Plato`s Theory of Knowledge

Transcription

Plato's Theory of Knowledge
Norman Gulley
Universidad de Navarra
Servicio dr:
B~bli8~ec::.:~.
First published in 1962
by Methuen & Co Ltd
This edition first published in 2013 by Routledge
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Plato's
Theory of Knowledge
BY
RONtledge is all illljJrillt of the '((/)'/01' & Frallcis Groll/!, all illforma blf.SillesJ
© 1962 Norman Gulley
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utilised in any form or by any electronic, mechanical, or other means, now
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information stomge or retrieval system, without permission in writing from the
publishers.
NORMAN GULLEY
Senior Lecturer in Classics and Ancient Philosophy
in the University "'of Bristol
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Contents
page vii
PREFACE
THE THEORY OF RECOLLECTION
I
2
Socratic Doctrine in the Early Dialogues
TheMeno
3~n~
II
THE CRITICISM OF PERCEPTION
Introduction
The Symposium
3 The Republic
4 The Cratylus
5 The Theaetetus
48
48
49
53
67
76
I
KNOWLEDGE AND BELIEF
108
Recollection and the New Method of Dialectic
The Evaluation of Perception in Plato's Later Theory
3 Knowledge and Belief in the Timaeus
4 The Sophist's Account of Statement and Belief
IV
I
4
~
2
III
I
I
108
2
120
MATHEMATICAL KNOWLEDGE
Mathematics in the Natural Sciences
Mathematics and the Forms
3 The Objects of Mathematical Knowledge
4 Conclusion
139
148
169
I
169
2
172
177
186
NOTES
188
INDEX
201
v
Preface
In this book I have tried to give a systematic account of the development of Plato' s theory of knowledge. So far as I am aware, no previous
book in English has tried to do this. There have been books on Plato's
theory of Forms and on his method of dialectic which have contributed
much to the understauding of his theory of knowledge. But it has not
been their concern to deal comprehensively with that theory. They
have discussed only those aspects of it directly relevaut to their subject. I
hope that the comprehensive examination attempted by this book will
do something towards filling the gaps aud that it will help at the same
time to a clearer understauding of the originaliry aud variety of Plato' s
contributions to the theory of knowledge.
The pIau of the book is a straightforward one. It begins with a consideration of Socratic aud other influences which determined the form
in which the problem of knowledge first presented itself to plato. It
then works through the dialogues from the Meno to the Laws aud
examines in detail Plato's progressive attempts to solve the problem.
The order in which the dialogues are examined is, with one exception,
the same as that which I assume to be the probable order in which
they were written, i.e. Meno, Phaedo, Symposium, Republic, Cratylus,
Theaetetus, Phaedrus, Timaeus, Sophist, Politicus, Philebus, Laws. The
exception is the Politicus. This dialogue is certainly later thau the
Sophist. But it best suited my exposition to examine the relevaut passages in it in conjunction with my examination of certain aspects of the
doctrine of the Phaedrus and the Timaeus.
If Symposium, Cratylus, Phaedrus, aud Timaeus were taken out of my
list I assume that there would be little, if auy, disagreement between
scholars abont the order I have given (the views ofleading students of
the subject are summarised in the first chapter of Sir David Ross's
Plato's Theory of Ideas). Something must be said briefly about my
placing of the remaining four dialogues. It would be agreed that the
Symposium belongs to the middle period of Plato's thought, which is
vii
viii
PREFACE
specifiable roughly as the period betweeu his first visit to Sicily (389388 B.C.) and his second (30-366 B.C.), and that it is later than the
Meno and earlier than the Republic. The only problem which remains
is, therefore, whether it precedes or follows the Phaedo. And this
problem seems to me to be of little importance in considering the
development of Plato's theory of knowledge. My main reason for
putting the Phaedo first is that the manner of its introduction of the
theory of Forms as an important new feature in the development of
the theory of recollection suggests that the theory of Forms is being
introduced here for the first time. In the Symposium the transcendence
of the Form of Beauty is assumed without any suggestion that this is
a new assumption or one which demands explanation. The place I have
given to the other three dialogues has been determined largely by my
views about the development of Plato's theory. Thus my main considerations in each case have been either the dialogue's close affinities in
doctrine with a dialogue which can firmly be allotted to a certain period
of Plato's thought, or some marked advance in its doctrine which
indicates that it is later than such a dialogue. The result is that I take the
Cratylus to belong to much the same period of composition as the
Theaetetus, the Phaedrus to be later than the Theaetetus, and the Timaeus
to be later tl!an the Theaetetus and the Phaedms but earlier than the
Philebus. I am well aware of the hazards of using for this purpose a
criterion based on a personal interpretation of the development of
Plato's theory. I hope that the arguments I have put forward in support
of my interpretation will show that I have been sufficiently cautious in
my use of it.
I am grateful to Professor W. Beare for his generous help in reading
the proofs of this book. I am grateful also to Miss Elizabeth Oatley for
her preparation of the typescript. Finally I would like to thank the
publishers for the good advice which they gave me with regard to the
presentation of my arguments. By persuading me to make my paragraphs much shorter and to introduce sub-headings within each chapter
they have considerably eased the task of the reader. For faults of any
kind which remain I alone must be blamed.
N.G.
Bristol
Octo her 1961
CHAPTER I
The Theory
r.
of Recollection
SOCRATIC DOCTRINE IN THE EARLY DIALOGUES
In Plato's early dialogues one of the n
h
. .
time most significant features f S lOst c ,a:actenstlc and at the same
·h h
0
Ocrates mquiri . h
w hIC t ey give to general defmitions In
es IS t e attention
Euthyphro, and the Hippias Major the ~im t: taches, the. Ch~rmiJes, the
usmg a question-and_an
h d
t e dISCUSSIOn IS to reach
swer met 0 the deli . .
f
'
UUtlon 0 a familiar moral
or aesthetic concept. Aristotle wasr' 'h
attention on defmition
. Ig t to emphaSIse tbat this fixing of
sluping of Plato's thear; ;a; an l1~ortant Socratic influence in the
But in addition to pointin o;:s ( etaphysics987br_7, I078br7-3r).
the objects of knowledge ~ e w~y to a theory of the nature of
.
.
' OCrates concern with d Ii '.
.
questions
ill
epistemolo
which
.
, e lllltlOllS raIsed
first explicitly formulatg~ hi h occupted Plato s attention before he
h' h
e s t eory of Form I . th
w IC must first be considered Th
s. t IS ese questions
ey
Socratic search for defiUU'tI'
'. h ( larose from the association of the
onSWlt i th' h
.
ledge; (ii) the advocacy of a p . 1 a eSlS t at VlItue was kuo wartlcu ar method of
as the hest means of attaining ku 1 d '
cross-examination
.)
T
h
'
ow e ge.
(1
e theSIS that virtue is kno 1 d '
.
whe ge 18 the theSIS not merely that to
be good it is necessary to ku
Ow w at IS good ,but
th
k
.
d.
IS goo 15 necessarily to do h .
a t to now What
good and yet to do what is~ adt IS good, or at least that to kuow What is
h' h . .
a IS to act mvolunt il A
.
t IS t eSls IS the thesis that nobod vol
.
ar y. SSoclated with
Y untarily does what is bad. This
embraces cases where the
agent merely think
b l'
· .
h
t mg IS good witho t h '
ku
s or e Ieves that some
. . 1
'
u avmg
owledge of h .
'!'
at IS good. SubJectlve y, everyone does what he su
pposes, accordmg to his own lights
to be good. It is 'n t' h
d) , h
0 In uman nature' to
d
th'
'
358 . T ose who are ignorant of h . b; 0 erWIse (Prolagoras
bad, but only what they thO uk b w at IS a do not desire what is
o
that those who are ignorant' of i: ~ g~.: .though in fact it is bad; so
the good' (Meno n d- e). Thus th~h t .' It good are clearly desiring
eSls that nobody voluntan'1y dOes
1
2
PLATO'S THEORY OF KNOWLEDGE
what is bad is, strictly, the thesis that nobody does what he either
thinks or knows to be bad. If what he does is in fact bad, then he is
acting in ignorance of what is good, and he is morally responsible, it
is assumed, for what he does in that it is in his power to rid himself of
this ignorance. Now these Socratic doctrines may be viewed, initially,
simply as statements of what is implicit in the normal Greek view of
'good' (agathon). 'The good', as the most general end of human action,
was invariably identified with 'happiness' (eudaimonia), so that 'to say
that happiness is the chief good seems a platitude' (Aristotle, Ethica
Nicomachea I097b). Thus the statement that nobody voluntarily does
what he thinks or knows to be bad means that nobody volnntarily
does what he thinks or knows to be conducive to his own misery
(Meno 78a). The combinationofthiswithwhat seemed to be the equally
obvious truth that to be good it is necessary to know what is good is
the basis of the Socratic thesis that virtue is knowledge.
But the thesis is more than an emphatic restatement of the utilitarian
outlook implicit in the use of Greek ethical terms. It assumes further an
ideal of determining what is good by a systematic method of inquiry
which is directed principally to the definition of the commonly
accepted 'virtues'. This method, it is assumed, will yield knowledge of
what is good/as opposed to the many and various opinions as to what is
good. Using again a deliberately paradoxical form as a means of
emphasising his tenets, Socrates states in the early d~al~gues that knowledge of what courage is, or of what temperance lS, 1S fundamentally
knowledge of what good itself is (Charmides 174a-<:, Laches 199d). For
in defiuing the particular virtues one is led to a conception of good as a
single end which 'uuifies' all the virtues, in the sense that it is common
to each of them that full knowledge of it implies knowledge of what
good is. Thus good itself is assumed to be definable. The additional
testimony of Xenophon and Aristotle confirms that Socrates' ideal of
knowledge was closely associated with his search for defiuitions.'
Aristotle adruirably summarises this ideal when he says that Socrates
believed that knowledge of virtue was the end, and inquired what
justice is and what courage is, and so with each of the parts of ~rtue.
And he did this with good reason. For he thought that all the Vlrtues
were forms of knowledge, so that to know what was just was at the
same time to be just. For to have learnt geometry and house-building
3
is at the same time to be a geometer and a housebuilder. That is why
Socrates inqnired what virtue is, and not how and from what conditions it comes into being (Ethica Eudemia 1216b3-IO).
The Socratic ideal of morality is, then, an 'intellectualist' ideal. It is
principally, an ideal of knowledge through defmition, and, moreover:
through real defmition. For in seeking to define the 'virtues' or virtue
itself Socrates is seeking to formulate a moral ideal. And it is in emphasising that real definitions are the object of the discussions of the
early dialogues that Plato begins to use the terminology later used for
the metaphysical theory of Forms. Thus the attcmpt to defme piety is
represented a~ an attemptto defme a single 'form' (eidos) possessed by
all partlcular ~stances whIch are properly described as pious (Euthyphro
5d, 6d-e). It lS assumed that there are certain general characteristics
whi~h constitute the real nature or 'essence' (ousia) of this 'form'; these
are Us defiuing cha~acteristics, and are to be distinguished from merely
accidental charactenstlcs (Euthyphro na). The implication is that the
term piety designates a real thing, a 'form', which is the definiendum.
Thus the knowledge sought by Socrates when he said that virtue was
kn~."'ledge is described by Plato as a knowledge of 'forms', in this sense.
(11) How, then, is this knowledge to be attained? The Socratic answer
would seem to be that it is attained by a question-and-answer method
of discussion, seeking a defiuition which can be considered adequate if
it
1S
accepted as correct
by the interlocutors.
No firmer criterion than
this is suggested in the early dialogues. The rules of the Socratic method
as there presented, indicate that its aim is to promote consistency of
opinion between the speakers. The rules are that there should be no
disagreement between questioner and answerer, and that any opinion
expressed sho~~ not c~nfli~t, either itself Or in its consequences, with
any other op1111on. which lS held just as strongly. 2 What is Plato's
attItude towards :IUs method? The difficulty in answering this is the
dIfficulty of decldmg where, in the early dialogues, Socratic portraiture
ends and Platonic interpretation begins. There are several features of
the discussions of the early dialogues which suggest that the method
practised is recognised to be very limited as a means of gaining knowledge: The discussions are inconclusive, and Socrates is represented as
desparrmg of ever reaching any definite truth. He would like to have
the arguments 'immovably settled' (Euthyphro nd), but all propositions
4
seem to be shifting and transitory. They all seem to have in them
ambiguities and inconsistencies, so that they 'run away' from any
systematic attempt to substantiate their truth (Euthyphro 7b-d, lIb-e).
Added to this is an insistence on the Ignorance of Socrates. The resnltant picture is of a Socrates who himself disclaims knowledge, and
habitually shows a lack of confidence in realising it in the mmds of
others by his method of cross-examination. All that he. claIms to be
able to do is to show others that they are ignorant. Ouly m the mIddle
dialogues, after the introduction of the theory of reco~ection: does
plato venture to present Socrates as an intellectual midwIfe, brmgmg
to birth positive truths in the minds of others (Theaetetus 150h-d). N~w
since the testimony about Socrates of writers other thau plato contams
practically nothing which suggests that Socrates habitually professed
ignorance and scepticism, 3 it seems reasonable to .conclude that plato
had more serious purposes in introducing these traIts than the deme to
preserve a realistic portrait, and that, if not invented by lum, they are
given very special emphasis by hIm as an I~dlc~tlOn ofhlS own attItude
towards the Socratic method. Thus plato s mSlstence on these traIts lS
an insistence on the limitations of the method, and may reasonably be
taken to imply an appeal to the need of a constructive theory of know1 d e which will provide a more adequate cntenan of truth than that
e g which the Socratic method relies. It is some confilrmatlon
. 0 f t h'15
upon
view that when, in the Meno, plato introduces such a theory and thus
reaches a position which the evidence of Xenophon and ArIStotle
sufficiently shows to he an advance in doctrine beyond the p~sltlon
reached by Socrates, he introduces it as a solution .of the difficultIes mherent in the Socratic method as a means of attammg knowledge. The
Meno makes clear, in fact, that the form in which the problem of knowledge first presented itself to plato was determined hy his reflections on
the limitations of the Socratic method.
2. THE MEND
a1Introduction of the theory of recollection
.
The Meno marks a transition from the thought of the early dIalogues,
which are largely designed to present and to evaluate the teachmg of
Socrates, to a much more constructive and theoretical level. plato 15
5
now putting forward his own positive theory, as an aIlSwer to problems
implicit in the discussions of the early dialogues. As yet he is not ready
to put forward a metaphysical theory; he does this for the first time
when he introduces the theory of Forms in the Phaedo, which is later
than the Meno. 4 The problem of the Meno is primarily the problem of
whether knowledge is possible at all, and not the problem of specifying
the nature of the objects of knowledge.
The dialogue begins as an attempt to define virtue. Its first part
follows much the same course as those earlier dialogues which aim to
define a general term, though it is noticeable that Plato indicates what
he considers to be the principles of general definition more clearly, and
with more effective and varied illustration, than had been the case in the
earlier dialogues. It is to be noted too that, after explaiuiug that what
he seeks to determine is 'the one identical form which all virtues have,
whereby they are virtues, and to which it is well for the answerer to
look in revealing to the questioner what virtue really is' (72c-d), plato
points out that this principle of distinguishing between a single common
'form', as the dejiniendum, and the many particulars characterised by it
applies to everything (74b), i.e. to all cases where 'many things are
called by a single name' (74d). As for the definitions of virtue put forward in the discussion, each of these is shown to be inadequate, either
as failing to satisfy one or other of the principles of definition, or as
involving a contradiction. Meno, whom Socrates is questioning,
finally confesses that he is utterly perplexed, and becomes sceptical
about the possibility of any defurite conclusion. He doubts whether
any criterion of truth exists. If, he says, you do not know what a thing
is at the begimring of an inquiry, how are you to decide which is the
one YOll are looking for? (Sad). How are you to distinguish a true
solution from one which is untrue but plausible?'
To meet Meno's argument the theory is now put forward that the
process of gaining knowledge in this life is a process of recollectiug
what the soul knew prior to this life. Thus it is a theory that knowledge
is a priori in the sense that its source is independent of the experience of
this life. The idea of recollection is first introduced in terms of Orphic
and Pythagorean religious beliefs. Plato then presents his own theory
in the course of a dialogue in which Socrates leads a slave to the solution
of a geometrical problem; this dialogue is meant to provide at the same
time a practical demonstration of the truth of the theory.
6
PLATO'S THEORy' OF KNOWLEDGE
b1 The religious background of the theory
The first thing to consider is the general backgrouud of the theory. The
principal ideas which it contains are that it is the soul which has kuowledge, that the soul existed prior to incarnation, and that the source of
kuowledge is independent of present incarnate experience. So far we
have seen that an important Socratic influence on Plato's thought was
that it led him to consider the problem ofkuowledge, and especially of
kuowledge through definition, as the fundamental problem in ethics,
and at the same time to reflect on the adequacy of the Socratic method
as a means of attaining kuowledge. This is the context within which
Plato's adoption of a theory of 'transcendent' kuowledge must be considered. Convinced as he was that permanent kuowledge was attainable, and yet finding in practice that the Socratic method of inquiry was
unable to yield it, he was perhaps already predisposed to welcome ideas
which suggested that the source of kuowledge was to be looked for
beyond the experience of this life. Amongst these ideas may be counted
the Socratic doctrine of the 'caring of the soul' which, in its association
with the thesis that virtue was kuowledge, identified the soul with
man's moral and rational' self'. 'In associating with the soul the intellectual activity which yields kuowledge, and making this activity the
soul's proper function, plato is clearly influenced by this Socratic
doctrine. Aud this doctrine, in its turn, reflects in part earlier religious
ideas about the soul. It is the influence of these ideas which plato
explicitly ackuowledges in introducing his theory of recollection, and
it is important to examine them in some detail.
This is Plato's description of them in Meno 8ra-e. They are said to be
the views of
those among priests and priestesses whose care it has been to give a
rational account of their practices. There is Pindar too, and among
poets who are divinely inspired there are many others. As for what
they say, it is as follows; consider carefully whether you think they
are speaking the truth. They say that the soul of man is immortal, and
that at one time it comes to an end (which is what they call dying),
and at another is born again, but is never destroyed. That is why it is
necessary, they say, to live one's whole life as righteously as possible.
Since then the soul is immortal and has been born many times, and
has seen both things here on earth and things in Hades, everything in
THE THEORY OF RECOLLECTION-
7
fact, there is nothing which it has not learned. It is not surprising
therefore that it can recollect all that it kuew previously, both about
virtue and about everything else. For since the whole of nature is
akin, and the soul has learned all things, there is nothing to prevent a
man who has recollected one single thing - this is what men call
learning - from discovering everything else, if he pursues this
search with courage and does not weary of it. For it seems that
research and learning are entirely recollection.
We may take this passage to be an expression of Plato's indebteduess
to religious ideas for such foreshadowings of his own theory as can be
found in them. The reference to 'priests and priestesses' is almost
certaiuly to the Orphics. 7 We kuow from other explicit references in
Pl~t08 t~at a b~dy of literature associated with the name of Orpheus
eXisted ill plato s time, and that the Orphics held (i) that the soul, in its
life ?n earth, .,,:,as. imprisoned.in th.e body as a punishment, and (ii) that
ill tItes of nutlatlOn and purificatIOn lay its hope of avoiding further
punishments in Hades and of achieving blesseduess. From references in
later authors ~d from .insc~iptions· it becomes clear that the Orphics
beheved too ill transnugratlon, and that their ultimate ideal was the
eternal release of the soul from imprisonment in the body. Similar
religious beliefs are attributed to Pythagoras and his school, and it is
probable that some kind of sacred literature akin to that of the Orphics
existe~ within the school.'° It is within the Pythagorean school, with
ItS philosophlCal as well as religious interests, that a more systematic
development of these religious ideas may reasonably be looked for.
There IS, unfortunately, very little evidence l1 to show how far the
Pythagoreans developed the ideal of the 'purification' of the soul beyond a purely formal and ritualistic one by associating it with their
more specifically philosophical and scientific studies. It is reasonable,
however, to assume some initial connexion between the religious and
scientific ideals, however much the two tended to separate later; both
Burnet and Cornford12 considered the evidence enough to show that
the id~al of ~urifi~ation ;was developed by adding 'the practice of
catharsIS by SCIence and the purification of the soul by theoria, the
contemplation of the divine order of the world'.
The spread of these religious ideas from the sixth century onwards
seems to have been specially marked in Attica, and in Southern Italy
8
and Sicily. plato himself, reflecting on the implications of Socrates'
teaching, and possibly only recently having gained a ~loser and fuller
acquaintance with these religious ideas durmg his VlSlt to Italy and
Sicily in 387 B.C., welcomed them readily, since he saw that they
provided the foundation of a theory of the nature of soul ~o. set agamst
the materialistic interpretation of mind and soul charactenstlc of much
pre-Socratic philosophy. The general assumption of pre-SocratIc
philosophy had been that the soul and mmd were of matenal composition and that their fuuctions were to be explamed m material terms.
The fuuctions of the human soul were considered to be all those
belonging to consciousness, especially sensible perception and feeling;
some philosophers, e.g. Heraclitus, ascribed also to the soul mtellectual
activity, but the general tendency was to distinguish between ~oul
(as 'consciousness' or simply as 'life') and nlind, while at the s~m.e urn:
making correctness or acumen of thought dependent on the mlXture
or 'harmony' of the elements of which the soul was composed .. Hence
Aristotle's frequent, though unfair, criticism of the pre-Socratlcs that
they virtually equated soul and mind, or perception and knowledge, by
treating both as rypes of physical interaction (e.g. De Anima 404a27 1£;
Metaphysics I009a22 If.). This type of philosophy would appear to b:
irreconcilable with the Orphic-Pythagorean Ideas we have discussed,
yet the mixture of religious and scientific thought in Empedocles and
within the Pythagorean school suggests perhaps that awarene~s ofthe
inconsistencies was not always felt. 13 To Plato, however, the ImplIcations of the two ways of thought were such that they represented alternatives fuudamentally opposed to one another. It is significant that ~n
the PhaeJo, where he puts forward his own conceptlOn of soul m
declared opposition to the earlier materialistic interpretatIons, the
influence of the religious tradition of thought IS most clearly marked.
And here in the Meno their influence is acknowledged, and a r~admess
is expressed to put trust in their truth in conducting the mqlllry l~to
the nature of virtue (8Ie). In preCisely the same way, m the Gorglas,
after the myth abont the judgement of the souls of the dead: plato
expresses his readiness to put trust in its truth (S24bI). That hIS conviction that the soul was immortal included also a belief m re-m~arna
tion is clear from the familiar passage at the end o~ the myth ~ the
PhaeJo (II4d), a myth including the doctrme ofre-mcarnatlOn..
As an influence of a more particular kind, plato suggests now m the
9
passage of the Meno translated above that these ideas embody a rudimentary theory of recollected knowledge. Though it is clearly wrong
to look here for Plato's own formulation of the theory, it is important
to consider what are the earlier forms of the theory to which plato
alludes. Plato introduces the idea that the soul can recollect its knowledge 'of virtue and everything else' as derivative from the theory that
the soul is immortal, alternating in its existence between states of 'life'
on earth and of 'death' in the other world; 15 for the latter theory is
taken to imply that in the course ofits numerous 'lives' and 'deaths' the
soul has learned everything (8IC). The idea of the possibility of such
recollection from previous existence is, as Burnet says,16 an easy step
from the doctrine of Rebirth. For this doctrine quite naturally gave
rise to the idea of aWareness of the continuity of the soul's existence, and,
further, to the envisaging of men of exceptional knowledge who had
retained in memory all that they had experienced in a succession of
existences. Empedocles refers to such an exceptional person (Pythagoras is probably meant), and claims to remember his own previous
existences;" and Pythagoras himself is said to have claimed that he
retained the memory of his previous re-incarnations." plato does little
more than repeat these ideas in the present passage. The idea that 'all
nature is akin' (8Id) - introduced to explain further how everything
can be recalled from the remembrance of a siugle thing _ is again
dependent on previous theory; it reflects the view ascribed to the
followers of Pythagoras and Empedocles that the one spirit which
pervades, like a soul, the whole nuiverse, establishes a commnuion
between Gods, men, and animals.1' Plato may well have in mind too
the much more profouud Pythagorean conception of the Harmony
which so orders the elements of the world that they form a systematic
uuity, thus enabling the mind, through number, to know all things in
their universal 'communion' with one another.20 But for the moment
he is concerned only with the presentation of more specifically religious
ideas, and it is the former view to which he is presumably referriug.
These then are the antecedents of Plato's own theory of recollection.
But it is easy to over-rate his indebteduess in this particular respect.
Though it is possibly true that the Pythagoreans linked their religious
and scientific ideals in a very general way, there is no evidence to show
that earlier thinkers had formulated anything which can be called a
philosophical theory of recollection, and certainly none to support
B
Burnet" and Taylor" in their view that the idea of remembering
previous existences was developed by the Pythagoreans into a theory
of the recollection, through the suggestions of sensible objects, of a
transcendent mathematical reality. It is precisely the distinctive
character of Plato's theory that he uses it to show how we come to a
knowledge of a transcendent reality. On the other side, it is important
not to assume that this distinctively Platonic theory was not yet envisaged by plato at the time of the Meno. Several scholars, whose views
will be examined later, have been at pains to use the language of the
passage we have been discussing to support a purely empirical interpretation of the theory of recollection of the Meno. Others, while
recognising the religious tone and form of the passage, and thus avoiding the mistake of constructing from it any precise philosophical theory,
have been content to dismiss recollection, as presented in the Meno, as
being for plato at this time a simple religious belief, lacking the
rationale given to it later by the theory of Forms. Thus Frutiger"
contrasts the 'mythical exposition' of the Meno (the whole section on
recollection, from 80d-86c, is taken, without discrimination, to be
'mythical') with the 'dialectical exposition' of the Phaedo. The fundamental mistake of both these kinds of interpretation is that they fail to
separate the introductory passage (8Ia-e) from what follows.
What must be recognised is that in this introductory passage plato is
not presenting his own theory, but using religious ideas to introduce
the idea of recollection as a possible description of 'what men call
learning' (8Id), acknowledging at the same time his indebtedness to
these ideas for such adumbrations of a theory of recollection as can be
fotmd in them. There is no conception within the circle of these ideas
of differing levels or kinds of experience, but only the ideal of a progressive accumulation of personal experience at the same level and of
the same sort. Thus 'recollection' (anamnesis) is simply the recalling,
from the storehouse of personal memory, of the experiences ofprevious
existences. It is certainly true that Plato here orders these ideas to suit
his purpose of introducing the idea of recollection. And it is, I think, an
exaggeration to say that the idea that everything can be recalled from
the remembrance of one single thing is nothing more than 'mythical
symbolism'.24 Plato is adding here his own suggestion of the possibility
of recalling ideas in a continuous chain, the link at each successive
point being the association in memory of two ideas. But the suggestion
is made within the circle of religious ideas, and provides no reason for
taking this introductory passage as a presentation of Plato's own
theory.
IO
II
1
c Demonstration that knowledge is recollection
The nature of his own theory is made clear in the course of a dialogue
between Socrates and a slave-boy, which Plato presents immediately
after the introductory passage. The aim of Socrates is to lead the slaveboy, prompted by his questions, to the correct solution of a geometrical
problem. The problem is to discover the length of the side of a square
which will have twice the area of a square with sides two feet long. The
detail of the steps in the solution need not concern us. What is first to
be noted is the general effectiveness of Plato's use of a particular geometrical problem as an illustration of the process of recollection. An
ignorant slave is chosen for the purpose, as one who clearly has had no
previous instruction in geometry. Further, a problem for solution is
chosen which will strikingly illustrate the slave's initial disillusionment
as he confidently gives the wrong answers. For the problem does not
allow an exact arithmetical solution. The solution is that the length of
the side of the reqnired square is the length of the diagonal of the
original square. And since the square root of 2 is incommensurable
with I, the slave is always wrong in his attempts to give an exact
arithmetical solution. 25 Yet the problem is, at the same time, one which
lends itself so readily to the use of simple sensible diagrams that the
slave is immediately made to realise at each point that he is wrong. The
method which then leads him to a true solution of the problem combines the use of a sensible diagram with a series ofleading questions
which suggest most pointedly to him what the solution is. This may,
perhaps, seem inconsistent with the profession that no instruction at
all is being given (82e).26 Yet it does nothing to invalidate Plato's main
point, which is that a previously untutored slave is able to recognise as
indubitably true (or false) propositions brought to his notice for the
first time.
As for the use of sensible diagrams, this is in accordance with the
normal procedure of Greek geometers." I doubt whether any special
significance is to be attached to their use here. If plato had meant in
this way to suggest the value of sense-experience as an aid to recollection, it is surprising that no mention at all is made of sense-experience
I2
either in the dialogue with the slave or in the subsequent discussio~ of
its signiflcance. The emphasis is exclusively on systematic questlOmng
as the means of eliciting truth (82eS; 84cII-d2; 8SC10, d3; 86a7); and
when plato does go on to consider the part played by sense-expenence
in recollection, in the Phaedo, he introduces this aspect of the the?ry as
something quite new, and different from what had been said m the
Meno (Phaedo 73b).
Plato's purpose then, in the dialogue with the slave, is to show that
by a method of systematic questioniug it is possible to eliCIt the recognition that certain propositions are indubitably true. And he argues that
the fact that, without any previous instruction in geometry, the slave
is able to recognise the truth of certain propositions in geometry
implies that this 'truth' waS a possession of the soul before the soul w~s
incarnate in human form (8se--86a). It implies further that the truth IS
still 'in' the soul in this life (8sc, 86a); it is innate; otherwise there
would be no possibility of eliciting it in this life. The fmal step is the
argument that what is true of mathematics is true also of 'all other
branches ofleaming' (8se). Thus Plato's claim is that all kno",:ledge IS
a priori, in the sense that its source is independent of the experIence of
present incarnate experience. And If th,SIS so, then the hope that ~e
inquiry of the Meno iuto the nature of Virtue Wlll yIeld knowledge IS
justified and Meno's argument is m~t. .
.
..
The direction of Plato's argument m th,S part of the Meno IS an mdIcation of one further important influence in the development of hIS
theory of knowledge - the achievements of Greek mathematics. The
Meno is the first dialogue to show a pronounced mterest m mathematics. Not only is a geometrical problem chosen for the demonstration of the fact of a priori knowledge, but it is to a geometrIcal method
of analysis that plato likens the method of hypothesis whIch he mtroduces as a method of philosophical analysis later in the dlalogne
(86e--87b ).28 There is little evidence in dialognes earlier than the Meno
of this interest in mathematics." Possibly the important part played by
mathematics in the Meno is a reflection of Plato's closer acquaintance
with Pythagorean mathematics gained during his visit to Southern
Italy and Sicily in 38711.C. However that may be, it is clear that by the
time of the Meno plato saw that in mathematics, the one field where
any systematic and organised knowledge had been achieved, he had
found an example of the permanent and exact truth which he sought
13
in ethics; and the argument of the Meno suggests that reflection on the
nature of mathematical truth was perhaps the decisive factor in Plato's
adoption of the theory of recollection as a general theory of knowledge;
already led by reflection on other problems and ideas to seek a 'transcendent' source of knowledge, the theory of recollection must have
seemed to him perfectly fitted to be an explanation of mathematical
knowledge. It is in this field that he attempts to demonstrate the truth
of the theory, before arguing for its validity in 'other branches of
learning'.
d] Stages in the process of recollection
One other feature of the theory which must be considered before its
metaphysical implications are discussed is Plato's division of the process
of recollection into three main stages. The first stage, illustrated in the
first part of the dialogue with the slave (81 e-84c), is the process of
disillusiomnent, a negative stage which elicits the recognition that
propositions which at first are believed to be true are in fact false. The
significance of this is that by explicitly affirming that this process is the
first stage in the process of recollection, and assuming that, if the
questioning is systematically continued, knowledge will eventually be
acquired, Plato makes quite clear that the theory of recollection is
introduced as a foundation for the Socratic dialectic. With this basis the
method can pass beyond the merely 'purgative' stage and lead to the
discovery of truth. For if knowledge is recollected knowledge, then
a criterion of truth above mere consistency and individual agreement
is available to guide inqniry and save the discussion from inconclusiveness. What this necessary initial process of disillusiomnent does is to
stimulate the search for truth by eliciting a confession of ignorance
(84b- c).
The second stage in the process of recollection is the recognition that
certain propositions are true, but not as yet why they are true. This
stage is illustrated in the second section of the dialogue with the slave
(84c-8sb). The level of apprehension now reached is described as 'true
belief' (8sc, 86a). The distinction made here between true belief and
knowledge (8sc-d, 86a) must not be confused with the distinction
made later in the Republic (477-480), where the distinction between
belief (doxa) and knowledge is said to imply a difference in kind
between the objects of knowledge (identified with Forms) and the
14
objects of belief (identified with sensibles). This latter sense of 'belief'
is a specialised sense which Plato continues to use in later dialogues side
by side with the non-specialised sense which we fmd in the Meno. The
distinction between knowledge and belief in the specialised sense is
primarily a distinction between a priori and empirical knowledge, the
term doxa (belief) being adopted by Plato to describe the latter because
of his decision to restrict the application of'knowledge' to a priori levels
of apprehension; but the distinction between them in the Mella, and
later in the Theaetetus and Politicus, assumes the same kind of distinction
as does modern English usage, there being no implication of a
difference in kind between the objects of belief and those of knowledge.
Thus, in the Meno, to have 'true belief' is to believe, correctly, that
something is the case, without being able to justify a elaim to know
that it is the case by giving 'good reasous' why it is the case. Towards
the end of the dialogue, when plato takes up again the question of the
status of 'true belief', he illustrates the distinction by a distinction
between a person who acts as guide to a place using his own experience
of the route, and one who does so relying only on reports about the
route which happen to be correct (97a-b). The former has knowledge,
the latter true belief. ao The nature of the distinction is then explained in
general terms which describe how true belief is convertible to knowledge. True belief, it is agreed, is unstable, since it is never able to meet
criticism by an explanation of the grounds for its truth. To become
knowledge it must be 'tied down' by 'a chain of causal reasoning' or by
'thinking out the reason why' (97d--98a). 31 The reference back (9 8a4-5)
to the earlier distinction between true belief and knowledge in the
dialogue with the slave shows that what is said here about the principle
of distinction is true also for the earlier distinction. And plato emphasises
during the dialogue with the slave that the conversion of true belief
to knowledge is dependent on a process of repeated and systematic
questiouing (8sc-d, 86e).
How, then, precisely, does plato envisage that the slave, who at the
end of the dialogue with Socrates has attained only 'true belief', will
attain knowledge? We may give greater precision to Plato's phrase 'a
chain of causal reasouing' by associating it with a particnlar method of
analysis, the aint of which is to find the antecedent conditions for the
solution of a problem or for the truth of a proposition. There are good
reasons for making this association. The method appears for the first
IS
time in the Meno, and, moreover, is introduced immediately after the
section on recollection (86e if.). It is said to be a method practised by
geometers, and the geometrical example given is of a diorismos, the
determination of the conditions for the possibility of the solution of a
problem." More generally, Greek geometrical analysis was a method
of assuming to be true a geometrical proposition which it was required
to prove, or assuming a geometrical problem to be solved, and attempting, by analysis or 'resolution backwards', to reach a proposition known
independently to be true, or a construction which it was possible to
satisfy. And it may fairly be assumed from all the evidence on geometrical method in Aristotle, in Proelus, and in the Greek commentaries on Aristotle, that it was primarily in relation to the ideal of
reducing geometry to a system that th~ -Greek geometers viewed the
function of non-deductive analysis,33 and that their formnlation of the
method, as it was known to Aristotle, reflected principally its function
of systematising geometrical knowledge and co-ordinating results by
leading propositions back to first principles - to axioms or definitions
or something already demonstrated. In the light of this, it is significant
that Plato, immediately after arguing from a demonstration of the a
priori nature of mathematical knowledge to the a priori nature of
knowledge in 'other branches oflearuing', shonld attempt to apply to
an ethical problem a method of geometrical analysis. It suggests, not
only that he envisages the possibility of applying the same exact method
of analysis in ethics as was practised in geometry, but that it is in terms
of this method that we should interpret the phrase 'a chain of causal
reasoning' which is used later in the dialogue as a description of the
method by which knowledge is to be attained. Thus the slave, who has
acquired merely a number of 'true beliefs' in solving a particnlar
geometrical problem, has still to grasp the proper connexion of the
various steps in the solution; he has still, further, to grasp the significance
of the solution as an instance of a general theorem, the theorem of
Pythagoras; and, taking into account now Plato's great interest, in the
Meno, in a method of geometrical analysis as a valuable method of
explanation and demonstration, it is probable that plato here has
in mind also the ideal of continuing the analysis until those first
principles are reached on which the truth of the theorem itself is
based.
Thus at the level of 'true belief' certain propositions are recognised
16
to be true, but as yet they are isolated truths in that they have not been
recognised as elements in a coherent system. Knowledge is the comprehension of a system, within which all the elements of the system frnd
their explanation. Thus the status of 'true belief' in the Meno is akin to
the status granted to 'uuderstanding' (dianoia) in the Republic (5IIc-e,
534a), a level of thought which plato represents as especially characteristic of contemporary mathematics; like 'true belief' in the Meno, it
does not 'give an account' of its assumptions (Sloe, 533c), but is con-
vertible to knowledge if it conf,rms its assumptions by showing them
to be derivative from higher principles. There is a further point of
similarity between the relationship of 'understanding' to knowledge
in the Republic, and that of true belief to knowledge in the Meno. It is
that in each case the difference between the two levels of apprehension
is a difference in degree of comprehension, and not a difference based on
a difference in kind between the objects apprehended. In the Meno both
true belief and knowledge are gained by recollection, and there is
nothing to suggest that they are concerned with different kinds of
objects. Thus both true belief and knowledge represent apriori levels of
apprehension.
el The objects of true belief and knowledge
What, then, is Plato's conception, in the Meno, of the objects of true
belief and knowledge? On this important point the Meno gives no
explicit guidance. The argument is not a metaphysical argument - it is
not concerned to determine the nature of the reality which is known,
but to demonstrate the possibility of acquiring knowledge at all.
Caution is necessary, therefore, in attempting to draw inferences from
the argument to Plato's metaphysical views at this time. One question
which immediately arises is whether the metaphysical theory of
Forms is here implied. The Meno makes no mention of the Forms in
connexion with recollection. Plato does say at one point that 'the truth
of things' is always in the soul (86b), and some scholars have taken this
to be a certain reference to the Forms, comparing Phaedrus 247C and
249b for similar language in description of the world of Forms. 3 ' By
itself, this argument from terminology is uuconvincing. What has ftrst
to be considered - and this is clearly the central problem - is whether
or not the theory of recollection, as presented in the Meno, implies the
conception of a transcendent world of reality, transcendent in the sense
17
that it is the object of an experience of the soul different in kind from
and superior to, the experience of this life. Ifthere is no such implicatio~
it would follow that the theory envisages no difference in kind between
the experience - and the objects of experience - of the non-incarnate
soul in a prior existence, and the experience of present life.
O.ne argument for the view that the theory does imply some conceptlon of a transcendent reality is that the theory necessarily implies
such a conception, since, without it, the theory leads to an in£nite
regress. 'If all our previous lives were on a level with the present, the
problem of t~~50rigin of know~edge would not be solved, but ouly
thrown back.
This argument lS much more obviously applicable to
the Phaedo doctrine of recollection than to that of the Meno. In the
Phaedo the fact that sensible things can remind us of Forms is said to be
explicable ouly on the assumption that the Forms were known in a
previous existence. It follows that in that previous existence the Forms
were known independently of the snggestion of sensible things. Thus
'the theory of anamnesis logically involves belief in transcendent
For~s'. 36 In the Meno theo:y, on the other hand, the Forms are not
mentIOned, and no attempt IS made to draw a distinction between percep~ual and conceptual levels of apprehension, the distinction on
whICh the argument of the Phaedo is based. Yet there is, I think, in the
Meno, a comparable distinction between levels of experience which
will allow the argument from an infinite regress to be applied equally
well to the doctrine there.
It is important, in considering this distinction, to recognise as two
separate ~nd different presentations of the theory of recollection the
present:tlOn of it in terms of religious ideas (8ra-d), and the presentatIOn of It on the baSIS of the dialogue with the slave (8re-86c). As we
have already seen, we do not have, in the ftrst presentation of the
theo;y: Plato's own ideas at all. The importance of recognising this is
that It IS on the language of this introductory presentation that scholars
often base the view that in the Meno Plato makes no distinction between
the experience of the soul in this life and its experience prior to this life.
And the assumption of these scholars is that the second presentation of
the theory presents fuudamentally the same theory as the ftrst and is, at
th~.most, merely complementary to it. 37 Now even apart from the
1~It1allmprobability that plato is using the dialogue with the slave
SImply as a demonstration of the truth of ideas which are in no way
18
distinctively his own, there are many serious difficulties in this assumption. In the first place the whole orientation of this demonstration and
of the inferences drawn from it is different from that of the introductory
passage. There (8ra-<1) the argument is that the possibility of recollection can be deduced from the religious doctrines of the immortality of
the soul and of re-incarnation. In the subsequent presentation (8re-86c)
the direction of the argument is the opposite of this. It proceeds, from
a demonstration of the fact that knowledge can be recollected (8Sd), to
deduce that the soul must, at the very least, have existed prior to its
present life in the body (8sd-e). It reflects, in fact, the direction of the
argument from recollection in the Phaedo where plato discusses a
further aspect of the doctrine. And the reason for the complete reversal
of the direction of the argument in the second presentation of the
doctrine of the Meno would appear to be that plato is now presenting
the doctrine in an entirely new form which is distinctively his own.
The whole language of this presentation, and the introduction here of
ideas which, as we have seen, point forward to the thought of later
dialogues, suggest the same conclusion. Everything suggests, indeed,
that Plato is using the dialogue with the slave for a purpose beyond that
of illustrating the 'religious' conception of recollection - the idea that
embodied soul and the soul simpliciter. This again implies a distinction
between two radically different kinds of experience. Thus the recollection theory of the Meno, though not directly a metaphysical argument,
does imply a transcendent reality as the object both of true belief and of
knowledge.
This does not, however, allow us to infer that at the time of the
Meno plato had already formulated a metaphysical doctrine of Forms.
None of the metaphysical distinctions associated with that doctrine
when it is explicitly presented in the Phaedo and later dialogues are to
be found in the Meno. Thus no attempt is made in the Meno to distingnish the perceptual and conceptual elements in experience, or to
contrast the instability and imperfection of sensibles with the fixity and
permanence of a separate world of nott"sonsible objects. Nor, indeed,
in the section on recollection, does plato associate his theory of a
priori knowledge with any of the logical distinctions which were made
in the earlier part of the dialogue in the attempt to work out principles
of definition. It may, of course, be argued that since Plato is arguing in
the Meno from the possibility of attaining knowledge in mathematics
to the possibility of attaining it in other 'branches ofleaming', among
which he presumably includes ethics, and since, in particular, he wishes
to show that it is possible, through recollection, to know the 'form' of
virtue, then the recollected knowledge of a transcendent reality, if not
exclusively knowledge of 'forms', includes knowledge of 'forms'. Yet,
if this is granted, it is difficult to argue further that this amounts to ilie
assumption of a metaphysical doctrine of 'forms'. There is, as we have
recollection is based on the accumulated experience of previous lives,
experience no different in kind from that of present life. The choice of
a mathematical problem is surely, too, very significant. plato is singling
out mathematical knowledge as a distinctive kind of knowledge. His
point is that in this field propositions can be recognised to be true
independently of all formal instruction in the subject, independently,
indeed, of the experience of this life altogether, except for the need of
systematic questioning to elicit the recognition. And since, for Plato,
the existence 'in' us, independently of the experience of this life, of this
distinctive knowledge entails the pre-existence of the soul, the conclusion seems inescapable that he is explaining the a priori nature of
mathematical knowledge by appealing to a distinctive type of apprehension, which was granted to the soul in a previous existence and is
superior to the experience of this life. To be noted also is tile distinction
in 86b between the time when we were human beings and the time
when we were not. As Taylor remarked,38 this 'way of speaking about
our ante-natal condition as "the time when we were not yet men" is
characteristic of the Phaedo', and implies a distinction between the
seen, no explicit association between recollection and 'forms',
19
and no
evidence in the dialogue that plato had given any consideration to the
question of the metaphysical status of 'forms', as contrasted with
particulars. His primary concern is to show that knowledge is possible,
and ilie important feature of his ilieory is that it appeals to a transcendent source of knowledge and implies a transcendent reality as the
object of knowledge, transcendent in the sense that it is superior to and
different in kind from the 'reality' which belongs to the objects of the
incarnate experience of iliis life. But no attempt is made to analyse this
latter experience or to specify the nature of its objects; in particular no
attempt is made to associate it with specifically sensible experience. Such
specification, together with specification of the objects of knowledge,
comes with the theory of Forms.
20
Before leaving the question of the metaphysical implication~ of
Plato's theory of knowledge in the Meno, it is importaut to deal :",th a
particular argument in favour of a purely empirical interpreta:1On of
the theory. As we have seen, the difference between true belief and
knowledge in the Meno is a difference in degree of comprehe~Sl?n,. and
not a difference in their objects. It is sometimes argued that this m ItSelf
is enough to show, not only that the metaphysical theory of Forms is
not to be looked for in the Meno, but that no implication of a transcendent realiry is to be looked for. Since the argument i~ that the theory
of the Meno is inconsistent with the theory of Forms, It would appear
to be assumed that the fact that the theory of Forms is the first explicit
presentation in the dialogues of a theory of a transcendent reality entails
that until Plato formulated this theory his theory of knowledge was
a naive empirical theory substantially the same ~s that implied i~
the Orphic-Pythagorean religious ideas ~escribed 1U SIa:-d. But thIS
assumption is clearly groundless. There IS no such ent~ent: Nor
indeed is the argument valid against the view that the Meno Implies the
theory of Forms. It is argued 39 that, if that was the case, t~en plato
would be assuming that belief, as well as knowledge, was dIrected to
Forms and thus would be contradicting a fundamental theSls of the
theor; of Forms, the thesis that there is an absolute distinctio~ between
knowledge and belief in that knowledge has Forms as objects, and
belief sensible,. But it is not the case that, once the theory of Forms has
been formulated, plato consistently uses 'belief' (doxa) with the implication that its objects are exclusively sensible objects. As ~as already
been noted such a use of 'belief' is a specialised one which IS found 1U
dialogues from the Republic onwards side by side witlt the nonspecialised use which we have in the Meno. Even 1U the R:publtc, where
the distinction between knowledge and belief in the specIalised sense IS
first clearly presented, 'true belief' is also used without any of the
implications belonging to the specialised sense (4I3a; cf. 603a). ,. It IS,
in any case, quite clear that a special application .of 'belief' adopted by
plato when marking the distinction between sensIbles and .Form~ has no
necessary relevance to the interpretation of its meamng. 1U a. dialogue
from whim sum a distinction is absent. The fmal step 1U this type of
argument is
(i)
to assume that the apparent inconsistency in the view
that the Meno appeals to a transcendent world of Forms imp~es that
Plato's theory is as yet at the stage of a naive empiricism, and (11) to use
21
the language of the religious ideas introduced in SIa-d as direct
evidence from the text for an empirical interpretation of the theory of
the Meno. Yet there is, as we have seen, every reason for discounting
this passage as an expression of Plato's own ideas. There is, consequently, no ,force in the appeal to the indiscriminate ~atu:e of th~
reference to all things, both things here on earth and things 1U Hades
(SIC), to support the view that plato makes no distinction between
what is experienced in this life and what is experienced prior to incarnation;" nor in the appeal to the reference to 'seeing all things' (SIC), to
support the view that Plato's theory embraces no kind of experience
other than sensible experience."
f] The argument for the immortality of thisoul
There is one further step in Plato's argument to be considered. When
the geometrical problem has been solved, Plato argues that the slave
must either have acquired at one time the knowledge he now has, or
have always had it (sSd). He then argues for the second alternative,
and, since he assumes that it is the soul which has this knowledge, infers
that the soul must be immortal (S6b). The steps in the argument are as
follows: (i) Since the slave has never been taught geometry in his
present life, he must have been in possession of tlte trnth when he was
not of human form. (ii) Since the trutlt is clearly 'in' his soul during
this life, needing only tlte stimulus of systematic questioning to elicit
it, it follows tltat he has possessed the truth botlt when he was of
human form and when he was not.
(iii)
'Time when existent as a man'
plus 'time when existent not as a man' = all time (S6a), which means tltat
for all time the truth has been in the soul. (iv) The soul is, therefore,
immortal. Step (iii) is clearly invalid. If we grant (i) and (ii) we may
infer tltat tlte soul existed for some indefmite time prior to its incarnation. This is, in fact, all that Plato thinks it legitimate to infer from the
argument from recollection in tlte Phaedo (77a-c). And in the Meno the
reservations which he immediately makes (s6b-c) after his 'proof' of
immortality clearly indicate tltat tlte 'proof' is put forward quite
tentatively, without any great confidence in its validity. The interest of
the argument for immortality is tltat its obvious inadequacy suggests
that Plato is only just beginning to consider what tlteory of the nature
of soul is implied by his theory of knowledge. Later in the Phaedo a
clearly formulated metaphysical tlteory, based on a distinction between
intelligibles and sensibles, is linked with a clearly formulated theory of
the nature of soul, based on a distinction between soul and body as the
seat of reason and of the senses respectively. And recognising the distinctive characteristics which must be attributed to soul as being that
in us which allows us to have knowledge of Forms, plato is now
reasonably confident that he can prove the immortality of the individual
soul. In the Meno a radical dualism of this kind is absent. Yet we do have
an appeal to a transcendent source of knowledge; we do have an
implicit distinction between the soul simpliciter and the soul incarnat~;
and Plato, in granting to soul the capacity for a priori knowledge, IS
already recognising this distinctive ability as a ground for thinking of
the soul as immortal.
IS m mathematics. Yet his conviction remaills that knowledge is
attainable, and there is 110 reason to doubt that this cOllviction extends
to ethical knowledge. plato does not, however, attempt in the Meno to
specify the extent of a priori knowledge. All that he says is that what is
true of mathematics is true of all other branches oflearning (mathemata:
8se). This is a question-beggiug phrase," siuce the theory of recollection in the Meno has been concerned to show that learning, or the
acqnisition of knowledge, is to be equated with recollection. It indicates
one of the ways in which Plato's theory of knowledge is, as yet, lacking
in precision. What is needed now, if the question of the extent of a
priori knowledge is to be seriously faced, is a more precise determination
of the nature of a priori knowledge and, as complementary to this, an
examination of the nature of non-a pri~nevels of apprehension, most
particularly of the nature of sense-perception and its status in relation
to knowledge.
22
gJ Plato's reservations about the theory of recollection
The discussion of recollection closes with an indication by plato that the
theory is put forward quite tentatively. He emphasises his conviction
that truth is attainable, but at the same time appears to express doubt
as to whether the theory of recollection is adequate as a justification for
this conviction (86b-c). This note of reservation occurs again in 98b,
with perhaps even stronger emphasis on the conjectural nature of the
theory that recollection is able to provide a criterion of knowledge.
These expressions of doubt should be taken as expressions of Plato's
own feelings, and not as a dramatic compromise in favour of Socrates'
agnosticism. Thus we need not assume that the reservations extend ouly
to the religious ideas of 8Ia-d, or to the proof of the immortality of the
soul in 8sd-86b.43 Plato is putting forward a positive theory of knowledge for the first time, in a form which suggests that many of its
implications have still to be worked out. A tentative approach is therefore natural, and plato is right to emphasise this. It is, indeed, noticeable
that in the rest of the dialogue the discussion of the question whether
virtue can be taught is conducted with much less confidence and succeSS
than had been the case in solving the geometrical problem. We should,
perhaps, take this last part of the dialogue as an illu~tration of th~ initial
stage in the process of recollection, an exploration of the different
aspects of the problem and the difficulties involved, prior to the
approach to a positive solution. Perhaps, too, plato is ill~strating the
point that the application of an exact method of analYSIS to ethic~1
questions is not, in practice, so straightforward and clear-cut as It
3.
23
THE PHAEDO
aJ
The moral orientation of the argument
The Phaedo, with its introduction of the theory of Forms and its new
approach to the theory of recollection, makes some attempt to deal
with these points, although there is no systematic examination of them
as problems in a theory of knowledge. Indeed, the moral fervour which
permeates the whole of the discussion in the Phaedo and the practical
moral significance which is assumed to belong to the arguments may
be said to constitute a hiudrance to any disinterested attempt to deal
with these points. It is essential, before trying to assess the developments made in the Ph.edo, to describe very generally the nature of this
moral background.
. In the frrst part of the dialogue, where Socrates is stating the assumptiOns on which he bases his conviction that the philosopher welcomes
death as a separation of the soul from the body, a radical contrast is
made between the soul, as the seat of 'pure reason' or 'pure thought',
an~ the body, as the seat of desire, pleasure, and the senses (64d-{56e).
It IS assumed that the life of philosophical 'reasoning' and 'thought',
which are activities of the soul, is a good life, and that the life of bodily
indulgence is bad, in that it is a hiudrance to the good life. Thus it
PLATO'S THEORY' OF KNOWLEDGE
deprives men of the leisure for philosophical thought (66c); in a later
reference it is argued further that indulgence in bodily pleasures results
in a false conception of the truth (83c-d), which presumably means that
it results in a false conception of what good is. Now it is within this
general condemnation of the body that the senses are morally condemned
as a hindrance to the life of reason. 'Reality' is not apprehensible by the
senses, but only by 'pure and simple' thought, uncontaminated by the
senses, which are inaccurate, uureliable, and convey no truth (65b-66b).
This tone of moral condemnation would seem to be singularly inauspicious for any subsequent attempt to evaluate sense-perception
from a more specifically epistemological point of view. Indeed, an
apparendy paradoxical aspect of Plato's position here is that, while he
is ready to condemn morally the body, its 'flesh' and its senses, and to
identify man's good with the soul's activity of disinterested pursuit of
truth through 'pure reasoning', yet he represents 'the good itself' (65d)
as something to be known by the soul as a result of its inquiry, as if the
goal of its inquiry here is to justify its assumption that its 'good' lies in
the activity of' pure reasoning'. He appears, in fact, to be prejudging the
issue. This is perfecdy true. Yet it is important to add that this first part
of the Phaedo is merely a statement of Plato's assumptions, and that the
order and 'irrationality' which justifies his assumption that man's
'good' is to direct his activities to knowing the Forms, to live the life
of philosophy. For the affinity of the individual soul's function to that
of the co~mic soul, the activity .of which is implied, for Plato, by the
fact of rational deSIgn and order ill the world, implies that its 'goodness'
is to be achieved by assimilating its activity to the activity of the cosmic
soul, since the cosmic soul is 'good' in that it is directed to the main-
24
remainder of its argument is the first instalment of a task, continued
throughout the dialogues, directed to the substantiation of these
assumptions. It is also important to examine briefly the reasons for the
emphatically moral orientation of the arguments of the Phaedo.
An obvious influence here is the body of religious ideas which had
already influenced plato in the Meno, especially the ideal of the 'purification' of the soul from bodily contamination as a preparation for
future discarnate life. The association of this ideal with the intellectualism of the Socratic thesis that virtue is knowledge does much to
explain Plato's conception of the soul's activity as an essentially
intellectual or theoretical activity, his association of this activity with
'goodness', and his moral condemnation of bodily activities. His own
justification of this ideal, on the basis of his own theory, links the soul's
activity with knowledge of Forms and, further, with a teleological
conception of the 'goodness' of the order and intelligibility of the
world, a conception which first assumes prominence in the Phaedo. It
is, indeed, in the last resort, his assumption that the systematic order of
the world, which alone permits its intelligibility, is 'better' than dis-
25
tenance of an order assumed to be 'good', and uses, as its 'model', the
world of Forms. These very general assumptions are not all explicit
in the Phaedo, but it is certainly within the teleological conception of
the 'goodness' of an ordered and intelligible world that Plato, in the
Phaedo, wishes man's individual goodness to be assessed.
This explains several important aspdts of the moral orientation of
much. of Pla:o's theory of knowledge, especially as it is developed in
the mlddle. dIalogues. It explains, in the first place, why it is possible, in
the RepublIC, to present knowledge of 'the good' as the culmination of
dialectical investigation. Within the broad conception of the'goodness'
of the systematic order of the world, knowledge of 'the good' is the
systematIC comprehensIOn of the world of Forms, which alone makes
the ord~r of the ph~sical wor!d fully intelligible. It presumably includes
the realIsatIon that goodness IS constItuted by the systematic order of
the world of Forms, and that the 'goodness' of the order of the physical
world IS denvatlve from this. It explains at the Same time that, although
Plato tends to approach the question of the conditions for the attain-
ment of knowledge from a moral point of view and with moral
assumptions which seem to us inappropriate to an examination of
problems in a theory of knowledge, yet it is not specifically moral
knowledge, as opposed to other fields of knowledge which is being
considered. It is a mistake to think of Plato's theory ~fknowledge in
the mIddle dIalogues as bemg very specially concerned with the question
of the nature of knowledge of specifically moral principles or of
specifically moral Forms. The theory of Forms, and the th~ory of
knowledge associated with it, are, as we shall see, theories of a wide
general application. Though Plato, from the point of view we have
now examined, thinks of the activity of soul which aims to gain knowledg~ of Forms as a 'good' way of life, the content of this knowledge is
not ill any w.ay speCIally restr:cted to what is specifically moral. Thus
the moral onentatlon of plato s theory in the Phaedo does not affect in
c
26
any way his conception of the extent of a priori knowledge. Where it
does affect his theory is in its assessment of the cognitive value of senseperception. The result is an inconsistency on this point throughout the
middle dialogues. On the one side is a moral condemnation of the
senses as systematically misleading and inaccurate. On the other is a
more serious assessment of the value of sense-perception and its objects
as aids to knowledge. In this respect it is not, I think, an exaggeration
to say that in the middle dialogues Plato's moral puritanism bedevils
his theory of knowledge.
One further influence must be briefly considered before the theory
of the Phaedo is examined. In the Metaphysics Aristotle states that an
important factor in the development oEplato's theory of Forms was an
acquaintance, through Cratylus, with the Heraclitean doctrine of
universal 'flux', which led plato to the conviction that, since all sensible
things are always in flux, then they cannot be the objects of knowledge,
and, conseqnently, that there must be other things to serve as objects of
knowledge which are not sensible and not subject to changes (9 87a32-4;
1078b12-16). There are no adequate grounds for questioning the
general truth of Aristotle's statement. Plato, as we shall see later, did in
fact accept the Heraclitean doctrine of flux as true for sensibles, and
there is no reason to doubt that consideration of this doctrine first led
him to reflect on the adequacy of sensibles as objects of knowledge. Nor
need we doubt Aristotle's further statement that Plato was led to the
formulation of the theory of Forms by combining reflection on the
Heraclitean doctrine of flux, as applied to sensibles, with reflection on
the Socratic search for general defInitions. Yet though Aristotle says
that Plato became acquainted with the Heraclitean doctrine in his
youth, the dialogues suggest that only at a date subsequent to the time
of writing the Meno did reflection on the application of the doctrine
to sensibles begin to influence the development of Plato's theory of
knowledge. There is no consideration of, indeed no reference at all to
sense-perception in the discussion of recollection in the Meno, and there
is no metaphysical doctrine of Forms. And it is difflcult to imagiue that
Plato's fIrst theory of knowledge would have taken the form of the
Meno theory if he had already come to any conclusions at all about the
relation between sense-experience and knowledge, much more difficult
if he had already formulated the doctrine of Forms. The important
thing to note here is that Plato's theory of knowledge as a priori is
THB THEOR.Y OF RECOLLECTION
27
iuitially quite independent either of a theory of Forms or of any theory
about the nature of sense-perception. It is ouly when he tries to give
greater precision to his theory of knowledge that he introduces, as a
newly developed doctrine, a doctrine which tries to give a more clearcut distinction betweeu a priori knowledge and non-a priori levels of
apprehension by basing it on a distinction between non-sensibles and
sensibles, and, from the epistemological point of view, between concepts and percepts. This is the signifIcant development made by the
theory of recollection in the Phaedo, which makes, for the first time, a
distinction between sensibles and transcendent Forms." A fmal point
to be made about the influence on Plato's theory of his consideration of
the application of Heraelitean doctrine to sensibles is that acceptance of
the doctrine as true for sensibles does nOt itself imply acceptance of the
view that sense-perception is systematically misleading and erroneous,
or that sensibles have no determinate characteristics, both of which
views are put forward in the middle dialogues as derivative from the
flux theory of sensibles. In the late dialogues it is no longer assumed that
acceptance of the flux theory carries with it acceptance of these views.
Thus it is especially in considering the middle dialogues that we have
to recognise that Plato's disparagement of sensibles is sometimes a moral
disparagement of them, and that this factor cannot be neglected in
accotmting for the exaggerations into which he is sometimes led.
bl Recollection and the Forms
The detail of the theory of recollection in the Phaedo must now be
exantined. The discussion begins by repeating what the MenD had said
about the way in which knowledge is elicited. Proper questions will
elicit correct answers about everything (73 a); this points to the existence
in us of knowledge and of 'a right account'.46 The way in which geometrical problems can be solved provides, it is suggested, the clearest
proof of this. Having thus briefly reviewed the theory of the Meno,
Plato now introduces an entirely new development in the theory of
recollection, indicating its novelty by his suggestion that, if Simmias is
not convinced by it in its presentation so far, then perhaps he will agree
if it is presented in another way (73b). plato begins by considering
examples of association, where the present perception of something
remiuds a persou of something else, not at the moment perceived,
which is associated in his mind with what is perceived, either by
28
1
PLAT0 S THEORY OF KNOWLEDGE
resemblance (e.g. the association between a portrait and its original) or
by contiguity (e.g. the association between a lyre and its owner). In thIs
way recollection comes from things 'either like or uulike' \74a), and IS
possible ouly if a person has prior knowledge of what ~e IS .reru:nded
of (73C). In caseS of association by resemblance the questIOn mev:tably
arises 'whether the similarity between the object and the thing It
reminds us of is defective or not' (74a). It is at this point that plato
introduces a special case of the distinction between perceiving and conceiving. In the earlier illustrations this distinction (73C, d) seems to have
been viewed by plato as a distinction between the present perception of
a particul~r sensible thing and the calling to mind of a particular
memory image. We now h:ve a distinction between t,he present per~
ception of particular equal things and the conception of the equal Itself
or 'equality' (74c); being reminded of the latter by the.for;"er IS taken
to be a case of association by resemblance. This IS a dlstmctlon between
Forms (though the technical term is not introduced until ;"uch I~ter in
the dialogue) and sensible particulars. The logical baSIS of ~t IS a dISWlCtion between universals and particulars, and, from an epIstemologIcal
point of view, between concepts and percepts. With the ~dded metaphysical assumption which Plato makes (74a, 7Sd, 76d), I.t becomes a
distinction between what is perfectly real, havmg an mdepender;t
existence and constituting an ideal standard or archetype, and what IS
necessarily inferior, resembling the archetype but o~y a~proximating
to it in its perfection (74a--c, 7sa-b). The dlStmCtlon IS of ge~eral
application valid for all cases where we apply to the general term our
seal and m~rk as being "the thing itself" , (7sd). On this distinction
plato bases his argument for the pre-existence of th? soul. ~e assumes
that in ordinary experience it is inevitable that sens'~le particulars are
recognised to be defective in their resemblance to the Ideal standards or
Forms (74d-7Sb). He assumes further that no Form can be recollected
withont the reminders given in sense-experience (74b, 7sa-e, 76d- e).
And since reference to an ideal standard, which all perception involves,
implies previous knowledge of the standard, then mat knowledge, it is
argued, must precede the first use of the senses; it must, therefore, have
.
been possessed before birth (74e-7S c).
This argument relies on a distinction between sensa.tl~n a?"d a conceptnallevel of apprehension. But the appeal to the dlStinctl,:e nature
of conceptual thought does not inlply that any concept deSignates a
29
Form. What it does, apparently, imply is that all concepts which have
sensible instances designate Forms, but no others do so.4' This is a very
general claim, and its implications must be carefully considered.
In the first place, what is the precise nature of the ideal standards or
Forms? The Phaedo theory of recollection clearly falls down unless they
have separate existence, in a non-sensible form. 'The doctrine of
ananmesis, if it is to be of any use, implies a previous direct knowledge
of disembodied Ideas.' "It implies their separate existence in this form,
since if in a previous existence 'we knew them ouly on the suggestion
of things of sense, the reference to a former existence does nothing to
explain the process of coming to know them' .4' plato acknowledges
that the postulate that Forms exist is \he fundamental premiss of his
argument (76e-77a). In what way, then;-does he make the distinction
between Forms and sensibles?
As an argument for the view that sensible instances of a Form are
distinct from the Form itself and necessarily imperfect exemplifications
of the Form, he says that whereas equal stones or pieces of wood sometimes seem equal to one man, but not to another, 50 though they have
not changed, yet 'equals themselves' never appear to be unequal, nor
equality to be inequality (74b--C). Since it is said that the two sticks or
stones are in fact equal and remain so, it is presumably meant that it is
some difference in perspective or some difference between me individual percipients which leads one to judge that they are equal, the
other that they are unequal. Thus it is difficult to see the force of the
argument as an argument for the imperfection of the objects of perception. For it implies that there is noming inconsistent in two iliings being
perfectly equal and at the same time appearing equal to one man and
unequal to another. Yet there is no doubt that this type of argument
was considered by Plato to constitute an inlportant reason for postulating the existence of non-sensible Forms, and for condemning sensibles
as 'imperfect'. To postulate a Form is to postulate the existence of
something which, unlike sensibles, can never have its contrary predicated of it. The principle by which Forms are thus postulated as nonsensibles is that
each pair of opposites contains two members, different from one
another, and hence, since experience shows that any sensible deserving to be called by the name of the one opposite may with equal
30
propriety be called by the name of the other opposite, no such
sensible is genuinely identical with either of the opposites (otherwise
they would not be two at all, but coincide with one another
contra hypothesim). 51
What makes the use of the principle particularly surprising in the
present passage of the Phaedo is not only that plato carefully specifies,
and hence recognises, the particular conditions which allow a pair of
contraries to be here predicated of the same sensible instance, but also
that he makes the fact that the sensible instances are instances of one
contrary, and not the other, the foundation ofhis argument for recollection. For having used, in 74b-c, the argument that equal sticks or stones
sometimes seem to possess a pair of contrary predicates as an argument
for distinguishing 'equality itself' from sensible instances of equality, he
then proceeds (74c-7Sb) to show that the equal sticks, in that they are
equal, do possess the detetruinate characteristic of equality, and do not
possess the characteristic of inequality. As far as the sensible objects
themselves are concerned, the imperfection is said to be their failure to
exemplify perfectly in their characteristics the standards constituted by
the archetypal Forms, and this imperfection does not include the
exemplification of the contrary of the Form to which they approximate. Moreover, the theory of recollection here is that the function of
the senses is to prompt recollection of Forms through experience of
sensible instances which are imperfect in this sense. Thus the argument
of 74c-7 5b makes perfectly clear that the earlier argument of 74b-c is
now left out of account, and that plato is not suggesting that the
experience of apparent unequals can just as well remind us of equality
as the experience of apparent equals. What he is presenting is the conception of Forms as ideal standards or archetypes, and of sensibles as
'copies' or 'images' (though these descriptions are used only in later
dialogues) which resemble the Forms. It is the fact of this resemblance
which allows the possibility of recollection of Forms from experience of sensible particnlars. Later in the dialogue the relationship between Forms and sensible instances of Forms is described in different
terms, but in a way which implies a relation of resemblance or
similarity between Forms and sensibles in respect of the determ~te
characteristics which sensibles possess. Thus the reason why a particular thing is beautiful is said to be that it participates in 'the beautiful
31
itself'; it is the 'presence' of the Form which makes it beautiful
(rooc-d).
The assumptions, then, on which the theory of recollection in the
Phaedo is based are (i) that non-sensible Forms exist: (ii) that sensible
instances of Forms are imperfect 'copies' of Forms: (iii) that these
instances, in virtue of their resemblance to Fornls, are able to act as
'reminders' of Forms. Thus the ability to recognise instances and to apply
concepts to experience is given a metaphysical interpretation, and
becomes the basis now of Plato's theory of knowledge. The concept of
knowledge is prominent in the discussion, both in the initial illustrations of association in terms of a distinction between perceiving and
conceiving (73c-d), and in the followi1(g argument (74b-c). It is, says
Plato, from the experience of sensible instances that knowledge is
acquired. It is unfortunate, therefore, that, having established as fundamental for his theory the relation of resemblance between Forms and
particulars, plato should complicate this thesis uunecessarily by adding
that 'so long as the sight of one thing leads you to conceive another,
whether like it or unlike, a case of reminder must have occurred'
(uc-d). Comparison of the phrase 'like or unlike' with similar phrases
in 74a and 76a shows that Plato is referring in this phrase to association
by resemblance and association by contiguity respectively. Thus it
appears that Plato now wishes to include within his theory of how
recollection of Forms is effected the factor of association by contiguity,
which he had mentioned earlier in order to illustrate the idea of association (73d-e) but had then left aside when he went on to make association by resemblance fundamental to his argument. It appears, in fact,
that he is now saying that it does not matter whether you are reminded
of equality by seeing two equal sticks or reminded of it by seeing a box
which you associate with equality because it once happened that you
saw two equal sticks in it. Iu that case the theory of recollection includes
cases where a Form is recollected from experience of sensible particulars
which are not instances of the Form, but are instances, presumably, of
another Form related in only a trivial and accidental way to the Form
of which they are 'reminders'. It would have been much better for his
argument if plato had restricted his use of the idea of association by
contiguity to the illustrations of73d-e. 52 To introduce it as part of the
theory of recollection is to introduce something which not only is
unnecessary to the argument, but also complicates it in a way which
tends to divert attention from the fuudamental point of the theory.
And the fundamental point is that recognition of sensible instances is
made possible by their resemblance to a Form, and that this recognition
is not only the indispensable basis of the possession of a Form in this life
(75a), but in fact implies that possession prior to this life (74e, 75a).
Indeed, immediately after introducing the above complication, plato
goes on to stress that the judgement of the deficiency of sensible
particulars to Forms necessarily follows upon our application of concepts to experience, and that the ability to apply concepts to experience
thus implies, for each concept, the possession of a standard of reference
whose perfection is to be contrasted with the imperfection of the
particulars (74d-75b). And in making this point he reaflirms that the
relation between Form and sensible instances is one of resemblance. For
it is the relation of imitation which is implicit in Plato's remarks when
he says here that sensibles strive to achieve perfect realisation of the
Form.
This examination of the theory of recollection in the Phaedo has
attempted to show the kind of metaphysical interpretation which
Plato gives to the fact that sensible characteristics are recognisable. He
assumes that this recognition is possible only at a conceptualleve! of
apprehension, and that the ability to apply concepts to what is given in
sensation implies the possession of a Form, an ideal standard or archetype which sensible instances resemble but never perfectly exemplify.
The main distinction employed in the argument is between percept and
concept, or between sensation and a conceptual level of apprehension.
The function of the Form as a universal is not Plato's concern here,
though he always assumes that it is a universal in the sense that it is
applicable to all its sensible instances (Cf.74aII-12, 75a2, b1-2, 7-8).
Now the distinctions which plato makes in this part of the Phaedo are
important distinctions for his theory of knowledge , but before they are
considered further from this point of view it is important to consider
briefly the difficnlties in his conception of Forms as ideal standards or
archetypes.
The principal difficulty, as far as the theory of recollection is concerned, is clearly stated by plato himself in the Parmenides (1J2d-133a),
the first part of which is devoted to a criticism of the theory of Forms
as it is presented in the Phaedo. The difficulty is that if sensible characteristics are explained in terms of 'participation' of sensible objects in
33
Forms, and if, further, this 'participation' establishes a relation of
resemblance between sensible objects, in respect of their characteristics,
and Forms, then an infinite regress arises. For the resemblance between
all ~en~ible instances of a Form is explained, on Plato's theory, as
derIvatIve; they have a common resemblance to the same Form. But
the prin~iple that the resemblance between two or more things is to
be explamed as thus derivative is applicable to cases of resemblance
between Form and sensible instances of Form. Hence the infinite
regress. Thus the implicit criticism is that to conceive the Form as an
archetype which its sensible instances resemble is to conceive it as a
perfect particular object possessing the same characteristic as its sensible
instances. Later in the Phaedo plato does in fact aflirm that 'the beautiful
it~elf' is .bea~tiful (IOOC). If the criticis~isvalid then Plato's attempt to
dlStlngmsh, m h~s theory of recollection, the Form from the objects
whIch resemble It, and to separate it from the class of those objects,
fads, and the theory Itself, as a theory of knowledge as a priori, falls
~OWll. And the criticism is, in fact, valid against Plato's theory here,
In so far as he fails to distinguish between the Form and perfect
mst.nces of the Form. One indication of this is that he refers to the
Form, of Equality indiscriminately as 'equality' and 'the equals themselves. (74c), the latter phrase bemg used because 'a perfect instance of
EqualIty 15 not one single perfectly equal thing but rather a pair of
things that are perfectly equal to one another'. 53 Later in the dialogue
Plato further ascrIbes to the Forms, in contrast with sensibles the
characteristics of being simple, non-composite, immutable, and et~mal
(78c- d). Yet these further distinctions are not sufficient, or indeed of
the right kind, to rid Plato's theory of the difficulty we have been
discussmg. They serve rather to reaffirm that Plato conceives the Forms
as ideal. objects, d a kind which makes it difficult for them to perform
the logIcal funct10ns which Plato apparently assumed that they could
p~rfor".'. For It must be remembered that it was by appeal to the
dlStlnct1ve nature of a conceptual level of apprehension that plato
argued for the existence of archetypal Forms as the objects of thought.
;IDd though the Form is distinct from the concept, Plato assumes that
It shares, as an object of thought, the virtues of the concept, as a unit
o~ thought, m the task of acquiring knowledge. Yet in attempting, in
this later part of .the Phaedo, to distinguish it as a non-sensible object
from senSIble objects by ascribing to it, in terms which point to
34
Parmenidean influence, 54 characteristics chosen as opposites to those
which belong to sensibles, he is at the same time in danger of depriving
it of those characteristics of complexity of structure and of relation
which would seem to be indispensable to it as an object of thought, at
least if the ideal of systematic knowledge put forward in the Meno is
to be realised.
1
c The contribution of sense-perception to knowledge
It is now time to examine more fully the implications for his theory of
knowledge ofPlato' s conception of Forms and their relation to sensibles.
We have seen that Plato's argument is that sensible instances of a Form
resemble the Form, and that it is in virtue of this resemblance that
sensibles can act as 'reminders' of Forms. There is, further, the apparent
assumption that to be reminded of the archetype by the sensibles which
resemble it is to acquire knowledge of the archetype (74b-c). In
discussing this argument elsewhere" I argued that the assumptions
necessary to justify the r6le which plato here assigns to the senses were
'(i) that there are Forms, (ii) that the soul has at some time known
them, 56 (iii) that the sensible world, in all relevant" instances, is a
sufficiently approximate copy of the world of Forms to be able to give
correct suggestions of that world, and (iv) that the senses arc to be
always trusted'. And I concluded that the main fault of the theory was
that 'plato is apparently assuming that the fact that we attain a conceptuallevel of apprehension automatically affords a recollection of
Forms, and tlms implicitly assumes also the impossibility of false
judgement' .
Professor Hackforth agreed that this conclusion is 'undoubtedly
justified' if the references to knowledge in 74b-;; are taken 'at their
face value', but argued that there is no need so to take them. 58 I accept
this argument. But I did in fact argue then that, even if we assume
that knowledge is not there being used in a sense which implies that the
Forms are known as fully as they can be known, Plato's argument still
appears to lead to the above conclusion. My argument was that if we
assume that the Phaedo implies a very wide gap between (a) the ability
to recognise sensible instances and to apply concepts to experience as a
mark of that recognition, and (b) knowledge of Forms, yet the validity
of Plato's argument from recollection still depends on stage (a) being
an accurate pointer to stage (b).59 Thus I would still defend assumption
35
(iii) above. It may be argued, against it, that it is enough for Plato's
argument if some sensible instances are sufficiently approximate copies
to act as 'reminders' of Forms, or, more generally, that the argument
for the pre-existence of the soul rests on the possibility of recollection
of Forms, so that it is enough for the argument if we ever recollect
Forms. Yet Plato's argument in fact attempts to establish much more
than this minimum reqnirement. He makes it clear that the relation of
resemblance between Form and sensible instances exists in the case of
all 'things-in-themselves', and that it is ouly through sense-perception
that recollection can be initiated (7Sa-d, 76d-e). And remembering
the very general distinction between conceptual and perceptual
apprehension which is the basis of the argument, it would appear
to follow that any sensible particulars t),which a concept is applicable
arc, ipso facto, in respect of any given characteristic, instances of a
Form, and consequently resemble the Form. In other words, any
recognisable characteristic which belongs to sensibles qualifies the
sensibles, in respect of that characteristic, to be a copy of a Form.
And the fact that the resemblance is said to belong to all instances of a
Form, and that the fact of this resemblance is assumed to be unaffected
by any variability in the conditions of perception, implies that in all
cases sensibles are 'sufficiently approximate copies'. Otherwise they are
not, on Plato's premisses, instances of anything, and do not comc
within human cognisance at all.
As for assumption (iv) - that the senses are to be always trusted - my
thesis here, I would now agree, needs further clarification. In stating
it I did not, of course, wish to suggest that plato was unaware that
people make mistakes and misapply concepts, or that he was consciously
arguing that any application of a concept to experience is a correct one.
What I did wish to suggest was that the generality of the distinction
which is the foundation of Plato's argument leaves the possibility of
making mistakes Ollt of accOlmt, in that it does not include any criterion
for distinguishing genuine cases of being reminded of a Form from
spurious cases. Thus, if plato is assuming that 'copies' of Forms are
not always seen as they actually are, he is assuming that recollection
supervenes ouly when the 'copies' are seen as they actually are, and
that apparent cases of recognition of sensible characteristics where the
characteristic does not in fact belong to the sensible object are not cases
of recollection of Forms (assuming, as we must, that recollection of a
Form means correct recognition). If this is the case, then there is an
implicit distinction between one class of instances of recognition
(incorrect ones), and another class (recollection of Forms). But the
distinction between sensation and a conceptual level of apprehension
on which Plato's argument rests does not include this distinction, so
that unless it is given further qualification the argument is one which
treats all cases of recognition as a single class, and, further, as cases of
recollection of Forms. It is on this basis that I argued that assumption
(iv) is an implicit condition of the validity of Plato's argument. I might
add that it is implausible to assume that Plato is arguing that correct
and incorrect recognition constitute recollection of Forms, in that even
incorrect recognition puts us in mind of some Form, even though the
sensible stimulus is not an instance of it. For his argument is that
recollection is dependent on actual resemblance between sensible
instance and Form.
If, however, assumption (iv) is an implicit condition of the validity
of the argument, yet it is one which plato seems to have been unaware
of. It is logically implied by his argument, but clearly not an indication
of his views on the reliability of sense-perception. This may readily be
granted. But, even allowing that plato intends no more than that
recollection supervenes only when the 'copies' are seen as they actually
are, his argument, in the claims which it makes for sense-perception
and its objects as pointers to reality, remains inconsistent with earlier
and later passages in the dialogue where the senses are condemned in
a tone of fierce moral disparagement as unreliable, inaccurate, and
devoid of all truth, and their objects condemned as devoid of all truth
and constancy (64d-66e, 79C, 83a-b). For his argument presupposes at
least a relative stability and constancy in sensibles, and also presupposes that the senses are not ineradicably and systematically misleading.
As Cornford remarked, in commenting on 79C, 'the fact that sensible experience may be the occasion of Recollection is lost sight of'. 60
In this examination of Plato's conception in the Phaedo of the relation
between sense-perception and knowledge it is now necessary to consider whether plato says or implies anything in his account of the
method whereby knowledge is attained to show that he conceived
knowledge to be something more than the immediate apprehension
of a Form following the prompting of a sensible reminder. In 74b-c
he says that to recollect a Form, in the way that he has described, as a
37
result of the :re~ders' given in sense-perception, is to acquire knowledge. How 1S tillS to be interpreted? The first thing to note about the
contributio~ of sense-perception to knowledge, according to Plato's
argum~nt, .IS that plato does not have in mind any process of reasoned
generali~atlOn from repeated sensible instances, or any process of
systematIC use of sense-perception in acquiring knowledge. He interprets
conceptualapprehension as being remiuded of an archetypal Form by
anyone of Its senSIble copIes. Perception of a single instance is assumed
to be snfficie~t as a r~minder, and the question of reflective comparison
and progressIve clarificatIOn does not enter into the argument. Now
if the knowledge mentioned in 74b-c is taken to mean full knowledge
of Forms, the argument would imply a direct and immediate transition
from a single instance of perception t~ knowledge, or from sensible
to Form. Wh~t grounds are there for ascribing this apparently implausIble doctnne to Plato? It might be argued that in his argument
~or recollecMn plato is postulating Forms only for simple characterIStics of ,sensIble things, characteristics which, in that they have no
compleXIty, are ~ot, able to be analysed, and that this is implied by his
subsequent descnptlOn of Forms as simple, non-composite objects.
'Absolute Simplicity, would belong only to Forms of qualities, hot,
cold, etc., w~t things having a derivative reality from these and
hencemfact bemg composite would not perhaps be counted as Forms.'6l
In that case, recollection of Forms from sensible remiuders could be
said t? afford full and immediate knowledge of Forms, as a direct
acquamt~ce with ,.bs,olutely simple Forms. There is, admittedly, a
c,ontradlctlon ill thinking of analysIs of objects which are absolutely
~Imple, But there is nothing at all in Plato's argument from recollection
ill the Phaedo to suggest that he means to restrict the number of Forms
In this way, and the evidence of the dialogues indicates clearly that it
:was not until later dialogues that he became aware of the difficulties
illvolved in his conception of the analysis of 'simple' Forms, It is true
that m hIS argument he has particularly in mind terms for qualities
and relatIOns r~ther than terms denoting concrete 'things', i,e, commou
nouns: But he IS clearly nN thinking of them here as essentially simple,
and hIS argument, from 1tS very nature, is not in fact restricted in its
application, to terms of this kind,
'
, Assuming, th;n, tha: n,o such restriction is implied, what evidence
IS there ill plato s descnptlOn of recollection that his conception of the
process of attaining knowledge goes beyond the conception of a direct
recollection of Forms from sensible reminders? At 76b he says that
knowledge of Form implies the ability to 'give an account' of it. This
seems to suggest that knowledge is something more than what is
afforded by reminders from sense-perception. It is in asking the
question whether we are born with knowledge or recollect what we
knew before birth that plato says that a condition of knowledge is
that a man should be able to 'give an account' of what he knows. And
since it is agreed that all men cannot give that account, it is concluded
that they do not have knowledge now, but must recollect what they
once learned; what they knew is forgotten at birth and has to be
recovered. Does the phrase 'to give an account' indicate the method
of analysis introduced in the Meno, and further described later in the
Phaedo (99d-I02a; the phrase 'to give an account' is in fact used in
lOId and interpreted as the process of analysis earlier described in the
Meno)? If so, then 'giving an account' of a Form would presumably
be analysing it so as to explicate its meaning. In this way knowledge
of the Form would be acquired. And if this were the case then the
question of the extent of the contribution of serue-perception to knowledge would become the question of the extent of its contribution to
this process of 'giving an account'. Now whether the phrase 'to giv:e
an account' should be interpreted in terms of the method of analysIs
described in the Fhaedo at 99d-I02a is a question which can better be
aruwered after a detailed examination of that passage. But it is worth
while at this point to'consider at least what is implied about the r6le of
sense-perception in the attainment of knowledge by Plato's conception
of the relation between Forms and seruibles, assuming that the Form
is amenable to systematic analysis.
In the first place systematic analysis would be possible ouly if the
Form was complex. Now if the Forms are archetypal objects, and
sensible characteristics are •copies' of Forms and resemble them, it
would seem to follow that the sensible 'copies' resemble the Forms in
their complexity. In other words, the fact of being a 'copy' of a Form
would seem to entail a relation of complete, though imperfect,
resemblance between' copy' and Form. The imperfection would consist only in the fact that the 'copies' never perfectly, or exactly, match
the ideal standard constituted by the Form. I think it is quite clearly
implied in Plato's argument that the imperfection or deficiency of
39
seruibles is imperfection in this sense. Thus if the recollection of a Form
is effected initially by perception of anyone 'copy' of a Form, and if
the complexity of the Form is reflected in the complexity of its 'copies',
then there would seem to be no reason why the recollection of tlle
complexity of the Form should not be similarly effected by perception
of the complexity of the 'copy'. Now this implicit assumption of a
parallelism in structure between archetypal Form and sensible instances
serves to emphasise a major difficulty in Plato's theory. He has
formulated his conception of a priori knowledge in terms of the
characteristics of archetypal non-sensible Forms as objects of that
knowledge. But the Forms have been conceived in such a way in
their relation to particulars that it bec~mes immediately implausible
to assume that the propositions which would figure in the analysis of
the Form have a formal validity which makes their truth independent
of sense-experience. The' copies' are tied too closely and systematically
to the Forms, and hence similarly is sense-perception tied to knowledge,
to make plausible a thesis that knowledge is a priori. Indeed, if we add
the fact that Plato's theory fails to distinguish, as it should have done,
between Forms and perfect instances of Forms, it becomes clear that
his analysis of recollection in the Phaedo attempts an analysis of conceptual experience and of recognition of sensible characteristics which
is more consistently plausible as part of an empirical theory of knowledge. It is an analysis very much akin, in its implications, to what
Professor Price has called the Philosophy of Ultimate Resemblances
which, instead of explaining the resemblance between sensible objects
in respect of given characteristics as derivative, from the fact that the
characteristics are instances of the same tuliversal, explains it in terms
of standard objects or class-exemplars within the class of sensible
instances. 62 As we have already seen, Plato himself, in the Parmenides,
questioned the legitimacy of raising the Forms, as conceived by him
in the Phaedo, to the rank of independent universals, separate from the
class of their sensible instances. Even if we grant the legitimacy of this
the fact remains that the distinction on which Plato's theory rests, the
distinction between, on the one hand, universal and sensible particular,
and, on the other, concept and percept, is far too general a distinction
on which to base a theory of knowledge as a priori; the theory needs
such further qualification as will distinguish further, witkin the field of
conceptual thought, a priori from non-a priori truths.
40
As it is, the impression left by the middle dialogues is that Plato,
after presenting the relation of Forms to their sensible instances as a
relation of archetypal objects to sensible 'copies', strives, at the cost of
much inconsistency, to keep Forms radically separate from sensibles,
and kuowledge radically separate from perception (i) by a fierce
disparagement of sensibles as utterly untrustworthy, and (ii) by
assuming that the analysis which yields kuowledge of Forms is entirely
independent of perception and appeal to empirical evidence. (i) is
already clearly evident in the Phaedo. (ii) also, it may be argued, is
already implicit in the passages where plato, while disparaging the
sellSes, gives high moral praise to the activity of 'pure reason' or 'pure
thought' which belongs to the soul (64d-66e). But it is in fact only
much later in the dialogue that plato properly considers the question
of philosophical method, and presents the best method explicitly as a
method whose practice is independent of perception and appeal to
empirical evidence.
d] The method of hypothesis
The significant thing about this later passage is that the method is
described and assessed independently of the theory of Forms, in a way
which clearly suggests that plato has not, at this stage, integrated the
method and the theory, and, consequently, that he has not yet begun
to consider the possible inconsistencies which would arise from any
attempt to integrate them. This point is an important one in assessing
the development of his theory of kuowledge, and this passage of the
Phaedo (99d-I02a) deserves detailed examination, the more so since
there has often been confusion in the interpretation of it.
plato has just argued that the method of previous mechanical types
of scientific explanation was a method of direct sensible observation.
He now presents as an alternative and preferable method and type of
explanation the method of analysis of propositions (logoi, 9ge). This
involves, in the first place, an examination of the logical consequences
of the initial hypothesis, in order to see not only what those consequences are, but also what inconsistencies with other propositions
acceptance of the hypothesis entails, and whether there is any contradiction implicit within the hypothesis itself. It involves further an
analysis which will discover the propositions from which the hypothesis itselfis deducible (Iooa, IOId-e). If we take the illustration of the
41
method of analysis in the Meno (86d-89a) as evidence for the form f
tJ:e .analysis mentioned in the Phaedo, then the analysis will be a syll~
g~stlc analysIs. w~~h seeks the premisses necessary to substantiate a
given ~~ncluslOn. The Ideal put forward here is, then, an ideal of
proposItional analysis.
Now when Cebes, to whom Socrates is explaining it, confesses, not
unnaturally, that he would welcome further clarification of Socrates'
meaning, Socrates immediately goes on to introduce the thesis that the
Forms are 'causes' of the sensible characteristics of the world, since it
is by 'participation' in Forms that sensibles possess characteristics
(Ioob-lOIC). The difficulty is to see in what way this thesis clarifies
the thesis that 'studying things in propositions' is a better method than
studying things by observation of senSible objects. The only way in
which Plato connects them with one another seems to be that th
. h F
"
.
e
theSIS t at orms are causes of sensIble characteristics is treated as an
in:<tance of a hypothesis to be examined in the way deseribed (IOIC-d),
With the added suggestion that the hypothesis that Forms exist will
possibly yield the conclusion that the sonl is immortal (roob). And
the stateme~t In 100a that the method of hypothesis follows the same
procedure whether the question is about causes or anything else'
appea;s to emphasise that, although the present argument is about
~ausality and although it is as 'causes' that the Forms are presently
mtroduced, the method does not derive its virtues from its association
with any particular assumptions about ~causes', whether in terms of
Forms or not. Hence there appears to be some ground for the contention that the ~ethod of hypothesis, as introduced here, 'seems a
mere excrescence, and that Its cOllllexion with what precedes and with
the following thesis that the Forms are 'causes' seems 'perfectly
accidental'." For if the connexion between the method and th th .
thF
".
eeSlS
at or~s are caus.es IS merely that this thesis may be selected as a
hypotheSIs for exammation, then the connexion is accidental.
. Moreover, when it might have been expected that Plato would
munediately contra~t the physicists' mode of explanation through the
study of se~slbles With his own mode of explanation through the study
ofnon-s~~slb~e Forms, It appears surprising that he should first contrast
the P~yslcls~s proced~e with a method which can be practised just as
well ill conjunction With that procedure as in conjunction with his
own postulate of the existence of Forms. It is this point, however,
n
42
which plato refuses to concede. He makes clear that the method is
incompatible with the physicists' procedure of relying on sensible
observation. We need not concern ourselves here with the question
of the historical justification of Plato's argument that a method of
direct observation was characteristic of pre-Socratic thought. 65 The
important thing to note is that plato assumes that if you rely on
sensible observation as a criterion in determining 'the truth of things',
then you cannot at the same time rely on a method of propositional
analysis. For he assumes that the method of propositional analysis
entails the rejection of any empirical criterion of truth; this is made
clear in 99d-Iooa. Logical consistency is now the criterion, with the
qualification that the interlocutor must agree that there are no grounds
for doubting the truth of the 'primary assumptions' (the 'adequacy'
mentioned in rare appears to mean adequacy in the Sense of being
satisfactory to the interlocutor). Thus the aim of the new method, and
the criteria on which it relies, are the same as those of the Socratic
method which we examined earlier, but plato adds (i) a systematic
formulation of the method, incorporating the procedure of finding
by analysis the prior assumptions on which the truth of the initial
assumption depends; (ii) a radical contrast of the method with the
method of direct observation. He then goes on to say that this is the
method to use in the examination of any question, whether about causes
or anything else (rooa). How far is it true to say, then, that the introduction of the method of hypothesis is 'a mere excrescence?
It must clearly be granted that the method has an important relevance
to Plato's argument. His purpose is to satisfy Cebes' request for a
demonstration that the soul is immortal (9Sb), and the relevance of
the description of the method of hypothesis to this is the obvious
relevance that it prescribes the method winch plato intends to follow
in the demonstration. Thus it shows to Cebes that the 'demonstration
will eschew any appeal to sensible observation and that it will be
effected in accordance with the rules of this method. And against the
objection that the natural place for its introduction would have been
at the very beginning of the argument, it can reasonably be said that
it is perfectly legitimate that Plato, since he intends to contrast the
method with the method of explanation adopted by the phySIcal
scientists, should first give a full account of the scientists' method.
This does, however, over-simplify Plato's purpose in describing the
43
scientists' method. For he wants his description to serve a double
purpose, and it is his failure clearly to separate these two purposes
which is responsible for the apparent confusion in his argument and
for the impression that the introduction of the method of hypothesis
is an excrescence. It can be counted an excrescence only if it is assumed,
wrongly, that the scientists' mode of explanation is described for the
single purpose of making a contrast with the mode of explanation
offered by the theory of Forms. In fact Plato has two purposes in
describing it: (i) to contrast it with the method of hypothesis, and
(ii) to contrast it with the explanation of the characteristics of the
world in terms of the Forms, as 'causes' of those characteristics; but
apart from the fact that they are each incompatible in their assumptions
with the scientists' mode of explanation, the method of hypothesis
and the thesis that Forms are 'causes' are c01l1lected ouly accidentally
in Plato's argument. Only when these two purposes are distinguished,
and the nature of the c01l1lexion between them realised, is it possible to
assess the siguificance of his argument for his theory of knowledge.
The first point to note is that Plato's treatment of the thesis that
Forms exist as a postulate subject to examination by the method of
hypothesis is simply one indication among others in the dialogue that
plato is not putting forward the theory of Forms or the theory of
knowledge which depends on it dogmatically, as theories of which he
considers there are no grounds for criticism or further examination.
He is sufficiently confident of the truth of the postulate that Forms
exist to use it as the basis of a theory of recollection, or as the basis
of his final attempt in the dialogue to prove the immortaliry of the
soul. It is a postulate which 'deserves acceptance' (92e), but is subject,
as the 'primary postulate' ofany argumentissubject, to further examina_
tion and criticism (ro7b). plato recognises, moreover, the limitations
of the method of hypothesis, and of human argument in general, as
a means of establishing with certainry the truth of any postulate. Short
of 'divine inspiration', the method of hypothesis is, for Plato, the best
philosophical method for attaining knowledge, but he acknowledges
that certainry is either impossible or extremely difficult to attain by
any method of human argument (Ssc-d, I07b).
Yet this profession of an ideal of disinterested inquiry, ready to
examine systematically all assumptions, is qualified itself by one
Importallt assumption. Plato assumes that in practice the method is
44
independent of sensible observation, and assumes that this makes it a
better method than the method of using sensible observation as a guide
to 'the truth of things'. The two methods are, for him, incompatible.
Moreover, this assumption about the method is made independently
of the theory of Forms. The conuexion between the method and this
theory is, as we have seen, accidental; the theory that Forms exist and
that they are the 'causes' of sensible characteristics is introduced as a
postulate which may be used as the starting-point in an application of
the method. This rules out the idea that when plato introduces the
theory of Forms as 'causes' he is suggesting that the way to get to 'the
truth of things' is to analyse, by the method he has just described, the
meaning of 'good', 'great', 'unity', and so on, and thus to attain
knowledge by coming to know the Forms by an analysis conducted
without any appeal to sensible observation. All that plato says is that
the postulate that Forms exist may be examined by the method he
has just described and thus without appeal to sensible observation - he
has particularly in mind the demonstration of the immortality of the
soul from tI,is postulate. The important point here is that the merely
accidental conuexion between the method of hypothesis and the theory
of Forms shows that plato is not ready to integrate them by making
the theory of Forms and the theory of recollection based on it the
basis of the method and the condition of its successful practice. He is
ready to do this in the Republic and hence to assert that the task of the
method is the examination of the world of Forms. And previously in
the Meno it was clearly implied that the systematic conversion of true
belief to knowledge, which is the final stage of the process of recollection, was effected by means of a method of analysis which in
its essential features is clearly the forerunner of the Phaedo's method
of hypothesis. There is no theory of Forms in the Meno, but at least
the conception of a transcendent reality is inlplicit in its theory 'of
recollection. Thus the assumption that the analysis which will yield
knowledge is part of a process of recollecting is the assumption that
recollection affords that recognition of truth which will guide the
steps of the analysis and ernure the correctness of its results. We noted,
however, that plato makes important reservations about his belief in
the theory of recollection, and stresses its very tentative nature. And
these doubts affect his view of the efficacy of the method of analysis.
For doubt about the theory of recollection is doubt about the founda-
45
tion on which rests the conviction that analysis will convert true belief
to knowledge. The position in thePhaedo is that the theory ofrecollection
is now ba.sed on the postulate that Forms exist, but that the theory is not
Imked With the method III the way implied by the Meno. It is linked
only accidentally, in the sense already examined. And we may reasonably assume that If Plato had made the link more than an accidental
one by making the theory of recollection a presupposition for the
effective practice of the method, and the world of Forms the objects
of its analysis, then his doubts about the efficacy of human argument
would have largely disappeared.
As it is, the virtues of the method and of the theory are assessed
independently, and this. itself i.s an indication that Plato has not as yet
begun to consider them III reiatlOn to one another except in an accidental
w~y, and thus has not begun to consider the possible inconsistencies
art~mg from an ..ttempt to integrate them. Plato's appreciation of the
serIOus difficulties lllvolved in integrating them is subsequent to a
tranSltlOn III hl5 thought from a position where he treats the theory of
Forms and the theory .of recollection as hypotheses to be examined by
the method to a posltlon where he treats them as presuppositions for
the :ffectl:e pracnce of the method. The former position appears to
be his ~oSluon ill the Phaedo. The latter position is his position in the
RepublIC, where the method of hypothesis is the science of dialectic
which explores the world of Forms. 66 But only in the late dialogues
does he begill to appreCIate the difficulties in the assumption that a
method dIVorced fro,:" sense-perception is the best method for analysing
Forms related to sernlbles III a way which suggests that in the process of
the recove~ of knowledge perception is the key to their analysis.
What 15 partIcularly Slgmficant about his position in the Phaedo is that
it sh~ws that his assumption that the method of hypothesis is to be
practISed Without resort to sensible observation is made in assessing
the method independently of the theory of Forms. And when the
method la:er .becomes the instrument of the analysis of the world of
Forms, thl5 llldependent assumption about it is retained, without
at. first any awareness of its apparent contradiction of what is im?lied by the theory of Forms and the theory of recollection based on
It.
1
e Giving an account of the Form
We may now return to the point from which this discussion beganPlato's assertion during his presentation of the theory of recollection
that knowing a Form implies the ability to 'give an account' of it
(76b). The results of this discussion should make us hesitate to interpret the phrase in terms of the Republic's conception of dialectic, and
then to say that it means to state a Form's 'resemblances to and differences from other - ultimately all other - Forms',67 thus implying that
a condition of knowledge of any Form is the comprehension of the
whole system of Forms, which is called in the Republic knowledge of
the Good. Indeed any interpretation in terms of the method of analysis
described in 99d-I02a would now seem to be implausible. A much
less ambitious interpretation must be looked for.
At TSC Plato has established that knowledge of 'the equal' (and of
'everything upon which we fix our seal and mark as being "the thing
itself" ': 7Sd) must have been possessed before birth. He now wishes
to establish as a feature of the theory of recollection that this knowledge
is forgotten at birth, and has to be recovered. The alternative, inconsistent with the recollection theory, is that the soul's prior knowledge is unaffected at incarnation, and is retained throughout incarnate
existence (76a). This alternative is refuted ifit is not the case that everyone Can 'give an account' of any Form, since it is assumed (i) that
everyone's soul knew the Forms before birth, and (ii) that the ability
'to give an account' is a condition of having knowledge. Since it is
agreed that it is not the case that everyone can give such an account,
then it must be that knowledge is recollected (76c). Thus it is assumed
that recollection brings with it the ability 'to give an account' of what
is recollected. Now it is reasonable to assume that in his presentation
of the recollection theory Plato's use of the term knowledge, whether
precise or not (i.e. whether implying full knowledge of Form or not),
is at least consistent. Hence, if to know a Form brings with it the ability
'to give an account', and if to know a Form is to be reminded of it by
the sensibles which resemble it (74b-c), the 'giving of an account' must
be explicable within the conception of 'knowledge' implied in the use
of the term in 74b-c. This suggests that 'to give an account' is to explain
one's possession of a Form by showing that it is necessarily implied by
that judgement of the 'deficiency' of sensible characteristics which
47
arises as soon as they are recognised. The fact that some people are not
able 'to give an account' of a Form means that they have not yet
realised it for themselves in this way, so that the concept which
designates it has no meaning for them.
There is one further point. 'To give an account' of a Form in this
way is at the same time 'to give an account' of the sensible characteristics which are recognised. These characteristics are explicable only
by reference to the archetypal Forms, whose 'presence' in sensibles is
thecause' of the characteristics (IOob-e). Thus it appears that, whereas
the process of 'thiulcing out the reason why' (aitias logismos) in the
Meno's recollection theory or the process of 'giving an account' within
the Phaedo' s method of hypothesis are, both to be explained in terms
of the analysis of propositions, yet within the theory of Forms, as far
as it is taken in the Phaedo, the only type of account possible is one in
terms of a relation of resemblance between archetypal Forms and
sensible characteristics or in terms of the 'participation' of sensibles in
68
Forms. And since it is assumed both in the Meno and the Phaedo that
a method of propositional analysis is the best means of attaining knowledge, while at the same time it is assumed in the Phaedo that the objects
of knowledge are the Forms, to be recognised through their sensible
'copies', it becomes clear that a consistent development of Plato's
theory of knowledge from this position will depend on the consistency
with which plato can reconcile the above two types of 'account'. In
attempting to trace this development in the remaining chapters the
fi:st aspect of It to be considered will be the developments in Plato's
VIews on the cognitive value of sense-perception. The incoruistencies
in his views about this ill the Phaedo are serious incoruistencies and it
is important, having first coruidered evidence from other ;";ddle
dialogues which indicates more precisely the natute and extent of this
~nco.nsistency,. to see to what extent Plato is able to remedy this fault
In hIS theory 111 the late dialogues.
49
2. THE SYMPOSIUM
CHAPTER II
The Criticism of Perception
I. INTRODUCTION
In Greek the general term for perception, aistMsis, is imprecise, and the
possibility of giving any exactness of meaning to it depends entirely
on the context in which it is used. Thus in the Phaedo, where it is clear
that Plato is distinguishing between sensation and a conceptual level of
apprehension, itis possible to say that aisth~sis means sensation (7Sa-b).
Again, in certain parts of the examination of aisthJsis in the Theaetetus,
it is possible, as we shall see, to allot this meaning to it. In other contexts
it has that much wider sense of perception which includes judgement.
When plato condemns perception it is usually the case that he is
including in his condemnation both 'the sensations and the judgements
in accordance with them'.! Thus in the Republic belief (doxa), as plato
calls the level of apprehension which has only sensibles as its objects,
includes judgement and is apparently assumed to be propositional.
And the reasons for treating it as unstable and unreliable are substantially the same, for Plato, as those for treating sensation as unstable
and unreliable. Sensation, perception, and belief (in the above specialised
sense) have a common basis in the 'experience' (pathos) which resnlts
from the interaction between the physical senses and external sensible
objects, and each is equally inadequate to afford insight into 'reality'
to the extent that this basis is inadequate for this purpose. In the middle
dialogues it is only in the Theaetetus that there is any detailed examination of the nature of this basis. Outside the Theaetetus discussion of
sense-perception and its objects is of a very general kind, with little
detailed analysis. What I propose to do in this chapter is to examine
what Plato says about sense-perception and its objects in the Symposium,
the Republic, the Cratylus, and the Theaetetus, and to consider in the
light of this what developments in his theory of knowledge can be
traced in this middle period of his thought.
48
The important passage in the Symposium is that in which plato describes
the 'ascent', through progressively more abstract levels of generalisation, to the apprehension of the Form of beauty (2toa4-212a7). In this
passage he states more clearly and emphasises more insistently than
anywhere else in the middle dialogues that the process of acquiring
knowledge of Form is a process of generalisation and abstraction. Thus,
at tlle initial level of sensible exemplification of beauty, sense-experience
of repeated instances of beauty brings first the recognition of the
similarity of one instance to another (2IOa7-bI), and then the recognition of beauty as a general characteristic or universal (2IOb2-3). This
process of generalisation is repeated ltt-progressively more abstract
levels of exemplification of beauty, and sense-experience gradually
ceases to play a part in it. It is at least implicit that sense-experience
plays no part at the higher levels of abstraction. After the generalisation
which follows the recognition of instances of beauty in 'occupations
and laws' (2IOC3-S), a much wider (d4) field of exemplification of
beauty is found in the intellectual 'beauty' which belongs to the various
sciences; and at this level the ability to recognise the similarity of the
different scie~ces as instances of beauty and from this to recognise
beauty as a uruversal character is said to result in knowledge of Beauty
itself (21oc6-e1; 2IIc6-d1).
It is clear from what Plat? says here that knowledge of Beauty has
the same Wide comprehenSion as knowledge of the Good has in the
~public; it is a .comprehension of the whole field of knowledge which
is a: the same t!~e a rec?gnition of its Goodness or Beauty. And just
as, m the Republtc, the highest level of apprehension is divorced from
~ense-perception., so, we may assume, are the final stages of the 'ascent'
m the ~ymposium. Yet if the Symposium invites comparison with the
Republtc m this respect, there is a radical contrast between the two
di"!"gu~s in respect of the method prescribed for attaining knowledge.
ThlS ames from a difference in the points of view from which the
app;oach to knowledge is considered. The Republic is concerned to
depict the method of systematic analysis by which the dialectician
explores the content and structure of the world of Forms and fmally
compr~hends that world as a single system; the Symposium is concerned
to depIct the process of generalisation from particular instances to
50
universal, and though it is no doubt assumed that, at the 1110st abstract
level of instantiation, the recognition of particular 'branches oflearning'
as instances of beauty is possible only at the conclusion of a comprehensive analysis of these 'branches of learning', it is the generalisation
marked by the recognition that beauty is a universal which the
Symposium emphasises, and not the prior analysis which makes such
recognition possible.
Moreover, though it is true that the Symposium describes the
generalisation from particulars to universal at various levels of abstraction, it is primarily the generalisation from present sensible particnlars
to non-sensible Form which it is concerned to emphasise. And in
emphasising this plato contrasts, in much the same language as he had
used in the Phaedo in contrasting Forms and sensible instances of Forms,
the permanence, immutability, purity, and uniformity ?f the Form
with the transitoriness, mutability, and imperfection of Its partIcular
instances, which present different appearances to different people at
different times and in different relations (zIIa-b, e). The language of
'participation' to describe the relation between particulars and Form
also recurs (zIIbz). One further and important similarity between the
Phaedo and Symposium is that the Phaedo's doctrine of recollection and
the Symposium's account of the 'ascent' to the Form of beauty both
describe the way in which the Form is apprehended in terms of the
recognition of a 'perfect' and uniform object, and not in t~rms of t~e
analysis of propositions. Yet there is an important difference m emphaS!s
between the two dialogues. The Symposium emphasises, unlike the
Phaedo the function of the Form as a universal; for whereas the Phaedo
explaU:s the recognition of a Form as being reminded of it by any
one of its sensible instances, the Symposium makes it dependent on a
generalisation from the experience of several instances recognised as
like one another. Does this mean that there is an inconsistency here
between the Phaedo and the Symposium? It is true that, granting the
premisses of the theory of recollection, that theory, as put forward in
the Phaedo, is able to explain the recognition of Forms without appeal
to a process of generalisation and hence to the p~rsonal memory ~f
previous sensible instances. The Phaedo is thus argumg that the expenence of more than one instance of a Form is not a necessary conditlOn
of the apprehension of a Form, and the Symposium is apparently arguing
that it is a necessary condition. In other words the Phaedo, m basmg
51
recognition 011 a relation of similarity between a previously known
archetypal Form and a present sensible instance of it, seems to be
assuming that the Form can be apprehended without awareness that
it is a universal. The Symposium, on the other hand, makes the initial
recognition a recognition of the similarity between two sensible
instances; the recognition of the Form is subsequent to the recognition
of several instances and is the recognition of it as a universal, as the
result of a generalisation. This inconsistency between the two dialogues
underlines the difficulty of reconciling the nature of the Form as an
archetypal object which resembles its instances with its function as a
universal. If, on the one hand, the apprehension of the Form is the
result of a generalisation from particulars, it is difficult to see the
justification for postulating its separate existence as a perfect archetype.
On the other hand, if recognition is explained as the recognition of a
Form from the experience of a single sensible copy of it, not only is
this not an account of how a general characteristic comes to be
recognised, but the relation of resemblance between archetype and
copy makes it difficult to avoid the argument from an infmite regress
raised later in the Parmenides (Ipd-I33a) if an attempt to maintain
that the Form functions as a universal is based on this account of
recognition.
We must now consider further what part is allotted by the Symposium
to sense-perception in the process of apprehending the Form. Implicit
in the Symposium is the same relation of similarity between perfect
Form and imperfect particulars as is explicit in the Phaedo. And though
plato stresses, as a mark of the imperfection of particulars, that they
present different appearances to different people at different times and
in different relations, yet he assumes at the same time that the relativity
of the appearance of sensible particulars to the individual percipient
and to particular circmnstances does not affect the status of the particulars themselves as 'images' of Forms, and assumes further that the
perception of these particulars is the initial basis of the generalisation
to the Form. Now this is to grant an important r61e to sense-perception
in the attainment of knowledge. It is true that in the case of the Form
of beauty with which the Symposium is concerned the process of
generalisation is extended to levels beyond the range of direct perception. But this Form has, as we have seen, an extremely wide
extension, comparable to that of the Good in the Republic, and is to
52
be treated as a special case. If we consider other examples of Forms it
is clear that there are very many cases where the process of apprehending the Form will rely throughout on sense-experience. Thus many
Forms designated by concrete terms - and the Phaedo theory assumes
that such Forms are properly postulated - will, it would follow from
the Symposium doctrine, be apprehended as the result of a generalisation from the perception of a number of their sensible images. And
though the Symposium does not represent the apprehension of the Form
as something achieved by au analysis of the complexity of a universal
but only as the recognition that it is a 'perfect' and 'uniform' universal,
it seems clear that any possible analysis of the Form subsequent to its
abstraction from particulars would rely on sense-perception of the
particulars. Indeed the Symposium, by combining a doctrine that the
Form is apprehended through generalisation from particulars with a
doctrine that the Form is an archetypal object which particulars
resemble, comes dangerously near to bridging the wide gap between
Form and sensibles which the theory of Forms wishes to maintain.
For it is implicit in that theory that no abstraction of Form from
sensible particulars is ever possible.
In this way the Symposium raises even more emphatically than the
Phaedo had done the problems introduced into Plato's theory of knowledge once the objects of knowledge are specified as archetypal Forms.
For it must be remembered that the theory of Forms is meant to give
greater precision to the thesis first put forward in the Meno - that the
only real knowledge is a priori knowledge. It is to be noted further
that the fIerce moral condemnation of the senses which characterises
parts of the Phaedo is absent from the Symposium. It is not argued in
the Symposium that the senses are utterly unreliable and deceptive.
What is argued is that sensibles are imperfect when measured by the
standard of the Forms, and the arguments here (2ua-b) are comparable with those within the Phaedo's theory of recollection, and
quite different in their purpose and doctrine from those other passages
of the Phaedo which so fiercely condemn the senses and their objects
from a moral point of view. Is it the case, then, that plato consistently
holds throughout this passage of the Symposium (2Ioa-212a) that the
perception of sensible characteristics is an adequate guide to the
apprehension of the Form? The general impression given by the
passage is that he does hold this view. But he does in fact make one
53
reservation, which is repeated in the Republic. It is that the 'ascent' to
the apprehension of the Form must be made under another's guidance
(2Ioa6-7; c2-3, 6-7; e3). The fact that plato makes several appeals
here to the need of a gUIde or director suggests that he considered this
point to be of some importance. But since it recurs in the Republic
any further ~ssessment of its importance is best postponed until after
an exammatlOn of what the Republic has to say about perception and
'images' of Forms.
3.
THE REPUBLIC
aJ Perception and the method of dialectic
'- ~
~~ is in ,the ~~public t~at Plato begins to speak regularly of 'copies',
Images, or likenesses of Forms. 2 This in itself indicates that he continnes to think of the relation between Form and particulars in the
same way as when he first formulated the theory in the Phaedo a
relation ~f rese~blance between archetypal Form and 'copies' of it, 3
and this IS expliCIt at 476c-d. Moreover in the Republic the theory of
recollection is implicit in Plato's remarks about the nature of education
at the begimIing of Book VII. Thus the language used to refer to the
kn~wledge residing in the soul immediately recalls the language in
which the theory of recollection is introduced in the Phaedo 4 and the
do~trine that education c?nsis~s not in putting knowledge in:o the soul
as if one w~re puttmg SIght mto blind eyes but in turuing the soul
already. havrng latent knowledge in the right direction is a doctrine
?resentmg, as Adam noted, 5 fundamentally the same view as that
Implied by the theory of recollection.
. But although the language of 'images' of Forms is prominent in the
dialo~ue and althoug~ a theory of recollection is implicit in it, the
doctrme of the RepublIC about the contribution of sense-perception to
~~wledge .appears in many important respects to be opposed to what
I' Implied m the Phaed~' s theory of recollection. In the first place
plato, .Ideal.of philos.ophical analysis, or 'dialectic', which yields knowledge, IS an I~eal which repudiates empirical aids to knowledge (Slob,
suc, 532a), Just as the method of hypothesis of the Phaedo had done.
But whereas the method of hypothesis in the Phaedo was connected
only accidentally with the theory of Forms, the method of dialectic in
PLATO'S THEOltY OF 1r.NOWLPiDGE
S4
the Republic is essentially a method which has Forms and nothing else
as the objects ofits interpretation and analysis (SIC-SU). The truth of
the theory of Forms is now assumed to be a guarantee of the certainty
of the truths which dialectic brings to light. Hence dialectic has no
need to rely, as the method of hypothesis of the Phaedo had relied,
merely on personal agreement as a criterion of truth. Yet it retains
certain important characteristics of the method of hypothesis of the
Phaedo - (i) it is a method of analysis of 'hypotheses' and hence, as is
clear from its affinities with the method both of the Phaeda and the
Meno, a method of analysis of propositions, and (ii) it is independent in
practice of perception. Plato's ideal of dialectic here is an ideal of 'pure
thought', which is aware that its objects are non-sensible Forms and
is able, without resort to sensible 'images', confidently to prosecute
its work of analysis with a clear recognition of the correctness of its
results at each step until a systematic comprehension of the whole
world of Forms is achieved.
It is primarily in order to emphasise the distinctive virtues of this
highest level of apprehension that plato contrasts it with lower levels
which rely in differing degrees on sensible 'images' of Forms. Thus
below the level of 'pure thought' are (i) a level of thought which is
aware that its proper objects are non-sensibles but has not achieved
that independence of perception which will allow it to dispense with
sensible images of Forms as an aid to thinking; it is 'compelled' to use
sensibles (Slob-sua); (ii) a level of thought, lower than (i), which is
not aware of Forms at all, but takes sensible images of Forms as constituting 'reality', and hence lays claim to knowledge from experience
of sensibles (476, 479-80, S09d-SIOa). And the task of education, as
Plato envisages it in the Republic, is to effect a 'conversion' of the soul
by leading it to the highest level of thought. It is clearly assnmed here
that the possibility of attaining knowledge of any Form is dependent
on the possibility of attaining a level of thought which is entirely
independent in its operations of sense-perception. Moreover, plato
does not suggest that the process of acquiring knowledge of Forms
begins with the experience of 'images' of Forms, in the way described
by the Phaedo in its theory of recollection. When he describes the two
levels of thought mentioned above ( (i) and (ii) ), he does not recommend them as stages in the acquisition of knowledge, but criticises
them as those most commonly mistaken to be the levels of thought at
SS
which knowledge is acquired or becomes possible. What we now have
to consider is what Plato's examination of these two levels of thought
reveals about his views on sense-perception and its objects.
b] Perception and mathematics
Level (i) is first described (sIOb-sud) as one of the subdivisions in
the, divided Line, the diagram used by plato in an attempt to schematise
the various levels of apprehension inferior to that which the practice of
dialectic affords. It is the level of contemporary mathematical thought,
and is called by Plato dianoia ('understanding') in distinction from that
highest level of intelligence or nous which yields knowledge (sud,
S34a). It was natural that he should giv~ g~eat prominence in the Line
to the procedure of contemporary matnematics. This was the main
field in which the Greeks were making systematic advances towards
the ideal of a precisely organised body of knowledge, and it was here
that a claim to have reached certainty seemed most justifIed. But it is
Plato's thesis that only for the results of the practice of dialectic can a
claim of certainty be fully justified, and he makes it a principal criticism
of the mathematicians' procedure that it fails to substantiate the
assumptions on which the truth ofits results depends. Further analysis,
he argues, would show that what the mathematician uncritically takes
for granted is in fact derivative from higher principles. Thus the
mathematicians' claim that their results are certaWy true rests on
nothing more than the uncritical acceptance of the truth of the premisses from which those results are deduced. To this criticism that
the mathematicians' results are never more than deductions from
'hypotheses' simply assumed to be certain, plato adds the criticism
that the mathematician always uses sensible 'images'. By 'unages' he
means 'images' of Forms. While criticising this use of images, he grants
that the objects of mathematical thought are non-sensibles, and his
description of examples of these as 'the square itself' and 'the diagonal
itself' is characteristic of his way of describing Forms (sIOd). Moreover
he grants that these objects, though apprehended at the level of dianoia
~o lo~g as the assumptions about them are left uncriticised, are fully
rntelligtble when apprehended 'in connexion with a first principle'
(sud). In other words, the distinction between tlOUS and dianoia is a
distinction between levels of apprehension of the same kind of objects,
and not a distinction implying a different kind of object for each level.
56
The 'images' which he has in mind are especially geom~tric ~gu~es,
but he implies further (SIoc3 with sIods) that arIthmetical th~king
is tied to sensible images (presumably the visual repre;~nt~tIon of
numbers by dots); also at SIOC3 he implies the same for. snnilar subjects', no doubt the subjects of astronomy and harmomcs which .he
describes later with a consideration of the kind of sensible alds which
they use (S27d ff.).
These then are the two criticisms which he makes of contemporary
mathem'atical'thought. I see no reason to doubt that plato is giving
here a fair description of the actual practice of contemporary mathematicians. It may seem, perhaps, that the insistence that the. mathematician invariably uses sensible images as an aid to thought IS rather
exaggerated through a concern to make the distinction between contemporary mathematics and dialectic as clear-cut. as pOSSIble. F?r
though the point that the geometrician always relies on the spatl~l
intuition provided by sensible figures. may .r:adil.r be. granted: t~
appears more questionable that the arIthmetIc:an ~varIably ha
rely on sensible intuition. But Plato's contentIo,,: '~ at least unde~
standable if we assume, as is reasonable, that he IS inJluenced III his
description here by Pythagorean theories of figured n~bers and by
the general Greek manuer of representing. un~ts by p~mts.6 Hence,
while allowing that there is so!"e exaggeration m Pl~to s st~tement of
the extent of the arithmetician s reliance on sensIble unages, we need
not doubt that he is giving in this passage what he considers to be a
fair description of contemporary mathematical practice. And he condemns it as bad practice. It is quite wrong to mterpret this part of the
Line as granting to mathematics a specially valuable st~tus a~ the Ideal
intermediary between sensible and intelligible worlds,. Ideal m that ItS
use of sensible 'images' is more efficacious in promptmg the mmd to
recollect the Forms than is the case with sensible images of nonmathematical Forms.' For when plato later discusses (52 sa ff.) the
way in which mathematics can serve as a useful 'handmaiden' in leading
the soul to the highest level of apprehension he makes clear th:t tl1lS
usefulness is dependent on the divorce of the mather,natI~al sC!e~c~s
from perception. Thus his criticism of the use of senSIble. I.mages III
arithmetic, geometry, and 'similar subjects' is not a
Cntl~lSm
of an
essential and ineradicable feature of the method of these SCIences, b~t
a criticism of a feature of contemporary practice which can be erad,-
57
cated, and must be eradicated if these sciences are to lead the soul
towards the attainment of knowledge. Hence it is not the case that
plato, in the diagram of the Line, 'insists on the necessity of diagrams
for the study of geometry', nor is it the case that he there 'opposes'
both empirical and rationalistic theories of the nature of geometrical
knowledge.' What he does oppose is contemporary practice, and what
he advocates subsequently (S2sa ff.) is 'the rationalistic or logistic
theory' of the nature of the mathematical sciences.
In this later section of the Republic he assesses the value of arithmetic,
geometry, astronomy, and harmonics, the last two being, almost
certainly, the subjects he had in mind when he referred in the Line,
after arithmetic and geometry, to 'similar subjects'. And what he
envisages is a unification of these sciertees as the result of an inquiry
which reveals their mutual relationship and 'kinship' (SlId), a result
clearly dependent for plato on the possibility of treating each of them
as different but related branches of pure mathematics. Moreover the
value of these sciences in turning the soul towards knowledge is
dependent on the attainment of this result (5lId). This amounts to a
repudiation of the use of sensible images in this field as a gnide to
knowledge. The point is made explicitly in Plato's discussion of the
particular sciences, and is in fact most explicit where it is least plausible
- in the case of astronomy and harmonics. 'AstronOlny,' says Plato,
'like geometry, we shall pursue by the use of problems, and leave the
heavens alone' (S30b), and he immediately points out the radical
change from the methods of contemporary astronomy which this
demands. Similarly he advocates a purely rational study of harmonics,
condemning the appeal to sensible observation and recommending
again the use of problems; the student must investigate 'which numbers
are consonant and which not, and for what reasons' (53IC). In the case
of astronomy plato does indeed grant that there is a strilting constancy
and regularity in the movements of the heaveuly bodies, but insists
that this falls far short of the exactness which a mathematical description
affords (529c-d, 530a-b), and concludes, not simply that all results of
investigation in this field should ideally be expressed in mathematical
terms, but that the only true results are attained through a purely
mathematical study which dispenses with observation. In the previous
discussion of arithmetic and geometry there is the same kiud of contrast
between empirical and rational methods of study as in the discussion
E
of astronomy and harmonics. It is 'numbers themselves' which the
arithmetician must study, not allowiug any discussion which deals
with 'numbers with bodies that can be seen or touched' (525d). So in
geometry the proper object of study is what is etemally real, and not
'what comes to be and passes away' (527b). Hence, plato asserts, the
normal language of geometry, which is fitted to describe methods of
practical construction, is quite ludicrous as an expression of its true
purpose. Here again we may assume that he is recommending what he
recommends for the other sciences - a method of pure mathematics, a
recommendation clearly implied for geometry at 530b.
We are now able to see that in this part of the Republic plato is
sketching a programme of research which is intended to eradicate at
least some of the faults which, he had asserted in the Line, belonged
to contemporary mathematics, and it is natural to associate what he
envisages here with some programme of mathematical research being
prosecuted within the Academy.' But the Republic makes it clear that
its mathematical studies are ouly a 'prelude' to dialectic (53Id). In
many ways this attempt to maintain a distinction between mathematics
and dialectic appears at this point to have lost the justification which it
had in the Line, and to remain merely as an artificial division to suit
the plan of separating a programme of progressive education into
distinct 'grades'. For the inferiority of contemporary mathematics to
dialectic, as described in the Line, was essentially an inferiority in
method, and this inferiority appears to have been largely eradicated
from the method of the mathematical sciences described in 525a ff.
The 'etemally real' is now studied without reliance on sensible observation, and is studied with a systematic thorouglmess which will obviously
demand an extensive use of that type of analysis which the Line represented as the exclusive mark of dialectic.'o In what way, then, does
plato now mark off mathematics from dialectic? He says only that the
mathematician is still 'unable to give and receive an account' {53 Ie).
And this must mean 'unable to give and receive afinal account', in the
sense that the mathematician is confmed in his investigations within
the limits set by his acceptance of the primary assumptions of his
science. Within these limits his procedure shares the characteristics of
dialectic - independence of observation, and systematic analysis. And
what remains as the distinctive mark of dialectic can only be an extension in the scope of analysis whieh will take it beyond the primary
59
assumptions of the mathematical sciences and allow it to complete the
task of systematisation by a discovery of the systematic unity of the
whole world of Forms. Thus plato assumes that there is a point at
which the mathematician ceases to be a mathematician and becomes a
dialectician. This does not, I think, imply that at this point the mathematician ceases to deal with specifically mathematical Forms, but rather
that at this point he begins to relate mathematical Forms to nonmathematical Forms within a more compreheruive analysis. And this
implies that the distinction between dialectic and the mathematical
sciences as conceived in 52sa ff. is essentially a distinction between
degrees of comprehension of Forms, the assumption being that knowledge of any Form is possible only within the comprehension of all
Forms as a single system.
'- If this is the case, it is reasonable to assume that what is true of
mathematics is true also of' all other branches oflearuing', as the Meno
would put it. For we must remember that the theory of Forms is a
theory of very wide application, and that it is a principle stated in the
Republic that the existence is assumed of one Form for each set of
things to which the same name is applied (596a). And since it is Plato's
invariable assumption that the only objects of knowledge are the
Forms, it is a fair inference that what Plato says about the progressive
stages of comprehension necessary in attaining knowledge of mathematical Forms is true also for all other, non-mathematical Forms. As
Ross has pointed out ill regard to Plato's description of contemporary
mathematics in the Line, 'in principle his account (so far as the use of
hypotheses is concemed) is applicable to all sciences which study a
particular subject without raising ultimate questions about the status in
reality of the subject-matter, and its relation to other subject-matters'.l1
And we can fairly say, in a similar way, of the account of the mathematieal sciences in 525a ff. that in principle this account is applicable
to all Forms, and that for all Forms there are two main stages in the
comprehension of them - firstly the comprehension of them within
the limits of various groups of Forms which constitute general 'subjects' and into which the Forms are initially separable; secondly the
fuller compreheruion of them within the single system which relates
all 'subjects' and hence all Forms to one another. As for Plato's choice
of mathematics as an illustration of what may fairly be taken to be a
general thesis, this is explained by the fact that mathematies was at
60
this time the only subject studied systematically enough to provide
such an illustration. A consequence of this generalisation would be that
plato makes the method of attaining knowledge of any Form, even
at the lower level of comprehension, completely independent of
perception.
Against this it might be argued that the choice of mathematics to
illustrate the lower stage of comprehension is a mark of Plato's
recognition of its distinctive features as a subject which, unlike others,
can be studied from the earliest stage by purely rational methods, and
that consequently (i) it is for this reason that mathematics alone is
fitted to be a 'prelude' to the purely rational method of coming to
know all Forms at the dialectical level; (ii) the choice of mathematics
as a 'prelude' implies nothing about the method by which the approach
to knowledge of non-mathematical Forms is made below the level of
dialectic, and thus cannot imply that that method is divorced from
perception. There is much plausibility in this argument. Yet it can be
objected to it that (i) it is not only by a generalisation from what
plato says about mathematics that it can be established that the approach
to knowledge of any Form is made independently of perception; there
is other evidence to support such a thesis; (ii) since it is not in doubt
that plato conceives the attaimnent of knowledge of Forms as the
culmination of a process of comprehending them within an everwidening field of relations, it is quite naturally assumed, apart from
any consideration of Plato's explicit description of the process in the
particular Case of mathematics, that the earlier stages in the comprehension of any Form will be a tracing of the more obvious relations
with other Forms which establish its place within the limited system
of a particular 'subject'. Together (i) and (ii) afford the same conclusion as is afforded by the generalisation from Plato's description of
the mathematical sciences, and thus suggest that the generalisation is
justified. It remains only to consider the' other evidence' mentioned
in (i).
There is, in the fmt place, the evidence provided within the
description of the mathematical sciences in S2sa if. What is especially
remarkable here is, of course, Plato's failure to make any clear distinction between pure and applied mathematics. The distinction was,
however, a difficult one for plato to make within the theory of Forms,
in view of the association made by that theory of a distinction between
61
Forms and sensible instances of Forms with a distinction between
a priori and empirical knowledge. Thus we find that arithmetic,
geometry, astronomy, and harmonics are treated on essentially the
same footing as sciences which investigate an eternally real world of
perfect objects which are imperfectly instantiated in the sensible 'copies'
of the physical world, the main distinction in each Case being between
the empirical and practical type of study directed to sensibles, and the
theoretical and non-practical type of study directed to non-sensibles.
And the most unfortunate consequence of the failure to distinguish
between pure and applied mathematics is the assnmption that the truth
of the applied mathematical systems of astronomy and harmonics can
be established independently of sensible~bservation. The significance of
this for our prese~t argu,ment is that in studies where Plato acknowledges
that the senSIble Image of the model constituted by the relevant Forms
is, though imperfect, closer in its approximation to the perfect standard
of the model than is the case with other sensible 'images', it is yet
emphaSIsed that the method of study must be independent of sensible
observation. Thus he asserts that in the heavenly bodies and their
movc~ents we have what i~ m~re beautiful and perfect than anything
ehe v~sIble (S29c-d), but stIll mSIst~ that in studying astronomy 'we
Will dIspense With the starry heavens (S30b-c). Hence it can be argued
a fortiori that, the study of other F,orm~, in that their sensible copies
will be less beautIful and perfect, wIll be mdependent of sensible
observation.
cJ Perceptioll and 'belie{' (doxa)
Plato's remarks on perception outside his discussion of the mathematical
sciences point to the sarne conclusion. We have already seen that one of
the levels of apprehension ranked by plato below the level attained at
the dialectical stage, and also, quite certainly, below the level attained
by the systematic study which is a 'prelude' to dialectic, is the level
which ~akes sensible images of Forms as constituting reality and hence
lays claim to knowledge from experience of sensibles. Plato describes
this l~vel as doxa (belief). In the passage (476a if.) in which he distmgUlshes doxa from knowledge he associates this distinction with a
distinction between types of object, arguing that whereas knowledge
IS d,rected to Forms, doxa is directed to sensibles. His explicit assumption
here IS that the fact that knowledge and doxa are distinguishable implies
r
62
that their respective objects are distinguishable (477e-478b). And on
this assumption he associates, by analogy, the certainty and infallibility
of knowledge with the invariability and permanence of the Forms,
and the inconstancy and fallibility of doxa with the inconstancy and
inconsistencies which belong to sensibles (477a If.). The nse of doxa
here is in every wayan nnfortunate one. Its departure from normal
usage would have been pardonable ifplato had consistently maintained
this specialised usage after its first introduction. But in fact he continues
to use doxa elsewhere, as we saw in the last chapter, in the normal sense
which carries no implication that its objects are diJferent in kind from
those of knowledge. In view of this, it is important to note that the
specialised use of the term does not imply, as the normal use does for
Plato, the possibility of converting doxa to knowledge by 'giving an
accoune which will establish that what is 'believed' to be the case is
in fact the case. Wherever Plato uses the term in its specialised sense,
he neither says nor implies that this is so. Hence we must not read into
his use of it in this passage of the Republic the implication that it is
possible to substautiate what is asserted to be true at the level of doxa,
i.e. an empirical proposition, and thus to know it to be true. The best
way to understand Plato's distinction here between doxa and knowledge
is as a distinction between empirical and a priori knowledge, carrymg
with it the clear implication that the one is not convertible to the other.
Plato's decision to use the term knowledge for a priori knowledge ouly
is not always consistently maintained in later dialogues, but when he
does use it of empirical knowledge he is using it in a general nonspecialised sense, and is not in any way contradicting what he s~ys in
the Republic, and repeats in dialogues of the latest penod, the T,maeus
and the Philebus, about the distinction between knowledge and doxa.
The next point to consider is what plato says in the passage of the
Republic we are discussing about the objects of doxa, which are, as we
have seen, sensible objects. His arguments here are of the same type as
he used in the Phaedo (74b-c) and the Symposium (z!Ia-b) in giving
reasons for the imperfection of sensible particulars. Thus he argues that
each sensible particular can have contrary predicates applied to it, and
that this makes it impossible to have any firm conviction that one of
the contrary predicates is properly applied to the particular, to the
exclusion of the other predicate (479a-c). He concludes from this that
sensibles belong to a 'shifting intermediate world' between 'Being' and
'not-Being'; the world of 'Being' is the world of Forms (479c-d). His
argument here has no more validity than had his argument for the
imperfection of sensibles in the Phaedo (74b- c) , a passage which was
examined in detail in the last chapter. He makes no attempt to consider
the qualifications which would resolve the puzzle of this apparently
contradictory feature of sensibles; and it is particularly surprising that
he fails to note that some of the terms which he uses as illustration are
relative terms (double and half, great and small, heavy and light), for
in these cases the merely apparent nature of the contradiction is more
immediately obvious than in other cases. Plato's view is, then, that the
contradictions which appear in sense-experience imply that sensibles
are not fully 'real' in the sense in which~the Forms are fully 'real'.
But does this imply further that sense-perception is of no value as a
guide of knowledge? Both the Phaedo, in its theory of recollection,
and the Symposium had denied this, arguing that the status of sensible
particulars as 'copies' of Forms enabled them to prompt the recognition
of Forms, and thus to play an important part in eliciting knowledge of
Forms. The Republic, however, makes no such concession to the senses.
Having argued at 479C that contradictions in sense-experience make it
impossible ever to have any firm conviction that one rather than the
other of two contrary predicates is properly applied to a sensible
particular, plato returns in a later passage (523a-525a) to the discussion
of these contradictions. He argues that experience of them prompts
the mind to turn away from perception and to inquire, at a level of
thought divorced from perception, what 'the large' is and what 'the
small' is. The passage is in many ways an admirable illustration of the
stimulus provided to philosophical reflection by apparent contradictions and puzzles in experience. But what is important to note for
our present argument is that Plato assumes not ouly that the discovery
of 'what" the large" is and what" the small" is' is made independently
of perception, but also that what is established as the truth at this level
of thought is never in any way true of sensibles. For sensible particulars,
while they appear to be instances of two contrary characteristics at the
same time, are never in fact instances of either. Thns, while plato does
here credit perception with the useful function of stimulating the mind
escape from it, he denies that sensibles ever reflect in any way what
IS true, for he implicitly contradicts the theory of recollection in its
assumption that sensibles, as 'copies' of Forms, are able to prompt
;0
recognition of Forms and thus serve as a guide to the truth. It must be
Iloted, however, that Plato does not assert that all instances of perception have the contradictory feature we have just discussed. Yet far
from saying that in cases where no contradiction appears perception
prompts the recognition of Forms he says that in these cases perception
fails to prompt the mind to reflection of any kind on what is given in
perception, since in these cases the judgements made by perception
itself are 'satisfactory' (S23a-e). As an illustration he uses the case of the
perception of several fingers, and argues that though the mind is
prompted by contradictions arising from this perception to inquire
what is 'the light' and 'the heavy', 'the soft' and 'the hard', it is not so
prompted, since no contradiction here arises, to inquire 'what is a
finger'. Thus at a point where we might have expected plato to grant
a positive value to perception as an accurate indication of the truth,
he implicitly condemns it as useless since it fails to prompt the mind to
seek the truth in independence of perception. It is not possible, of
course, to argue that plato, since he asserts that in cases where no
contradiction arises the judgements of perception are 'satisfactory', is
here commending perception as itself providing a full answer to the
question 'what is a finger'. His point is that the perception is 'satisfactory' to most (523d4) percipiellts in the sense that they readily
accept what is given in perception without being prompted to inquire
at all 'what is a fInger'. Contradictions in experience, on the other
hand, 'compel' the mind to go beyond perception, and hence in this
respect are 'useful'. plato is thus emphasising yet again that only in
independence of perception can the truth be established, and that
perception is never to be used as a positive guide in seeking the
truth.
There is one final aspect of this argument to be considered. It can be
maintained with some plausibility that, although plato dismisses as
useless for stimulating thought cases of perception where the judgeInent of perception is 'satisfactory', yet it is implicit, in his assertion
that no contradiction is afforded by them, that they are perceptions
of 'images' of Forms, unlike the perception of sensibles which are
apparently 'images' of two contrary Forms at the same time but in
fact are 'images' or instances of neither. Yet even if this is granted it
does not at all imply that plato would assume that such 'images' are
therefore valuable as an aid to knowledge. All the evidence from the
65
Republic which has been considered so far shows that his position is
that all perceptIOn, whether or not its object is properly an 'image' of
~ Form; IS to be eschewed in seeking knowledge. The language of
Images IS ill fact very promment ill the Republic - in the Line, the
C~v,e, and elsewhe;e. Yet,. except where Plato uses the term 'image'
(elkon) for hIS own IllustratIve figures or examples, it is never suggested
that they are of value for the discovery of truth.
. Bef~re considering some of the passages where he is explicitly
discussmg In:ages, It ~s worth notmg briefly that an 'image' of a Form,
as the term IS used m the Republic, is not only a particnlar sensible
instance of a Form (as a particnlar dog is an 'image' of the Form 'd ')
'rm~ge"al
og.
IS ~o used'm the.'ense of verbal 'image', which appears to
be
eqUIvalent, m the Republtc, to an empirical proposition. Thus Plato
speaks of the 'images' of justice, beauty, and goodness, which are
taken to be real by men whose level of apprehension is the same as
;hat of the prison~rs in the Cave (SI7d, S20C), images represented by
Imperfect anal~gle~, popt;lar definitions, suggestive phrases, wellmeant laws and mstltutlOns .I' And this level of apprehension is doxa
for what plato says at 517b and 532a-c makes clear that the prisoner:
III the Cave have doxa only, which is said in the Line to deal with a
world of 'Becoming' and not of 'Being', a world of sensibles and not
of Forms (534a). The 'images' with which doxa deals are in fact those
described earlier in the Republic as 'the numerous conventional notions
popularly held about beauty and the rest' (479d); and these notions,
as the context makes clear, are based on sense":'experience. These references suggest that in t~e Republic doxa is 'propositional', including in
the scope of Hs expressIOn both particular and general statements, and
assunung as ItS baSlS a combinat~on of perception and thought which
reas~ns and sometImes luakes clever conjectures' (SI6d) from its
senSIble data, but is always tied to such data as the only criterion of the
truthof ItS results. Thus, as we noted earlier in the discussion of 476a If.,
the distmctlO~ ~etween dox~ a~d knowledge is essentially a distinction
betw~en empmcal and a priOri knowledge, and it is important to see,
esp~~lally for the purpose of contrasting Plato's position here with his
posmon m the Phaedo, that ~ust as by the intimate link which he
appears to make m the RepublIC between the Forms and the method of
hypothesis plato implies that knowledge is 'propositional', so by what
he says about doxa and the 'images' with which it deals he implies
66
THE CRiTICISM OF PERCEPTION
PLATO'S THBORY OF KNOWLEDGE
that doxa is 'propositional'. This represents an important shift from the
view taken in the Phaedo. There the distinction fundamental to the
theory of recollection was a distinction between sensation and a conceptual level of apprehension, and the apprehension of Form was
represented as a recognition of Form marked by the transition from
sensation to a conceptual level. Thus the doxa of the Republic would be,
according to the Phaedo doctrine, already a level of thought involving
apprehension of and reasoning about Forms. And this raises immediately
the problem of what distinctions can be made to separate sharply doxa
from knowledge consistently with the theory of Forms, especially with
its assumption of an archetype-copy relationship between Forms and
sensibles. This problem will be discussed in the next chapter. For the
present all that should be noted is that the main reason why the problem
is avoided in the Republic is that by his severe disparagement of perception and its objects and his refusal to allow perception to playa
positive part in the approach to knowledge plato suc:eeds, at the cost
of some inconsistency with his theory of Forms, rn keeprng doxa
sharply separate from knowledge.
,.,"
.
In the light of this discussion of doxa and the Images With which It
deals, we now see that 'image' is used to denote not only particular
objects of perception but also verbal 'images', particular or general
statements having their basis in perception. It is very difficult to say in
some places what weight should be placed on the use of 'image' in the
Republic _ whether it should be taken to mean 'image' of a Form il~ a
sense which implies that it properly reflects the Form and preserves Its
similarity to the Form, or whether it is used more loosely to describe
what appears to have this or that characteristic, or to be true of what
is perceived, but is in fact a ~alse and deceptive. 'image' of ;:hat i~
'real' (elsewhere in the middle dialogues plato certainly does use Image
(ddSlon) in this latter sense, e.g. The~etetus ISOC, Isoe, ISIC). ~ut i.t is
at least quite clear that, even where It can be assumed that he 18 usmg
'image' in the former sense, he considers images to be o~ no value
an aid to knowledge. At least it is only as a teaching :ud that he IS
willing to accord any value to them, his assumption being that only
with prior knowledge of the Forms is it possible to recognise whether
anything is an 'image' and what it is an 'iInage' ~f. The assumpti~n is
apparent in Plato's discussion of the early education of the gu,:"d,an~.
It is the business of the poet and artist, he argues, to produce 111 their
:s
work 'images' (40Ib, 402C) of goodness and beauty. The difficulty is
that such images c=ot properly be recoguised for what they are.
Thus the images may be images of the bad rather than the good, and
though the many impressions of sense may be formed imperceptibly
into some kind of unity, it is without conscious recognition of their
meaning (40Ib-c). And plato clearly implies that it is only when the
Forms themselves are known that it is possible to recognise the images
properly (402b-c). We can, in fact, be right, though without knowing
why, in our appreciation of images only if our training is rightly
directed from above (40rd-e). And those alone who have 'seen the
truth concerning what is beautiful and just and good' will 'know what
each of theimages is, and of what it is an image' (S20C). ltis, of course,
natural that within a context where an ei!ucational programme is being
discussed an emphasis should be placed on the use of images as aids in
teaching rather than in other ways. But plato insists that this should
not be taken to imply that images are of value outside this limited use
of them. Thus what he says about 'images' in these passages accords
with all the other evidence from the Republic about his views on perception and its objects. Advocating an ideal of 'pure thought', he
dismisses the claim that perception provides knowledge, and divorces
perception completely from the method by which knowledge is to
be attained. It is only by severely disparaging perception in this way
that he is able to maintain a radical distinction between doxa and
knowledge. For ifhe had seriously considered the claim that perception
provides knowledge in the light of the implications of the Phaedo's
doctrine of recollection, he would have been led to question the
adequacy of the theory of Forms as the basis of a distinction between
a priori and empirical knowledge.
4. THE CRATYLUS
aJ Plato's criticism of verbal 'images'
We must now consider other criticisms of perception made by plato
in the middle dialogues. In the Republic the only positive criticism is
that the objects of perception have the contradictory character of
allOwing two contraty predicates to be applied to them at the same
time. We may add to this the general assumption that the objects
68
studied by dialectic and the mathematical sciences have an invariability
and permanence which do not belong to sensibles. But no attempt is
made to offer an explanation. of the apparent contradictions arising in
perception. The Theaetetus is the first dialogue in which such an
attempt is made. Before examining it, however, the Cratylus, a dialogue
which has many clear affmities with the Theaetetus, must be considered,
for its discussion of 'images', more especially verbal 'images', as repre.,..
sentations of 'reality' is both relevant and important, and so too are its
remarks on the Heraclitean doctrine of flux.
It is in the Cratylus that plato first explicitly distinguishes the verbal
image as one important class of images. 13 It must be admitted that he
discusses the verbal image here in a particular restricted sense, since he
relates his discussion of it to a theory of 'natural' language which makes
a name significant by resemblance, resemblance between the form or
sound of the letters of which the name is composed and the thing which
the name signifies; the discussion explicitly assumes that single words
have significance apart from statements, and can be true or false (38 5c).
But towards the end of the dialogue (438a if.) the general question is
raised whether it is preferable to discover reality through verbal 'images'
of it or through the things which are themselves 'real', and it is clear
that 'the truth of things' must be discovered through a study of the
realities themselves. For since the difficulty of distinguishing true from
(and that this is so is suggested by the way in which the Forms are
introduced at the very end of the dialoguc) it is extremely difficult to
imagine how one can practise, independently of all words or symbols,
tl,e direct inspection of realities which Plato aSSerts to be the best way
to attain knowledge. The probability is that plato has been led to
exaggerate here in his concern to protest against the view that the
nature of reality can be discovered through a study oflanguage alone,
more particularly through a study of the Greek language of his time.
For the Cratylus seems to be mainly concerned to show the inadequacy
of existing language as an instrument of inquiry into 'the truth of
things', whether that language is interpreted from the point of view
that names are significant 'by nature' ,or~from the point of view that
they are significant 'by convention'. Plato clearly assumes the possibility
of a reform of existing language which will make it an adequate
instrument of inquiry. Hence his appeal to the dialectician as the ideal
'superintendent' in the task of reformation (390c-d). Against this
important assumption the question of whether language is 'natural' or
'conventional' is relatively unimportant. It is clear that Plato's view is
that it is impossible to interpret an existing language exclusively on
the basis of either of these theories, and that it is equally impossible to
restrict the reform of language to a pattern dictated by exclusive
adherence to either theory (43S b- d ).
If, then, plato thinks that language must be reformed to make it an
false images seems to arise in the case of all verbal images we cannot
adequate instrument of inquiry into 'the truth of things', what reasons
resort to other verbal images as a criterion but must have knowledge
of things independently of the use of verbal images if we are to decide
whether a particular verbalimage is true or false (438d-e). This answer
recalls the implicit assumption in the Republic that independent knowledge of the Form is essential to the recognition of the image. Ill. the
Republic, however, the assumption was made only for those verbal
'images' which were empirical statements. It was not made for the
propositions examined by the mathematical sciences and by dialectic,
does he give for this? In other words, what are the inadequacies that
he fmds in existing language? His answer here is important as an
explanation of his mistrust of verbal 'images', and points forward to
what h~ says in the The.aetetus in criticism of perception and its objects.
HIS mamcntlC1sm ofeXIsting language is that it possesses merely relative
SignIficance. Thus, on the theory that language is conventional, the
correctness of words becomes relative to the particnlar individuals or
particular societies establishing the convention (384c-39Ia, 433 e). Plato
does not c?nclude f~om this tha; convention should be allowed no part
In determmmg the correctness of words. He grants that it must play
a part (435b-c). But since his assumption is that it is possible to establish
a ~oc;bnlary which is adequate for the expression of 'the truth of
things he refuses to grant that the establishment of the 'correctness' of
words is properly left to 'any chance person' (390d)." And he argues
that in interpreting Plato's answer to this there is no need to restrict
the sense of 'image' to the narrow sense just described. His answer is
for though these too can be described as 'images' or 'representations'
of ,reality' plato does not suggest in any way that the study of them is
other than the best way of attaining knowledge. The Cratylus, then,
appears to make a much more sweeping condemnation of images than
the Rep"blic. Indeed, if one assumes that the realities are the Forms
r
70
that since the 'conventionalists' wrongly assume that their theory
implies that 'any chance person' is an adequate arbiter of correctness,
then a natural corollary of their theory on the metaphysical side is a
subjectivist theory of a Protagorean kind, which makes 'any chance
person' an adequate arbiter of what is 'real' (385e-;86a). Hence the
weakness of existing language, in so far as its vocabulary is established
by convention, is that its adequacy for the expression of the truth is .
entirely relative to what any ordinary person conceives to be the truth,
or to be 'real'. Much the same kind of criticism can be brought ifit is
assumed that words have a natural aptitude, through their form or
sound, to signify their proper objects. For the significance of the words
will be relative to a particular interpretation of the nature of the
'reality' which the language is to mirror, and will constantly be subject
to changes and transpositions dictated by individual fancy (4' 4c-d,
436b ff.). The Greek language, in so far as it reflects a particular conception of 'reality', suggests that it is largely based on a Heraclitean .
flux theory of the nature of the world (402a, 4ub-c, 439c); Plato's
remarks at 439C seem to make clear that he is putting this forward
serionsly as his own view.
b] Plato's assumption that sensibles are in flux
Now in criticising in these various ways the adequacy of current
vocabulary to express 'the truth of things' plato appears to be
advocating as an ideal of universal application what he had advocated
in the Republic in particular application to geometry, when he argued
that the normal language of geometry, fitted only to describe methods
of practical construction, was ludicrously inadequate as a description
of geometrical reality (527a). Thus he is advocating a general reform
of current language so as to make it adequate to express the truth as
he himself sees it, i.e. to describe the eternal and immutable reality of
the Forms. What is particularly significant in his criticism of existing
language is his view of the conception of 'reality' which is implicit in
its terminology and usage. In the fmt place he argues that existing
language can claim that it is consistently adequate to express the truth
ouly if it assumes a subjectivist theory of truth, such as that of Protagoras. In the second place he argues that, in so far as it does in fact
imply with at least some consistency one particular objective theory
of the nature of 'reality', it implies a Heraditean doctrine of flux. Thus
71
he links his criticism of the adequacy of existing verbal 'imagery' with
the two theories which he will subsequently show, in the Theaetetus,
to be essential to the conSistency of any claim that 'knowledge is perception'. And in the Cratrlus he sets against each of these theories his
own theory of Forms. Against the subjectivism of Protagoras he asserts
that things 'have a fixed reality of their own, not in relation to us nor
constituted by us' (386d-e). Against the flux theory of Heraclitus he
asserts that knowledge is impossible if all things are in flux, for what
is in flux is never in any determinate condition, and cannot significantly
be named at all (439d-e). Hence, once we grant the possibility of
knowledge, We must grant that its objects are not in flux, but are
immutable, and agree that 'the beautiful itself', 'the good itself', and
the other 'realities' are the objects ofkn'O",ledge (43g e-440c).
Here for the first time the theory of Forms is explicitly opposed to
the Heraclitean theory that all things are in flux. And what is to be
especially noted is that Plato, having argued that to accept that knowledge exists and hence that objects of knowledge exist is to accept that
knowledge itself and its objects are not in flux, assumes without
question that the objects of knowledge are 'beauty itself, good itself,
and all the other realities' (440b). For he is not argning simply that to
accept the existence of knowledge is to accept that its objects have
some stability. This in itself would give him no greater justification
for assuming that 'beauty itself', 'good itself', etc., 'realities' different
from sensible particulars, are objects of knowledge, and hence stable,
than for assuming that sensible particulars are objects of knowledge,
and hence stable. But in fact his argument begins with the assumption
that these' realities' exist, that they are clifferent from sensibles and that
they 'are always such as they are' (439c7-d6). He then argues that if it
is asserted that these 'realities' are in flux, then they cannot keep their
own, or indeed any determinate form, and hence cannot be known.
Indeed, he goes on, the existence of knowledge will have to be denied
if all things are in flux. But, he concludes, on the assumption that
knowledge, and hence objects of knowledge exist, and that 'the
beautiful, the good, and all the other realities' exist, then there do exist
things which are not in flux (44ob4-C1). Thus the argument begins
and ends with an assertion of the thesis that non-sensible realities exist,
and it is clear that plato considered the assumption of their existence
essential in opposing the flux doctrine.
Why is this assumptiou considered essential? It is obvious that plato
does not think it enough, in opposing the flux doctrine, to put forward
the logical argument that the doctrine has the apparently absurd consequence that nothing can be known, but thinks it necessary to select
one special class of objects, the non-sensible 'realities', and to emphasise
that these cannot be known if they are in flux. And his reason for
thinking this necessary must be that he considered that if these nonsensible 'realities' were in flux then it would in fact be the case that
nothing can be known. His argument thus implies his acceptance of
the flux doctrine as true for sensibles. Hence the assumption made at
the beginning of the argument - that there are non-sensible 'realities'
which 'are always such as they are' - is essential for plato in that only
on this assumption is knowledge possible. The important feature of
this argument for our present inquiry is its implication that plato
accepts the flux doctrine as true for sensibles. The need to stress that
this is clearly implicit in the argument arises ouly because an ambiguity
in the text at the beginning of the argument allows the possibility of
doubt as to whether plato is there explicitly asserting that he accepts
the doctrine as true for sensibles, and hence accepts as true for sensibles
what he asserts to be true for anything in flux. The ambiguity arises
at 439d4. Having asserted that there exists 'beauty itself, good itself,
and all the other realities', plato goes on: 'then let us consider beauty
itself, not asking whether a particular face, or anything of that sort, is
beautiful, and all these things appear to be in flux'. Is 'whether' (ei) to
be understood with the last clause (... and [whether1all these things
. . .)? Grammatically this would seem the more obvious interpretation."' Yet for the sake of the logical sequence of Plato's argument
there are very strong reasons for taking this clause in an explanatory
sense: '(for) all these things appear to be in flux'." So taken it is a
statement by Plato that he accepts the doctrine of flux as true for
sensibles. Such a statement is obviously called for at this point. For
since plato has just asserted that, in the argument against the flux
theory which is to follow, he is excluding sensible particulars from
consideration, it is natural to expect that some reason will immediately
be given for this exclusion. The clause 'all these things appear to be in
flux' would provide such a reason, and once accepted as the statement
of a reason for excluding sensibles from consideration it makes much
clearer than would otherwise be the case the purpose and sequence of
73
PLATO'S THEORY OF KNOWLEDGE'
the argument which follows. These, to me, are very good grounds for
interpretmg the clause in this sense.
Th~ position is, then, that Flato, atleast implicitly and almost certainly
expliCitly also, IS acceptmg the flux doctrine as true for sensibles. He
had, of course, earlier in the Phaedo made clear his view that sensibles
are ~onstantly changing and that this is a reason for condemning perceptlOn as mcapable of yielding truth (78c-80b, 83b). And that he
accepted the flux doctrine as true for sensibles is stated by Aristotle in
twO pa~sages m the ~etaphysics (987a32-b7, 1078bI2-17) where he is
explammg that Plato s acceptance of the flux doctrine as true for
sensibles led him to postulate non-sensible Forms in order to save the
possibility of knowledge. Moreover Aristotle's statement that Plato
continued in later life to believe that Sensibles were in flux seems to
be confirmed by passages in late dialogues such as the Timaeus (49 d- e)
and the Phdebus (59b), whIch affirm that sensibles are constantly
changmg. Thus tJ;e eVidence of the Cratylus is by no means the only
eVidence for Plato s acceptance of the flux doctrine. Yet it does deserve
special emphasis and consideration. For it is the only place in the
dIalogues where plato clearly shows that he considered the specifically
Herachtean doctrme of flux to be true for sensibles. The fact that in
the Theaetetus he n;akes
Heraclitean doctrine an essential part of
the baSIS of the claIm that knowledge is perception' does not itself
show that he himself accepted it as true for sensibles. But the evidence
of the Cratylus, confirming from the dialogues themselves Aristotle's
testimony, allows us to assume that in the Theaetetus too Plato accepts
the doctrme ,,:,d hence accepts the implications which he there finds in it.
This last pomt IS Important in assessing the severity of Plato's condemnatlOn of perceptIon and its objects in the middle dialogues. The
Cratylus and the Theaetetus are the only two dialogues where Plato
discusses the flux doctrine as a specifically Heraclitean doctrine, and
~n each case his attempt to reduce to absurdity the claim that what is
m flux can be known leads him to the extreme position of denying
that there are any determmate senSible characteristics. For his argument,
both m.th," Cratylus and the Theaetetus, includes a denial that what is
m flux IS m any way determinate. And this, assuming as Plato does
that sensibles are .in. flux, is a denial that there are any determinate
s~ns~ble characterlSl1cs. Thus in the Cratylus plato affirms that no
slgmficant deSCription can be applied to what is in flux' one cannot
till;
F
'
74
describe it as 'that' or as 'of such a kind', because it is never in any
determinate condition. The same argument appears again in the
Theaetetus (157b, 182d-183b; cf. 152d). Hence to agree that sensibles
are in flux is to agree that it is impossible to describe them. What
then becomes of the doctrine that sensible characteristics are' copies' or
'images' of Forms, that they are recognisable and hence are able to
prompt the recollection of Forms? This doctrine clearly assumes that
there are determinate and recognisable sensible characteristics; indeed
it is a doctrine that sensibles are determinate and recognisable in so far
as they 'participate in' and hence 'resemble' Forms.
There is a serious inconsistency, then, between this doctrine and the
consequences draWll by plato from the fact that sensibles are in flux.
It is an inconsistency which some scholars are reluctant to admit, and
attempts have been made to resolve it by denying that Plato ever
accepted the flux doctrine as true for sensibles. Thus it has been argued
that when Plato in the Theaetetus (I82d-I83C) attempts to reduce to
absurdity the thesis that 'all things are in flux' by showing that it
implies that no significant description can be applied to anything, and
that all answers to any question about anything are equally right, 'we
are taddy given to understand that these consequences are obviously
false and therefore the view which entails them must be false also'.17
So far there can be no quarrel with this argument. plato does intend
here to reduce to absurdity dIe view that 'all things are in flux'. But
to reduce this view to absurdity is not equivalent to reducing to
absurdity 'the proposition that everything in this world is always
changing', though the argument assumes this wheu it goes on to assert
that Plato's argumeut shows 'that there is something stable in this·
world. For a refutation of the proposition that everything in this world
is always changing both its place and character would be a proof of the
proposition that something in this world is sometimes stable in respect
of either its place or character or both.' 18 plato is clearly not, however,
refuting the proposition that everything in this world is always changing.
Both in the Gratylus and the Theaetetus it is perfectly explicit that the
thesis which plato attacks is 'that all thiugs are in flux', and in each·
case his main concern is to show that what is in flux cannot be known
(for it cannot even be described in any way), and hence that, if all
thiugs are in flux, nothing can be knoWll. But the possibility of using
the absurdity of this fiual consequence as an argument for the view
75
that 'there is something stable in this world' arises only if the thesis
'that all things are in flux' is associated with the thesis 'that all things
are things in this world' (i.e., presumably, sensibles). In that case to
argue, from the absurdity of its consequences, that the proposition
that 'all things are in flux' is false is to argue that one of two theses
is false - that either' all sensibles (= all things) are in flux' is false (hence
some sensibles are not in flux) or 'all things are sensibles' is false (hence
some things are non-sensibles and are not in flux). But the fact that
the view that 'all things are in flux' (where all things are sensibles)
entails absurdities does not itself allow us to assert which one of the
above two theses is false. Nor does Plato, in the Theaetetus, suggest
in any way that it does. In 18zd-I83c he is attacking the view that all
things are in flux as the basis of the thesls-that knowledge is perception,
and as the basis of such a thesis it can readily be admitted that the view
that all things are in flux appears to be associated with the view that all
things are sensibles; but all dIat plato concludes from the absurd consequences of the view that all things are in flux is that the thesis that
knowledge is perception is false in so far as it is based on that view
(r83c). Only by agreeing that 'all things are sensibles' must continue
to be accepted as true wonld he be able to argue further that 'all
sensibles are in flux' must be false, and hence that some sensibles are
not in flux. And he neither says nor implies that he agrees with this.
In fact, once we compare the argument of the Theaetetus with the very
similar argument at the end of the Cratylus, we see that what plato
accepts as true is that all sensible, are in flux, and hence that he can
argue from the absurdity of the consequences of the view that all
things are in flux to the falsity of the view that all things are sensibles,
and thus give reasons for assuming that there are non-sensibles which
are not in flux.
We may conclude, then, that the Theaetettls does not show 'that
there is somethiug stable in this world', and that the Gratylus dearly
shows that plato accepted the Heraditean doctrine of flux as true for
sensibles, and hence accepted as true for sensibles the consequences that
what is in flux has no determinate characteristics and can have no
significant description applied to it. As we noted earlier, it is only in
the Gratylus and the Theaetetus that plato exanrines the specifically
Heraclitean flux doctrine and only in those dialogues uses against a
flux doctrine a particular reductio ad absurdum type of argumentimplying
an extremely severe condemnation of sensibles. But this does not,
I think, imply that his acceptance of the Heraclitean view as true for
sensibles is to be differentiated from his view that sensibles are constantly in change, a view which he expresses in later dialogues without
any of the severe condemnation of sensibles characteristic of the middle
dialogues. In other words I do not think that at one time Plato thinks
of sensibles as subject to a sort of change which precludes the possibility
of describing them, and at another time thinks of them as subject to
an essentially different sort of change which allows them to be significantly described. The truth appears to be that, while in later dialogues
he acknowledges that the fact that sensibles are in flux is not inconsistent
with their ftmction as 'images' of Forms, his attitude of severe disparagement of sensibles in the middle dialogues leads him to exaggeration in examining the consequences of the fact that they are in flux,
and thus leads him to a view of them inconsistent with the view that
they 'participate in' and 'resemble' Forms. In this respect the Cratyius,
with its introduction of arguments from the doctrine of flux, illustrates
even more strikingly than the Republic had done the serious difficulties
which arise for Plato's theory of knowledge from his uncompromising
attitude of contempt for perception and its objects. And it is as well
to recall, in concluding this examination of the Cratylus, that Plato's
argument at the end of the dialogue is a criticism of the flux theory as
a theory representing that conception of 'reality' which is, plato
appears to assume, implicit in the present form of the Greek language.
Hence his final remarks associate a condemnation of the flux doctrine
with a plea not to put trust in names (44oc-d). Thus, when we note
further that he asserts that what he says about the adequacy of single
names to represent 'reality' is true also for propositions (logai: 43Ib),
we can see that his criticism of existing language as an adequate
instrument of inquiry into 'the truth of things' implies ultimately that
all propositions expressing what is apprehended at the empirical level
described as doxa in the Republic are meaningless.
5.
aJ
THE THEAETETUS
The thesis that kllOwledge is perception
This examination of the Cratylus has enabled us to dispose of one of
77
the difficulties which arise from the discussion of perception in the first
part of the Theaetetus. For the evidence of the Cratylus that plato
~cc~Pts the Heraclitean doctrine of flux as true for sensibles clearly
Justifies the inference that hts argument in the Theaetetus that what is
in flux is valueless as a basis of knowledge represents his own conviction
about sensibles. The point is, as we have seen, important. For the fmt
part of the Theaetelus is not a direct presentation of Plato's views on
the nature of perception and its objects, but rather an examination of
the assumptions necessary to make fully consistent the thesis that
'knowledge is perception'; and the fact that Plato, having stated the
assumptlOns, attempts to reduce them to absurdity obviously does not
imply that he ~ccepted any of them, qr ~any part of any of them, as
true of perceptton or of the objects of perception. This purpose of the
first part of the dialogue mak~" it, indeed, an excellent example of the
apphcatlOn of the method of hypothesis' to a particular thesis.
. The 'hypo;hesis' fr~m which the discussion starts is that 'knowledge
IS perceptton. Plato mterprets this as a claim that whatever anyone
asserts to be the case on the basis of what he is at the moment percelVlng or ~f what he has perceived in the past is necessarily true, and
not only this. but that this basis in perception is both a necessary and a
suffiClent baSIS of knowledge; there is no knowledge other than what
is based on perception. It is true that Plato's examination is directed
initiall! to 'pure' sensation, but it becomes clear that 'perception', in
~he claIm that 'knowledge is perception', is meant to include memoryImages (~63d:-I66c) and judgement (I58b, I6Id, 178b, I79c). Once the
hypotheSIS IS mterpreted m the above sense, and it is recognised that it
is impossible to know and yet to be wrong (I52C), the hypothesis is
~e",: to be assummg that perception is infallible. plato therefore makes
It his first task to see what further assumptions must be made to allow
this assumption to be :onsistently maintained. He says firstly that the
claim that knowledge IS perceptIOn Implies acceptance of the thesis of
Protago~as that 'man is the measure of all things' (I52a). For it follows
from this theSIS that perception is infallible, which is assumed in the
ch,m that knowledge is perception. Thus, according to Protagoras,
what appear~ to be the case is the case, and hence what is perceived to
be the case IS the case, for all mstances of perception (I52a- c). Plato
. argues further that the Protagorean thesis rests in turn on the thesis
that all things are in motion and perpetually changing (I5 2C- I 53 d).
79
This latter thesis is not, of course, implied by the Protagorean thesis,
which in fact denies the validity of any daim to be able to specify the
general characteristics of an external 'real' world which is common to
everyone as the object of their perceptions. However, plato is no doubt
sincere in his contention that it is only if everythiug is in fact in flux
that the thesis that knowledge is perception becomes consistently
tenable, and for this reason, having already argued that the daim th~t
knowledge is perception implies acceptance of the Protagorean thesIs
that 'man is the meaSure of all things', he develops the Protagorean
thesis as a thesis based on a flux doctrine, though there is no reliable
independent evidence that Protagoras himself based his thesis on such
vidual, and hence are private and peculiar to that individual. The confusion here is in the interpretation of 'nothing is ever the same'. If
everything is perpetually changing, then it is true to say that 110 particular event in a process of change is 'the same' as the one inunediately
preceding it or the one immediately following it, and that no particular
event ever remains 'the same', in the sense that it preserves its identity
and is not subject to change; it must necessarily be succeeded by another
and a different event. In these two senses of 'the same' the doctrine of
perpetual change appears to entail that 'nothing is ever the same'. But
it does not entail that no particular event or series of events recurs or
is repeated at another time or in another place at the same time. Hence
it does not entail that no particular eve,\!: or series of events is ever 'like'
(see 159b) any other event or series of events; in this sense it does not
entail that 'nothiug is ever the same'. Later, in the Timaeus (49d- e),
plato came to recognise this, but here in the Theaetetus he apparently
does not. If he had done, he would have seen that the individual's
percepts, viewed as the result of the interaction between constantly
changing sense-organs and constantly changing enviromnent, may
be 'like' the percepts of another individual, possibly of all other individuals, and that they are not necessarily 'nnlike' those of any other
individual, and hence private and peculiar to him.
If, however, there is some confusion in the way in which plato links
the thesis that 'man is the measure of all things' with a doctrine of flux,
it is not difficult to see, from his discussion, what considerations initially
led him to assume a connexion between the two doctrines. It is significant that in illustrating the connexion plato relies almost exdusively
on the fact of the relativity of the individual's percepts to his bodily
condition. Thus changes in bodily condition imply changes in the
percept, and a perpetually changing bodily condition implies perpetually changing percepts. Socrates-ill, says Plato, has different percepts from Socrates-well, and so on (158e-15ge). This immediately
establishes one sort of connexion between the concepts of change and
of relativity, and it is clearly one to which plato attaches great importance. And his earlier remarks in 154a ahnost suggest that this sort of
connexion constitutes for him an ajortiori argument for the view that
the percepts of each individual are private and peculiar to him in a
way which excludes the possibility that they are 'like' the percepts of
any other individual. For having given the first summary account of
78
a doctrine.
In what way, then, does a flux doctrine support the claim that
knowledge is perception? According to plato the infallibility of perception can be shown to be a consequence of the doctrine that all ~gs
are in flux. For if everything is in flux, theu, assuming that perceptlou
implies an interaction between the individual percipient and h.is environment, it will follow that all percepts are the result of an mteractlon
between constantly changing sense-organs and a constantly changing environment (I53d-I54b, 155d-I57C). The relativity of the percept at
once to the individual percipient and to particular circumstances could,
of course, have been argued independently of any theory of flux. And
this relativity, since it points to the diIlicnlty of trying to justify the
daim of anyone 'perception' over another to yield knowledge, could
plausibly have been used to support an argument that all cases of perception have an equally strong claim to be able to yield knowledge,
and hence are all equally 'true'. What, then, does the assumption that
all thiugs are in flux add to the plausibility of such an argument? The
flux doctrine itself does not entail that each individual percipient is
restricted in what he perceives to a private world different from that of
any other percipient. In other words it is not a doctrine necessarily
inconsistent with the doctrine that what is perceived is the same for
all percipients in the same situation. It is dear, however, that P~ato
does consider that the two doctrines are inconsistent. His assumptions
appear to be: (i) if everythiug is in flux, then 'nothiug is ever the same';
(ii) if 'nothiug is ever the same', then no two percepts are ever the
same; (iii) if no two percepts are ever the same, then the percep.ts ~f
one individual are always all different from those of any other mdl-
80
the percept as the result ofinteraction between sense-organ and external
'motions' (153 d-I 54a) he assumes immediately that this account implies
that percepts are peculiar to the individual percipient (I54a). And to
counter any possible doubt about the truth of this consequence, he
asserts that one can actually affirm with certainty that not even to
oneself does anything ever appear 'the same', since one is never in the
same condition. Aristotle too, in the Metaphysics (ro09b), presents the
fact of the relativity of the individual's percepts to his bodily condition
as the principal argument in support of the subjectivist view that what
appears to the senses must be true."
So far, then, Plato has argued that the thesis that knowledge is
perception, implying, as he interprets it, the infallibility of perception,
must, if it is to be consistently tenable, assume the truth of the Protagorean doctrine that 'man is the measure of all thiugs', and that this
doctrine in turn assumes that everything is in perpetual change. His
reason for interpreting it as a thesis that perception is infallible is presumably that he considered that only in that sense could it plausibly
be maintained in the face of all the apparent contradictions and inconsistencies arising from perception. For he is concerned to emphasise
that, once it is interpreted in that sense, then any apparent contradictions and inconsistencies are resolved (154b-155d, 157e-158e). It
seems possible to argue, therefore, that plato is honestly trying to make
out as consistent a case as possible for the claim of perception to yield
knowledge, and that any confusion in his manner of associating it with
a doctrine of flux is inadvertent confusion rather than deliberate
perversion.
Yet in one respect at least it is difficult to avoid the conclusion that he
is deliberately weighting the scales against perception. Thus he refuses
to apply the term 'is' or 'being' to what is perceived; 'nothing is,. but
is always becoming' (I52d-e, I 57a--b, 157d). 'Becoming' is associated
(I57b) with 'being produced', 'perishing', and 'changing'; it is contrasted with what is defmite or determinate, Plato's assumptions being
(i) that only to what is defmite or determinate can the terms 'is' or
'being' be properly applied, (il) that 'becoming' excludes 'being determinate' (Iszd-e, 157a--c). By this manner of presentation he is already
preparing the way for his criticism later in the dialogue of the thesis
that knowledge is perception, in particnlar for the argument that 'being
determinate' is a condition of 'being known',
81
In considering this stipulation about the proper application of 'is' it
is imFo~tan,t, in the first place, to distinguish it from the stipulation
that Bemg (to on) IS to be ascribed to Forms but not to seusibles
which belong to a world of 'Becoming' (geneSis). For this latte:
~t1pulatlOn does n~t mclude the stipulation that 'becoming' excludes
bemg determmate . It uses genesis as a general description of a world
?f changmg and .hence impermanent characteristics, this change and
Impermanence bemg contrasted with the immutability and permanence
which plato assumes to belong to the 'really real' (to ontds on). For as a
te~m properly use.d. to describe the process of attaining some determ~nate state, genesIS IS naturally associated with change, and hence is a
sUltable enough term for Plato's purpose here. This is of course a
stipulation :vhi~h would become unwieldy if an attemp; was mad; to
adhere to It WIth rrgorous consistency in discussion as Plato well
r~alised, 20 and h~ does ll~t pretend to maintain
rigorous con~lstency: I~, partIcular, smce this distinction between 'Being' and
Becon:rng ,IS not m~ant to imply that 'Becoming' excludes 'being
determmate , he IS qUlte ready to use 'is' and 'being' for what is determinate in the w.orld of 'Becoming', and to use 'becoming' for the
process of attammg a determinate state, a narrower sense than that
given to it in the original distinction. Moreover, he makes clear that
the world of 'Becoming', withiu which this subsidiary distinction
between 'bei~g' and 'becoming' is made, is a world of perpetual
change. Thus m the Fhaedo, where he emphasises that the visible world
IS one, of pe~pet~al.ch:ng~ (~8c-7?c), he discusses the causes of 'comingto-be and, pe~shing w~thiu t~s world (96a ff.), or, more fully, the
c~u:'es of commg-to-be and perrshmg' and 'being' (97c). And in
gIVlllg his own explanation in terms of the theory of Forms he sees his
task as th~t.of explaining the fact of the determinate, yet impermanent
.
charactenstlCs of senSIble things. Thus he says that the onl
hich
thin'
Y way m
w
any
g comes to be' is 'by participation in the proper reality
of any gIven form m which it participates' (roIC).21 For example,
~nythm~ that IS to be two (to mellonta duo esesthai) must participate in
d~ality , and SImilarly anythmg that IS to be one must participate in
UlUty (IOIC). Here Plato accepts the fact that the world of 'Becoming'
has. determma,te .ch~ractef1St1cs and readily uses the verb 'to be' to
deSignate the bemg of the determinate characteristics which are the
end result of the process of 'coming-into-being' (geneSIs). The same
such
kind of distinction is found later in the Phi Ie bus when plato is again
explaining the determinate characteristics of the world of 'Becoming'.
Here the process of 'coming-into-being' is described not simply as
genesis, but more fully and precisely, so as to distinguish the process of
'becoming' from the resultant 'being', as gmcsis eis ousian (26d); the
same distinction is fotUld also in the phrase used to describe this resultant
'being' - gegen~men~ ousia (,the being that has come to be': 27b). In
the Philebus too it is made clear that the world to which the two terms
in this distinction are applied is a world of perpetual change (59 a- b ).
Now that we have distinguished (i) the stipulation that 'Being' is to
be distinguished from 'Becoming' as the permanent and immutable
(Forms) from the impermanent and changing (sensibles): and (ii) the
subsidiary distinction, within 'Becoming', of'becoming' and 'being' as
a distinction between 'coming-to-be determinate' and 'being determinate', it is clear that it is the distinction in (ii) which is relevant to
the assessment of Plato's argument in the Theaetetus. For his argument
is that what is in perpetual change and motion is never in any determinate condition, and that consequently 'being', as defined in (ii), is
never applicable to it. Hence he says that no predicate can ever be
properly applied as a description of what is in flux, so that to say 'it
minate condition as an argument for postulating the existence of nonsensible 'realities' not subject to change, on the ground that otherwise
knowledge is impossible. Thus at the same time he asserts that Forms
exist and denies that the sensible world has any determinate characteristics. This in itself is implicitly to acknowledge that the argument that
'being in flux' is incompatible with 'being determinate' is equally valid
whether or not it is assumed that Forms exist. Nor indeed is it the case
that when plato accepts that the sensible world has determinate
characteristics and explains these in terms of 'participation' in Forms
he is thereby absolving them from change and impermanence. It is
part of the 'imperfection' of these sensible 'copies' of Forms that they
lack the constancy and permanence of their archetypes, and there is
no warrant at all, as we shall see in mote~detail when considering the
Timaeus, for assuming that 'copies' of Forms are not subject to change
and are permanent, and thus resolving the inconsistency between the
Theaetetus and other dialogues; the determinate characteristics of the
sensible world are characteristics of a perpetually changing world and
are themselves perpetually changing; this the Phaedo, Timaeus, and
Philebus quite clearly assume. Thus, in the light of the inconsistency
between these dialogues and the Theaetetus, it becomes clear that plato
is ready to use against the thesis that knowledge is perception an
argument which, except in the Cratylus, he invariably assumes to be
invalid when he is presenting his own theory of Forms. And this
suggests that he is deliberately weighting the scales against perception.
is X' of any part of the flux, where 'it is X' means 'it has the determinate
characteristic X', is always improper (I52d, I 57a-b). Thus he is contradicting what he says in the Phaedo and the Philebus; whereas in those
dialogues he fmds no incompatibility in the view that a world of
perpetual change has determinate characteristics, he asserts in the
Theaetetus that 'being in flux' is incompatible with 'being determinate'.
It is no doubt true that for plato the only explanation of the existence
of determinate characteristics in the sensible world is in terms of Forms,
and it may be argued that this has led him to believe that to hold that
everything is in flux and thus not to accept the existence of Forms is
to exclude the possibility of the existence of determinate sensible
characteristics. It is possible, I think, that this kind of reasoning may
have influenced plato in his presentation of the case for perception in
the Theaetetus. But it does nothing to resolve the serious inconsistency
between what plato says in the Theaetetus and what he says in other
dialogues such as the Phaedo and the Philebus. For, as we saw in considering the Cratylus, plato does accept that the sensible world is in
flux, and nses the argument that what is in flux is never in any deter-
bI Plato's criticism of the thesis
So far we have considered the manner of Plato's presentation of the
claim that knowledge is perception, and concluded that, although in
general it may be considered a fair presentation in the sense that it
appears to be a serious attempt to state the assumptions which would
make the claim as consistently tenable as is possible, it does in one
important respect seem to be less than fair. We must now consider the
criticisms which plato makes of the claim, as thus presented.
In the first place he develops the point that 'being in flux' is incompatible with 'being determinate', arguing that, since what is
perpetually changing both its place and character is never in any
determinate condition, then what is perpetually changing cannot be
known. And since it has been shown to be a necessary assumption of
85
the claim that knowledge is perception that what is perceived is thus
perpetually changing, then whatis perceived cannot be known (I8Ib183c). Thus the claim that knowledge is perception is disproved in so
far as itis based on the view that all things are in flux (I83c). The main
point which he makes in the course of this argument is that unless what
is perceived has some stability and fixity it is impossible to apply any
significant description to it, and he assumes that unless this possibility
exists, it is impossible to claim to know that something is the case. He
is clearly thinking of simple perceptual judgements of the kind 'this is
and sameness, oneness and twoness, likeness and unlikeness, evenness
yellow' or 'this is a stone' (I82d, 183a). Now we have already seen.
and oddness, beauty and ugliness, goodness and badness are instances of
in considering the argument at the end of the Cratylus, that this
argument, which is closely similar to the present argument in the
Theaetetus, shows that plato accepts as true that all sensibles arc in
flux, and hence can argue that if knowledge is to be possible it is
s11ch characteristics (r85a-I86a). These are 'common' characteristics in
necessary to assume the existence of some determinate non-sensible
'realities'. Though the Theaetetus does not make this explicit, it is
legitimate to say, on the evidence of the Cratylus, that it implies it.
It would follow that any significant judgement, however simple,
implies the existence of such non-sensible 'realities'. It wonld follow
also that such judgements have no application to the sensible world.
This last consequence is, however, apparently denied in Plato's next
argument (I84b-I87a). He begins it by pointing out that we see and
hear, not with onr eyes and ears, but through them. There is a unitary
'soul' with which we perceive all the objects of perception through the
senses as instrUlnents (I84d). Perception (aisth~sis) is, however, limited
to the isolated 'impressions' (patMmata) which are conveyed to the
'soul' through one or other of the particular senses, and it is the
distinctive feature of the perceptual activity of' sonl' or mind 22 that
each impression is conveyed through a single sense-organ. plato is here
attempting to specify the purely perceptual elements in cognition, and
he now goes on to distinguish as non-perceptual the 'thought' (diauoia)
and 'reasoning' (syllogismos) of the mind when it is 'occupied with
things by itself' independently of any bodily 'instrument' (I8sa ff.).
This is an important distinction, and enables Plato to defme aistMsis
with some precision before considering whether knowledge is aistMsis
as thus defmed. Examples which he gives of the 'impressions' to which
aistMsis is limited, and which are exclusive to one or other of the
particular sense-organs, are warm, cold, hard, soft, light, sweet, white,
black (r84b-e, r86b, d). These, he says, can be perceived by animals as
wellas men from the moment of birth (r 86c). Contrasted with aisthisis
are the thought and reasoning of the mind 'by itself', and the nature of
this independent activity of mind is defmed in the following way. If
there IS a characteristic applicable to the objects of more than one
se~se-organ, that characteristic is apprehended by the mind per se,
WIthout the medIatlOn of the senses. Being and non-being, difference
the sense that, unlike perceived characteristics, they are applicable to
the objects of m~re.than one of the sentes (r8sb-e). And they may be
descnbed as a priOri, ~n the sense that, though certainly applicable to
perceIved cha:actenstIcs (e.g. 'white is different from black'), they are
never, according to Plato, given in perception but apprehended independe~tly o~ It. It IS by parucular appeal to the characteristic of 'being'
thatthlS dlStmctlOn IS used to refute the thesis that knowledge is perception. Thus, since
(a) 'being' is an instance of a 'common' character-
~stic and hence, b~ defmition, not given in perception, and (b) to know
IS to know what IS or what IS true, and hence to apprehend 'being' or
truth (I86c, e), then knowledge is impossible if apprehension is limited
to the isolated impressions of one or other of the particnlar senses.
plato concludes that knowledge is not to be fonnd in the 'impressions'
afforded by perceptIon, but in the mind's reflection (syllogismos) about
them (I86d). This reflcctlOnlllcludcs all discrimination and comparison
not only of what is given in perception (r86b-c), but also of the commo~ char~ct~ristics themselves (I86a), and is subsequently described
as b~V11lg. (doxazein, I87a). More precisely, belief is the result of
;eflectlOn, which IS further described in r8ge-r90a as an internal debate
m the mind issuing in affirmations or denials, nnspoken statements
(log~t). These statements are expressions of doxa or belief, and it is the
theSIS that knowledge is true belief which now replaces the thesis tllat
knowledge is perception.
T~e point of similarity between this present argument and the
prevIOus argument against the doctrine of flux is that each is assuming
that the problem o~ !",owledge is to be approached initially as the
proble~ of the ~onditIons for the application of predicates significantly
to what IS perceIved. The argument against the flux doctrine was that if
86
everything is in flux, then no significant description can ever be ap~lied
to what is perceived, so that even the simplest judgements such as this
is yellow' or 'this is a stone' become inapplicable. And it appears to.be
assumed that knowledge includes judging significantly that something
is the case a condition of the significance of the judgement being that
its referen~e is to what is determinate. Since it is impossible to satisfy
this condition if the flux doctrine is true, then the thesis that knowledge
is perception is refuted in so far as it rests on that doctrine. The thesis,
as we have seen, does not limit perception (aisthesis) to 'sensation', ~ut
takes it to include 'sensations and the judgements in accordance Wlth
them' (I79c). In this argument against the flux doctrine plato has concerned himself primarily with what he distinguishes in hIs next. arg~
ment as strictly perceptible qualities. He now goes on to show, I~ thIs
next argument, that, even if it is assumed that ~ere are determmate
sensible characteristics, yet aisthisis cannot legltlmately be saId to
include anythiug other than the isolated 'impressions' of these characteristics, conveyed by the senses to the mind, since to go bey~nd the
impressions and to make 'judgements in ac~o~dance :,,:th them mvolves
an independent activity of mind; hence It IS illegItimate t~ constru~
aisthisis as 'sensations and the judgements in accordance WIth them.
And since it continues to be assumed that knowledge includes Judgmg
significantly that something is the case, then, since any judgement
involves an independent activity of mmd, knowledge cannot be
equated with perception.
. .. .
We have already seen that in making this dlStmctlOn b~tween
aisthisis and the 'thought' and 'reasoning' of the mind plato IS pnmarily
concerned to show that there are concepts which, though not denved
from perception, are nevertheless applicable to --;hat is percdved.
'Being' (ousia) is such a concept, and in assummg ItS applicability to
strictly perceptible characteristics (IS sa, . I86b) plato seems, to. b~
contradicting what he had argued earlier m refusmg to apply bemg
to what was in flux (I 52d-e, I 57a-b, I82b, I83a), and h~nce to
sensibles. It might be argued that this assumption is simply an mstance
of the bad habit of using the term 'being' loosely, a habIt which Plato
recognises in I57b as one responsible for a lack of preci~ion at several
points in his exposition so far. Thi~ is a pos~lble and m some w~ys
plausible explanation. But I am mclined to think that the explanatIOn
is that plato readily and naturally assumes, as he did earlier in the
Phaedo, that there are determinate sensible characteristics, overlooking
the fact that in his previous argument he had implicitly denied their
existence. And he is now arguing, as we have seen, that, assuming that
there are determinate sensible characteristics, yet aistMsis itself never
affords knowledge.
It is, I think, important to note that Plato is not arguing that, while
some knowledge is derived exclusively from perception, some is not.
His argument is that no knowledge is derived exclusively from perception. Thus, to take again the examples 'this is yellow' or 'this is a
stone', plato would say that, while 'yellow' and 'stone' are perceptible
characteristics, the simple jndgement 'this is yellow' or 'this is a stone'
includes the application of 'being', whkhis apprehended by the mind
independently of perception. It is true, of course, that the 'is' in these
examples is not used existentially. Yet it is clear, from Plato's previous
discussion of the distinction between 'being' and 'becoming' in the
Theaetetus, that 'this is yellow' is, for Plato, an implicit assertion of the
'being' of yellow, in the sense of 'being a determinate characteristic',
and this is equally clear from the discussion of the distinction between
'being' and 'becoming' in the passages of the Phaedo and the Philebus
examined earlier. Moreover in I87a plato describes as doxa the level of
apprehension attained by the mind when its activity is directed to
'things' (ta onta) independently of perception. I am not convinced,
incidentally, that it is right to translate doxa here as Judgement'. I have
myse1ffrequently used the term Judgement' in discussing Plato's argument, but without intending it to be assumed that it is a translation of
Plato's doxa. I prefer to translate doxa as 'belief'. The way in which
plato illustrates the distinction between true doxa and knowledge in
20Ia-c, and his phrase 'true doxa with an acconnt' as a proposed
defmition of knowledge (zord ff.), both suggest that he is using doxa
in the Theaetetus for 'belief', in the non-specialised sense in which it is
regularly distinguished from knowledge in other dialogues by its inability to 'give an account' ofitsel£ Doxa, in this sense, does, of course,
include judgement, but ouly an explicit distinction between doxabelief and doxa-judgement would justify a translation of doxa as judgement, either here in the Theaetetus or later in the Sophist. Now Plato's
point that doxa is a proper description of the mind's level of apprehension when it is occupied with things 'by itself' indicates that in his
view any belief that something is the case involves the application of
88
characteristics which are apprehended independently of perception,
and, of course, his argument that the fact of this independent form: of
apprehension refutes the hypothesis that. knowledge IS pe;cepnon
indicates that any knowledge that something IS the case similarly mvolves
such application, and hence is never derived exclusively from perception.
.
..
The question which now arises is whethe; thIs argu;uent IS mtended
to imply what the previous argument Imphed - that If we assume the
possibility of knowledge it is necessary to assu~e the. eX1ste~ce of nonsensible 'realities'. For since plato has expliCItly dlstmgmshed some
characteristics as apprehended a priori, in the sense that the apprehensIOn
of them is independent of perception, it is natural to ask .w~ether he
considers that they have a 'reality' independently of the mmd s ~ppre
hension of them. Clearly the argument itself does not
him
to any definite view on this question. If it is granted that ",sthe"s IS
limited to the isolated 'impressions' conveyed through the. senses, ~nd
that knowledge necessarily involves an independent act1Vlt~ of. ~d
not included in sensation, then the thesis that knowledge IS a"theSls
is refuted, no matter what further interpretation is given to the
mind's independent activity. And though I consider it highly probable
COm;ult,
that Plato's argument is meant to point to the need to aSSlmle no~
sensible 'realities' if knowledge is to be possible, I do not feel there IS
sufficient warrant for assuming that he is here consciously arguing
from the standpoint of his theory of Forms. The validiry and importance of the argument should be assessed quite independently of that
theory.
.h
h
It is interesting, however, to COlnpare what he says here WIt w at
he has said earlier about knowledge of Forms, especially as regards the
part played by perception. We have seen that in the RepublIC' the
existence is assumed of one Form for each set of things to which the
same name is applied. It is further assumed (i) that knowledge IS of
Forms, and Forms only; (ii) that there is an inferior level of apprehension which is not directed to Forms at all but, exclUSIvely t~
sensibles; Plato calls this doxa, and clearly takes It to be proposmonal,
(iii) that perception has no contribution to make to knowledge. In the
Phaedo there is far less consistency in Plato's argument. Though Plato
appears to make assumption (iii) when condemning the senses from a
moral standpoint and when discussing the method of hypotheSIS, he
asserts in his discussion of Recollection that perception of sensible
'likenesses' of Forms is essential to the recognition of Forms. As for
his view of the extent of the world of Forms, this is not made so
explicit in the Phaedo as in the Republic. But he does at least assume that
each Form has perceptible instances. If we compare the Phaedo and the
Republic in these respects with the Theaetetus, it is clear in the first
place that the Theaetetus is introducing distinctions which are not found
in either the Phaedo or the Republic, and which it wonld be difficnlt to
incorporate within the theory of Forms of either the Phaedo or the
Republic. Thus if we assume, as we have good right to assume, that the
hypothesis that at least some knowledge is derived from reflection
about sense-impressions is intended tobe a serious contribution to the
question of the nature of knowledge, th'enthe hypothesis is at variance
with the thesis of the Republic that perception has no contribution to
make to knowledge. On the other hand, if compared with the Phaedo's
doctrine of Recollection, which does acknowledge the value of perception as an aid to knowledge, the hypothesis is at variance with the
apparent assumption of the Phaedo that each Form has perceptible
instances and that these initially prompt recognition of the Form; for
it maintains that independently of perception the mind apprehends
'by itself' characteristics which, unlike others which are perceptibles,
are not given in perception at all. There is, finally, the interesting
question whether the hypothesis is at variance with the thesis of the
RepubliC thatthereis a 'propositional' level of apprehension (to describe
which the Republic uses doxa in a specialised sense) which is distinctively
empirica~ directed exclusively to sensibles. According to the hypothesis
this level of apprehension would, from its 'propositional' nature, include the apprehension by the mind 'by itself' of some things not given
in perception and thus wonld, in that respect, be a priori. It is true that
the Theaetetus emphasises that a fnll understanding of what is apprehensible only by the mind 'by itself' is the resnlt oflong and intensive
study (186c). Hence it could be maintained that the doxa of the Republic,
while including an independent activity of mind, never includes any
fnll apprehension of what is distinctively intelligible, and never perceptible, and is thus still properly described as empirical. This would,
however, be a doxa which it is possible to convert to knowledge, at
least to the kind of knowledge envisaged in the hypothesis of the
Theaetetus, for its nature wonld imply that the dividing line between
G
90
what is doxa and what is not doxa is determined by the degree of comprehension of the distinctively intelligible elements present in any
doxa. Thus the doxa of the Republic, in that it is meant to exclude the
possibility of conversion, even in part, to an a priori level of apprehension, cannot consistently be interpreted in terms of the distinctions
of the Theaetetus.
The fact is that the argument of the Theaetetus which we are considering, advanced independently of the theory of Forms, points not
only to a reinterpretation of what plato has hitherto taken to be
exclusively perceptual judgements, but also to a reformulation of the
distinction between such judgements and exclusively a priori judgements. And if this new approach is to be formulated in terms of a
theory of Forms, it follows that new distinctions within the theory of
Forms of the Phaedo and the Republic are necessary. It is, in the first
place, impossible, on the basis of tlle argument of the Theaetetus, to
distinguish doxa (in the Republic's sense) from knowledge by correlating
each with a different sort of object. For doxa is now shown necessarily
to involve the apprehension of 'objects' which, according to the
Republic, were exclnsively objects of knowledge; I assume here that if
the argument of the Theaetetus is formulated in terms of the Forms
theory plato would atIeast grant that what is, according to the Theaetetus,
apprehended a priori in any judgement has the status of a Form. And if
it is granted that doxa, while being about sensibles, includes the apprehension of Forms, its difference from knowledge will presumably be
that knowledge is about Forms, and not at all about sensibles, being
exclusively a priori. Now to maintain this distinction consistently within
a theory of Forms Plato, ifhe is to retain his thesis that apprehension of
Forms is an a priori form of apprehension, and that any other form of
apprehension is of something other than Forms, appears to be committed to disallowing the clainl to designate Forms of some concepts
which, according to the Phaedo and the Republic, do designate Forms.
For the argument of the Theaetetus appears to be distinguishing types of
concepts, specifying some as empirical and others as a priori. Empirical
concepts are those which are applicable only to the objects of a single
sense; a priori concepts are those applicable to objects of more than one
of the senses and hence, according to Plato, apprehended by the mind
'by itself'. It is true that Plato does not deal at all in his argument with
the question of the way in which characteristics other than those
91
apprehended by the mind 'by itself' are themselves apprehended. It
does in fact follow from his reduction of aisthesis to bare sensation that
to possess those concepts which designate sensible characteristics involves an independent activity of mind, since any comparison and
generalisation necessarily involves such activity. Yet Plato has no need,
for the purpose of defining independent activity of mind, to distinguish
between the isolated impressions of the senses and the explicit abstraction of the concepts describing those sensa. And the premisses of his
argument, even if such a distinction had been made, would still imply
a radical distinction between concepts which simply describe what is
given through the senses and concepts applicable to the objects of more
than one of the senses. Thus, if the elistinction between empirical and
apriori concepts implies that apprehension of the former is not a priori,
it would seem difficult to continue to maintain that they designate
Forms. Hence the argument of the Theaetetus, if used as the basis of a
revision of the theory of Forms, suggests the rule that the existence of
a Form is to be postulated only for concepts which satisfy the condition that they are applicable to the objects of more than one of the
senses. The evidence that plato attempted any such revision in later
dialogues is not, however, very strong. There is, as we shall see, Some
suggestion in the Politicus that concepts can be distinguished as empirical
and a priori, and that only the latter designate Forms. Apart from this
Plato, while recognising the importance of distinguishing types of concepts, seems reluctant to disallow the claim of the 'empirical' concepts
of the Theaetetus to designate Forms; thus a distinction which assumes
inlportance in later dialogues and which has some correspondence with
the distinction of the Theaetetus is a distinction between Forms which
have 'clear sensible images' and those which have not.
cJ False belief
This argument of the Theaetetus is the final criticism which Plato makes
in the dialogue of the claim that knowledge is perception; the only
other serious criticism is the criticism of it as a thesis inlplicitly based
on a doctrine of flux. One further question which must now be considered is whether the argument is fruitfully developed in the rest of the
dialogue once it has prompted the new hypothesis that knowledge is
definable as 'true belief'. What we might reasonably have expected
would have been, as a preliminary to the examination of the claim of
92
trne belief to constitllte knowledge, further illustration aud elucidation
of the relation berween what is contributed by the senses aud what is
contributed by the independent activity of mind in coming to believe
that something is the case. This expectation is, however, disappointed,
and little of the discussion of the rest of the dialogue appears to be a
development of the ideas in the final argument against aistMsis. The
principal reason for this is that the rest of the discussion is limited to
an examination of knowledge as knowledge of particular objects; this
raises entirely new problems which seem to have little connexion with
the problems implicit in the criticism of aisth~sis, when plato was
apparently treating knowledge in a much more general way as knowledge of facts, withont any restriction of it to knowledge of particular
objects.
The first new problem which the discussion raises is the problem of
how false belief is possible. Limited as it now is to au examination of
knowledge of particular objects, the discussion construes true belief
as the correct identification of a person or thing, Hence false belief
is incorrect identification - confusing one thing with auother; it is a
belief that a thing is other thau what it is (allodoxia, r89b). Now if it
is assumed that a person either knows or does not know the objects
confused, in the sense of being acquainted with or not acquainted with
them, the problem arises of how confusion is possible berween two
objects when it must be the case that a person is either acquainted with
one aud not acquainted with the other or acquainted with both or not
acquainted with either (rS8a-c). It is to be noted that before dealing
with this problem Plato dismisses the objection that, since to believe
falsely is to believe 'what is not', to believe falsely is impossible. While
agreeing that, if 'what is not' is interpreted as 'what has no being at
all', then believing 'what is not' is believing 'nothing' aud hence not
having a belief at all (r88e-r89a), he assumes that to believe falsely is
to believe 'something' aud that consequently 'to believe falsely must
be something different from believing what is not' (I89b). With this
assumption he describes false belief as a belief that something is other
thau what it is (r89b)," and returns to what he considers to be the
main problem - how the confusion cau arise which will result in a
false beliefas thus construed. plato sees his main task as that of examining
the kind of apprehension a person has of each of the rwo objects confused in cases of incorrect identification. The initial assumption was that
93
a person either knows or does not know the objects confused, and since
confusion seemed to be impossible on this assumption au escape from
this apparent absurdity would appear to depend on either discovering a
sense of 'knowing' and 'not-knowing' which does not yield the absurdity or revising the initial assumption so as to allow that at least one of the
objects is apprehended in a way not equivalent to either 'knowing' or
'not knowing'.
Considering first the former alternative, plato has no difficulty in
showing the possibility ofconfusing two things 'known' (where 'knowing' is 'having acquaintance with and retaining in memory a direct
uimpression" '); the confusion call arise when one or both of the
'known' objects are subsequently perceived indistinctly. With the same
sense of 'knowing' it is easy to show how indistinct perception cau give
rise to confusion between a 'known' and an 'unknown' object (r9 rbr94b ). Thus the 'known' Theodorus may be confused with the 'known'
Theaetetus or with an 'unknown' person. But plato is not satisfied with
this, even though, grauting his definition of knowledge, it is a satisfactory reply to the present objection t1lat false belief is impossible. It
is not simply that he considers his explanation too narrow to cover all
cases of false belief; he considers that unless some other aud more
satisfactory explanation is given of false belief, the initial problem has
not been resolved in the slightest degree (r96c). He appears to assume,
in fact, that the appeal to indistinct perception is an appeal to merely
aCCIdental CIrCUmstances which have no proper relevance to the
knowing/not-knowing distinction which he is exploring. He therefore suggests another sense of'knowing' which will allow the possibility
of confusmg one known object with auother known object. He distinguish?s berween (i) 'possessing' and (ii) 'having' knowledge, thus
recogmsmg that knowledge is a 'disposition' (possessing) which may
be 'actuali~ed' (having) in particular instances of its application (r97 b19 8d). ThIS will allow the possibility of the misapplication of what is
'known' (in sense (i) ), resulting in a false belief which may be interpreted as a confusion between one 'known' thing (knowledge which is
misapplied) and another 'known' thing (knowledge which would
correctly be applied in this particular case). To illustrate this plato
takes as i~stauces ,of 'known' things intelligibles rather thau perceptibles.
HIS. tw~ known things are the numbers I I and 12, aud he says that if
I I IS gIven as the answer to the question what the sum of 7 and 5 is,
94
the answerer is confusing I I with 12 and thus believing falsely that
II is 12. This remarkable illustration serves to emphasise the extent of
Plato's preoccupation with the idea that knowledge is knowledge of
individual objects. It further emphasises his tendency to assimilate all
knowledge to acquaintance with individual objects. Just as a perceptible object is 'known' once acquaintance with it through perception has stamped an 'impression' of it in memory, S0, it appears,
an intelligible object is 'known' once acquaintance with it has introduced a new conception to the storehouse of the mind. It is as if Plato
is assuming that once an object is before the mind, or 'possessed' by
the mind, no matter whether it is a perceptible or intelligible object,
then it is 'known' (cf. 188a). A consequence of this kind of approach
to knowledge is that, although plato asserts at the beginning of his
discussion that belief is 'propositional' (18ge-190a), his preoccupation
with the question of what it is to 'know' particular objects leads him
to neglect what had already been suggested in the final criticism of
aisthesis - the importance of examining the complexity and structure
of what is known. It is true that the suggestion there is not made as
explicit as we should have liked. Indced it could be argued that even
there Plato, in distinguishing between a priori and empirical Concepts,
tion of false belief on the basis of the assumption that a person either
knows or does not know the objects confused in false belief. This
attempt breaks down because Plato concludes that the distinction
between 'possessing' and 'having' knowledge is just as unsatisfactory
as his earlier conception of knowledge in terms of memory-images as
a means of resolving his difficulties about false belief. For, mistakenly
assuming as he does that the false belief held by the person who answers
that the sum of 7 and S is I I is the belief that I I is 12, he refuses to
accept the possibility that a person should lnisapply what is known,
since this is equivalent to confusing two 'objects' with both of which he
is acquainted (199c-d). Consequently, having failed to discover a sellSe
of 'knowing' and 'not-knowing' which does not yield the result that
false belief is impossible, he appears to fall back On the alternative
method of escape - revising the initial assumption so as to allow that
at least one of the two objects is apprehended in a way not equivalent
to either 'knowing' or 'not-knowing'. This leads him to suggest that
an object cannot be known unless an 'account' (logos) can be given of
it, the implication being that false belief arises when at least one of two
objects confused is not 'known' since this new condition of knowledge
with regard to it is not satisfied. Thus Plato is still preoccupied with
the problem of the nature of knowledge of particular objects, and he
decides to abandon altogether at this point his examination of false
belief, and to examine further the nature of knowledge of particular
objects without regard to any elucidation it might afford of the nature
of false belief. Bis new hypothesis that to know implies the ability to
give an 'account' is, of course, one which he has often adopted preVIOusly when specifying a distinctive mark of knowledge. In theMeno
it was used to distinguish knowledge from true belief. And Plato does
in fact now suggest that knowledge may be defined as 'true belief with
an account' though the hypothesis that knowledge is true belief has
not yet been examined on its own merits; indeed 'true belief' re-enters
the discussion rather unexpectedly, as part of an old formnla which
Plato wishes to test in application to the problem of what it is to
know a particular object.
Now what he has said so far about this knowledge has given no
positive indication of what he considers to be the cognitive value of
perception. Be has fIrst attempted to explain false belief by examining
cases where perception contributes to the formulation of the false
is thinking primarily in terms of a distinction between different sorts of
particular 'objects' - those apprehended a priori and those apprehended
empirically. Yet the general impression which his examination gives is
that heis viewing knowledge as the result of some sort of interpretation
by the mind of what is given in perception, and his specification of the
various ways in which the mind contributes to this interpretation
appears to mark a recognition not only of the complexity of what is
known but also of the fact that the structure of what is known is an
important factor in assessiug the nature of knowledge.
d] Knowledge as 'true belief with an account'
In the final part of the Theaetetus he does, however, enlarge the conception of knowledge which governs his discussion of false belief by
exploring the hypothesis that knowledge is acqnired as the result of an
analysis of a particular perceptible object, and he attempts to specify
the method of analysis which will yield this result. The hypothesis is
put forward after the breakdown of the attempt to discover a sense of
'knowing' and 'not-knowing' which will allow a satisfactory explana-
9S
96
belief He has then attempted to explain it by examining cases in which
he seems to assume that perception contributes nothing to the formulation ofit. Both attempts fail. But in now trying to specifr the 'acc~unt'
which will yield knowledge, he introduces a theory which, despite ItS
limitation to cases of knowledge of individual objects, does seem to
have some connexion with what he had said in his final criticism of
aisthisis. He suggests that an 'account' (logos) is possible 0111y of what
is complex. Thus, to use the analogy of letters and syllables, syllahles
are complexes of single letters and can have an account gIVen of them,
an analysis into their simple components, the letters. But no a~count
can be given of the letters, which cannot be analysed mto Simpler
components. They thus rank as absolute simples. Hence, says Plato,
complexes are knowable, simples are unknowable (2?2b). He further
states that the simple components of a complex are (I) ~ameable, but
incapable of having any predicates applied to them, (n) percepuble
(aisthita) , but incapable of being an object of either true belief or knowledge. What he says about (i) suggests in many ways a rerurn to. the
sort of approach made in the final criticism of aisthi!sis, espeCIally smce
what he says about nameables is true, in view of (ii), of perceptlbles,
only. Thus, he says, a name is all there is tbat belongs to a Simple
element. Even to say 'this is an X', where X
1S
the name,
1S
n?t ?~~
missible since to 'attach existence to it' or to apply the term this IS
to appl; predicates which, 'running about', are attached to ~verything
and are distinct from the things to which they are applied (202a).
Hence it is impossible to describe simples in a statement (logos); here
it seems clear that Plato is using logos in the same sense m which he
had used it in 19oa. Now, remembering that simples are percepubles,
much of this inevitably invites comparison with the f,:,al argument
against aisthlisis, which had limited aisthlisis to sensaUon, ":,d had
specified 'being' and various other predicates as ones which belong
to everything', and which are not percepuble, the. apprehensIOn of
them being ascribed to an independent activity of mmd which reflects
'about' sensibles and issues in statements (logoi). And as m that argument
Plato had shown that perception itself cannot yield either true belief or
knowledge, so in this present argument he asserts that simples are perceptible only, and never the object of either true beli~f or ~owledge
(202b-c). What plato is now doing, it would seem, IS making much
more explicit than in the earlier argument the pomt that knowledge,
97
unlike the direct apprehension of what is 'given' in sensation, is propositional and thus necessarily of what is complex. Hence there appears
to be some justification for linking Plato's argument with 'the fanliliar
Aristotelian and mediaeval doctrine that the "complex enunciation",
or proposition, is the unit of knowledge' ," and assuming that his main
point is to contrast the 'simplicity' of what is directly apprehended in
sensation with the complexity of what is known and expressed in
propositions (logoi).
Yet, though there is much in the manner of Plato's distinction between
what is nameable only and what is expressible in a logos which suggests
this interpretation, the rest of what he says about the nature of this logos
shows quite conclusively tllat his main point is something quite different
from this. Thus in 202b he says that corresponding to the complex
thing or object compounded of simple elements which are nameable
only is the complex logos or statement, which is a combination of the
names of the elements. When he speaks of a 'combination of names' as
constituting the logos it is obvious from the context that he means a
combination of the names (onomata) of the simple elements, each of
these names being peculiar to a particular element. It is impossible that
he is arguing that the combination of names is a combination of the
type 'this is an X' where X is the name of a simple element and 'this',
'is', and 'an' are names of the other simple components of the complex
described in the logos. For he has already excluded such an interpretation
since (i) by a 'name' he means a name peculiar to each simple element,
alld (ii) he has specified 'is' and 'this' as terms not peculiar to one
particular object or one particular class of objects but 'attached to
everything and distinct from the things to which they are applied'. It
is clear, in fact, that the main distinction which Plato is trying to make
is between the physical complexity of particular objects and the simple
constituents of those objects. Thus the fact that knowledge is propositional is irrelevant to the meaning of logos, and this is made explicit
at 206d-e. To construe logos, says Plato, as the expression of one's
thought in speech 'with names and verbs' is to neglect the fact that
the .bility to give a logos or account was introduced as a distinctive
feature of knowledge, as opposed to true belief; any sense of logos
therefore which ascribes a logos to both true belief and knowledge is
inadmissible. In this case, since both true belief and knowledge are
expressible in speech 'with names and verbs', it is inadmissible to
98
construe logos in that sense. The conclusion must be, then, that the
principal meaning which plato is giving to logos when he uses the
analogy of letters and syllables to distinguish simples and complexes
is an account or explication of a complex object which specifies and
enumerates its simple components. It is assumed that, if this is done,
the object is 'known'. To have 'true belief' with regard to it will be
to identify it correctly but without any analysis of it; this will be
expressible in the form 'this is X' where X is the name of the complex.
It is now possible to see that in the passage 20rd-202c plato is using
logos in two different senses. In the first part of the passage, where he
is arguing that simples are nameable only (20rd-202b2), logos means
statement. Both true belief and knowledge are expressible in logo; or
statements, and this sense of logos, as we have seen, is irrelevant to the
distinction between belief and knowledge. In the second part of the
passage (202b2-cs) logos is a specified kind of account or description
of a complex object - an enumeration of its simple components. It is
this logos which is relevant to the distinction between true belief and
knowledge, and Plato, in stressing at some length its relevance to this
(bs-cs), indicates that it is the conception of this sort of logos which he
is primarily concerned to put forward in the passage 20rd-202c as a
identification or express any other truth about the object). Perception
is wider in scope. All simples are perceptible, and there is nothing in
Plato's argument to exclude the perceptibility of complexes. Moreover, it is entirely consistent with tbis argument that perception should
contribution to the discussion, which is, we must remember, a discus-
sion of the new hypothesis that knowledge is definable as 'true belief
with an account (logos)'. Moreover, since the rest of the discussion is
concerned exclusively with the problem of knowledge of physical
objects we may reasonably assume that in his present argument plato
would accept as a proper illustration of it the analysis of a complex
physical object by enumeration of its simple component elements.
The fact that he says that simples are perceptibles is some confirmation
of the assumption that he is here thinking of analysis of physical objects,
as also is the fact that he says that the simple elements are' elements of
which we and all other things consist' (20re). Thus the result of Plato's
argument is severely to restrict the scope both of knowledge and true
belief. The only cases of knowledge will be those where this kind of
enumerative 'account' has been correctly given, and the
only cases of
true belief will be those where this kind of account is possible, but not
given, and where a complex object has been correctly identified (the
complexity of what is believed is the complexity of the object identified
and is not the complexity of the propositions which express the
99
be the criterion of whether or not the enUlllcrative 'account' of the
simple constituents, which is a condition of knowledge, is a correct
account and yields knowledge, and that perception should be the
criterion of whether or not the belief that the complex is identifiable
as this or that is true. And plato does clearly assume that simples, which
are perceptible only, are correctly identified. Hence, it would seem,
the statement 'this is X', where X is the name of a simple, is assumed
to be true as a direct report of what is given in perception, though it
fails to qualify to be the expression of a 'true belief' since plato has
extended his restriction on the application of knowledge to the application of' true belief', with the result that, for him, 'true belief' is possible
only with regard to complexes (202b). It is true that at the beginning
of the passage plato has said that the 'elements' are nameable only,
which would make the statement 'this is X' inapplicable to an element.
Yet since in the latter part of the passage he is giving a different interpretation of logos or 'account', the objections which he earlier made to
saying of an element that 'this is X' become irrelevant. For the conception of the analysis of a particular physical object into its physical
elements which now gives meaning to complex and simple makes it
absurd to apply to simples in this later context the earlier rule. 25
What we have, then, in this new approach to the problem of knowledge is an attempt to distinguish between three forms of apprehension
- perception, true belief, and knowledge, in relation to a particular
physical object. An obvious criticism of it would be that its extremely
narrow conception of the 'account' (logos) which converts true belief
to knowledge, coupled with its assumption that recognition of and
correct identification of simples is exclusively the work of perception,
makes the distinction between knowledge and perception a merely
trivial distinction. And Plato's criticism of the new theory shows
clearly that he recognises this. Thus, using again the analogy ofletters
and syllables, the syllable is either all its letters or a single entity distinct
from the letters. In the first case it will follow that to know the syllable
is to know its letters. But since the letters have been assumed to be
unknowable, then the syllable too will be unknowable. In the second
100
case the syllable, as a distinct unity, caunot be analysed into parts, and
will thus be simple and unknowable for the same reason as the letters
are (203a-205e). Since Plato clearly finds these consequences of his
theory unacceptable and yet continues to assume that to know includes
the ability to 'give an account', one possible solution of his difficulties
would be to assume that simples as well as complexes are knowable
and to frnd the 'account' not in any form of analysis but in verification
in perception. This solution makes the distinction between simple and
complex irrelevant to the question of what constitutes knowledge. It
is not, however, a solution which plato bothers to explore, the rest of
the discussion showing that he continues to assume that the 'account'
must be found in some form of analysis. Now since an assumption of
the Theaetetus, from the beginning, appears to have been that it is
relevant to the inquiry into the definition of knowledge to examine
particular hypotheses (e.g. that knowledge is perception) as to what is
a satisfactory criterion for knowing, it might seem that in failing to
explore the above solution plato is deliberately turuing his back on it
because it assumes that perception provides a satisfactory criterion [or
knowing, and that in continuing to seek a defrnition of knowledge in
terms of a particular form of analysis he is assuming not simply that
knowledge, in that it implies an ability to provide a precise conceptual
analysis of its object, is superior to perception as a level of apprehension,
bnt also that the provision of this precise analysis itself constitutes a
criterion for knowing which is quite independent of perception. My
own view is that Plato is making such an assumption. The general
impression given by the dialogue as a whole is that, having once refuted
the hypothesis that knowledge is perception, Plato's subsequent concern is to fllld some criterion other than perception, and that, even
where the discussion leads to a point where the recognition of perception as a criterion would seem to be the most plausible solution of
difficulties which have arisen, Plato is unwilling to reassess its claims.
Thus such recoguition would have allowed him to use the distinction
between distinct and indistinct perception to explain how false belief
is possible. And such recognition would, as we have noted, have
allowed him to offer a plausible solution of the difficulties in the theory
put forward in 20Id-202C.
If; then, he is unwilling to resort to a solution of this kind, what
solution does he actually offer? Retaining his view that the 'account'
lor
which converts true belief to knowledge is some form o[ analysis of a
complex, and continuing to restrict his discussion to the problem of
knowledge of particular physical objects (a cart, a person, the sun),
plato first re-emphasises, by using the illustration of the analysis of a
cart into its physical components, the triviality of the distinction
between knowledge of the complex and acquaintance with its components if the analysis is a simple enumeration of components (207a20sb). He then finally suggests that to know a thing is to have a true
beli;f with ;~gard to it (correctly identify it) plus the ability to give
an account rn the form of a statement of the differentia which distinguish?s it from. other things (20Sc-e). The objections that (i) the
correct ldentificatlOn of the thing necessarily includes the correct
identification of the differentia; (ii) to say that knowledge is true belief
plus knowledge of the differerltia is to give a circular definition, are
allowed to stand and to bring the dialogue to an inconclusive end.
These objecti~ns indicate that plato has not yet succeeded in finding
a satIsfactory cntenon for knowledge which will clearly dissociate it
from perception. The essence of the objections is the same as of those
brought against his earlier attempts to specify the 'accmmt' which will
convert true belief to knowledge - that the 'account' of the complex is
such as to make only a trivial distinction between knowledge of the
complex and direct acquaintance through perception either with the
components of the complex or with the complex itself. For it is to be
n~ted,th~t ~n this last attempt to specify 'account' Plato is still dealing
wlth mdIVldual and perceptible objects. His example is the person
Theaetetus, whose differentia is 'snubnosedness', and his difficulty is to
distmg~Is~ knowledge o~ Theaetetus from acquaintance with him and
Wlth .hIS snubnosedness. But it is clear that, though the difficulty
r~m~ms here .unresolved, this last attempt to specify 'account' gives a
SIgnIficant pomter to the solution which plato offers in later dialogues
It is clear in the first place that by the end of the dialogue plato i;
very near to thinking of 'account' in terms of defrnition. Moreover
though i~ his last example he is certainly not thinking as yet in term;
of d:fi~t1on of speCIes and making a distinction between genus and
specles, It IS not dIfficult to see that his specification of 'account' in
terms of the method of division (diairesis) in later dialogues is the fmal
result of the inquiry in the Theaetetus and closely linked with the final
part of that inquiry. Thislinkis seen not only in the common assumption
that the 'account' of a thing is to be found in its defInition, and that
defInition is through specllcation of differentiae. It is seen also in the
common terminology of the distinction in the Theaetetus between
complexes and their simple components or parts, and of the description
in later dialogues of Forms as complex 'wholes' divisible into parts
(moria, mer~).26 It is a distinction between complex and relatively unanalysable and simple which is preserved within the method of division.
For in any defmition or in any scheme of classllcation by diairesis the
infimae species are indivisible (atomon); 27 they constitute the limit of the
analysis necessary for the determination of the 'essence' of a particnlar
Form or for the purpose of the classifIcation. And just as they are
indivisible relatively to these ends, so they are simple relatively to their
genera, the genera being for plato at once wider in extension and richer
in complexity than any of their subordinate species, since they necessarily embrace and contain within themselves a greater number of
species and sub-species than does anything subordinate to them. Yet
though the Form is thus relatively indivisible and simple, it does possess
a complexity of structure, and this allows an 'account' to be given of it
which will separate it and distinguish it from all other Forms. Thus
plato felt that the method of diairesis made it possible to recoguise the
complexity of what is known, and at the same time to retain his conception of Forms as indivisible and simple. In the Phado it was the
indivisibility and simplicity of the Forms which had been stressed.
They were uniform (monoeides, 7Sd, Sob) and incomposite (asyntheton,
78c ), characteristics associated by Plato, tmder clearly Parmemdean
influence, with the immutability and permanence of the unitary Form
as contrasted with the mutability and impermanence of the many
particulars. And it is just these characteristics which in the Theaetetus
are said to exclude the possibility of knowing the objects to which they
belong (205a-e). Thus it is argued that the elements of a complex are
unknowable since they are each uniform (monoeides) and incompoSlte
(asyntheton), and that the complex too, if regarded as a unity over and
above its elements, is itself uniform and incomposite and hence unknowable. Of neither can an 'account' be given. This precise correspondence of terminology between the argument of the Theaetetus and
the description of Forms in the Phaedo" clearly establishes an important
link between the discussion of the latter half of the Theaetetus (201C21Ob) and the theory of Forms. And since the difficulties raised in the
Theaetetus about the possibility of knowing what is 'uniform' and
'incomposite' are now seen to be directly relevant to the problem of
knowledge of Forms, we have further confIrmation that Plato's subsequent development of a new method of attaining knowledge of
Forms should be regarded as au answer to the problems raised, but
not solved, by the Theaetetus.
It is important to note, fInally, that these problems are such as to
lead plato to a re-affrrmation of the existence of Forms as the basis of
his solution of the problems. A brief review of his position at the end
of the Theaetetus will make this clear. He has recoguised that the object
of knowledge is necessarily complex, and has abandoned as untenable
the view that it is absolutely simple and incomposite. But he has not
yet found a satisfactory way of distinguishing between perception, true
belief, and knowledge. Throughout the discussion of false belief he had
apparently assumed that all knowledge was knowledge of individuals
by direct acquaintance and had found it impossible, as we have seen,
to explain on this assumption how confusions could arise. His subsequent attempt to distinguish knowledge from both perception and
true belief breaks down because the discussion is still restricted to the
problem of knowledge of individuals, and it proves impossible to make
anytlling more than a trivial distinction between knowledge of the
complex individual and immediate experience either of this individual
as a 'whole' or ofitssimple 'parts'. Thus plato has abandoned the earlier
conception of knowledge as direct acquaintance but has failed as yet to
distinguish it satisfactorily from direct acquaintance. The discussion
has, however, brought him to the point where he is seeking a satisfactory method of definition as a solution to his problems. And the
fundamental step towards Plato's solution is the recognition that
defmition is not of individuals but of species, not of the particular
but of the general. This, it might well be said, in view of the essays
in general defInition in some of the earliest dialogues, is hardly a point
which Plato needs to be led to realise. But we must remember that in
the Theaetetus Plato, having disposed of the thesis that knowledge is
perception, makes a new approach to the problem of knowledge by
examining cases of acquaintance with individuals or particulars and
endeavouring to find at this level a satisfactory distinction between
perception, true belief, and knowledge. What he is led to realise as a
result of his failure to fmd this is the relevance to the problems raised
102
103
104
of the point that definition is not of individuals. The perceptible
individual or particular is unknowable because it is indefinable. The
way is now clear for the re-introduction of the Forms as the objects
of knowledge; and with the further introduction of the method of
division plato is now able to find his 'account' in a precise and universally
applicable method and on this basis to distinguish clearly between
perception, true belief and knowledge.
It is easy to see how attractive this solution of the difficulties of the
Theaetetus would appear to Plato. The new method oflogical analysis
for defining Forms clearly seemed to him to provide a demonstration
of the nature of tlle Form; and the certainty thus yielded could be
plausibly interpreted as a result of the exercise of reason rather than of
perception, and, further, as a confirmation of the superiority of reason
over perception. Moreover, in the light of this, plato could explain the
triviality of any distinction between knowledge and perception which
assumes that knowledge (a) is knowledge of individuals and (b) implies
an ability to specifY either the constitutive elements or the peculiarities
of the individual. The distinction is trivial since the merely contingent
nature of the combination of perceptual characteristics which make up
the 'being' of the particular or its peculiarity seemed to Plato to allow
no other method of coming to 'know' the particular than that of
enumerating the perceptual characteristics as they were given in perception. And such an 'account' yields only a trivial distinction since,
for plato, it involves only a trivial application of reason to the interpretation of what is perceived. Hence, since no other 'account' than
this is possible for providing knowledge of the particular, and since the
claim of perception to provide knowledge has already been dismissed,
plato is ready to conclude that the sensible particular is unknowable. It
is not amenable to the systematically rational 'account' which is possible
for the Form, and Piato can thus relegate it to the level of the indeterminable, below the limits of the exercise of the method of
diairesis.29 In this way the difficulties of the Theaetetus lead plato to a
re-affirmation of the 'reality' of the Forms as objects of knowledge
and of their superiority to sensible particulars. At the same time they
lead him to a recognition of the need to reconcile the earlier assumption
of the simplicity and incomposite nature of the Forms with the present
assnmption that knowledge is the result of an analysis of the structure
of its object and hence is knowledge of what is complex. It is the new
105
method of definition by diairesis which shows plato how the reconciliation can be effected. Thus it allows him to meet the difficulties in his
theory of knowledge which we raised at the end of the first chapter.
There we saw that m the Phaedo the virtues of the theory of Forms
and of the method of analysis of propositions were assessed independently of one another, and that Plato had not yet begun to consider
the possIble mconsistencies arising from an attempt to integrate them.
Wlthm the theory of ~orms, as far as it was taken by the Phaedo, the
only possIble type of account' either of the Form or of its sensible
instances was ?nc in terms ~f a relation of resemblance between simple
archetypa! objects and senS1ble characteristics, or in terms of the 'partICIpatIon ~f sensibles in the perfectly real archetype. And we suggested
that a C.onS1stent development of Plato's theory of knowledge from
thlS POSltlOtI would depend on the consistency with which he could
reconcile this type of 'account' with the ideal of giving an 'account'
m terms of a precise method of analysis. To this reconciliation the
Theaetetus, as we ha:e now seen, points the way, and in implicitly
reJectmg the conceptIOn of knowledge as direct acquaintance it rejects
the conceptIon of knowledge which would seem to belong naturally
to the Phaedo' s conception of the Forms.
The objection can readily be raised, of course, that Plato's solution
through the method of diairesis is no solution at all, that he has simply
substItuted a theory of Forms as complex and composite objects of
kn~wledge for hIS earher theory of Forms as simple and incomposite
objects of knowledge, and that there is strictly no 'reconciliation'
between the earlier and later theory. The further objection can also
be ralsed, as Aristotle raised it,80 that the Form, as an individual archetypal object, remains indefrnable and unknowable for the same reasons
for whIch the sensible individual is indefmable and unknowable, and
hence that the argument for appealing to Forms as objects of defInition
and kno;rledge involves an infInite regress. Certaiuly plato never meets
these objectIons properly, though it would seem that he was aware of
difficulties in his proposed solution.3I But the important thing for our
present purpose has be~n to see how the problems about knowledge
ralSed by the attempt m the Theaetetus to distinguish knowledge of
partIculars from both true belief abollt them and perception of them
lead plato back to the theory of Forms, but lead him also to a new
conception of the structure of Forms and the method of attaining
H
knowledge of them. Whatever the objections which can be raised
against his proposed solution of his difficulties, there can be no doubt
that it marks an important development in his thought.
perception of these characteristics is an essential first step to the attainment of knowledge. There is a fundamental inconsistency here, and
the first task in the next chapter will be to see to what extent this
inconsistency is resolved within the new conception of dialectic in the
late dialogues; this will serve as a preliminary to a discussion of the
problem of the relation between belief and knowledge in those
dialogues.
106
e] Summary
In concluding this examination of the Theaetetus an attempt must be
made to review briefly its results. It has been rightly said that 'while
the dialogue is concerned not with metaphysics but with epistemology,
it furnishes the strongest argument Plato gives anywhere for the
foundation of his metaphysical theory'. 32 We have just seen in what
way the difficulties raised in the latter half of the dialogue in the
attempt to discover a criterion for knowing other than perception
point the way to a re-introduction of the theory of Forms, in conjunction with a new method of dialectic, as the basis of the solution of
these difficulties; thus the latter half of the dialogue may plausibly be
said to point implicitly to the need to postulate the existence of Forms
ifa satisfactory account of knowledge is to be given. The first half of the
dialogue, through its refutation of the thesis that knowledge is perception, points the same way. More systematically than in any other of
the middle dialogues it examines the nature of perception and its
objects, and attempts to reduce to absurdity the claim that perception
yields knowledge. Its criticism of perception is an extremely severe one,
its most important criticisms being (i) that the thesis that knowledge is
perception, in so far as it rests on the assumption that all things are in
flux (and Plato himself accepts the flux theory as true of sensibles),
implicitly denies the existence of determinate sensible characteristics
and hence the possibility of knowledge; (ii) that perceptiou (aistMsis)
is strictly limited to the isolated 'impressions' of the particular senses
and cannot be equated with knowledge since any knowledge includes
the apprehension by the mind 'by itself' of non-perceptual characteristics. Thus the Theaetetus matches in the severity of its criticism the
Phaedo, which had condemned perception and its objects from a moral
point of view, and it reflects generally the Republic's attitude of uncompromising renunciation of perception as a guide to knowledge.
We have noted at several points in this examination of perception in
the middle dialogues the difficulties of reconciling the major criticisms
of perception made there with the assumption of the theory of recollection that sensible characteristics are 'images' of Forms and that
CHAPTER III
Knowledge and Belief
I. RECOLLECTION AND THE NEW METHOD OF DIALECTIC
The first formal exposition of the methods of collection and division
is fOlmd in the Phaedrus. It is now generally agreed by scholars that this
dialogue is later than the Republic.' It is also generally agreed that in
several important respects its doctrine links it with the group of late
dialogues which begins with the Sophist.' As for the question ofwhether
it precedes or follows the Parmenides and the Theaetetus, I have already
attempted to show how Plato's new method of dialectic is designed to
meet problems raised, but not solved, in the latter half of the Theaetet"s,
and this, in my opinion, is good reason for assuming that the Phaedrus
is later than the Theaetetus. 3
Together with the new method of dialectic the Phaedms re-introduces the theory of recollection. The close link between method and
theory is established at 249b-c, where plato first describes the method of
collection (synagogJ) in its application to sensible particulars, a process
of generalisation and abstraction culminating in the recognition of a
single common Form. This recognition is then said to be the recollection of that 'true reality' which the soul once knew. And though
recollection is mentioned ouly with this first description of collection it
is clear that this first description is closely related to the later description
of it in z65d ff., where it is linked with the method of division; and this
passage is closely related in turn to descriptions of the method in the
Sophist (253d) and the Politi",s (z85a-b). It is to be noted too that,
although it is to 'collection' as a process of direct abstraction from
sensibles that recollection is explicitly related, Plato indicates that this
process of abstraction is simply a first step in recollection, to be followed
by a further stage of methodical analysis (249c-d). The obvious implication, once we take into account the relation between the earlier and
later descriptions of 'collection', is that this further stage in the process
of recollection has as its instruments the methods of collection and
lOS
109
division. And the descriptions of these methods, in the Phaedrus and in
later dialogues, suggest that fundamental in the process of recollection
will be the recognition of relevant resemblances and differences between
Forms in attaining knowledge of any particular Form. It is extremely
important, I think, to see that there is this close association between the
new conception of dialectic and the theory of recollection. Many
scholars have argued that the theory of recollection is abandoned in the
late dialogues. And it is essential to any examination of Plato's theory
of knowledge in the late dialogues to consider first the evidence for and
against this view. This will lead to a discussion of Plato's evaluation of
perception within his new conception of dialectic. And this discussion
in turn, by bringing to light the problems involved in Plato's retention
of the distinction between knowledge and belief, will lead to an examination ofwhat plato has to say about the distinction in the late dialogues.
We have already seen that the descriptions of the new method suggest
that fundamental to the successful practice of the method in attaining
knowledge of Forms is the recognition of relevant resemblances and
differences between Forms. This concept of 'likeness' or 'resemblance'
(homoiot8s) has an important place in the dialectic of the late dialogues.
It is used not only with reference to sensible particulars which have
derivative resemblances to one another as instances of the Same Form
also, in conjlmcti~n with its opposite 'dissimilarity' (anomoiotes):
b~t
WIth reference to specIes of the same genus; and the genus itself is describable as a 'likeness' in that it constitutes the common point of re-
semblance between its different species.' And from thePhaedrus onwards
this terminology is associated, within the new methods of dialectic
with the t:rminology
~Ckind' (genos) and 'part' (meros) as descriptiv;
ofForn:s. Together WIth these new methods and the new terminology
whIch IS used to descnbe them there is a significant change in Plato's
~ssessment of the.cognitive value of perception. This change is apparent
In the first place 111 the fact that the severe disparagement of the senses
which w~s characteristic of the middle dialogues virtually disappears in
the late dIalogues. As we shall see in detail later Plato gives in the late
dialogues a much more consistent and much more favourable assessment of perception and its objects. Thus in the Timaeus his evaluation
of sen~ible'in:ages' in relation both to Forms and to Spaceissopointedly
atvanance WIth what had been put forward in the Theaetetus as a major
CntlClSm of perceptIOn that it is difficult not to cOllclude that it is
IIO
PLATO'S THEORY' OF KNOWLEDGE
designed as a correction of the views of the Theaetetus.
is in the
Timaeus that Plato explains the efficient cause of the ability of sensible
particulars to function as images or likenesses of Forms, and most
emphatically asserts the value of perception in suggesting the way to
knowledge of the structure of the universe and ofthe laws which govern
its movements. 7 In other dialogues too Plato's discussion of'visible likenesses', taken in conjunction with his descriptions of the methods of
collection and division, suggests that he is now making a much more
consistent assessment than in the middle dialogues of the claims of perception.' And a point of special significance which seems to be implied
by this evidence is that the new methods of collection and division, in
so far as they assume the complexity of the Form to be defined and
assume also that the Form has perceptible instances, thereby assume the
complexity of the perceptible instances of the Form. Thus these instances mirror in their complexity the strncture of the Form and for all
characteristics relevant to knowledge have a complete, though imperfect, resemblance to the Form. And this immediately points to the possibility of a systematic use of perception in acquiring knowledge. At the
same time Plato feels that he is able to maintain the superiority of the
Form to sensible particulars. The sensible particular remains indefinable
and nnknowable, its individual peculiarities falling below the limit of
the systematic ordering which the new methods afford.. It is the Form
or 'Kind' which is definable and knowable.
But does plato still maintain his doctrine of recollection? The doctrine is not mentioned after the Fhaedrus, and some scholars argue that
Plato's new conception of dialectic and his reassessment of the claims of
perception lead in the late dialogues to a modification of the theory of
Forms which makes the doctrine superfluous as part of his theory of
knowledge. Their arguments make a radical distinction between recollection, as an earlier technique of coming to know Forms, and division,
as a later 'technique of relation' or of 'specification'!· which supersedes
recollection. Recollection is associated with the view that the relation
between sensible and intelligible worlds is one of radical separation
and that this permits no systematically ordered means of 'mediation',
division with the view that no such radical separation exists and that
the structure of 'reality' can be revealed through an exact analysis of
class-concepts and their relations, with no further need 'either for a
transcendent dialectic or for reminiscence, which is the necessary means
6 And it
III
to it' .11 Thus, on the one side, recollection is envisaged as a sort of
'intuition' of a simple object, effecting an immediate transition from
the sensible to the intelligible world, and representing the only possible
means of bridging the gap between the two; on the other side division
is envisaged as a systematic means of 'mediation' between worlds no
longer radically separate, and designed to serve the needs of a theory of
knowledge which is now giving serious attention to perception as an
important source of knowledge."
Now as a preliminary to the discussion of this thesis it is worth recalling what sort of qnestion the theory of recollection was designed to
answer. It was the question of how one is to know that a proposition is
trne, and thus save an inquiry from being inconclusive (Meno 80d-8Ia).
Similarly, when the theory is associated with the theory of Forms in the
Fhaedo, it sets Out to show what assumptions are necessary for the Forms
to be recognised. Thus in the middle dialogues the possibility of knowledge is dependent, for Plato, on the assumptions of the recollection
theory.
If, then, the theory is abandoned in the later dialogues, on what alternative assumptions does the possibility ofknowledge now depend? One
apparent assumption, according to those who claim that recollection is
abandoned, is that the method of division, provided that it satisfies in
practice the formal requirements which necessarily belong to it as a
particular method of analysis, itself affords a guarantee of the correctness oEits determination of 'reality', and hence of knowledge. There is
certainly no doubt that plato was impressed by the apparently demonstratlve force of the method. But there is no ground for thinking that
this entails that plato thought that by 'mere analysis', by a process of
descending by stages of 'pure thought' independently of any criterion
for knowing external to the method itself, it was possible to attain
knowledge of the Forms.!3 In fact Plato illustrates abundantly in practice and acknowledges in theory that the method is not, in itself, infallible." Thus it may distinguish, within a genus, a 'part' for which
there is no Form, in which case the division is not a 'natural' one.lO
Admittedly he does not elucidate further here what sorts of'parts' have
Forms, and what sorts have not, but he does at least make clear that
merely to satisfy the formal requirements of the method is not sufficient
for the determination of 'reality'. Hence' the formal method alone may
lead to any number of definitions of the same thing unless one has the
II2
additional power of recognising the essential nature that is being sought
(Sophist 23rc-232a). In short, diairesis appears t~ be only an ald to
reminiscence of the idea.' 16 One might add that It IS essential to have
'the additional power', at every stage in the practice of the methods of
collection and division, of recognising and selecting 'real' resemblances
and differences, those which are resemblances and differences between
Forms (Politicus 28Sb). The possibility of knowledge cannot, then, be
made to depend on diairesis as a self-sufficIent Criterion.
And it is certainly not the case that perception now becomes the
criterion for knowing. Nor do those who claim that the recollectIon
theory is abandoned pretend that it does, though they certainly as~ume
that the fact that perception and its objects are now valued more highly
in relation to knowledge and the Forms has an important relevance t~
the question whether the recollection theory is abandoned: But what IS
this relevance? As far as the metaphysical status of senslbles m relatIOn to
Forms is concerned the thesis of the late dialogues is distinguished from
that of the middle dialogues rather by its greater consistency th~ by
any important change in doctrine. Thus the theory of rec~llectlO~ m th~
Phaedo had assumed that Forms have sensible instances whIch are copIes
resembling their archetypes, and on this assumption had granted to
perception the cognitive value of facilitating the recogmtlOn ~f Forms.
And since plato thus acknowledges the eXIstence of determmate sensible characteristics he quite properly describes them as h~ving :being'
without in any way contradicting the assumptions of hIS dlstmctlOn
between Being (the perfect or 'complete' Being belonging to Form.sto pallteMs on) and Becoming (the most appropriate comprehensl~e
term with which to characterise the changmg sensIble world m distinction from the world of Being in the above sense). Any possible confusion is avoided once we distingnish, as plato distingnished, (i) the
distinction between Being and Becoming, as above, (ii) the distinction,
within Becoming. between the derivative 'being' of determinate. s~n
sible characteristics and the 'becoming' which is the process of attammg
this determinate state of 'being'. This point we discussed in detail in the
last chapter in exa1l1ining Plato's criticism of perception in the Theaetetus. Now these distinctions are preserved in the late dialogues.': T~ey do
not make their appearance there for the first time as an mdlcatlOn of
some important development in doctrine. When plato assun:es there
the 'being' of determinate sensible characteristics he IS assummg only
II3
what he had earlier assumed in the middle dialogues as part of his theory
of Forms. Unfortunately his criticism of perception in the middle dialogues had led him into inconsistencies. It had led him at times to deny
any cognitive value to perception and to deny too the existence of
determinate sensible characteristics. It is failure to recognise this serious
inconsistency in the middle dialogues which has allowed scholars to
maintain thatin the late dialogues thereis an important change in Plato's
assessment of the metaphysical status of sensibles." For they fail to
recognise that what plato says in severe condemnation of perception
and its objects in the Phaedo, the Republic, and the Theaetetus is inconsistent not only with what he says of perception and its objects in the late
dialogues but also with what he says about them in other places in the
middle dialogues and, most particularly, with the assumptions of his
theory of recollection, as presented in the Phaedo. Finally, by associating
the distinction between Being and Becoming (distinction (i), above)
with the middle dialogues only, as a distinction marking a severe disparagement of sensibles, and the distinction between 'being' and 'becoming' (distinction (ii), above) with the 'maturer doctrine' of the late
dialogues, they wrongly assume an incompatibility between distinctions (i) and (ii). Once these confusions iu their thesis have been noted,
it is possible to see that all the positive evidence which they adduce for
the view that in the late dialogues Plato assumes the 'reality' of determinate sensible characteristics is simply evidence that in the late dialogues Plato is underlining more emphatically and maintaining more
consistently than in the middle dialogues what was assumed from the
start in his theory of recollection." Hence it is evidence irrelevant in
itself to the question of whether or not recollection is abandoned in the
late dialogues.
There is one passage, however, which demands special consideration,
since the mallller of its presentation of the function of the method of
division and its subsequent analysis of 'being' in terms of the Pythagorean concepts of Limit and the Unlimited have made it the passage
most commonly appealed to as evidence for the advance in Plato's
theory which removes the doctrine of recollection from the late dialogues. For it is argued that it is most clearly in this passage that the
method of division can be seen to be a method which 'bridges the gap'
between sensibles alld intelligibles, and here too, in the analysis of the
generation of 'being', that the problems raised by the 'separation'
II4
lIS
KNOWLEDGB AND BELIEF
between the two worlds can be seen to have been removed. The passage
is in the Phi/ehus (Isa 1£). The method of division is here presented as
one which supplies 'intermediaries' between the genus and the infinitely
numerous particulars. The problem raised at the beginning of the passage appears to be that of the consistency of postulating the Form as a
One, and yet subjecting it to division and making it a Many." But
Plato goes on to state that the problems of postulating the Form as a
One are: (i) do these Ones or monads really exist? (ii) can they retain
their unity and permanent identity if they 'come to be' in an infinite
number of particulars? 21 The method of division is then introduced as
a method which will illustrate the 'one-many' distinction in a form
which will prevent the 'one-many' problem from confusing the proposed discussion of the nature of the genus pleasure and its varieties. 22
And it is introduced here as a method of classification, not of definition
in terms of genus and specific differences. What the method does, says
Plato, is to show precisely what and how many species there are of a
given genus. The initial division of the genus into species is followed by
subdivision of these species, and the process is continued until no further
subdivision is possible, the 'total number' of species within the genus
having now been discerned. This number is fInite, and the species making up this finite number are described as 'intermediary' between the
One genus and the infmite1y numerous particulars. 23 Plato, making use
here of the Pythagorean concepts of Limit and the Uulimited, associates
Limit with the finite number ofspecies of the genus, the Unlimited with
the infmite number and variety of particulars. And in saying that only
when the total fmite number of species has been determined is it permissible to 'let each of these species pass away into the unlimited', he
clearly implies - and this is confirmed by his subsequent illustrations that with the limits of exact specification there has been reached also the
limits of the intelligibility of the particular, the'infmity' of their number and of their individual differences being alike irrelevant to their
determinate nature. In this analysis it is clear that the element of 'unlimited' is located in the realm of particulars, and not at all in the realm
of Forms. At the same time it is clear that particulars are characterised
by 'limit' to the extent that they are amenable to the systematic ordering
made possible through an analysis of Forms completely determinate in
structure. Thus it is possible to say that, in so far as it is assumed that the
method of division makes it possible to explicate precisely the structure
of a complex Form, it is correspondingly assumed that the determinate
nature of sensibles which are instances of the Form is specifiable in a
more precise and 'scientific' way than is possible if their determinate
nature is specifiable ouly in terms of separate and isolated characteristics
designating the various Forms in which the sensibles 'participate'.
Yet it is obvious that this assumption contributes nothing to the solution of the problem raised in Isb - how the Form, a monad which is
'always one and the same', can retain its unity and yet be present in an
indefmite number of particulars. Nor does it contribute anything to the
solution of the problem which'jieems to be implicit in Isa - how such
Forms can retain their unity when they are subjected to analysis by
division and their complexity of structure revealed; it merely raises the
problem. What is shown by the raising in Isb of the problem of the
splitting up of the Forms amongst many particulars is that the theory of
Forms is still maintained in a form which engenders this problem;
plato does not think that the existence of this problem, which he had
earlier recognised in Parmenides 13 Ia-e, has made it necessary to modify
the theory. And all that the subsequent account of the methods of
collection and division shows is tbat the problem of 'the One which is
Many' raised by the recognition that there are varieties of pleasure and
of knowledge (I4c) is at once clarified and prevented from being a
source of confusion in the argument (I6a-b) by being viewed in the
light of an exact method of classification which shows that a generic
One is divisible into a finite number of species and sub-species, and
distinguishes this number from the indefiuite number of particular
members of the genus arid its species. The method is clearly not intended to 'bridge the gap' between intelligibles and sensibles, nor does
it do so. Plato does speak of the fmite number of species as 'intermediate' between the generic One and the infmite number of particulars, though without making clear what particular emphasis he
wishes to be given to the term. Certainly no metaphysical significance
can be attributed to it. Indeed Plato's exaggerated emphasis in this passage on the numerical distinction between the fmite number of species
and the infinite number of individual members of the genus almost
suggests that he is using 'intermediate' in a trivial numerical sense. And
even if we interpret it as an indication that a description of particulars in
terms of the infimae species to which they belong is a closer specification
of their particularity than is a description in terms of wider genera,
n6
we do not thereby bridge a metaphysical gap between Forms and
sensibles.
It is argued, however, that the metaphysical significance of the present passage is to be interpreted in the light of Plato' s later illustration of
the nature of the 'mixture' of Limit and the Unlimited in 23C-27C. I
doubt whether this is justifiable. plato is dealing now with a question
quite different from the question which led him to introduce his
account of the method of division, and, further, is using the concepts of
Limit and the Unlimited in quite a different way. Moreover this later
passage, even if used to interpret the metaphysical significance of what
Plato says earlier about the method of division, does not itselfhave such
metaphysical significance as would show that the method 'bridges the
gap' between intelligibles and sensibles. Plato here explains, in terms of
specifically mathematical determination, that the 'being' of such
qualities or conditions as beauty, health, strength, good climate, etc.,
is the product of two factors - Limit and the Unlimited, the former
signifying what is definite or determinate, the latter what is indefmite
or indeterminate. He is explicitly concerned with 'things which come
to be' (gignamena) (27a), and not with Forms, and all his instances are
instances of 'things which come to be' in time." And the fact that he
refers to the 'being' of the qualities or conditions which are the result
of the 'mixture' of Limit with the Unlimited is in no way incompatible
with the fundamental distinction which he makes in other dialogues
and, indeed, later in the Philebus itself,25 between Being (Forms) and
Becoming (sensibles). To argue that it is thus incompatible is the result of the confused interpretation which we have already examined the interpretation which associates the distinction between Being and
Becoming with the middle dialogues only, as a distinction marking a
severe disparagement of sensibles, and assumes that the ascription of
'being' to sensibles is a mark of a more mature doctrine belonging to
the late dialogues.
It is this confused interpretation that provides the basis for the fmal
part of the argument that Plato's new dialectic 'bridges the gap' between sensibles and intelligibles. The contention is that 'reality' or
'being' (ausia) is no longer the 'reality' constituted by a world of
separate non-sensible objects, the Forms, but the 'reality' constituted
by a system of relations explicated by the method of division and
realised in particular cases. The basis of the distinction between sensible
117
and intelligible reality is consequently found in 'exactitude or lack of
exa?titude in .kn~wledge of relations', the supremacy of intelligible
rea!tty conSlstmg m the fact that the constitutive relations of the Form
are exac~y or 'scientifically' defined as a fmite system of relations,
whereas u: the case of the sensible particular this exact defmability is
never possIble. Thus sensible realities are not 'specifically separate' from
Forms, nor Forms from sensibles. It follows that there is no need for the
'transcendent' dialectic of the middle dialogues, and consequently no
need for what was a necessary means to it - recollection. It follows too
that the problems raised in the first part of the Parmenides about the
'participarion' of sensibles in Forms are solved in that the theory of
Form~ has. been. so ,modified that these problems no longer arise. The
only partlC1patlOn, It IS argued, now relevant to the constitution of
:being: is par~icipation as a relation between Forms. This principle of
partlC1p~tlOn, for:nally;nunciated in the Saphist, 26 is the principle that
a Form IS able to share m other Forms or to combine with them. It
marks the explic.it recognition by plato of the complexity of the Form
~ ItS relatlOns WIth other Forms, and is necessarily assumed by a dialectic whl~h alms to dIscover the organisation of the system of Forms and
to exp!tc~te the structure of each of them. 27 The point of the appeal to
It as a prmclple of fundamental metaphysical siguificance in the 'later'
theory of Forms is easy to understand. For it can quite properly be
argued, Wlthout any assumption which discounts the radical dualism
of Plato's metaphysical theory, that the constitution of the determinate
'being.' of se~ible ~art~cul~rs is in each case to be interpreted in terms of
a part1cnlar combmatlon of Forms in certain specifiable relations to
one another. When it is further assumed, in the way we have indicated
~bove, that sensible realities are not 'specifically separate' from Forms,
It c.an further be argued that it is this 'participation', and this only,
which constItutes the determinate 'being' of sensibles, and that the
'earlier' principle of the 'participation' of sensiblesin Forms is no longer
~elevant to ~his determinate 'being', for it is a 'being' no longer to be
Interpreted ill terms of separately existent non-sensible Forms.28 The
argun:ent is, in:ffect, the argument that Plato's theory of Forms in the
late dialogues IS a theory which, while continuing to maintain the
;eality the Foru:s, now treats them as class-concepts which have no
separate reality, I.e. no reality apart from the particular things to
whlCh they apply." Yet the foundation of any such elaborate thesis is.
0:
lI8
as we have seen, an interpretation of the significance of Plato's ascription of 'being' to sensibles which is demonstrably false. There is the
clearest positive evidence in the late dialogues that plato continued to
assume the separate existence of the Forms, ascribing to them a 'perfect'
reahty of a distinctive kind in radical contrast to the 'being' which
belongs to the sensible world. 30 The Philebus itself provides such positive evidence, and furthermore makes clear that nothing in the preceding dialogues has provided a solution to one of the major problems
raised in the Parmenides about the 'participation' of sensibles in separately existing Forms.
So far we have seen that the argmnent that the doctrine of recollection is abandoned in the late dialogues is based on the thesis that the
disappearance in the late dialogues of the theory of separate 'transcendent' Forms removes the need of a 'transcendent' dialectic and hence
removes the need of a doctrine of recollection. And we have seen that
this thesis rests on a misinterpretation of what plato says about the
'being' of sensibles and is in fact contradicted by Plato's explicit statements in the late dialogues themselves. The fact that the separate reahty
of the Forms is still assumed and the absence of any kind of alternative
answer to the question which the doctrine of recollection was initially
designed to answer do not in themselves, of course, entail that the
doctrine of recollection is still maintained. Yet together they constitute
a very good reason for thinking that the doctrine is still maintained. It
is worth recalling that the postulate of the 'transcendence' of the Forms
is the primary postulate of the doctrine, and that it is just this transcendence which, Plato argues, makes necessary an appeal to the preexistence of the discarnate and intelligent' soul' as a basis of any theory
of how the Forms can be known. Now both these essential ingredients
of the recollection doctrine - the transcendence of the Forms and the
pre-existence of the soul- are retained in the latest dialogues. 31 And
terminology and form of argmnent, very clearly imply such a doctrine.
Thus Plato, far from claiming that recollection is replaced by the new
'technique' of specification afforded by the methods of collection and
division, first closely associates the one with the other in the Phaedrus.
Then later, in the Politicus, he introduces a discussion of the significance
of the fact that some 'realities' have 'visible likenesses' (28 Sd-286b), a
discllssion which has so many striking similarities in argument and
vocabulary with the passage in the Phaedrus which discusses recollection
(249 b-2sod) that it clearly confirms that Plato still retains not only that
since, moreover, the recollection doctrine provides an answer to the
objection raised in Parmenides 133a-134C - that the postulate of transcendent Forms makes the Forms unknowable to man - and is in fact the
only answer provided in the dialogues,32 there is very good reason for
assuming that in the late dialogues the postulates of the transcendence
of the Forms and of the pre-existence of the soul carry with them the
doctrine that coming to know the Forms is a process of recollection.
There are indeed several passages in the late dialogues which, in their
II9
conception of sensibles as 'copies' or 'likenesses' of Forms which is
characteristic of his theory of transcendent Forms from the beginning
but also the doctrine of recollection. 33 And in the Politicus, as in the
Phaedrus, the discussion of 'visible likenesses' is closely associated with a
discllssion of the new methods of dialectic. Again, in the Timaeus, this
characteristic terminology recurs, and again there are clear pointers to
the doctrine of recollection. Thus in stressing the value of perception in
so far as it suggests the way to a knowledge of the structure of the
universe (47a if.) Plato indicates that in this study of the nature of the
universe it is the function of perception to put us in mind again of the
reality revealed to us before incarnation." There can be little doubt
that Plato has the doctrine of recollection in mind. In particular the
image of the souls set
in stars 'as it were in chariots' (4 Ie) seems
obviously intended to recall the myth in the Phaedrus, where the soul is
granted a vision of the realm of Forms. 'Here in the Timaeus the souls
are shown "the nature of the universe". Such knowledge of reahty as
they will acquire in earthly life will be gained by Recollection.' " The
significance of these and other relevant passages in the Politicus and the
Timaeus will be considered further when we come to examine in detail
developments in Plato's theory of knowledge in the later dialogues. But
It was Important to try to dispose, in advance of this, of the view that the
doctrine of recollection plays no part in Plato's later theory, and that the
theory of Forms is now no more than a 'synthetic logic', proof against
the criticisms of the Forms made in the first half of the Parmenides.
There is, as we have now seen, no good evidence to support such a view,
and plenty of good evidence to refute it. Certainly the criticisms of the
Forms in the Parmenides are serious criticisms, and certainly it is reason-
able to expect that Plato would subsequently try to meet them and to
modify his theory of Forms if he found no adequate answer to them.
120
But he does not do this. And though it is true, as we shall see, that some
of the difficulties in the theory of knowledge of the later dialogues arise
from his failure to do this, these dialogues give us no warrant for equating their doctrine with the doctrine which we think that plato should
have propounded to meet the criticisms of the Parmenides.
2. THE EVALUATION OF PERCEPTION IN PLATO'S
LATER THEORY
aJ The Phaedrus alld the Politicus
It is in connexion with the retention in the late dialogues of an absolute
distinction between knowledge and belief (doxa, in the specialised sense
defined in the Republic) that the major difficulties in Plato's theory of
knowledge are best considered. And this distinction itself must be considered in the light of certain important developments in Plato's later
theory which serve to emphasise the difficulties involved in the retention of the distinction. Most directly relevant to the appreciation of
these difficulties are developments in Plato's evaluation of perception.
The theory of recollection, as it is presented in the Phaedrus, provides
the best starting-point for an examination of these developments.
The setting of the theory in this dialogue is mythical. In order to
explain the nature oflove as a type of 'divine madness' plato has turned
to an examination of soul and, having established its immortality
(245c-246a), he now describes its nature in a myth (246a ff.). Its highest
and most proper function is contemplation of the reahn of Forms, the
'colourless, shapeless, intangible, truly real Being, seen by reason alone,
the pilot of the soul' (247c), a realm to be contrasted with the reahn of
Becoming and Belief, with which the soul comes into contact once it is
incarnate (247d-248b). And the aim of the incarnate soul, now 'bearing
a full load offorgetfulness' (248c), must be to recoverits knowledge of
reality, the 'truly real being' of the Forms. The discussion of the possibility of recovering this knowledge begins at 248e. plato first points out
that it is a distinctive mark of human understanding, dependent on a
pre-incarnate knowledge of the Forms, and, at the same time, a condition of the attainment of human understanding, that this understanding
is 'by way of what is called a Form'. The initial step in the attairunent of
knowledge of Form is a process of'passing from many perceptions to a
121
~nity gathered together by reasoning' (249b), and this understanding is
a recollectlOn of the thmgs which our so1l1 once saw' (249c). That this
merely an initial step towards knowledge becomes clear when plato
:m;nediately goes on to descri~e the final insight into reality as an
lruUatlOn mto perfect mysteries, 36 envisaged as the goal of a long and
contllluous process of recollection which depends for success on the
:right use', of such 'reminders' of reality as experience affords (249c). By
right use plato presumably means the correct methodical analysis of
the initial recollections, where the correctness of the analysis will itself
depe~d on the criterion afforded by recollection; for this 'rightness'
(orthos) of procedure we may compare the frequent use of orth8s in the
description of the progressive stages of the 'ascent' in the Symposium,
210a-2IIC. Thus W. H. Thompson" was right to recognise that what
Plato describes ~s 'passing from many perceptions to a unity' represents
but a first stage III recollectlOn, and substantially right in his view of the
later ~tages as an ascent to 'exact scientific knowledge';38 how far he
IS
was nght ill construing the first stage as a transition from sensation to a
conceptual level of apprehension is the first point to be considered in the
detailed interpretation of the passage.
The main significance of this first stage of recollection is, as has
already been noted, that it links recollection with the method of 'collection', and, by implication, through its connexion with other passages
~ th~ Phaedms and later dialogues, with the complementary method of
dIVlslOn. There
ar~ tw,o possible interpretations of Plato's meaning
when he speaks of pas,smg from many perceptions to a unity gathered
together by reasonmg . He may meall (i) an essentially pre-analytical
stage of recolle~uon,. whereby a slllgle lUllversal, through a gradual
proe.es.s of familiansatlO~ wlth and recognition of sensible particulars, is
exp~Cltly abstracted; this.would be an essential first step in the 'possessl?n of the Form, precedmg any:nalysis ofitsstructure: or (il) a recogmUon of the genenc likeness of different species, and the' collection' of
these species into a single genus. (ii) presupposes the ability to recognise
particulars as Instances of a species; 'individual things must first have
be;n brought under the unity of one of the Ideas', so that 'abstraction'
IS cOlllcldent With the subordination of lower kinds under a h' h
'''Th
r··,
Iger
one.
us CornlOrd mSlsted that collection must not be confused
With the Socratic muster of individual instances (epag8ge). Collection is
a survey of speCific Forms havmg some prima facie claim to be members
I
122
of the same genus.' 40 The context of the passage points to (i) rather
than (ii), since Plato, in speaking of 'understanding by way of what is
called a Form', appears to be stressing that the distinctive mark of man,
as against beast, is that man can attain a conceptual level of apprehension. And the statement that it is a necessary condition of human understanding that it should be 'by way of what is called a Form' most
naturally suggests that when plato describes the way in which tlns form
of understanding is initially realised in man he is referring to (i) rather
than to (ii). We may assume, then, that it is in terms of (i) and not (ii)
that we should interpret the initial stage of the process of recollection.
It represents the first realisation of the Form iu the understanding. The
later description of collection in 26Sd41 as a process of 'gathering into
the unity of a single Form things that are widely scattered, seeing them
all together' also suggests (i), though here there is no explicit emphasis
on sense-perception, aud the context indicates that collection, though
iucluding (i), includes also the bringing of the Form as a species under
its nearest genus, and the continuation of ills process until, in conjunction with division, it can provide a full analysis of the complexity of the
Form, an analysis guided by recognition of'similarities' and' differences'
(26Ie if.).42
A question which immediately arises is that of the extent of the aid
given by perception in the process of recollection. The way in which
the formula of 249b ('passing from many perceptions to a unity
gathered together by reasoning') is presented seems to imply that it is a
formula to which there are no exceptions - the initial realisation of any
Form in the understanding must conform to it. Yet, having thus made
perception the necessary basis of the possession of the Form, plato
immediately goes on to make reservations about the adumbration of
Forms in the sensible world and about man's ability to recognise such
adumbrations as there are. A great difficulty here is the mythical setting
and modes of expression of his account, and it is fortunate that a closely
similar argument in the Politicus allows us, by comparison, to give
some precision to the interpretation of Phaedrus 24ge if. Here Plato first
asserts that the soul has only a dim perception of ' images' (homoi8mata)
of the Forms (2 soar -bI). He then introduces an important distinction.
In the case of some Forms, he argues, the images on earth have no
'lustre' or brightness. Instances are justice, temperance, and 'all the other
things precious to souls'. Wisdom is added as an example at 2sod, where
123
plato says that this Form and 'all the others that are beloved' are not
given to sight; they have no such 'clear image' (enarges eidSlon) as is
afforded to sight. To Beauty however a distinctive status is granted as
the Form most manifest in its images to sight, and the most clearly
adumbrated in the sensible world. Now as we saw in our discussion of
the Symposium at the beginning of the last chapter this Form has a
special significance in Plato's thought; it is the object of the philosopher's 'love' in his intense desire to attain full insight into the world of
reality. And taking into account also the mythical setting of the discussion of the Phaedrus, it is clear that the distinctive status granted here
to Beauty should not be takeu as au indication that the 'images' of one
particular Form constitute the class of' clear sensible images'. It is more
plausibly construed as an indication of a more general kind - that there
are' clear sensible images' of some Forms, but not of others. A closely
similar passage in the Politicus (28sd-286b) appears to confirm this
interpretation. Here plato says that the highest, most important realities
have no clearly adumbrated sensible image to which a person can point
in order to satisfy someone who inquires about their nature. The terniinology here is exactly the same as that of the Phaedrus. 48 But in some
cases, Plato argues, 'sensible likenesses' (285e) are available. In these
cases adequate understanding of the object of the inquiry can be gained
simply by referring to the sensible likenesses, without any verbal
account or explication of its nature (28sd-286a). The 'most important'
realities, however, are clearly apprehensible by reason alone (286a).
Thus both the Phaedrus and the Politi",s appear to be making the same
distinction - between Forms which have clear sensible images and
Forms which have not.
Moreover there is some suggestion that some Forms have no sensible
images at all. It is true that in speaking of the lack of ,lustre' or brightness in the images of some Forms plato is not necessarily indicating anything more than relative clarity. Again in the Politi",s his point that the
'most important' realities have no clearly adumbrated sensible images
and are clearly revealed by reason alone suggests 'that the subject under
discussion is not the absence of sensible images, but a pervasive lack of
clarity in them'." Yet plato doesstress, at 2sod, that wisdom (phronlsis)
and 'all the other things that are beloved' (which are quite certainly the
Forms described in 250b as 'precious' and as having images with no
'lustre') are not given to sight. And this clearly means that some Forms
I24
12 5
have no visible images, and this in turn has very naturally been taken to
imply that some Forms have no sensible images at all. 45 It cannot mean,
vites comparison with the passage in the Sophist (254c) where the
however, that some Forms have no images, for plato assumes that
Forms of Existence, Sameness, Difference, Rest, and Motion are des-
Forms which do not have visible images do have 'likenesses on earth'
(250b) of some kind. Unfortunately his remarks on the way in which
these 'likenesses' are apprehended are very obscure. He says that men
approach these 'likenesses' through 'dull organs' (250b). The contrast
here is with sight, described later as the 'sharpest' of the senses (250d).
And in view of the implausibility of assuming that it is through hearing
or touch or any other of the senSes that the likenesses are apprehended,
there is much to commend the suggestion that the 'dull organs' are' the
inadequate reasoning powers of man'. 46 In that case the 'likenesses'
would presumably be verbal images, the kind of image which Plato
seemed to have predominantly in mind when referring to images of
moral Forms in the Republic. The alternative to this kind of interpretation is to assume that in speaking of' dull organs' plato has no specific
'organs' in mind, but is using the phrase merely to point out the
obscurity of the path to knowledge of Forms in some cases. Whatever
view we take on this point, it is at least clear that the Phaedrus maintains
that some Forms have' clear sensible images', and that some (though not
necessarily all those which do not have clear sensible images) have no
visible images at all; the Politicus agrees with this to the extent that it
l1uintains that some 'realities' have clear sensible images and some have
not. In both dialogues the main distinction seems to be between Forms
which can initially be possessed by direct abstraction from perceived
instances or 'images', and Forms which cannot be so abstracted. And
tlus suggests that the formula of Phaedrus 249b ('passing from many
perceptions to a unity gathered together by reasoning') is not in fact a
formula to which there are no exceptions.
As for the question of which Forms have no visible images, the
Phaedrus affords little guidance. The instances which it gives suggest that
it is especially moral Forms which are considered to have no visible
images. In a later passage (263a-c) 'good' and Just' are specified as instances of words which have no clear and accepted application to particulars, in contrast with words such as 'iron' and 'silver' which can be
applied directly and without doubt to particular instances. The Politicus
passage, in its description of Forms with no clear sensible images as
'most important and most valuable' (megista, timi8tata; 28se-286a), in-
cri~ed as 'most i?,portant' (megista). And taken together these indic~t'~ns .as to which Forms have no visible images suggest that the
dlStmct,on between these Forms and Forms which do have visible
images has some affinity with the distinction made in the Theaetetus
between percept~al and non-perceptual characteristics (184b-187a);
th,s1att~r dlStmctJ.On appeared to imply, as we saw in the last chapter, a
dlStmc:lOn between empirical concepts (instantiated in perception in
the objects of a smgle sense-organ) and a priori concepts (apprehended
mdependently of perception by the mind and as 'common terms' not
restricted in their application to the objects' of one particular s~nse
organ).
The.re is, I think, quite certainly some affmity between the distinction
made m the Theaetetus and that made in the Phaedrus and the Politicus
But it is to be noted that Plato's purposes in introducing the distinctio~
m the Phaedrus and the Politicus are different from his purpose in the
Theaetetus. In the. Theaetetus the distinction was made for the purpose of
refutmg the thests that knowledge is perception. And assuming, as he
had done in his earlier criticism of the thesis in so far as it rested on a
'/I~x' theory, that knowledge includes judging significantly that somethmg lS the case, plato had shown that, since any judgement involves an
apprehension by the mind of 'realities' not given in perception, then
knowledge cannot be equated with perception. The interest ofhis argument here, as we. sa:v ~ our detailed examination of it in the last chapter, lay not only m ':s ,.mplicit distinction between perceptual and nonper~eptual charactemt'cs but also in its suggestion that Plato was now
begmrnng t~ approach the problem of knowledge on the basis of an
analyS1~ of Judgement, having especially in mind here judgements
whtch mclude terms for perceptual characteristics and distinguishing
the perceptual and non-perceptual elements in such judgements. There
seem to be no suggestions of this kind in the Phaedrus or in the Politicus
passages. The purpose of the passage in the Phaedrus is to show that
recollection of Forms from perceptible 'images' of Forms is limited by
the fact that many Forms do not have 'clear sensible linages'. The purpose of the passage m the Politicus is a different one, for, though it
appears to make the same distinction as the Phaedrus did between Forms
with 'clear sensible images' and Forms without, its purpose lS to suggest
that the study of 'realities' which have clear sensible images may point,
through these images, to analogies for the interpretation of 'higher'
realities which have no clear instantiation in the visible world. Thus the
Politicus does indicate one way in which perception may be of value in
the analysis of Forms which have no 'clear sensible images'. Yet here,
as in the Phaedrus passage, Plato's attention is firmly fixed on the question of how we come to know particular Forms; he is not concerned to
illustrate the relation between 'realities with clear sensible images' and
'realities without clear sensible images' in particular judgements, but to
base on the distinction a distinction between two ways of coming to
know particular Forms. Thus, granting that there is an affinity between
the distinction of the Theaetetus and that of the Phaedms and the Politims,
the use of the distinction in the two later dialogues suggests perhaps that
the application of it to judgement in the Theaetetus was a special application in support of a particular argument against perception, and that
subsequently Plato's main interest in the distinction lies in its relevance
to what seems to him to be a more general and more important problem
for his theory of knowledge - the method by which knowledge of
particular Forms is to be gained. It remains, in any case, a distinction of
considerable importance, and the extent of the affinity between its
immediately suggests that plato is here referring to those 'most important' realities which, he has just asserted, have no clearly adumbrated
sensible images, it seems natural to take this latter half of the passage as
a statement that while knowledge of Forms without sensible likenesses
is gained by 'reason alone' since no sensible aids are available, knowledge of Forms with sensible likenesses is not gained exclusively by
reason but is facilitated by the use of sensible likenesses. The objection
to this interpretation is that Plato does not say that 'of incorporeal
things those which are the noblest and most important are clearly revealed by reason alone', which would have implied the existence of
other 'incorporeal things' ofless importance. He says (and there is no
ground at all for doubting the text) that 'incorporeal things, which are
the noblest and most important, are clearly revealed by reason alone'.
This implies a contrast with things of less importance which are not
'clearly revealed by reason alone' and not incorporeal; and these things
ofless importance must, evidently, be the previously mentioned 'realities' which have sensible likenesses. It would seem to follow that
since 'incorporeal' is a term surely applicable to any Form, then 'realities:
which have sensible likenesses are not Forms. Thus the passage appears
to be repeating the implicit distinction of the Theaetetus between a
posteriori and a priori concepts; the latter designate transcendent Forms,
the former do not and have no 'reality' apart from the particular things
to which they apply. The ouly way to make the passage consistent as a
distinction between Forms with sensible likenesses and those without is
126
earlier and later occurrence deserves careful examination. In particular
it is important to ask whether the implicit distinction in the Theaetetus
between a priori and a posteriori concepts is reflected in any way in the
passages of the Phaedrus and the Politicus. And to ask this is, of course, to
question whether it can certaiuly be established that in the Phaedrus and
the Politicus plato is distinguishing between two classes of Forms - those
with clear sensible images and those without. Ifhe is, then it is necessary,
I think, to conclude that knowledge of Forms of either class is a priori.
The Politicus passage, though not the Phaedrus passage, undoubtedly
lends itself in some part to an interpretation which yields quite a
different distinction. In this passage Plato first states that some 'realities'
(to onta) have 'sensible likenesses' but that the highest, most important
realities have no clearly adumbrated sensible images (28 5e-286a). Then,
after saying that exercise in the analysis and defmition of realities of each
kind is essential, he asserts that 'incorporeal things (ta as8mata), which
are the noblest and most important, are clearly revealed by reason
alone', and that it is easier to practise in small matters than in great. And
since the description of'incorporeal things' as 'most important' (megista)
12 7
to take 'incorporeal' (as8mata) in the sense of 'not having visible
(bodily) likenesses' ;47 bnt this is a sense without parallel in Greek, and
to adopt it seems to me to be a desperate expedient. Thus the text as it
stands is most consistently interpreted as a distinction between (i)
'realities' which are incorporeal and have no clear sensible images, and
(ii) 'realities' which are not incorporeal and do have clear sensible
images; the 'realities' in
(i)
are most naturally taken to be Forms.
Now we saw at the beginning of this chapter that the late dialogues
provide clear evidence that Plato retained there his doctrine of the
'transcendence' of the Forms. Are we then to take the present passage
of the Politicus as an indication that, while retaining this doctrine, he
restricted the number of transcendent Forms to the number of nonperceptual characteristics, as defined in the Theaetetus? It is at once clear
that this position cannot be taken as representative of the doctrine of the
128
129
late dialogues. In the Tintoeus and the Philebus, where the radical distinction between Being (Forms) and Becom.ing (sensibles), a characteristic indication of the 'transcendence' of the Forms, is fOlmd, together
with other equally significant indications, the examples given of Forms
are examples which quite certainly fall within the class of Forms with
clear sensible images. Such examples are natural kinds, like Man and Ox
(Philebus 15a), and material elements, like Fire and Earth (Tintaeus
51 b-c). And the Tintaeus, as we shall see in detail later, makes clear that
the class of independently real Forms with clear sensible images is a
wide class. Moreover, although there was certainly much discussion in
the Academy on the question of the limit to be imposed on the class of
things of which there were Forms, and although there is some discrepancy between Aristotle's testimony on this question and the evidence of the dialogues,48 all the evidence is decisively against the suggestion implicit in the Politicus passage about the kind of limit to be
imposed. I think there is little doubt that if Plato had consistently
developed in his theory of knowledge the distinction which appears to
be implicit in the Theaetetus and the Politicus he would have been able
to formulate a much more satisfactory theory of the distinction between
a priori and empirical blOwledge. But the fact remains that he did not
so develop it. And it is reasonably argued, especially in view of the
radical conflict between the passage of the Politicus as interpreted above
and the evidence of the other late dialogues and of Aristotle, that (i) the
passage is able to yield such an interpretation only because plato has
been inexact in his formulation of the distinction between Forms with
clear sensibleimages and Forms without; (ii) the precise correspondence
in vocabulary at many points between this passage and the earlier passage in the Phaedrus (250b-d) is in itself a strong argument for the
view that the Politicus is making the same distinction as the Phaedrus between transcendent Forms with 'clear sensible images' and transcendent Forms without 'clear sensible images'.
The discussion so far has shown that in coming to know Forms
which have clear sensible images it is by a method of direct abstraction
from the perceived images that the Form is initially possessed. It has
shown too that, while the distinction in the Theaetetus between perceptual and non-perceptual characteristics is clearly akin to the distinction between two classes of Forms in the Phaedrt" and the Politicus and
thus suggests a criterion for determining which Forms have clear seu-
sible images and which do not, it is not the case that we should exclude
'realities' with clear sensible images from the class of transcendent
Forms. It is now necessary to consider the further stages in coming to
know these 'realities'.
The Phaedms, as we saw, recognises two main stages, and indicates
that the stage which succeeds the initial realisation of the Form in the
understanding is the analysis of it by means of the methods of collection
and di:,ision, with defmition as the aim of the analysis. As a guide in this
analysts appeal to the perceptible instances of the Form is recognised by
Plato to be of great value. For in cases where the Form has visible
images, these images mirror in their complex structure the structure of
the Form and have a complete, though imperfect, resemblance to the
Form. If we tnrn to the Politicus again, we have a clear indication of the
extent of the help given by perception in the analysis of these Forms.
Just before the passage examined above, Plato, in a description of the
meth?ds of collection and division, shows what part is played in the
practlce of these methods by perception of the visible images mentioned
m 285e-286a. He says (285a-b) that
when a man ~rst perceives
(aisthhai) what is common to a great
nnmber of things he must not desist until he sees, within what is
common to them, all those differences which are differences between
Forms. Again, when he sees the differences of all kinds which exist
in a multitude of things he must not fight shy and give in Ulltil he
has embraced in the unity of a common resemblance all those which
are really cognate, thns comprehending them in the real unity of a
common Form. 49
Now since Plato immediately goes on to develop his view of the part
played by vlSlble likenesses m the analysis of Forms it is reasonable to
assume that :what is the~e said about visible likenesses is directly relevant
to what has Just been SOld about the practice of the methods of collection
and division. '0 what plato says about visible likenesses is that the fact
that some 'realities' have visible likenesses makes the analysis of the
structure of those realities comparatively easy and at the same time
valuable in suggesting analogies for the analysis of realities which do
n~t have visible likenesses. And what he says about collection and
d1:'lSlon suggests ~ery pointedly, in its terminology, that plato is descnbmg the analySls of Forms where visible likenesses are available. It is
I30
the repeated reference to 'seeing' and 'perceiving', taken in conjunction
with the reference to 'multitudes' of things, which suggests that it is
specifically sense-perception of visible particulars which Plato has in
mind, thinking of such perception as a valuable guide to the comprehension of the Form not only at the initial stage of direct abstraction
but also at the stage of explicit conceptual analysis which follows the
initial 'realisation' of the Form in the understanding. Thus in the process
of acquiring knowledge 'the illustrations of sense, instead of deluding
us, are declared to conduce, wherever they can be had, to the clearness
and facility of the process'. 51
The high value placed here on perception, and particularly the
assumption that it is possible to use perception systematically in acquiring knowledge, are natural developments in a theory of knowledge
which continues to think of knowledge as recollected knowledge, continues also to assume that, at least in the case of Forms with visible likenesses, recognition of Forms is prompted by perception of these visible
likenesses, and assumes finally that the resemblance between visible
'copy' and complex Form is a complete, though imperfect, resemblance. Nor is there any radical inconsistency in Plato's attitude to perception in the late dialogues, as there was in the middle dialogues.
Plato still assumes that the sensible world is in continual change, but he
no longer assumes that this entails that the sensible world is devoid of
determinate and recognisable characteristics. That he recognised that
he was wrong to make that assumption in the Gratylus and the Theaetettls is indicated in the course of his careful evaluation of the sensible
'image' in the Timaeus. Nowhere does Plato give a fuller and more
systematic treatment of sensible 'images' than in the Timaeus, and an
examination of what he says there will enable us to see the reasons for
the high value placed on perception in the Politicus and elsewhere, and
will provide at the same time further illustration of the extent of the
class of Forms with 'clear sensible images'.
bI The Timaeus
The fundamental assumptions made by Plato at the beginning of his
account of the nature of the physical world are stated (Timaeus 27d ff.)
as follows: (i) there are two orders of existence - the eternal, unchanging world of Forms, to be apprehended by reason, and the sensible
world, which 'comes to be and passes away' and is the object of'belief'
13 I
(doxa); (ii) the sensible world is 'good', the meaning of this assmnption
being that the sensible world exhibits rational order and design in its
processes (30a). It is this 'goodness' which implies - plato appeals here
to the analogy of the human craftsman - the existence of a permanent
'scientific' model (paradeigma), i.e. the system of Forms; (iii) it follows
from (ii) that the sensible world is an 'image' (eik8n) of the eternal; (iv)
the existence of 'soul' in the world is also implied by (ii), since the
presence of intelligent order and design implies the presence of 'soul'.
This concept of a cosmic soul is a characteristic feature of the late dialogues. The Phaedms first indicates the change in Plato's interest from
soul in its relation to individual morality to soul in relation to change
and process in the world as a whole. In 24sc-e the 'essence and definition' of soul is said to be self-motion, and in 246b, e there are already
suggestions of the way in which this conception of soul is to be developed as the basis of a theology. Explicitly in the Laws (893b ff.) the
conception of soul as that which moves itself and is the source of movement of all bodies is the basis of a demonstration that the order of the
world is attributable to the control of a perfectly wise and good
supreme soul." It is the activity of soul so conceived, producing a
world 'like' the Forms, as copy to model, which explains, in the Timaeus,
the way in which the 'participation' of things in Forms is effected.
Later in the dialogue (48e-52d) Plato returns to the distinction between model and copy, and introduces, in an attempt to specify more
exactly the nature of the sensible image, a new element - 'the Recept-
acle of all Becoming' (49a) or Space (S2a). This is a qnite independent
element of reality, not fashioned after any model as sensibles are but
permanently existing as that in which sensible characteristics make their
appearance. Plato stresses that space or extension necessarily belongs to
all that is sensible; it is essential to the existence of sensible 'images' that
they are extended in space (S2C). It is probable that his insistence on the
importance of extension for a proper appreciation of the mode of
existence of sensibles, and on the importance of trying to grasp the way
in which extension itself is to be apprehended in abstracto (SIb, 52b),
independently of both sensibles and Forms, is prompted principally by
his conception that it is the geometrical structure of the particles of the
material elements which determines the distinctive characteristics of
those elements. " The fact that sensible images are extended in space is,
then, one important condition of their existence. And in a difficult
132
passage beginning at 49b plato attemptstocharacterisefurtherthenature
of the seruible image and to indicate the proper way of describing it. 54
He first notes the apparent perpetual transformation into one another of
the material 'elements' - earth, air, fire, and water - and then goes on
(49 d- e):
Since in this way none of these things eVer presents the same
appearance, of which of them can one confidently assert, without
shame, that it is any definite 'this' and not any other thing? It is not
possible, but by far the safest course is to speak of them in the following way. Whenever we see a thing continually changing its appearance, fire for example, in every case we should not call fire 'this', but
'what is of such and such a kind', nor water 'this', but always 'what
is of such and such a kind', nor anything else' this', as though it had
some permanence, among the things which we point to with the use
of the words 'this' or 'that', thinking that we are indicating something. For it slips away, not waiting to be called 'that' or 'this' or any
term which indicts it of being stable. We must not in fact apply any
of these terms; the description we must apply, in each and every
casc, is 'the such and such which is perpetually recurring as similar';
thus we should call fire 'what is always such and such', and so with
everything that comes to be.
The argument here is, briefly, that the visible world is one of perpetual change and that it is necessary to distinguish between a right and
a wrong way of describing it. 'TIils' or 'that' is always wrong, since
these terms suggest a reference to something substantial and permanent,
whereas in fact the sensible world is a world of transient, yet recurrent,
characteristics or groups of characteristics (subsequently called 'copies'
or 'likenesses' of the Forms; soc, 5Ia) which are properly described as
'of such and such a kind'. Thus the fact that the visible world is in
continual change does not entail that it is devoid of determinate and
recognisable characteristics, but it does entail that there are no substantial permanent 'things' in it. Now the Theaetetus and the Craty/us
assumed, as we saw in the last chapter, that the fact that the visible
world is in continual change does entail that it is devoid of determinate
and recognisable characteristics, and both dialogues made clear that it is
as illegitimate to apply the term' of such and such a kind' to any part of
it as it is to apply the terms 'this' or 'that'. The Theaetetus argued that if
I33
everything in the sensible world is continually changing in respect of
both place and character then no description can meaningfully be
applied to it, since it possesses no determinate characteristics which can
give any description significance (I82C-I83c). Not even the words 'so'
or 'not-so' can be used to describe any aspect afit (183a), nor 'trus' nor
'that' nor 'any other word that brings things to a standstill' (157b;
c( I52d). In much the same way the Cratylus asserted (439c ff.) that
what is in perpetual change cannot properly be referred to as 'this' or as
'of such and such a kind', for it is never in any determinate condition
(439 d). Thus the Timaeus passage contradicts what is said in the
Theaetetus and the Cratylus, and shows clearly, I think, that plato has
recognised the need to correct what he had earlier propounded as
implications of the theory (and he holds this theory to be true) that
the sensible world is in flux.
Moreover, in making clear that in the sensible world there are
determinate and recognisable characteristics, the 'copies' of the Forms,
plato stresses that the appearance of these copies in space is recurrent.
They are copies describable as 'of such and such a kind' and they
'perpetually recur as similar'. This serves to correct another argument of
the Theaetetus about the doctrine of flux. In the Theaetetus plato had
linked the flux doctrine with the subjectivist thesis of Protagoras, arguing that this thesis aSSUmes that all things are in flux. In particular he had
argued that when the flux doctrine is used as the basis of an analysis of
perception it is possible to demonstrate that no two percepts are ever
the same, the percepts of each individual being always themselves in
change, always all different from those of any other individual, and
hence private and peculiar to the individual. Thus his argument was
that to accept the flux doctrine as true for sensibles is to accept that
perception is necessarily subjective. His argument rested, as we saw in
the last chapter, on a confusion in the interpretation of 'nothing is ever
the same'. In one sense it is true to say that the doctrine of flux entails
that 'nothing is ever the same'. But, as we pointed out when examining
Plato's argument, it does not entail that no particular event or series of
events recurs or is repeated at another time or in another place at the
same tilne, and hence does not entail that no particular event or series of
events is like any other event or series of events. If an individual's percepts are similar to or 'the same as' the percepts of another individual,
even of all other individuals, this is not necessarily inconsistent with the
I35
doctrine that all things are in flux. Now in the Timaeus Plato clearly
continues to accept the flux theory as true for sensibles, and just as
clearly denie, that perception is necessarily subjective. In particular, as
part of his contention that there are determinate and recognisable
sensible characteristics, he emphasises that these copies of the Forms
'perpetually recur as similar' in space, and thus firmly rejects an essential
part of his argument in the Theaetetus that the flux doctrine is necessarily
linked with subjectivism. And Plato's account here of the nature of
these recurrent sensible characteristics must be viewed within his
broader picture in the Timaeus of the 'goodness' of a visible world
which exhibits, as a copy of an intelligible model, rational order and
design, and hence makes possible an approach to knowledge through
perception. In several other passages in this dialogue he indicates the
importance of the part played by perception in the recovery ofknowledge. These passages must now be considered. They will confIrm that
Plato's view that the sensible world is continually changing no longer
has any association for him with the subjectivist thesis which he propounded in the Theaetetus.
There is, firstly, the eulogy of sight at 47a-b as 'the cause of the
highest benefits to us'. Here plato affirms that
previously known reality. And though in 47a-b plato gives special
prominence to the heavenly bodies in speaking of the study of the
nature of the world, he indicates that the efficacy of perception extends
to the whole field of this study.
In other passages the same general assumption is apparent. One
essential part of this assumption is, of course, that sensible characteristics
are 'good' images of the Forms, in the sense that they do not distort in
their appearances the reality which it is their function to mirror. That
they are 'good' images iu this sense is clearly implied at 50e. Here Plato,
in arguing that the Receptacle itself is characterless, says that' if it were
like anyone of the things that come in upon it, then, when things of
contrary or entirely different nature came, in receiving them it would
reproduce them badly, intrnding its own features alongside. Hence
that which is to receive in itself all kinds must be free from all characters.' 57 Thus plato assumes that sensible characteristics are 'well' reproduced in space as 'copies' of Forms. And this same assumption
governs the whole discussion of the structure and transformation of the
material elements (53c-6rc). Postulating a theory of the geometrical
structure of the particles of the material elements plato explains in the
light of this theory the principal varieties and compounds of the elements, showing the manner of the determination of the main distinctive characteristics of the material world as they are presented to the
senses. These characteristics are 'real' and clearly distinguishable features
of the sensible world. And when plato goes on, in 6rc-68d, to consider
in some detail particular characteristics perceived by the senses, he
assumes that the' appearance', in each case, is precisely determined by
I34
no word of our present discourse about the universe could ever have
been spoken had we never seen stars, Sun, and sky. Bnt as it is, the
sight of day and night, of months and the revolving years, of equinox
and solstice has caused the invention of number and bestowed on us
the notion ~f time and the study of the nature of the world; whence
we have derived all philosophy, than which no greater boon has ever
come or shall come to mortal man as a gift from heaven. 55
There are two points to be noted here. The first is the special importance
accorded to the movements of the heavenly bodies. It is Plato's view
that the rational ordering of the universe through the activity of the
cosmic soul is most conspicuously and most perfectly manifested in this
sphere." The second is that the refereuce to 'the study of the nature of
the world' in 47a is a clear reference back to 4Ie, where it is said that
'the natnre of the world' was revealed to the sonl before incarnation in
human form, and where the imagery used immediately invites comparison with the Phaedms and its doctrine of recollection. Thus the
function of sight, it would seem, is to prompt the recollection of a
an interaction between sense-organ and object, and that an exact corre-
lation always exists between each 'appearance' and particular definite
characteristics of the object of perception. Again at 42e-44d there is the
implication that all men have the capacity to interpret correctly what is
sensibly perceived. Here plato describes the confusion which reigns in
the soul when newly incarnate in the infant, one manifestation of this
being persistent error in the interpretation of what is perceived, resulting in false statements as to 'what is the same as this or different from
that' (44a). At this stage the soul is 'without intelligence'. But it is
immediately made clear that this stage is naturally outgrown and that
the capacity belongs to all men, when physical maturity is reached," to
'give their right names to what is different and what is the same', the
basis for the attainment of knowledge (44b-c). This capacity belongs to
the human soul in virtue of its composition from the same ingredients
as those of the cosmic soul (35a-37c, 4Id) 59 which, having a form of
existence intermediate between that of the Forms and that of the sensible world, is able to apprehend both of these worlds and to observe
the distinctions within them (37a-c). And it is as an 'intermediary' of
this kind that the soul, though admittedly less 'pure' in composition
than the cosmic soul itself (4Id), is able to use what is perceived as a
guide to the recovery of knowledge.
There is one other factor which must be considered in assessing the
efficacy of perception and the 'goodness' of the images which are its
objects. It is the factor of 'Necessity'. That which 'comes about of
Necessity' (47e-48a) is what comes about as the result of the intractability of the material medium in which soul works; mechanical and
unordered' causes' operative in this medium resist complete subordination to an intelligent and purposive' cause' working towards a good end
(46c-e). Fully to achieve this end would be to make the physical world
a perfectly ordered 'image' of the invisible 'real' world. Yet this concept of Necessity is never used by plato to suggest that the sensible
characteristics of the world are insufficiently determinate or insufficiently 'like' the Forms to be properly recognised and described. Consistently throughout the dialogue he assumes the opposite of this, as we
have seen. As far as its relevance to the problem of knowledge is concerned the restriction imposed by the factor of Necessity would appear
to lie (i) in the fact that the visible world never perfectly exemplifies
the systematic order of the world of Forms; the presence of what is
'disordered' or contingent is the mark of this imperfection: (ii) in the
fact that the human soul is associated with bodily sensations and desires
which cut off its direct insight into reality and make its recovery of
knowledge a long and indirect one through perception. It is not that
Necessity is responsible for a misleadingly inadequate presentation of
sensibles to the soul or necessarily for confusion in the soul's recognition of what is thus presented to it, but that it is a necessary liinitation
on the soul's approach to knowledge that this approach has to be made
through perception. And in the way in which he points to the moral
significance of this approach Plato implies that any confusion and misinterpretation are to be referred primarily to the uses to which the
individual puts his sensations and desires (,l2a-e, 44b-c; cf. 90a-d), To
137
use them rightly is to use them to further the study of' the nature of the
world', and th~ responsibility for this lies with the individnal (42 e).
What the T,maeus further shows us is the very wide extent of the
class of Forms with clear sensible images. According to the Timaeus the
physical world is ~ copy or iu:age of an eternal model which is a system
of Forms contammg every kind of thing found in the physical world
(3 0C-3 Ib). Moreover the physical world is a visible world (28a-c, 30b ,
etc.). Thus all mstances of all kinds of things within the four main
classes specified by Plato as making up the visible world will be sensible
Images of their corresponding Forms - 'the gods in the heaven'
(pl~ets, Earth, and fixed stars), birds, fishes, beasts, and men (3g e).
~gall1 the four materIal elements, earth, air, fire, and water, are sensible
Images of Forms of earth, air, fire, and water (5Ib-e). And it would
appear from the important passage 48e-52d, in which Plato attempts to
specIfy the nature of the sensible image in relation to the Forms and to
space, tha; all phy~ical a~d visible characteristics having extension in
space are senSible Images of Forms. Nor need we hesitate to identify
thIS class with the class of 'clear sensible images' recognised in the
Phaedrus and the Politicus. The only necessary condition suggested by
those two dialogues for. the 'clarity' of a sens,ible image is that the image
IS perceptIble through SIght, Sillce tlllS is the clearest' (enargestate) of the
senses.
But it has been argued further that the class of Forms with visible
images (= 'clear seflSible images) is in fact the class constituted by the
system of Forms wh,ch plato describes in 30d as a 'living Being' which
is intelligible (noeton), the model for the physical world, which is a
perceptible 'living being'. 'We have no warrant for identifying it (the
mtelllgible model) with the entire system of Forms, or with the Form
of the Good m the Republic, or for supposing that it inclndes the moral
Forms ?f dialectIC or the mathematical Forms, or even the Forms of the
four pnmary bodies.' It is 'the system of Forms that are, together with
the ForltlS of the primary bodies, relevant to a physical discourse, because they are the patterns of which the things we see or touch are senSible Images, coming to be and passing away in time and space. We are
not here concerned with the moral Forms, of which there are no sensible hnage~: 60
own view is that the 'intelligible Living Being' is
to be. Identified WIth the entire system of Forms. Plato's picturesque
descnptlOn of the system as an 'intelligible Living Being' is dictated by
Mr
K
139
his conception of it as the archetype of a physical world which owes its
characteristics and systematic form to the activity of the cosmic soul,
and the phrase itself cannot be taken to imply that the archetypal
system contains only certain kinds of Forms. In fact plato makes quite
clear that the physical world, as a system, exemplifies in its structure
and processes certain general characteristics which must, since the
physical world is a copy of an intelligible model, have their counterpart
in that model. Thus the physical world exemplifies beauty and goodness
(2ge-30b, 34b, 68e, 87c, 92C). In structure the particles of its material
elements are geometrical, and here again it is presumably the case that
the copy reflects its model. There are also other concepts of a very
general kind relevant to the interpretation of the physical world, e.g.
existence, sameness, and difference, and we must assume that the nl0del
contains these too as Forms (34b-37c). Indeed in 35a plato is clearly
treating them as Forms and at the same time as 'relevant to a physical
discourse'. Thus it would seem to be the case that according to the
Timaeus the physical world is fully explicable only if its model is the
whole system of Forms.
The model will, then, contain Forms of both perceptual and nonperceptual characteristics, or, to use the phraseology of the Phaedrus
and the Politicus, both Forms with 'clear sensible hllages' and Forms
without. And one particularly valuable contribution of the Timaeus is
that it elucidates the question of both the nature and the extent of the
class of clear sensible images, and in correcting, through its examination
of the sensible image, the faults in the criticisms of perception and its
objects made in the middle dialogues, it provides the theoretical ground
for the consistently favourable attitude towards perception which is, as
we have seen, characteristic of the late dialogues. It shows too that
Forms of non-perceptual characteristics, while they are not instantiated
in perception as Forms with visible images are, are yet contained in the
model of which the physical world is a 'copy'. This means in the first
place that these non-perceptual characteristics are applicable to what is
perceived and relevant to the interpretation of what is perceived.
According to the Theaetetus their non-perceptual character means that
the apprehension of them is entirely independent of perception. The
Timaeus does, however, show that, while non-perceptual characteristics
do not have the concrete visible instantiation which perceptual characteristics have, sight does serve to elicit the apprehension of them
(47a-b). But plato does not develop in any way in this dialogue the
question of the differences in the way in which knowledge is attained
of these two classes of Forms, or the question of the ways in which they
are related to one another. The principal distinction which he is concerned to make is between intelligible model and physical copy and his
distinction confirms what we have already seen to be indicated by the
other late dialogues so far considered - that he still assumeS that all
Forms arc separate non-sensible realities.
3. KNOWLEDGE AND BELIEF IN THE TIMAEUS
The Timaeus also shows that he still assumes an absolute distinction
between knowledge (which is of Forms) and belief (doxa, which is of
sensibles) (27d-29d, 5Id-52a). The same absolute distinction is found
also.in the Philebus (s8e-S9c). It is a distinction which gives rise to
serious difficulties in Plato's theory of knowledge; these difficulties
must now be considered.
As a preliminary it will be useful to review briefly what we have so
far tried to establish as the main features of Plato' s theory of knowledge
in the late dialogues. Two of its main features arc features belonging to
it from the time of the first introduction of the theory of Forms in the
Phaedo - (i) that knowledge is of separale non-sensible realities, the
FornlS, and (ii) that c0111ing to know these Forms is a process of recollecting what was previously known. But there are important refmements and developments in Plato's conception of how knowledge is to
be attained. The methods of the dialectician are now the methods of
collection and division, and appear to plato to offer a solution to
difficulties in his theory of knowledge raised by the Theaetetus. In particular he feels that they enable him to maintain the unity and the
incOlllposite nature of the Forms consistently with a recognition of their
complexity of structure. And with this recognition goes a recognition
of the corresponding complexity of the sensible 'copies' of the Forms,
whieh in itself suggests the possibility of an extensive use of perception
as an aid in the recovery of knowledge. plato attempts to show precisely how extensive this use of perception is (i) by a careful assessment
of the status and function of sensible' images'; (ii) by distinguishing two
main stages in acquiring knowledge of Form - (a) the initial realisation
140
of the Form in the understauding as the result of direct abstraction from
perceived instances or 'images'; (b) the analysis of the structure of the
Form by the methods of collection and division, directed either to
definition of the Form or to systematic classification; (iii) by distinguishing two main classes of Forms - Forms with visible images (=
clear sensible images) and Forms without such images. He further shows
that in attaining knowledge of Forms with visible images perception
is a valuable, indeed an apparently indispensable guide, throughout
both of the stages specified Ullder (ii). As for Forms without visible
images he acknowledges the comparative difficulty of analysis in these
cases, but he assumes that these Forms are sometimes analogous in
structure to Forms with visible images and hence he values the analysis
of these latter Forms as 'examples' (paradeigmata) for the analysis of the
former. For the rest the Timaeus appears to assume that sight does serve
to elicit the apprehension of Forms without visible images. Without
sight we should not be prompted to the initial recollection of them, but
we certainly do not apprehend them initially in the way in which Forms
with visible images are apprehended - by direct abstraction from perceived 'images'.
In the light of these developments iu Plato's theory let us now consider his conception of the distinction between belief and knowledge.
Knowledge is of the unchangeably real, the Forms; the object of belief
is the changing sensible world. Forms, says Plato, are apprehended by
thought conjoined with a rational account, while sensibles are apprehended by belief in conjUllction with perception, which is 'irrational'
or'tmreasoning' (alagon) (28a-c). This same term - alagon - is used in
5 I e to describe, not perception, but 'true belief' itself, which is contrasted, as 'irrational' (i.e. incapable of yielding any rational accoUllt of
its object), with knowledge, a form of apprehension which can always
provide a true accoUllt (logos). And again in this later passage the distinction between belief and knowledge is associated with the distinction
between sensibles and Forms as their respective objects. Finally, on the
basis of these distinctions, plato makes one further distinction. He says
(29b-c) that 'discourses' 61 are akin in character to that which they
expound; thns, while discourses about what is 'abiding and stable and
apprehensible by thought' will themselves be abiding and Ullchangeable, discourses about what is merely a likeness or copy of the abiding
and stable will themselves be only 'likely' (eik8s). It follows that his
141
own discourse about the nature of the physical world in the Timaeus
will be merely a 'likely story' (29d)."
. This suggests that, in thus relating the merely likely status ofhis, and
mdeed any, physical discourse to the fact that its object is a sensible
'likenes~' or copy, plato is afftrming that nothing propounded in physical
theory 1S ever exactly or certainly true, and is attributing this deficiency
to the fact that physical theories are 'discourses' about a physical world
which is an imperfect copy of a non-sensible intelligible model and
never in any part exactly or perfectly conforms to the standard constituted by that model. And since in the Timaeus plato is using doxa in
the speCIalIsed sense, which indicates that his distinction between knowledg~ .and doxa is intended to be a distinction between a priori and
empI~Ical knowledge, it is tempting to elaborate the significance of the
descnptIOn of physical theory as merely 'likely' in terms of modern
conceptions of the distinction between a priori and empirical knowledge. Thus it seems plausible to argue that Plato's point is that in cosmology and biology and 'pure physics itself it is impossible to be
rIgorously exact and arrive at the finality which is possible in 'absolutely pure mathematics', since in each case the 'account' is of the
empirically existent and must introduce empirical premisses. Interpreted in this way Plato's distinction between knowledge and belief
:ests on a distinction between the necessary and the contingent. What
IS known1S, necessarily true, not dependent for its truth on experience
of the phYSIcal world and free from any condition that it should have
apphcatIOn to the physical world; what is 'believed' is contingent, for
the 'matter' o~fhysics is contingent, as any empirically existent 'matter'
IS contmgent. But can this type of mterpretation be made consistent
with Plato's conception of (i) the relation between the Form and its
sensible 'images', and, on a more comprehensive scale, between the
syste~ of Forms as a 'model' and the derivatively 'real' system of the
phys~cal w~rld, a 'copy' of that model; (ii) the part played by perceptIon m attammg knowledge of Form?
It is first necessary to consider what the differences are between the
procedure of the philosopher and that of the physicist which explain
why the first IS able to attain knowledge and the second is necessarily
restncted to the attainmentof'belief', although each starts from experience of a common physical world which is an 'image' of an eternal
world of Forms. The procedure of the philosopher will presumably be
142
the employment of the methods of collection and division for the purposes of definition and classification. This will enable him, with such
assistance from perception of visible 'images' of the Forms as we have
already indicated, to attain knowledge of Forms and of the system of
Forms as a whole. That the system of Forms and, derivatively, the
system of the physical world are envisaged in the Timaeus itself to be of
a kind which makes the methods of collection and division appropriate
to their explication is clearly indicated by thelanguage of 30C-3 la. Now
within this field of specifically 'philosophical' interpretation it is not
difficult to specify the nature of the distinction between knowledge and
beliefin the non-specialised sense, but it is extremely difficult to specify
the nature of the distinction between knowledge and belief in that
specialised sense which assumes that its objects are exclusively sensibles
and never Forms.
First let us consider the former distinction. Here belief is regularly
distinguished from knowledge by its inability to 'give an account'
which will substantiate the truth of what is believed to be the case. In
the Meno and the Theaetetus plato discusses, iudependently of the theory
of Forms and without any suggestion that there is a difference in kind
between the objects of knowledge and those of belief, the nature of the
'account' which will convert belief to knowledge. Within the theory
of Forms the 'account' is specifiable in terms of those methods of dialectic which will explicate the structure of the Form and its relations to
other Forms through definition and classification. In the later dialogues
tllese methods are the methods of collection and division. A passage in
the Politicus is instructive on the question of the status of belief in the
non-specialised sense. At 277d-279a, where plato is discussing the
nature of 'exatnples' (paradeigmata), there are several references to
'right belief', the context making it clear that 'belief' is used in each case
in a non-specialised sense. 'Right belief' is used not only for correct
identification but also for the recognition of similarities or analogies in
cases where what has been correctly identified in simpler contexts is
enconntered in contexts of a radically different and more complex kind.
Thus the correct identification of the elements of weaving and the
analysis of its structure may point by analogy to the recognition of the
elements and structure of the art of statesmanship. The existence and
recognition of sueh analogies are assumed to be of great value to the
dialectician, and the possible use of them in reasoning to be extensive
143
(27Sc-d). And what the passage 277d-279a suggests, taken in conjunction with the subsequent description of the methods of collection and
division and the discussion of'visiblelikenesses' (28sa-286b), is that the
dialectician attains knowledge only when analysis has reached a point
where full explicit definition of the Form in question is possible, and
that at all the preceding stages of the analysis of the Form through
identification, comparison and discrimination ofits 'parts' he has belie£
Thus one will be able to 'give an account' (286a) of a Form, and hence
to know it, only when one is able to defme it. This is, of course, only
one particular specification of 'account', and the lnore conlprehensive
the dialectician's aims in systematic classification the more comprehensive will be the 'account' which yields knowledge. There are, in fact,
varying degrees or levels of comprehension which can, for Plato, be
ranked as knowledge; in the final 'acconnt' knowledge will be the comprehension of all Forms within a single system. In relation to knowledge, belief will vary in its scope with the differing levels of comprehension ranked as knowledge. And its objects will be the same as those
of knowledge - the Forms. It is not suggested in any way in the Politicus
that knowledge and right belief differ in the kind of objects to which
they are directed. Nor does Plato ever suggest, when distinguishing
knowledge from belief in the non-specialised sense, that they differ in
this respect. And in the light of what we have seen to be the scope of
beliefin relation to knowledge, it is easy to see further that the assumption that belief is a level of comprehension of Forms is entirely consistent with what Plato has said elsewhere in the later dialogues about
how we come to know the Forms. Thus Plato's descriptions of the
process of abstraction whereby the Form is initially realised in the
understanding (Phaedrtls 249b-c; c£ Politicus 28 sa-b) show that he is
still thinking of the distinction between sensation and a conceptual level
of apprehension as one between sensation and a level of apprehension
directed to Forms. And this level of apprehension, we must remember,
is assumed to be prior to any explicit conceptual analysis, and to represent a lower level than those attained in the further analysis. A jortiori,
therefore, belief is directed to Forms. Plato, then, is able, consistently
with his theory of Forms, to maintain the distinction between knowledge and belief in the non-specialised sense first introduced in the
Meno.
But can he, with equal consistency, continue to maintain a distinction
I44
between knowledge and belief in the specialised sense? We have previously argued that the intelligible 'model' of which the physical world
is a 'copy' is to be identified with the entire system of Forms. Now
plato emphasises in the Timaeus that the system of the world of Forms
and the systematically ordered physical world which is a 'copy' of it
are each unique (3 ra-b). Thus the interpretation of the system of Forms
is at the same time a deftnitive interpretation of it as a theory about the
physical world in so far as that world is a 'copy' of the 'model' constituted by th~ Forms. And though Plato certainly, in stressing the
independent reality of the world of Forms, appear~ to. assume that the
system of Forms is free from conditions which reqmre Its mterpretatlOn
to be limited by its reference to a world outSlde the system, hlS assumption that the systematically ordered world of Forms and the systemaucally ordered physical world are each unique ~d at th~ same Ume are
related as 'model' to 'copy' does in effect make It lmpoSSlble to construe
the distinction between the philosopher's and the physicist's interpretations in terms of a distinction between necessary and contingent truths.
The sphere of the contingent is, in fact, for plato the sphere of the
operation in the physical world of what he calls NeceSSlty, a term
strikingly paradoxical if construed in terms of modern conceptlons of
the distinction between necessity and contingency but Ul fact associated
by plato with what is erratic and disorderly, wi~h what acts a~ a con-
straint on the systematising activity of the cosmIC soul. And smce the
sphere of the contingent is thus restricted and since th~ phY~lcal world,
in so far as it is systematically ordered, is thus far a copy of the llltelligible 'model' of the world of Forms, it follows for plato tha~ the
interpretation of the order of the physical world in ~erms of Forms 15 a~
interpretation which will be necessarily true. Th~s It beco',"-es ,mmed,ately implausible to suggest that, whereas the phIlosopher s lllterpr~t~
tion issues in knowledge and in what is necessanly true, the phySlclSt s
interpretation is restricted exclusively to the contingent. What ,,:ust be
recognised is that Plato's distinction between necessary and. conu~ge~t
truth canuot be applied in the way in which the modern dlStm~uon 15
applied. plato does not indeed anywhere make a clear d1St11lctlon between necessary and contingent truth. However, I think that he wou:d
assume to be necessarily true what is established by the philosopher, III
explicating the system· of the world of Forms, through the cor~ect
application of what he (Plato) affirms to be specifically philosophical
145
methods. And he wonld assume to be merely contingently true anything which falls outside the scope of the philosopher's analysis. Thus,
as we have seen, all the order ofthe physical world is derivative from an
intelligible 'model' of Forms and hence is amenable to the philosopher's
analysis. All that is disorderly and erratic is not so amenable, and is to
be thought of as 'contingent'. The important respect in which this distinction between necessary and contingent differs from the modern
distinctioll which we have discussed is that it does not entail that the
content of physical theory is contingent.
In the light of this distinction we must now consider Plato's assertion
that any 'discourse' about the physical world cannevcr be more than
a 'likely story'. Consistently with his conception of the model-copy
relation between Forms and physical world and with his conception of
the distinction between necessary and contingent Plato can maintain
that the results of the philosopher's analysis are necessarily true but are
never in fact perfectly realised in an imperfectly ordered world. Yet
consistently with these conceptions he cannot maintain also that the
resnlts of the investigations of the physical scientist camlOt be necessarily
true because they are interpretations of an imperfectly ordered world,
though this is what he seems to be trying to maintain in the Timae"s.
For it is difficnlt to see why Plato shonld assume that the physical
scientist, starting as the philosopher does from experience of a visible
copy of the model constituted by the Forms, is inevitably debarred
from that privileged rype of interpretation which alone yields knowledge and from which Plato attempts to exclude everyone except the
philosopher. Thus it is natural to ask why the physical scientist is not
prompted by sensible 'likenesses' to a recognition of Forms, and why it
is not possible that in the generalisations which he makes and the
theories which he formulates he should never be recognising or 'recollecting' the nature of Forms and the relations between them. The
difficulty of Plato's position becomes an acute one as the result of his
reassessment of the cognitive value of sensibles in the later dialogues. In
the middle dialogues it had been possible, at the cost of some inconsistency with the theory of recollection, to keep 'belief' sharply distinct
from knowledge by severely disparaging the cognitive value of perception and by assuming that the philosopher's analysis was independent of
perception. It could there be maintained that any proposition which had
its basis in perception was either false or at most was no more true than
other propositions which contradicted it or were inconsistent with it,
and that perception was useless either as a means to the initial realisation
of the Form in the understanding or as a guide in the subsequent
analysis of the Form. In the later dialogues, however, perception is no
longer considered useless in these ways, and the reassessment of perception, coupled with the assumption of a parallelism in structure between the systematic order of the world of Forms and the systematic
order of the physical world, raising as it does the problem of keeping
'belief' (in the specialised sense which assumes that its objects are exclusively sensibles) distinct from knowledge, raises thereby the problem
of maintaining a further radical distinction, based on the distinction
between 'belief' and knowledge - the distinction between the theories
of the physical scientist and those of the philosopher. We have seen
already the patent implausibility of the suggestion that any pronouncement of the physicist is to be relegated to the realm of contingent statements. For it is patently implausible to suggest, given Plato's conception
of the distinction between the necessary and the contingent, that the
physicist, confronted in experience with a visible world in which every
element of order reflects an intelligible' model', should be so systematically misled that his theories invariably fail to reflect accurately any part
of that order. And this is equivalent to saying that it is patently implausible to suggest that the physicist should be so systematically lnisled
that in his theories he invariably fails to gain insight into the intelligible
order of the Forms and is restricted to the empiricallevd of 'belief'.
The conclusion must be that Plato has failed adequately to distinguish the procedures of the philosopher and the physical scientist in a
way which will justify his ascription of knowledge and certainty to the
first, 'belief' and probability to the second. Thus when he describes perception and 'true belief' as 'irrational' (alogon) or incapable of yielding
a rational 'account', we have to interpret 'account' strictly as the
privileged type of account reserved for the philosopher. And we find
that Plato gives no proper reason why one particular method or
'account' is privileged (there is only the assumption that the structure
of the intelligible world is such that it can be explicated by no other
'account' than this), and no properreason why all theories which aim to
iuterpret the physical world other than the philosopher's theories are
necessarily limited to 'belief' and probability. The inadequacy of rIato' s
doctrine here is, quite clearly, the inadequacy of the theory of Forms as
I47
the basis of a distinction between a priori and empirical knowledge. It
was a consistent development in his theory of recollection that plato
should recognise the possibility of a systematic use of perception as a
guide to the analysis of Forms, and should recognise the important
status of sensibles as 'images' of Forms. But a result of the development
of his theory of knowledge in these directions is that the correspondence
between the system of Forms and its visible' copy', the physical world,
becomes at once too close and too wide to be used as a satisfactory basis
for a distinction between a priori and empirical knowledge, or, in
Plato's terminology, between knowledge and 'belief'. The appeal to a
privileged method of analysis as a specifically philosophical method is
in itself inadequate for the purposes of this distinction, since its practice
assumes the close and wide correspondence we have noted. A much
more satisfactory distinction would have been possible if plato had
developed further the distinction implied in the Theaetetus between
a priori and a posteriori concepts. For this might well have led him to
realise, from a consideration of different kinds of Forms and different
modes of 'combination' of them, the need to reformulate the principle
whereby Forms are designated as 'separate' ina way which would allow
the distinction between a priori and empirical to be specified within the
world of Forms. But since he fails to reformulate the principle in any
such way his theory of Forms continues to be an inadequate basis for the
absolute distinction which he makes between knowledge and 'belief'.
This absolute distinction, it is to be noted, is found in the Phi/ebus as
well as in the Timaetls, and tllere is no evidence to show that plato ever
abandoned it.
Is it the case, then, that the distinction between Forms and sensibles
and the corresponding distinction between knowledge and 'belief',
coupled with the assumption that there is a privileged philosophical
method of analysis of Forms, constitute Plato's final answer to the
problem of the distinction between a priori and empirical knowledge?
The possibility that he did, in developments in his philosophy of
mathematics in the latest phase oEhis thought, give a more satisfactory
answer will be considered in a final chapter. But before this it is
important to consider further, from a review of the discussion in the
Sophist, the difficulty of using the theory of Forms as the basis of any
answer.
4.
aJ
THE SOPHIST'S ACCOUNT OF STATEMENT AND BELIEF
Statement
The concern of the Sophist is to establish the possibility of false statement and false belief. Plato assumes that the main difficulty involved
in false statement and belief is the apparent contradiction in stating or
believing that 'what is not is' or that 'what is is not' (240d-24Ib).
Hence he considers that in order to establish the possibility of false
statement and false belief he must show that it is possible to assert
without contradiction that 'what is not' is in some respect (kata ti) and
that 'what is' is not in some respect (24Id). And to show that this is
possible is to contradict Parmenides' pronouncement that it is impossible
to prove that 'things that are not are' (237a).
That plato considered the problem of false statement and belief to
be one which raised important metaphysical issues is suggested by his
association of false statement with 'appearance' (as opposed to reality:
236e) and with the problem of the existence of 'images' of reality
(240a-c), as well as by his assumption that a resolution of the problems
involved in false statement and belief demands a critical review of
different types of metaphysical theory (242b ff.). And this suggests that
his elucidation of the problems raised by false statement and belief will
serve to elucidate problems in his own metaphysical theory. plato does
not, however, dr2.w any explicit conclusions for his metaphysical theory
from his substantiation of the thesis that false statement and belief
'exist'. Nor is it easy to see for the most part what he means to be
implied for his theory by the arguments which he uses in support of
the thesis. There is, certainly, no difficulty in seeing that his main
argument is relevant in one respect to his metaphysical doctrine. Thus
his elucidation of the significance of is not as equivalent to is other than
in negative statements of the type 'x is not white' (257b-c) can be
used to guard against one type of objection to his theory of Forms,
the objection that to ascribe 'reality' to Forms but not to 'images' of
Forms is to exclude the existence of 'images' since they are not 'real'.
And the fact that he applies his elucidation of negative statements to
the explanation of false statements (260b ff.), together with the fact
that he links false statements with 'images' of reality, might be taken
as an indication that he did think of his argument as an answer to
such an objection.
149
Yet the malUler of Plato's association offalse statelnents with 'images'
of reality is such that it would be wrong to seek in it any particular
metaphysical implication. Indeed, his application of the distinction
between deceptive and non-deceptive 'images' (235a-236c), introduced
to mark the distinction between false and true statements is so inconsistent that the language of imagery eventually beco';es merely
confusmg. Thus the sophist's art, conceived as the USing of false statements to induce false belief, is initially said to have as its tools deceptive
verbal images (eid8la or phantasmata), merely apparent likenesses as
opposed t~ genuine or 'real' likenesses (eikones or mim~mata). Merely
apparent hkenesses are, then, £tlse statements, and genuine likenesses
are true statements. That both true and false statements are described
as 'images' or .'likenes~es' is consistent with what Plato has already said
about verbal Images 11l the Cratylus - they are 'images' or symbolic
representations of the 'reality' to which they refer and are themselves
other than this 'reality'. And their 'existence' is assumed to depend on
their havrng reference to some 'reality'. Hence Plato assumes that to
show that it is possible without contradiction to assert what is false
is to demonstrate at the same time that deceptive verbal images (eid8la
?~ phamasmata) exist, on the ground that they have a reference to 'what
IS even though they express what is not the case. But Plato's use of
the term 'inlage' as verbal image is not, as is clear from its use in the
Cratylus, associated with a particular conception of the nature of the
're~tyj :vhich is imaged, and hence differs from his use of 'image' as
senSible Image, which has a special significance within the theory of
For.ms. We cannot, therefore, infer anything about the 'reality' of
whic~ true and false ~tatements are 'images' from his use of 'image' to
descnbe statements m the Sophist. It is true (as we saw in the last
chapter) that in the Republic his references to images are often to verbal
l~:ge~J and that. ~ these cases he treats verbal images not only as
eidola ill the SophISt s sense, i.e. as essentially deceptive or false images,
~ut . at t~e. same tim~ ~s empirical propositions, expressing what is
believed, ill the speCialised sense of that word. Here the deceptiveness
of the Image as an eid8lon is attributed to the fact that its reference is to
a particular kind of object which is other than 'real' objects, the Forms.
It IS difficult to say ho,: the Sophist's distinction between deceptive and
~on-decepuve verbal Images would be applied in the Republic consistently With the Republic's conception of eid8la. It is questionable
150
whether the Republic would allow what seems to be the most natural
application - using mim~mata (non-deceptive verbal images) for true
empirical propositions; possibly mim~mata would be used for a priori
propositions, having Forms as their reference. Yet though the Republic's
references to verbal images show that their status as images is closely
associated with the fact that their reference is to sensible images there
is no ground for reading into the Sophist a sense of eidSlon similar to
that found in the Republic. That plato in the Sophist attaches no particular metaphysical significance to the term is indicated by his indifference to maintaining the distinction between eidSla or phantasmata
(for false statements) and eikones or mim~mata (for true stateulents)
after its initial introduction. He subsequently uses all four terms indiscriminately to describe false statements or false beliefs (239d, 240b,
241 e, 264d). We must, then, dissociate the language of imagery in the
Sophist from the theory of Forms; the language in itself tells us nothing
about Plato's conception of the 'reality' which is the reference of both
true or false statements; more particularly it does not imply in any
way a distinction in kind between the objects of false statement and
the objects of true statement.
If we turn, however, to the argument of 25 Ia-26ob we find some
positive indication as to the sort of 'reality' of which true and false
statements are 'images'. Here plato introduces, as a principle essential
to his demonstration that 'what is' is not in some sense and that 'what
is not' is, the principle that Kinds (gen!') or Forms (dd!') are capable of
'combination' or 'communication' with one another. And at the conclnsion of his argument he insists that if 'combination' was not possible
and each Form was isolated from every other, i.e. not related in any
way to any other, then all 'discourse' (logos) would be impossible. This
does not imply that any statement is an expression of a particular
'combination' of Forms, since (i) 'combination' is possible only between
compatibles (thus Plato's principle is not that any Form is capable of
'combination' with any other; he recognises that some Forms are incompatible with one another and hence cannot 'combine'; 25 Id-2sze);
(ii) there are (false) statements which do not express a 'combination' of
Forms, but rclate incompatibles. And it is to be noted that at 25ge
Plato asserts that it is the 'weaving together' of Forms (symplok~) which
makes discourse possible; and since he goes on to specify the 'weaving
together' of noun with verb as a necessary condition of a minimum
15 1
statement that can be true or false (26Id-262e) and, further, gives as
an illustration of such 'weaving together' a false statement which relates
incompatibles (263a-d), it becomes clear not only that the 'weaving
together' of Forms includes the weaving together of both compatibles
and incompatibles, but that any significant statement, whether true or
false, is an instance of a 'weaving together' of Forms. plato is not, of
course, saying that the principles of compatibility and incompatibility
between Forms are sufficient to determine the truth or falsity of statements, but only that they govern the possibility or impossibility of the
truth of statements. And, more generally, he is saying that the intclligibility of any discourse depends on acceptance of the principle that
Forms are related to each other in certain ways; he shows in the
passage 25Ia-26ob that the very general relations of compatibility,
incompatibility, and implication are necessarily presupposed in the
application by the philosopher of specific methods of analysis (253 d- e)
of the system of Forms.
If, then, any significant statement is an instance of a 'weaving
together' of Forms, are we to assume that by Forms he means separate,
archetypal Forms in the sense initially specified in the Phaedo? The
Sophist by itself certainly does not allow us to say this. Its principal
arguments do not demand such a postulate and to substitute 'concepts'
for Kinds (gen!') or Forms (eid!') in interpreting the arguments does
not introduce any difficulties. But this does not constitute an argument
for the view that plato is no longer thinking of Forms as non-sensible
separate realities. There are, I think, very good grounds for assuming
that he is thinking of Forms in that Sense in the Sophist. The passage
in which the 'friends of Forms' are criticised (248a-249d)64 shows at
least that Plato assumes the fixity and immobility of the objects of
knowledge (249b-c). And the fact that gell!' and eid~ are used as
synonyms cannot be taken to imply that he is now thinking only in
terms of the analysis of class concepts and their relations without the
assumption of a transcendent reality. The terminology of 'Kinds' in
reference to Forms is common from the Phaedrus onwards. And in
the Phaedrus and later it is found together with the assumption of a
transcendent reality constituted by the Forms or Kinds. Moreover our
earlier discussion ill this chapter has shown that in the Phaedrus, Politicus,
Timaeus, and Philebus the doctrine of transcendent Forms, as well as
the doctrine of recollection, is maintained. And if this is the case for
dialogues of the late period which precede and follow the Sophist it is
reasonable to assume that it is the case for the Sophist itsel£ There is,
finally, the point that in introducing in the Sophist the principle of the
itself), and to predicate Difference is to deny its identity with something ehe. At the same time he shows that, since these predicates can
be applied to any Form, it is possible both to assert the existence of
any For~ an.d to deny its identity with any other Form, e.g. to say
that M~tlOn IS and to say that Motion is Itot Rest (254d-257a); and he
eInphasIses that In thIS sense is /lot = is d!fferel1t from and does not = is
colltrary to what exists (257b-258c). Hence it is possible to assert without
152
'combination' or 'intercommunion' of Forms plato is taking up a
problem previously raised by the Parl1lenides (I29d-I30a) about the
transcendent Forms - whether Forms themselves such as Likeness and
Unlikeness, Plurality and Unity, Rest and Motion can be 'mixed with
and separated from each other'. And there is nothing in his subseqnent
explication and illustration of the principle to suggest that to answer
the Parmenides' question about the transcendent Forms involves an
abandonment of their transcendence.
Plato's illustration of the principle takes the form of an examination
of the relations which exist between five of the greatest or most
inlportant FornlS - Motion, Rest, Being, Sameness, alld Difference.
As a preliminary to this examination he introduces an important
distinction. Using the analogy of the relation of vowels to other
letters of the alphabet when letters are combined to make words,
Plato says that some Forms are predicable of all Forms and that without
these Forms no 'combination' of Forms with one- another is possible,
nor any distinction of one Form from another. Earlier in the Theaetetus
(18 sa-e) he had specified existence, sameness, and difference as examples
of common terms which apply to everything. The principle of selection
of these Forms is, however, not the same in the Sophist as it was in the
Theaetetus, where the definition of 'independent activity of mind'
allowed a wider class of 'common characteristics' than the class of
Forms which make possible the combination of Forms with one
another and their 'separation' from one another. In the Sophist plato
is concerned only with those 'common characteristics' in terms of
which he will be able to distinguish certain general forms of combination or separation. That he gives only a limited analysis of these Forms
is attributable largely to the fact that his particular purpose here is the
restricted one of showing that 'what is noe is in some sense and that
'what is' is not in some sense. Taking Being, Sameness, and Difference
as the three Forms which are able to combine and to separate all other
Forms, he shows, by conjoining each of them in turn in statements
with Motion and/or Rest, that to predicate Being of anything is to
assert its existence, to predicate Sameness is to assert its identity with
itself (he limits his examples to assertions that a thing is the same as
I53
contradiction that 'what is not is' and that 'what is is not', and thus to
refute Parmenides' dictum (25 8c- e).
Plato's analysis here does clearly distinguish between the existential
and non~existential use of 'is'. A~ld since in 254d-257a Plato appears
to treat IS not throughout as eqmvalent to 'is not identical with' one
might argue that he is distinguishing between the existential 'is' and
the 'is' which marks identity. Yet his recognition of the 'is' of identity
does not appear to be a recognition which allows him to distinguish
It from other non-existen;ial uses. In 257b-258c he seems to be thinking
of statements of the type apes are not beautiful' Or 'mice are notlarge';
he. does not distinguish this 'is' from the 'is' which marks identity, and
thIS suggests that he thinks melevant, or has failed to see, the distinction
between the 'is' of identity and the 'is' as copula. 65 The analysis is,
however, sufficient for his particular purpose.
It is iu:portant to note that plato considered that the principles of
combmatlOn and separatlOn of Forms which he elucidates were the
principles of the science of dialectic, described in 253d-e as the methods
of collection and division of Kinds or Forms, and that it was for this
:eason,.as w~ll as for its applicability to the particular problem of how
what 15 not can be, that he thought it important to assert the general
pnncIple that Forms stand to one another in certain relations which
combine and distinguish them. It is clear from his description of the
philosopher's science of dialectic that his ideal is still that of the explicatlOn of the structure of the world of Forms as a hierarchical system by
the claSSIficatory methods of collection and division, and that knowledge .of the Forms of~eing, Sameness, and Difference is highly valued
e~sen:,ally because It YIelds understanding of those principles of combmatlon and separation of Forms which are fundamental to the
methods of collection and division. Thns we must recognise that the
mterest 111 the form of particular statements shown in Plato's analysis
of these Forms and in his selection of them as three of 'the greatest'
L
154
Forms (in that they make possible the combination and separation of
Forms) is subservient to the ideal of knowledge through defmition
and classiftcation of Forms which has dominated his theory of knowledge from the Fhaedrus onwards. Hence it is misleading to say that, in
distinguishing here between formal and non-formal concepts, Plato's
primary concern is with 'propositional forms'. More particularly, it is
not the caSe that Plato is arguing that Being, Sameness, and Difference
are 'not terms in propositions we think, but the forms of the combinations of those elements into propositions'. 66 These are substantive
Forms, represented as 'elements' in a proposition equally with the
other Forms contained in it. Indeed plato emphasises (258b-c) that
Not-Being is a single substantive Form, and as such it is an element
or 'part' in a complex of other Forms which are 'parts' of the logos or
statement in which it is itself contained. And this is characteristic of
his approach to the problem of the complexity of statements and
judgements, which is always analogous to his approach to the problem
of the complexity of the Forms themselves. He treats the complex
statement as separable into 'parts' each of which designates a 'part' of
reality, and his analysis of each 'part' and his elucidation of its relations
to other 'parts' are always guided by his conception of a system of
substantive (realities' hierarchically organised.
That this is so is conftrmed by the manner of his analysis of false
statements. Having shown, in the passage we have discussed above, that
it is possible to assert without contradiction that 'what is not is' and
'what is is not', he applies this conclusion to the problem of false
statement and false belie£ Its possible relevance to this problem is
immediately suggested by the fact that to believe or to state what is
false is to state or believe that something is the case which is not the
case, or to state or believe that something is not the case which is the
case. But before he examines the problem Plato asserts that only when
words are 'fitted together' in a certain way do they express a significant
statement. A string of names or of verbs is nonsense, and does not
constitute a statement at all. But combining a name with a verb yields
a significant statement, the simplest type of statement (26Id-262c). He
says further that statements are significant in a way in which names by
themselves are not. They' do not merely name something but get you
somewhere' (262d). This certainly suggests that plato is about to make
the relation of statements to facts the basis of his explication of false
ISS
statement, and not to analyse false statement in terms of the particular
'realities' designated by the elements of the statement taken separately,
Thus it suggests an approach to the question of the distinction between
truth and falsity which is not dominated by a conception of knowledge
in terms of definition of particular Forms or of the classiftcation of them
within a hierarchical scheme. Yet we find that the manner of his
demonstration that false statements 'exist' as 'images of real things'
is quite out of keeping with the apparent tenor of his preliminary
remarks.
His demonstration is directed against the argument that any statement or beliefis an assertion of'something' or a belief about 'something',
and that to asSert or believe what is 110t is to assert or believe nothing,
and hence is not to be ranked as a statement or belief; thus there are
no false statements or beliefs, since stating or believing what is false is
stating or believing what is not. 67 plato takes as his example of false
statement the statement 'Theaetetus (who is present and is correctly
identified) flies', when it is the case that Theaetetus is sitting. He then
says that this statement, though false, is of or about 'something', since it
refers to Theaetetus, and that, though it states about Theaetetus 'what
is not', it does so only ill the sense of what is different from 'what is'
in this particular case and not in the sense of what does not exist at
all (263a-d). Thus Plato, assuming that false statements are shown to
'exist' as 'images of real things' once they are shown to refer to some
'reality', to 'what is', considers that he has achieved his purpose if he
takes subject and predicate separately and shows that each refers to
'what is', But it is no answer to the objection that false Statements
are about 'nothing' to select as the subject of the false statement
analysed an individual person actually present and correctly identified
and then to say that this is a false statement and it is about'something' .
plato appears in this respect to be creating an unfair advantage for his
own argument by his selection of this statement rather than e.g. the
statement 'Pericles is sitting here', Nor is his application of the result
of his previous examination of negative statements to the analysis of
the predicate 'flies' a very happy one. He had previously shown that
to assert that 'Motion is not Rest' or 'mice are not large' is not to assert
that Motion or mice do not exist. He now suggests that the falsity of
ascribing 'flying' to Theaetetus when he is in fact sitting may be
expressed in the form of the negative statement 'Flying is 1101 what
156
is the case here and now in respect of Theaetetus', and that this state~
ment does not imply that 'flying' does not exist. He asserts in fact,that
'flying' is 'a thing that exists'. But what he says here about the predicate
gives no more satisfactory answer to the ObJcctlOn that. false statements
are about 'nothing' than what he had said about the subject, The proper
application of the is/is not antithesis is not to isolated elements of the
statements and their references, but to the facts which the statements
express, and the question to be asked in terms of this antithesis is
whether there is or is not a fact to which the statement corresponds.
It is clear from the exposition in the Etlthydemtls (283e-284c, 285<1-286c)
of the thesis that false statement is impossible that this thesis assumes
that statements are expressions or descriptions of facts (pragmata) and
that a false statement is an expression of 'what is not a fact at all', of
'what is not' [a 'fact' (pragma) being 'what is' (to on)]. To Plato's
argument the advocates of this thesis could readily reply that a faJse
statement is simply a statement of wh7t IS not the case, and that, to
argue that 'what is not the case' means what
IS
other than the cas~
1S
not to show the possibility of there being a fact (pragma) or something
which is (to on) as the reference of the state~ent but to exclude such
a possibility, For what is other than the case IS what IS other tha~ what
is the case, and it is impossible for 'what
IS
other than what
IS
to be
ranked as 'what is' at all. Hence their claim that faJse statements
express 'what is not' is rightly construed if the 'is' is ~aken existenti~lly,
and the claim itself is rightly made. To take subject and predicate
separately and to construe 'what is ~~t' in a non~exist~ntial sense in
application to these is not only to nusmterpret their claim but also to
misinterpret the nature of false statements.
Now this wonld be a sound rejoinder to Plato's argument. The
mistake of those who argued that false statements were impossible was
not in their analysis of faJse statements as expressions of 'what is not'
but iu their inference from this that ±alse statements are Impossible aud
that all statements are true. Plato's mistake in attempting to refute thiS
argument was that he attacked it at the point where it was right and
neglected to attack it at the point where it was wrong. Heassumed that
he could show that false statements' exist' only by showmg that they
are 'images of things that are' (264d) and he avoided the problem that
there is no fact to which the false statement corresponds by Ignormg It,
for he was thinking throughout his analysis not in terms of facts but
157
in terms of the 'real' objects designated by the constituent 'parts' of the
statement. This recalls the analysis of false belief in the Theaetetus, which
similarly takes as its starting-point arguments for the impossibility of
false belief and false statement and attempts to explain false belief as a
confusing of one 'reaJ' thing with another 'real' thing, within the field
of things which are in some sense known; it eventually abandons the
examination of false belief in order to concentrate on the problem of
what it is to know a particnlar object. Subsequently, as we have seen,
plato felt that the methods of collection and division, directed to the
systematic classification and definition of Forms, provided a solution
to this problem as it Was raised by the Theaetetus, enabling his theory of
knowledge to maintain the unity and incomposite nature of the Forms
as the objects of knowledge consistently with the recognition of their
complexity of structure. And we have now seen that in his analysis of
faJse statement in the Sophist he overlooks what seems to be the obvious
application of the is/is not antithesis to true and false statements, and
continues to centre his attention on the particular 'realities' designated
by the different constituent 'parts' of the statement.
He does, however, recognise that any statement is an example of a
'weaving together' of Forms; and this entails that 'Theaetetus sits' and
'Theaetetus flies' are examples of a 'weaving together' of Forms. What,
then, is the significance of this for his analysis of false statement? Plato
has already suggested, in expressing in the form of a negative statement
his account of the falsity of applying the predicate 'flies', that he is
thinking of the relation of incompatibility between this Form and other
Forms. Thus 'flying' and 'sitting' are for him here incompatibles and
mutually exclusive. But it is not only this which is suggested. Though
his demonstration that false statements 'exist' as 'images of real things'
is made possible only by taking subject and predicate separately and
showing that they have a 'real' reference, it is indicated at the same time
that it is the correctness of the connexion of predicate with subject
which distingnishes the true statement from the false. And if both
statements are instances of a 'weaving together' of Forms we must
assume that it is in terms of relations between Forms that plato intends
this connexion to be interpreted, Hence it has been plausibly suggested
that 'the judgement that "Theaetetus is flying" is false because it cannot
be reconciled witl, the definition of man, and attaches to him a m~ Oil
(what is not) - a quality from the wrong side of the Division'."
IS8
PLATO'S THEO'RY' OF KNOWLEDGE
Certainly as an instance of a 'weaving together' of Forms the statel,:ent
is rightly construed as asserting a connexion between Man and Flymg.
And it is some support for the view that plato is treating the statemeut
as false because it implicitly asserts the compatibility of what are in fact
incompatibles that the previous discussion of the 'intercommunion' of
Forms has given prominence to incompatibility between Forms and
indicated the importance of this and other very general relations for
the philosophical method of division. It is significant, too, I think, in
considering Plato's selection of 'flies' as predicate, that later in the
Politicus he divides animals into walking and flying animals (264e,
266e). There is, finally, the obvious implansibility of assuming that
plato envisages that the false belief occurs when Theaetetus is seen and,
whether from indistinct perception or some other present circumstance,
is mistakenly believed to be flying.
If, however, the falsity of this statement lies for Plato in the fact that
it asserts the compatibility of what are in fact incompatibles, this does
not, of course, mean that in his view principles of compatibility and
incompatibility alone determine the truth or falsity of statements, for
he is certainly not suggesting that 'Theaetetus sits' is made true by
the fact of the compatibility of 'man' and 'sits' or that all false statenlents are false for the reason for which 'Theaetetus flies' is false. But
it does meau that his assessment of particular statements is a limited
one in that it is an assessment of their possible contribution to knowledge of a particular kind, i.e. knowledge of Forms attai~ed by mea.ns
of the methods of collection and division. Its importance IS that, while
the 'parts' of the statement are still considered to be separable'parts'
designating Forms, it is recognised that within the statement Itself a
relationship between Forms is expressed. Thus all partlcular true statements are to be interpreted as expressions of relations between Fonns.
Not all particular true statements, however, are of the same value for
the purpose of attaining knowledge. It is by the extent to :"hlch they
can contribute, wher interpreted as expressions of class relatIonshIps, to
the general 'scientiflc' knowledge of the philosopher that they are
valued. In this way the method of division, with the complementary
method of collection, becomes for plato 'an instrument which may
bring experienced fact within his conception of knowledge'. 69
I59
b1Belief
We must now relate this discussion in the Sophist to the problem of
the distinction between knowledge and belief (in the specialised sense).
We bave seen (i) that the doctrine that all statements (including all
particular statements based on present perception) are instances of a
'weaving together' of Forms implies that all true statements express
correctly relations between Forms: (ii) that Plato's ideal of knowledge
continues to be an ideal of knowledge by definition and classification
of Forms through the methods of collection and division, and that
this ideal is a restrictive influence on his analysis of false statements:
(iii) that there is no good evidence that in the Sophist either the transcendence of the Forms or the conception of knowledge as a priori
knowledge of Forms is abandoned; it is consistent with the doctrine of
the other late dialogues that the passage 248a-249d70 emphasises that
'being' is properly predicated of the world of Becoming and not
exclusively of the world of ' immovable' Reality and thus suggests that
in the Sophist the derivative reality of the world of Becoming as a 'copy'
of the world of Forms has the same significance for the practice of the
methods of division and collection as we have found it to have in the
other late dialogues we have examined. From (i) and (iii) it would
seem to follow not only that all class relationships exemplified in the
world of Becoming exemplify, in so far as that world is a copy of the
world of Forms, real relations in the system of Forms but also that the
possibility of the truth of all statements about the sensible world is
antecedently determined by real relations in the system of Forms, in so
far as
all such statements can be interpreted as expressions of relations
between Forms; hence there are true statements which can properly be
said to be about the sensible world and which are at the same time
necessarily true statelnents which 'weave tog~ther' Forms. Thus the
discussion in the Sophist leads by a different path to the question
prompted by the Timaeus - the adequacy of the theory of Forms as
the basis of a distinction between a priori and empirical knowledge. It
is with this question in mind that we must examine what Plato goes
on to say about beliefin the Sophist after he has disposed of the problem
of false statement. And since it is clear from (ii) that the Sophist continues to grant a highly privileged status to the methods of collection
and division it is important to keep in mind also the question of the
160
r6r
adequacy of the appeal to these methods as the only means of attaining
a priori knowledge.
The Sophist's remarks about belief are introduced at 263d. Here plato
argues that from the demonstration that there are false statements it
follows that there are also false beliefs. Belief (doxa) arises, he says, when
the mind makes assertions and denials in the course of silent and
'independent' thinking. It is the 'conclusion' of a process of thinking.
This description of it follows closely the description in Theaetetus
189e-I90a, where it is concluded that doxa is a statement (logos) pronounced, not to someone else or aloud, but silently to oneself. And the
Sophist says that it is because belief is 'of the same kind' as statement
that it is necessary to conclude that there is false belief as well as false
statement (264b). In both the Theaetetus and the Sophist the word logos
is used in two senses. In one sense it means statement. In the other sense
it means 'discourse', which is the equivalent in speech of the thinking
(dianoia) which precedes belief and statement; this thinking is described
as a silent dialogue carried on within the mind. Belief, then, is closely
associated with logos in both senses; it is the unspoken statement which
is. the conclusion of a process of thinkulg or silent 'discourse' within
the mind.
One point which needs clarification in Plato's account is the point
that it is in the course of the mind's illdependent thinking that assertion
and denial occur (Sophist 264a). 'Independent' means 'independent of
perception'. But what does 'independent of perception' mean? In the
Theaetetus the thought and reasoning of the mind 'by itself' are contrasted with aisth~sis (perception), and 'by itself' is defined by the rule
that if there is a characteristic applicable to the objects of more than
one sense-organ that characteristic is apprehended by the mind 'by
itself' without the mediation of the senses (184e-185e). Subsequently
the process offormulating beliefs (doxazein) is given as the description
of 'what goes on when the mind is occupied with things by itself', the
result of the process being, as we have seen, the belief that sometlling
is (or is not) the case. Now this description is put forward generally
as valid for all cases of belief; it follows that even beliefs based on present
perception are the result of 'what goes on when the lnind is occupied
with things by itself'. And this, if considered in the light of the fuller
account of the process of thinking which precedes belief (18ge-190a),
points to a broader conception of the independence of the mind's
activity than that which thinks of the independence exclusively in
terms of the mind's apprehension of non-perceptual characteristics. It
suggests, conformably with the conception of aisth~sis as bare sensation
in the final criticism of perception (I84b-186e), that the whole of the
mind's reflection and reasoning, i.e. the whole of its activity apart from
~ts perceptual f,mction as the recipient of isolated impressions of sense,
15 an mdependent activity; in other words ouly at the time that it is
receiving present sense-impressions is the mind's activity' dependent'.
As we noted in examining in the last chapter Plato's fmal criticism of
perception, his reduction of aistMsis to bare sensation implies that the
'independent' activity of the mind is exercised in coming to possess
any concept, whether designating non-perceptual or perceptual charactenstlcs, .s~ce any comparison and discrimination necessarily involve
suc~ actIVIty. We can see, then, that there is no case for interpreting
the mdependence of the mind's activity in a way which would rule
out the mind's reliance on sense-impressions and memory of senseimpressions, as data for its 'reflection' and 'reasoning'. The Sophist,
although, Irke the Theaetetus, taking the mental activity by which
bdlefs are formed to be indepelldent of perception, marks off by a
dl~erence 1ll termmology cases of belief where the mind's activity is
IUltlated by present perception from cases of belief where it is not.
The former a~e said to be cases of phantasia ('appearance'). The term
IS us~d e~rher In the Theaetetus, where it is equivalent to aisth~sjs (perceptlOn).m that sense of aistMsis which includes judgement (r5 2c). In
the SophISt plato says that phantasia is 'a blend of perception and belief'
(264b). He reserves the term doxa (belief) for cases where the mind's
activi:y is not initiated by present perception. 71 He further says that
only ill these latter cases is the mind's activity 'independent'. But since
phallt~sia includes doxa and hence includes the mental activity whereby
dox~ 15 formed we are to take this as meaning that in cases of ph""tasia
the mdependence of the mind's activity is not so complete as it is in
cases where present perception is not involved.
In th~ Philebus Plato illustrates the formation of a belief where presellt
percepUon15 mvolved (38b-40d), i.e. of a belief which, in the terminology of the Sophist, is a phOl1tasia. In such a case it is perception and
memory (the latter having been defined previously, 34a, as 'the preservation of se:rs.ation') which give rise to the attempt to form a belie£
And m deSCrIbIng the formation of the belief a Case of indistinct
162
PLATO'S THEORY 01' KNOWLEDGE
perception is deliberately chosen as best suited to illustrate the process of
questioniug within the miud which precedes the fmal unspoken assertion constituting belief, the process earlier described in the Theaetetus
and the Sophist. The case is of a person who sees an object at a distance,
and tries to form an opinion as to what it is. Prompted by the
suggestious of perception and memory the miud's 'dialogue with
itself' finally results in the assertion or denial which, if unspoken, is
a belief, if spoken, a statement. plato likens the work of iuterpretation
to the work of a scribe, said to be writiug 'discourses' (logo i) in the
'book' of the mind; it is when what is written is true that 'true belief'
results. There is one further factor. Independently of present perception
memory-images of beliefs or statements may be retaiued in the mind,
the truth or falsity of the images being dependent, of course, on the
truth or falsity of the originals (39C). And these images have their part
to play iu the formation of other beliefs and statements.
I have translated doxa as belief, rather than judgement. It might be
argued that Plato's description of doxa as the unspoken assertion or
denial which is the conclusion of a process of reasoning more naturally
suggests the meaniug 'judgement', and that his analysis of the way in
which we arrive at doxa does not imply iu any way that doxa, if true,
is never an instance of knowing, but always only of belief. Yet it is
clear that in the Theaetetus doxa means belief rather than judgement.
Thus in concluding (200d-201d) that knowledge cannot be defmed as
true doxa plato points out that the lawyer's skill is directed to makiug
people believe (doxazein) what he wants them to believe, and that ill
some cases what they are persuaded to believe happens to be true, bnt
that in these cases they do not have knowledge, bnt only true belief
(doxa). Only if a satisfactory account of or reason for (logos) the truth
of what they believe is given will they have knowledge. Here it is
obvious that plato is using doxa and doxazein in the sense of 'belief' and
'believing', as contrasted with knowledge and knowing; his distinction
between true belief and knowledge is similar to the distinction between
them made earlier in the Meno. Thus the hypothesis he is here refuting
is that knowledge is true belief, and since the analysis of the forming of
doxa in 18ge-190a is part of his attempt to distinguish false from true
doxa in examining this hypothesis it follows that that analysis is an
analysis of the forming of belief. And belief here is not belief in the
specialised sense which assumes tl,at the objects of belief are sensibles
16 3
and different in kind from the objects of knowledge. It is belief in the
non-specialised sense, the belief which lacks the systematic comprehension which is the mark of knowledge bnt is directed to the same
kind of objects. One fmther point to be noted is that the discussion of
the Theactetus entails that the logos or 'discourse' which is the spoken
equivalent of the thiuking which results in belief is never an adequate
gronnd for claiming that the resultant assertion or denial is an instance
of what is known to be true. For the fact that it results in belief implies
that an 'account' (logos) has to be added to the beliefifitis to be converted to knowledge, and this logos is, whenever it is given, additional
to, and thus distinct from, the logos which is the spoken equivalent of
the thinking or reasoniug (dianoia) which belongs to the formation of
any belief; it is also, of comse, distinct from the logos which is the
statement expressing the belie£ Now the description of the formation
of doxa in the Sophist follows closely, as we have seen, the description
of the Theaetetus. It would consequently seem to be implausible to
assume that in the Sophist plato is using doxa in a sense different from
the sense in which he uses it in the Theaetetus. Hence doxa will mean
belief in the Sophist in the same sense of belief as in the Theaetetus,
i.e. the sense which implies, for Plato, that, while lacking the systematic
comprehension which is the mark of knowledge, belief has the same
kind of objects as knowledge.
Btlt in the Sophist it is possible to give a more precise specification
of the nature of doxa and its objects than was possible in me Theaetetus.
The methods of collection and division are now established as the
methods of the dialeetician and have solved for plato the problems
about knowledge raised but not solved by the Theaetetus. And the
nature of doxa can now be assessed in the light of Plato's claims for
this method and, more particularly, in the light of his explication in
the Sophist of those Forms which make possible the' combination' and
'separation' of Forms and his doctrine that any statement is an instance
of a 'weaving together' of Forms. Thus we can say firstly that, since
belief has the same kind of objects as knowledge, then the objects of
belief are Forms; secondly that, since any statement is an instance of
a 'weaving together' of Forms, then belief, which asserts or denies
that something is the ease, is a form of apprehension which relates
Forms in certain ways. Thus it is essentially as a process of thinking
which attempts to establish relations between Forms that the work of
interpretation which has its conclusion in belief is to be construed. And
before its analysis of statement and belief the Sophist has shown what
are the principal kinds of relation between Forms and shown too that
they are the basis of the methods of division and collection through
which alone knowledge is attainable. This establishes what form of
interpretation goes to the formation of belief. And our previous discussion of the nature of the distinction between knowledge and belief in
the non-specialised sense has indicated how extensive is the possible
scope of belief. In this respect, i.e. in respect of the scope of the interpretation which goes to their formation, particular beliefs will differ
considerably, though the form of the interpretation will be the same
for all true beliefs. Thus the picture given to us of belief is a picture
of a form of apprehension which, using the memory whether of past
sense-inlpressions or of what has been believed or asserted in the past
and sometimes the suggestions of present sense-impressions, interprets
this experience in terms of relations of compatibility, incompatibility,
and implication between Forms, widening experience guiding the
selection, frOln cases of those relations, of the ones essential to the
definition and systematic classification of Forms through the methods
of collection and division. This very general description of belief may
perhaps be thought a much too ambitious interpretation of what is
implied in Plato's analysis of particular statements and beliefs. Yet the
argument of the Sophist points clearly, I think, to an interpretation of
this kind. Thus eVen in the relatively simple case of the interpretation
of a present sensation where the purpose is the identification of a
particular object, it is clear that the interpretation which goes to the
formation of belief is envisaged as a process of testing the applicability
of an identifying Form to this object by a method which assumes that
the object is of a certain kind and, with reference both to perception
and memory, considers what other Forms may be implied to be present
assuming the presence of this Form and with what other Forms this
Form is compatible or incompatible, the aim being to reach a fully
consistent belief about the nature of the object based on an insight into
real relations betweell Forms.
What we now have to consider is the problem of how to interpret
Plato's conception of belief in the specialised sense consistently with
this conception of belief in the non-specialised sense found in the
Sophist. The problem can be put in this way. If belief in the non-
16$
specialised sense is, however limited in particular cases the process of
thinking leading to its formation might be, relating Forms in certain
ways,. what precisely are the distinctive characteristics which justify
marking It off from a doxa which too is 'propositional' and is the result
~f an interpretative process of thinking bnt is excluded from insight
mto Forms? The only possible answers to thisseem to be: (i) the person
who has this latter doxa is committed to a metaphysical theory which
does not accept the existence of transcendent Forms and assumes that
sensibles are the only reality, or (ii) he is following a different kind of
interpretation from the uniquely privileged kind affording insight into
relattOns between Forms and hence calmot be said to have Forms as
the objects of his apprehensiQn.
By itself (i) is clearly an insufficient answer. Certainly plato considers
that. the person with this doxa does assume that sensibles are the only
reahty, but does not consider that it is for this reason that he cannot be
said ever to gain insight into Forms. Or at least he considers that the
assumption is inevitably abandoned once a particular method of analysis
1$ adopted. Hence. we come to (ii). The Sophist lends some plausibility
to thIS. The SophIst not only makes explicit the 'propositional' nature
of behef but asserts that statements are significant in a way in which
names by themselves are not, for they 'do not merely name something
but get you somewhere' (262d). And this significance lies, as we have
seen, in the fact that statements 'weave together' Forms in certain
ways. A statement, luoreover, is the expression of a belief which has
in its formation, traced the relations with other Forms of the Form~
fmally 'woven together', and it is in these links with the system of
F~rms that plato looks for the fuller Significance of any statement, its
m~lmum ,slg~ficance being that it relates in a certain way the Forms
whIch are Its d,rect and immediate reference. The emphasis throughout
IS on th~ necessity ,of tracing relations between Forms if any insight into
Form~ IS to be g~med. It thus becomes possible to argue that, correspondmg m plato s thought to the VIew that significance is to be found
mstatements rather thanin'names by tllemselves' and that the minimum
si~nificance of a. st.atement is that it relates Forms in a certain way, is the
VIew that the mmmlUm level of insight into Forms is the recognition of
cert~mrelattOns between Forms and that this level of insight marks the
begmrung of the realisation of the Form in the understanding. Thus the
pomt at whIch a Form can be said to be possessed by the mind and, at
166
the same time, at which thought can properly be said to be directed
to Forms is already a level of explicit conceptual thinking. Earlier in
the Phaedms plato had described the iuitial realisation of the Form
in the wlderstanding as a process of generalisation and abstraction
culminating in the recognition of a siugle common Form. And now,
it would seem, he is refmiug his conception of the level of abstract
thiukiug which constitutes this realisation of the Form and assuming
that some explicit conceptual analysis is a necessary part of the abstraction of the Form and not a process marked off as succeeding an initial
abstraction, as seemed to be implied in the Phaedrus.
This does not, however, allow us to find a place for doxa in the
specialised sense by identifyiug it with some less abstract level of
apprehension so closely tied to sensation that it lacks this mark of
explicit conceptual analysis. For to have attained ouly the level of the
doxa which has sensibles and not Forms as its objects is consistent,
accordiug to the Timaeus and the Philebus, with haviug elaborated
highly abstract theories of the nature of the physical world; and from
the beginniug this doxa has been assumed to be 'propositional'. But it
is at least possible to argue that, if the realisation of Forms as the
objects of thought is attained ouly as the result of a particular kind of
analysis of relations between concepts, then there can eXist a doxa,
which, though the result of an analysis of relations between concepts,
is the result of an analysis other than that which affords insight into
Forms, and hence still has objects other than Forms. And this, I thiuk,
is the only possible way of distinguishing the two· types of doxa. It
must be added that it is no longer possible to attribute the failure of the
interpretation which forms doxa in the specialised sense to afford
insight into Forms to its use of sensibles as an aid to interpretation, on
the groWld that perception is invariably misleadiug and Wlreliabl~ and
that it is a necessary condition of the ability of a method of mterpretation to afford insight into Forms that it never uses sensibles as
an aid. For the late dialognes consistently assume that the use of sensibles is a valuable aid to the analysis of Forms, as we have seen. Hence
the fact that sensibles are used as an aid to interpretation is common
to both types of doxa and cannot be appealed to as a mark which
distiuguishes one from the other. The conclusion would seem to be
that doxa in the specialised sense is precluded from having Forms as. the
objects of its thought by its use of a wrong method of lIlterpretatlon,
wrong iu the sense that it is other than the methods of collection and
division which, Plato assumes, alone can yield insight into Forms and
which, he also assumes, the philosopher alone is capable of practising.
What reasons, then, does he give to save this distinction between
right and wrong methods of interpretation from being a merely
arbitrary one? He continues to assert that the reasons why the method
of interpretation on which doxa in the specialised sense is founded is
wrong are that it uses sensibles as an aid and that its results are abont
a sensible world. Yet, ifhe is to be consistent with the developments in
his theory of knowledge in the late dialogues, he is no longer able to
appeal to these factors as marks of distinction between a method of
interpretation which has sensibles as its objects and one which has
Forms as its objects. For the effect of these developments, as we noted
immediately before our discussion of the Sophist, is to break down the
distinction between empirical knowledge (doxa in the specialised sense)
and a priori knowledge (of Forms). Begiuniug from a distiuction
between Forms and sensibles which corresponds in his theory of knowledge with a distiuction between sensation and a conceptual level of
apprehension, plato was led in the middle dialogues to a position where
he could keep radically distinct knowledge of Forms and empirical
knowledge only by assumiug that the only correct and properly
systematic conceptual analysis was completely divorced from perception, while continuing to assume also an archetype/copy relation
between Forms and sensibles and a theory of knowledge as recollection
in which that relation was fundamental. It is his attempt in the late
dialogues to remove the inconsistencies inlplicit in this position which
make it dillicult for him to maintain any longer the radical distiuction
of the middle dialogues. For his recognition of the close and wide
correspondence between the system of Forms and its visible 'copy',
the physical world, and with it the recognition of the value of perception as an aid in the work of systematic analysis of Forms now
make it inconsistent to continue to maintain in the Timaeus and the
Philebus the earlier distinction between empirical and a priori knowledge. To maintain it plato has to try to make good his claim that the
physicist's methods are inadequate to afford insight into Forms by
condemning these methods for reasons for which the specifically
philosophical method which he now advocates as the unique means
of affording insight into Forms can equally well be condemned. It
168
follows that he now has no satisfactory grounds for according to the
methods of collection and division this unique privilege of affording
a priori knowledge. All that remains to support his distinction between
empirical and a priori levels of apprehension is a con~iction that the
only correct and properly systematic conceptual analysIs IS analySIS by
these methods. And this reduces his selection of these methods as the
only ones yielding insight into Forms to a merely arbitrary selection.
It is to be noted finally that, though there are good reasons for
assuming that doxa in the Sophist is used in the non-specialised sense
and that its objects are Forms, plato asserts that statements which are
the spoken expression of doxa 'give information about what IS or has
been or will be' (262d). In the Philebus too, in the passage (3 8h:-40d)
in which he illustrates with an example where present perceptlOn IS
involved the process of the formation of doxa described earlier in the
Sophist, he points out that doxa has reference to 'what is or has been or
will be' (39c-40c). These remarks of the Sophist and the Philebus should
not, however, be taken as an indication that the discussions of doxa
both in the Sophist (263d-264d) and in the Philebus (38b-40d) are
discussions of doxa in the specialised sense, the doxa exclusively concerned with the events of the temporal world and uever with the
timeless world of Forms. Only if these remarks were inconsistent with
the thesis that Joxa is there used in the non-specialised sense and that
its objects are Forms would they constitute an effective .objection to
that thesis, which has, as we have seen, strong arguments l111ts favour.
There is however no such inconsistency. For Plato's conception of
the relation betwe:n the system of Forms and the physical world w~ich
'copies' that system makes it consistent to assume that a :rue doxa 1~ at
once a truth about the sensible world and a truth assertmg a relatlOn
between Forms. And this is in fact what plato does assume in the Sophist.
It is not an assumption which should lead us to doubt in any way the
very good evidence that in the late dialogues plato r~tamed hIS doctrme
of transcendent Forms. Rather is it a mark of the madequacy of that
doctrine as the basis of a distinction between a priori and empirical
knowledge so long as a model/copy relation between. Forms and
sensibles is assumed. If it is difficult to find m the SophIst any clear
and explicit metaphysical doctrine the dialogue at least serves to underline the difficulties in Plato's distinction between knowledge and belief
in the specialised sense which we discussed earlier
CHAPTER IV
Mathematical Knowledge
I. MATHEMATICS IN THE NATURAL SCIENCES
It remains to consider whether developments in Plato's latest doctrine
allowed him to overcome these difficulties. In examining in the last
chapter Plato's distinction between a priori and empirical knowledge
we examined it initially in terms of his distinction between the aims
and methods of the philosopher and those of the physical scientist. In
the Timaeus and the Philebus he associates physics with 'belief' and
probability, as opposed to the knowledge of the philosopher, and his
attitude to physics, when he compares it with philosophy, retains some
of the disparagement with which 'belief' was treated in the Republic,
despite the revaluation of perception in his later thought. From other
parts of the Timaeus and the Philebus, however, and later from the
Laws and the Epinomis there is evidence of a gradually increasing respect
for the natural sciences as a field of empirical study. More particularly
there is increasing emphasis on the ideal of a mathematically formulated
science of astronomy as essential to the understanding of the 'divine'
governance of the world and hence as essential to the attainment of
piety. It would appear from this that plato is now recognising that
empirical knowledge ('belief') can be much more systematic and
precise than he had hitherto allowed. Moreover the increasing
attention which he now gives to the implications of the fact that its
results can be mathematically formulated appears to be reflected in
the mathematical orientation of his latest metaphysical theory. What
we must consider is whether this latest theory affords the basis for
a lllore satisfactory distinction between a priori and empirical knowledge.
Beginning with the Timaeus we will fmt examine briefly the nature
of the mathematical approach to the natural sciences in the late dialogues.
In the Timaeus (S3b ff.) the ideal of a mathematical formulation of
physical theory is already evident in the account of the geometrical
M
r69
structure of the material elements and the explanation of the transformation of one element into another in terms of geometrical structure. Plato asserts further that the analysis which assumes that rectilinear
triangles are the basis of the structure of the elements is not a fmal .
analysis. Further analysis will reveal still simpler principles to explain
the determination of the 'basic' figures themselves (53d). And he has
already asserted at 53b that a fixed and definite structure is given to
the material elements by geometrical shapes and by numbers. In the
Philebus we find again this appeal to mathematical determination in
explaining the ordered structure of the world. Here plato uses the
Pythagorean concepts of Limit and the Unlimited, the former signifying precise mathematical determination and the latter the indeterminate
or indefinite. And just as in the Timaeus that which is 'without proportion or measure' (53b) is given definite structure by means of
geometrical shapes and numbers, so in the Philebus the Unlimited is
given precise determination by the introduction of Limit, described
as 'whatever is a number in relation to a number or a llleasure m
relation to a measure' (25a-b). Thus Limit is identified with mathematical ratio; and the emphasis put on numerical ratio is indicated by
the subsequent description of the 'family of the Limit' as 'all that puts
an end to the conflict of opposites with one another, making them
well-proportioned and harmonious by the introduction of number'
(25d-e).
It is in astronomy that plato considers that the mathematical interpretation of the world can be most fruitfully and most exactly applied.
His reason for this is that the rational activity of the cosmic soul in
ordering the world is most perfectly exemplified in the regular and
eternal movements of celestial phenomena. Thus in the Timaeus he
asserts that this rational activity is supremely manifested in the sphere
of the fixed stars (36c, 40a-b, cf. 47b). And the stars are regarded as
'gods'; they are 'divine and everlasting living beings' (4ob). plato
aSsumes further a correspondence in structure between the imnl0rtal
soul in man and the cosmic soul, the 'harmony' of the structure being
constituted by a system of numerical ratios (3 5a-36d, 4I d). This allows
the possibility of an assimilation of the rational activity of the individual
human soul to that of the cosmic soul. And since it is assumed that an
ordered universe is better than chaos (30a) and that the cosmic soul's
activity is directed to this good end of ordering the universe it becomes
I71
possible to argue that the goodness of the human soul is most fully
attained when its rational activity is most fully assimilated to the
rational activity of the cosmic soul, which is, as we have seen, most
perfectly exhibited in the regular movements of the heavenly bodies
(47b--c, 90c-d).' Hence the individual, to attain goodness, must apply
his reason to the scientific study of astronomy; ouly in this way is the
full assimilation of the rational activity of his soul to that of the cosmic
soul possible.
Later in the Laws and the Bpinomis' plato re-affirms his conviction
that the study of astronomy is of the highest valne. Thus in the Laws
arithmetic, geometry, and astronomy are to be studied by all citizens
(8I7e ff.). It is especially important in the study of astronomy, Plato
argues, to realise that the movements of all the heavenly bodies are
strictly regular. In particular the notion that the sun, moon, and other
'planets' are irregular and 'wandering' in their courses must be eradicated. An indication of Plato's special interest in astronomy in his later
years is found here in the statement (821 e) that only recently has he
himself come to appreciate the right explanation of the regular orbits of
the' planets'. And a final indication of the high value which astronomy
now has for him is that a knowledge of it is said to be indispensable for
all members of the 'nocturnal council', the body which has the
supremely important function of both comprehending and realising
the main purpose for which the proposed state is to be put togetherthe goodness of its citizens. Essentially-the same reasons for treating
the study of astronomy as of the highest importance are given here
(966c if.)' as were given in the Timaeus. It is emphasised that the
exactness and regularity of the movements of the heavenly bodies can
be accounted for only by assuming that they are ordered by the rational
activity of the soul which pervades the world and is the source of all
its movements and order. And a necessary preliminary to the study of
these movements is training in mathematics.
Finally, as an appendix to the Laws, the Bpinomis describes more fully
the programme of education for the members of the nocturnal council.
The question of what the basis of this education should be is introduced
as the question of what form of knowledge must be possessed to entitle
a man to claim that he is really wise (974d-976d). Plato's answer is that
it is knowledge of number (976e if.). His primary reason for selecting
knowledge of number is that it is the key to the science which he
considers to be of the highest value - astronomy (977b), and, having
once again given his reasons for treating astronomy as a study of the
highest value, he proceeds to explain in detail how fundamental knowledge of number is for this study (990a ff.). In a very difficult passage
(990c--991b)4 he stresses the importance of studying the theory of proportions as the key to the understanding of the connexion of the study
of numbers with geometry and with the science of astronomy. His
ideal is the unification of our scientific knowledge of the universe.
'Every geometrical diagram, every numerical series, every harmonic
combination and the single harmonious system of the revolution of
all the heavenly bodies must become clear to the man who learns by
the right method. And they will become clear if he learns rightly by
looking towards unity. For reflection will reveal a single bond of
nature linking all these things' (991e).
2. MATHEMATICS AND THE FORMS
We have now seen how prominent in Plato's latest doctrine is the
ideal of a mathematically formulated science of astronomy. This is
presented as the one form of knowledge which will qualify its possessor to be really wise and at the same time make him pious and good.
It appears, moreover, to be knowledge of a different kind from the
knowledge of Forms which belongs to the philosopher. It is attained
by different methods and is expressed in exclusively mathematical
terms. Yet, though apparently different from the philosopher's knowledge of Forms, it is assumed to have the supreme values which have
previously been assumed to belong only to the philosopher's knowledge. It confers both wisdom and goodness on its possessor.
Thus in Plato's latest doctrine there appear to be two different views
about the right way to attain wisdom and goodness. It is difficult to
imagine that plato is simply putting forward alternatives and assuming
that each is sufficient for the attainment of the same ends. which of
the two, then, is to be taken as his final doctrine? The Laws and the
Epinomis would appear to give some plausibility to the view that the
new ideal of a mathematical astronomy has displaced in Plato's thought
his ideal of a dialectic which will yield knowledge of Forms, that
'dialectic has given place in his mind to the joint ascendancy of
theological sentiment and Pythagorean
arithmetic'. 5
173
But if we accept
thIS VIew, what are We to assume the relation to be, if any, between
astronomy and dialectic? In the Republic the reasoh for granting
supre,:"acy to the science of dialectic was that its analysis was a final
analySIs which went beyond the limits of the analysis possible within
the mathematical sciences (including astronomy) and was alone able
to achieve full knowledge of reality (the Forms). In the late dialogues
from the Phaedrus to the Philebus this supremacy continues to be
accorded to the science of dialectic, its methods being now specified
as those of collection and division. In the Politicus (283c-28sc) and the
Philebus (s6d-S8e) its supremacy over mathematics is explicitly reaffirmed. If it is argued that in Plato's latest doctrine the science of
astronomy displaces the science of dialectic as the supreme science this
might mean (i) that plato has abandoned or at least is sceptical about
the metaphysical assumptions of the science of dialectic, and that the
supremacy given to astronomy is an acknowledgement that the 'fully
real' is to be found in the sensible world: or (ii) that Plato, recognising
~he preClSlOn and exactness obtainable in physical science, and especially
m astronomy, through formulation in mathematical terms, has been
led to modify his theory oEForms, with the result that he now conceives
the system of Forms to be a mathematical system and abandons the
methods of collection and division as the methods which will yield a
final analysIs of reality. On this interpretation it would not be strictly
true to say that the science of dialectic has been 'displaced'. The
argnment would be that the old conception of dialectic has given
place to a new one which reflects Plato's preoccupation with astronomy
and nlathematics.
From the latest dialogues alone it is impossible to substantiate either
(i) or (ii). Both in the Laws (963c if.) and the Epinomis (991C) there are
descriptions of a ,;,ethod r~cognisable .as the method associated preVlO:1Sly With tl,e dialectiC of the philosopher; the terminology is
suuIlar and there is emphasis on the method of' collecting' particulars
uuder a single form (idea, eidos) or species under a single genus. But
neither the Laws nor the Epinomis gives any indication of the metaphysical significance of their reference to 'forms', or of the relation
betwee~ the method which they describe and the science oE astronomy.
The testimony of Anstotle does, however, allow us to rule out (i) above.
Though there are good grounds for criticising Aristotle's account at
174
many points as a misrepresentation ofPlato' s doctrine, ids inconceivable
that he either failed to appreciate or dishonestly concealed the abandonment by plato in his latest doctrine of the posmlate which is the
principal object of his criticism - the postulate of the separate reality
of the Forms. We must accept his testimony that plato never abandoned
this postulate. As for (ii) above, any consideration of it will have to
take into account Aristotle's testimony about Plato's 'unwritten
doctrines'. 6 It is clear that Aristotle was acquainted with Platonic
doctrine not recorded in the dialogues. His testimony about it is,
therefore, of very great importance.
A reference by Aristoxenus 7 to Plato's lectures on the Good indicates
that in lectures which we know from the Greek commentators on
Aristotle to have been concerned with the ultimate principles of Plato' s
metaphysical theory great prominence was given to mathematics and
astronomy. Quoting Aristotle, Aristoxenus relates that most of those
who attended the lectures were disillusioned when they found that it
was with mathematics that Plato was dealing - numbers, geometry,
and astronomy. This in itself suggests that the prominence given to
'numbers, geometry, and astronomy' in the Laws and the Epinomis is
reflected in the structure of the metaphysical theory expounded in his
lectures. We know, moreover, from Simplicius8 that a feature of
Plato's lectures on the Good was an exposition of the principles from
which the Number-Forms were derived, a further indication of the
mathematical orientation of Plato's metaphysical theory. There is,
finally, Aristotle's testimony that Plato held that all Forms were
numbers." Thus Plato's latest metaphysical system is, it would seem,
predominantly mathematical in its features. And what we have to ask
is whether the modifications made in the theory of Forms were deSIgned
to make the theory consistent with the view, found in the late dialogues,
that the characteristics of the physical world are mathematically determined and that physical theory is to be formulated in mathematical
terms. For that view, if we assume that in retaining the postulate of the
transcendence of the Forms plato retained also his assumption that the
system of Forms was an 'intelligible model' of the physical world,
appears to demand as its complement a conception of the system of
Forms as a specifically mathematical system.
The theory of Forms had, of course, assumed from the begimilng
that there were Forms of numbers. These Forms were Forms of the
175
positive integers. Thus in the Phaedo (101 b9-c9) Forms of Oneness,
Twoness, and so on are postulated. And as Aristotle's testimony
shows,!o plato assumed that the Number-Forms were ordered in a
series; there was a relation of 'priority' among them. Aristotle also
asserts that plato described them as 'incomparable', meaning strictly
that they cannot be stated as fractions one of another; but in the context of Metaphysics I080a20 their incomparability appears to mean
more generally that they cannot enter into arithmetical relations with
one another - be added and subtracted, multiplied and divided. l l In
the dialogues the Number-Forms are not accorded any privileged status
in the world of Forms, nor does plato anywhere state what he conceives
to be the relation between Number-Forms and other Forms within the
system of Forms. What, then, does he conceive this relation to be when
he maintains that all Forms are numbers?" There is nothing in Aristotle's testimony about this doctrine to suggest that the range of
distinctive Forms other than the Number-Forms was limited or determined in any way by the association made between Forms and numbers.
Thus it is not suggested that the Number-Forms of the earlier theory
are the only Forms. We have to assume, therefore, that the doctrine
was a statement of the principle of relation between Number-Forms
and other Forms.
Unfortmlately no consistent principle can be found in what Aristotle
says about the doctrine. l3 There is, however, a passage in Sextus
Empiricus14 which ascribes to Plato a definite principle for assigning
numbers to Forms. Sextus says that
the Forms, which are incorporeal, are according to Plato prior to
bodies, and each of the things that come into being does so because
of its relation to them; but they are not the first principles of existing
things, since while each Form taken separately is said to be a unity,
yet in so far as it embraces another or other Forms it is said to be
two or three or four, so that there is something higher than their
nature, namely number, by participation in which 'one' or ~two' or
'three' or yet higher numbers are predicated of them.
Sextus is here illustrating the argument that though the principles of
imperceptible bodies (e.g. atoms) must be incorporeal it does not follow
from their incorporeality that they are first principles. And his immediate appeal to Platonic theory as the initial illustration of the
177
argument, and his clear and definite statement of the theory, make it
unlikely that he is here giving a merely personal interpretation of
are mathematically determined and that in the fmal analysis physical
theory lS to be formulated m mathematical terms. The answer would
seem to be that they are not so designed, for in themselves they do not
m fact make the theory any more or less consistent with that view
than it was before, assuming that consistency is determined in relation
to the postulates that determinate sensible characteristics are 'images' of
the Forn:s and that the system of Forms is an 'intelligible model' of
the phYSIcal world. Thus the sense in which Forms are now said to
be numbers is an entirely trivial one as far as the structure of the Forms
is concerued; nothing is thereby added to the nature of the Forms or
of the system d Forms as a whole which converts that system to one
which reflects In Its structure the order of the physical world as conceIved by the n:athematical theory of the late dialogues. The possibility
of such co~verslOn, whatever principle is adopted for assigning numbers
to Forms, IS mdeed excluded by Plato's conception of the nature of the
Platonic doctrine. Moreover there is some confirmation of the correct-
ness of Sextus's account in the fact that the only passage in other
writers clearly indicating a principle whereby plato assigned numbers
to Forms is in one of Plato's late dialogues, and that the principle there
indicated is the same as that described by Sextus.
The passage is in the Philebus. Here the description of the science of
dialectic is dominated by the idea of number, and this idea is associated
with the Pythagorean concepts of Limit and the unlimited. Both in
the initial description of dialectic (1OC-17a) and in the illustrations of
its application (I7a-1Sd) the aim of the method is said to be the
discovery of a definite number. The number to be found is the determinate number of species and sub-species in a genus when classifying
and defining Forms. It was no doubt natural for Plato, in emphasising
the unifying function of the concept, to make a numerical distinction
between the One Form or 'monad' and the indeflnite number of its
particular instances. But he shows himself unduly preoccupied with
the idea of number when he conceives the distinction between determinate and indeterminate principally in terms of a numerical distinction
between the determinate number of species and sub-species of a genus
and the indefmite number of its individual members. The probability
is that the Pythagorean influence already evident in the use of the
concepts of Limit and the Unlimited is now leading Plato to think
that to relate Forms to numbers from the results of the analysis of
their structure by division is to add significantly to our comprehension
of them. And since the principle described by Sextus for assigning
numbers to Forms is identical with the principle indicated by the
Philebus Sextus's account suggests that it was in following the line of
thought expressed in the Philebus that Plato reached the position where
he granted to the Number-Forms a higher status than other Forms
and asserted that all Forms were numbers. Finally, by taking the analysis
one stage beyond this, plato attempted to show what the principles
were from which the series of Number-Forms was itself derived."
These late developments in the theory of Forms must now be considered in relation to the question raised earlier - whether the developments were designed to make the theory consistent with the view
found in the late dialogues that the characteristics of the physical world
Nmuber-Forms, for he assumes that the arithmetical operations neces-
s~ry for the development of the mathematical theory of the late
dIalogues are not possible in the case of the Number-Forms. 16 We
must conclude, therefore, that the latest developments in Plato's theory
of the nature of the Forms themselves and of the system of Forms were
not directed to the end of making that conversion possible.
3· THE OBJECTS OF MATHEMATICAL KNOWLEDGE
There is, h.owever, one further development in Plato's metaphysical
theory which IS plaUSIbly interpreted as an attempt to answer the
problem we have been discussing. It seeks to explain mathematical
knowledge by postulating that its objects are neither sensibles nor
Fon~s but objects 'intermediate' between the two, higher in metaphYSIcal status than sensibles but lower than Forms." And it is because
this postulate is the ?nly part of Plato' s latest theory which can provide
a metaphYSIcal baSIS for. his Ideal of formulating physical the0ry in
mathematIcal terms that It becomes plausible to assume that this ideal
was at least one important influence in prompting him to introduce
the postulate into his metaphysical theory.
The Philebus is the best starting-place for a discussion of this point,
for ItS doctrme not only shows III a most definite way the gap in Plato's
179
metaphysical theory so long as it provides no basis for this ideal b1:lt
also points the way to the means fmally adopted by plato to ftil the
gap. The relevant passages are those in which plato discusses (i) the
principle of Limit (16c-26d) and (ii) the difference between dialectic
and mathematics (sse-S9c). As for (i), the important point here is
that the treatment of the principle of Limit in relation to the Forms
themselves (16c-17a) is separate from and different from its treatment
as a principle of explanation of the determinate characteristics of the
physical world (2Jc-26d). As for (ii), the important point is that
dialectic, as the science which investigates the Forms themselves, is
treated as separate from and superior to 'philosophical' mathematics.
And what our discussion is concerned to do is to show the connexion
between (i) and (ii).
The difficulty about (i) is that Plato, having discussed and illustrated
the significance of the principle of Limit in two different fields, says
nothing about the relation between one significance and the other.
Thus, (a) in relation to the Forms the distinction between Limit and
the Unlimited is, as we saw in an earlier discussion of the passage, a
distinction between the definite or 'limited' number of species and
sub-species within a genus, and the 'unlimited' number of the individual members of the genus; (b) the distinction in relation to the
the Forms, it has to assume further, since Limit as a principle of determination of physical characteristics is defined in terms of mathematical
ratio, that it is mathematical ratio which gives definite structure to the
Forms. But this is to contradict what plato has previously said about
the principle of Limit in relation to the Forms themselves (16c-17a)
when he specifies it in terms of the defmite number of species and subspecies within a genus, as established by the philosophical method of
division, a conception of the structure of Forms clearly incompatible
with a conception of structure in terms of mathematical ratio. Thus
to interpret in terms of Forms a principle of Limit defined in terms
of mathematical ratio is to try to equate two radically different conceptions of Limit. We have to recognise, then, that the Philebus
describes two different principles of determination or Limit. In
describing the first (16c-17a) Plato is concerned to emphasise the
definiteness and fixity of the structure of the Forms, but it is clear
that what he says here of the principle of Limit in relation to the
Forms will be true also derivatively of the determinate nature of the
characteristics of the physical world inasmuch as that world is a 'copy'
or 'image' of the world of Forms. In describing the second (2Jc-26d)
plato is explaining the determinate nature of the characteristics of the
physical world in terms of mathematical ratio and not in terms of the
principles applicable if this determinate nature was derivative from
the determinate nature of the Forms as explained by the first principle;
phenomenal world is a distinction between, on the one hand, precise
lluthematical determination in the form of numerical ratio and, 011
the other, the indeterminate, a state such as is imagined in the Tin~aeus
as prevailing before any 'measure' or 'proportion' had been introduced
into the world to give it a definite structure. Plato, as we have noted,
has nothing to say about the relation between the two distinctions.
Moreover incompatibilities arise from any attempt to correlate one
with the other. Such attempts usually take the form of attempts to
interpret distinction (b) in terms of Forms. Thus many scholars have
equated the function of Limit in respect of the determination of the
characteristics of the physical world with the function of the Forms
in the same respect, thus assuming that Limit signifies the defmiteness
and fixity of the Forms. This kind of interpretation is understandable
enough, for the Forms 'may be said, as defining and determining the
character of the sensibles which "partake" of them, to function as
"limits"
'.18
It is, however, a demonstrably false interpretation. For,
assuming as it does that Limit signifies the definiteness and fixity of
to try to identify the 'mixed' class of characteristics which result from
the imposition of Limit on the Unlimited with the class of 'copies' or
'images' of Forms gives rise to the same incompatibility as arises from
the attempt to equate the two principles of Limit. Thus the position
is that, unlike the first principle, this second principle of explanation
of the determinate nature of physical characteristics is unrelated to the
theory of Forms. It is unrelated to any metaphysical postulate. It is,
however, already implicit that if the principle is to include a metaphysical postulate, then that postulate must be (a) other than the
postulate that there are Forms, (b) designed to explain specifically
mathematical kuowledge.
What indications are there, then, in the Philebus itself of Plato's
views on mathematical kuowledge, and, more particularly, on the
metaphysical status of the objects of mathematical kuowledge? A
passage later in the dialogue (sse-59c), in which plato attempts to
180
classify the various forms of knowledge on the basis of their degree
of exactness and purity, distinguishes 'philosophical' mathematics both
from 'popular' mathematics and from the science of dialectic. The
distinction between the two kinds of mathematics is explained in terms
ofa distinction between the kinds of units with which the' philosophical'
and the 'popular' arithmetician deal. Thus the 'popular' arithmetician
deals with 'unequal' units, sensible numbered things; in each calculation
he arbitrarily selects as 'units' things which are 'unequal' and which for
the purposes of other calculations may not be units. The 'philosophical'
arithmetician, on the other hand, deals with absolutely equal units; in
any calculation the units are all exactly the same, no one being in any
way distinguishable from another (56c-e). plato adds that there are
infmitely many units of this kind. An analogous distinction is assumed
between 'philosophical' and 'popular' geometry, the assumption
apparently being that the former deals with perfect non-sensible
geometrical lines and figures, the latter with inexact drawn lines and
figures (c£ 62a-b), used for practical purposes such as house construction. Plato concludes that philosophical mathematics represents a
higherlevel of exactness and purity than other 'arts', including 'popular'
mathematics, which are essentially empirical in method, in the sense
that they rely on the rough and ready distinctions afforded at the level
of sense-experience. The highest level, however, belongs to the science
of dialectic, for it is the distinctive mark of dialectic, as contrasted with
all other sciences, including the science of philosophical mathematics,
that it affords knowledge of perfect and permanent reality (58a). Hence
philosophical mathematics deals with neither sensibles nor Forms. That
it does not deal with sensibles is made abundantly clear by the account
of its distinction from popular mathematics. That it does not deal with
Forms is made clear by the statement that it is the science of dialectic
alone which has as its object what is absolutely real and eterual (58a).
It is implied, then, that mathematical knowledge is knowledge of
objects lower in metaphysical status than Forms but higher than
sensibles.
Thus this implicit metaphysical postulate satisfies the two conditions
which Plato's earlier discussion of the two principles of Limit has
already implicitly shown to be the conditions which have to be satisfied
ifhis conception ofthe second principle of Limit as precise mathematical
determination is associated with a metaphysical postulate. We clearly
I8r
cannot conclude with any certainty from this alone that Plato introduced this postulate primarily in order to give a metaphysical basis to
his ideal of a mathematical interpretation of the determinate characteristics of the world. But at least, if we leave aside metaphysical considerations, it is difficult not to conclude that such an interpretation is
already associated by Plato with the science of philosophical mathematics audnot with dialectic. And, granting this, it is surely significant
that m a d1alogue where the principle of mathematical determination
is first dearly presented as a principle distinct from the principle of
determmat10n by the standard of Forms there is also the clearest indication so fur given by the dialogues that the science of mathematics deals
with objects different in kind both from sensibles and from Forms.
Together these features of the dialogue suggest that Plato has already
recognised the insufficiency of the theory of Forms for the purposes
of an explanation of the intelligibility of the physical world in mathematical terms, and has already been prompted by this recognition to
think of the reality known to the mathematician as different in kind
from the reality constituted by the Forms.
It is now necessary to consider more precisely the nature of the
objects of mathematical knowledge. While the Philebus shows that
plato was then assuming that these objects arc different from and lower
in metaphysical status than the Forms, its evidence is insufficient to
show that he had already fully elaborated the doctrine of the 'interInediate' class of mathematical objects ascribed to him by Aristotle.
But at least what he says about numbers is close to his doctrine of
Mathematical Number as described by Aristotle. Just as the Philebus
says ~h~t the units of philosophical arithmetic are absolutely equal and
that 11 15 w1th un1ts of thlS kmd that arithmetical calculations (logismoi,
57ar ) are made, so Aristotle says that in mathematical numbers all
units are .'u~l<li~erentiated' and 'associable', meaning that they are in
no way dlStmgmshable from one another and that a set of units selected
indiscriminately constitutes a mathematical number, and assuming that
1t 1S these characteristics which allow arithmetical operations to be
performed which are not possible in the case of the Number-Forms."
What Aristotle say~ further (Metaphysics 987bI4-I8) is that the objects
?f m~themat1cs (anthmetIc and geometry) 'differ from sensible things
m bemg eternal and unchangeable, from Forms in that there are many
alike, while the Form itselfis in each case unique'. Thus there are many
182
instances of each mathematical number for each Number-Form, and
many instances of geometrical objects (lines, circles, squares, etc.) for
each geometrical Form. The eternal and unchangeable reality of the
objects of mathematics was no doubt for plato a corollary of the
exactness and permanence of the truth which he found in mathematics.
And the contrast between the uniqueness of each mathematical Form
and the plurality of instances of each corresponding mathematical object
is a further indication ofllis reasons for thinking that no explanation
of mathematical knowledge was possible so long as it was assumed
that its objects were Forms. Thus, in the case of arithmetic, the uniqueness of the Number-Forms seems to have been taken by plato to be
incompatible with the thesis that they are the objects with which the
arithmetician deals, not only because their uniqueness seemed to entail
their 'incomparability' but also because, thinking as he always was of
the objects of arithmetic as objectively real 'things', he concluded that
arithmetical operations were impossible unless there were many
instances of each number and infmitely many units to constitute them.
The one connexion between Number-Forms and mathematical
numbers is that mathematical numbers are considered to be perfect
instances of the Number-Forms. This is not, however, a type of
instantiation comparable to that whereby sensibles are 'copies' of
Forms. It is not simply that in the one case the instances are perfect
and non-sensible, in the other imperfect and sensible. It is also that,
with the exception that the series of Number-Forms is parallel to the
series of mathematical numbers, no systematic parallelism is assumed
between the relations of numbers in 'philosophical' arithmetic and
either the relation of the Number-Forms to one another or the relation
of Forms-as-numbers to one another within the system of Forms as a
whole, whereas such a parallelism is assumed between the system of
Forms and the order of the physical world, in so far as that world is a
'copy' of the world of Forms. That there is no systematic parallelism
in the fornler case is, of course, essential to Plato's distinction between
N umber-Forms and mathematical numbers, for to admit the parallelism
is tantalnount to admitting that mathematical numbers, as a separate
class of entities additional to the Number-Forms, are superfluous for the
purposes of explaining mathematical knowledge. And though they are
in fact superfluous for that purpose Plato felt unable to admIt this, for
the reasons we have already indicated.
In one important respect his conception of Number-Forms did show
a valuable insight into the nature of number; it has been compared,
with some plausibility, to modern conceptions of the positive integers
as 'properties of sets'.20 But
he did not see that numbers in the sense of properties of sets are the
only numbers needed and that the relations and operations of arithmetic can be defined for numbers in this sense in such a manner that
the commonly accepted arithmetical statements are verified. As
regards the arithmetical relations and operations he seems to have
been unable to conceive auy other defmitious than those which
fitted solely his Mathematical Numbers."
The postulate of the existeuce of ' intermediate' mathematical objects
does, however, have oue important advantage over the theory of
Forms, as far as Plato's theory of knowledge is coucerned. It allows
Plato to escape, in the field of mathematics at least, the difficulties
created for his distinction between a priori and empirical knowledge
by the model/copy conception of the relation between Forms and
sensibles. For in this one field alone an explanation of the distinction
between a priori and empirical knowledge is now possible which is
quite independent of a model/copy conception of the relation between
their respective objects.
In the first place, although the 'intermediate' mathematical objects
are thought of as instances of the mathematical Forms, it is not the case,
as we have seen, that this exclusively determines the structure of and
possible developments in philosophical mathematics; no such systematic
'copying' is assufl1_ed here as was assumed in the case of the relation
between Forms and sensibles. In the second place the relation between
philosophical mathematics and the structure of the physical world is
not envisaged as the type of model/copy relation assumed in the
Timaeus to exist between the system of Forms and the sensible world.
Thus it is clear that in the Philebus plato envisages philosophical
mathematics as a science of pure mathematics, distinguished from the
mathematics of the 'popular' kind which is applied for particular
purposes to the sensible world, e.g. by the architect or the engineer
(s6b-S7d). He goes on to say that the majority of arts are limited in
their apprehension to 'belief' (doxa, in the specialised sense), a strictly
empirical level of apprehension having only the changing things of
sense as its objects (58e-59a). In this majority plato is certainly including
the applied mathematical techniques which he has earlier specified, and
just as certainly is excluding from it the science of philosophical mathematics. He adds that the study of physics is likewise limited to the realm
of 'belief' (59a). And though he is doubtless thinking here of preSocratic cosmology, yet it is true, as the Timaeus Inakes clear, that his
own theoretical account there in mathematical terms of the structure
of the physical world Can claim no more than probability and represents no higher level of apprehension than 'belief' (29c-d).
The significance of this for the assessment of the status of philosophical mathematics is clear. Just as it is independent, for its structure
and development, of the system of Forms, so too, though it is applicable
to the physical world for the purpose of formulating the theory of the
structure and order of that world, it is free from any necessity of being
so applied and thus free from any conditions requiring its development
to be limited by the purposes of that application. And it is because the
postulate of the existence of 'intermediate' mathematical objects allows
plato to make philosophical mathematics an independent science in
both these respects that he is able to make a much more satisfactory
distinction between apriori knowledge and empirical knowledge (doxa)
in the case of mathematical knowledge than in other fields, where the
model/copy conception of the relation between Forms and sensibles
was still maintained. Thus, on the one hand, the knowledge attained
in the study of philosophical mathematics, conceived as a science of
pure mathematics with the 'intermediates' as its objects, is a priori
knowledge in the same sense in which knowledge of Forms is a priori.
On the other hand the knowledge attained in the study of the physical
world is empirical knowledge (doxa). plato conceived this study, as we
have seen, as one which in the final analysis formulated its theory in
matheluatical terms. Moreover it is clear, if we associate what is said
in the Timaeus about the merely probable truth of the results of this
study as so conceived with what is said in the Philebus about the
distinction between pure and applied mathematics, that plato is thinking of physical science as a science of applied mathematics, distinct
from the science of pure mathematics. We cannot, of course, assume
that when he wrote the Timaeus Plato had already developed his
doctrine of the 'intermediate' mathematical objects and hence we cannot assume that he is thinking of the geometrical shapes and numbers
MATHEMA TICAL KNOWLEDGE
I8S
mentioned at 53b as 'intermediate' mathematical objects. But we can
surely assume that once this doctrine was deVeloped then plato would
henceforth interpret the applied mathematics of the Timaeus conformably with that,doctrine an~ thus assmne those geometrical shapes
and numbers to be Illtermediate mathematical objects. This makes the
applied mathematical theory of the Timaeus a 'real' intelligible model
dIfferent from the model constituted by the Forms, and thus allows
Plato to overcome the difficulties which in the absence of the doctrine
.belong to the metaphysical theory of the Timaeus - the difficulties of
maintaining an adequate distinction betwee.n a priori and empirical
knowledge and of associating a theory of the nature of the physical
world formulated III mathematical terms with a 'model' constituted
by a system of Forms which is itself non-mathematical in structure.
Recognisi~g t~lat the ,Precision and permanent truth belonging to the
mathematIcal model are never III fact perfectly exemplified in the
phYSlCal world, Plato continues to maintain that physical science can
attain nothing higher than empirical knowledge. On the other hand
philosophical mathematics, while in its application to physical science
It 1S able to supply an 'intelligible model' of the order and structure
of the physical world, is a field in which knowledge is a priori; it is
as a SCIence of pure mathematics that plato conceives it.
It must be added that conformably with this distinction between
a priori and empirical knowledge in the Jield of mathematics and its
appI~cations Plato's increasing appreciation of the precise order of the
phYSIcal world and the regularity of its processes, especially in the
sphere of astronomy, leads him to put a very high value on the
empmcal knowledge gained by a study of the physical world. The
study of astronomy becomes, as we have seen, the focal point in the
educatIon of the philosopher. In the light, however, of our discussion
of the latest developments in Plato's metaphysical theory it is now clear
that the prominence given to the study of astronomy as a science of
applied mathematICS does not imply either that the doctrine of transcendent Forms is abandoned or that, though retaining that doctrine,
Plato has radIcally changed his conception of the structure of the world
of Fon~s. For his doctrine of 'intermediate' mathematical objects
allows hIm to keep the science of dialectic which yields knowledge
of F~rms mdependent for the most part of the sciences of pure and
applied mathematIcs. Thus the interpretation of the order of the
"
186
physical world in specifically mathematical terms and its interpretation
in terms of Forms represent two quite different and separate levels of
interpretation. Both types of interpretation arc highly valued by plato
for the knowledge which they yield, but it is significant that in his
latest work there are indications that for the first time he is beginuing
to envisage the former type of interpretation as a discipline with an
independent right to be the basis of true piety and goodness. It demands
the study both of pure mathematics and of the physical sciences,
especially astronomy, as applied mathematical sciences. It demands
also the study of the Number-Forms themselves and the principles
from which they are derived (cf. Epinomis 990d). But it does not
demand the study of the system of Forms as a whole through the
science of dialectic, for it is not concerned with Forms other than
mathematical Forms. This last study becomes for Plato, it would appear
from the Laws (96Sb-c) and the Epinomis (991C), a necessary complement to the other studies for those who are to be completely pious
and good, but no longer does it hold the centre of the stage.
4.
Forms in the unrestricted form which continues to fmd in the distinction between universal and particular or, from an epistemological
standpoint, between concept and percept, an adequate basis for its
distinction between a priori and empirical knowledge. It is true, [mally,
that in his latest thought Plato develops a metaphysical theory restricted
to the explanation of mathematical knowledge which provides a more
satisfactory explanation of the distinction between apriori and empirical
knowledge than does the theory of Forms found in the dialogues; we
might well think that this late development should have prompted
plato to abandon the more general explanation. of the nature of a priori
knowledge which the theory of Forms had hitherto provided. Yet, if
we accept, as we should, Aristotle's testimony, we must accept that
Plato did not abandon that more general explanation. In. the case of
all knowledge other than the knowledge gained in philosophical
mathematics that explanation continned to be the distinctive feature
ofhis theory of knowledge.
CONCLUSiON
This discussion has been primarily a discussion of the evidence for the
development in Plato's latest thought of a more adequate theory of the
distinction between a priori and empirical knowledge than was afforded
by the theory of Forms. It has tried to establish that only in the field
of mathematics was plato able to dissociate the distinction from the
distinction between Forms and sensibles and to make the distinction in
a form which would avoid the principal difficulties of the original
distinction. But there is no evidence to show that outside mathematics
Plato modified his conception of a priori knowledge of Forms so that
those difficulties were avoided. It is true that there were important
developments in the late dialogues in his theoryofknowledge. Together
with a reassessment of the cognitive value of perception there IS a new
conception of the science of dialectic which e:rlicitly recognises ~he
complex structure of the Forms and th~ diverSIty ~f :ela~lOns eXlstmg
between the Forms and recognises also Important dlStffictlons between
kinds of Forms. It is true also that these developments themselves serve,
as we have seen, to accentuate the difficulties in retaining a theory of
:1
i
NOTES
Notes
NOTES TO CHAPT.ER I
See Xenophon, Memorabilia, III, 9; IV, 2, 6. For the Aristotelian references,
with an excellent discussion, see Deman. Le Temoignage d' Aristote sur Socrate
(Paris, I942), pp, 83 If. See also John Gould, The Development of Plato's
Ethics (Cambridge, 1955), Chapter I, for an interesting discussion of the
thesis that 'virtue is knowledge', Gould argues, using Ryle's distinction,
that Socrates' ideal was 'knowing how' to act, and not an ideal of theoretical 'knowing that' (knowledge of facts and principles).l would agree that
Aristotle tends to over-emphasise, for the purposes of his own arguments,
the 'pure intellectualist' aspect of Socratic ethics, but his testimony, supported as it is by Xenophon and Plato, cannot be dismissed as a c~mplete
misrepresentation. See Philosophy, XXXI, p. 377, where I have d1scussed
Gould's thesis more fully.
2. See Richard Robinson, Plato's Earlier Dialectic (2nd ed., Oxford, 1953).
pp. 15-17 77-82, for full references and discussion. Chapters II-V oftbis
book are ~xcellent on the Socratic method of cross-examination.
3. See my article in Classical Quarterly, N.S., VoL II, pp. 74-S2, particularly the
references in note I, p. 75.
4. Phaedo 73a-b almost certainly refers to the recollection theory of the Meno.
5. In Grote's words (Plato, 1865, Vol. II, p. 16).
6. See especially Apology 29d-30b, 40c-41C.
7. For general literature on the Orphics, see M. P. Nilssc;>n in Harvard Theol.
Review, XXVIII (1935), pp. 181 ff.; W. K. C. Guthne, Orpheus and Greek
Religion (I935), and The Creeks and Their Cods (I950), Ch. XI; I. M.
Linforth, The Arts of Orpheus (1941). Linforth has argued convincingly
that the evidence is weak for the view that an organised Orphic sect, with
a deftnite body of literature to express its .creed, existed.in Greece be~ore
Hellenistic times. But all that concerns us 1S that Plato himself recogmsed
certain religious beliefs as 'Orphic' and acknowledged that they were an
influence on his own thought.
8. Cratylus 4oob-c; Republic 364e-36sa. For other p,ossible :eferences see Ket;-I.
Orphicorum Fragmenta, pp. 81-90, and Shorey s note 1U What Plato Said,
P·447·
9. See Guthrie, Orpheus, pp. 171 ff.
10. Die1s-Kranz, Die Fragmel1te der Vorsokratiker, 5th edition (subsequently referred to as DK.): 14, 8; 14, 8a; 44 B 14, B 22; 14, 19; 18, 3; 18, 4.
II. See DR. S8 D I, 2.
12. Burnet, notes on Phaedo 61a3, 67CS, and Greek Philosophy, Pt. I, pp. 41-2.
Cornford, Classical Quarterly, XVI, pp. 145-50.
13. L. Robin, Revue des Etudes Grecques'l XXXII, pp. 452-5,..
. .
14. Cf. the remarks in Epistle VII. 335a: we must always mallltam a real beliefm
the ancient and sacred doctrines which proclaim that our soul is immortal.
and pays full requital for its deeds, as soon as a man has left behind the
body'.
188
1.
15· See Phaedo 70c ff. for this idea of alternation.
16. Creek Philosophy, Pt. I, p. 43.
17· DK. 31, B 129 (probably referring to Pythagoras), B II7.
18. Diogenes Laertius, VIII, 4-5; DK. 14, S.
19· Sextus ~piri:us, A~ersus Mathem~ticos ix. 127. See also DK. 14, Sa ad fin.
rot
anmterestmg note (op. Clt., Vol. II, p. 17), illustrates as a Leibnizlan VIew ~he thought 'that the human mind, by virtue of its interdepend_
ence or kindred with all nature, includes a confused omniscience'. It is the
pare.nt of t~e Stoic conception of'sympathy'.
20. See ~hilolaus 1ll DK. 44, B 6, B II. Cf. Plato, Gorgias S07e-s08a.
21. op. CIt., p. 43.
22. Plato, the Man and his Work, p. 186, n. 2.
23. Les Mythes de Platon, pp. 70-6.
24. Shorey, op. cit., p. 43.
25· It seems clear that in choosing this problem Plato had in mind the incommensurability of the diagonal of a square with its side. The square root of
2 seems to have been the ftrst irrational to be discovered. See Heath, Greek
Mathematics, Vol. I, pp. 90-1, IS6-7.
26. Bertrand Russell, History of Western Philosophy, p, 112, complains that Socrates
here 'has t~ ask leading questions which any judge would disallow'.
27· In the Republtc (SIOb, sua) Plato goes so far as to say that geometry is compelled to make use of sensible 'images', an indication of the reliance of
contemporary geometrical procedure on sensible ftgures. See Ross, Plato's
Theory of Ideas (Oxford, I951), p. 49.
28. For a sununary of the mathematics in Plato, see Heath, op. cit., pp. 294-3IS.
Cf. Proclus, In Bud. (ed. Friedlein), p. 66, 8- I 4.
29· Cf. Euthyphro I2d; Gorgias 4SIb-c, S07e-50Sa.
30. It is of no. epjste~ological signiftcance for Plato's theory that his illustration
~en~ di~tlllgU1shes between empirical knowledge and true belie£ Cf. a
sl1U11ar Illustration in Theaetetus 201a-c.
31. The ftrst phrase is Tho~pson's translation of the Greek aUlas logismos (The
Meno of Plato (Macm1llan, 1901), p. 22I); the second is Taylor's (Plato the
Man and his Work, p. 143).
'
32. See Thomas~ Greek Mathematical Works, Vol. I, PP.,394-'7 (Loeb).
33· Non-deduct1ve, as opposed to the deductive form of analysis which deduces
consequences from the initial assumption and, from the last step in the
analys1s, repeats the steps of the analysis in reverse order to reach the initial
assumption .. The requirement of this method is that the implications at each
step a~e reCIprocal. In the non-deductive form, which clearly influenced
Plato 111 the development of his philosophical method, the procedure is not
~o. s~e what follows from the initial assumption, but to see from what the
1ll1t1al assumption follows. Here it is only the synthesis which is deductive,
and n~t also the analysis. For a full discussion of this distinction, a review of
the eVldence on geometrical analysis, and an examination of its relation to
what .t~e Gree~ commentators describe as philosophical analysis and
syllOg1st1C analYSIS, see my Greek Geometrical Analysis, in Phronesis, Vol. 3,
1958, pp. I-'4.
34· Thompson, op. cit., p. 143. Chemiss, Review of Metaphysics, Vol. IV, p. 421,
n.62.
3S· Thompson, op. cit., p. 127.
36. Ross, op. cit., p. 35. See also p. 2S.
37· So Klara Buchmann, in Die Stellung des Menon in der platonischen Philosophie
(Leipzig, I936), p. 6r.
9 :,111
NOTES
38. op. cit., p. 138, n. I.
39. Buchmann, op. cit., pp. 63, 67-8.
40. Cf. the reference to 'true belief' in th~ Politictls (:-78.c), :v~ere t~e context
makes it clear that 'true belief'is not m any way linuted m Its objects to the
world of appearance. Cherniss, however, exaggerates w~en ~e says tha~ this
passage alone (278c-d) is enough to show that wh~t IS SaId a~out true
belief' in the Meno 'does not distinguish Plato's doctrme at that tIme from
his doctrine in the latest dialogues' (lac. dt., p. 421).
41. Buchmann. op. cit., pp. 65. 70. She is followed by MugIer, Platon et la
recherche mathimatique de son cpoque (Strasbourg: HeItz, 1948),. pp. 3?7. 373·
4 2 • MugIer, op. cit., p. 369. Thus in explaining the status of true belie~s as lsolat:d
data lacking orientation (pp. 302-3. 368-9. 373). he finds thelr source In
sensible experience in a previous life. Initially they are 'the result of an
abstraction based on experience in a previous life' (p. 370 ).
•
43. Cornford (Plato's Theory qf Knowledg:. p. 3) .thought that the reservatlo~
extended only to 'the details of re-lllcarnatlOn, purgatory, and ,so forth,'
I have argued fully elsewhere against th~ tendency. to explam Plato s
reservations as expressions of the uncertalllty and diffidence proper to
Socrates (Classical Quarterly, N.S., Vol. II, pp. 74-82) .. Plato'~ r:luctance to
dogmatise is explicit in dialogues where an explanatlOn of It 1U terms of
Socratic portraiture is quite impossible (e.g. Timaeus, 72d. Cf. the language
of Laws 64Id).
.
44. It must not, of course, be taken as a reference to branches of mat?e~at1cs oth~r
than geometry, to the exclusion of o~her 'branches oflearru~g.. In Plato s
use of it it does not mean 'mathematlcs'. When he does use lt m reference
to the ~athematical sciences, it is always clear in the context, that the
mathematical sciences are 'branches of learning' amongst other branches
oflearning' (e.g. Laws 817e).
.
45. See Hackforth, Plato's Phaed? (Cambridge, 195~), pp. 3-II. I would, wlth
him, place the Phaedo earlier than the Sympostum. .
.
46. Possibly a reference to the ability to comprehend things sy~em~tIcally, the
mark of knowledge as opposed to true belief. Cf. the cham of causal
,
.
reasoning' in the Meno (98a).
47. Cf. Taylor, op. cit., p. 188, n. I, and A. Wedberg, Plato s Ph.losophy of
Mathematics (Stockhohn, I955), p. 33·
48. Ross, op. cit., p. 35.
49. Ross, ibid., p. 25·
,
1
50. I accept Burnet's Oxford text reading here, and transl~te as equa to one ma~.
but not to another', rather than as 'equal to one thl,ng, but. not, to ano~her,
the fonner being preferable in view of the questIon which Immediately
follows about 'equals themselves' or 'equality' - whether THEY ev~r
appeared to you (Simmias, or, it is implied, anyone else) to be unequal (m
the way that equal stones sometimes appear to some people to be unequal).
See further W. J. Verdenius, Mnemosyne, S. IV, V~l. XI (1958), p. 2IO.
For a discussion of the whole passage see K. W. Mills, phronesls, Vol. 2,
pp. 128-47, and Vol. 3, pp. 4~58. The va~iant,readlng tote men ',' . tote. de
(at one time ••• at another) ,IS awkw~rd 1U Vlew of the preceding ent~te
(sometimes). But see Verdemus, loco Clt., pp. 20g-ro, for a defence Oflt.
S!. Mills, loco cit., Vol. 2, p. I45, commenting on Republic 523e-S24d. Other
similar passages are cited by Mills in the same place.
52. If it were not for the recurrence of the phrase 'like or unlike' in 76a. ther~
would be reasonable grounds for bracketing 74cII-d3. Burnet, 1ll his
edition of the Phaedo (p. 56), defends the inclusion of this part of the
NOTES
53.
54-.
55.
56.
57.
19 1
argument, but for the wrong reasons. Plato is not implying here that 'the
equality of sticks and stones must either be like or unlike real equality', and
that it has still to be shown in the argument which follows that the equality
of sticks and stones is 'like' real equality. The relation of resemblance, as
opposed to association by contiguity, has been assumed from the beginning
(74a5).
Wedberg, op. cit., p. 98 (Chapter III of this book gives a most lucid and concise account of the theory of Forms). Plato dearly uses the phrase 'the
equals themselves' as equivalent to 'equality', and there is no ground for
arguing that Plato does in fact here distinguish between Forms and
perfect instances of Forms. Cf. ParmenidesI29a-e. See Verdenius, Ioc. cit.,
p. 2IO, for other similar references, and for reference to further modern
discussions of the point.
See Hackforth, op. cit., p. 84.
In Classical Quarterly, N.S., Vol. N (1954), p. 198.
These first two assumptions are, of course, made explicit (75b-e, 76c-77a,
92d-e). The 'primary postulate' is the existence of Forms.
Though Plato's argument is not concerned with the question of the extent of
the world of Forms, its implication is, as we have seen, that all concepts
which have sensible instances designate Forms.
op. cit., p. 75.
loco cit., p. I99.
58.
59.
60. Plato's Theory of Knowledge, p,6.
61. L. Robin, Les Rapports de I'Etre et de la Connaissance d'apres Platon (Paris,
1957), p. 89.
62. Thinking and Experience (Hutchinson, I953), pp. I3-23.
63. There are obvious affinities here with Aristotle's conception of the syllogism
as a method of scientific explanation, the premisses being the 'cause' of the
conclusion, and offering a scientific explanation of it. The Analytics reflect,
in their title, that conception of the direction of scientific investigation
which views it as a search for the premisses which give the 'cause' of the
conclusion. For references see my discussion in Phronesis, Vol. III, pp. 4-9;
also Ernst Kapp, Greek Foundations qf Traditional Logic (Columbia University Press, New York, 1942), pp. 70-3.
64. Richard Robinson, op. cit., p. 143.
65. His argument here has, in fact, little historical justification. The aim of logical
consistency, which is the aim of Plato's method of hypothesis, is more
characteristic of much pre-Socratic theory than is the aim of verification by
detailed observation.
66. This does not, of course, mean that after reaching position two Plato abandons
for good examination of the theory of Forms itself. The first part of the
Parmenides shows dearly that he does not. And in the late dialogues, and
particularly in the Timaeus, he attempts an examination of those very
general assumptions about the order and intelligibility of the world which
place the theory of Forms within a wider perspective and thus serve to give
reasons for Plato's conviction that the postulate that Forms exist is a sound
one. All that the present argument asserts is that position two appears to
come later in the development of his thought than position one, and that
this is an important factor in assessing the development of his thought.
67. Hackforth, op. cit., p. 72, n. 2.
68. Cf. Julius Stenzel, Plato's Method cif Dialectic, trans. by D. J. Allan (Oxford,
1940), p. 8.
I92
NOTES
NOTES
NOTES TO CHAPTER II
Plato's phrase at Theaetetus 179C.
2. See Ast's Lexicon Platon/cum (2nd ed., I908). s.v. eikSlt, eidolon, and HliffJ~ma.
3· In the Phaedo Plato does not speak of 'images' or 'copies' of Forms in his discussion of recollection, but expresses the relation of likeness between Form
and sensible instances of Form by the adjective hOfnoion and the verb
1.
proseoikenai.
4· Republic 5I8b, c. The enousa epistflne of 51gb is to be compared with the
episteme enausa of Phaedo 73a; cf. the references to 'innate' true beliefs in
Meno 8SC4. 6; 86a7.
5· The Republic of Plato. edited by James Adam, Vol. II, p. 98.
6. On the theory of figured numbers see Heath, Creek Mathematics, Vol. I,
PP·76- 84·
7. So Taylor, op. cit., p. 285.
8, Ross, op. cit., pp. 48-9.
9. Cf. Produs, In Bud. i (ed. Friedlein), pp. 66-8.
IO. For the application of geometrical analysis in the kind of study which
Republic VII envisages see my remarks in Phrouesis, Vol. 3, No. I, pp. 5-9.
II. op. cit., p. 52.
12. Paul Shorey, Republic, Vol. I, p. 412 (Loeb Classical Library).
13· 430a ff. Mimema, eikotl, and de/Sma are the terms used for 'image' or'representation' in words.
14. At this point Plato tends to confuse his argument by associating his advocacy
of expert knowledge in establishing 'correctness' of words with the
advocacy of a 'natural' theory oflanguage in preference to a 'conventional'
theory (390d-e). But his position is subsequently made quite clear.
15. Stallbaum and Meridier so took it.
16. Ficinus took it in this sense, and has been followed, I think rightly, by many
other scholars. I see no necessity to adopt Heindorf's reading kai gar to get
this sense.
17. Richard Robinson in Philosophical Review, LIX, 1950, p. 9.
IS. ibid., p. ro. Robinson's italics in each case. Robinson's argument is directed
against Cornford's view that the arguments of the Theaetetus, while not
mentioning the Forms, are meant to point to the need to postulate them
as objects of knowledge. He does not in fact conceive his purpose to be the
resolution of an inconsistency in Plato's theory of knowledge, but his
argument deserves examination in some detail as an ingenious attempt to
show that in the Theaetetus Plato is refuting the view that sensibles are in
flux. Emil Weerts (Philologus, Supplement XXIII, I, 1931) does, however,
notice the inconsistency in Plato's thought if it is asswned that Plato (i)
held the doctrine of flux to be true for sensibles, (ii) accepted what he
asserted in the Theaetetus to be an implication of this - that determinate
sensible characteristics do not exist, and yet (iii) affirmed that they do exist,
in his doctrine of the 'participation' of sensibles in Forms. But Weerts,
instead of accepting the fact that there is this inconsistency, attempts to
resolve it by denying (i). Thus he discounts Aristotle's testimony that (i)
Was an important influence in Plato's metaphysical theory, and argues (a)
that Plato's reason for thinking sensibles inadequate as objects of knowledge was not that sensibles were in flux but that they exhibited contrary
characteristics; (h) that it was this latter feature of sensibles which led Plato
to postulate a non-sensible reality (p. 39). The influence here, he says, was
Eleatic (cf. Parmenides 127e-130a). The clear and abundant support given by
I93
th~ ~ialo~ues the~selves to Aristotle's testimony on (i) sufficiently refutes
thIS mgemous them; moreover, as ~e shall see in examining the Timaeus in
the llext chapter, Plato there recogruses that (i) is compatible with (iii) and
does not e,ntail (~). There ~s thus no need to try and resolve on Plato's
behalf an mCOllSls~ency whIch he himself later recognised and resolved.
See further Chermss, Aristotle's Criticism ~f Plato and the Academy, Vol. I,
pp. 21S-19. n. 129.
19· C£ Proceedings ~f the Classical Associatioll, Vol. LI (1954), pp. 53-4, for my
remarks on Metaphysics I009bI2-!4.
20. Compare his remarks on the difficulty of adhering to the stipulation made in
the Theaetetus (157b).
2r. Burnet's translation.
22. 'Mind' is the nearest English equivalent for the Greek psyche here and will be
used for ,p~yche in, the rest of the discussion of this argument. '
23. He thus antICIpates hIS fuller treatment in the Sophist of the distinction between
~wo senses of 'what is not' - (i) contrary to what is, (ii) different from what
1S
(258b).
24. A. E. Taylor, op. cit., p. 345. There has been much recent discussion of this
passage (201d-202C) of the Theaetetus. See especially Winifred Hicken in
Phroflesis, Vol. 3 (1958), pp. 126-45, and the references there.
25. To do so would ?e equival~t to saying that what is a simple within the
second conception of logos IS shown to be a physical complex once it is
grant;d that the s~atement 'this is X' is applicable to it. The confusion in
Plat~ s argument I~ understandable when it is seen that in his presentation
o~ his ~rs,t c:mcept.lOn of log~s as statement he is assuming that to say of a
thmg this IS ~ IS to aSCrIbe complexity to it, the complexity being
at:alogous fo: him to the complexity of a physical object made up of
dlffe~nt speCIfiable elements or 'parts'. Compare the use which he makes
of this type of argument in criticising the Parmenidean 'One' in the latter
half of the Parmenides and in the Sophist (244b - 24Se ).
26. Phaedrus 265b-266b; Politicus 260b-z63a, 2S5a~b; Sopllist 219C 220b 245a
253 c-d, 266a, etc.
'
,
•
27· Phaedrus 277b; Sophist 229d. Cf. Phi/ehus 16c-f7a.
2S. See Stenzel, Plat~'s M.ethod if Dialectic (trans. by D. J. Allan), pp. 72-95, for
an excellent discusslOn of the relevance of the problems raised in Theaetetus
~0Ic-210b to the theory of Forms, and to the new method of diairesls.
29· Phtlebus 16d-I7a.
30. Metaphysics I040a8-b4.
3 I. Cf. PhOebus I sa-b.
32. Ross, op. cit., p. 103.
NOTES TO CHAPTER III
See Robin, Pheare ,(Collection des Universites de France, 1933), pp. ii~ix;
Hackf~rth, Pl~to s Phaedrus (Cambridge. 1952), pp. I-7; Festugi{:re, Contemplatlon et vie contemplative selon Platon (2nd ed Paris 1950) P 9
2. See Robin, ibid.
"
,
•..
1.
3· It is impossible to say wh:re the Parmenides stands in relation to the Theaetetus
and the Phaedrus. ,In vl,ew of t~e 12rominence given in the Phaedrus to the
new method of di~ectlc I am Inclined to the view that the Phaedrus stand
chlose:- ~o the SophIst and the Politicus than does the Parmenides and hena:
t at It IS later than the Parmenides
'
N*
.
NOTES
I94
NOTES
4. Phaedrus 249h-250d, 26re ff., 26Sd-z66b, 273d-e; Sophist 253d-e; Politicus
278a-c, 28sa-b; Philebus nb-I3d.
5. Phaedrus 263b-c. 26sa-266b, 27Ib-d. e~c..
.' .
.
6. Especially Timaeus 49d-e. I have exammed thIS passage m detail III American
Journal of Philology, LXXXI ('960), pp. 53-64.
. b
7· 47a-<:.
8. Phaedrus 249b. 250d, with Politicus 28sa-286b; Phileb,ls r6c-18d. Cf. Phlle us
38b-39 C •
9. Philebus ,6d-e.
10. L. Robin, Platon, pp. 89-90.
II. L. Robin, Revue des Etudes Grecques, XXXII, p. 459·
12. J. Stenzel, Plato's Method ofDialeelie, PP. 55--64. I37-48? I5~-6. A more ~ecent
presentation of the thesis that the theor~ of recollectlOn 15 ab~doned m the
late dialogues is that of M. Vanhoutte 1U La .M!tho~e Ontologtque- de Pl~to~
(Louvain, 1956), pp. 36-8, a work extensIvely mfluenced by Robm s
Platon.
13. See Stenzel, op. cit., pp. 90-2, 109-10.
14. See]. B, Skemp, Plato's Statesman (Routledge & Kegan Paul, 1952), pp. 67-8;
H. Cherniss, Aristotle's Criticism of Plato and the Academy, Vol. I, pp. 46-7.
252-3.
IS. Phaedrus 26sc; Politicus 2S9d, 262b, 263b; cf. 28Sb.
16. Cherniss, op. cit., p. 47.
17. Timaeus 27d-29a, 3Sa, 5Ie-52d; Philebus 26d-27b, 59,a-b, 6Id-e.
.
18. e.g. Robin, Platon, pp. I5S-6. A. E. Taylor a~so, cO!1S1dc:cd that the grantmg
of ,being' to determinate sensible charact,ensttcs, m Phllebus 26d~27b marks
a 'maturer doctrine' which is incompatIble with the conceptIon of the
relation between Being and Becoming found in the Phaedo and the
Republic (A Commentary on Plato's Timaeus (Oxford, 1928)~ p. 86).
19. In addition to a passage in the Philebus (23C-2?C) to be consl~ercd shortly
there is one other passage in the dialogues ,whic~ calls for sp~<:I~l com,?-ent.
It is a passage in the Sophist (248a-249d) 111 which Plato CrItICIses phllosophers whom he calls 'the friends of Forms', philosophers who say that only
Forms are real and that they are known by the soul throug~ reflection or
reasoning (logismos). The principal aim of~s argument her~ IS, apparently.
to establish that 'motion' as well as 'rest' 1S real, but there IS 1Uldoubtedly
some confusion in the argument. He ar~ues that 'in~elligence' (n,ous) <:annot
be excluded from 'what is fully real (to pantelos on): that ,mte~gence
implies life, that these both imply s~ul. an~ th;tt the reall~y o~ mtelligence.
life, and soul implies that 'what is In motion and ~otlOn Itself are real
(248e-249b ). The significance of the a~peal to nous IS then m~de ~lear ..If
only what is immobile (the Forms), IS real, then nous, >yhich Implies
motion, has no reality; hence, if the ,e~stence ofknowl~dge IS to be saved,
the theory that only what is immobile ~s real mus~ be rejected. At th,e same
time Plato insists that to accept the reality of,nous ~s to ~~c~pt the fmty ~nd
immobility of its objects (249b-c). Hence hIS, mam cntlclsm so far of the
friends of Forms' would appear to be that, In
far ~~ they assume the
existence of knowledge, they must asswne that, 111 addItion to the Forms,
1tOUS is 'fully real'.
,
In his final summing up of the argument, however, he sugg~sts that he IS
criticising them on another ground. ,He says that we, must reject bo~h the
doctrine that all that is real is immobIle and the doctrme that all that IS real
is in motion and declare that reality includes 'all things immov,able and all
things in mdvement' (249d). And in saying this he seems to suggest that the
:0
20.
21.
22.
23.
24.
25.
26.
27.
I95
distinction between Being (ousia) and Becoming (genesis) made by 'the
friends of Forms' is open to criticism if it implies a denial of any reality to
the world of Becoming. But it is inconceivable, unless we assume it con~
ceivable that he should in a single passage flatly contradict everything else
he has anywhere said on the subject, that he is suggesting that everything
that is in movement is 'fully real'. Certainly when he speaks of 'the
perfectly or completely real' (to panteMs on) in 248e-249a he appears to be
using the phrase in the sense in which he uses it in Republic 477a; the Greek
will not naturally yield any such translation as 'the sum of all that has
being'. Hence it would follow that in arguing for the reality of nous he is
arguing that it is as 'fully real' as the Forms are. But in extending his
argument to the world of Becoming, he speaks now simply of 'Being'
(to on) and 'the whole' (to pan) of reality. We are to think of his argument
here as an argument that 'being' is properly predicable of the world of
Becoming, and, most probably, as a correction of that 'false and dangerous
disparagement of all particulars, in the supposed interest of Forms' (Ross,
op. cit" p. 39) which had led him in the middle dialogues to deny to
perception any cognitive value and to deny the existence of determinate
sensible characteristics. In that respect certainly Plato was 'a friend of the
Forms', a phrase used to describe those who, like Plato himself at times,
have unduly exalted the reality of the Forms to the exclusion of the claims
of everything else. And in that respect Plato's criticism of Ithe friends of
Forms' is a useful corrective to the views of those who had adopted the
doctrine of certain parts of the middle dialogues as their metaphysical
theory. His other criticism serves to make explicit what had not been made
explicit in the middle dialogues - that nous and soul are 'fully real', though
this can hardly be said to be a 'correction' of any of Plato's earlier views.
Now Plato's criticisms do not go beyond this. He is not replacing the
distinction between Being and Becoming by some other doctrine. He is
not bringing sensibles any <closer' to Forms than he had done in the
recollection theory of the Phaedo. And he is certainly not ascribing life
and change to the Forms. The sophistications of some modern views of
the way in which life and change can be said to belong to the Forms are
in themselves attractive, but derive no support from the text. For the
extensive literature on this passage see especially' A. Dies, Le Sophiste
(Collection des Universites de France, 1925), pp. 286-90; C. J. de Vogel
in Proceedings of the Eleventh International Congress oj Philosophy (Brussels,
'953), Vol. XII, pp. 6,--'7; H. Chemiss, op. cit., pp. 437-42, 452-3.
Isa. 'Suppose you venture to take as your One such things as Man, Ox, the
Beautiful, the Good, then you have the sort of unities which involve you
in dispute if you give them your serious attention and subject them to
division,' (Hackforth's translation: Plato's Examination of Pleasure (Cambridge, '945), p. '9.)
ISb.
I6a-b.
I6e, I7a.
This in itself should warn us against reading into the passage the doctrine of
the Igeneration' of the Number-Forms, ascribed by Aristotle to Plato (see
especially Metaphysics 987bI8-25). and using this to interpret the 'being'
mentioned in 26d and 27b as the 'being' of Forms.
59'; 6,d-e.
2SId-253c.
253c-e.
NOTES
28. For the arguments see especially L. Robin, PlatO/t, pp. 88 ff., 154 ff., and Les
Rapports de l'Etre et de la COllllaissallce d'apres Platon (Paris, 1957), pp. II427, 144-5; cf. Stenzel, op. cit., pp. 137-48, and G. E. L. Owen, Classical
Quarterly, N.S., Vol. III (1953), pp. 82--6. Owen mistakenly assumes that
the absolute distinction between Being and Becoming excludes the 'being'
of sensibles, and argues that the fact that the Timaeus maintains this
absolute distinction is one reason for abandoning the almost universally
accepted view that the dialogue is one of the late dialogues. He would
place it in the middle dialogues. This, and his other arguments, are effectively criticised by Cherniss in American Journal of Philology, LXXVIII
(1957), pp. 225-66.
29. Robin claimed, ineffectually in my opinion, that his interpretation did not
imply the substitution of a 'conceptualist' for a 'realist' point of view in
Plato's later thought (Les Rapports • •• I p. !I8). Cf. his statement that
'after the Parmenides the theory of Forms is, in effect, a synthetic logic,
which "constructs" realities' (ibid., p. 100).
30. Especially Timaeus 27c-29d, 48e-52d; Philebus 59a, 6Id-e.
31. See references in note 17, supra. For immortality of soul see Laws 713e,
891e ff., 959a-b, 967d.
32. See Festugiere, ContemplatiolJ et vie contemplative selon Platoll (2nd ed., Paris,
1950), p. 189, n. 2.
33. I previously noted this similarity between the two passages, and compared
them in some detail, in Classical Quarterly, N.S., Vol. IV (I954), pp. 201-4.
34. A comparison of the ten tou pantos p/tysin of 4Ie2 with the same phrase in
47a7 shows that what is to be revealed to us in this life through the suggestions of sense is the same as that which was initially revealed to us before
inca1'l1ation.
35. F. M. C01'l1ford, Plato's Cosmology, p. 144.
36. Cf. Symposium 2Ioa.
J7. Ed. Phaed",s (1868), p. 56.
38. ibid. He spoiled his argument, however, by basing it on an unfortunate
distinction (following Ast) between eidos (as 1Iotio universa vel genus) and
jdea (taking ideai as 'realities'). The eMos is apprehended, he argued, in the
first stage of recollection, the idea at the end of the second and final stage.
39. Stenzel, op. cit., pp. I55-6, in commenting on this passage.
40. Plato's Theory oj Knowledge, p. I86.
41. Cf. 273e.
42. The descriptions of collection and division in the Sophist (253d-e) and the
Politicus (28 5a-b) are closely related to the description of them in the
Phaedrus (265d-266b) and to the discussion in the Phaedrus of knowledge
of resemblances and differences (261e ff.).
43. timiOtatois in 286a1 corresponds with the timia ofPhaedrus 250b, and eidolon • ••
eirgasmmon margos in 286aI-2 corresponds with the marges damon of
Phaedrus 250d.
44. G. P. Henderson, commenting on my argument (Classical Quarterly, N.S.,
Vol. IV (I954), p. 204) that according to the Phaedrus some Forms have no
sensible images (Paideia kai ZO;, No. 48 (Athens, April 1956), p. 70}.
45. Cornford (Plato's Cosmology, p. 41) took Phaedrus 250d to mean that 'there
are no sensible images' of some Forms.
46. Hackforth, Plato's Phaedrus (Cambridge, 1952), p. 95.
47. SO J. B. Skemp (op. cit., p. 175), who translates ta as8mata as 'the existents
which have no visible embodiment'.
48. For Aristotle's testimony and references to modern literature on the subject
NOTES
197
s~e especially Ross, Aristotle's Metaphysics, Vol. I (Oxford, 1924), pp. xlixh, 191-J (on Met. 990bII), 199 (on Met. 991b6), and Plato's Theory of Ideas,
Ch. XI. The evidence is not sufficient to establish that Plato abandoned
in the late dialogues the principle of Republic 596a - that a Form is to be
postulated for every set of things called by the same name. It is true that
he assumes a distinction between 'natural' and 'artificial' divisions in the
practice of diairesis, and assumes that some 'parts', are Forms and some are
not (Politicus 262b-263b; cf. 259d, and Phaedrus 265e). But it may well be
that the use of the terminological distinction between Forms and nonForms is here relative to the questioll of what constitutes the definition of
particul.ar Fo~ms, distinguishing 'real parts', in the senseof'parts' which will
be specified 111 the definition of a particular Form, from 'non-real parts', in
the sense of 'parts' which will not be so specified, but without implying
that what is a 'non-real part' of one Form cannot ever be a 'real part' of
other Forms.
49· Cf. Sophist 253d-e, with Stenzel's analysis (op. cit., Ch. VI), and Comford,
Plato's Theory of Knowledge, pp. 267-8.
50. So Stenzel, op. cit., p. 132.
51. Grote, Plato, Vol. II (1865), p. 472. Grote rightly emphasised that 'sensible
perception' is here highly valued, and rightly compared this passage with
Ph~edrus 249c, 265d-e. But he was wrong to conclude that the granting of
an Im~ort~nt role, h~re t~ perception il?-dicates that the Form is now thought
of as logIcally distmgUlshable from Its particulars, but having no reality
apart from them' (P.471).
52. See also Sophist 248a ff., 265c ff.; Philebus 26e-3 ra.
53. See Tayl~r, A, Comme~tary on Plato's Timaeus (Oxford, 1928), pp. 312-13.
54. In an artIcle ill Amencan Journal if Philology, LXXV (1954), pp. !I3-30,
P~ofessor H. Cherniss offered a translation of this passage substantially
~erent from my own, and argued. both in that article and in a subsequent
arude (AJ.P., LXXVIIl (1957), p. 245), that it was through mistranslation
that It be~e pOSSIble to find a dIscrepancy between this passage and those
p~ssag:s ill the T.h~aetetus (I82C-d) and the Cratylus (439d) where Plato is
~hscusslllg, as he IS III the Timaeus passage, how we are to designate what is
111.change. I hav~ critici~e~ Cherniss's translation and interpretation of the
Ttmaeus passage 1ll detaillll AJ.P., LXXXI (1960), pp. 53-64. and given
reasons for preferring the translation I now make.
55. Cornford's translation in Plato's Cosmology, pp. 157-8.
56. 36c, 4oa-b, 47b.
57. Cornford's translation, op. cit., p. 186.
58. See Taylor, Commentary, pp. 272-3, for the interpretation of the clause "otan
de • .. rheuma (44b).
59. I accept Grube' ~ interpretation of the difficult passage (3 5a) on the composition
of the cosmI~ soul (Classical Philology, XXVII (I932), pp. 80-2).
60. Cornford, op. CIt., p. 41.
61. This is Taylor's rendering of logoi (Commentary p. 74). It is best to avoid the
translation 'accounts', since Plato has just pointed out that both perception
an~ tru~ belief are inc~pable of yielding any rational 'account' (logos) of
theIr objects. Thus while explanatory descriptions of 01' 'discourses' about
the J?hysical world as a wh<;le may be put forward, the form of appre.
henslo~l (doxa) of ~he phYSIcal wo~l~ which. these 'discourses' yield is,
a,ccording to ~lat~, 111c~pable of pr~V1dUlg a ratIOnal 'account' of its objects
SUlce n~, finaIJust~~atlon of:vhat IS taken to be the truth is ever possible.
62. That the likely stones of phYSICal theory represent a level of apprehension
NOTES
,<53.
<>4.
<55.
<56.
·67.
-6S.
69.
70.
71.
which is merely 'belief' (in the specialised sense) is indicated at 29c. See also
Philebus :59a, where the physical scientist is said to have only 'belief'.
Taylor (op. cit., pp. 59-61, 73). In presenting this type of arg~ment I have
simply summarised Taylor's much longer account, keeplllg as far as
possible to his terminology.
For an examination of the whole passage see note 19, supra.
But see J. L. Ackrill in Journal of Hellenic Studies. LXXVII (1957). pp. 1-6.
who argues that 2:56alo-b4 implies the distinction.
Gilbert Ryle in Mind. N.S. XLVlII (1939). p. 146.
See Euthydemus 2S3e-2S4c, 2S:5d-2S6c; Theaetetus 167a, ISSd-189 c.
Stenzel, op. cit., p. 127.
Stenzel, ibid., p. 109.
See note 19 supra.
.. .
Since instances of both phantasia and doxa are instances of doxa the dlstmctlon
is not, in its terminology. a very happy one.
NOTES TO CHAPTER IV
For the affinity between human soul and cosmic soul, and the significance of
this for human goodness, see also Philebus 26e-3U.
2. There are no good grounds for condemning the Epinomis as spurious. For the
literature on this question and a good brief discussion see J. Harward, The
Epinomis of Plato (Oxford, 1925), pp. 26-5 S.
.
3. Plato also refers back to the theological doctrine earlier expowlded III Book X.
See particularly 897b-899b.
.
.
4. An excellent recent examination of the passage IS made by A. R. Lacey III
Phronesis, Vol. I, pp. SI-104.
5. Grote. Plato. Vol. JII. p. 454.
6. Aristotle refers to them in Physics 209b14. Ross (Plato's Theory of Ideas,
Ch. IX) effectively answers Prof. Chemiss's thesis that f1ris~ot1e, wheneyer
he appears to go beyond the doctrine of the dialogues, IS m~sunderstanding
or misrepresenting what he found in the dialogues ('0e ~Iddle ?f t~e Early
Academy, Univ. of California Press, 1945). Chenuss s theSIS IS most
persuasively argued, deriving its strength not only from the fact th~t
Aristotle does frequently misinterpret Plato but also from the fact that his
testimony frequently assumes for its proper interpretation a knowledge of
the details of Plato's latest doctrine which we do not possess and thus
prompts us to find a clue to its interpretation i~ the sugge~tions and
implications of Plato's latest dialogues. But the testimony of Anstotle and
of the Greek commentators on Aristotle shows beyond doubt that Plato
gave oral instruction in the Academy which went beyond the doctrine of
the dialogues.
7. Harm. EI. ii, 30-1 (The Harmonics of Aristoxenus, ed. H. S. Macran (Oxford,
1902), p. 122).
8. In Phys .• p. 453. 25 ff. (Die1s).
9. De Anima 404br8 if.; Metaphysics 99rb9-992brS, ro73aI7-19, roS6aII-13,
1090aI6-17.
ro. Metaphysics IoSobII-14; cf. 1OSoa30-35·
II. Ross, Aristotle's Metaphysics, Vol. II, p. 42 7.
12. The fullest and best discussion is that ofL. Robin in La Thiorie platonicienne
des Idees et des Nombres d'apres Aristote (Paris, 1908). pp. 450 iT.
13. For references to passages in which Aristotle assigns particular numbers to
Forms see Ross, Plato's Theory of Ideas, pp. 2IS-20.
I.
NOTES
199
14· Adversus Mathematicos x. 258; quoted by Ross, ibid., p. 216.
IS· C£ Theophr~st~s, Met~physjcs 6b.II-!4. ~e says that Plato, in reducing things
to first pnnC1ples, linked senslbles WIth Forms and Forms with numbers,
and then proceeded from numbers to first principles. Although the
obscurity of the evidence makes highly conjectural any interpretation of
the manner of the derivation of the numbers from the principles of the
One and 'the great and small', the important point for the purposes of
the present discuss~on is one which is not a matter of conjecture - that the
numbers to be denved from these principles and ordered in a series are the
Number-Forms, the characteristics of which we have already examined.
Ross, op. cit., Ch. XII, gives an excellent review of modern interpretations
of the manner of derivation of the Number-Forms.
16. Wedberg (op. cit.• pp. 131-5) rightly emphasises the importance of Phaedo
rOIb-d for this characteristic of the Number-Forms. We noted earlier
,note II, su1?~a) a reference in Aristotle's Metaphysics (loSoa20) to the
'mcomparability' of the Number-Forms in a context which indicates that
their incomparability excludes the performing of arit1lnletical operations
on them.
17· Aristotle ascribes the doctrine to Plato by name in Metaphysics 987b14-IS and
102Sbl9-21. For other references to the doctrine in the Metaphysics see
Ross, Aristotle's Metaphysics, Vol. I, p. r66.
IS. Taylor, Plato, the Man and his Work, p. 417.
19. Metaphysics 1080<121-23; roSU5-7, IS-21.
20. By Wedberg. op. cit•• p. 7721. Wedberg, ibid., p. 7S. I am much indebted, in my discussion of the distinction
between Number-Forms and mathematical numbers, to Wedberg's valuable examination of the distinction, but I cannot agree with him that as
early as the Phaedo Plato was clearly aware of the distinction. It seems to me
that o~¥ in the Philebus d~es it first become clearly implicit that Plato is
recogrusmg that mathemattcal knowledge cannot be explained in terms
only of Forms. And in a passage in the Metaphysics (1078b9-I2) Aristotle
appears to imply ~at the doctrine of 'intermediate' mathematical objects,
as well as the doctnne that Forms are numbers is a late and not an original
•
feature of Plato's metaphysical theory.
Index
Ackrill, J. L., 198
Adam, J., 53. 192
Analysis: geometrical, 14-16, 189. 192;
as enumeration of simple compo-
nents,
96-IOI.
See also Hypo-
thesis
Aristotle: on Socrates, 1-3; on preSoctaties, 8; on geometrical analysis, IS; 011 theory of Forms, 26-7.
73. 105. 128. 173-4, 196-7; on
theory of £lux, 26, 73; on subjectivism, 80; on syllogism, 191;
on Plato's 'W1written doctrines',
174 ff., 195, 198, 199
Aristoxenus, 174, 198
Astronomy, 56-7. 61, 134, 170-2,
1 84-6
Being: distinct from Becoming, 80-3.
86-7. II2-13. II6, 130-1, 159
Belief (doxa): two senses of, 13-14.
62; distinct from knowledge, 1321, 87-90, 139---47; distinct from
judgement, 87-8, 162-3; false,
91-5. 160; as result of reflection,
85. 160-4; and account (logos), 16,
62, 94-105; and perception, 61-7.
140-1, 160-1, 164-8; and physical
theory, 141-7, 169, 184
Buchmann, K., 189, 190
Burnet, J., 7, 9, ro, 188, 190-1,
193
Cherniss, H., 189, 190, 193. 194, 195,
196, 197, 198
Collection, method of, 108-12, 120-2,
142, 153-4
Compatibility, ISO-I, 157-8
Comford, F. M., 7, 36, 121, 188, 190,
19 6, 197
Definition, 1-5, IOo-5, 140, 159
de Vogel, C. J., 195
Diels, H' I 188, 189. 198
Dies, A" 195
Diogenes Laertius, 189
Division, method of, 101-6, ro8-12,
142. 153-4. 157---9, 164, 173. 176
Empedocles, 8, 9
False statement, 154-8
Festugiere, A. J., 193. 196
Flux, Heraclitean doctrine of, 26-7,
70-80, 82, 132-4, 192-3
Forms. 24 if., 49:ff.. 64-7. 71-3, 76, 84,
88-91, 102-6, II4 ff., ISO fL.
194-5; and Numbers, 174 If.
Frutiger, P., ro
Good, nature of, 1-3, 23-6, 131, 170-1
Gould,J.,I88
Grote, G.• 188, 189. 197, 198
Grube, G. M. A., 197
Guthrie, W. K. C., 188
Hackforth, R., 34, 190, 191. 193. 195.
19 6
Harward, J., 198
Heath, T. L., 189, 192
Henderson, G. P., 196
Heraclitus, 8. See also Flux
Hicken, W., 193
Hypothesis, method of, 15-16, 40-5,
53-5, 77
Images: sensible, 30-40, 49-57, 62-7.
II2-I3. 122-39; verbal, 65-7.
68-70, 149-50
Kapp, E., 191
201
INDEX
202
INDEX
Lacey, A. R., 198
99d- 102a
Limit, principle of, II3-I8, 170, 176,
178-80
Linforth. I. M., 188
lOIb--c
40-45
175
Plato: Timaeus-continued
42e-44d
135
47a-b
119, 134, 138-9
47e-48a
13 6
48e-52d
131-4. 137
49d-e
73, 132-3, 194
51d-52a
139 If.
53b
170
53c-68d
135
Symposium
210a-2I2a
49-53, 121
Republic
Mathematics, II-I3, 14-15. 55-61,
135, 169 ff.; objects of. 55. 175.
177 If., 189
Mills, K. W" 190
Mugler, Ch., 190
Necessity, 136--7; and contingency,
141, 144-5
Nilsson, M. P., 188
Numbers; see Forms
Orphics, 5. 7. 8, 188
Owen, G. E. L., 196
Parmenides, 34. 102, 148, 153
Perception: in Phaedo, 28-41; in
Symposium, 49-53; in Republic,
53:ff.; in Theaetetus, 76 if.; in
Phaedrus, 120-30; in Timaeus, 130139; in Sophist. 160-1, 164; in
Politicus, 123-30; in Philebus, 161162; distinct from sensation, 48,
77; distinct from thought (dianoia).
84-7. 160-1
Philolaus, 189
Physical science, 134-8, 141-6, 169-72,
184-6, 197-8
Plato: main passages discussed:
Euthydemus
285d-286c
Meno
Phaeda
64d-66e
73 a- b
a-77a
76b
78c-80b
66-7
53
13-14, 61-3
53-6
192
63-4
56-61
59
Sophist
235a-236c
240d- 24Id
24 8a-249d
251a-260b
254C
261d-262e
263a-d
263d-264b
Cratylus
385e-386a
386d-e
390c-<l
435b-<l
438a-e
439c-440d
70
71
69
69
68
Theaetetus
ISld-160e
181b-183C
182d-183c
I84b-I87a
187e-I 99d
201d-205e
20sa-e
207a-21ob
76-83
83-4
74-5
84--91, 125--9, 160-1
92-5
96-100
102
101-4
Parmenides
129a-e
129d-130a
I31a--e
132d-l 33 a
133a-134c
1-2
6-II
II-23
'4
23-6,36,40
188
n
73. ID2
245c-246a
246a-248e
249b-d
24ge-250d
263a-c
265d-e
191
152
Timaeus
27d-3 0C
30C-3 1b
3Ia-b
35a-37c
4
'e
120, 131
120
14-3
142-3, 190
112, 129-30
123-8, 143
Philebus
15 a- 17a
16c-18d
23C-27C
25a-e
26d-27b
38b-40d
sse-59c
59b
817e if.
893b If.
963c if.
965b-c
966c if.
32-3, 51
II8
122-4124
108, 122
277d- 279a
285a-b
285d-286b
Laws
lIS
108-9, 120-2,
'49
148
151, 159, 194-5
150-4125
'54-5
155-8
160-8
Politicus
7 1- 6
Phaedrus
283e-284C
77d-78a
Sra-e
Sre-86c
97'-98a
401-402
476c-<l
477-480
510-5II
5I8b, c
523a-5 2sa
525a If.
596a
Epinomis
990a if.
991C
II3-16
176, 178
II6-17. 178-9
170
82
161-2. 168
179-8473
171
131
173
186
17 1
Price, H. H., 39
Proc1us, IS. 189. 192
Protagoras, 70-1. 77-80, 133
Pythagoreans, 5, 7-ID, 12, 15, 56, II3 ..
170, 173. 176, 189
Recollection, theory of: in Meno, 4-23 ~
in Phaedo, 27-40; in Republic, 53;
in Phaedrus, ID8-ro, 120-30; in
Timaeus, II9, 134-S; in PolitictlS,
1I9. 123-30; retained in late
dialogues, 108-20
Robin, L., 188, 191, 193. 194, 196, 198.
Robinson, R., 188, 191, 192-3
Ross, W. D., S9, 189, 192, 193. 197.
198, 199
Russell, B., r89
Ryle, G., 188, 198
Sextus Empiricus, 175-6, 189
Shorey, P., 188, 192
Simplicius, 174
Skemp,]. B., 194, 196
Socrates, 1-4.6, 188, 190
Soul: immortality of, 6-g, 21-2. 120 ..
196; cosmic. 25, 131, 136, 170-1
Space, 131-3, 135
Stenzel,}., 191, 193, 194, 196, 197, 198
Taylor, A. E., 10, 18, 189, 190, I92 ..
193. 194. 197, 198, 199
Theophrastus, 199
Thompson, W. H., 121. 189
Vanhoutte, M., 194
Verdenius, W. J.. 190, 191
172
173, 186
20J
Wedberg, A., 190, 191, 199
Weerts, E., 192-3
Xenophon, 188
130-1, I39~1f.
137
144
136
II9, 134
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Plato`s Theory of Knowledge

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