its
activities, to discover to us a universal and eternal vovs,
which manifests itself in the cosmos just as surely as our
minds find expression in our bodies, and which, when
conceived of as functioning in unrestrained perfection,
is the ethical ideal in imitation of which the world, with
all the creatures contained therein, was created. From
47 E onwards, however, Plato addresses himself to the
task of examining the material universe itself, in the
hope of laying down, if possible, certain definite
principles, which may be said to govern the operations
of the universal soul in the visible world. Having given
dogmatic utterance to his conviction that vovs and
yfrvxv ai*e the ultimate cause of all phenomenal things,
he now endeavours to support it by a minute examina-
tion of phenomena. His attitude, therefore, has changed ;

5—2

6$ THE IDEAS AS 'Aptd/JLOL

all his attention is now directed towards the material
universe itself, in order that he may find therein the
proof of the belief that he has just proclaimed. This is,
indeed, the only course open to him ; it is inevitable
that he should begin with the world of time and space,
in which he finds himself. It is only through using
material objects as images that we may hope to assume
the existence of the ideas, which are the goal of all
knowledge. If we would try from the outset to look
straight at the sun, we should only make for ourselves
darkness through excess of light.

Plato, accordingly, begins this second part of the
dialogue by declaring his intention of retracing his
steps in order to set forth the nature of dvay/crj and the
irXavcofjievT] ah la, which share with vovs the responsi-
bility for the material order of things. In particular,
he is desirous of enquiring into the nature of air, earth,
fire, and water, whose existence was assumed from the
first as being essential to the materiality of the universe,
but of which no explanation has yet been given. This
new method and point of view necessitate a fresh
classification of existence, based upon a different principle
of division. Instead of having two classes, the vot\tqv
and the oparbv, the irapaheiyfia and the fxifjurifjia, we
now have three, viz., the vo^tov, the oparov, and the
vTroho^rj yeveaeco?, an elbos which is ^aXeirov and
d/jivSpov. To define this latter, the Substrate of
Becoming, is an extremely difficult task. Its nature can
scarcely be expressed in positive language ; in fact, it
cannot be described at all without calling to our aid the
phenomena of which it is the receptacle. Now we see
that fire, water, and all substances that are possessed of

THE IDEAS AS 'ApudfJioi 69

sensible qualities, are forever in a process of trans-
mutation ; water is continually changing into earth or
air, and air in turn becomes fire ; the flux is ceaseless,
and it is impossible to call any of these bodies by any
definite term, since one is never sure that it has not
already become different. But one may conceive of
something in which all these varying phenomena arise,
and to which, in virtue of its permanence, a name may
safely be assigned. In order to understand the nature
of this receptacle we may take the illustration of gold,
which in the hands of the craftsman takes upon itself
in turn all manner of forms and shapes, but which in
strictness can be termed gold and nothing else. In like
manner the virohoxv receives within itself all material
bodies, and puts on all manner of varying appearances,
while it is itself utterly devoid of body or form. This
is its sole function, and it is eternally true to that
function. The ever-varying bodies that enter into it
are likenesses of eternal existences, copied from them in
a strange and mysterious fashion which will hereafter
be explained. Meantime we are satisfied that the
universe may be said to consist of three kinds : to
jtyvofjievov, to iv Sjiyv6Tacy and to 8' 66ev atpo/xocovfjievov
<bv€Tai to yiyvofjuevov.

Here Plato pauses to answer a supposed objection.
Are you right in mentioning likenesses and models in
this connexion ? Is there, for example, such a thing as
TTvp icf)' iavTovy the likenesses of which enter into the
v7ro8oxv ? And are there ideas of all the other bodies
which we have been calling fxi^irjixaTa tcov del ovtcov ?
The answer is decisive. If vovs and Soga a\7]0rj$ are
to be eternally distinct, then assuredly there are ideas

70 THE IDEAS AS 'ApiOfiOL

of this kind, entirely separate from the sensible objects
which Ave perceive, avaiaOrjTa v<$> tj/jlcov elS?;, voovfjueva
fxovov. We therefore re-affirm our classification. There
is, first, the invisible and immutable idea, to be grasped
by vorjais alone/ secondly, its copy, which is subject to
ceaseless flux, and apprehended by aiadii<ri$, and,
thirdly, eternal x^Pa> the eSpa of all Becoming, which
is grasped XoyiafMp rtvt vo6(p. It is this %a>pa, adds
Plato, which is always perverting our judgment when
we are considering immaterial things. Because a
material body, being a perishable copy, must perforce
arise in something, in order to come into existence at
all, we must needs apply spatial relations to the ideal
world too; whereas reason should tell us that the natures
of idea and copy are so essentially distinct that the
conditions of the one are in no wise applicable to the
other.

Proceeding with his analysis, Plato goes on to say
that the v7ro$oxv> being ceaselessly filled with earth, air,
fire and water, is continually disturbed, and is subject
to a vibratory motion due to the diversity and inequality
of the bodies which enter into it. This vibration reacts
also upon the objects by which it is caused, and has the
effect of separating and sifting them, so that similar
things are gradually drawn together.

We have now to learn the explanation of the
generation of fire and the other elements, which we
were led to expect at 50 c. In order to make them as
fair as possible, the creator from the first shaped them
with forms and numbers. Now, seeing that they are
material bodies, and that material bodies require depth
and therefore surface, it is plain that these elements

THE IDEAS AS 'kptOfiol 71

have surface, of which the simplest example is the
triangle ; and all triangles may be resolved into two, the
rectangular isosceles and the rectangular scalene, which
we accordingly affirm to be the bases of the elements,
although we acknowledge that there may be apyaX even
beyond these, known to God alone, and such as are
friends of God. Our task now is to choose the figure
appropriate to each element, and to decide upon the
dpidfiol or proportions in which the constituent triangles
are combined iolov Se etcaarov avrclov yeyovev eZSo?
fcal 0; oacov avfjureaovrcdv dpcO/idov1). To begin with
fire, we find that six rectangular scalenes combine to
form an equilateral triangle, four of which may be placed
together to form the first regular solid, the pyramid.
This figure we conceive to be the typical form of fire,
and we may therefore say that fire is composed of six
primal scalenes combined together four times, or a total
of twenty-four primal scalenes. The form of air is the
octahedron, and is made up of six multiplied by eight,
or forty-eight primal scalenes. Water, which is repre-
sented by the icosahedron, is composed of 6 x 20, or
120, of the same primal triangles. These three elements,
being all capable of transformation into one another, are
accordingly furnished with the same base. Earth, which
stands apart from them, has as its element the rectangular
isosceles, which, when combined in six sets of four, gives
rise to the cube, the eZSo? of earth. Earth, then, is
formed of 4x6, or 24, of the rectangular isosceles
triangles.

This apportioning of the regular solids to the
different elements is justified by a comparison of the

1 54 d.

72 THE IDEAS AS 'Apidfioi

attributes of the figures with those of the elements
they denote. As earth is the most stable of elements,
so the equilateral triangle and the square are the most
stable of plane, and the cube of solid, figures. Fire too,
being the keenest of the four elements, is well repre-
sented by the pyramid, which is the sharpest of solid
figures.

These, then, being the figures of which fire, air,
earth and water are constituted, we must first conceive
of each of them as being in isolation too small to affect
the eye ; only when gathered together in great multi-
tudes can they be supposed to give any impression of
magnitude. Next, all these bodies, three of which
may have ceaseless generation into one another, must
be regarded as continually changing their positions,
owing to the vibration of the vttoSo^t], and as being
inevitably carried towards the others of their own kind,
inasmuch as similar things are always attracted to-
wards one another, and there is no arbitrary distinction
of " up " and " down." In the course of this vibration
and attraction it may happen that the octahedrons of
air, or the icosahedrons of water, become divided by
the keenness of the pyramids of fire, and the octahedron
thus changes into two particles of fire, and the icosahe-
dron becomes one particle of fire and two of air. Earth,
however, can only be dissolved into its parts, which
thereupon drift about till they can be united once more.
But on this principle alone it would seem that kindred
particles would speedily become associated, and all need
of further disintegration would cease. There is, accord-
ingly, another force at work, which prevents such stag-
nation, viz., f] rod ttclvtos irepiohos, which compresses the

THE IDEAS AS 'AptO/jLOL 73

matter of the universe with such all-pervading force that
no intervals are suffered to remain between the kinds,
and consequently one is continually being compelled to
interpenetrate the other. These two forces, then, the
vibration of the u7roSo%r/, and the iriXrjat^ of the
revolving universe, combine to produce eternal move-
ment and disturbance among the kinds.

The remainder of the dialogue is occupied by a
minute examination of all the kinds that arise by
combination of these four elements, together with
a physiological analysis of the senses and the bodily
functions. Within the elements themselves, we are
told, there are distinct yivrj, which owe their variety to
differences of size in the primal triangles of which they
are composed. But, apart from these, there are in-
numerable compound substances, such as stone, earthen-
ware, salt, formed of different proportions of the four
elements. Animal and vegetable bodies, both in whole
and in part, arise out of one or other combination of
fire, air, earth and water1. Marrow, bone, flesh and
sinew are all compounded in this fashion2. Everything
in the universe, in fact, as far as its materiality is
concerned, may be built up out of fixed proportions of
these ingredients.

It is now time to turn back and follow up the course
of Plato's argument in order to set down in plain
language the results at which he has been aiming. If
we are to take 50 c seriously, Plato's intention has
been to show us in some measure how the elatovra
teal itjiovra, the ever-varying flux of phenomena, may
be regarded as the representatives in space of im-
1 73 b-e. 2 74 c, d.

74 THE IDEAS AS WpiOfioi

mutable etSr/, which exist eternally and are independent
of actual relation to space and time. Our object then
must be, first, to come to some understanding con-
cerning the viroSoxr], in which phenomena are said
to arise, and, secondly, to discover the nature of the
elSr] of fire, etc., which are introduced in such an
emphatic way at 51 B. We shall then be in a position
to draw some conclusions regarding the aim and objects
of knowledge, according to Plato's latest utterance on
the subject.

Those who would interpret the Timaeus literally
seem to be disposed to treat the vttoBoxv as an actual
K€v6v, or void, like that of Democritus, in which
actual atoms did, at some prehistoric period or other,
float about in the way described. This view is of
course excluded by our general treatment of the
dialogue, but there are besides two serious considera-
tions that make it absolutely impossible to hold it for
a moment. First of all, one cannot conceive of Plato
as being willing to imitate the Atomists after the
wholesale contempt which he has poured upon them,
not only in previous dialogues, but in the Timaeus
itself1. The open enemy of the Atomists is not likely
to adopt their materialistic bases and automatic process-
es in trying to account for an orderly world. Secondly,
the whole development of the conception of the vtto-
Soxv is opposed to any such view. Plato is obviously
taking the material world as it is, and gradually
abstracting from it everything of a bodily nature.
The Kevbv is an abstract conception, which is reached
only after laborious thought ; it is not, like that of
1 See 46 d ; 55 d. Cf. Soph. 265 c, d.

THE IDEAS AS 'ApidfiOL 75

Democritus, assumed as the primary condition of the
universe. From pages 49 A to 51 B, which are devoted
entirely to the gradual unfolding of the notion of %copa,
we learn that it is that which remains of the material
world when it is divested of all body, shape and
quality. It is that underlying principle which remains
permanent amid their everlasting mutability, and may
be illustrated by the example of gold, upon which all
manner of shapes are continually impressed and as
continually obliterated. It is plain that Plato's whole
endeavour here is to get a firm grasp of the notion of
space by abstraction, for he can only conceive of it by
ridding his mind of the actual world he sees. So far
from describing a material process from space and
atoms to actual existence, he presents us here with
a logical progression from actual existence to space
and the geometrical elements.

What then is the nature of this %wpa, when it has
at length been reached ? Enough has been said to
show that it was not intended for an actually existent
void. Let us, therefore, try to elicit from Plato's
further treatment of the subject some information
regarding its nature. Plato, having conceived the
notion of the substrate, immediately fills it with
certain elementary triangles, which combine in certain
fixed modes to form figures, which are the apxaL °f
the four elements and their combinations. Xcopa also
allows of the activity of certain forces, which unite to
keep the dpxai in a state of continual disturbance.
Now, these rpiycova are manifestly the plane triangles
of geometry, the perfect, ideal triangles which the
crude triangles of our diagrams affect to represent,

76 THE IDEAS AS "KptOfjuoi

the del ovra of Republic 527 B, which are a stepping-
stone in our mental progress towards the I8ea rdyaOov.
This conclusion is not only the natural inference from
Plato's express statement at 53 c, where he makes it
perfectly plain that the geometrical laws conditioning
the perception of solids are his sole consideration, but
it is the only explanation that tallies with the details of
Plato's exposition. Mr Archer-Hind, at pp. 203, 204
of his edition of the Timaeus, has pointed out that no
solid bodies could fulfil the requirements made for the
pyramids, octahedrons, and other figures in c. 22. Two
solid pyramids could not possibly be transmuted into
a solid octahedron, but, according to the geometrical
law regulating pyramids and octahedrons, two pyra-
mids consist of eight equal planes, and thus supply all
that is theoretically necessary to the constitution of an
octahedron.

The triangular planes, then, and the figures alike
are to be conceived of as the ideal triangles and figures
of geometrical definition, the perfect and immutable
laws which form the foundation of the sciences called
geometry and stereometry. They are eternal and
immutable, in contradistinction to phenomenal things
which are apprehensible by the senses alone ; and yet
they are iroWd, inasmuch as their multiplication is
theoretically essential to the production of more ad-
vanced figures. These, then, are the arj^fiara which
Plato's viroho'xr) is destined to contain, and, difficult
though it be to define its nature, we are assured
that our explanation of it must be consistent with
the nature of the rpiycova, and the more complex
etSrj, which it is made to contain. It is, accordingly,

THE IDEAS AS 'AptOfioi 77

impossible either to regard the v7roSoxv as an actual
void, or to connect it directly with the world of
ytyvofieva at all; Plato has indeed taken great pains
to divest it of all trace of the phenomenal. It is an
ideal x^Pa> the X°^Pa w^ich is logically necessary for
the operations of the ideal rpcycova and TrvpafdSe? of
true geometry ; it is a %ft>pa which exists in the mind
alone, Xoycp TrepiXrjTTTov.

It will be remembered that we noticed some attempt
at a similar analysis in the Philebus. There Plato
conceived of the vXtj ig ov yiyveTai to irav as sensible
qualities, abstracted from the objects in which they
were made to inhere by the mind. But the distinction
between the vXrj e£ ov and the vXtj iv & was evidently
unconsciously present to his mind, for he spoke of a
ehpa, in which these qualities (to /jl&XXov re /cat tjttov)
arise, so that in the background of his thoughts there
was evidently the notion of a vXrj iv & as well as of a
vXt) e£ ov. In the Timaeus the sensible qualities, the
vXr) it; ov, have been entirely superseded. Plato seems
to have become more and more convinced of their
relative and secondary character. At 61 E ff. he informs
us that all such qualities are simply the varying effects
which the different structures of the elements make
upon our senses. He appears to have examined these
qualities, and to have discovered that they may all
ultimately be reduced to two, or rather that they all
depend ultimately upon the principle of two, viz., to
fiel^ov /ecu apbucpoTepov. Spatial extension and size are
the fundamental attributes of everything bodily, and
accordingly we may in our present examination discard
vXr) il; ovy and concentrate our attention upon vXrj iv

78 THE IDEAS AS 'KpiOfioi

w. It may be noted that Aristotle1, ignoring Plato's
ultimate rejection of antithetical qualities as vXrj, chose
out hot and cold, wet and dry, as the proximate vXrj of
material bodies, probably in imitation of the Philebus.
The Tpiycova of the Timaeus were not calculated to
appeal to his practical turn of mind.

As Plotinus2 indicates in the Enneads, one thing
may be said to be in another quite apart from any
question of spatial relation, just as many things in-
here in mind, and hence the v7ro8oxv possesses only a
(jydvracrfjLa of 07/co?. From chapter 20 onwards, there-
fore, we have before us the conception of geometrical
space, containing within itself the dtSta rpiycova, and
the figures formed of these, which are the ideal counter-
parts of the four elements of the universe ; and these
apyai inhere in it not in a state of rest, but they are
evermore subject to two forces, which Plato felt to be at
work in the material universe. The vibration and the
iriXricrLs, too, have been abstracted from the confusion
of the visible objects which they are seen to affect, and
transferred to a geometrical region where their opera-
tions may be viewed in the clear light of the intellect,
and set down in fixed and unambiguous formulae. One
is forcibly reminded of the ov ra%09 and the ovaa
fipaSvrrjs of Republic 529 D, also of the true heavens,
wherein there moved true stars. Plato's whole object
in this exposition of physical phenomena has been to
arrive at exactitude of some kind, to be able to state in
some fixed language the principles of order that underlie

1 SeeAr. de gen. et corr. B. 1. 329 a 24; 2. 329 b7; 3. 330 a 30.

2 Plotinus, Enneads ii. 4. 11 (xii. 11 Kirchhoff).

THE IDEAS AS "KpiQjXOi 79

the yty vofieva of the universe. Hence the whole totality
of physical yevecris has been translated into ideal being
in terms of mathematical and geometrical relations.

If this be so, what are we to say about the ideas of
fire, etc., to which special attention was drawn at 51 B ?
In considering this question we should bear in mind
continually the fact that Plato's point of view has
changed since we last heard of ideas at 39 E, and that
the three-fold classification into ov, yiyvopuevov, and
vnrohoxv must needs affect to some extent our view of
to ov. For to ov is now the father, and %(£>pa the mother,
ofyeveais ; the idea is not wholly responsible for its copies,
but must enter into relation with x^Pa f°r their pro-
duction. The idea, accordingly, must be expressed in such
terms as would render the simile appropriate. The
function of the v-iroSo^rj is to afford room for yeveais ;
it is the recipient of all that is spatial ; the idea, then,
must be conceived as far as possible in terms consistent
with spatial relation. Plato, immediately after he has
affirmed the existence of ideas of fire and the rest,
proceeds to give an account of the Starafjis, or arrange-
ment, of each of these bodies. Fire, it is discovered,
has as its intelligible apxv the pyramid, and the
pyramid is inevitably composed of four sets of six
primal scalene triangles. Similarly, the octahedron and
the icosahedron, being the apyai °f air an(i water
respectively, are the result of the combination of eight,
and twenty, sets of six primal scalenes. Earth has for
its apx*l the cube, to compose which six sets of four
rectangular isosceles triangles are always required. ,Thus
the law governing fire -form at ion is that 24, or 6x4,
primal scalenes shall combine to form a pyramid, the

80 THE IDEAS AS "AptOfjioi

dpxv of foe. Air, water, and earth are likewise subject
to similar laws ; and Plato, by taking up every variety
of material body and substance in turn, might have
found similar laws to regulate them all. In the case of
stone, flesh, bone, and the like, he has shown us how
the principle works out. The more complex structures
of the bodies of animals, however, have not been
directly dealt with, but that Plato conceived them too
to be composed of primary triangles combined in
varying ways is obvious throughout the physiological
discourse.

These material laws, then, that govern all the kinds
within the material universe, I hold to be the ecSy i^
eavToov mentioned at 51 B. Such a view finds confirma-
tion from many sources. First, one cannot but feel that
material bodies such as fire, air, water and earth, and
their combinations, which exist simply to be perceived
by sight and touch1, and are mere modes of matter,
stand on quite a different footing from the fe3a, that
have within them the very principle of life, and should,
therefore, receive a different treatment. We cannot,
accordingly, include these ideas of fire and the like
among the first-mentioned ideas of 39 E, the vorjra £o3a,
which were special aspects of the supreme and ever-
active vovs. At the same time, though the elements
are not as intimately connected as the £g3<z with the
great alria, voi>s, that underlies all phenomena, they
are none the less eternal manifestations of noetic force.
The 0€os made them fair, and brought them into order
according to definite and eternal laws. These laws,
therefore, are not unworthy of the title of etBrj ; they

1 31b.

THE IDEAS AS 'ApidfJiOl 81

are unbegotten, imperishable, invisible, objects of
thought alone.

Secondly, our investigation of the Philebus resulted
in the conviction that the ideas there were to be found
in the class of fierpia, the eternal laws of proportion,
which depend for their realisation on mathematical
Trocrd. All existing fiucra, we found, could be resolved
into two elements, of which the v\rj of sensible qualities
was one, and the ideal law of proportion the other,
while universal vovs, as alria rr)<; /u£e<«>9, was the
reality yet further back to which their existence could
be traced.

A third confirmation lies in the fact that the ecSrj
as dpcO/jiol were a phase of the ideas which attained
considerable importance in the later days of Plato's
school, and which was always said by Aristotle to have
originated in the teaching of the master himself, in
spite of all the accretions of the Platonists that tended
to obscure it. A minute analysis of the evidence on
this point awaits us in a later paper; but it is quite
clear that these formative laws are nothing else but
dpi0fioL Each elSos is said to consist of definite
dpi0/jLoi, or proportions, of primary triangles, and Plato
himself uses the word twice in his exposition of the
subject (etSeal re teal dptdpiol^, 53 B; ig oaoov av/jL7re-
aovrcov dpiO/n&v, 54 d). All these chapters, indeed,
breathe the spirit of the mathematician. Never since
the Republic has Plato given the subject so much
attention, or assigned to it so lofty a function.

Finally, have we now reached the limit of human
knowledge ? From the first the eiSrj ifi eavrdov were to
be objects of human knowledge, and now the possibility
w. 6

82 THE IDEAS AS 'AptOfMOL

of knowing them has been realised beyond dispute.
But are we to stop there ? Are we to be content with
knowing the fixities inherent in matter, eternal and
immutable though they be, and never penetrate
further ? We were told in the earlier part of the
Timaeus that there was an ultimate airia for all
Becoming, a irapdhecy/jLa for all creation. Is this ever
to be known or realised ? There are considerations
which seem to show that Plato did not despair of
attaining even this ambition. It must be remembered
that Plato has been trying to work back to the
subjective dpyal °f matter, and has reduced the
various material kinds to the primary notions on
which our apprehension of them, as matter, depends.
After all, dpidfioi, though they prove to us the presence
of vovs in the world, are not in themselves ultimate ;
number is simply a necessity of our mind, as essential to
its working as the categories of Same and Other. Hence
Plato, in resolving matter into dptOjjioi, has resolved it
into its subjective factors, thereby taking us to the
limit of the analysis the finite mind can reach. May
mind, qua infinite, go a step further, and pass beyond
the subjective dp^al to the absolute dp^v of all ? At
53 D we are told : ra$ & ert tovtwv dp^ds dvcoOev Oebs
oZSe, teal dvSpoov 09 dv etce'iva) fyiXos fj. In this we can
only see a hope that the human mind may some time,
somehow, through a diligent pursuit of the etBrj as
dpiOfiol, rise to a still higher form of knowledge, and
know by direct intuition the votjtov £coov and the
vorjrd £wa, which represent the ideal in its highest
form. As in the Republic, dpcOfjiol are to be the
stepping-stones to the realisation of the Good ; but the

THE IDEAS AS 'ApcdfMOL 83

apc0/jLol have now a greater importance than formerly,
since they represent the highest actual point which
human knowledge has yet reached. Ac6 Bij, says Plato,
XPV Sv alrias ecSr] Siopu^eaOat, to fiev avay/calov, to
8e 6elov, kcli to /Jbev Oelov ev airaac ^r/Telv kttJ<j€oo<;
€veica evSatfiovos ficov, tcaO' ocrov rjficov rj (pvarts ivSe^eTac,
to Se dvay/caiov i/ceivcov y&piv, Xoyi^o/xevov, a>? dvev
tovtcov ov SvvaTCi avTa i/celva, i<f> ols o~7rovSd^ofji€V}
nova KCLTavoeiv, ovS av \aj3elv, ovh" aWco? 7TO)?
jjb€Taax€W- (68 E — 69 A1.)

Before we conclude the subject of the apiQyioi,
there are two points which would seem to demand
some further elucidation. The first is concerned with
the objective reality of space. We realise that the
X<*pa of the Timaeus is not an actual void, but an ideal,
mathematical x^pa. May we then draw any conclusion
as to whether Plato considered space to have independent
existence, or whether it was to him a mere illusion ?
Here, of course, one feels the inappropriateness of making-
Plato speak in Berkeleian phraseology, and yet it is
impossible to suppose him to believe that space was
anything in itself. The whole universe, and time too,
are always but shadows that appeal to the senses alone.
Fire, air, water, and earth, which constitute the material
universe, only exist for the sake of being seen. Qualities,
which, after all, are what we have most in mind when
we allude to the material world, are just affections of our
senses, caused by something, it is true, but by something
of alien nature to the things we see. When one divests
the universe of these qualities, one has left indeed the
vttoSoxv yevecreoy^, the hvvafiLs of yevecns, within which

1 Cf. 59, 60.

6—2

84 THE IDEAS AS 'Kpt9fioi

to reconstruct ideally the eternal principles of matter,
but this has no objective existence ; it is a (pdvraafjba.
With the reduction of qualities to their subjective
factors, one rejects the independent reality of the whole
material universe, and consequently of extension too,
for extension can never have actual existence apart
from extended objects.

The second subject referred to is that of the doiovra
kclI i^Lovra, which have usually been identified1 with
the /maOrj/jbari/cd, or rpiycova, of c. 20. This identification
I believe to be impossible for the following reasons. In
the first place, there is nothing whatever in the actual
context of 50 c to lead one to associate the elatovra
teal i^iopra with fia 0tj fiar lk a at all. There has as yet
been no mention of geometrical forms. Plato's sole
aim here is to reach a conception of pure space by
stripping the world of every visible and variable
quality. Space is that ev w iyyvyvofieva del etcaara
avToov (pavrd^erac koX irakiv iiceZOev diroXkyrat^. It is
f) rd TrdvTO, hexo^evq croo/jLara cj)v(TL<;d, which nevertheless
fiop(f)rjv ovSe/jblav irore ovSevl rdov eiatovrcov ofioiav
€t\r)(f)€v ovhafifj ovSa/jLws*. Hence it is not a question of
triangles at all, but of ytyvofieva, which are in continual
flux.

Secondly, the triangles are not elcnovra teal igcovra;
they do not come into being and vanish, for they are
regarded as filling up every nook and cranny of the
vtto8oxv> so tlmt} void may be as far as possible non-
existent. To this it may be replied that the particular
combinations of triangles — pyramids, octahedrons, and

1 e.g. Adam's Republic, vol. ii. p. 161.

2 49 e. s 50 b. 4 50 c.

THE IDEAS AS 'AptOfjLOL 85

the rest — come and vanish ; but even so the vttoSoxv
does not rid itself of fjuaOrj /xan ted, the constituent
triangles being always constant1, and the cube does not
suffer destruction at all. How could the elaiovra teal
e^uovra, which are admittedly always coming and
going, be identical with fiadrj part ted, or the Trepas
e^ovra of the Philebus, which are directly opposed to
that which is in flux ? The eiatovra teal igtovra are
akin, if to anything, to the direipa, which are subject
to unceasing fluctuation. But fjuaOrj/jLarcted represent
measurement and definiteness, and are of a totally
different nature.

Thirdly, mathematics have always held an exceed-
ingly high place in Plato's esteem, their objects being
del ovra, and akin to the ideas. It is inconceivable that
he should here degrade fiaO^fiartted to the level of
phenomena, and say that they are merely, like them,
jjUfjLrjIiaTa to)v del ovrcov 2.

The reason why these elaiovra teal egtovra have been
taken for naOrj panted is apparently that they have been
confused with the fiopfyal and axv^^cc which occur in
the simile of the gold, which is employed as an illus-
tration. In the simile the shapes impressed on the
gold are the counterpart of the elaiovra teal e%i6vray
because the gold has to correlate with the substrate ;
but since the substrate has to be devoid, not only of
shape, but quality of every kind, it is impossible to con-
clude that shapes alone are supposed to enter, and
vanish from, the virohoxrj. Plato certainly does not say
so ; he calls the viroho^rj 77 rd irdvra Se^o/juevr] acofiaTa
<f>v<TL<;, and the ao^/jbara that come and go are generally
1 56 d. 2 50 c.

86 THE IDEAS AS 'ApiOfJLOL

styled ra elatovra /cat i^iovra. The use of i8ea and
eZSo9 occasionally at 50 D, E, and 51 A, need not be taken
to imply that shape alone is intended, since the language
here is particularly affected by the simile of the gold
previously referred to, and form is for the nonce regarded
as the typical attribute of body. The simile of the
unguents1, to produce which varied scents are imparted to
a scentless fluid, apparently serves Plato's purpose just
as well as that of the gold. Shape, consequently, is not
the essential point in the simile ; if any further proof
were wanted, the final moral of the passage at 51 A should
suffice : Sid Srj ttjv tov yeyovoros oparov ical iravro)^
ataOrjTOv fjarjrepa /cal vttoBo^tjp fjbrjre yrjv /mrjTe depa

/JL7]T€ 7TVp /JLT/Te vScOp \€<y(D/ji€V, /JL7]T€ OCTCl €K TOVTCOV, firjT6

ef cop ravra yeyovev (i.e. the qualities of the Philebus).
That is, the elacovra koX i^tovra of the vttoSoxv^ as
opposed to those of the gold, are visible air, earth,
fire, water, and their constituents and compounds, not
/jLa0r)fjLaTLfca at all.

Looking backward over the road that we have
travelled since a theory of knowledge was first stated in
the Republic, we find that Plato has done much to justify
the hope which he there set before us. The dialectician
was to start from the world of sensible objects, and,
through the continuous assumption of immutable elhrj,
rise to the highest idea of all, an apxv avwirodeTos. In
the interval he has concluded that many things of which
he then posited ecSrj are but instruments to help us
along the road to knowledge ; they can never serve as
its end and goal. Antithetical qualities, for instance,
are but the terminology of the senses. The Good and

1 50 e.

THE IDEAS AS 'Apcd/JLOi 87

Beautiful are, generally speaking, the leading predicates
of the science of aesthetics. The categories of Same
and Other are not ideas, though they are of the utmost
importance to the operations of vovs and acadrjat^ alike.
They are the basis of all classification, and through them
alone can we hope to climb the ladder of knowledge at
all. They are the foundation of the mathematical
sciences, which lead us to the very forecourt of the
dya06v, and which, in default of the dyaOov itself,
furnish us with intermediate elh-q. He who would
make the ascent to the supreme idea must, there-
fore, begin with the scientific classification of the
objects of sense, through which such information and
intellectual power may be acquired as to enable him to
posit the existence of mathematical ideas, hypotheses
whose truth can only be assured when they have found
confirmation in the dpxv dwrroderos. Having attained to
them he already has an ideal explanation of phenomena,
and by diligent study he may hope to imitate in ever-
growing perfection the motions of the dXrjOivo? ical
deios 1/01)9, and realise in some degree the end and aim
of being, the dyaOov, b S?) Sido/cec fxev airaaa ^f%?} teal

TOVTOV €V€/Ca TTaVTCL 7TpdTT€C, d7TOfiaVT€VOfl€Vr] TL €LVCU,

diropovaa he teal ovtc eyovcra \a/3elv l/cavoos ri ttot early
ovhe TTiGTei xprjaaadaL /xovifMcp, 01a teal irepi rd\\a, hid
Tovro he diroTvyydvei /cat twv dWcov, el rt o<pe\o$ tfv.
(Rep. 505 E.)

ESSAY V.

THE PYTHAGOREAN *Api0fiol AND THEIR RELATEON
TO THE PLATONIC IDEAS.

The subject of Plato's indebtedness to Pythagorean
philosophy is one which most authorities agree to disre-
gard and minimise as far as they consistently can. This
is due partly to the fact that the mists of neo-Platonism
and neo-Pythagoreanism, creeping in between Plato and
ourselves, have so obscured the original outlines of the
two schools that it seems well-nigh impossible to discover
where Pythagoreanism ends and Platonism begins, and
partly to the difficulty one always experiences in trying
to elicit from Aristotle, our only accredited witness, any
unbiassed account of previous schools of thought. The
whole question, in fact, is one that calls for the exercise
of the critical faculty rather than the laborious collection
of evidence. In the present paper, therefore, I do not
intend to investigate and catalogue the latent resem-
blances between the two schools so much as to indicate
the great advance which was made by the theory we
were last considering upon the early fancies of the
Pythagoreans. My first task will be to try to come to
some definite conclusions as to what the Pythagoreans
really held ; my second to compare their views with the

THE PYTHAGOREAN 'ApiOfjbOL 89

mature doctrine of dptO/jLol which Plato had reached in
the latter half of the Timaeus.

The evidence for the genuine beliefs of the Pytha-
goreans is perforce restricted to that afforded by
Aristotle in various parts of his Metaphysics. All other
writers, such as Strabo, Stobaeus, and Alexander
Aphrodisiensis, who give details concerning their
doctrines, lived at too late a date to escape the con-
tamination of the neo-Pythagorean craze of the first
century B. c. Confining ourselves then to Aristotle, let
us set down the substance of the Pythagorean doctrine
as stated in c. v. of Metaphysics A and elsewhere.
From the earliest times, we learn, the Pythagoreans
were expert mathematicians, and their chief, and,
perhaps, earliest, dogma was that all things are number.
To quote the account in Metaphysics N1 : "The Pytha-
goreans, because they perceived many of the attributes
of numter~totnTiere in visible bodies, held that existing
things were numbers ; and these numbers were not
separate from, but immanent in, things. And why ?
Because numerical relations are inherent in harmony,
and in the heavens, and in many other things.' We
gather, then, that Pythagoras and the Pythagoreans
were impressed by the potency and utility of number,
in the first instance, through their mathematical and
musical experiments. In music, Pythagoras himself
had tested its value by his discovery of the chief
intervals of the scale2 : the quality of different notes was
found to depend upon the proportionate lengths of the
monochord which was struck to produce them. Philolaus,
their great astronomer, had made plain the intricate
1 Met. N. 3. 1090 a 20. 2 Cf. Diog. Laert. viii. 12.

♦••

90 THE PYTHAGOREAN 'ApiOflol AND THEIR

harmony and regularity with which the heavenly bodies
performed their courses. It was borne in upon them
in general that the numerical properties of a thing were
its essential attributes, the most definite account that
could be given of it. Consequently they were led to
affirm boldly that things are number, and that the
opposite characteristics that appertain to things are but
varieties of the ultimate opposition of odd and even.
We are told in Metaphysics A, c. v., that some Pytha-
goreans, notably Alcmaeon of Croton, resolved number
into two constituents, the odd and the even, or, in
geometrical terms, the finite and the infinite, and
declared that these constituents, under a variety of
names, were the constituents of all existing things.
Alcmaeon was so interested in this point that he drew
up a lengthy table of the most striking oppositions of
this kind ; and the antithesis in the first column was
invariably regarded as the source of good, that in the
second as the origin of evil, in the things which it helped
to constitute.

But what was their precise meaning when they said
all things are number ? Aristotle tells us plainly enough
that they regarded numbers as the material cause of
things1, and that the numbers, instead of being yodpiaTa,
were actually immanent in the things themselves ; nay,
the things were number. He thereupon proceeds, in
c. viii.2, to draw a ludicrous picture of the Pythagorean
universe, in which the absurdity of the theory is made
manifest. The Pythagoreans, he says, made the whole
universe to consist of number, and it was primarily the
heavens, the heavenly bodies, and all the inferior objects
1 A. 6. 987 b 27. 2 A. 8. 990*19.

RELATION TO THE PLATONIC IDEAS 91

of perception, that they sought to explain by an elaborate
use of their dpyai Even thus far one can scarcely
follow them, seeing that they leave motion entirely
unexplained ; but what are we to think, says Aristotle,
when they extend their theory even to things that are
higher in the category of reality than visible objects, to
abstract conceptions, to 86%a, tcaipos, dhiKia, Kpicns or
tufys? For they have shown conclusively that each
of these, too, is a number. How can we accept this,
knowing that there is only one kind of number, that of
which external nature is composed? One would expect
to find at least two different classes of dpiOfjuol, one
appropriate to visible objects, and another to be reserved
for vorjrd. Are we to imagine a universe in which are
to be found, not only the numbers of all alaOrjTa, but
the numbers of all vorjrd too ? Dire overcrowding would
be the result ; yet they cannot surely refuse to admit
into their world the number of 86%a} when they say
that all numbers alike have fieyeOos, and are inseparable
from the world of sense.

This criticism unmistakeably breathes the Aristo-
telian spirit. One instinctively feels that the writer is
not only captious, but biassed by his scientific point of
view, and that one may be reading a mere travesty of
Pythagorean ideas. One has only to recall the material-
istic account of the ^v^oyovia of the Timaeus1 to realise
that the most philosophical conceptions may at times be
set down by Aristotle as sheer materialism. It is, there-
fore, imperative to examine Aristotle's statements
regarding the Pythagoreans thoroughly before accepting
them as an authentic account of the facts.
1 De An. A. 2. 404 b 16.

92 THE PYTHAGOREAN 'Aptd/nol AND THEIR

First of all, he classes the Pythagoreans with the
Ionian nature-philosophers as seeking for reality in
alaOrjTa rather than in vorjra, and then immediately
taxes them with inconsistency in admitting vorjrd into
the sphere of their studies, and accounting for them on
the same principle as alaOrjrn. Now if the Pytha-
goreans tried to account for voijrd and alaOrjrd alike, it
is at once obvious that Aristotle has little or no justifi-
cation for classing them with the nature-philosophers of
Ionia, who concerned themselves with alaO^rd alone.
Quite apart from the question whether their explanation
of things sensible and spiritual was reasonable or not,
the mere circumstance that they took account of
spiritual phenomena is sufficient to separate them from
the early Ionians, and in all probability Aristotle is doing
them an injustice in criticising them as if they looked
at things from the same point of view as these. The
fact that Aristotle at the beginning1 cites as typical
examples of their dpid/juol the numbers of Stfcaioavvr],
/cacpos, and vovs, and never instances numbers of sensible
things, shows that spiritual phenomena were no mere
appendage in their system ; they cannot have been
introduced, as some think, as "a mere sport of the
analogical fancy2." In fact, I regard this two-fold
application of the Pythagorean numbers as the funda-
mental objection to any view which makes them in any
sense a materialistic system.

The opposite theory, however, is so strongly main-
tained by Prof. Burnet in his Early Greek Philosophy
that it would be as well to consider for a moment the

1 Met. A. 5. 985 b 29.

2 See Burnet, Early Greek Philosophy, p. 317.

RELATION TO THE PLATONIC IDEAS 93

arguments by which he supports it. His opinion is
based mainly on the belief that the Pythagoreans were
the originators of the doctrine that the point is identical
with the monad or unit, that the line, being the first
increase of the point, is duality, that the surface is the
increase of duality to the number three, and so on.
Thus, by identifying the point with the Pythagorean
monad, which, according to Aristotle l, had fjueyetfos, and
regarding the line as the material increase of this to two
units, Prof. Burnet thinks a reasonable origin may be
found for Aristotle's statement that the Pythagoreans
made number the material cause of things. But surely,
if a point be regarded as having fjueyeOos, it is to all
intents and purposes not a point, but a solid body, and
the three increases from point to line, from line to
surface, and from surface to solid, are no longer neces-
sary to produce a three-dimensional body. Therefore,
although it is possible that the Pythagoreans 2 had not
yet reached an abstract conception of the point, the
line, or the surface, I cannot agree that they held the
view indicated by Prof. Burnet. On the contrary, the
resolution of the point into the monad, and of the line
into duality, would naturally belong to a period in which
the science of geometry had been subjected to speculative
analysis ; and this period could hardly have been that
of the Pythagoreans, seeing that Aristotle himself
agrees that they were entirely unversed in logic3, or
dialectic, in any degree. It is far more likely that the
view in question arose in the time of Plato 4, or that of
his immediate predecessors.

1 See Met. M. 6. 1080 b 20, 32 ; M. 8. 1083 b 13.

2 See R. and P. 105 a.

3 Met. A. 6. 987 b 32. « Cf. Rep. 528 a sqq. ; Laws 894 a.

94 THE PYTHAGOREAN "ApiOfMol AND THEIR

Moreover, when one comes to examine the evidence
for this so-called spatial character of the Pythagorean
theory, it is found to consist entirely of Aristotelian
references which either do not apply conclusively to the
Pythagoreans, or are to be discounted either because of
Aristotle's materialistic bias, or for other reasons. The
references in which Aristotle1 is supposed to say that
the Pythagoreans identified the line with duality
cannot by any stretch of language be proved to point to
the Pythagoreans ; on the contrary, the text seems to
indicate that the later Platonists alone can be intended,
and the same criticism applies to the passages2 in which
the Pythagoreans are supposed to make the monad and
the point identical. As for the statement that the
monad or unit, according to the Pythagoreans3, had
/jieyedos, here Aristotle is simply telling his old story
over again, and representing the Pythagorean number
as a material basis, without inspiring any additional
confidence in his view, or taking account of the funda-
mental objection which was mentioned before. The
passages in Aristotle's Physics4, in which the Pythago-
rean void is identified with the aireipov, prove nothing,
since the term aireipov might quite well be applied to
the void without indicating necessarily that the airetpov
is inevitably a res externa, or that number, of which it
is sometimes a vToiy/iov, is invariably, or originally,
spatial. The reference to Eurytus5, in which the latter
is said to have tried to arrive at the numbers of man,

1 Met. Z. 11. 1036 b 12. Cf. de An. iii. c. 4. 429b 20; de Caelo a.
1. 268a7.

2 Met. Z. 2. 1028b 16. 3 See p. 93.

4 Phys. T. 4. 203 a 7 ; A. 6. 213 b 23.

5 Met. N. 5. 1092 b 10. Cf. M. 8. 1083 b 18.

RELATION TO THE PLATONIC IDEAS 95

horse, etc., by sketching their outlines, and counting
the number of pebbles required to produce them, comes
nearest to supporting Prof. Burnet's theory. In isola-
tion, however, it cannot be said to carry conviction,
since, in the first place, the process described is
extremely obscure, and it is hard to say exactly what
Eurytus was aiming at, and, secondly, one can quite
well imagine the Pythagoreans using childish methods
of this kind to arrive at the numbers of concrete things,
without asserting that their whole theory arose in this
way. The particular method ascribed to Eurytus was
very likely only one of the ways which the younger
Pythagoreans employed to give the master's theory a
universal application. I cannot, therefore, regard any
of this evidence as conclusive in proving that the
number-doctrine had a spatial or geometrical origin.
It will appear that little or no satisfaction is to be
had by regarding the Pythagorean philosophy through
the eyes of later schools. A truer insight, it seems to
me, may be gained if we go back in thought to a period
anterior to that of Pythagoras himself, and endeavour
for a moment to view him rather as the heir of Egyptian
and Babylonian mysticism1, than as the forerunner of
Plato. Here, of course, one is approaching a field of
research which is as yet only beginning to yield definite
results, and from which a rich harvest may be expected
in the future. Sufficient evidence, however, is to be

1 I am of course using " mysticism " here in the sense in which it
is most applicable to Eastern beliefs, as the association of divinity
with certain material symbols for purely fanciful reasons, quite apart
from any intellectual process. (See Inge, Christian Mysticism,
Appendix B.)

96 THE PYTHAGOREAN 'Api6fiol AND THEIR

found in hieroglyphic and hieratic literature 1 to make it
practically certain that the Egyptians in ancient times
attributed not merely to numbers but to the spoken
word in general a curious and mysterious potency which
is wholly foreign to western nations. In the Pyramid
Texts, in fact, we find mentioned a god called Khern,
i.e. "Word" (compare \0709). That which to us is simply
an instrument of expression, created by man to serve the
necessities of human intercourse, was regarded by them
as belonging to an independent order of existence with
a vitality of its own, and endowed with all the at-
tributes that compose the description of a living thing.
The "word" had a personality like that of a human
being2, and, provided it were pronounced in the proper
manner, and in the proper tone of voice, was powerful
in the service of him by whom it was uttered. The
creation of the world was due to the interpretation in
words by Thoth of the will of the deity.

Number especially seems to have been invested by
the Egyptians with these peculiar powers. By the
four-fold repetition of their curse-formula, under proper
conditions3, the speedy realisation of their desires was
ensured. This potency of four is connected by some
with the gods of the four points of the compass, but it may
have a far less obvious explanation. Their all-powerful
and beneficent deities were classed mainly in groups of
odd numbers4, especially of nine and seven, and, of course,
the famous three. This preference for odd numbers in

1 See Dr Budge, Egyptian Magic, preface, pp. x., xi.

2 See Dr Budge, translation of Book of the Dead, p. 147.

3 Dr Budge, Egyptian Religion, p. 107.

4 Dr Budge, Egyptian Religion, pp. 89-91.

RELATION TO THE PLATONIC IDEAS 97

representing divinity seems to indicate that the odd
numbers had with them, as with the Pythagoreans after
them, a pre-eminence over the even as being a power
for good. Seven also played an important part in their
rites and ceremonies. The Book of the Dead tells of
the seven Arits or halls1 in each of which three gods
were seated, guarded by seven doorkeepers, seven
watchers, and seven heralds, and of the seventh formula
which, when recited, procured entrance at the door of
any one of the seven mansions of Osiris.

The Babylonians, too, apparently, gave special
prominence to number ; like the Pythagoreans they
realised its value in the practical sciences of calculation,
and they also regarded it as of mystical significance.
There is evidence to prove2 that their multiplication
table was remarkably well-developed, that they counted
up to 12,960,000, and that their tables of weights and
measures were very far advanced. Their measurements
of time seem to have been based on the division of the
zodiac into twelve parts3 : thus the Babylonian day was
made to consist of twelve double-hours, as the faces of
our clocks still indicate. That they assigned magical
properties to number and preferred one number over
another is plain from the fact that they invariably
regarded some days as lucky, others (particularly the
seventh) as unlucky. The importance of the number
seven, not only among the Babylonians, but with the
Eastern nations generally, is of course abundantly

1 Egyptian Magic, p. 165.

2 See Hilprecht, The Nippur Expedition, pp. 28 ff.

3 Cf. Winckler, Die Weltanschauung des Alten Orients (Leipzig,
1903).

w. 7

98 THE PYTHAGOREAN 'ApcOfjiol AND THEIR

illustrated in the Old Testament writings — in the seven
towers of Babel, and the numerous repetitions of seven
in the instructions regarding Jewish ritual (e.g.
Leviticus 4. 6; 14. 16, 51; Numbers 23; Ezek. 40.
22).

Now, although the evidence which has as yet come
to light is but slight, it is at least clear that the
Egyptians and Babylonians assigned to number a great
importance, and attached to it the functions of an
independent agency in a fashion that appears strange
to western minds. They regarded it as something
endued with power to heal or to harm, to create or to
destroy, according as its nature, being good or bad,
prompted. Like the " word," it could be described by
attributes, favourable or unfavourable, such as were
applied to human agents themselves. If this, then,
was the general attitude of the East towards number
in ancient times, if it was regarded almost with the awe
and reverence due to Deity itself, it would be little
wonder that there should arise a school, peculiarly
subject to Oriental influence, whose leading tenet was
that number is the sole arbiter of life. There is no
need to prove that Pythagoras ever had actual dealings
with Egypt, Babylon, or any other Eastern country ; it
is undeniable that his system was chiefly a farrago of
religious and mathematical precepts, which are ana-
logous to Eastern, rather than Hellenic, thought.

The remarkable importance assigned by the
Egyptians to the more general "word" seems to
have borne fruit at a later time, and to have led,
directly or indirectly, to a form of the Heracleitean
philosophy which gave to words and names a per-

RELATION TO THE PLATONIC IDEAS 99

manence which was denied to the visible things of the
universe. The Heracleitean Cratylus1, who thus saw in
ovofiara the inmost reality of the fluctuating objects of
sense, could not conceivably be termed a materialist.
Why then should Pythagoras, the heir of Egyptian and
Babylonian mysticism, be accused of materialism for
declaring that numbers, to which the learned people of
the East had always attributed the greatest magical
significance, are the truest reality of things, that things
are really number ? An assertion of this sort did not
necessitate any art of ScaXeKn/ctj, which we know
Pythagoras lacked ; to make it there was needed only
the impetuous logic of the religious enthusiast, which
Pythagoras certainly was. The induction which he drew
was neither that of the physicist, nor of the philosopher,
but that of the mystic.

My contention, therefore, is that the Pythagorean
doctrine described by Aristotle is far more reasonably
regarded as the natural development of a mystical view
of numbers than as a truly philosophical or physical
system. Aristotle, impatient as he was of everything
pertaining to the occult, might quite well describe such
a system in the obscure and self-contradictory language
which we have noted. The point upon w^hich he insists
throughout is that the Pythagorean numbers were not
abstract conceptions (xcoptard), like those of Plato.
The Pythagoreans had not, in fact, advanced sufficiently
in scientific speculation to make the abstract calculations
of our own time : when they counted it was always
apparently with a reference to external objects of one
kind or another. Aristotle, therefore, concludes that
1 See Plato, Cratylus 386 d, e ; 390 d, e.

7 9

100 THE PYTHAGOREAN 'ApiOfiol AND THEIR

their doctrine that things are number can only mean
that number was to them a material cause, and that
each unit had a {leyedos which contributed to the bulk
of the thing. But if the alternative offered us by
Aristotle is such a reductio ad absurdum, surely he has
misunderstood the point at issue. The Pythagoreans
certainly did not conceive of number abstractly, but
might they not have regarded it vaguely as the
mystical cause of things, and have allowed their
statements to vacillate, after the manner of mystics,
between assertions that things are reflexions of number,
and bolder proclamations that things are number itself?
Aristotle certainly assigns to them both doctrines
indiscriminately1, without any consciousness that the
two views are mutually destructive. If the Pythago-
reans did make use of both forms indifferently (and we
have no reason to doubt it), then Aristotle is assuredly
mistaken in classing them as materialists. By far the
more natural supposition is that their vague and
mystical modes of expression were to him incompre-
hensible, and the simplest solution for him was to set
them down as materialists, although on this hypothesis
the extension of their doctrine to immaterial things was
a source of constant irritation. The fact that the
symbolical element and the doctrine of yui^ai^ did
undoubtedly play their part in the Pythagorean
system seems to me to make it almost certain that
the Pythagoreans were mystics rather than philo-
sophers.

This conclusion appears to me still more likely when
one considers the subordinate clause of Pythagoreanism,
1 See Met. A. 5. 985 b 27 ; 987 b 11.

RELATION TO THE PLATONIC IDEAS 101

viz., that the odd and the even, being the constituents
of number, are the constituents of all existing things.
Since all existence has its source in the antagonism
of opposites, whatever object we may care to consider
is to be regarded as a composition of the opposing
forces of odd and even. Now here we have the
popular notion of the contradictions of life, which
recurs in Heracleitus' yeveats e£ ivaprccov, brought
into line with the empirical division of number into
odd and even. There are two sides, said Alcmaeon,
to most things in life ; there is the finite and the
infinite, good and evil, male and female, right and left,
rest and motion. Number, too, the essence of things,
has two phases, the odd and the even ; hence it must
be that the antitheses of existing things are but
variant forms of the ultimate antithesis of odd and
even. But this odd and even are also said by Aristotle1
to have been regarded by the Pythagoreans as material
elements. This view seems at first sight to be even
harder to justify than the preceding; yet the explana-
tion becomes perfectly easy when once we suppose
Aristotle to be understanding mystical and semi-
religious formulae in a literal sense. Number once
exalted as the mystical basis of things, nothing is more
natural than that its fundamental division into odd and
even should be regarded as the mystical origin of all
the multitudinous antitheses of existing things. If
number works good or ill according as it be lucky or
unlucky, odd or even, and if number is, somehow, the
reality of things themselves, then assuredly the good

1 e.g. Met. N. 3. 1091 a 15.

102 THE PYTHAGOREAN 'ApiOfiol AND THEIR

qualities of things must be caused by oddness, the bad
qualities by evenness, in number.

Finally, if one views the Pythagoreans as mystics
rather than philosophers, one has no difficulty in the
fact that their scheme took account of immaterial, as
well as material, phenomena. The mystic is not con-
cerned to make distinctions of this sort. The smaller
the barrier set up between spiritual and material the
better for his purpose. A theory that is based on
fancy and dogma does not need to be tested by
philosophical distinctions.

Before passing on to the consideration of Plato, we
have to note that although the original idea of Pytha-
goreanism probably had its source in the Orient, the
members of the school apparently worked it out in
detail according to their own methods, relying chiefly
on superficial analogies. " The Pythagoreans," says
Aristotle at A. 5. 985 b 27, " believed that they detected
in numbers certain resemblances (ofMOLco/xara) to
existing and phenomenal things," and immediately
afterwards : " Phenomena indeed appeared to them
to be copied from (dcj)cofioi(oa-6ac) numbers/' The
reasons given by later commentators for their choice
of particular numbers for particular things are fanciful
enough. Some of them may also, as Aristotle indicates,
have had recourse to the absurd tactics of Eurytus in
order to arrive at the numbers of material objects.
These details are of slight importance ; they only go
to show that the school soon lost what serious scientific
interest it had possessed. The main result of our
enquiry is that the Pythagoreans were not in the strict
sense philosophers, that they upheld number, in a vague

RELATION TO THE PLATONIC IDEAS 103

and mystical way, as the source from which all things
proceeded, and that the obscure and indefinite form of
their statements, and the indiscriminate application of
their theory to material and spiritual things alike,
show that they had not any exact knowledge of the
nature either of number or of form.

Our next task is to compare this doctrine with
the numbers of Plato, and to estimate the difference
between them. That Plato was steeped in Pythago-
rean fancy, and extremely familiar with Pythagorean
teaching, cannot be doubted by those who are ac-
quainted with his dialogues. Their cardinal doctrines
of the transmigration of souls, and of the destruction
and reconstruction of the world in definite periods,
appear again and again in his works. He is constantly
referring to them and adducing them as authorities on
matters that appertain to mathematics. That a great
gulf, however, yawned between their system and his
cannot but appear when one recalls the highly
developed mathematical theory that was put forward
in the last part of the Timaeus. There we found Plato1
making a new beginning, and pitching his song in a
different key. The greatest part of his message,
perhaps, had already been delivered; he had pro-
claimed his belief in a universal mind that is the
ultimate source of all phenomena. The dyadov, which
in the Republic represented the goal and aim for
which the whole creation strives, has resolved itself
into a Belos fcal ak-qdivos vovs, and the divine ideas,
which have held his imagination captive so long, are
but certain aspects and determinations of that Reason.

1 Tim. c. xvii. p. 47 e.

104 THE PYTHAGOREAN 'ApiO/jLol AND THEIR

But the dya06i>, with Plato, was not to be a mere
hypothesis ; it was to be known and realised ; it
was the goal of all knowledge. How then is he to
attain to it ? How is he to prepare himself to come
into relations with the irapaheiyfjua of all existence ?
He can only begin, as the Republic suggested long
before, with the world of phenomena around him,
the world which he perceives through acaOrjai^ — that
perverted mode of apprehension which belongs to the
animal kind alone, and which is the inevitable conse-
quence of the deliberate degeneration of souls, and
their transmigration through endless ages into ever-
varying forms of life. Starting, then, with the world
of sense, Plato endeavours to rise from the perception
of body to an intermediate class of ideas which will
serve as objects of knowledge until the supreme vov? is
within reach. In order to describe these ideas, he is
forced to delineate an entirely new conception, that of
abstract space, the viroSo^rj yeveaeax;, within which he
builds up mentally the things of time and space,
conceived in terms of their geometrical construction.
He shows us that all the perceptible objects of the
world around us are only perceived subject to con-
ditions of geometrical relation1, and that the exact
expression of these varying relations is the highest
mental interpretation of the things they denote.
The mind translates into its own terms the materials
of sense, and when this happens we are journeying
from the material towards the ideal. All the phe-
nomena of nature, therefore, may on this view be
regarded as copies of a mathematical idea, according

1 Cf. Laws 894 a.

RELATION TO THE PLATONIC IDEAS 105

to which a certain dptOfjuos of primary triangular forms
is supposed to constitute the characteristic elSos or
shape of the particular thing.

Now the first and obvious distinction to be drawn
between Plato and the Pythagoreans is that the former
considered number, form, and space, too, in the abstract
and not in the concrete. Number, he tells us in the
Parmenides1, is generated as soon as any notion, of
whatever kind, comes before the mind for consideration.
The mind is forced to count, as soon as it begins to be
active. Number is, consequently, of a subjective nature
only ; it cannot have an independent existence apart
from the thinking mind. As to form, we know that he
had always in his mind's eye the ideal triangle and the
ideal pyramid of yecofjcerpta, which, although they had
been conceived of course before Plato's day, were almost
certainly unknown to the Pythagoreans, whatever later
writers, such as Proclos, may say to the contrary. There
is, at all events, no sure or conclusive evidence that they
had advanced to a conception of abstract geometrical
forms. As for the conception of pure, abstract space,
it is extremely doubtful whether any of Plato's prede-
cessors had attained to such a clear or complete notion
of it as that which we find in the Timaeus.

Once Plato had reached these highly abstract
conceptions, he could indeed reconstruct the world
mathematically without any fear of the ridicule that
attended the attempts of the Pythagoreans. Anyone
that allowed the truth and reality of mental con-
ceptions would, under these conditions, permit him
to have dpiOfjuol and yet be sane. It may be objected

1 Parm. 143 d, e.

106 THE PYTHAGOREAN 'ApiOfiol AND THEIR

that something of the mystical element remains in the
hope, vague though it be, that he may some day be
enabled, through a diligent pursuit of the apiOfjboi, to
rise to the knowledge of the supreme reality itself.
Such an aspiration may perhaps be termed mystical,
in so far as it makes an assertion without affording
visible or reasonable justification, but if it be mysticism
at all, it is the mysticism1 of the man who thinks, the
man who realises and does not confound, as the Pytha-
goreans did, the means and the end. 'ApiBfiol to him
are only a stepping-stone. While pursuing them he
never loses sight of the great reality beyond, which a
man must seek icrrjaea)^ eveica evSai/juovos Blov.

Let us endeavour, then, to sum up the difference
between the Pythagorean theory and that of Plato.
Plato inherited from the Pythagorean school the doctrine
that the real essence of a thing is not material air,
'earth or water, as the case might be, but a certain
number, of which the thing was, in some mysterious
and inexplicable way, a likeness. The only reason
which the authors of the doctrine could give for their
assumption was the fact that they had fancied certain
resemblances to exist between number and things, and
that they had, moreover, been astonished at its efficacy
in their musical and mathematical experiments. They
could assign no reasonable basis for their faith ; they
were more mystics than metaphysicians. Plato, pur-
suing diligently the study of mathematics, came to

1 Mysticism in this sense would be identical with Inge's conception
of it in his Christian Mysticism — the " formless speculation " which
comes to the aid of philosophy against materialism and scepticism.
(See Christian Mysticism, Lect. i. p. 22.)

RELATION TO THE PLATONIC IDEAS 107

the same general conclusion, namely, that number
plays a great part in our experience of phenomena. It
would have been unnatural for him, however, to rest
content with this vague generalisation. The severe
discipline to which he subjected himself in the Par-
menides, the Sophist, and kindred dialogues, had made
clear to him the nature of mind and its mode of
operation. Sensation, with him, was a degenerate
form of apprehension, arising from the body, with
which the soul is clogged. It can never give accu-
rate information concerning the universe. Sensation \
told him that the universe is bodily ; whereas his \
reason knew that its truest and highest nature was
that of mind and soul. The philosopher must, however,
begin with the data of sensation, for thence he may, by
the activity of pure 1/01)9, discover the conditions and
principles which underlie the ever-varying illusion of
sense. Geometry comes to his aid first, and teaches
him the ultimate laws of bulk and surface ; then, by
the help of pure arithmetic, he is enabled to express in
the language of the intellect the entire sensible world.
And this, he feels, is not mere imagination ; he is
approaching the truth of things. For the universe,
after all, is real, and it is the only object of knowledge;
only it is not just what our senses perceive. Therefore
the more intellectual our account of it becomes, the
nearer we are to knowing it as it really is. And
the individual soul is a copy of the universal irapa-
Sevyfjia, the Oeco? vovs, though the resemblance is for
the present obscured through the adverse power of sin.
It must inevitably, some day, return to its first estate,
if only it cultivates diligently the activities of reason

ION THE PYTHAGORKAN 'AptOfiol

that have been planted within it, and models its life
upon that of the great Soul of the universe.

Such a view is surely not unworthy of the greatest
philosopher of antiquity. The mathematical ideas,
with him, did not, as with the Pythagoreans, represent
the final analysis of the universe. They were fiera^v
ti, an intermediate stage merely, to prepare the soul
for the comprehension of the supreme irapdhety^a.
Let us not set down to him the absurd accretions which
were superimposed upon him by his feeble and literal-
minded followers, who, engrossed with the thought
of ideal numbers to the exclusion of all else, confused
their master's doctrine hopelessly with that of his
Pythagorean predecessors, thereby casting an un-
merited cloud upon the brilliancy of his philosophical
reputation. For the Pythagoreans were children,
playing with pebbles upon the shore of the vast ocean
of knowledge ; but Plato had already embarked, with
his sails full-set for the open sea.

ESSAY VI.

THE ARISTOTELIAN CRITIQUE OF THE IDEAS AND
NUMBERS OF PLATO.

Any account of the Platonic system, particularly in
its maturer form, would be imperfect without some
reference to the Metaphysics of Aristotle ; for in them is
to be found the only contemporary evidence extant
respecting the nature of Plato's doctrine at a time
when he himself had ceased to commit his thoughts
to writing. To ignore them entirely would, indeed,
be a serious error, when one considers that a man's
published work is not always the most accurate
representation of his mature conclusions, but that
his ultimate views are often reserved for the inner
circle of friends or pupils, who may, if they will,
record them after his death. Objection is frequently
made to the testimony of Aristotle in this connexion
on the ground of his personal antipathy to the idealist
point of view, and the consequent unfairness, not only
of his criticism, but of his statement, of Plato's teaching.
This, however, is not sufficient reason to deter us from
interrogating Aristotle as far as we can, provided we
assess his evidence at our own valuation. When all

110 THE ARISTOTELIAN CRITIQUE OF

due allowance is made for the philosophical bias of
the witness, there will surely remain a residuum of
information which will contribute something to the
discovery of the true state of affairs. Therefore, since
our aim is to come to some conclusions regarding the
Platonic system itself, our endeavour will be to review
the information with which Aristotle supplies us, rather
than to attempt any estimate of his critical ability,
although the character of his criticisms must necessarily
reveal itself, to some extent, in the course of our examina-
tion; also, for the sake of clearness and convenience,
his account of the Platonic system in general should
claim our attention before the detailed exposition of
the numbers in Books M and N, and in other isolated
passages.

Following Aristotle's frequent statement1, then, we
find that the ideal theory, as originally conceived,
before it became connected with the nature of numbers,
was promulgated as a complementary article to the
Heracleitean doctrine of flux. Its supporters were
convinced that if there was to be eiriarr)p,r) or (frpovrjo-K;
of any kind, there must be existences, other than peovra,
endued with the permanency in which these were
lacking ; and whereas Socrates, intent on morality and
ethics, was content to seek this knowledge in the defini-
tions of general notions merely, which definitions were
obtained through peovra, Plato and his followers posited
certain permanent existences separate from peovra
(Xoopto-rd), which they termed ideas, and of which, as
distinguished from peovra, the definition was given.
The consequence was that they supposed ideas to exist

1 Met. A. 6. 987 a 29 seq. ; Met. M. 4. 1078 b 9; 9. 1086* 35.

THE IDEAS AND NUMBERS OF PLATO 111

of every general predicate, after the fashion of a man
who, in making a calculation, believes it easier to count a
larger number than a smaller one ; and the relation which
obtained between these ideas and peovra they termed
fjbWe^L*;1. These, of course, are the ideas as described in
the Republic and Phaedo, where they are assumed for
the express purpose of clearing up the mystery of pre-
dication, and they meet with the same objection (that
of the rpiros av6 pwiros;) from Aristotle that Plato him-
self urges against them in the Parmenides. But, apart
from that, Aristotle continues, the doctrine is very
unsatisfactory, because, in the first place, the argu-
ments used by the Idealists do not carry conviction,
and, in the second, their contentions result in our
having ideas of things for which we do not recognise
ideas. The latter criticism is justified by references to
dialogues in which are given the accounts that conflict
with the orthodox system. Thus, if one accepts their
arguments regarding the sciences, there will be an idea
for every science (cf. Rep. 476 e); according to their
explanation of the ev eirl iroWcov, there will be an idea
for all negations (Rep. 596 a); also, in virtue of the
possibility of votjo-ls concerning things dead, we must
accept ideas of (f>0aprd (Parm. 132 B, c). But orthodox
Platonists apparently do not have ideas of these things.
Moreover, the most accurate expositions postulate ideas
of relations2, of which we present-day Platonists refuse
to admit ideas, and in another case the rpiro^ avOpwiro^
argument itself is brought against the ideal theory.
Another inconsistency is found in the fact that, whereas

1 Met. A. 6. 987 b 9.

2 Phaedo 74 a. » Parm. 132 a.

112 THE ARISTOTELIAN CRITIQUE OF

the Platonic teaching makes the ideas responsible for
yeveais of any kind, there is yeveats of some things, such
as SatcrvXtos and oUta1, of which the Platonists say
there are no ideas. The Plato whom Aristotle knew
apparently claimed ideas of natural objects only, such
as Trvp, crap!;, /cecfxiXr/ (Sib Br) ov tca/co)? 6 UXdroyv e(f>r}2
on elhrj iarlv oiroaa cfrvaei,, elirep eanv elhrj.,.olov irvp,
cap!;, K€(j)a\7]), and these ideas were pre-eminently of a
numerical nature, composed of the same <jToiyelaz as
visible things, viz., the ev and the dopccTos Sua?, or,
to fxeya teal to fiucpov. Hence the absurdity of those
accounts which posit ideas of a multitude of things, for,
according to these, number, and not the dyad, is first
in importance, and the darling theory of the Platonists
is overthrown.

Such, in brief, is the substance of the rambling
sketch given by Aristotle, and the writer of Books M
and N, of the Platonic system in general. Disjointed as
it is, however, it furnishes us with several conclusions
regarding Aristotle's relation to the Platonic teaching.
In the first place, he certainly was not aware of any
single harmonious theory in which all the statements
in the dialogues, written at different periods in Plato's
career, were to be reconciled. On the contrary, the
dialogues furnish him with constant occasion for
discontent; they contradict one another, and militate
for the most part against the received Platonism of
the day. Aristotle, therefore, did not hold, with certain
modern critics, that the ideal theory was a single con-
ception that remained essentially the same throughout.

1 Met. M. 5. 1080 a 5. 2 Met. A. 3. 1070 a 18.

3 Met. A. 6. 988 a 11.

THE IDEAS AND NUMBERS OF PLATO 113

Secondly, he speaks as one who has read the dialogues
for himself, as a self-imposed task, without any
illuminating aid from the one who wrote them. They
are a problem which he does not seem able to solve.
Clearly, then, Aristotle could not at any time have had
the advantage of hearing Plato himself lecture on the
subject of the dialogues; he could not have known
the ideal theory at first hand during its various
developments. By the time he came to the Academy
the theory must have suffered material alteration, and
apparently no great pains were taken to make the later
phase consonant with the former. All Plato's strictly
philosophical dialogues wrere probably already written,
and his work lay chiefly in discoursing personally to
his pupils on the subject of the ideas as apiQyioi — so
at least one gathers from the numerous references1
to the aypacjya Soy/jbara and aypacfroi, avvovcriai made
by Aristotle and later writers. At any rate, it is the
dpiO/jLol that loom largest on Aristotle's horizon ; the
Platonists of his day devoted themselves to them alone,
and schism even arose in their ranks on account of
their conflicting views regarding them. It is quite
natural, therefore, that Aristotle, being steeped in the
contemporary views of the school, should display con-
siderable ignorance regarding the evolution of Plato's
thought during the interval between the Phaedo and
the Timaeus, and should fail to realise the value of
that deliberative and corrective process which we have
examined in previous essays. That the ideal theory was
not in the beginning identical with its latest phase, he
assures us; but of the intervening stages he knows
1 See Ar. Phys. A. 2. 209 b 15 ; Procl. in Tim. p. 205.
W. 8

1 14 THE ARISTOTELIAN CRITIQUE OF

nothing. But, although we may be disposed to regard
him as a dubious authority on the ideal theory at large,
we cannot rob him of his importance as a contemporary
student of Platonism, when we are examining the latest
stage of that theory.

This so-called number-theory, as described by
Aristotle, is so full of difficulty, and the dissensions
among its supporters are of so intricate a nature, that
a complete examination of the evidence is necessary
before one can hope to disentangle the views of Plato
from those of his successors; and for this purpose it
will be wiser to postpone the consideration of the
condensed and confused statements of Book A till we
have weighed the more detailed accounts of Books M
and N. The author of M and N, writing perhaps more
as a Platonist than as Plato's contemporary, describes at
great length the conflicting tenets of the Platonists of
his day. There were, apparently, at least three different
sections 1 among the Platonists of that time, one school
postulating the existence of two kinds of numbers, the
ideal and the mathematical, which were widely different,
although alike yjapiGTa, another affirming that /jLaOrj/jba-
rt/ca and ISeat are one nature, and that the Iheat find
expression in mathematical terms, and yet a third, who,
according to M. 1086 a 2 and N. 1090 a 17, discarded ideas
altogether, and sought refuge in fxad^/jLariKa simply,
declaring, like the Pythagoreans, that things are really
numbers.

The first of these theories is a complicated one2, for
these Platonists believe that the ideal, as opposed to the

i See M. 1. 1076 a 16 ff. ; M. 8. 1083 a 21 ff . ; M. 9. 1086 a 2 ff . ;
N. 3. 1090b16ff.

2 See M. 6. 1080a15ff.

THE IDEAS AND NUMBERS OF PLATO 115

mathematical, numbers, differ one from the other in
quality, and are do-vfjiftXrjToi, i.e., no mathematical
operations, either of addition or multiplication, can
take place in regard to them. Whereas mathematical
numbers are formed by the addition of a plurality of
units, all of equal value, the units of ideal numbers are
in each case distinct, and cannot enter into combination
with those of other ideal numbers. This at least seems
to Aristotle the most plausible explanation of the word
do-vfifiXrjTos, though he acknowledges that it may be
construed to mean that even the monads of each ideal
number itself, if it has any, are not to be added to one
another, in which case, of course, the ideas of number
will not have the properties of number at all. It is
hard to believe, as Aristotle justly points out, that
there can exist a number which is not to be formed by
the addition or multiplication of units ; and, on the
other view of ao-u/x/3\?; to 9, it would seem necessary to
make, not only the monads, but the triads, pentads, and
all the other constituents of the numbers, to be
dav/jLfiXrjToi as well — a truly complicated task (M. 7.
1082 a 1 seq.). The first doctrine, then, is characterised
by ideas of number, which are ranked in a qualitative
order (rov fxev eyovra to nrporepov ical varepov rds
l&eas, M. 1080 b 12), together with mathematical
number, apart from the ideas and alaOrjrd. These
ideas are generally styled irpoyroi dpcOfiol1, in con-
tradistinction to the numbers of the second school,
and are not made to consist, like the ideas of the second
school, of the ev and the indefinite dyad (see N. 3. 1090 b
34 : cf M. 8. 1083 a 32). Mathematical number, more-
1 See M. 7. 1081 a 4, 21.

8—2

116 THE ARISTOTELIAN CRITIQUE OF

over, was regarded by them as jiera^v rod elhrjrucov fcal
rov alaOrjrov, holding the same position as the /jlclOt)-
jjuari/cd of the Republic, except that it is now considered
to be something between ideal and material number
exclusively. The old multitude of ideas, representing
everything which can be predicated of anything, have
dropped into the background, and the ideal numbers are
the only ideas, and, in virtue of being ideal numbers, are
also the ideas of material things. Such, at least, seems
to be the necessary inference from the discussion in
M. 8. 1084 ab, where the avrol dpiOfiol, or ideal, as
distinguished from ordinary, numbers, are certainly
referred to (1084 a 19, 23), and it is implied that each
of the avrol dptOfjuol stands for the idea of an animal or
the like. There it is also hinted that the ideal series
ends with the Se/ca?, but this is not advanced as a
compulsory part of the creed.

Opposed to the Platonists, who posit the two classes
of numbers, is the school (least commendable of all, says
Aristotle1) who say that the ev is the dp^rj and aroiyelov
of all things, and that by its combination with the 8vd<;
dopurTos2 number is produced. These apparently agree
wTith the former school in making numbers ^topiard,
but their numbers are not, like the ideal numbers of
the first school, dav/ji^Xrjrot. They saw the folly of
having two distinct sets of number, and their contention
seems to have been3 that the ideas took the form of
numbers, or were expressible in numbers, for they
refused to agree with the more Pythagorising section
that numbers are in themselves ovcrta4. They seemed
to justify their position by their speculative analysis,

1 M. 8. 1083 b 2. 2 M. 6. 1080 b 6.

3 M. 9. 1086 a 7. 4 M. 9. 1086 a 2; N. 3. 1090 b 17.

THE IDEAS AND NUMBERS OF PLATO 117

not only of number, but of all /juadrj/jbaTL/cd. After
generating number out of the ev and the dopuaro^
Svds, they proceeded to generate /meyedo^ out of number
and v\r), or ^iwpa1, in virtue of their resolution of the
solid into 4, the surface into 3, the line into 2, and so on.
They are also represented2 as in some instances generat-
ing the various aspects of fxeyeOo? out of varieties of
the dopLaros Sua?, or to /jueya kcli to yaKpov, which is
the ultimate basis of number and all things.

The third section, who, fearful of the hvayepeta2, that
beset the ideas in general, took refuge in fiadrjfjLaTt/cd
alone, seem to have been infected with the taint of
Pythagoreanism, though apparently they did not go so
far as to make numbers a material cause, as Aristotle
would put it (M. 1. 1076 a 35). They did not indulge,
like their contemporaries, in the speculative analysis of
number into the ev and the dopiaTos Svds ; but they
are represented instead as evolving all number from
the addition or multiplication of eV4.

Now it is at once obvious that of the three theories
the first is by far the most complicated, inasmuch as
it is at pains to draw fine distinctions between the
el&rjTi/col and the /iadrj/juaTL/col dpcd/Liol, and applies
different phraseology to the two kinds. The eiBrjrifcol
dpc0fjLol are 7rpa)T0t aptO/uoc, and are incapable of
mathematical operation of any sort, whereas the
fiaOrj/jLaTLtcd are /jueTa^v, and are subject to mathe-
matical calculation. The upholders of this view,
moreover, did not seem to endorse the theory of
number as being compounded of the ev and the
dopiaTos Sua?; they seem, in fact, to have left the

1 N. 3. 1090 b 21. 2 M. 9. 1085 * 9. 3 M. 9. 1086 a 3.

4 M. 8.1083*21.

118 THE ARISTOTELIAN CRITIQUE OF

details of their theory unexplained, not even trying to
give an account of the fjuaOrj/jLart/col dpiOfioi1. We may,
however, draw several inferences regarding this section
of the Platonic school. The fact that fjuadrj/jbartKa, on
this view of the numbers, are almost always termed
/jL€rai;v, has already led Prof. Cook Wilson2 to infer that
the ideas of number referred to here are identical with
the earlier doctrine of the Republic. While allowing
that the discussion of fxaO^fianKa in Book B, and
perhaps a few other passages, may refer to the theory
of the Republic alone, I believe that the details
concerning the davfjLfiXrjTot apiOfjuol in M and N cannot
but belong to the late theory of numbers, which, in the
hands of one section of Platonism, was contaminated
with the mathematical teaching of the Republic^.
There, it will be remembered, there is an eternal and
immutable idea of every mathematical notion, besides
the abstract conception of which the scientific definition
treats. This later school of Platonists, as far as we
can judge, took over this portion of the educational
scheme of the Republic, and, ignoring for the most
part the geometrical, astronomical, and other /xera^u
(A. 9. 992 b 13), used it to explain the difference
between ideal and mathematical number. The theory
of the Republic, however, was assuredly pressed into
the service of the later number-theory, in order, no
doubt, to afford a plausible justification for having
idea-numbers at all4. The davfji/3\r]Tot dpiOfiou, since
each represented a unique entity, were ev, and not
iroXkd, and were, therefore, not subject to the objection

1 N. 3. 1090 b 34.

2 See Art. by Prof. Cook Wilson, Class. Rev. vol. xviii. p. 247.

3 Rep. 525 a ff. 4 See M. 7. 1081 a 6ff.

THE IDEAS AND NUMBERS OF PLATO 119

raised by Aristotle, that if any number could be an
idea, the ideas for each object would be multitudinous.
It is at any rate clear that these Platonists thought
their ideal numbers to be the ideas of things. The
writer of Book M1, referring at c. 8 to the Trpcoroc
apiO/jiOL, which he shows to be subject to the same
absurdities as ordinary apcO/iou, gives as hypothetical
instances of the numbers that stood for ideas of things
fj r€Tpa<; avrrj and rj 8vd$ avrrj, thereby showing
clearly that the supporters of the irpoyrot dptOfiol used
them to express the reality of visible things. In
common with the rest of the school, they held that
number was the highest expression of reality, but it
was not mathematical, but ideal, number that was so
distinguished.

To this section of the school, undoubtedly, belongs
that curious article of belief which Aristotle attributes
to the Platonists in the sixth chapter of the first book
of his Ethics2. The later Platonists, he says, did not
admit the existence of an idea to correspond to a group
of things whose members were in the relation oiirporepov
zeal varepov to one another (i.e., they did not accept the
doctrine of the Republic in toto, and allow an idea of
every predicate), and, consequently, did not recognise a
single idea of number to correspond to the group of ideal
numbers, which were in the relation of irporepov /ecu
varepov to one another. These Platonists, in short,
utilised a part only of the machinery of the ideal theory
of the Republic. The assumption of an idea for every
predicate was for them unnecessary, since the logic of pre-
dication, thanks to Plato's dialectical zeal as exemplified

1 M. 8. 1084 a 23 seq. 2 Eth. N. i. vi. 1096 R 17.

120 THE ARISTOTELIAN CRITIQUE OF

in the Parmenides, the Sophist, and elsewhere, was not
to them a mystery, such as it had been to the Eleatic
Zeno and his contemporaries. They retained apparently
ideas of numbers only, and these ideas had the pre-
eminent virtue of representing the reality of all existing
things ; and, although they constituted an ideal series,
they were to be exempt from the original rule that
every group of particulars has an idea corresponding
to it.

The second class of Platonists did not feel com-
pelled to have recourse to these shifts for main-
taining the doctrine of the ideas as numbers. There
did not seem to them to be any absurdity in supposing
that the ideas should be represented as ordinary dptO/jLoc,
and that the highest expression of the reality of the
universe was to be found in mathematical formulae.
They laid great stress on the derivation of number from
the ev and the dopicrTos Svds, which were the arot^eia,
not merely of number, but of all existing things. In
fact, it was in virtue of thus containing in their essence
the elements to which all existing things must
ultimately be reduced, that numbers were marked
out by them as the ideal prototypes of things. Of
these two GToiyela, it is the unit that is the aToiy/lov
par excellence, since it furnishes ovaia to the number
that is generated, whereas the indefinite dyad acts as
the vXrj or 8vva/j,L<;. The statements made regarding
this latter mysterious conception are somewhat vague,
and not always consistent, and it would appear that the
Platonists held varying beliefs regarding it. In general,
however, it may be said that it is the potentiality of
quantity, of excess and defect. Some of the schools

THE IDEAS AND NUMBERS OF PLATO 121

called it Svottolo?1, that which duplicates whatever
it operates upon, rov yap 7ro\\d rd ovra elvac alria
avrrj? rj (frvcrts2; and Simplicius adds: tcaOo yap Sua? icrrt,
ttXtjOos teal oXiyoTTjra Xaj(ev ev eavrf)* icaOo fjuev to
8t7r\dai6v icrnv, ev avrfj 7r\rj0os.../ca06 Se rjpnav
6\iy6rr)Ta3. This tenet, however, was, I believe, the
result of a misconception regarding the origin of the
term Svds, as will appear later. The ordinary phrase for
the Svds, applied, we are told, in the first instance by
Plato, was to [xeya icaX to /jatcpov, but some Platonists pre-
ferred to call it by the general name ttXtjOo^] whereas
others chose to employ a variant of the original fieya
teal fxiKpov which seemed to them to be more appropriate
to the nature of the Svds, viz., to virepeyov icai to
virepeyop.evov 5.

The third, Pythagorising, school need not detain us
long. Dropping all compromise, they maintained boldly
that things are numbers. To them possibly belonged
Xenocrates 6, who, interpreting p. 35 A of the Timaeus,
affirmed that the generation of the soul out of the
d/jLepcaTos and the fxepiaTrj ovaia was simply the
generation of number out of ev and 7r\f}0os, and that
the soul was therefore only a number that moved itself ;
and if we are to believe the account of Met N. 5. 1092 b
8 ff., there must have been very little to choose between
them and the Pythagoreans.

It is now time to turn to the consideration of the con-
fused statements in Book A, with a view to determining

1 M. 7. 1082 a 14 ; M. 8. 1083 b 36.

2 M. 8. 1083 a 14. 8 Simp# in Ar> Phys, 104 B.

4 N. 1. 1087 b 30. 5 N. 1. 1087 b 18.

6 Ar. de An. A. 4. 408 b 32 ; Plutarch, irepl rrjs ev Ti/xaiy \pv\oyov las
c. 2.

122 THE ARISTOTELIAN CRITIQUE OF

how much of this number-doctrine can be legitimately
fathered upon Plato, who is there said to have originated
it. After various details regarding the ideas as origin-
ally described in the Phaedo and Republic , we are told
that1 Plato regarded the /jlclOt} pari tea as being fxera^v
roiv irpay/jiaTcov, and apparently at the same time held
that, since the eiSrj are the causes of peovra, their
aToiyela must accordingly be the GToiyela of existing
things also ; and these GToiyela were two, &>? /xev ovv
vXrjv to fieya /ecu to /ju/cpov elvai dpyd<$9 go? S' ovcriav
to ev. This statement, on the face of it, proves that the
writer was not careful to distinguish the different stages
of Platonic doctrine. How could a belief in /jiaOrj/jiaTi/cd
as fi€Ta%v between ideas and sensibles be held in con-
junction with the doctrine that ideas are numbers
composed of numerical GToiyela ? Our investigation of
the two leading doctrines described in M and N showed
us that the two positions were quite incompatible,
inasmuch as the first school made their numbers
davfjb^XrjTOi, whereas the latter made no such condi-
tion. A further confusion, moreover, is to be found
in the phrase to pueya /ecu to fju/cpbv elvai dp^ds.
According to N. 1. 1087 b 14, the view that made to
fjueya Kal to /ju/epbv two separate dpxal belonged to a
very late sect of Plato's followers, and could not with
accuracy be ascribed to him at all. The account of
Plato's doctrine given here is, therefore, by no means
clear or exact. The statement, however, that Plato
made the ideas as numbers to consist of the ev and the
/jieya /cal pu/epbv is one that demands our attention, for
it is borne out by other passages such as Physics
T. 4. 203 a 10, A. 2. 209 b 33. But since Aristotle is so

1 A. 6. 987 b 15.

THE IDEAS AND NUMBERS OF PLATO 123

lacking in precision concerning the divergences of
the schools, and fails so often to point out where
Plato ends and Platonism begins, the utmost caution
must be exercised in attributing to Plato himself any
of the number-doctrines mentioned by Aristotle, even
when they bear his name. Only when we find con-
firmation in the dialogues themselves can we with
certainty assume that Plato himself was the author of
any of these views.

That Plato in the Timaeus has given to fjuaOq/jbaTC/cd
an important place in his ideal reconstruction of the
universe will not be denied by those who have accepted
the results of Essays ill and IV. Let us then compare
to /jL€<ya /cal to /ju/cpbv of Aristotle's critique with the
parallel conception in Plato, which was delineated first
in the Philebus as to fxaXXov t€ /cal tjttov, and de-
veloped later into the x°*Pa °f the Timaeus. Plato
began, as we found in Essay II, with a realisation of
the vast multitude of antithetical qualities in terms of
which the flux of sense is for the most part to be
expressed. The typical instances of these were to
OepjJLOTepov /cal yjrv^poTepov, to ^TjpoTepov teal vypoTepov,
and to nel^ov /cal o-fitfcpoTepov, the comparative degree
marking the infinite variability of the attributes them-
selves and of the flux which they represented. The
mere isolation of these qualities, however, from their
environment seemed to imply the existence, tcaTa
\6yov, at any rate, of something within which they
arose and perished, and consequently we heard of rj tov
fiaXkov t€ /cat tjttov ehpa, within which the antithe-
tical qualities found a home, that which made their
existence possible. In the Timaeus we found the

124 THE ARISTOTELIAN CRITIQUE OF

conception of the eSpa still further developed; Plato
there, in fact, had sketched1 for us in clear language
the abstract notion of space, within which these
qualities arise, together with the objects which they
compose (to Se ottolovovv ti, Oepfiov rj Xev/cbv rj /ecu
OTtovv toov evavTicov teal iravff ocra i/c tovtcov). Plato
also had utilised this conception in order to give an
intelligible representation of the ideas of natural
objects; within this abstract x^Pa he caused to
appear the ideal counterparts of fire, air, earth and
water — geometrical structures composed of triangles
combined in various proportions, the highest expres-
sion of the eternal laws of Becoming.

Now it is extremely probable that the phrase
doptaros Sua?, so much used by Aristotle, arose while
the theory of space was taking shape, and was based
on the description in the Philebus, in which we are
presented with the picture of two extremes in ever-
varying degrees of approximation to, and divergence
from, each other. The writer of N practically ac-
knowledges this when he speaks of rj rov dvlaov
8vd$ rod /xeyaXov koX /M/cpov2. If the phrase had
originated as an arithmetical term simply, i.e., as the
equivalent of the duplicating force, it would not have
been conjoined invariably with those two antithetical
adjectives. Moreover, when Plato's analysis of matter
developed still further and was found to consist ulti-
mately in the notion of abstract space, it is quite
conceivable that the %oopa, the Svpcljulls or v\rj of size
and extension, should be popularly described in the
school by the dopiaro^ 8vd<; most appropriate to it,
1 Tim. 50 a. 2 N. 1. 1087 b 7.

THE IDEAS AND NUMBERS OF PLATO 125

viz., that of to jjuel^ov tcai afiiKporepov or to fxeya teal
to ixacpov ; for the tendency of the Timaeus was to
make all these sensible qualities but variations of the
fundamental opposition of to fieya /cat to fjuicpov, as
the exposition of 61 E ff. particularly shows. The
qualities of hot and cold, hard and soft, and the like,
are dependent upon the geometrical structure of the
elements which produce them ; they are secondary
effects1 of the primary differences of shape in the
elementary figures, and consequently to fjteya teal to
fjuKpov is the fundamental opposition of matter. But,
after the date of the Timaeus, while the Platonic
number-theory was rapidly developing in various di-
rections, the phrase to /xiya ical to fjuc/cpov undoubtedly
came to be used in a somewhat restricted sense, and in
a fashion that to the writer of M and N appeared
inaccurate. It was applied to the vXrj of apc0/u,ol as
such, which to many contemporary Platonists2 seemed
to be represented better by the words to 7ro\v ical
to oXiyov, or to virepe-^ov ical to virepeyp^vov. Some
indeed repudiated to fxeya ical to fu/epdv altogether,
and substituted the simpler ttXtjOos. All, however,
agreed in making the ev the other aToi^elov, and re-
garding it as the source of ovaia in the numbers that
were generated.

Now is there any indication that Plato himself wras
responsible for this extension of the phrase to /xeya ical
to ixacpov?. In c. 6 of Book A, previously referred to,
he is not only said to have employed it in this way,
but the reasons for his doing so are given in a passage
that abounds in reminiscences of the Timaeus. '' The
1 Cf. M. 9. 1085 a 10. a N. 1. 1087 b 16 ff.

12() THE ARISTOTELIAN CRITIQUE OF

second crTo^etor," says Aristotle1, " they made a dyad,
because the numbers, with the exception of the nrpwroL
apiOfioi (i.e., the ideas of numbers advocated by the
first of the Platonic sects), were easily generated out
of it, as it were from an itcfjuayelov" "And yet,"
Aristotle goes on to say, " the Platonic account is not
in harmony with facts, for in actual life one eZ8o<?
generates many things out of many substances, not
from one v\rj, as the Platonists say; neither is their
simile of the father and the mother consistent with
their doctrine." Here we have obviously the argument
and the imagery of Timaeus 50 A — E reproduced in
a condensed form, and transferred from the conception
of x(*>Pa> t° which they were originally applied, to that
of a SvvafjLLs of plurality, out of which, with the aid of
the unit, dpidfioi are evolved. Not only, then, may
we suppose the existence of a %oopa, within which all
manner of geometrical figures are generated, but even
the more select science of number must have as its
foundation a conception of an arithmetical vXr], an
arithmetical aireipov, from which, with the aid of the
" atomic " unit, the whole army of numbers is to be
created.

This extension of geometrical terms to the science
of number is by no means surprising. It was the
recognised scientific method of the day. From the
first geometry had been called into requisition to
exemplify the technical differences of number, as the
mathematical demonstration of the Theaetetus2 clearly
indicates. If the square, the oblong and the gnomon3

1 A. 6. 987 b 33. 2 Theaet. 147 d seq.
3 Cf. Ar. Phys. T. 4. 203 a 14.

THE IDEAS AND NUMBERS OF PLATO 127

each represented a mathematical principle which is
valid for the science of number, no less than that of
surface, why should not the abstract, ideal %w/oa,
within which these figures arise, also have its counter-
part in arithmetic ? What is it that makes the gene-
ration of number possible ? The point, which forms
the original basis of all superficial and solid figures,
is, in arithmetic, the unit, the arty/jurj aOeros1. The
%ftSpa, or the fjueya teal yuKpov, then, of number, is that
which provides for the multiplication, the pluralisation
of the unit, the vague hvvaya^ of amplification, of
quantity, which is best described as to virepkyov real
to vTrepe^ofievov2.

It is not at all incredible that Plato may have been
the author of this development in mathematical science,
but it is more difficult to believe that he associated it
with his ideal theory of numbers, and said that the
mathematical ev and the doptcrTos Svav of number
were the <7T0£%e?a of the ideas and all existing things,
as Aristotle indicates. In Essay IV we had reason to
believe that in the Timaeus he posited the existence
of certain mathematical ideas — the mathematical laws
which governed the existence of all perceptible things,
and which, for him, represented their truest reality,
inasmuch as they were the eternal and intelligible
counterparts of the things of flux. But these laws of
matter depended for their expression on geometrical,
no less than arithmetical, formulae. The science of
number, indeed, supplied the proportions which were
necessary to the formulation of the law; number was
in a manner its ova la, but the no less essential v\rj
1 M. 8. 1084 b 26. 2 Cf. Ar. Phys. V. 6. 206 b 27.

128 THE ARISTOTELIAN CRITIQUE OF

took the form of primary geometrical triangles, in-
volving, of course, the /neya kol fiLtcpbv of space. And
some Platonists seem to have adhered to this view to
the end, if we can trust the evidence of M. 9. 1085 a 33,
where it is stated that some preferred to think of the
ideas as composed of the arty fir) and a spatial vXtj.

It is just possible, however, that Plato may have
analysed the aroix€^a °f his mathematical ideas yet
further, and announced that the ultimate elements of
all were the numerical unit and the numerical doptaro^
Svds;. At N. 3. 1090 b 21 the adherents of the second
school of Platonism are represented as generating
mathematical /neyeOr) (which are the equivalent of the
mathematical ideas of the Timaeus) out of apiO^bs and
v\rj, through their identification of the point with the
unit, and so on, and deriving number itself from the ev
and the aopiaros St/a? as apyai. Moreover, it is quite
conceivable that Plato would have concurred in the
view, given at B. 1002 a 4, that the surface is prior to the
solid, the line to the surface, and the point and monad
to the line. Seeing, therefore, that Plato in all proba-
bility did regard1 the fundamental conceptions of
geometry as varieties of the corresponding arithmetical
notions, by his identification of the point with unity,
the line with duality, and so on, it may be that he
finally decided that the ultimate bases of the mathe-
matical ideas were the unit and the arithmetical }ieya
kcu /M/cpov. Some such modification of view is declared
by Aristotle in his Physics to have taken place. In the
fourth book of the Physics2 we are told that Plato's

1 See Rep. 528 a, b. Cf. Phys. T. 6. 206 b 27.
2 Phys. A. 2. 209 b 11.

THE IDEAS AND NUMBERS OF PLATO 129

account of vXtj, or to fxeTaX^irTiKov, in the Timaeus
was different from that given in the aypafya Soyfiara :
Sco kclI UXdrcov rrjv vXrjv real rrjv ^ojpav ravro (f>r]atv
elvai ev ra> Tifiai(p' to yap /jLeTaXrjTTTitcov teal tt)v yu>pav
ev /cat tclvtoV) aXXov Be rpoirov eicel re Xeycov to
/n€raXrj7rTL/cbv teal ev tols Xeyo/jbevots aypd(f)OL<; Boyfiaacv.
Similar affirmations from other commentators on Plato
or Aristotle are too numerous to mention. If these
considerations, then, are to be accepted as proof, we
may say that Plato's own later views are to be assigned,
if to any, to the second of the Platonic schools which
we have been considering.

We may then, I think, regard it as certain that
Plato, in his latest stage, paid great attention to
certain mathematical ideas, or laws, governing mate-
rial existences, and as highly probable that he proved
these mathematical proportions to be capable of being
analysed into two ultimate elements, the ev and the
indefinite dyad. Immediately after his death, however,
and possibly before, the Platonists seem to have fastened
on the number-theory as a fit medium for all manner
of Pythagorean extravagances, which the philosophical
Plato could not have entertained for a moment. This
they accomplished partly by amalgamating with the
number-doctrine certain Pythagorean traditions, such
as the attribution of special virtue1 to the numbers ten
or seven, and the derivation of good and evil from the
ultimate irepa^ and aireipov in number, and partly by
interpreting certain passages in Plato's dialogues in too
literal a sense. It would seem, in fact, that a regular
school for the interpretation of the dialogues started

1 See N. 6. 1093 a 28 ; M. 8. 1084 ■ 12 ; N. 4. 1091 b 34.
W. 9

130 THE ARISTOTELIAN CRITIQUE OF

soon after Plato's death. Xenocrates' interpretation of
Timaeus 35 A has already been touched upon ; and the
wide-spread view that the Svds was the cause of evil,
and the ev consequently of good, was in all probability
based upon passages like Timaeus 53 B, where the
v7ro8oxv> before the introduction of method and
measure, is said to have been the reverse of fcdWtarov
and apiarov. The combination of the ideas of the
Republic with the number-theory, as illustrated in the
doctrine of the first school of Platonists, is also a case in
point. Moreover, the people1 who fancifully attributed
the number one to 1/0O?, two to eV^o-r^/A??, three to ho%a,
and so on, were probably interpreting the Timaeus in
a fashion of their own. The principle that soul is
composed of the same elements as the things upon
which it operates, which Plato presumably enunciated
in his story of the creation of ^frv^v ou^ °f Same, Other,
etc., gave rise to the inference that aLorOrjais, like the
aicrOrjTov, is represented by the number 4, whence, by
Pythagorean analogy, the numbers one, two, three, were
assigned to the other activities of soul.

Such, then, is the sum of the information to be
obtained from Aristotle's critique. In the course of
our enquiry we have found confirmation for the belief
that Plato's ideal theory changed its character from
time to time according as his knowledge, and particularly
his logical knowledge, grew, that, although for him the
assumption of eternal ideas was always obligatory, he
latterly no longer retained them for the explanation of
things whose mystery was easily solved by the logic of
ordinary intelligence, and that his account of the idea
1 De An. A. 2. 404 b 20.

THE IDEAS AND NUMBERS OF PLATO 131

at the end of his life was materially different from that
of the Phaedo and the Republic. In Essays in and iv
we had reason to think that, at the end of his days, he
recognised two distinct classes of ideal existences, the
first being at once the eternal cause of all Becoming
and the ethical ideal of every living soul, the second
being a mathematical law governing material bodies,
the direct criterion of physical beauty. Of the former
Aristotle takes no account ; but from his exhaustive
treatment of the latter it would appear that the
mathematical ideas, being the more tangible, took the
fancy of the school, and attracted greater investigation.
And our conclusion that these mathematical ideas were
restricted to natural objects only, to the exclusion of
qualities, relations, (ncevaard and such-like, has found
abundant confirmation in Aristotle's own words. It
has also become clear that the nature of the ideas, as
they were conceived successively in such dialogues
as the Sophist, Philebus, and Timaeus, was not in
the least comprehended by Aristotle, since he expects
them to be in every respect identical with those of
the Phaedo and the Republic, and complains when he
discovers that they are not. The only phase of the
ideal theory on which he can speak with any confidence
is the very latest stage, the doctrine of numbers, and
even there, as we saw in our examination of A. c. 6, he
is not careful to distinguish between Plato's own view,
and those which are elsewhere acknowledged to be
subsequent accretions.

To follow Aristotle in detail through his criticisms
of Plato and the Platonic point of view would be an
unprofitable as well as a tedious task, for nearly every

132 THE ARISTOTELIAN CRITIQUE OF

objection is levelled from the authors scientific point of
view, and with an idealist would have no weight at all.
The scorn which is heaped upon the ideas in general is
directed largely against the metaphorical processes of
fieOegts and /jll/ultjo-l?1, which Plato used in describing their
functions ; as Plato himself would have acknowledged
these to be mere /jL€Ta<f>opal TroirjTt/coi, the criticism is
hardly useful. The ideas as numbers are chiefly
criticised because they imply the priority of apcO/juS?2*
which is a <rv/jL/3e/3r)/c6s, to the avvo\opy which is ovala.
This taunt is, of course, dependent upon Aristotle's
classification of categories, in which ovaia precedes
iroaov — which is scarcely a fit criterion to use in
reviewing a predecessor, whose whole point of view was
opposed to such a classification. Another objection
consists in the statement that, even if the idea is a
number8, it must be apiOfxh^ tlvcov, of some material
ingredients — which in itself shows how materialistic
was Aristotle's point of view, and how utterly he had
failed to grasp the subtlety of Plato's speculations in
the Timaeus. There are a few points, indeed, which
might justly be made by any man of science, but the
criticism on the whole is so absurdly literal that it
scarcely merits serious reading. The attack4 on the
Sua? aopiaros, for instance, is based largely on the
notion that it is literally a dyad, which we know to be
inaccurate. In fact, Aristotle is the last authority to
look to for a fair and liberal account of Platonism.

1 A. 9. 991 a 10, 20 ; M. 5. 1079 b 25.

2 B. 5. 1001 b 26; M. 9. 1085* 20.

3 A. 9. 991 b 20; N. 5. 1092 b 22.

4 M. 7. 1081 b 17 ; 8. 1084 b 37.

THE IDEAS AND NUMBERS OF PLATO 133

Under these circumstances there was, of course,
little likelihood that Plato's system, especially in its
latest form, should be handed down to us in the form
in which he himself evolved and formulated it. Every-
thing has tended to obscure both the expression and
the content of the number-theory, and one may almost
agree with Berkeley, and say that " Aristotle and his
followers have made a monstrous representation of the
Platonic ideas, and some of Plato's own school have
said very odd things concerning them1." The aim of
this paper has been to show that, in spite of all these
obscurations, one can detect a certain residuum that
may fairly be ascribed to Plato himself, and that the
number-theory cannot be summed up placidly as an
elaborate fiction concocted by Plato's successors for the
mere purpose of deceiving posterity.

1 Berkeley, Reflexions and Inquiries, § 338. (Bohn's edition vol. iii.
p. 325.)

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