An Examination of
Plato's
Volume Two
PLATO ON KNOWLEDGE
1. M. CROMBIE
, 'o.n ;.. s'uti^s and discusses
'',:" V) say on the more tcch-
t; .s of philosophy. This
-'Je metaphysical and logical
topi*, . iicory of knowledge., philos-
ophy of nature and the methodology of
science and of philosophy,
The book is intended for the student
of philosophy, and assumes no knowledge
of Greek.
Reviewing Volume Onc 3 Plato on Man
and Society*, the Oxford Magazine says
of Mr, Crombie: 'He is clear and candid,,
often amusing, usually interesting. His
style of interpretation is generous and
favourable to Plato. The book is good :
readable, stimulating, useful.*
Reviewing Volume Two for Philos-
ophical Books ) A. C. Lloyd wrote ; c Mr.
Crumble has completed his ambitious
i ask ot' exploring in a framework that
makes sense to current English-speaking
phifosiophy the whole of Plato 1 j>
or the one might say
i if how far this can be done,
Th& second seems to me to be
very indeed and one which deserves
la be called important* 9
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An Examination of
PLATO'S DOCTRINES
REALITY
. . , ,,. ,*,.. I .... ..,., ., ..., ,,
Internationa! Library of Philosophy
and Scientific Method
EDITOR: TED HONDERICH
A Catalogue of books already published in the
International Library of Philosophy and Scientific Method
will be found at the end of this volume.
An Examination of
PLATO'S
DOCTRINES
by
I. M. Crombie
Fellow of Wadham College, Oxford
ii. PLATO ON KNOWLEDGE AND REALITY
LONDON
ROUTLEDGE & KEGAN PAUL
NEW YORK : THE HUMANITIES PRESS
First published 1963
by Routledge & Kegan Paul Ltd
Broadway House, 68-74 Carter Lane
London, EC4V 5EL
Printed in Great Britain
by Fletcher & Son Ltd, Norwich
I. M. Crombie 1963
No part of this book may be reproduced
in any form without permission from
the publisher, except for the quotation
of brief passages in criticism
Second impression 1967
Third impression 1971
ISBN 7100 3633 7
CONTENTS
PREFACE page fx
GLOSSARY x
1. THEORY OF KNOWLEDGE
I. AISTHESIS
A. The machinery of sensation I
B. The epistemological status of sensation (the Theaetetus) 3
/". The discussion of Protagoras 4
iL The discussion of Heraclitus 10
HL The equation of knowledge -with sensation 13
iv. The perception theory of the Theaetetus 14
v. Our knowledge of the external world 26
II. DOXA AND EPISTEME
A. The concept 0/doxa 33
B. The contrast between doxa and episteme; introduc-
tory 34
C. General impressions of the contrast between doxa
and epistSmd 35
D. Doxa and episteme; anticipation of conclusions 41
E. Knowledge and belief in the Meno 50
F. Knowledge and belief in the Republic 53
/. In Republic 5 53
ii. In Republic 6 and 7 70
JK. In Republic 10 103
G. Knowledge and belief in the Theaetetus 105
H. Knowledge and belief in the Seventh Letter 122
/. The formal question: "What is knowledge?" 127
/. The material guestion: " What can we know?"" 128
III. THE DOCTRINE OF ANAMNESIS 135
APPENDIX. FURTHER POINTS CONCERNING THE PASSAGE IN
THE FIFTH BOOK OF THE REPUBLIC 148
2. COSMOLOGY AND THEORY OF NATURE
I. THREE PRESUPPOSITIONS 153
IL THEPffAEDO 156
III. THE REPUBLIC 171
V
KANSAS CITY (MO.) PUBLIC LIBRARY
7315623
CONTENTS
5. PLATO'S CONCEPTION OF PHILOSOPHICAL
METHOD
I. GENERAL CONSIDERATIONS 517
II. HYPOTHESES AND DIALECTIC 528
A. Hypotheses in the Meno and Phaedo 529
B. Hypotheses and dialectic in the Republic 548
III. THE CONCEPT OF DIALECTIC 562
IV. CONCLUSION 567
INDEX 571
viu
PREFACE
FOR an account of what I have tried to do in this book I would
refer the reader to the Preface and Introductory Notes to the first
volume. This second volume contains my account of Plato's treat-
ment of the more technical problems of philosophy. I have tried to
make it self-contained; this has entailed some repetition of matters
already treated in Volume 1. 1 repeat the acknowledgments made in
the earlier preface. In particular my thanks are due to my colleagues
and pupils for what I have learnt from them; to Professor Ayer who
kindly read my manuscript and persuaded me to remove some of its
faults; to Mr. B. G. Mitchell who read and commented on an earlier
draft of Chapter 1 ; to Mr. J. C. B. Gosling, from discussions with
whom I have learnt a very great deal about the topics treated here
(though I doubt whether he will agree with many of my conclusions);
to Mr. R. M. Hare, whose article on Philosophical Discoveries (Mind
1960) has helped me to crystallise some of the things that I wanted to
say; to Professor Ryle, whose studies in Plato, published and un-
published, have done so much to breathe life into the discussion of
Plato's later work.
I. M. CROMBIE
Oxford
IX
GLOSSARY
The following crude equivalences may be found useful as aide-memoire.
Agnoia, ignorance
AlsthSsis, sense-perception
Aitia, cause, reason, explanation
Akribeia, accuracy
Aletheia, truth
Anamnesis, recollection
Ananke, necessity ("brute fact")
Arche y beginning, source, principle
Chora, space
Diairesis, division, separation
Dialektik$, dialectic.
Dianoia, thought
Doxa, belief, opinion, impression
Eikasia, conjecture, likening
Eikon, image
EpistSme, knowledge
Genesis, a becoming, happening,
coming to be
Gignomenon, something that be-
comes
Gnosis, knowledge
Kalos, noble, fine, beautiful
Kinesis^ change ("motion")
Logismos, calculation, thinking out
Logos, account, definition, argu-
ment, proposition, etc.
Meros, part, bit
Noesis, intellectual apprehension
Nous, mind, intellectual apprehen-
sion
Opsis, sight
Paradelgma, exemplar, illustration,
archetype
Pathema, something undergone
Phronesis, wisdom
Pistis, belief, grounded confidence
Sapheneia, clarity
Sophia, wisdom
Sunagoge, drawing together, collec-
tion
I
THEORY OF KNOWLEDGE
THE discussion of epistemological questions was begun, I suppose,
by the fifth century Sophists and in particular by Protagoras: but
there was a good deal left for Plato to contribute. It will be con-
venient to discuss his contributions mainly in terms of three central
concepts, namely aisthesis (perception or sensation), doxa (belief,
opinion, judgment) and episteme or gndsis (knowledge or under-
standing).
I. AISTHESIS
A. The machinery of sensation
Plato was well aware of the difference between a philosopher and a
physiologist, and did not feel called upon to offer a physiological
account of perception. In the Timaeus however (45-6 and 61-8)
Timaeus is made to say how he supposes the senses to work. The
account which he offers is of the same type as that which is given
by a modern physiologist, though of course the details are very
different. It is important to have some idea of the physiological
picture which Plato thought probable and we will therefore look
briefly at Timaeus' account of sight (Timaeus 45-6 and 67-8).
There is, then, a certain type of fire which cannot burn in other
words, light. This substance is to be found outside us, and there is
also a supply of it inside the body. This internal light flows out
through the eye when the eye is surrounded by light outside (it can-
not get out at night when the eye is surrounded by darkness). The
beam of light which flows out through the eye coalesces with the
light straight ahead of it, and forms a sort of solid cone with its
point at the eye and its base at the surface of the object which is
being looked at. Being solid, this cone of light acts as a sort of rigid
body and transmits any motions which there may be at the surface
of the object back to the eye of the percipient and thence to his mind.
1
THEORY OF KNOWLEDGE
(The movement of this solid cone of light thus does the work of light
rays in modern optics in that it stimulates in the eye disturbances
which correspond to the disturbances at the surface of the object).
The colour of the object seen depends on the size of the particles
emitted by the object, particles of different sizes having different
effects on the cone of light, and therefore on its effect on the
eye.
Plato is not committed to the details of this account, and they are
not perfectly clear. But in general the position is that both the
percipient and the perceived object must be in a state of activity, the
one emitting light through its eyes, the other particles from its
surface, and that this activity is not what we see, but the cause of
our seeing. Our seeing is a pathema or something which we undergo
when the disturbances set up in the eye are large enough to be
transmitted to the psuche or mind.
When Plato turns to a philosophical discussion of the problems
of perception in the Theaetetus he seems, as we shall see, to accept
this kind of generalised version of the optics of the Timaeus as the
basis from which epistemology must start. Epistemological pictures
can be crudely divided into cognitive pictures and causal pictures.
According to a cognitive picture we somehow use our senses to find
out what things are like. The colours and other sense-properties of
things belong to them quite independently of our perceiving them;
in perception we discover but in no sense create the properties which
things have. According to a causal picture on the other hand our
sense-data are simply the results of the stimulation of our sense-
organs. The sensible properties of things are therefore joint products
of the activities of the sense-organ and of the perceived object; and
in that way colours and tastes and so on are partially created (so to
speak) by our sense-organs in perception. The colour of a thing is
the way in which it affects our senses and the true properties of the
thing are those properties, whatever they are, which enable it to
affect our senses in that way. A causal picture is commonly adopted
by those who take seriously (or, some would say, naively) the dis-
coveries of the physiologists; and it is I think important, if we are to
understand Plato's attitude to empirical knowledge, to remember
that he seems to have taken a causal picture for granted.
To take only one respect in which this may be important: a causal
picture enhances what I will call the formal rather than the qualita-
tive aspect of our sensory information. Thus there is a formal
correspondence, but no qualitative resemblance, between the shape
of the groove in a gramophone record and the sound which comes
out of the loudspeaker; a certain type of sound corresponds to a
certain pattern of groove, but a high note (for example) is not in any
2
THEORY OF KNOWLEDGE
other way like a sharply serrated groove. If our sense-organs are
thought of as mechanisms, as gramophones are mechanisms, this
might at least make it easier to believe that it is the shapes, sizes,
velocities and other "primary qualities" of things which are essential
to them as they are in themselves.
(One might illustrate the difference between the causal and the
cognitive pictures of perception by the difference between two types
of mechanism, a gramophone and a magic lantern. In the case of a
gramophone you feed in a series of jolts to a stylus and get out
something quite different. In the case of a magic lantern you feed in
a picture and get out the same picture enlarged on a screen; the
mechanism hardly creates the picture but merely renders it visible
to a large audience. If our senses are like magic lanterns, windows
or telescopes then clearly the world is very much as it seems; if
however our senses are more like gramophones then clearly there is
a sense in which we shall be misled if we suppose that they tell us
what the world is really like),
B. The epistemological status of sensation (the Theaetetus)
Plato's discussion of aisthesis or sensation is to be found in one of
his most brilliant dialogues, the Theaetetus. In form this dialogue is
a search for a Socratic definition of knowledge (episteme), and the
search is unsuccessful. In practice however the point of writing the
dialogue was not to fail to define knowledge, nor to show that it
cannot be defined, but to illuminate certain other matters. Perhaps
the chief of these is that our knowledge 1 of the external world is not
a matter of undergoing sense-data but of interpreting them. This
result emerges from a long and complicated discussion which takes
the form of distinguishing aisthesis or sensation (which consists of
things which happen to us as a result of the stimulation of our
sense-organs) from doxa or judgment (which comes about through
the comparison of sense-data with each other and which consists
in treating them as manifestations of an external world).
The discussion is, as I say, long and complicated. The section we
are concerned with is from 151 to 187. It opens when Theaetetus
(having begun by defining knowledge in terms of its instances, and
having been told that this is not the proper way to define) says that
a man who knows anything perceives or senses it and that therefore
knowledge is perception or sensation (aisthlsis).
Socrates' reaction to this is striking, for he proceeds rapidly to
1 Here and elsewhere I shall, where convenient, allow myself to use "know-
ledge" in places where Plato would perhaps regard epist$m$ as strictly inappro-
priate.
3
THEORY OF KNOWLEDGE
identify this Definition firstly with Protagoras' doctrine that there is
no distinetion (in terms of truth and falsehood) between illusion
and reality, and secondly with Heraclitus* doctrine that there is no
stability in the world (panta ra, or "everything is in flux").
These identifications seem bold, and the second of them far-
fetched. In order to understand what is in Socrates' mind we must
remember that Theaetetus' proposed definition "knowledge is per-
ception" is to be read as an equation, and therefore as entailing
both: "Every case of perception is a case of knowledge" and also:
"Every case of knowledge is a case of perception." Now if every
perception is a case of knowledge, then evidently there are no illu-
sions, and where there is an empirical disagreement, say between
Jones who finds the wind chilly and Smith who finds it warm, both
must in a sense be right. On the other hand if every case of knowledge
is a case of perception then there must be complete instability and
randomness in the world. For if there are constant relations between
sense-data, and we can be aware of them, then there are things other
than sense-data that we can know, namely the constant relations be-
tween them. Therefore if our knowledge consists of nothing but the
having of sense-data, these constant relations cannot exist; in other
words everything is in flux. It must I think be in this way that Socrates
makes Theaetetus* definition imply the Heraclitean dDCtrine of flux
(though it must be confessed that the connection is not made clear
in the text).
We must go into this in rather more detail. Since Plato feels that
the Protagorean and the Heraclitean doctrines belong very much (at
the least) to the same stable, he does not disentangle them completely
and we shall not be able to do so either.
(i) The discussion of Protagoras
Protagoras* treatise apparently opened with the sonorous aphorism
"Man is the measure of all things", and his "relativism" seems to
have boxed the philosophical compass. Whatever seems to a man to
be so, is so to that man whether it is a matter of wine seeming sour,
or of an institution seeming unjust. There are unusual sense-data
and deplorable opinions but there are no illusions and no false
beliefs. Plato seems to imply, however, that this general relativism
had its roots in a doctrine of perception according to which nobody
ever perceives anything but his own sense-data, and grew from these
roots into a universal doctrine. This extension may well have taken
place in both of two ways. Firstly Protagoras may have felt that all
beliefs that a man holds must in the end be based on his experience,
so that differences of opinion about, say, politics, or agriculture
derive ultimately from different ways of experiencing the world.
4
THEORY OF KNOWLEDGE
Secondly, and perhaps more importantly, the words for seeming in
Greek as in English (dokein and phainesthaf) are ambiguous in having
both a sensory and a non-sensory use. Thus the wine may seem sour
in the sense that it tastes sour, or it may seem to be stolen in the sense
that it is reasonable to believe that it is stolen. It is possible then that
Protagoras began by asserting that all sense-data are in the same
ontological boat; the wine really has as many different tastes as
there are people to whom it tastes different. It is not the case that
the wine is really sweet, though it tastes sour to Jones ; rather it is
really sweet-to-Smith, sour-to-Jones, tasteless-to-Green and so on.
Expressing this in the form "whatever seems to a man is to that
man", Protagoras may have felt obliged to go on to say that all
opinions are equally true, just as all sense-data are equally valid,
simply because an opinion too is something which "seems to a
man".
However this may be, we can distinguish in Protagoras what
we may call his central and his extended thesis, his central thesis
being that all reports of immediate perception are equally valid,
his extended thesis that all beliefs whatever are equally valid. This
distinction Socrates gradually draws in the course of the present
discussion.
Theaetetus, then, proposes (151) that knowledge is perception, and
Socrates tells him that this amounts to the Protagorean doctrine that
man is the measure of all things. This doctrine in turn, he says, rests
on the further doctrine that: (a) there are really no individual things
having properties of their own (whatever seems to have one property
can also seem to have the opposite property); and (b) everything is
a product of motion and activity. Thus the whiteness of an object,
for example, is "a resultant of the contact of the eyes with the
appropriate motion" (153 e 6). Since this can be applied to every
property of a thing, the objective existence of things is dissolved away
and we are left with a world of sense-data, each private to a given
percipient. We know from our own experience that a thing which
looks one colour on one occasion may well look another colour on
another occasion; a fortiori we can infer that what looks one colour
to one man may well look different to another man. There is there-
fore no reason why any sense-datum should be regarded as more
veridical than any other, and thus the distinction between reality
and illusion is done away with as Protagoras* thesis requires.
What has happened is this. Theaetetus has suggested that know-
ledge is perception. But if that is so then there is truth in every
perceptual judgment. Yet perceptual disputes occur; the stone which
one man finds warm seems cold to another. Therefore we can only
say that both of these perceptual judgments are true, if we say that
5
THEORY OF KNOWLEDGE
what each man perceives is private to himself the warm stone
private to the one man, the cold stone private to the other. Each
man will be correctly reporting the properties of his private stone.
But we cannot have an indefinite number of private physical stones
In the same place at the same time. The only way therefore in which
this can be rendered plausible is to get rid of the physical stone.
If the stone is nothing but a collection of the sense-data which lead
us to speak of the stone, then there is no reason why one man's
sense-data of the stone should agree with another's. The only physical
thing involved in the transaction is some process or other whose
interaction with our bodies gives rise to the sense-data which we take
to represent the stone to us. Physical things are thus got rid of in
favour of physical processes and the sense-data begotten of their
interaction. This is justly said to be a Heraclitean conclusion.
We know that Plato was influenced by Heracliteanism in his
youth; and according to Aristotle he never fully shook it off. It is
not surprising therefore that Socrates goes on (153-5) to find things
to say in defence of this doctrine. The first is the general observation
that activity is beneficial and sloth harmful; this presumably gives
some measure of support to the view that nothing in nature is at
rest, since it shows nature to be on the side of activity. More seriously
Socrates next observes that if a sense-property such as whiteness were
located in the object it is difficult to see how it could ever seem any
other colour; while if it were supposed to characterise the visual
sense of the percipient he would presumably see white all the time.
It seems inevitable to regard the whiteness as a product of the inter-
action between the object and the percipient. These arguments are
of some weight and as Plato produces no answer to them it is natural
to suppose that he accepted the sense-datum theory to which he
makes them point. Then finally Socrates is made to observe that the
conventional view that properties belong in an absolute way to the
objects to which they are commonly ascribed gives rise to paradoxes.
For if A is larger than B or more numerous than C, it can without
change in itself become smaller than B (if B grows) or less numerous
than D (if D is a larger group). Needless to say if this is meant as an
argument in favour of the view that sense-properties are products of
interaction it is a very bad one, for whiteness is not at all the same
kind of property as largeness. Perhaps however it is intended not so
much as an argument, but more as an aperitif. Get a man to admit
that Jones's shortness does not belong absolutely to Jones, but exists
only as a relation between Jones and the average man, and you will
have him in a more amenable state for persuasion that the stone's
whiteness belongs not absolutely to the stone, but is begotten of the
intercourse of the stone with the percipient's sense-organs. Common-
6
THEORY OF KNOWLEDGE
sense holds, does it, that stones are really grey ? But it also holds that
Little Tich was really short. 1
Socrates now goes on (156) to reveal what he calls the Mysteries
of the Protagorean and Heraclitean thinkers. A philosopher's
"Mysteries" must be doctrines which he never published, and so we
may infer that what Plato offers us under this title is the theory of
perception which he took to underlie views of this kind. It is roughly
as follows.
Nothing exists except kinesis (activity, change, process). There are
two kinds of process, the one capable of affecting, the other of being
affected that is of sensing. (This distinction as Socrates says is only
relative. B may be an object in one transaction but a subject in
another. When I see Jones, Jones is the object, but when Jones sees
the tree he is the subject). But processes may be divided not only into
subjects and objects, but also into slow and fast. Both subjects and
objects percipients and the things they perceive are slow processes,
but when a subject and an object come together, two quick processes
occur. There are, as Socrates says, "twin offspring of the intercourse"
of the two slow processes, namely a sense-quality (e.g. whiteness) and
the perception of it ; and these "twin offspring" travel rapidly between
the two parties so that the stone (for example) becomes white and
the eye comes to see it. Every sense-datum exists only as the object
of a particular act of sensing and every act of sensing only as the
correlate of that particular sense-datum. There is nothing continuous
in the stream of sense-data nor in the sensings which are correlated
with them. Every pair of "twin offspring" exists only momentarily
having no necessary relation to its predecessors or successors, and
owing its character entirely to the momentary condition of the two
"slow processes" involved in the transaction.
This theory, Socrates goes on to observe, deals admirably with the
phenomenon of "illusion" or perceptual disagreement with the sick
man to whom wine tastes bitter or with the mad man who sees things
which are not there. What we see, hear or otherwise perceive is
always a sense-datum, and sense-data owe their qualities to the
momentary state of the two interacting processes. It is not to be
wondered at, therefore, if a piece of physical environment which
produces nothing but an image of a blank wall in the visual field of
a sane man produces an image of a scarlet toad in the visual field of
a madman. We have no access (this seems to be essential to the theory,
though it is not explicitly stated) to the real nature of the other "slow
1 The idea that Plato failed to see that such properties as shortness are rela-
tional, or that he confused relational with non-relational properties seems to me
groundless. Phaedo 102 where he is sometimes said to treat shortness as a non-
relational property seems to say the opposite (see 102 c 7).
7
THEORY OF KNOWLEDGE
process" whose interaction with our own produces our sense-data,
but only to the sense-data which are the "twins" to our acts of
sensing. This being the case, the external world to which we have
access is a world of momentarily existing sense-data only; physical
things are simply "collections" of these (157 b 9). The result of this is
that while, as a matter of fact, our sense-data are normally regular
and can be "collected" into what we call men or rocks, there is none
the less nothing ontologically inferior, so to speak, about the irregu-
lar sense-data suffered by people in abnormal conditions. All are
equally "true", all perception is infallible (since there is nothing to
check it against, no reality apart from each man's private reality);
and therefore all perception is equally knowledge.
(We may notice in passing that this is a somewhat cavalier treat-
ment of the phenomenon of "illusion". The water which feels hot to
a cold hand is easily explained in this way, but Socrates is surely
wrong to include, as he does, dreams and complete hallucinations
under the same umbrella. Given that when I am asleep I am not in
the same condition as I am when I am awake; but what is it that is
supposed to be interacting with my sleeping organism to produce
the marble halls I seem to see?).
Socrates has now (161) completed his exposition of the Protagorean
theory and of the Mysteries which he deems it to rest on, and he
turns to criticism. Plato was extremely conscious in his later years of
the facility and danger of criticising aupiedde la lettre, and he goes
out of his way in a number of places to denounce it. This is one such
place, for he makes Socrates offer a number of criticisms which he
then condemns on the ground that they rely either on appeals to
emotion or on unsympathetic interpretation of his opponent's words.
There is however one important point which emerges from this
criticism. Socrates says that when one hears people talking in a
foreign language, one hears, but does not know, what they say; and
to this Theaetetus replies that one hears and knows the sounds, but
neither hears nor knows their significance (163), He is commended
for this reply and it is left on one side. It is of course a pointer to
Socrates* essential objection to the view that knowledge is percep-
tion, namely that to acquire information about the external world
we need not only to have sense-data but to interpret them.
The Protagorean thesis which Socrates has expounded is what we
called Protagoras' central thesis, namely that all reports of immediate
perception are equally valid. When, however, Socrates turns to
serious criticism it is the extended thesis, that all beliefs whatever
are equally valid, that he attacks. He begins by putting into Prota-
goras' mouth an ingenious "pragmatist" answer to the obvious
objection that some men are surely wiser than others. That this is
8
THEORY OF KNOWLEDGE
so Protagoras concedes, but he Is made to reply that the wisdom of
a wise man consists not in the truth of his beliefs but in their benefi-
cial character; a wise man is one who can make his plants or his
farm stock or his fellow humans experience their environment in a
healthy and fruitful way. Whatever a man thinks right "is right to
that man" (whatever exactly that means); but the things that some
men think are right are bad and unprofitable things, and it is desirable
that these men should be brought to see things differently.
Socrates' reply to Protagoras' extended thesis makes two main
points. The first is that the thesis is self-refuting, for, by claiming
that all beliefs are true, it is forced to concede truth to the almost
universal belief, that some beliefs are false. Protagoras must concede
then that at least some error is possible, namely the error of his
opponents. This established, Socrates goes on to admit that Prota-
goras' relativistic view of morality is not repugnant to common
sense. It is commonly held that opinions about right and wrong are
no more capable of being corrected in the light of an objective
standard than are reports of immediate perception. The man with
eccentric moral views, like the man with some abnormality of sense,
is out of step with the majority but cannot be said to be wrong.
Though he admits that this doctrine is not repugnant to common
sense, Socrates does not of course accept it. He does not however
attempt to refute it. Rather he meets it with a long and splendid
passage (172-7) contrasting the litigious and practically-minded
man with the speculative and practically incompetent philosopher.
The upshot of this praise of the philosophic life seems to be that
men in general fail to understand the true reward of virtue and
punishment of vice. The common conception of justice is a querulous
conception based on self-seeking, and it is no wonder that this is
thought to have no objective foundation. But the man who realises
the sordidness of material ends will have a motive for goodness
escape from sordidness and assimilation to the divine which could
not be dismissed as merely conventional. However, as Socrates says,
this will cut no ice with the tough-minded, so he allows that it is
tenable that "what a man or community thinks fair and right is so
to him". But he denies that what a man thinks beneficial is so to him.
"Beneficial" as he says means "likely to do good" and his point is
a general one about prediction. To allow that all reports of present
experience are equally valid is one thing, to allow that all predictions
of future experience are equally valid is another. Every man can tell
whether he is enjoying his meal, but it takes a cook to know whether
a meal is likely to be enjoyable.
This establishes a large class of beliefs beliefs about what is likely
to do good, beliefs about what is likely to happen within which the
9
THEORY OF KNOWLEDGE
beliefs of the expert are much more likely to be right than the beliefs
of the non-expert. That is why the expert is trusted. In this sphere
at least the distinction between true and false beliefs is needed, and
therefore Protagoras' extended thesis fails.
Plato has his pulpit moments and his philosophical moments. In
his pulpit moments he calls down universal curses on any line of
thought whose tendency he distrusts. This is decidedly one of his
philosophical moments, for this criticism is very economical. Prota-
goras* extended thesis goes too far, but Socrates concedes that the
central thesis is left untouched. "Concerning what happens to a man
at any given moment, and the sensations to which that gives rise,
and the beliefs based upon these sensations it is not so easy to show
that these are not true." Perhaps beliefs based on present experience
have the "clarity" which entitles them to be called knowledge (179 c).
To decide whether this is so it is necessary to examine the Heraclitean
doctrine of the instability of all things.
(ii) The Discussion ofHeraditus
Socrates begins his discussion of instability by distinguishing two
kinds of it, namely motion and change (181). He then reminds his
hearers that the doctrine they are examining is: that when contact
is established between subject and object, a twin progeny is begotten,
namely a sense-quality (e.g. whiteness) and the appropriate sensation ;
and that these travel between the two parties so that the object
becomes white and the subject comes to see it.
Now, he continues, if the instability doctrine confined itself to
asserting that everything is in motion, all would be well. For in that
case a given thing might persist in, for example, "flowing white".
Or, in other words, it does not matter making the sensible properties
of things resultants of motion so long as you allow that the motion
in question conforms to a stable pattern in such a way that the object
continues to manifest the same sensible properties for a reasonable
period of time. In that case it will be possible to describe things.
However incessantly active the plate may be behind its placid appear-
ance, so long as the activity, by virtue of which it "flows white**,
persists unchanged, it will be possible to call it a white plate. But the
Heraclitean cannot allow this, for he asserts that everything is
unstable. But there is no point in saying that everything is unstable
if you merely mean that everything results from instability; for if
you allow that the instability of objects conforms to a stable pattern
so that the same sensible property is manifested over a period of time,
then you have admitted that something is stable, namely the pattern
and the sensible property in which it results. Therefore the Heracli-
tean must either reduce: "Everything is unstable" to the tame
10
THEORY OF KNOWLEDGE
doctrine: "Some things are unstable and some stable", or else he
must claim not only that things "flow white", but also that "white-
ness itself is in flux", or in other words that sensible properties not
only result from, but are themselves subject to, continuous change.
But to say this is to say that neither percipient subjects nor per-
ceivable objects are ever in the same condition in any respect in two
consecutive moments. But in a world in which that was true all
propositions (except perhaps negations) would be false (183 a-b).
A plate cannot be said to be white if it is the next moment some other
colour. Nor would there be in such a world such a thing as percep-
tion; for "sight", for example, is presumably the name of some
constant and unchanging activity. There is therefore this dilemma for
the Heraclitean: either his thesis is tenable but trivial, or he is com-
mitted to a world in which there is no such thing as a describable
object, nor such an activity as perception, nor therefore (if perception
is knowledge) such a thing as knowledge. (See below pp. 27-33).
The blunder, which has led the Heracliteans (if there were any)
who embraced the latter alternative to this absurd conclusion, is
that of confusing: "All properties result from change" with: "All
properties are subject to change". Perhaps an illustration would
help. An electric bulb glows (we will suppose) because of some kind
of incessant activity in the filament. But although the glowing is a
process which results from activity or change it is not in itself a
process of change, in the way in which a continuous flickering could
be said to be a process of change. The Heraclitean doctrine which
Plato is refuting amounts to the doctrine that, since the incandescence
of the bulb is due to activity in the filament, there can never really
be a steady glow but only a flickering one.
The argument establishes that whatever views you may hold about
the nature of the mechanisms underlying the phenomena, it cannot
seriously be disputed that there are many constant phenomena in
the world. The comment which Socrates makes upon this result is:
"this emancipates us from Protagoras; ... we cannot agree that
perception is knowledge, at any rate along the lines of the doctrine
that everything is unstable" (183 b-c).
This is an odd comment. Socrates had said that beliefs based upon
present perception might be true and might count as knowledge; the
doctrine of instability would have to be examined to decide that.
Now it has been examined and found wanting, and Socrates con-
cludes that "Perception is knowledge" fails, meaning presumably
thereby that beliefs based upon present perception cannot count as
knowledge. This may seem plain sailing; Protagoras* central thesis
entails Heraclitus' thesis; Heraclitus' thesis is false; therefore Prota-
goras' central thesis is false. But in fact it is not so simple as that,
11
THEORY OF KNOWLEDGE
With Heraclitus, as with Protagoras, one can distinguish two
theses, which we will call normal and rampant. Normal Heraclitean-
ism asserts that all properties result from activity, rampant Hera-
cliteanism draws the absurd conclusion that there are no stable
properties. Now in the discussion of Protagoras his view had been
shown to require something like the normal Heraclitean thesis. The
denial of illusion makes sense only if all sense-data are momentary
resultants of the interaction of two processes. But Protagoras' view
has not been shown to require (and does not require) the rampant
Heraclitean thesis. Yet in the discussion of Heraclitus the normal
thesis has been treated as tenable, and only the rampant thesis
refuted. But since Protagoras does not require the rampant thesis, the
refutation of the latter should leave him unscathed. What has
happened?
The truth is, I believe, that Socrates has not yet given his reasons
for denying that beliefs based upon present perception can be
counted as knowledge. His reasons, to be given in the sequel, are
that a belief which was based strictly and only on present perception
would be simply an expression of one's private sensations and would
have no reference to an objective external world. How then does
rampant Heracliteanism come into the picture? Only, I think, be-
cause if it were true, we should have to concede the status of know-
ledge to beliefs based on present perception. Protagoras does not
entail Heraclitus, but Heraclitus does entail Protagoras. In the actual
world, in which there is in fact considerable stability, I cannot be
said to know anything on the basis of my present perceptions alone.
To know that there is a white plate on the table is a good deal more
than to know that there is a round white patch in my visual sense-
field. It is at least to know also that such a white patch has been and
will be available to myself and others at this and other times. What
can be called belief (and a fortiori what, if anything, can be called
knowledge) about the external world is something much more than
awareness of present sensations. But in a rampant Heraclitean world
this would not be so. There being no constant patterns in such a
world, there would be nothing whatever to know except present
sensations, and no point in reserving the title "knowledge" for
something else. In the actual world expressions such as "true** and
"knowledge" must be kept to characterise beliefs not about sense-
data but about real things (however precisely these may be related to
sense-data) ; in the world of rampant Heracliteanism there would be no
real things and therefore no such use for these expressions. The de-
struction therefore of the rampant Heraclitean thesis does not directly
destroy Protagoras' central thesis ; rather it takes away the only prop
which could sustain it against the criticism which is forthcoming.
12
THEORY OF KNOWLEDGE
The position then so far is as follows. Theaetetus' equation of
knowledge with perception has been shown to involve the Protagorean
denial of the distinction between reality and illusion; and it has been
argued that this denial can only be sustained on the basis of some
kind of a sense-datum theory of perception. Protagoras' extended
thesis has been discussed, and it has been shown that while parts of
it are acceptable to common sense parts of it are certainly untenable.
Protagoras' central thesis however has so far been left untouched,
and so has the theory of perception which was worked out to support
it. The theory of perception has also survived the scrutiny of Hera-
cliteanism; for it is more or less equivalent to what we have called
the normal Heraclitean thesis, whereas Socrates' criticisms were
directed against the rampant thesis alone. There are therefore two
extremist theories refuted at this stage, and two (Protagoras* central
thesis and the perception theory associated with normal Hera-
cliteanism) still in the field.
(iii) The equation of knowledge with sensation
Having disposed of the authorities whom Theaetetus might have
invoked in defence of his equation of knowledge with sense-percep-
tion, Socrates turns to discuss the equation in its own right (184-7).
His,reason for rejecting it is essentially that what the senses give us,
strictly speaking, is no more than sensation, and that we do not
know anything about the real world by having sensations, but only
by interpreting their significance.
He begins by saying that we ought strictly to say that the mind
perceives the external world through the medium of the senses. The
senses are not independent receptors of information, "located in the
body like the Greeks in the belly of the Trojan Horse"; they are
abilities or tools through which the mind becomes aware of the
world. 1 Each sense has its own proper range of sense-qualities; thus
sight is correlated with colours, hearing with sounds and so on. But
we are capable of noticing other things beside the proper objects of
a particular sense; we can for example notice about two of the
latter that they both exist, are not identical with each other, and do
(or do not) resemble each other. These additional facts concerning
existence, identity, number, similarity and so on are not the objects
of any particular sense but are noticed by the mind without the aid
of the senses. Goodness and nobility, similarly, with their opposites,
"are pre-eminently things whose existence is observed . . , by the
mind, by a process of reckoning up past and present in relation to the
future". Any animal, however young, can perceive bodily distur-
bances (pathematd) which penetrate into consciousness ; what needs
1 184 c-d. I think that this is the correct account of this rather obscure passage.
13
THEORY OF KNOWLEDGE
to be learnt is the necessary calculations (analogistnatd) which have
to be made concerning these with reference to "existence and utility"
(186 c 3). However without this process of calculation the percep-
tions of the organism do not make contact with existence, and hence
cannot be called true, nor count as knowledge. "Knowledge therefore
is not to be found in the sensations we undergo, but in our thought
about them; it is only by the latter that we make contact with
existence and truth" (186 d).
What this amounts to is, I think, as follows. If we suppose an
organism merely to have sensations, then all we can say of it is that
it has sensations. Unless it notices that they are occurring (this I
take to be what is meant by "noticing their existence"), discriminates
them, notices which resembles which, and the patterns in which they
recur, it will be completely without information. Its sense organs will
be undergoing things and it will be in a sense conscious of what they
undergo, but it cannot be said to be in a state of knowledge or belief.
Things are happening to its consciousness but it is not intelligently
aware of them. Intelligent awareness is something which only arises
when one critically surveys the significance of what happens in
consciousness.
To put it at the lowest, the point is being made that there is a
non-sensory component in empirical knowledge. This seems quite
clear. There are however difficulties in detail about the interpretation
of Plato's version of this truth which we shall consider in the next
section. Meanwhile we can round off this section by giving the
conclusion of the discussion, which is that knowledge is not to be
looked for in the sphere of sensation but in the sphere of "properly
mental activity about the world" (187 a 5); and this, Theaetetus says.,
is called the sphere of doxa or judgment.
(iv) The perception theory of the Theaetetus
The concept of aisthesis or sensory activity has now been discussed
in relation to doxa or judgment and epistgmd or knowledge, and it
has been shown that aisthesis is essential to, but not identical with,
doxa. Meanwhile it seems that a theory concerning the status of the
objects of perception has been implied in the discussion, and we must
now consider what this theory is.
There are two places where a theory is stated or implied. There is
firstly Socrates* account of the Mysteries of the Protagoreans and
Heracliteans (153-60, and a repetition, 182), and there is secondly
the passage we have just considered (184-7) where the relation
between judgment and its sensory component is discussed,
The question arises whether Socrates is committed to the theory
outlined in the first of these two places. The answer seems to be that
14
THEORY OF KNOWLEDGE
he is not. He says, and rightly says, that Theaetetus' definition re-
quires some such theory, and this is a sufficient reason for Ms stating
it. On the other hand the rejection of Theaetetus* definition leaves
the Mysteries untouched. Unless therefore it can be shown that the
theory of the Mysteries is implied in the final and constructive dis-
cussion, it seems to be impossible to determine Socrates' attitude to
the Mysteries. From the fact that Socrates gives a sympathetic and
plausible account of the theory, and subsequently offers no refutation
of it we can no doubt infer that Plato was at least not hostile to it;
but we cannot at the moment go further than that.
Is it the case then that the theory of the Mysteries is implied in
the constructive discussion at the end of the section? We must look
at this discussion more closely.
The argument, as we have seen, is that the senses do not (by
themselves) inform us of the existence of their objects, and that that
which makes no contact with existence makes no contact with truth,
so that there are no truths which we owe to the senses alone. So far,
so good, but what is meant by "the existence of their objects*' ?
What does Socrates mean when he asks : "With what sense do we
notice the existence (and also distinctness, number and similarity or
otherwise) of a sound and a colour?" (185 a-b)? One is tempted to
suppose that the point is that sense-data are subjective occurrences,
and that we do not therefore, by having sense-data, get into touch
with an objective physical world. The contribution of the mind on
this view would consist in referring our sense-data to the external
world, in treating them as manifestations of independent entities;
the mind would get us across the gap between a subjective world of
Lockeian "ideas" and an objective world of physical things. Sensory
activity by itself would not get us into touch with the real world, but
only a world of private experience, and the "protocol-sentences",
such as "I am now sensing a red patch", which would express its
meagre information would be without "ontological commitment",
and hence would not deserve to be called true. Epistme or "know-
ledge", and with it aletheia or "truth" are reserved for awareness of
a reality independent of oneself.
Socrates may mean this, but his words do not bear this interpreta-
tion. What the mind notices according to him is not that the colour
belongs to an independently existing object, but that the colour exists.
The mind also notices that the colour is not identical with the sound,
and that it does or does not resemble it; and if we Interpret "that the
colour exists" as "that the colour belongs to an independently
existing object", we shall find it impossible to give a parallel inter-
pretation of these two additional observations (for a colour and a
sound do not necessarily belong to two distinct objects). Therefore
15
THEORY OF KNOWLEDGE
the distinction that Socrates is making seems to be the distinction
between (a) passively undergoing sense-experience, and (b) noticing
that it is occurring, distinguishing its items, detecting resemblances
between them and so on. It is this contribution which the mind makes,
and it must be this which is enough to bring us into contact with
ousta or reality and to give our observations the status of true beliefs.
In that case a man who takes a detached and observant attitude to the
events of his dreams, while not knowing that he is dreaming, could
presumably be said to be making contact with reality.
This conclusion seems odd ; so odd that, while I think that this is
what Socrates says, I have admitted that it may not be all that he
means. There is however a way of escaping this conclusion. We may
say first that Plato is not talking about dreams but about sense-
perception, and that although he has himself raised "the old chestnut:
'How do we know we are not now dreaming?' " (158 b 8), he is not
himself troubled by this kind of Cartesian doubt. Then we can say
next that Plato talks, not about "sense-data" or anything of the
kind, but about sounds and colours. If then we suppose that Plato
takes a Naive Realist view of sense-perception, according to which
the colours which we see are normally "parts of the surfaces of
material objects", the situation is saved. On this view when we notice
that a colour exists we are not noticing that we are having a visual
sense-datum, but that there is a coloured expanse out there in the
physical world. What we sense then on this view is not sense-data
but physical things. The contribution of the senses is to put us de
facto into touch with physical things, the contribution of the mind
to make us aware that we are in fact in touch with them.
This line of escape is attractive, but has its difficulties. For Socrates
distinguishes not only seeing colours from noticing their existence,
but also suffering pathemata or undergoings from "reckoning them
up with reference to existence and utility" ; and it seems clear that
these two distinctions are roughly the same, and in particular that
colours, sounds and so on are identical with the patMmata which
we suffer. But a Naive Realist who speaks of the things we see and
hear as pathemata, or things that happen to us, is surely giving away
his case. As recent writers have argued, to treat perception as if it
were a form of sensation (in the way in which a pain or a tickle is a
sensation) is to take the high road leading to sense-datum theories
of perception. But there are without doubt places (e.g. 186 c 1)
where Plato writes as if he took the objects of sensory awareness to
be, or to be the results of, bodily disturbances which penetrate into
consciousness, or in other words as if he took awareness of a colour
to be analogous to awareness of a tickle or a pain. "New-born men
and animals," he says in that place, "are endowed by nature with
16
THEORY OF KNOWLEDGE
the ability to perceive such pathemata as reach through the body to
the mind." But if the objects of vision and of the other senses are, or
result from, bodily disturbances stimulated by the impact of external
objects, then the question surely arises: How are these immediate
objects of experience related to the external objects which stimulate
the senses and thus give rise to them? And in the context of the
Theaetetus it is difficult to believe that Plato would have overlooked
this question, since it seems to be so germane to the theory outlined
in the Mysteries.
In the Timaeus (61-8) Plato seems to treat the colours, tastes,
smells and so on that we are immediately aware of as things which
arise in the mind as the results of bodily disturbances; and this, as
far as it goes, supports the view that pathemata in the present passage
are to be understood in the same way. Again in the Theaetetus
itself, in the discussion of Protagoras, Socrates treats the awareness
of cold, burning, pleasure, pain, desire and fear (156b), and also
apparently memory (166 b) as if they belonged to the same class as
the five senses, and as if their objects were the same sort of thing
as colours and sounds. It is true that this occurs in the discussion of
Protagoras, for whom of course this was so ; but the point is that
Socrates makes no bones at all about lumping together these different
things, and it is difficult to believe that a writer who meant us, a few
pages further on, to take a Naive Realist view of the five senses
would do nothing to mark the discomfort which he would be bound
to feel at this "assimilation of the concept of perception to the
concept of sensation" and indeed to that of emotion as well.
We seem then to have two possible interpretations of the theory
of sensory awareness which Socrates relies on in order to distinguish
the latter from judgment; and each of them has its difficulties. The
one interpretation gives us a Realist theory. Through the senses we
are directly aware of physical objects, or their sensible properties,
and the contribution of the mind is to recognise them as such and
to assess their significance for us. The other interpretation gives us
a theory which is compatible with Phenomenalism or with a Lockeian
Causal Theory of perception. According to this interpretation what
we are aware of in sensation is sense-data, and the contribution of
the mind lies in noticing that they are occurring and in constructing,
so to speak, an objective external world by observing the patterns
in which they occur. The empirical world in this view (as in Pheno-
menalism and in the Causal Theory) is the orderly system of sense-
data which we experience. In neither of these interpretations, it may
be noticed, does the mind enable us to cross the gap between private
sensations and physical objects. The one interpretation begins with
physical objects, and the other ends with private sensations. The third
17
THEORY OF KNOWLEDGE
interpretation according to which we begin with private sensations
and end, through an act of the mind, with physical objects had to be
rejected because it did not conform to the text.
Which of these interpretations ought we to take? The sense-datum
interpretation, according to which this account of perception is in
line with the theory of the Mysteries, or the Realist interpretation
according to which it is not? Here, as so often, the truth may well be
that it would be historically inaccurate to choose. The truth may well
be that Plato was not completely clear in his own mind and that the
theory is an unstable amalgam. If however I were forced to choose,
the interpretation I would reject is the Realist interpretation.
Provisionally, then, the theory implied in this passage is some form
of sense-datum theory; and this conclusion brings what we have taken
to be Plato's own views more or less into line with the theory which
he calls the Mysteries of the subtle thinkers. We must now look more
closely at this latter.
The theory is stated in terms of kinesis, a word for which I have
used various equivalents, such as "change", "process", "instability"
and "activity". "Process" is perhaps the most convenient in this
place. There are then four kinds of processes mentioned, namely
two kinds of slow processes, that which can affect, and that which
can be affected, and two kinds of quick process, namely that whereby
an object comes to have some sense-quality, and that whereby a
subject comes to sense it. Let us try to interpret this.
We will suppose that the two slow processes involved in a per-
ception-transaction are the perceiving subject (say Jones) and the
perceived object (say a stone). To describe Jones as a slow process
would indeed be a strictly improper use of the abstract noun kinesis
(Jones's life might be a process, but not Jones himself); but this I
think is not an impropriety which would have worried Plato very
much. Jones and the stone are called processes, we will suppose,
because for perception to occur each must be in a state of activity.
Jones, we might say, must be emitting light from his eyes and the
stone particles from its surface, as in the Timaeus. And anyhow since
the theory is being stated in a Heraclitean context a thing can well
be called a process as a concession to Heraclitus. Here, then, are our
two slow processes, Jones and the stone, and they are slow because,
in themselves apart from anything that they do, they remain much
the same over a period of time. But when they get near enough to
each other their two gradual and placid activities impinge on each
other and create some kind of a disturbance. Jones's cones of light
from his eyes, perhaps, collide with the particles given off by the
stone, and this sets up a rapid two-way process, or pair of rapid
processes, by which Jones comes to see and the stone to be white.
18
THEORY OF KNOWLEDGE
It is easy to see that on this interpretation the theory given as the
Mysteries is a generalised version, uncommitted as to physical and
physiological detail, of the account given in the Timaeus. But there
are difficulties in this interpretation.
Firstly this is not a Phenomenalist account of perception, but a
version of the Causal Theory; it mentions two physical objects,
namely the two slow processes, Jones and the stone. Now if Jones
and Smith both look at the same stone, the same physical object is
interfering with, and giving rise to sensations in, both of them. In
one sense they have a common object. No doubt their sense-data
are private, and Jones sees the stone as grey whereas Smith, who has
jaundice, sees it as khaki; but it is the same stone which affects them
in these different ways. Now at times in his exposition Socrates talks
as if this was the picture he is trying to paint; but at other times he
does not. When talking of wine which tastes sour to a sick man (159)
he speaks of the same object interacting with different subjects, the
normal and the sick, and thus begetting different progeny. But there
are other places where he speaks in different terms. Thus in 157 b-c
he says that men and stones and other objects ought strictly to be
spoken of, on the theory, as collections (hathroismatd) of the things
which come into existence only momentarily and in relation to each
other; and it is clear from the context that these momentary entities
are sense-data and the awareness of them. But this whole Hera-
clitean denial that there are any persistent things which exist in their
own right, but only a world of momentary sense-data and their
correlative sensations, is, verbally at least, inconsistent with the
Causal Theory. According to the Causal Theory my glimpse of the
stone, indeed, exists only in relation to me, but the stone itself exists
in its own right and endures through time whether anybody is seeing
it or not. It does not come into existence when it is seen; it has to be
there beforehand in order to cause the seeing.
Now this objection may not seem very serious. It is true that, on the
Causal Theory, there do exist enduring and independent objects
constituting the physical world, but it is also true that we can never
be directly aware of them. As Locke saw it is necessary to locate the
causes of our sensations in space and to attribute to them some kind
of activity ; but as Locke also saw 1 it is logically incoherent to ascribe
to them any sensible properties. (This is the point of the famous
distinction between primary and secondary qualities, and it is also
the reason why the Causal Theory, though taken for granted by
many scientists and by educated common sense, is seldom popular
among philosophers). But if we cannot attribute sensible properties
to the physical objects which are postulated as the causes of our
1 Though not, perhaps, quite clearly.
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THEORY OF KNOWLEDGE
sensations, then obviously they form no part of the world of our
experience. As Berkeley said, even if you suppose that they exist, you
have to admit that our experience might be precisely the same though
they did not. Therefore it might be argued that, when Socrates says
that, on the theory he has outlined, there are no enduring and
independent objects, he is speaking loosely but perfectly naturally.
For the independent objects that the theory postulates never enter
into our experience. When we talk of the tree, we are talking of the
tree as we experience it, not of whatever it is that causes our experi-
ence; and the tree as we experience it is a collection of momentarily
existing sense-data. Provided that "the world" means "the world of
experience" it is perfectly true that the world contains nothing but
collections of momentary entities.
This is all very well, but one would have expected Socrates to
throw a sop, now and then, in the name of accuracy to the enduring
physical objects that the theory postulates, if that is indeed the correct
interpretation of the theory. And there is worse than that. Not only
does he often speak of the world as if the causes of our sensations
did not exist, there is one place where he actually says about the
causes things which ought only to be said about their effects. This
is 160c4-5, where Socrates says: "Therefore, since that which
affects me" (to erne poioun, the phrase which, on this interpretation,
means "the cause of my sense-data") "exists to me only, I also alone
perceive it."
I do not want to make too heavy weather of this. No doubt it
can be dismissed as a slip. But surely it at least suggests that if Plato
intends an interpretation along the lines of the Causal Theory he is
not perfectly clear in his own mind of the logic of his theory.
But there is a further difficulty about this interpretation, and it
concerns the rapid processes. For Plato talks of two rapid processes,
and, though I tried to conceal it in niy exposition above, we have
really only found one. If the rapid processes are the effects of the
two objects on each other, the effect of the stone on Jones is clear
it gives him a sense-datum but what is the effect of Jones on the
stone? No doubt his cones of light could be thought to cause some
disturbance at its surface as they collide with the particles it gives
off; but this is clearly a negligible effect, and anyhow it is not the
effect which Socrates describes.
What precisely does Socrates say about the rapid processes? He
says the following (156-7): "the slow process or activity carries on
its activity (kinisis) in the same place and in relation to its environ-
ment". This means, I think, not that the slow processes never move,
but that their activity does not consist in moving; and that their
activity consists in their effects upon their neighbours. Then he says
20
THEORY OF KNOWLEDGE
that when two of these slow processes come together their inter-
course begets a twin offspring, and that these twin offspring are
quicker, travel, and exercise their activity in travelling. Thus, he goes
on, when an eye meets an appropriate object (summetrori) they beget
a sense-quality, e.g. whiteness, and the corresponding sensation;
and the sight travels from the eyes and the whiteness travels from the
object, so that the eye becomes full of sight and sees, while "the other
parent of the colour" is filled with whiteness and becomes white.
Looked at close to, this is a very odd account. One puzzling feature
is the use of the abstract nouns "whiteness" and "sight" as names
of things that travel between the two parties. For Plato is writing
carefully here; thus he troubles to say that the eye becomes "not
sight, but a seeing eye", while the object becomes "not whiteness,
but white". Clearly then when he uses the words "whiteness" and
"sight" he uses them on purpose, whatever he means by them.
"Sight" is perhaps not too troublesome, for the stream of light is
referred to in the Timaeus (45 c 3) as opseos reuma or a stream of sight ;
but what can "whiteness" stand for? If we make "sight" stand for
the light flowing in one direction, what is supposed to be flowing
in the opposite direction and to be called whiteness? No doubt it is
the particles given off by the object; but these are odd candidates for
the name "whiteness". Then again there is something odd about the
direction of travel. For sight travels from the eyes (pros with the
genitive; it seems hard to translate this "towards") and whiteness
from the object, and the result of this is that "the eye therefore be-
comes full of sight and sees at that moment, and becomes not sight
but a seeing eye, while the other parent of the colour is filled with
whiteness and becomes, not whiteness again, but white" (156 e 2-5).
But if the whiteness travels/row the stone, why does the stone thereby
become filled with whiteness ? If water travels from a tap it is the
bucket and not the tap that gets filled.
Perhaps the best we can do towards a physical picture is the
following. When the Timaeus comes to talk of the perception of
colours (67-8) it speaks of colour as "a flame flowing off from every
object, having its particles appropriate (summetra) to sight in relation
to perception" (67 c 6-7). The theory seems to be that different kinds
of fire correspond to different colours, the different kinds of fire
having particles of different sizes, some of them being larger, some
smaller, and some the same size as the particles constituting the
opsis, the stream of light from the eyes called sight. As the opsis and
the flame of colour flow through each other in opposite directions,
the jostling effect of their particles on each other varies with the
variations of the particles constituting the colour-flame, and that is
how we see different colours. Clearly in that case it would not be too
21
THEORY OF KNOWLEDGE
far-fetched to use the word "whiteness" as the name of that kind of
flame whose particles are such as to make us see white. Then white-
ness, in the sense of the appropriate flame, would travel from the
object along the beam of sight, and the beam of sight would travel
from the eyes to the object. But this still leaves us wondering why
the eyes are filled with sight and the object with whiteness, and not
the other way round. Obviously if "the eyes are filled with sight" is
simply a florid way of saying "the eyes see", and if "the stone is
filled with whiteness" just means "the stone looks white", all is well.
But if we take that interpretation we make Plato use "sight" and
"whiteness" to stand for two different things (streams of particles,
and the sensations that their interaction results in) in consecutive
sentences in a passage in which he makes almost a parade of precision.
This is unsatisfactory, and it tempts one to abandon a physical
picture in favour of a metaphorical one. For the stone, as we have
just seen, can easily be said to be filled with whiteness in a meta-
phorical sense.
Let us then try a picture more in accordance with Phenomenalism,
or Russell's Neutral Monism, than with Locke's Causal Theory. In
this picture the two slow processes are not two physical objects in a
state of steady physical activity, but two sets of sensory phenomena.
Jones is a gradually growing biography of sense-perceptions, and the
stone a gradually growing history of sense-data. Jones is the sum of
his experiences and the stone is the sum of the experiences of which
it would ordinarily be called the object. To talk of the stone is to
talk of the views, pressures and so on that people have of it, to talk
of people is to talk of the experiences that they have. In this picture
"when two slow processes come together" means something like
"when their histories intersect". The rapid processes which there-
upon occur are no more than Jones's view of the stone. This is indeed
the same thing as the coming together of the two slow processes, but
in a metaphorical account this does not perhaps matter. Jones's view
of the stone, which occurs instantaneously when Jones sees the
stone, is described as two rapid processes because the sight of
something can be analysed into two, logically distinct, components,
the sense-datum and the sensing of it. Sight is said to travel from the
eye because of course it is the eye that sees, and whiteness to travel
from the stone because the whiteness seen is thought of as "coming
from over there". The eye is filled with sight in an easily understood
metaphorical sense, and the stone is filled with whiteness analogously.
Since the travelling of the sight and the whiteness is purely meta-
phorical the difficulties about the direction of travel no longer
arise.
This picture has the advantage that it abolishes the physical objects.
22
THEORY OF KNOWLEDGE
If this seems too daring, we may remember that Plato denied the
status of onta to material things ; and there seems to be one place
(Symposium 207 e-208 b) where he is prepared to treat human minds
as consisting of nothing but the sum of what would ordinarily be
called their acts and experiences, where men are nothing but a stream
of transient thoughts, feelings and sensations. This interpretation,
then, Is not too daring for Plato; and of course it suits the present
context very well. For as we have seen the Causal Theory of percep-
tion does not strictly allow one to say the Heraclitean things which
Socrates deduces from what he says in this passage. The meta-
phorical interpretation, by giving us a Phenomenalist or Neutral
Monist picture, does Indeed delineate a world in which nothing en-
dures (except in the way in which a stream endures) nor exists in Its
own right, but everything Is a collection of momentary entities, such
as sense-data and sensings of them, existing only in relation to each
other.
This is a strong argument in favour of the metaphorical inter-
pretation of the doctrine of the Mysteries, but the interpretation is,
nonetheless, untenable. The trouble is this. When Socrates turns to
refute rampant Heracliteanism he first carefully distinguishes kinesis
into motion and other kinds of change. He then recalls the doctrine
of the Mysteries in words which make it perfectly cleai that the
travelling of the sense-quality and its appropriate sensation between
the object and the subject is supposed to be a case of motion (182 a
3-6 and c 9 and d 5). In face of this it is impossible to maintain
that the metaphorical interpretation tells the whole story.
We are forced therefore to fit the slow processes and the rapid
processes into a physical picture. No doubt the two slow processes
will have to be Jones and the stone, described as slow processes
because they exert a steady effect on their environment. And no
doubt the two rapid processes, being cases of motion, will have to
be the streaming of light from Jones's eyes and of the flame of colour
from the stone. The picture is still a blurred picture, both for the
reason given above, that the eyes are filled with the "sight" that
streams from them, and also because the only travelling that we can
find, namely the travelling of the two sets of particles, is surely not
something that "is begotten", and rapidly happens, when the two
slow processes approach, but something that goes on all the time.
We still want, for the rapid processes, something that happens instan-
taneously when and only when perception occurs. The interference
between the two sets of particles is no doubt such a happening; but
how do we make this into two processes, each travelling rapidly in
the opposite direction?
What happens rapidly or instantaneously when a subject and an
EPD B 23
THEORY OF KNOWLEDGE
object come Into range is that the object Is perceived and that the
subject perceives it; and this is how we naturally want to take the
two rapid processes. But if we do take them in that (metaphorical)
way the conclusion follows that Plato's doctrine is inconsistent with
itself; and that is probably the right conclusion.
Perhaps the following is the best account of the matter. What
Plato intends to put forward is a version of the Causal Theory, but
he does not fully understand the logic of the theory, which requires
two sets of terms, one to stand for things as they are in themselves,
the other for things as they are perceived. Let us call the stone as it
is in itself the physical object and the stone as it is in perception the
empirical object, and let us make a similar distinction between Jones
as the physical subject and Jones as the empirical subject. This
duplication of terminology does not of course mean a duplication of
entities; it only means that there are on the theory two ways of
considering every object. We are supposing that there is some kind
of activity located at a certain point in space which causes in us the
sense-experiences which we call views or feels of the stone, and this
activity is not perceived (we do not see the particles which are sup-
posed to stream off the stone; we see the grey expanse which they
cause us to see). And similarly there is some kind of activity going on
in ourselves by virtue of which we are enabled to perceive, and this
activity again is not itself an object of perception.
Now when the physical subject and the physical object are in a
certain spatial relationship to each other the physical activity of the
one interferes with the physical activity of the other, producing
various disturbances in the nervous system, and ultimately in the
brain of the physical subject. The result of this is the birth of a "twin
progeny", namely the sensing by the empirical subject of a sense-
datum belonging to the empirical object. Since, on the theory, our
sensations are due to, but are never of the physical activity of the
physical object, it follows that no sense-qualities can be ascribed to
this physical activity. One cannot talk, for example, of the emission
of white particles, but only of the emission of the kind of particles
which produce white sense-data in normal percipients. The scientist
who wants to advance a detailed explanatory hypothesis to account
for perception will want to offer some kind of description of the type
of physical activity correlated with a particular type of sense-datum;
but he will find that he can only do so, at best, in terms of primary
qualities shape, size, velocity and so on. This Plato does in the
Timaeus in terms of shapes and sizes of particles, and the modern
physicist in terms of wave-lengths, frequencies and so on. Primary-
quality words such as "triangular" may therefore be usable both on
the physical and on the empirical side, but secondary-quality words
24
THEORY OF KNOWLEDGE
such as "white" must be confined to the description of empirical
objects. 1
Plato however fails to observe this rule. He allows himself to talk
of whiteness travelling when he intends to refer to the travelling of
a certain kind of particle. Instead of saying something like: "when
the appropriate particles travel from the physical stone a white
sense-datum of the empirical stone is sensed", he says: "when
whiteness flows from the stone the stone is filled with whiteness."
This is puzzling language in itself, and what is worse it confuses the
physical with the empirical stone. This is dangerous for the following
reason. There are certain sentences in which the expression "the
empirical stone" can function as subject which are harmless enough
when taken in the right way ; for example : "The empirical stone exists
only when it is being perceived." Rightly understood this sentence
expresses a tautology, since it is no more than a round-about way of
expressing the definition of "the empirical stone" as "the stone as it
is in perception". But if the distinction between "the empirical stone"
and "the physical stone" is not drawn, trouble results. For "the
stone exists only when it is perceived" seems to be an acceptable way
of saying that the (empirical) stone is only filled with whiteness,
hardness and its other observable properties when it is sensed. Yet
it also seems to imply that there is no independent and enduring
(physical) stone. Thus the lack of a distinction between the "physical"
and the "empirical" stone allows the Causal Theory to topple over
into Phenomenalism, and encourages Plato to think that the Causal
Theory is able to bear the Heraclitean superstructure which he builds
upon it. It would seem therefore that the hypothesis, that Plato
intended to put forward a version of the Causal Theory, but failed
to conform to the logical requirements for doing so, explains all the
difficulties which we found in his account of the doctrine of the
Mysteries.
This conclusion also allows us to bring the doctrine of the Mysteries
into line with the account of perception which is drawn on by Socrates
when he comes to describe the relationship between sensory activity
and judgment. This is obviously a desirable result; for unless we were
allowed to draw on the former it would be difficult to understand
what Socrates meant by referring to sense-experiences as patMmata
or undergoings in the latter. There is then only one theory of per-
ception in the Theaetetus and since it is presupposed by Socrates
1 That Plato did in fact understand the relation between primary and secondary
qualities in this way is clear from the Timaeus (see below pp. 221-2). See also an
incidental remark in Laws X, 897 a, where he makes sense-properties such as
warmth and whiteness consequent upon physical activities of increase, diminution,
separation and combination.
25
THEORY OF KNOWLEDGE
when he is arguing in his own person we may conclude that Plato
intends us to accept it as his own.
(v) Our knowledge of the external world
What then is Plato's conception of our knowledge of the external
world? The activity of the things around us interferes with the
activity of our bodies, thereby setting up pathemata or disturbances
in our bodies. These disturbances we are said to perceive, and this
is aisthesis or sense-perception (186 c 1). This again is loose language,
for it suggests that we perceive the electrical impulses in our nerves
or whatever it may be that is set up by external stimulation. It is,
however, the same kind of looseness as that which we have just been
considering, for it consists in combining the physical and the empirical
vocabularies in an illegitimate way. We shall therefore confidently
emend it, and say that we do not perceive the disturbances caused
in our bodies by external stimulation but that we do perceive the
sense-data to which they give rise. This I think is not only what
Plato ought to say, but also what he means. This perceiving of
sense-data is common to all organisms, and it does not constitute
knowledge of the external world. Knowledge of the external world
only arises when we notice the occurrence of our sense-data and, by
comparison of one with another, assess their significance as pointers
to out future experience, when we notice for example that we are
perceiving the kind of objects to which we have learnt to give the
name "black clouds", and conclude from this that we shall shortly
experience what we have learnt to call rain. This means that know-
ledge of the external world is always knowledge of the significance
of our experiences and of the patterns to which they conform. Of the
real physical activity of the real physical things which give rise to
our experience we can have no knowledge, but are confined to plaus-
ible conjecture such as that given in the Timaeus (which repeatedly
stresses the conjectural nature of its doctrine).
The name which Plato gives to the having of sense-data is aisthesis,
the name which he gives to the activity of determining their signifi-
cance is doxa. It follows from this definition that aisthesis does not
by itself give rise to any propositions about the world, and that
predicates such as "true" cannot be used of it* It is simply something
that happens to us and can be used as the raw material of true (or
false) judgments. AisthMs therefore cannot be identified with
episteme. Episteme is to be looked for in the sphere of doxa, in the
sphere where "the mind concerns itself with things that are, itself
according to itself" (187 a 5).
(Verbally this is a bad description of doxa, for it suggests that doxa
or knowledge of the external world is something that the mind
26
THEORY OF KNOWLEDGE
achieves by its own resources; and this suggests the picture of
aisthesis and doxa as parallel "faculties", the former putting us in
touch with sensible objects, the latter giving us some kind of intel-
lectual intuition of onta or things that are really real. However
congenial this may be to certain conventional pictures of Platonism
it must be rejected. There is no reference in this passage to any
knowledge of supra-sensible entities and hence the idea that the
sphere of doxa is a sphere in which the mind dispenses with aisthesis
is quite out of place. Reality and truth are attained to by use of sense-
data, and it is within this "properly mental activity" that eplsteme is
to be looked for).
Note on the refutation of the extreme Heraditean thesis.
Something must be said to justify the view (whose truth I have assumed above)
that the Theaetetus contains an intended refutation of what I have called the ram-
pant Heraclitean view of the natural world. For it has often been held that this
is not the case, but that the Theaetetus resists the equation of aisthesis with
episteme by conceding to the Heracliteans that the natural world (which is the
object of aisthesis) is radically unstable, while hinting that there exist other
entities (viz. the forms) which are, being stable, fit objects of knowledge. So far
as I know this view was first effectively challenged in recent times by Mr G. E. L.
Owen in The Classical Quarterly for 1953.
In the vital passage (182 c 9-d 5) Socrates says: "If everything was in motion
only, but not changing, we should be able to say what-like sorts of things the
objects in motion flow. . . , But if 1 not even this is stable, namely that that which
flows flows white, but this too changes, so that there is flux of just this thing,
whiteness, and change into some other colour, in order that it may not be caught
staying the same, how then will it be possible to name any colour so as to speak
of it correctly?". I have taken this to mean that Socrates has no objection to an
account of apparently stable entities which makes them consist of particles 2 in
continuous motion or something of the kind, provided that their continuous
activity is such as to permit them occasionally to manifest stable sense-properties
over a period of time, this proviso being a necessary condition of the describa-
bility of physical things, and of there being such a thing as aisthesis for episteme
to be identical with. This interpretation may be challenged on the ground that
Socrates has earlier said (154 a 7-9 and 159 e 7-160 a 3) that no two sense-
perceptions are ever exactly alike, from which it might seem that we can infer that
he does not believe that anything ever does manifest stable sense-properties.
An alternative interpretation of the crucial passage may be preferred as follows.
Socrates is not concerned with the describability of the physical world. Physical
things, and even the activity of perceiving, may be totally in flux; but knowledge
is not. He is not concerned to say: "I don't mind inconstancy on the microscopic
level so long as I am allowed reasonable macroscopic constancy." He is willing
to consign the physical world, and ourselves as sentient beings with it, to the
Heracliteans; he only wants stability in the realm of the intellect. His argument
1 Literally "since" (epeide). But Socrates must mean "since, on the theory
which I cannot accept, , . .", for Socrates is now introducing the view which
leads to the unacceptable conclusion that all that one can ever say of anything
is that it is not-P.
2 For the introduction of particles see the last but one paragraph of this note.
THEORY OF KNOWLEDGE
is not that we could not describe a totally fluid world, but that we could not de-
scribe with totally fluid predicates. The "flux of whiteness" which he speaks of as
something which it would be difficult to allow is not what I have taken it to be
(namely that the plate is never on two successive occasions the same colour);
rather it is that whiteness is always changing into some other colour. The flux
in fact that Socrates cannot agree to is not an inconstancy in the whiteness of a
white thing, but an inconstancy in whiteness itself. We must insist that whiteness
is always whiteness 1 though we need not insist (indeed should deny) that anything
is ever continuously white. What would happen if whiteness were not always the
same is not that we could never describe any physical thing (it is strictly the case
on Heraclitean principles that we cannot in fact do this anyhow) but rather that
we could never "name" or "speak of" (proseipein and prosagoreuein, d 4-5) any
colour. The argument is in fact: "We have names for colours; therefore colours
must be constant", and not: "We speak of plates as e.g. white; therefore the
whiteness of plates must sometimes be constant." Things, that is, can be in-
definitely unstable, but properties cannot be unstable at all. It might be added by
those who favour this interpretation that, although whiteness and other colour-
properties are doubtless not themselves forms, one of the purposes of the demon-
stration that properties cannot be unstable is to remind us that forms have the
stability which is common to all properties, and hence are fit objects of knowledge.
In this way we can link up the view that what Socrates is doing in these sentences
is to tell us that properties cannot change with the "conservative" interpretation
of the Theaetetus according to which one of Plato's main purposes in writing it
is to hint to us that knowledge is always of the forms.
It must be allowed that this reading of the crucial sentences fits the text very
nicely at certain points.^Socrates asks for example (182 d 4-5): "how then will it
be possible to name any colour so as to speak of it correctly?", and not: "how
then will it be possible to name anything's colour . . . ?". (The view that we are
following has to take "any colour" to mean "anything's colour"). I agree also
that Plato wants to make the point that properties are not themselves subject to
change. This is probably what Socrates is getting at in 182 a 3-b 7; and it was of
course a necessary part of the task of extricating the notion of a property that the
point should be made that things change their properties, and that properties are
what change is from and to, and not what changes. But I do not think that this is
all that Plato wants to tell us in the passage under consideration, though it is
possible that he did not see clearly that the two points are distinct. 2 Like its rival,
the interpretation that we have followed can also be said to fit the text very
nicely at certain points. For example in 182 c 9-10 the words : "If everything were
in motion only but not changing, we should be able to say what-like sorts of
things (hoia attd) the objects in motion flow" seem to say: "Let A be in motion;
provided it is not also changing qualitatively we shall be able to describe it",
where this lends itself to the interpretation that things which are in motion (in
some sense) can be said to be, e.g. white if neither their motion nor the motion of
their particles nor anything else causes them to cease to be white. Again in d 1 the
words "that that which flows flows white" (which are used to express a proposi-
tion which is denied by the Heraclitean view under discussion) suggest not that
whiteness stays white, but that some admittedly flowing thing stays white -e.g.
1 This is of course logically necessary, in that the notion of whiteness becoming
some other colour makes no sense. It would be anachronistic to say in so many
words that this is Socrates' point, but on the interpretation that we are considering
this will be the modern version of his point.
2 For it might be rather easy for him to confuse "whiteness is constant" with
"Cases of whiteness are constant".
28
THEORY OF KNOWLEDGE
this plate. These words suggest, then, that Socrates Is attacking a view according
to which things which flow do not go on flowing in the same manner, i.e. is
arguing that things may flow, and yet flow in such a way as to be, for example,
continuously white. These words, then, seem to support our interpretation, even
if the succeeding words ("so that there is flux of just this thing, whiteness, and
change into some other colour") might seem to support its rival. And yet these
last words do not support the latter very strongly, for it is surely not too difficult
to take "flux of ... whiteness" as "flux of ... the whiteness of S". This is the
easier when ws remember that "flux of ... whiteness" is advanced as the alterna-
tive to "that that which flows flows white".
It seems then that neither reading fits the words of the text perfectly and that
each fits it tolerably. We shall have to try to decide between them on general
grounds. Perhaps the three most potent considerations which can be advanced
against the reading of this passage which accords with the "conservative" inter-
pretation are the following.
1. Whatever Socrates is doing here, it ought to be relevant to the truth of
Protagoras' central thesis, for it is this that the examination of Heraclitus'
doctrines is designed to test. On the conservative interpretation Socrates is
consigning the physical world to the Heracliteans. It might seem that this gives
us all the relevance that we need, on the ground that if the physical world is as
the Heracliteans say it is, then presumably all statements about it are strictly
speaking false, and then presumably none of them, not even those based on
present perception, will be true, nor count as knowledge. If this is acceptable
(about which I have doubts) it establishes the required connection between what
Socrates says and what he is supposed to be trying to show; but the overall re-
sult seems to be very much out of key with what Plato is trying to do in this part
of the Theaetetits, For he seems to be trying to examine rather carefully how we
get the information that we possess about the material world, which of our
beliefs about it are to be regarded as "objective", and so forth. To this end the
general statement that no empirical judgment is strictly true is of no use what-
ever. The blanket condemnation of all empirical judgments is just as anarchic as,
and in the end little different from, Protagoras' blanket endorsement of them all.
"All judgments about the natural world are false because each implies a per-
manence which does not in fact obtain" and "All judgments about the natural
world are true because each is about just one momentary private sense-occur-
rence" come to very much the same thing, and neither fits well with, for ex-
ample, the doctrine that the expert is more likely to be right about the future
than the non-expert. Plato seems to want to tell us that we derive our information
about the natural world not from just having sense-experiences but from intel-
ligent "reckoning-up" of the patterns into which they fall. To this purpose it is
helpful to point out that the instability of the natural world is not total; it is not
helpful to concede that it is.
2. The doctrine that objects are inconstant with respect to colour, but that
colours themselves are constant, must be allowed to be very mysterious. For
whiteness, for example, must surely be identified with the colour of white things.
It is unplausiblc to suppose that it is the archetypal white patch in the visual
sense-field of Eternal Reason. (The case would have been different if Plato had
given as his example of something constant an "intelligible" property such as
circularity, for we could then have supposed that circularity was something other
than the property common to objects generally called circular). This mysterious
doctrine could, I suppose, be understood in either of two ways. We shall have
to suppose that things which apparently stay white actually fluctuate within a
band of similar but not identical shades, and we shall have to suppose also either
29
THEORY OF KNOWLEDGE
that "whiteness" is the name of just one of these shades (with the result that
nothing is ever continuously white), or that "whiteness" is the name of the band
of shades within which an object is allowed to fluctuate without forfeiting its title
to the description "white" (with the result that things can stay white, but that
"staying white" does not entail "staying just the same"). The constancy of white-
ness will have to consist either in the fact that "whiteness" is the name of just one
shade, or in the fact that, although a number of shades fall under it (as a number
of visual appearances fall under the description "dingy"), nevertheless the
shades that fall under it are always just those shades; a word which is to be of
any use can be indefinite in meaning in that what falls under it may be a range
which includes considerable variation, but it cannot be indefinite in meaning in
that what falls under it is now one range, now another. It is true that the doctrine
that things are inconstant in point of colour, but that colours themselves are
constant, can be understood in either of these two ways (only the first of which,
incidentally, allows the point that Socrates is now making to contain the refuta-
tion of Protagoras' central thesis which we suggested above); but it is not true
that Plato gives us any indication how we are to understand his point, on the
assumption that this is the point that he is making. We are left to puzzle out for
ourselves how whiteness can be something constant when things are inconstant
in respect of colour.
3. On any view Plato does not make it clear quite how he thinks he has shown
that we cannot "agree that episteme is aisthesis, at any rate along the "everything
is unstable' road" (183 c 1 sqq.). On the interpretation we have followed the
point is that there are entities other than sense-data to be known (namely the
patterns into which they fall), this suggesting the conclusion that reports of
present sense-experience are on the wrong logical level, so to speak, to count as
cases of knowledge. It is true that this point is not clearly brought out, though it
has been fairly well indicated that Protagoras* views require a world of discon-
nected, atomistic sense-data, and that this requires that the world be as inconstant
as the rampant Heracliteans say it is. But it is a sound point; it is entirely con-
sistent with what was said earlier about hearing people talking in a foreign
language, and with what is to be said later about reckoning-up our sense-experi-
ences with reference to existence and utility; and it would seem to be about the
only way in which Plato could show that judgments based on present perception
are not all true and do not count as knowledge for we have been allowed to get
the impression that these are incorrigible, so that it is only if truth involves some-
thing more than incorrigibility that we can deny them truth. And it does depend
on showing that the physical world is not totally inconstant. But on the conserva-
tive interpretation what are we to say are Plato's grounds for denying that such
judgments count as knowledge, and thus finally getting rid of Protagoras? If his
grounds are to be valid they cannot really be what I suggested earlier that they
might be, namely that the objects of aistMsis are inconstant and hence cannot
have true statements made about them. For "This is now pink to me" can be
true however inconstant "this" may be. In other words, if we are considering the
hypothesis that all judgments based on present perception may be true since
such a judgment commits its maker to nothing about the future, or the past, or
any other sense-experience whatever except the one that is being currently de-
scribed, then it will not do to dismiss this hypothesis by arguing that such a
judgment would be false if It did imply constancy, i.e. if it did commit its maker to
something about the future or the past or someone else's experience. If therefore
we are to find for Plato a valid reason for denying that such judgments count as
knowledge, it cannot be, I think, that the objects of aisthesis are inconstant; it
must be that aisthesis itself is inconstant, and therefore cannot be a kind of
30
THEORY OF KNOWLEDGE
episteme, this being assumed to be something constant. Now on the conservative
view Socrates does not argue that, if the natural world is inconstant, sensory
activity must be so also, for what he is saying at 182 d 8 sqq., on that view, is that
if whiteness itself (as opposed to white things) were inconstant, then sensing
itself (as opposed to sentient activity) would, by parity of reasoning, be inconstant
also; and this does not come to the same tiling. 1 But it could be said that this has
sufficiently hinted that percipient subjects are in the same boat with the objects
of their perceptions, from which we could no doubt conclude that if the natural
world is unstable, then our sensory apparatus is so also. It must be allowed, too,
that the conservative view can argue with some plausibility that Plato might well
have assumed that readers who would not boggle at the inconstancy of the bodily
function of perceiving would boggle at that of the spiritual function of knowing,
and therefore reject the linking of the two ; but two difficulties remain. The first-
is that it is necessary for the argument that it should be shown that everything
changes in every way all the time; it is not enough that it should be conceded that
this may be so. It is only if aisthesis is inconstant that it cannot be a kind of
epist&ne. But Socrates does not in the least seem to argue that everything in the
natural world, including our sense-apparatus, does in fact change in every way
all the time; the most that the conservative view can claim is that he argues that
even if this is so, still properties themselves cannot change. But this is not enough
to show that sensing, being inconstant, cannot be a kind of knowing. (A version
of this objection also holds against the view that Plato's reason for denying that
aisthesis is a kind of episteme is that the objects of aisthesis are inconstant; for
the most that can be claimed is that it is conceded that this is possible, not that
it is said to be true). And secondly it is very difficult to believe that when Plato
subsequently comes to discuss the contributions of sensing and of reckoning-up
to our acquisition of empirical information, he writes as if he thought that what
goes on in our bodies is something totally inconstant.
The conservative view can get a measure of support from the fact that there
are other places in Plato where the natural world is said to be a theatre of change,
and where this is held to put difficulties in the way of our describing it. But it is
perhaps significant that in the Timaeus, for example, 2 Timaeus does not object
to describing things adjectivally; it is merely the application of substantives that
he finds strictly misleading. However this may be, the considerations we have
advanced tend to show, so far as this passage is concerned, that if Plato's purpose
is to deny, on the ground that the natural world is totally inconstant, that
aisthesis is a kind of episteme, then his argument is somewhat incoherent. Since
there are other interpretations which attribute to Plato a more coherent (and less
silly) train of thought, it seems that the conservative interpretation is to be re-
jected. What then is to be said about the two passages (154 a 7-9 and 159 e
7-160 a 3) 3 in which Socrates seems to say that the content of one sense-experi-
ence is never identical with that of any other? The answer will have to be that
what Socrates is here saying is that each sense-experience is independent of every
other, in that the parties interacting in the one are always different from those
which interact in the other. If, that is, I look at the table, and then look at it
again, both the table and I will have changed, in small ways at least, on the
second occasion, so that it cannot be assumed that the content of the two experi-
ences will be identical; and indeed if one includes enough in what counts as one
1 On any interpretation this particular sentence is counter-factual, i.e. is part
of what Socrates cannot allow.
2 Timaeus 49-50; see below p. 217.
3 1 am grateful to Mr. J. L, Ackrill for forcing me to clear my mind about these
two passages,
31
THEORY OF KNOWLEDGE
sense-experience, and demands sufficiently high standards of identity.it can almost
be assumed that the two contents will not be identical (something will have
moved, the noise of the wind will have changed, my ear will have started to
tickle, or ... or ... etc.). And the reason why Socrates is saying this is that he
wants to argue that perceptual disagreement between two different percipients
is not surprising, and that Protagoras is right, with certain qualifications, in
holding that in such a case we cannot say that the one percipient is right and the
other wrong. Each is having the sense-experience which was bound to arise from
the interaction of just those factors which are interacting, each pair of factors is
a unique pair, and therefore identity of offspring between one interaction and
another (i.e. identity of content between two sense-experiences) must be the ex-
ception rather than the rule. If it is thought that I am putting rather a deflationary
interpretation upon Socrates' words, I can perhaps retort that in the earlier of the
two passages at any rate (154 a 7-9) we must deflate what he says a little, since
Theaetetus accepts it without demur. Socrates and Theaetetus agree without
argument that nothing can ever seem the same to someone else as it seems to
oneself; indeed, they say, nothing can ever seem the same to oneself as it seemed
on another occasion, on the ground that one is in a different state. But if this is
accepted without argument, it must be meant as something fairly mild that no
two sense-experiences will ever be totally identical, or that it cannot be assumed
that they will. It is very difficult to believe that they suppose themselves to be
assenting to the paradoxical and dogmatic statement that the same thing never
looks exactly alike on two distinct occasions. Perhaps we can conclude, then,
that Socrates does not, in these two passages, mean to deny to the empirical
world the element of stability which we took him to be attributing to it in
182.
It may be asked "finally whether it is legitimate to construe "if everything was
in motion only " in 182 c 9 as I have construed it, namely as if it were **if every-
thing consisted of particles in motion only". I think that it is, for the following
reasons. Firstly I can see no point in considering the hypothesis that everything 1
is in motion as a whole, for, in relation to the earth at any rate, this house for
example plainly is not. It seems more worth while, therefore, to consider the
hypothesis "that this house is in motion" in a form in which it is not plainly
false, i.e. in the form in which it means that the house consists of nothing but
moving things. It is the easier to take Socrates' words in this way in that, when he
recently distinguished kinesis or activity into motion and qualitative change, he
reminded Theaetetus (182 a 5) that the sense-qualities of a thing depend on the
motions which pass between subject and object; a thing's "becoming white" on
being seen was a resultant of motions, the moving objects being, we decided, the
particles constituting the opsis given off by the beholder, and those constituting
the flame of colour given off by the beheld. In this context the hypothesis "that
everything is in motion" is very naturally taken to be the hypothesis that every-
thing consists of particles in motion. If it is objected that there will be on the
theory certain entities which may well be at rest (e.g. the stone whose surface
gives off the white flame), the answer must be that we have already seen that it is
characteristic of this whole section of the dialogue that Plato is a little uncertain
about the status of entities such as the physical stone. Certainly it is inaccurate to
say that we never see anything but swarms of particles, but this is just the kind of
inaccuracy which has troubled us throughout this argument.
I think we can conclude, then, that the purpose of this passage is to argue that
the sane parts of the doctrine of the Heracliteans do not justify the multi-
tudinous enigmatic apophthegms which, as Theodorus says at 180 a, these
1 Panta from c 4 seems to be the subject of the verb,
32
THEORY OF KNOWLEDGE
philosophers are wont inconsistently to shoot at one, without staying to give an
answer. 1 In other words, it is intended as a refutation of rampant Heracliteanism.
II. DOXA AND EPIST&M&
A. The concept 0/doxa
What Plato has to say about doxa is mostly said in the course of
contrasting it with aisthesis on the one hand or with episteme on
the other. We cannot of course assume that the word means precisely
the same in these two contrasts. A man who in one place contrasts,
say, feeling with thinking, and in another place thinking with knowing
may, without equivocation, easily intend "thinking" to be taken in
two rather different ways. "Thinking as opposed to feeling" may be
a wider notion than "thinking as opposed to knowing", just as
"animals as opposed to vegetables" is a wider notion than "animals
as opposed to men".
Doxa then is a term which is employed primarily in contrasts ;
Plato says little about the meaning of the word on its own, and
perhaps there is not very much that can be said. There is however
what follows.
In the passage we have just been examining doxazein the verb
and doxa the noun stand as we saw for the activity of assessing or
interpreting the significance of material; or rather, for the decision
in which that activity culminates. Socrates says a little further on
(189-90) that thinking (diandeisthat) is silent discussion and that
doxazein is the decision which the discussion comes to. A doxa
therefore is something one asserts to oneself, and it is based on some
kind of assessment of material.
That a doxa is based on silent discussion is not always an essential
part of the word's meaning. Commonly elsewhere (e.g. Theaetetus
201) it is said to be a mark of a doxa that one can be induced, per-
suaded or jockeyed into holding it. Knowledge must be taught but
doxa can be induced by any method which secures the victim's
assent to a proposition. Doxa in other words, like "belief", does not
strictly imply the existence of grounds.
On the other hand there are one or two places (e.g. Theaetetus 189)
which suggest that the verb doxazein is nearer to "judge" than to
"believe". For "judge" implies (more clearly than "believe") that
something is being assessed or interpreted; and so it is, I think, with
1 One gets strongly the impression from this speech of Theodorus' that Plato
thinks that some of the Heracliteans are rather silly. There is also the general
impression that he is mediating between the Heraclitean belief in total in-
stability and the Eleatic belief in total changelessness. These impressions militate
against the conservative view.
33
THEORY OF KNOWLEDGE
doxazein. The word is etymologically connected with the notion of
seeming (dokeiri) and retains some flavour of "putting an interpreta-
tion upon". This I suspect helps to create the problem of false beliefs
which puzzled so many Greek thinkers. For when I believe some-
thing false, I, in one sense, "judge what is not" ; but yet when I judge
I must judge something, so that I must in another sense "judge what
is". You cannot construct this contradiction with "believe", for I
believe what is not, but I believe it about something that is. 1
Doxa, then, though it is the general word for "belief ", tends to
carry with it the hidden, but sometimes operative, implication that
the belief in question is an assessment of something. This is an
important clue to the contrast of doxa with episteme, to which we
must now turn; for epistemg implies that the object is not being
interpreted or assessed, but grasped,
B. The contrast between doxa and episteme. Introductory
A great deal hangs on the contrast between doxa and episteme.
Indeed some will tell us that the fallacious distinction between these
two concepts is the root error from which the whole of Platonism
grew. What Plato did, they will say, is to notice that doxazein, "to
believe", does not mean the same as eplstasthai, "to know". What
he failed, very naturally, to see is that this is only because, when 1
say that Jones knows that S is P, I commit myself to the truth of
"S is P", whereas I do not do so when I only say that Jones believes
this proposition. Therefore I cannot say: "Jones knows that S is P;
but he may be wrong." Hence it appears that to know is to do some-
thing which is infallible (cp. Republic 477 e 6-7). Deceived by this
appearance, the argument runs, Plato assumed that believing and
knowing were the exercise of two different faculties, each with its
appropriate kind of object. He looked therefore for an infallible
faculty, and for objects upon which it could plausibly be exercised.
Since our beliefs about ordinary things can always be wrong,
special objects, having a special affinity to the mind, had to be in-
vented to become the objects of knowledge. For various reasons
universals and mathematical entities seem best fitted to play this
role, and hence a special brand of self-subsistent universals, and
perhaps mathematical entities, had to be invented. This is the origin
of the belief in forms.
I do not deny that Plato may have thought along these lines, but I
think that we shall find that there is a good deal more to it than that.
A contrast between two intellectual levels is very pervasive in
Plato's writings from the Gorgias to the Laws. The word for the
J For further discussion of the Paradox of False Belief see below, pp. 486-98
34
THEORY OF KNOWLEDGE
lower level is fairly constantly doxa, though in the Gorgias (454,
462-5 and 501) the words pistis ("conviction") and empelria ("experi-
ence") turn up instead. Episteme is commonly used for the higher
level, but we also find its near-synonym gnosis, and also such words
as noesis (which rather implies "understanding") and sophia (com-
monly translated "wisdom"). The looseness of language is of course
typically Platonic, but it is also perhaps due to the fact that the
higher level consists in the attainment of the intellectual goal, which
can be looked at in more than one way and called by more than one
name, whereas the lower level consists in a practically adequate
approximation to it.
The major discussions of doxa and episteme are to be found in the
Meno, Republic and Theaetetus', and there is an illuminating discus-
sion of episteme in the Seventh Letter. Before we turn to detailed
examination of these passages we shall describe certain general
impressions which can be got from them and also from the shorter
discussions in other dialogues.
C. General impressions of the contrast between doxa and epistm6
L Knowledge (if I may use the English words without necessarily
intending their English meaning) is of course superior to belief, and
its superiority seems to reside (a) in the directness (Republic Books
6 and 7) with which a man who knows is related to what is really the
case, and consequently (b) in the infallibility of knowledge. On the
whole what Plato seems to have in mind by "fallibility" is the
tendency of something which we only believe to let us down when
we come to apply it to a particular situation (cp. Meno 96-8, dis-
cussed p. 52 below). This suggests that he is chiefly, though not
exclusively, thinking of his contrast as one which is useful in the
context of pieces of general information; for it is general information
which can be applied in various situations.
2. Knowledge is bound up with understanding, and hence has to
be conveyed by teaching whereas belief can be induced by training,
persuasion and so on. We have already quoted this point from
Theaetetus 201, and it comes out in the discussion of the courage of
the soldiers in Republic 429-30. In this connection there is a note-
worthy passage in the Timaeus (51-2). Here Timaeus has been making
use of forms in his account of nature, and he pauses briefly in order
to justify doing so. Some, he says, hold that particulars are the only
realities, the universal of which they are said to be instances being
only "expressions we use" (logoi). His reply to this (which he admits
is summary) is that, if nous or intelligent understanding is not the
same thing as right belief, then there must be something which can
be grasped by the mind, though not by the senses, to be the object
35
THEORY OF KNOWLEDGE
of the former. But in fact these two states of mind are different.
Intelligent understanding is a rare state which can only arise through
teaching, involves an accurate account (alethes logos), 1 and is not
dislodged by persuasion. Right belief on the other hand is something
all men share in, is not rational, and is inculcated, and thus can be
destroyed, by persuasion. Therefore understanding and belief are
distinct, and therefore there exist self-consistent universals as the
object of the former, and changeable sensible particulars as the
object of the latter. This passage can clearly be used by those who
hold that the forms were invented to give knowledge an object.
Meanwhile, however that may be, it emphasises that knowledge (if
we may identify nous and episteme) is something which exists at the
rational level whereas belief is confined to the level (or levels) at
which sense-perception is decisive and at which emotional appeals
can be effective. Knowledge then is connected with understanding.
3. In particular it is connected with understanding why what is
the case must be the case with insight into necessity. This is said
in Meno 96-8, though it might be held that doubt is cast upon it In
the last section (201 onwards) of the Theaetetus.
4. A conflicting general impression. In some places it is implied
that what we can believe we can also come to know. In other places
it is implied that this is not so, that belief and knowledge have
different "objects" or spheres of operation.
Thus in the Meno one can believe or know a proposition like that
which describes the road to Larisa (97); and indeed the Meno gives
the recipe for turning belief into knowledge. Similarly in the Theaete-
tus (201) it is said that an eye-witness may be the only person who
can know the facts though the court may be induced to believe in
them. These two passages allow knowledge and belief to have the
same objects, and indeed allow that matters of empirical fact can
be known.
Elsewhere, however, and perhaps predominantly, this is not so;
knowledge has special objects, and matters of empirical fact are not
among them. The Meno, as we shall see, is hardly consistent with
itself and says things which make one wonder how it is possible, on
its terms, to know the road to Larisa. The Republic speaks quite
happily (Books 6 and 7) of the "sphere of belief", which seems to
be at least closely related to the empirical world. In the passage from
the Timaeus which we just looked at belief was connected with sensible
particulars, and knowledge with universals. The same thing is said
earlier in the same dialogue (Timaeus 27 d-28 a), where Timaeus
begins his discussion by distinguishing "that which is at all times,
1 This surely means an account which gives the reason for the fact in question,
an account which gives insight.
36
THEORY OF KNOWLEDGE
and never becomes" and "that which becomes at all times, and
never is", of which the first is "graspable by understanding (noesis)
with rational insight (logos), being always the same", whereas the
second "can only be judged by judgment (doxa), with non-rational
perception (aisthesis), since it comes and goes and never really is".
The same point, that that which changes cannot properly be known,
is made in the Philebus (55-9). Socrates is examining the various
branches of knowledge to test their purity, or in other words to see
how much real knowledge each involves. To do this he puts branches
of knowledge in order ofakribeia, a notion which involves accuracy,
but also more than that. Perhaps "finality" or "unrevisability"
would do. At the bottom go practical arts, those like carpentry which
involve mathematical techniques being preferred above those like
music which do not. Pure mathematics is on the floor above, but
the top stage is occupied by philosophy (dialektike), which alone
is unadulterated knowledge. The subjects on the ground floor are
put there (59 a) because they rely on beliefs ; not only music and
architecture, but also cosmology, are belief-ridden subjects because
they concern themselves with changeable particulars.
In the Epinomis (or thirteenth book of the Laws), however,
cosmology is promoted. In the first book of the Laws it is said that
a community needs some guardians of its laws who walk by wisdom
(phronesis) and some who walk by true belief. The astronomer-
philosophers of the Nocturnal Council are provided to supply the
former need. When the Athenian Stranger comes to consider the
education these men are to receive, he asks himself what branch of
knowledge entitles a man to be called wise (Epinomis 974-6). Every
other branch of knowledge is rejected for one reason or another (in
the case of medicine and rhetoric the reason being that these subjects
rely on beliefs) except for an astronomico-mathematical brand of
philosophy which involves a grasp of the perfect harmony of the
motions of the heavenly bodies. Here therefore it is clearly allowed
that certain changeable particulars can at any rate be the objects of
something higher than belief.
5. In one or two places it seems to be implied that knowledge
involves something like direct acquaintance, and thus goes beyond
the ability to describe correctly. The point is perhaps made in the
Theaetetus (208-9) in terms of a distinction between knowing who
Theaetetus is, and knowing only what sort o/man he is ; and a similar
distinction is made in the Seventh Letter (342-3). The idea that
knowledge is to be thought of after the model of direct acquaintance
could be made to take care of the man in the Meno who knows the
road to Larisa and of the eye-witness in the Theaetetus who knows
what the prisoner did.
37
THEORY OF KNOWLEDGE
To sum up these general impressions, then, knowledge is infallible ;
involves understanding in some sense, perhaps insight into why what
is the case must be so; is commonly, though not always, confined to
the sphere of things which do not change, which is a sphere from
which facts about the empirical world are excluded; and finally it
can be conceived after the model of direct acquaintance.
One view, then, is that we can only know things which do not
change, and that this means that we cannot know the physical world.
It is in the Timaeus that this view is most prominent, and it is to be
noticed that in this dialogue three classes of objects are identified :
(a) that which can be understood, (Z?) that which does not change, and
(c) that which cannot be grasped by the senses. Moreover the
Timaeus seems to argue that it is because physical things come into
and pass out of existence that they cannot be known; and the
Philebus seems to agree with it on this point.
This raises two problems. Firstly we remember that the Theaetetus
argues that, although it may be true that physical things are in flux,
the manner in which they are in flux does not make it impossible to
describe them; for the flux results in the stable manifestation of
properties such as whiteness. Now, whether or not the Theaetetus
is earlier than the Timaeus, it is almost certainly earlier than the
Philebus. But by the time of the Theaetetus Plato has seen that the
kind of change which can plausibly be ascribed to the physical world
does not render it indescribable; why then, one wants to ask, should
it render it unknowable? Is the position of the Theaetetus^ that the
physical world may be impermanent, but is none the less describable,
consistent with the position of the Timaeus and Philebus that its
impermanence renders it unknowable?
The second problem which arises concerning this latter position
is one of interpretation. What does it mean to say that the physical
world is unknowable ? If we are being told that there is no such thing
as (for example) "knowing the sun", what is it that is here being
denied ? And similarly what is it that is being said to be impermanent,
to "become and perish" ? Is it the sun itself which becomes and
perishes; and if so does this mean only that it is not an eternal object,
or does it rather mean that its material is continually consumed and
renewed? Or is it that nothing about the sun endures, that its size
fluctuates, its path wanders, its temperature varies, and so on?
There are three rather tempting ideas which suggest themselves in
the light of these difficulties. The first of these is that the Timaeus
does not mean to tell us that we cannot know facts about the sun
(to continue with that example), but only that there is no such thing
as "knowing the sun". Things are what we can perceive, and they
change; facts about things cannot be perceived by the senses but can
38
THEORY OF KNOWLEDGE
be grasped by the mind ; and facts about things, even about changing
things, do not themselves change. We can therefore know in what
path the sun travels, though we cannot literally see this; and we can
see, but cannot literally know, the sun itself. This is an attractive
idea. The conception that the senses put us into touch with things,
but that the mind puts us into touch with facts about them, reminds
us of the distinction between aisthesis and doxa In the Theaetetus.
But unfortunately there are two fatal objections to this idea. Firstly
if physical things are what we perceive, and if facts about physical
things are among the things that we know, what is it that we believe?
This objection may perhaps be answerable, but the second is not.
It is simply that the use Timaeus makes of his distinction between
knowledge and belief does not at all correspond to the suggestion
we are considering. That the sun is of such and such a size or travels
in such and such a path is not at all the sort of thing that Timaeus
describes as "something that always is, and hence can be known".
He introduces his distinction precisely in order to explain why his
account of physical nature is and must be conjectural Facts about
nature therefore are exactly that which can only be believed. It is
the rational necessities which must have determined the creative
activity of the divine Craftsman that can be known.
The second tempting idea is that physical things are not gignomena,
or things that become and perish, in the sense that they change, but
in a different sense, the sense in which this and allied notions were
used in the description of the Protagorean-Heraclitean Mysteries in
the Theaetetus. In this sense natural objects are gignomena in that
they only come into momentary existence when they are perceived;
the tree as we know it only "becomes" when there is someone in the
quad, and "perishes" when he goes away. The real physical activity
which gives rise to the sense-data which constitute empirical objects
is inaccessible except to conjecture; and the best that we can manage
with the natural world is a knowledge of the patterns to which
sense-experience conforms in fact what the Theaetetus calls doxa.
The trouble with this suggestion is that it is far-fetched. "Change
and decay in all around I see" is the natural reading of Timaeus'
language about becoming and perishing, and it is difficult to believe
that we were meant to understand anything else. It is possible that if
we knew more of the things that were written and said by Plato's
philosophical contemporaries we should see that "become and
perish" could naturally be taken in some other way; but we cannot
assume that this is so.
The third suggestion is on a rather different plane. It is that the
Timaeus should not be taken too seriously. The dialogue is more a
piece of cosmological speculation than of philosophy; the tone is
39
THEORY OF KNOWLEDGE
lofty and hierophantic and the philosophical issues it raises get
rather summary treatment. How would it be then to say that Timaeus
uses what looks like a clinching argument in order to make as briefly
as possible a point which does not in fact depend at all upon that
argument ? Plato's real point is somewhat as follows : Observation
and theories based upon it can never put us into touch with the
realities of nature; it can give us information about things as they
affect our senses but not about things as they are in themselves. If
we want a picture of things as they are in themselves the best we can
have is a conjectural one. The conjecture will be a kind of bridge
resting at one end on things that we can know and at the other end
on things that we can observe. We -can know the intelligible neces-
sities which must have determined the Creator's ends but we cannot
know how he may have set about realising them in the material
available. This we can only conjecture by constructing hypotheses
to explain the observed phenomena. Thus we can know that irregular
shapes are offensive to reason, and we can know how many regular
solids there are. We can know from this that the shapes of any three-
dimensional particles there may be will be from among the regular
solids. Reason will have decreed this. On the opposite bank we can
observe, for example, that fire bums. Between these two ends we
can build a bridge by supposing (as in Timaeus 56) that fire is made
of pyramidal particles and owes its destructive powers to the sharp
corners of the regular pyramid. However confident we may be of
such a theory it must remain an explanatory hypothesis, and the
intelligible facts (geometrical and other) which we can know are
somewhat remotely related to it. We do not need to suppose that this
is Plato's real point about certainty and uncertainty in the Timaeus^
for it is clear that it is. What we will suppose is that Timaeus in the
preface to his discourse wants to convey that what follows is a
conjectural edifice, and cannot, without anticipating what he is going
to say, describe the precise roles played in it by intelligible neces-
sities, facts of observation and hypotheses linking the two. But there
lies ready to hand what seems a clinching argument to show that
cosmology must be conjectural: cosmology is about the world,
the world is subject to change, and what changes cannot be
known.
It may be felt that "what changes cannot be known", as applied to
the world, rests on a fallacy exposed in the Theaetetus and that
therefore in the Philebus at least Plato should have known better.
One might perhaps reply to this that "what changes cannot be known,
and therefore the physical world cannot be known" is the sort of
error which is so natural that it can only be got rid of by frequent
refutation. Whatever Plato may have done in the Theaetetus the
40
THEORY OF KNOWLEDGE
error is hardy enough to reappear in the Sixth Book of Aristotle's
Ethics (E.N. 1139b22).
We shall have to return to this later when we have examined the
three major discussions of knowledge and belief. Meanwhile we can
note that this preliminary discussion has the folio wing result: The
doctrine that the physical world is impermanent and hence cannot
be known (a) may perhaps represent an over-simplification of Plato's
real thought into which he sometimes slipped and (b) is an unclear
doctrine in that we are uncertain both in what sense the physical
world is said to be impermanent and also what precisely it is said
that we cannot know.
D. The contrast between doxa and epist6m6; anticipation of con-
clusions
The three major discussions of knowledge and belief are so compli-
cated that a thread is needed to guide one through them. I shall try
to provide such a thread in this section by anticipating the conclusions
which I hope to come to.
The question: "what can human beings feed on?" admits of a
formal and of a material interpretation. Formally interpreted, the
answer expected is something like : "Any thing which can be absorbed
through the digestive tract and used to build and maintain the tissues."
But this formal answer having been given, the question can still be
put materially by asking: "Well, and what kinds of things are these?"
So with the question: "What can we know?" The answer to the
formal version of this question will lay down the conditions which
anything must satisfy in order to be knowable: the answer to the
material version will tell us what things satisfy these conditions. A
good deal of confusion can get into the discussion of what Plato says
about knowledge and belief if this distinction between the formal
and the material version of the question is not kept in mind.
Next we must remember that some of the things which Plato says
are said in terms of what is to us an unfamiliar picture of the relation-
ship between the knowing subject and the thing known. To avoid
unnecessary confusion it is important to get the right picture. Firstly,
what we would naturally claim to know are propositions, truths.
What Plato would naturally claim to know are things. We would
tend to say of a mathematician that he knows that triangles have such
and such properties, or indeed that he knows how to multiply or to
integrate. Plato would tend to say of him that he knows triangles and
numbers (cp. Theaetetus 198). Secondly, Plato tends to think of the
process of learning as one of acquiring or devouring (see again the
41
THEORY OF KNOWLEDGE
image of the aviary, Theaetetus loc. cit.). Thirdly, what the learner
needs to acquire or devour is some part of the real objective world.
Knowledge then, being the achievement of learning, is the devouring
of something real. The mathematician who knows all about triangles
(who "knows the triangle") has devoured triangularity; triangularity
has become part of his mental equipment. The school-boy on the
other hand who can assert some, but not all, of the truths about
triangles, and who can do so with a measure, but not a full measure,
of understanding, he has devoured not triangularity but a likeness of
it only; and his state is one not of knowledge but of belief. The
difference between the two states is that in knowledge what has been
devoured is an objective entity, whereas in belief what has been
devoured is no more than a likeness of such an entity. This is
important so we will repeat it in a little more detail.
There are really three states we are concerned with, namely know-
ledge, belief and what the Republic calls agnoia or ignorance. Now
to decide whether my state on a given occasion is one of knowledge
or of belief or of ignorance what you have to ask is what it is that
I have in my mind. Take the case of knowing Jones. Let us suppose
that my conception of Jones is faithful in all respects, so that Jones
himself, we might say, lives in my mind. What the Jones whom I
conceive of would do or think or say in a given situation is identical
with what the real Jones would do or think or say; there is no dis-
crepancy between the Jones in my mind and the Jones in the real
world. My Jones is identical with the real Jones ; and yet there are
not two Joneses, one in my mind and one outside it, so perhaps we
had better say that what exists in my mind is the real Jones. My mind
in this case has absorbed a real thing. This is a case of knowledge.
But now let us suppose that my conception of Jones, though based
on the real Jones, is all the same distorted, blurred, defective. I can
tell for example the kind of political views which Jones tends to-
wards, but I do not know him well enough to be able to say just
what he thinks about nuclear weapons; or perhaps I think I can say,
but am wrong. What exists in my mind now is not Jones, but an
eikon, an image or picture, of Jones something that owes its broad
outlines to his outlines, but is deficient (schematic and two-dimen-
sional, whereas he is in the round) and also perhaps distorted. This
is a case of doxa or belief, and in this case what exists in my mind is
not identical with., but is based on the real thing of which I am forming
a conception.
Finally let us suppose that there is nothing in my mind which can
be called a picture of Jones. Here my conception of Jones is nothing,
and here my condition with regard to Jones is one of agnoia or
ignorance. This can happen in either of two ways; either because I
42
THEORY OF KNOWLEDGE
have never heard of Jones and hence would not claim to have any
conception of him; or because the conception of him which I do
claim to have is so completely false that it cannot be called a con-
ception of Jones at all, but a complete figment, where the man whom
I conceive under that name has no existence outside my mind.
(Similarly there may be no picture of the Marble Arch in my sketch-
book either because I have not tried to draw it, or because, although
I have tried to draw it, the result is so hopeless that it must be dis-
missed as "not a picture of the Marble Arch at all". When is a
picture not a picture? When it is hopelessly unlike).
That to know something is to grasp or absorb some piece of
reality is of course only a picture. If we approach the consideration
of cognitive states in terms of this picture (as I am suggesting Plato
did) it will give rise to certain difficulties, of terminology at least,
which it will be worth our while to look at. We begin from the
position that he who comes to know something thereby absorbs
part of the world; starting there it is natural to go on to ask what it
is that has been absorbed by the man who is in a state of belief or
ignorance. To see the answers that might be given to these questions
we must consider in a little more detail what these two states con-
sist of.
The distinction between knowledge and belief which we sketched
above is roughly this. When I know something, say that Jones has
a moustache, there exists a complex in the external world, Jones-
having-a-moustache, or (we might almost say) Jones's moustache;
and this complex is actually before, or in; my mind. When I only
believe that Jones has a moustache I am not in direct touch with
Jones's moustache, or with the state of affairs Jones-having-a-
moustache. The position is rather that I affirm the existence of a
state of affairs which belongs to a certain range of states of affairs,
namely that range the existence of any member of which would
render true the proposition that Jones has a moustache. I am out
of touch with the actual individual condition of Jones's lip, 1 though
I very likely imagine some individual lip-condition and impute this
to Jones with the reservation that his actual lip-condition will re-
semble, but may not be identical with, the lip-condition that I
imagine. For my belief that Jones has a moustache to count as a
true belief it is necessary that there should be a reasonable degree of
resemblance between the actual condition of Jones's lip on the one
hand and on the other the condition that I impute to him in my
imagination, or rather perhaps the typical condition with which a
proposition to the effect that some man has a moustache is cor-
related. A belief can be regarded as reasonably reliable so long as
1 cp. Theaetetus 209 c 4-9, discussed below, p. 113.
43
THEORY OF KNOWLEDGE
such a resemblance holds ; in a sufficiently complicated case a belief
may be of some service even if there is a certain amount of positive
discrepancy between the actual situation and the expectations which
the belief leads one to form, even if the actual situation falls in some
ways outside the range of situations which is such that one of these
situations must be the case if the proposition which expresses the
belief is to count as perfectly true. Analogously a picture will be
recognisable even though it misrepresents its subject in certain
respects. 1 I shall not say that you are totally out of touch with the
actual situation just because the type of situation which falls plumb
under the meaning of the proposition to which you assent differs in
some ways from the actual situation. We do not therefore reach the
borders of agnoia or of being totally out of touch with what is going
on until we transgress the bounds of reasonable resemblance. With
regard to any topic, I may be said to be totally out of touch with it
if none of the contents of my mind has any reference to that topic,
or if some of the contents of my mind do claim to refer to it, but
totally misrepresent it. As we have seen we do not get a case of this
latter just because I say that Jones is clean-shaven when the truth is
that he has not in fact shaved for three days ; but we certainly will
get a case of it if I say that Jones is clean-shaven when the truth is
that his moustache is and has been for years the pride of the Ser-
geants' Mess. What happens in this case is that I assert a proposition
such that there is correlated with the truth of that proposition a
range of situations such that the actual situation falls clean outside
the boundaries of that range however tolerantly they are construed.
We have then certain factors which we can distinguish and which
we can use if we wish in the analysis of the cognitive relationship
between a man and a topic. We have first the mental state of the man
with respect to that topic. This may be one of knowledge, of true
belief, of false belief, or of being totally unaware of the topic. We
have next the mental correlate, or content, of the state in question.
In the case of knowledge, the absorption-picture requires that we
should say that this is the topic itself. In the case of true and false
belief it will be what we should call a proposition- In the case of
total unawareness it will of course be nothing. Next we have the
actual state of the topic, the actual condition of that to which the
mental state relates. In the case of knowledge this will be identical
with the content of the state. In the case of true belief it will be a
state of affairs which fits more or less comfortably under the meaning
of the proposition which expresses the belief. In the case of false
belief it will be a state of affairs which falls outside this range. In
1 Cratylus 430 affords an example of the use by Plato of the notion of a picture
in this kind of context.
44
THEORY OF KNOWLEDGE
the case of unawareness it will neither fall nor fail to fall within the
range of the proposition believed, for there is no such proposition.
Finally in addition to the actual state of the topic we have what we
may call the alleged state of the topic. In the case of knowledge the
alleged state is of course identical with the actual state of the topic,
and this in turn is identical with the content of the knowledge. In
the case of true belief the alleged state of the topic is the class of
states of affairs each of which would, if it existed, suffice to render
true the content of the belief, the actual state of affairs being one of
these. In the case of false belief the alleged state of the topic is again
the class of states of affairs each of which would, if it existed, suffice
to render true the content of the belief, but in this case the actual
state of affairs is not a member of this class. In true belief therefore
the actual state falls within the alleged state, in false belief it falls
outside it. There is of course no alleged state in the case of total
unawareness.
We have then four factors : a mental state, its mental correlate or
content, and two objective correlates, the actual and the alleged
state of the topic to which the mental state in question relates. Our
purpose in distinguishing these four factors was to use them in
trying to see some of the difficulties which might arise if we were to
start from the principle that that which is before the mind of the
knower is some actual state of affairs, and go on to ask what it is
that is before the mind of a man who is in a condition of doxa or
agnoia.
Today we tend to say that what is before or in the mind of the
believer is a proposition, true or false. But as we have seen Plato
tended to speak of knowing, not propositions, but things; and it
seems that he tended also at one stage to speak of that which is
before the mind of the believer and of the ignorant as if it were some
kind of thing. More accurately, perhaps, he tended to use the syntax
of connaitre for the case of knowledge, and to use the same syntax
for the other cases; and some of the difficulties in his account in
the Republic in particular can be construed as difficulties which are
due to thinking of belief and ignorance in this syntax. This gives the
impression that belief and ignorance are epistemologically inferior
faculties whereby we become acquainted with ontologically inferior
objects. One can of course assimilate the logical syntax of savoir to
that of connaitre by treating a that-clausQ as the name of a complex
entity. This in itself gives no trouble; trouble arises when we treat
as names of complex entities the tfzatf-clauses which occur in false-
belief statements. "That Jones has a moustache" can be regarded as
the name of a state of affairs so long as Jones has a moustache; if
however he is clean-shaven there is no such state of affairs for it to
45
THEORY OF KNOWLEDGE
name. Reflection on false belief thus induces us to introduce the
notion of a proposition as something distinct from a fact, event,
state of affairs or what you will (This does not mean of course that
it induces us, necessarily, to believe that there exist propositions
which serve as intermediaries between minds and facts. That it may
induce us to believe this is the objection to the notion of a proposi-
tion, for the idea that propositions are intermediaries has notorious
difficulties of its own. But reflection on false belief is likely to in-
duce us at least to introduce the term "proposition" as an analytic
tool).
It was Plato's achievement to make clear in the Sophist (and to
hint perhaps in the Theaetetus) that we need the notion of a proposi-
tion for the analysis of false belief. 1 But at an earlier stage he appears
to have followed what seems to have been the practice of his contem-
poraries and to have tried to manage without it. Let us try to see
where this would have got him to. The question was: "If some part
of reality is what is before the mind of a man who knows something,
what is it that is before the mind of a man in an inferior cognitive
state?". We will start with the case of false belief. The man in a
state of false belief has taken into his mind a proposition, and this
proposition is one which would be verified by the existence of any
one of a range of states of affairs, none of which exists. For the sake
of simplicity let us speak as if there were just one state of affairs
("the alleged state of the topic") whose existence would verify a
given proposition. In this simpler language we can say that the false
believer has taken into, or has before, his mind a proposition which
would be verified only by a state of affairs which does not exist.
Telescoping this by leaving out the proposition we can say that the
false believer has before his mind something which does not exist,
a non-entity. Notoriously this is what many Greeks did say, for it
is this which leads to the Paradox of False Belief since there are no
such things as non-entities, it would seem that the false believer has
nothing before his mind. 2
We will take next the case of true belief. If we bear clearly in mind
that there are many different states of affairs each of which is sufficient
for the truth of a given proposition, and only one of which, at most,
exists, we shall say, as we have said, that the alleged state of the
topic in the case of true belief consists of a range of states of affairs
such that the actual state of affairs is a member of that range. But
we might fail to bear this clearly in mind, especially perhaps if we
did not make use of the notion of a proposition. Without this notion
1 See pp. 492-8 for an account of the discussion in the Sophist and pp. 490-2
for an account of the possible hints in the Theaetetus.
3 For the Paradox of False Belief see Chapter 4, pp, 486-98.
46
THEORY OF KNOWLEDGE
we shall tend to say that belief affirms the existence of a state of
affairs. Since this "state of affairs" will have to include within itself
all the various possibilities which are compatible with the truth of
the belief, it will be an odd sort of entity, a kind of highest common
factor of the range of possibilities. If we ask how this "state of
affairs' 5 is related to the actual state of affairs, we shall say perhaps
that It resembles it or that it is an image or representation of it.
True belief therefore affirms the existence of a state of affairs which
is an image of the actual state of affairs. If the man who knows has
in his mind the actual state of affairs, the man who truly believes
has in his mind an image or likeness of the actual state of affairs.
What he has in his mind therefore is something which comes in
between the real entity which is grasped by the knower and the non-
entity which deludes the false believer. It is neither an entity nor a
non-entity, but something in between.
We can of course avoid this paradoxical result if we clearly insist
that there is no such thing as "the state of affairs which the true
believer believes". We do not believe states of affairs, we believe
that so and so; and the relationship between the //zn/-clause or
proposition and the world is that the rules of the language we are
using are such that the proposition would be true if the actual situa-
tion fell within a certain range, false if it fell outside it. The state of
affairs which the believer believes, the thing which is neither an
entity nor a non-entity, is something which we only get if we, so to
speak, treat the /to-clause as if it were a state of affairs. It is this
which makes us try to find an ontological status for it in between
those states of affairs which do, and those which do not, exist or
rather to use language which makes it seem that this is what we are
trying to do. It is the treatment of to-clauses as if they named some
complex in the world that makes us treat the /to-clauses which are
the objects of true belief as if they named complexes in the half-
world, and to treat those which are the objects of false belief as if
they named complexes in the non-world.
Finally we may round this discussion off by considering the case
where my ignorance of X consists in my being totally unaware of it.
Here clearly what exists in my mind with respect to X is nothing
whatever. If we are thinking of cognitive states in terms of the degree
of contact between the subject and the object it may well seem that
being deluded about X and being unaware of X are more or less the
same thing. The difference between them is that in the case of delu-
sion there is a reference to X (or more strictly to that locus which is
in fact occupied by X); but so far as contact with what is going on is
concerned this is equally missing in the case of unawareness and in
the case of delusion. It will be argued later that the Theaetetus shows
47
THEORY OF KNOWLEDGE
Plato becoming aware of the importance of the topic of reference, 1
and he is certainly aware of it in the Sophist. But if in the earlier
period he attached no great significance to this relationship, it might
well have seemed to him that delusion and unawareness could be
treated together under the title of agnoia, the common factor of the
two cases being that nothing with respect to X is present in the mind
of the man who is either deluded about it or unaware of it; and (if
delusion was the one of these conditions which attracted more of his
attention) it might well have seemed to him tolerable to use of both of
these kinds of nothing the title "non-entity" which belongs more
properly to a figment, i.e. to that kind of "nothing with respect to
X" which occupies my mind when I am deluded about it rather than
to the blank space opposite X which exists in my mind when I am
unaware of it.
I need not remind the reader that in recent paragraphs we have
been speculating about the sort of language which Plato might have
found himself using if he had thought of cognitive states in a certain
way that is, if he had thought of them in terms of the degree of
contact between mind and state of affairs which is present in each of
them. This speculation, I own, has not been entirely disinterested;
it has been guided by the interpretation which it seems to me neces-
sary to put upon certain texts, especially those in the Republic. But
I do not claim that in these paragraphs I have been reporting
doctrines that Plato explicitly advocated ; and I hope that I shall not
be accused of saying, for example, that Plato anywhere tells us in so
many words that knowledge is full contact between mind and object;
that he thought that what occupies the mind of the believer is, in
favourable cases, an image of the object; that he lacked the notion
of a proposition and thought that /^/-clauses were the names of
states of affairs, real, unreal or half-real; or any other things of
this kind. I have done no more than try to show what might have
happened if he had thought about certain topics in certain ways, in
the hope that, when we come to consider some of the things that he
said, we may find that the conjectures throw light on the facts. The
proposition which is essential to these speculations, namely that in
knowledge the known state of affairs exists in the knower's mind, is
not, let us say it frankly, to be found in Plato's writings. We do find
it explicitly stated by Aristotle, but not by Plato. I do not even say
that it is a proposition to which Plato would have given his assent.
He might have found it, as we find it, a proposition to which it is
difficult to attach a clear meaning. It is no part of my argument that
Plato thought that he knew what knowledge was but kept it as a
secret which he passed on to Aristotle to publish. Being less in-
1 Sec below pp. 110-1L
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THEORY OF KNOWLEDGE
cllned than Aristotle to believe that philosophical problems can be
solved by formulas, he may well have found himself to the end puzzled
about knowledge and unable to say what it is. I suggest no more than
that the proposition in question gives expression to the picture which
Plato took for granted in his reflection about knowledge and its
inferior states.
Remembering then that these are conjectures, let us take them a
little further. From those which we have made so far we are in a
position to extract an answer to the formal Interpretation of the
question: "What sorts of things can we know?" Since, when I know
something, I have in my mind the thing itself and not just a repre-
sentation of It, the things which can be known will be presumably
those which can be grasped or absorbed by, or which can exist in a
mind. But now the material Interpretation of the question arises In
the form: "What sort of things can exist in a mind?" In our dis-
cussion so far we have used various examples triangularity, Jones,
Jones's possession of a moustache, the road to Larisa. Are all of
these things which the mind can absorb ? Is it, for example, possible
for a man to have the road to Larisa in his mind ?
Metaphorically of course it is. The man who has often travelled
to Larisa certainly has the road in his mind. There is no significant
difference between his conception of the intervening country and the
intervening country as it is in reality. But literally the road to Larisa
Is a stretch of earth and rocks and trees and not a system of logical
necessities. Literally therefore a man cannot have the road to Larisa
In his mind but only a conception or series of pictures of it. What
he has in his mind logically cannot be more than an eikon or image
of reality. In the case of triangularity this is not so. Triangularity is
something more like a system of logical necessities, and as such it
is a noeton or intelligible entity, something which can itself be
absorbed by the mind. Strictly therefore in the case of triangularity
what a man has in his mind and the reality that he is thinking about
can be identical, whereas in the case of the road to Larisa they
cannot. Yet while in the latter case we strictly have to confess that
what is in the mind is an eikon, it may be an eikon which is capable
of no improvement. A perfect eikon is not Identical with Its original,
but if it is perfect there Is no point in stressing this. It follows from
this that, in terms of the conception of knowledge that we have
outlined, it will be perfectly natural, but strictly Incorrect, to speak
of knowing the road to Larisa. The conception of the road which
exists in the mind of the man who has merely been told how to get
there Is an eikdn in a far more significant sense than that of the local
inhabitant, so that if you want to bring this out you will say that
the visitor has correct belief and the local inhabitant knowledge.
49
THEORY OF KNOWLEDGE
The same point may be made in a different way. To want to know
Is to want to have insight into what really exists in the world. In one
sense the road to Larisa is one of the things that really exist in the
world, and therefore the man who is familiar with it can be said to
have achieved the goal of knowledge. But in another sense, used at
a more theoretical level of discourse, the road to Larisa is no more
than a complex of empirical objects; and, as we have seen more than
once, to be familiar with an empirical object is not to be in touch with
something ultimate. An empirical object is "in flux" In all the senses
which can be attached to that phrase. If we want to be strict we shall
reserve the title of an on, or of an ultimate reality, for that which
determines that the flux shall take, in any given case, the form that
it does. In this way therefore It Is strictly true that the man who Is
familiar with the road to Larisa is familiar with something derivative,
something that can be called an elkon. 1 Clearly therefore If we are
to reserve "to know' 5 for insight Into ultimate realities the man who
is familiar with the ordered series of sense-experiences which con-
stitutes the road to Larisa cannot be said to know. Equally clearly
however it would in some contexts be pedantic to insist on this point.
The upshot therefore of these last two paragraphs Is that it will not
surprise us if we find Plato using a strict sense of epistasthaim which
we cannot be said to know physical objects and a relaxed sense in
which, under favourable conditions, we can.
E. Knowledge and belief in the Meno
The first of the major discussions of knowledge and belief Is to be
found In the Meno, The topic pervades the whole dialogue but It is
to be found in concentrated form from 96-8, The context of the
passage is this. If goodness were some kind of knowledge, it would
be teachable. It seems that It must be knowledge, for goodness is
valuable, and therefore must involve knowing how to make use of
potentially valuable endowments. Yet in fact goodness does not seem
to be teachable. Socrates gets out of this dilemma by saying that it is
in practice just as useful to have right belief as it is to know, and that
it may be impossible sufficiently to inculcate right beliefs about life. 2
If then goodness depends on right belief, rather than knowledge, we
can understand both why it is useful and why it cannot be taught.
In detail Socrates says that one man may have done the journey
to Larisa and hence know the road, but that another man who has
not done the journey, and therefore does not know, may be an
1 This of course is a different use tfelkdn from that in the last paragraph. For
this double use of the word compare Phaedo 100 a,
2 The implication is of course that knowledge always can be taught.
50
THEORY OF KNOWLEDGE
equally good guide provided that his beliefs are correct. Right belief
is just as effective towards right action. Meno objects that right
belief does not always work, and Socrates retorts that it always works
when it is present, but that it does not always stick. It runs away
and needs to be tied down. This can be done by "working out the
explanation" (aitids logismos), which Socrates calls recollection
(anamnesis). When a belief is tied down in this way it is turned into
knowledge, which persists. Socrates adds that he is sure that right
belief is not the same as knowledge, but is only conjecturing the
difference between them. This is a significant comment, for it suggests
that Plato's starting point in the whole business was the conviction
that there is one state of mind which involves insight and hence is
unshakable, and another which does not.
Knowledge then must be teachable, it must involve understanding,
and for that reason it is not liable to "run away". A belief can be
converted into knowledge by "recollection", that is by working out
the explanation of the fact. What Socrates means by "teachable",
and why understanding the explanation of a fact is called recollection
has been explained earlier in the dialogue (80-6) where Socrates
gives an instance of how to teach by getting an uneducated slave to
prove a geometrical theorem simply by asking him the right questions
in the right order. The slave is thereby enabled to gather from his own
resources insight into the logical necessities of the theorem (it is
because the insight is gathered from within that the process is called
recollection). 1 The false beliefs that he had on the subject are thereby
expunged, and his true beliefs (this seems to be the point) are con-
verted into knowledge by being strung together in such a way that
they afford him understanding.
It is noteworthy that in this account "knowledge" and "belief "
are used to classify two attitudes of mind and not two classes of
proposition. There is no suggestion that only propositions about
universals can count as knowledge, propositions about particulars
counting as belief. In 86 a 7 the right answers that the slave gave
are called "true opinions" and it is said that they were turned into
"knowledges" (epistemai) when they were "awoken by questioning".
The implication of this is that what the slave tentatively put forward,
as what seemed to him the probably correct answer, became some-
thing of which he could be certain as the course of the questioning
showed him that no other answer was possible. Knowledge then is
the state of mind in which you are certain because you have seen why
the answer must be right. As in the Gorgias (501) and elsewhere
1 This is complicated by the additional doctrine that the resources which we
draw on when we understand something were garnered before birth. See below,
pp. 135-47.
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THEORY OF KNOWLEDGE
experience or luck may enable you to give the right answer, but
unless you can "give account" (logon didonai) you cannot be said to
know. Any belief, however, can be converted into knowledge by
working out the reason for the fact.
This catholicity is perhaps a little puzzling, for if the typical
instance of knowledge, and of insight into necessity, is given by the
understanding of a geometrical theorem, one wonders how it is
possible to know the road to Larisa. There could not be a theorem
proving with geometrical rigour that one must turn right at the pond,
No doubt it is true that the man who knows the countryside can give
account of why one has to follow a certain route, "but we shall still
have to say that in this dialogue the notion of insight into necessity
which is used to characterise knowledge is a very wide notion -em-
bracing the understanding of theorems and the understanding of
terrain. What the spotlight is trained on is not any particular type
of understanding nor any particular class of intelligible entities, but
rather the certainty that a man is entitled to have concerning some-
thing that he understands in any sense.
Understanding not only justifies certainty, it also prevents know-
ledge from "running away". Our discussion of the Protagoras 1 has
suggested that its doctrine is that people yield to temptation because
they do not understand the reason for their moral rules, and thus
find it easy to deceive themselves about their application to particular
cases. In the language of the Meno this is probably a case of a belief
"running away". The Republic (413) offers two other causes for the
loss of a belief in addition to temptation, namely persuasion and
simple forgetting. The point probably is that what a man merely
believes is no more than an impression that he has formed or a lesson
that he has learnt by rote. It has not been built into his mental out-
look nor is its true significance grasped, and for this reason its
applicability to a present situation can easily be ignored. The man
who merely believes that stealing is wrong without understanding
why it is wrong is in a better position than the man who has thought
the matter out to persuade himself that what he proposes to do would
not be a case of stealing.
Finally, although the Meno stresses the importance of understand-
ing to the notion of knowledge, it also, by citing the example of the
road to Larisa, gives some place to acquaintance. Perhaps we ought
to say that understanding is thought of after the model of acquaint-
ance. The man who knows, not by hearsay, but by following the
demonstration, that the square of the hypotenuse equals the sum of
the squares of the other two sides, has seen for himself these features
of squareness which bring this about.
1 See above, pp. 241-3 of Vol. 1.
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THEORY OF KNOWLEDGE
F. Knowledge and belief in the Republic
The contrast between episteme and doxa pervades the Republic.
There are two main passages where It is explicitly discussed and one
important subsidiary passage. The first main passage Is at the end of
the Fifth Book (474-80), and the second runs from the concluding
pages of the Sixth Book almost to the end of the Seventh (504-34).
The subsidiary passage is In the tenth book (601-2). Something has
already been said about these passages in the chapter on the Republic,
but they are difficult enough and controversial enough to call for
further treatment. I shall not attempt to do justice to the controversies
they have provoked or to justify my interpretation by scholarly
standards; but I must try to indicate what seems to me to be the
correct approach.
(i) Knowledge and belief in Republic 5 1
Having declared that philosophers must rule, Socrates tries, towards
the end of the fifth book, to distinguish true philosophers from "lovers
of sights and sounds" a derogatory title used to describe learned
persons as well as those who cultivate novel experiences. The mark
of philosophers is that they love aletheia. This word Includes the
Idea of truth, but also a good deal more. The central notion is some-
thing more like reliability, and therefore one can talk of the aletheia
of things as well as of propositions. The word carries a suggestion
of getting behind appearances to something ultimate and unrevisable
(it was probably in this spirit that Protagoras called his epistemo-
logical treatise Aletheia). We are being told therefore that the
philosopher is the man who wants to get down to bedrock, who will
remain dissatisfied until he sees things precisely as they are. That the
beliefs of the unphilosophical lack aletheia does not mean that they
are false in the natural English sense of the word. That heavy objects
fall is not false though the lover of aletheia would think Newton's
Inverse Square Law a much better statement of the matter.
So much for what aletheia is. Philosophers desire to have it, and
this, Socrates says (475 e) is dependent upon acknowledging the
existence of universals. The philosopher knows that beauty or weight
is a distinct thing with a nature of its own, and is concerned to
understand it in itself; and this he does not do by inductive observa-
tion of its instances. For any given universal is a single common
quality present to all the things which exemplify it; but qualities are
met with in the physical world only as the qualities of particular
things and not in isolation but "combined with each other". For
1 My view of this passage owes much to discussions with Mr. Gosling; see his
article in Phronesis, VoL 5.
53
THEORY OF KNOWLEDGE
this reason it is impossible to come to know what, say, beauty or
heaviness is by collecting facts about "the multifarious beautiful or
heavy things".
Those who try to do this a the lovers of sights and sounds"
are said to be living in a dream. This is a common Platonic metaphor,
and in this place he says what he means by it (476 c 5-7). The essence
of dreaming, Socrates says, is to mistake A for B when A merely
resembles B. Thus (I suppose) when I dream of St. Paul's I have an
experience which is like seeing St. Paul's, and mistake it for an
experience of seeing St. Paul's. Thus to concern oneself only with
"the multifarious beautiful things" and not with beauty is to make
the former identical with the latter when in fact they are only similar
to it.
This is important, but not clear. There are two problems in particu-
lar: what does Plato mean by saying that a universal resembles the
class which is correlated with it, and what precisely is the error of
which the non-philosophical learned are accused ?
Similarity-language is not uncommon in Plato in the context of
the relation between a common quality and its instances. 1 Such
language obviously cannot be taken literally, and this Plato points
out in the Parmenides (132). 2 Although he finds it necessary to make
this point, the absurdity of saying that animality (for example)
literally resembles the multifarious animals is so gross that one
cannot suppose that he is castigating a mistake he has himself made.
To see how such language arises, take an architect's plans for a
house, and take two houses built to those plans. The two houses will
resemble each other, and there will be some kind of affinity (we
should call it conformity) between the houses and the plans. Nor
would it be too far-fetched, especially in certain contexts, to speak
of the conformity in terms of likeness. Thus, to choose a phrase
which is paralleled in the Tlmaeus (e.g. 3 1 b 1), we should understand
what the builder meant if he said he had tried to make the houses
"as like the plans as he could**. Something like conformity then is
presumably the relation intended by the similarity-language which
Plato uses about common qualities and their instances.
This being so, what precisely is the intellectual error described as
identifying the two? Plato is trying, I think, to diagnose a logical
blunder which he takes to be implicit in contemporary thought-
processes. The blunder is too gross to be explicitly committed, and
1 It is especially common in the Timaeus, a dialogue written in a lofty tragical
manner. The references can be found in Ross: Plato's Theory of Ideas, pp. 228-
30.
2 The same point is obliquely made in the Republic itself (597), We shall have
more to say of all this in a later chapter, below pp. 267 sqq., 332 sqq.
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THEORY OF KNOWLEDGE
therefore I say that he is trying to diagnose a hidden confusion. I
shall try to state the blunder clearly and I dare say that, if I succeed
in making it clear, then I shall have taken the analysis a little further
than Plato had taken it, and in this way my account of his meaning
will be historically inexact. The blunder then is that of supposing
that, when it is true that S is P, the property P-hood is identical with
the properties of S which make us say that S is P. Thus many objects
(cp. Phaedo 100 d 1) owe their beauty to bright colouring, and in the
case of these objects bright colouring is the property which makes
us call them beautiful. Heavy objects observably tend downwards,
and it is because they tend downwards that we call them heavy.
Beauty then (according to the blunder) is bright colouring, heaviness
is a tendency downwards. Yet of course in the case of many properties
to follow this method of (we will say) "collecting universals induc-
tively" is to run into contradictions. A is beautiful because of its
bright colours, but bright colouring would spoil B's delicate outlines.
In the case of B then beauty is not bright colouring, but delicate
outline. Although this trouble does not arise in the case of heaviness
(for all heavy objects in our experience tend downwards), there is
another trouble which does; for, as Plato points out in the Timaeus
(62), "downwards" has no meaning in a spherical universe, and
therefore "tending downwards" gives no insight into the nature of
weight. Therefore the practice of collecting universals inductively
leads to either or both of two unfortunate consequences. The first
is that we refuse to believe in the existence of single self-consistent
properties. There is no such thing as beauty which is present in all
its instances; there are as many different beauties as there are sets
of properties which make us call things beautiful. The result of this
is that we do not try to discover what is common to them all. The
second unfortunate consequence is connected with this, namely that
we rest content with practically adequate but intellectually opaque
definitions such as "heaviness is tendency downwards". It is clear
that such definitions might have stultifying effects on thought
(relativity theory would not have developed if Einstein had not seen
that it will not do to say that two events are simultaneous if they
happen at the same time). And it is not too far-fetched to say that
these effects would come about from identifying, e.g. the multifarious
beautifuls with beauty, from thinking that the various general
statements that can be made about the "beauties" of the multi-
farious beautifuls are the most that can be said about beauty. The
cure of the error is to realise that whatever can be called beautiful
can also in certain circumstances be called ugly. For if a thing which
looks bright and therefore beautiful in one room looks harsh and out
of place in another, then its colouring is responsible both for its
EpD C 55
THEORY OF KNOWLEDGE
beauty and for its ugliness; and obviously therefore It cannot be
identical with either.
The point then is that nobody can be called a philosopher if he is
content with inductively collected accounts of properties. Since such
accounts are collected by noticing apparent (sc. obvious) features of
classes of objects, this means "if he is content with doxai or judg-
ments based on what is apparent".
Philosophers are awake, whereas ordinary men are asleep and
dreaming. This means that the thought of philosophers deals with
realities whereas that of ordinary men deals with some kind of
images. Socrates allots the names "knowledge" and "belief" to
these two states of mind respectively, and then proceeds to offer a
proof that the unphilosophical cannot be allowed to claim knowledge.
This is one of many places in Plato where he could probably have
been more convincing if he had tried to elucidate his point rather
than to offer a formal demonstration of it.
Socrates' methods are conversational and in setting his argument
out I shall slightly alter the order of exposition. Since much turns on
how we translate these key expressions, I shall use without trans-
lating: on (plural onto), literally "that which is" and me on (plural
m$ onto), literally "that which is not". The argument then is as
follows :
(1) A man who knows knows an on. (2) That which is fully on is
fully knowable; that which is totally me on is totally unknowable.
(3) Anything which was both on and me on would lie between the
two, and the state of mind corresponding to it would lie between
knowledge and ignorance. (4) Belief and knowledge are different
functions (dunameis), for the latter cannot be wrong, and the former
can. (5) Two functions are different if (a) they do different things, and
(b) they do them to different objects. (6) Therefore the objects of
belief are different from the objects of knowledge. (7) The objects of
knowledge are onta\ but the objects of belief cannot be me onta, for
a man who believes must believe something, and a me on cannot
properly be called something. (8) Since belief is a state of greater
darkness than knowledge and of greater light than ignorance, it
ought to be located between them, and its objects between on and
m on (see step 3). (9) Take the multifarious so-and-so's which the
unphilosophical believe to be the only realities, and which are not
changeless like universals. Now for any predicate P and its opposite
-P ("beautiful" and "ugly", "heavy" and "light"), it is always the
case that things which one has reason to call P can also be found to
be -P. None of the multifarious P's is definitely P and in no way
-P. Should they not then be said to be between on and in on,
"darker than on but better lit than me 0/2"? (10) "Therefore the
56
THEORY OF KNOWLEDGE
multifarious conventional opinions of ordinary men about beauty
and other such things roll about between on and me on" : and these
must be the objects of belief.
This argument is not easy to interpret. We may begin by clarifying
its purpose. This is to show that ordinary men cannot ever claim to
possess knowledge, and that the reason for this is that their opinions,
however correct, are always "inductive" (in the sense used in recent
paragraphs), and therefore have the status of doxai or beliefs. It
tries to show this by assuming (step 4) that since knowledge is in-
fallible and belief is not, knowledge and belief must be different
"functions" (dunameis) and therefore must have different "objects".
The purpose of this is to establish a logical chasm between knowledge
and belief, in terms of a difference between their "objects". The rest
of the argument is devoted to rendering this plausible by finding
suitable "objects" for belief, and by showing that the opinions of
ordinary men are concerned with these "objects".
What does Plato mean by "functions" and "objects"? We can
begin by noticing what seems to be a fatal flaw in the argument.
Two functions are the same if they do the same thing to the same
objects, and two functions are different if they do different things to
different objects (447 d). 1 But what, one asks, are we to say about
functions A and B such that they do different things to the same
objects (as, e.g., sight sees apples and pears, and smell smells them)?
Plato is trying to prove that knowledge and belief have different
objects on the ground that they do different things (knowledge doing
something infallible and belief something fallible). But if the two
functions can have the same objects and yet be different functions (as
sight and smell are surely different functions) then the argument will
not work. Knowledge and belief might have the same object (say the
world) although the one recorded it infallibly and the other fallibly.
If this is a mistake, it is a very gross one, and one looks for a
different interpretation. Fortunately there is one to hand. If we
assume that the "object" of a function is an "internal accusative",
the case of A and B which do a different act to the same object does
not arise. 2 Thus the internal accusative of "see" is "sights", of
"smell" is "smells"; and it is true that sight and only sight sees
sights and nothing but sights, that smell and only smell smells smells
and nothing but smells. With this conception of "what the function
does" and "what it does it to", Socrates' definition of sameness and
difference of function becomes correct. The possibilities are now only
two in number and the definition exhausts these.
1 The phrase for "object" is "that which the function is epi". Epi is a pre-
position which bears the general sense of "onto" or "on".
3 Nor does the case of C and D which do the same act to different objects.
57
THEORY OF KNOWLEDGE
It seems therefore worth considering whether that to which a
faculty is epf, the "object" of a faculty, may not, in this passage at
least, be its internal accusative. If we adopt this suggestion, then the
"objects" of belief and knowledge becomes beliefs and bits of know-
ledge, and in that case it will be beliefs themselves and not their
subject matter, which are said to be between on and me on. Or
rather, to use a phrase which we used above in our preliminary dis-
cussion, it will be the mental correlates of the state of belief; that
which is between on and me on will not be that which the belief is
about, but that which the believer's mind has grasped. This, as we
saw above, will not be precisely a proposition, or rather we shall
not expect Plato to speak of it in the language appropriate to pro-
positions. We shall expect him to speak of it as if it were that of
which a /to-clause is the name; and in the case of true belief, as we
saw, this is just the sort of entity which we should expect to inhabit
a half-world. The /to-clauses of knowledge name realities, those of
delusion figments ; and those of respectable opinion ought to name
something in between. It seems then worth considering seriously
whether the objects of these faculties may not be their "mental
correlates" in this sense. Textually indeed it is not at all far-fetched
to suggest that that which is between on and me on is something of
the approximate character of a belief or proposition, for this is
entirely in accordance with what Socrates says in step 10 in drawing
his conclusion. It is the multifarious conventional opinions of
ordinary men which he argues must roll about between on and tn
on, and these are what we should call beliefs. How it can be that
beliefs can perform the extraordinary feat of "rolling about between"
(this perhaps means "occupying some point anywhere on the scale
between") "the existent and the non-existent" has I hope been made
clear above. I certainly cannot imagine how the subject-matter of
beliefs (the things that we have beliefs about) could do anything of
the kind. That beauty is a matter of bright colouring is perhaps one
of the multifarious conventional opinions of ordinary men about
beauty, and the "quasi-fact" which this clause stands for (namely
beauty's being a matter of bright colouring) is not a fact or a reality,
but on the other hand it is not a complete figment either. It is between
being a fact or reality and being a figment, just as the corresponding
state of doxa is between grasping perfectly and being completely out
of touch.
Using this as a clue we can reconstitute the argument as follows :
(a) The mental correlate of knowledge is something which really
exists (=step 1 of the original argument), (b) Anything which really
exists can be a mental correlate of knowledge; any mental corre-
late which is totally a non-entity must be a correlate of ignorance
58
THEORY OF KNOWLEDGE
and not of knowledge (=step 2). (c) Any mental correlate which
is and yet Is not a reality will lie between these two extremes, and
the corresponding state of mind will lie between belief and Ignor-
ance (=step 3). (d) Belief and knowledge are different functions, the
latter being infallible and the former not (=step 4). (e) Therefore
(from the definition of difference of function) the mental correlates
of belief and knowledge are different (steps 5 and 6). (/) The mental
correlates of knowledge are realities. The mental correlates of belief
cannot be non-entities, because a believer must believe something,
and a non-entity is not something (=step 7. The present step is
clearly fallacious and this will be discussed below), (g) Since belief
is a condition of illumination intermediate between knowledge and
ignorance, its mental correlates ought to have a status intermediate
between that of realities and that of non-entities (=step 8). (h) We
need therefore to discover mental correlates having this status.
Bearing in mind that anything which is e.g. beautiful is also in
suitable circumstances ugly, and bearing in mind that conventional
opinions about beauty and so on are inductively based, we shall see
that these conventional opinions do indeed have that status (steps
9 and 10, the clause in italics being introduced to bridge the gap
between them).
Two questions arise. (1) What about step / of the reconstituted
argument? (2) What about the gap between steps 9 and 10 of the
original argument? Or in other words: How does step h of the re-
constituted argument work?
Step f of the reconstituted argument (478 b 3~c 1)
That which can be believed cannot be that which is, for that which is
is that which can be known. But one cannot, either, believe what is-
not. The believer must bring his belief to bear on something one
cannot believe, and yet believe nothing. But if the believer must
believe some one thing, and if what is-not is not some one thing,
then the believer cannot believe what is-not. This is the argument,
and it seems to be clearly fallacious, for it seems to argue from the
premise that every belief must have some content to the conclusion
that the content of a belief cannot be a non-entity, or in other words
a falsehood.
About this step there are two points which strike one. The first
is that it is fallacious, the second that it proves too much. For this
is a standard argument, deriving, it is said, from Protagoras, to
show that there can be no such thing as meaningful false belief, that
every meaningful belief must be true. But it is clearly no part of
Plato's purpose at this point (or indeed anywhere else) to assert this.
What he wants to show is that the beliefs of plain men cannot be
59
THEORY OF KNOWLEDGE
called fully true; to do this he has no need to deny that some beliefs
are totally false. Rather the reverse Indeed, for one has the impres-
sion that he wishes to make palatable the view that the beliefs of
ordinary men cannot count as knowledge by conceding at the same
time that they need not count as ignorance either. But in that case
surely there must be some beliefs the holding of which does count as
the opposite pole from knowledge, and these beliefs will have to be
false. It is therefore positively inapposite to have at this point an
argument showing that there can be no false beliefs.
Therefore we are not intended to find such an argument here. But
that is to say that, within the terms of this passage, what we should
call in English a false belief does not count as a doxa, nor the
entertaining of it as doxazein. Doxa in this passage is what is else-
where called ortM doxa or right belief.
One can begin to see how this happens if one translates doxa by
some such word as "interpretation" or "representation". To doxa-
zein, we might suggest, is "to represent something to oneself as".
Using language of this kind we can see that in the case of every doxa
there are two terms, the thing represented (beauty or whatever it may
be) and my representation of it. But there conies a point when a
representation of X can no longer be called a representation of X
at all, but of something else, Y. Therefore when I totally misrepresent
beauty to myself, what I have in my mind is not a doxa of beauty at
all. Therefore whenever a man has a doxa in his mind, what he has
is not a total misrepresentation a total misrepresentation is not a
representation, and therefore not a doxa.
This explanation of the use of doxa in this passage may seem un-
convincing. If it is, some other explanation will be needed, for
whatever the explanation it seems clear that in this passage doxa
bears the sense of "tolerable belief". If false beliefs belonged to the
sphere of doxa they would not belong to the sphere of agnoia, i.e.
they would not belong to the sphere of that whose correlate is me on.
But it is clear from many passages that it was the standard practice
to correlate falsity with me on (arguing for example that he who says
what is false says a me on), and this standard practice Plato does
not depart from, though he tries to rescue it from the paradoxes
which it sometimes bred. 1 To me it is incredible that he should have
correlated false belief not with me on, but with that which is between
on and me on. It seems to follow that false beliefs are excluded from
the sphere of doxa as Plato is using the word in this passage. It
would not indeed be to his purpose to include them, since what he
1 See the discussion of the Paradox of False Belief in Chapter 4, pp. 486-98.
Greek-speaking readers will notice that I treat mS and ouk as interchangeable for
our purposes.
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THEORY OF KNOWLEDGE
is trying to tell us is that the best that can be achieved by non-
philosophers must fall within the sphere of doxa. He is not trying
to tell us that blunders fall short of the status of onta> but that this
happens even to the highest achievements of the inductive approach.
Therefore his subject is respectable beliefs, beliefs which "have
something in them". If it is thought that this is not in itself enough
to explain how he could allow himself to use an argument whose
effect is to show that no doxai are false, some other explanation will
be needed, and this is what I have tried to supply.
This explains, then, why the argument does not prove too much,
It does not prove that there can be no false beliefs; rather it refuses
to call false beliefs doxai. A belief about, say, justice which deserves
the label "false" cannot count as a representation of justice to one-
self and is therefore excluded from the sphere of doxa. It need not
perturb us that the sphere of doxa is elsewhere extended to include
false beliefs. To take a somewhat analogous case, if I mistake that
rabbit for a stone, do I or do I not see the rabbit? One might some-
times give the one answer, sometimes the other.
So far so good, but the step is still fallacious. Plato could perhaps
have drawn validly the conclusion that he wanted to draw. If he had
made explicitly the point that we have just imputed to him, namely
that if I totally misrepresent something to myself my state cannot be
called doxa (but must be called agnoid), he could have argued that,
if a state is one of doxa, its content cannot be a me on or figment.
But he does not do this. The premise that "the believer (doxazori)
must bring his belief to bear on something; one cannot believe, but
believe nothing" (478 b 6-8) cannot be taken to mean that every
doxa must be a version of some reality; the reader could not be
expected to get this meaning out of this terse sentence. What we
have here as premise must be the logical truth that every belief must
have some content. But of course to say that every belief must have
a content is not to say that no belief can have a figment or non-
entity as its content. Socrates' statement (478 b 12) that a me on
is properly called nothing is false in the sense in which it has to be
taken. When I wrongly believe that Jones has a moustache, what I
believe is a non-entity (the non-fact that Jones has a moustache) and
yet it is also something (the proposition that Jones has a moustache) ;
so a non-entity can be the content of a belief.
Clearly, in that way of setting it out, there is an ambiguity in "what
I believe" ; it may be used to refer to what we called the alleged state
of the topic or it may be used to refer to the proposition which makes
the allegation. The former of these is a figment, a non-fact, a non-
entity. The latter is false, but it is not a figment or a non-entity
it is a certain proposition, namely that Jones has a moustache.
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THEORY OF KNOWLEDGE
Evidently what has happened is that, in the absense of a clear distinc-
tion between the proposition and the state of affairs which it alleges,
Plato has allowed himself to confuse together the predicates which
belong with logical propriety to each of these, and so he has allowed
himself to argue that if I believe something what I believe must be
something and therefore cannot be nothing and therefore cannot be
a non-entity.
He is not of course alone in this confusion. It was the standard
drill of the Paradox of False Belief. But as we have seen it is not to
his purpose to propound the Paradox here and we should not say
that lie is doing so. Rather we should say that he wants a reason for
refusing to correlate doxa with what is-not This he wants because
the state of mind which he is calling doxa, or which he is primarily
thinking of under that name, is not a state of total misrepresentation.
It is mental furniture such as sound but un-philosophical concep-
tions of justice that he is trying to locate between on and me on.
Wanting a reason why doxa should not be correlated with me on
he finds one ready to hand in the Protagorean armoury of arguments
purporting to show that whatever is believed is true. Because in this
passage he is making doxa bear a sense narrower than "belief " he
is not disconcerted by the thought that the argument shows that
there are no false beliefs because it seems to him only to show that
there are no false doxaL Nor, on this occasion, does he notice that
the argument is fallacious, for it seems to him to have a healthy
result, and he is without the clear distinction between proposition
and alleged state, given which the argument must have jarred on his
logical conscience. When used by Protagoreans to show that every
opinion must be true the argument worried him, but it was to be
some years yet before he began to see what was wrong with it, and
he did not do so before he distinguished the logos or proposition
from the subject that it "names", "belongs to" or refers to and from
the rma or allegation that it makes.
This explains, I hope, the fallacy which we found in step/, both
how it occurred and how it escaped detection. It is an instructive
slip because it does a good deal to show us what conceptual weapons
Plato is using.
We may conclude this section by drawing a comparison between
this passage and Symposium 202 a. Socrates is there arguing that
that which is not noble is not necessarily base; there is something in
between. Similarly, he says, there is something in between wisdom
(sophia) and folly or ignorance (amathia). This is orth$ doxa, right
belief. "To believe what is correct", he says, "without being able
to give account is, as you must know, not episteme (for how could
something irrational be episteme '?), and it is not amathia (for how
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THEORY OF KNOWLEDGE
could that which does not fail to hit to on be amathial). Orthe doxa
therefore is something which is of this nature, and is between
phronesis and amathia." If we may assume that in this passage Plato
has used as a parallel to his point about nobility and baseness
something which he thought to be a fairly obvious point about
wisdom and folly, then we can perhaps argue that the passage in
the Symposium throws light on what Plato took for granted when he
wrote the passage in the Republic. To do this however is to support
the view that doxa in the Republic stands for correct opinions ; for
it is orthe doxa in the Symposium which comes between wisdom and
folly. It can also, I think, be argued that to bring the two passages
together is to strengthen the interpretation of agnoia for which I am
about to argue namely that agnoia in the Republic is primarily
delusion. For the corresponding term in the Symposium is arnathia>
a word which perhaps tends to connote intellectual coarseness (cp.
Sophist 229 c, where it is used for the kind of agnoia which consists
in the possession of deluded doxai); and the phrase "for how could
that which does not fail to hit to on (to . . . tou ontos tunchanori) be
amathiaT might perhaps be said to imply that amathia is something
which aims at to on but fails to hit the target. But this is some-
thing which could be said more happily of delusion than of un-
awareness.
What is agnoia?
Agnoia is correlated with (epi) that which does not exist (to me on).
We have argued that that which a mental function is epi, in this
passage, is its mental correlate. Some say however that that which a
mental function is epi is that segment of the universe which it is
competent to deal with. They take to on to stand for the forms, and
they say that the doctrine that epist$me is in the ^/-relationship to
to on means that episteme is competent to deal with, and confined
to, the forms. That which is between to on and to me on they take to
be the physical world, which occupies this position on the ground
that it is only half-real; and it is doxa, on this view, which is the
mental function which is competent to deal, albeit fallibly, with the
physical world. We have seen above 1 that there are passages in
Plato, particularly in the Timaeus, which support the Allocation of
the functions of episteme and doxa in this way. But it is highly im-
probable that the first readers of this section of the Republic could
have read the Timaeus, and I do not believe that the innocent eye
could extract this meaning from this passage. I do not believe that
the spheres-of-competence view correctly interprets the primary
meaning of this passage, though I think I do see how Plato could
1 See pp. 35-41,
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THEORY OF KNOWLEDGE
have got to his formula about spheres of competence through putting
together what he says in this passage with what he says elsewhere
(roughly by putting together the formal and the material answers
to the question: "What can we know?"). More of this elsewhere; 1
meanwhile an argument against finding spheres of competence in
this passage can be got by reflecting upon the position of agnoia.
For on this view the sphere of competence of agnoia will have to be
that which is unreal. But we surely cannot say that there is a mental
function or state whose sphere of competence is the unreal. We can
say that there is a state whose content is the unreal, but to say that is
to take the view which I am advocating. If we want to find a sphere
of competence for agnoia, then, we shall have to say that it is the
non-existent, or in other words that agnoia has no sphere of compe-
tence, that whatever exists belongs either to the sphere of episteme
or of doxa. This last is harmless ; but if we treat agnoia and to me on
in this way it has the result that Plato's triadic structure is fraudulent.
He appears to be asking us to consider three different mental
functions or states, each of them being correlated with its own
correlate, but in fact, on this view, he is only really asking us to
consider two. There is no such thing as a state of mind whose pro-
vince is the non-existent any more than there is one whose province
is the unreal. The things that we are ignorant of are ordinary
existent things coming presumably from the province either of
episteme or of doxa. To say then that doxa is between episteme and
agnoia and its objects between to on and to me on is simply to say
that it is not quite ignorance and its objects not quite non-existent.
This would no doubt be a possible thing to say, 2 but it has about it
the awkward feature that the ^/-relation in the case of agnoia does
not relate a state to a special class of entities as it does in the other
two cases; saying that agnoia is in the e/?/-relation to to me on, if it
is not to tell us that there exists a class of fit objects of ignorance,
must simply be telling us that nothing is a fit object of ignorance, or
in other words that everything is a fit object either of episteme or of
doxa. The view that the ^/-relationship holds between a state and
its mental correlate preserves the triadic structure epist$m cor-
responds to facts, agnoia to figments, and doxa to things which are
neither quite facts nor quite figments. The view now under attack
fails to preserve this structure.
This argument is plainly not coercive; Plato might have failed to
see that his triadic structure was spurious, or seen and not bothered*
But I think it has some weight. So far as it goes however it is an
1 See pp. 49-50, 128-35.
2 Supporters of the view now being attacked can quote Timaeus 52 c 4 "clinging
somehow to existence" in support of this notion of being not quite non-existent.
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THEORY OF KNOWLEDGE
argument against taking agnoia to mean Ignorance in the sense of
unawareness. Does this matter?
Verbally there is no doubt that agnoia can mean simply Sfc not
knowing", but there is equally no doubt that it can also be used to
stand for the kind of ignorance which consists in false belief (e.g.
Sophist 229 c). There is equally no doubt that to me on, which is
here correlated with agnoia^ is a standard correlate of false belief.
There is therefore nothing forced in taking agnoia to stand for false
belief. Indeed the use to which (as we have argued) Plato is putting
the word doxa in this section might well make him hesitate to employ
the phrase pseudes doxa for false belief, and that would drive him
back on some such word as agnoia to express his meaning. Again
he might be led to avoid the phrase pseudes doxa by the thought that
the use of it would embroil him with the Protagoreans. It seems then
perfectly possible that false belief should be comprehended under
the meaning of agnoia; on the other hand it would be odd if unaware-
ness were excluded from its meaning, as the correlation with to me on
might seem to suggest that it is.
The answer to this has been sufficiently given, I hope, in our
preliminary discussion. The basic idea of the passage is that of the
subject's degree of contact with reality in each of the three states.
From this point of view delusion and unawareness come to the same
thing, for in each of these states the subject Is totally out of touch
with the reality in question. Therefore Plato does not trouble to
distinguish them. It may still be asked however why Plato gives as
the correlate of this two-fold condition of being out of touch a
correlate which belongs to one of its forms rather than the other.
We might reply to this that the correlate Plato gives is the one that
he wants for his triadic structure ; he wants to tell us that doxai are
superior to figments rather than that they are superior to unaware-
nesses. But why does he want to do this ? Possibly the answer can be
found if we remind ourselves of the topics the grasp of which he is
concerned with in this passage. For he is thinking after all about our
grasp of entities such as justice and beauty, and these are entities
about which many of us are grossly deluded, but few of us totally
unaware. He is talking of matters, being totally out of touch with
which consists normally not in never having heard of them, but in
having gross ideas about them. He is telling the unphilosophical
cultured, as it seems to me, that though they cannot claim to know
what justice is they need not suppose that they are, like the tyrant or
demagogue, totally ignorant of it; and the ignorance of these latter
consists in wrong ideas, not in no ideas at all. This might explain
why, in the context, he assigned to the condition of being quite
out of touch the correlate which belongs to delusion rather than to
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THEORY OF KNOWLEDGE
unawareness. He might also, of course, have done this the more
easily under the influence of the fact that the nothing which I have
in my mind with respect to S when I am unaware of S is after all
not something which exists, and can therefore be comprehended
under to me on with propriety if not with felicity. 1
For these reasons it seems to me quite feasible that Plato should
have used a word from whose meaning * 'unawareness" cannot be
excluded to stand primarily for "delusion". On the other hand it is
no part of my purpose to argue that Plato intended with perfect
clarity to say just one thing in this passage. My purpose is to diag-
nose his "dominant" intention, by which I mean the nexus of ideas
which led him to write the passage. I do not have to say, and do not
want to say that he would consistently have distinguished the inter-
pretation that he primarily intended from other possible interpreta-
tions of his words. Anybody who has ever written any philosophy
knows how easy it is to fail to do this. In particular I would suggest
that he might well have been deceived by the ambiguity of the re-
sounding phrase with which he introduces the discussion (477 a 3-4) :
"That which is altogether existent is altogether knowable, that which
is in no way existent is altogether unknowable." We have taken
this to mean : "That which is without qualification a fact is without
qualification a proper object of knowledge, whereas that which is
without qualification a figment is in no way a proper object of
knowledge." But on the other hand this formula could be (indeed
usually is) taken to mean that things which exist can be known,
things which do not exist cannot be known. We have argued that this
second interpretation cannot be the only correct one, because, if it
were, we should have to find a place for the objects ofdoxa "between
existence and non-existence" and that means nothing. But it may
well be that Plato did not nicely analyse what he meant by to me on
nor therefore what he meant by making agnoia correspond to it. The
"unknowableness of the unreal" may have comprehended both the
fact that it is only non-entities that we are utterly incapable of
1 Agnoia of justice might well include at least two things. One is the holding of
mistaken theories such as those of Thrasymachus and Callicles. The other is the
complete inability to distinguish the just from the unjust which is characteristic of
us all in so far as we are prisoners in the cave of Republic 7, Aristotle for example
seems to imply (Eth. NIC. 1110 a 26) that Alcmaeon in Euripides' play offered
totally spurious justifications of his murder of his mother. Those of his audience
who were taken in (as Plato supposes theatre audiences to be commonly taken in)
by such spurious justifications would be totally gullible in the matter of instances
of justice, and this might be thought to mean that they were totally out of touch
with justice. To stress this interpretation of agnoia is to bring it into close contact
with apaideusia or boorishness in Republic 7, and thus into close contact also
with eikasia in one sense of that word.
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THEORY OF KNOWLEDGE
grasping, and also the fact that falsehoods cannot be known (for
entertaining them is not knowledge, in however lax a sense of the
word, but delusion). This would have made it easy for agnoia to
cover both the mental vacancy which properly corresponds to things
which do not exist and also the delusion which we suffer when we
accept falsehoods.
The gap between steps 9 and 10; step h of the reconstituted argument
The next question we had to ask concerned the connection between
steps 9 and 10 of the original argument, or in other words the
cohesion of step h of the reconstituted argument. We want in fact
to know how, having defined the class of approximations, Plato
succeeds in showing that the opinions of ordinary men fit the defini-
tion. Every one of the multifarious beautifuls (etc.) can also seem
ugly (etc.); therefore the multifarious beautifuls are between being
and not being; therefore the multifarious conventional opinions of
ordinary men about beauty and so on roll about between on and
me on. This is the argument, and at first glance it seems a non-
sequitur. That it has some coherence none the less, I hope I have
already implicitly shown. Put to a plain man the question "What
is beauty?" (especially in Greek, where you will probably word it
"What is the beautiful?") and he might reply (for example): "Well,
Regency furniture is beautiful." 1 "Why," you ask, "is it beautiful?"
"Well, it is so delicate." "Is delicacy then beauty?" "Yes it is."
Or, to take another of Plato's examples, ask the plain man: "What
is it for one quantity to be twice another?" (in Greek "what is the
double?"). "Well," he might reply, "8 is twice 4, 10 is twice 5, and
so on." Now in each of these cases the thing which the plain man was
asked to define is not without influence on his mind; his grasp of
it is enough to make him give answers which are at least not in-
apposite. But he has of course no abstract understanding of it. His
conception of beauty is an amalgam of the various properties which
are in suitable circumstances relevant to the beauty of classes of
objects; his conception of duplicity consists of various successful
performances in the twice-times table. That his conception does not
amount in either case to "knowing the beautiful" or "knowing the
double" can be shown by prolonging the conversation. There are
contexts in which a Regency piece, being a delicate object, would be
out of place; therefore delicate objects are not always beautiful, and
delicacy is not beauty. Again 8 is just as much half 16 as it is twice
4; doubles are also always halves. Therefore a conception of dupli-
city which amounts to the ability to produce a string of doubles
cannot be said to be a case of "knowing the double itself according
1 See the Hippias Major for answers of this type to this question.
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THEORY OF KNOWLEDGE
to itself ". In general, because a thing which is P can always be shown
to be in some way not-P, therefore the man who says that P-hood Is
identical with the various properties which make us attribute P-hood
to things cannot be said to know it, although, if his attributions are
in general correct, he is not ignorant of it either. His state of mind
in relation to P-hood is between knowledge and ignorance; his
judgments occupy the ground which lies between on and me on.
This seems well enough, but this is a simpler argument than
Plato's. From the premise that every one of the multifarious beauti-
fuls can seem ugly we have inferred the conclusion that the opinions
of plain men about beauty fall between knowledge and ignorance of
it; and the link we used to join the premise to the conclusion was
the manner in which plain men form their ideas of general terms,
namely by identifying the multifarious beautifuls with beauty in the
manner discussed above. But this is not the link that Plato uses.
From the premise that every one of the multifarious beautifuls can
seem ugly, he infers that each of the multifarious beautifuls is be-
tween being and not being (479 c 6), and it is apparently from this
that he infers the conclusion.
That he says that each of the multifarious beautifuls is between
being and not being is the bastion of those who hold that Plato
believed that the physical world does not really exist. But it is a
cardboard bastion. He certainly denied to physical things the status
of onta, but this as we have seen does not mean that he denied their
real existence. Nor is this denial really apposite in the present con-
text. No doubt, writing an ambiguous language, Plato might often
in some degree have in mind all the various possible interpretations
of his words; but it is that interpretation of any given sentence which
makes it relevant to its context which is presumably responsible for
the writing of the sentence and which should therefore be called its
meaning. What is relevant here is not that a given beautiful object is
(like any other physical object) no more than a stable pattern mani-
fested in the flux of nature, but that it is and is not beautiful. For
that reason we surely ought to say that it is the predicative and not
the existential sense of "to be" which is uppermost when Plato says
that physical things are between being and not being. They do not
lack existence tout court, they lack existence-as-beautiful-things/
heavy-things or whatever it may be. In other words they are and are
not beautiful, heavy and so forth. This of course may have awkward
implications. It may seem to imply the (surely empty) notion that
there is something which can be said to be beautiful without quali-
fication; and this something must be beauty itself. 1 How Plato came
1 Whether this implication is really present will be discussed below, pp.
263-5, 309, 334-5.
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THEORY OF KNOWLEDGE
to write as if it made sense to call beauty beautiful is something we
must consider in a later chapter. If this blunder cannot be made
intelligible, that will no doubt cast doubt on the current interpreta-
tion. Since however I think it can be made intelligible, this does not
trouble me. We conclude therefore that the argument is : (a) that any
given beautiful thing is also not beautiful; (b) that therefore any given
thing is and is not whatever it is ; and (c) that therefore conventional
opinions about beauty and so on are between on and me on\ and the
link between (b) and (c) must be that which we supplied above.
Let us try to see the significance of this passage whose interpreta-
tion has cost us such a long discussion. Firstly Plato is not concerned
here with the question whether we can know facts about the physical
world. His purpose is to show that there are certain common states
of mind which cannot be classed as knowledge. People who do not
ask themselves the counter-inductive, abstract question "What is
beauty?", but collect their ideas of beauty from observing the
significant features of beautiful things cannot be said to know what
beauty is. This is so not only in the case of beauty, but in the case of
an indefinitely wide range of other properties. Plato does not say
whether he supposes his argument to apply to all properties. His
examples are all of properties such as beauty, justice, largeness and
so on in the case of which it is plausible to say that a thing which
has one of these properties also has its opposite; but he says nothing
which suggests that he saw that the argument might be less plausible
in the case of other properties. Can something which has the property
of being a table also in suitable contexts have the property of not
being a table? There is perhaps a passage in the Seventh Book which
suggests that Plato thought that his argument did not include
"substantival" properties such as that of being a finger (523 d).
This is perhaps not very important, for even if it is possible, as the
passage just referred to suggests, to collect an adequate idea of a
finger inductively, the fact that one cannot do this in the case of such
things as beauty, justice, size, weight and so on means that those who
collect their universals inductively are deprived of full insight into
the principles on which the world is ordered and on which they must
themselves order anything of which they are in charge. And the
immediate consequence of this is that they are not fit rulers for
society.
The material version of the question "What can we know?" is
not therefore answered in this passage. Formally speaking we are
told (it is taken for granted) that knowledge is the direct grasp of
something real, and on the basis of this we learn that in the case of
beauty and similar entities it is not possible to have knowledge of
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THEORY OF KNOWLEDGE
them unless you first admit the existence of these universal properties
as single self-consistent entities. We are not told whether it is possible
to have knowledge of the road to Larisa, nor what form such know-
ledge would take, nor whether it is available to locals or to philoso-
phers, nor anything of this kind. We are told something about the
knowledge of universal properties and how this differs from the
indirect apprehension of them in the doxai of the ordinary man;
and the point of telling us this is that we may see why ordinary men
are not fit to rule eschewing abstract philosophical thought they
have no insight into principles.
One final comment. "None of the multifarious justs but is also
unjust." Does this mean that there has never been a perfectly just
action? I think not. The type/token distinction is not drawn. When
Jones pays a debt his action may have been perfectly just. But to
make justice consist of debt-paying and other similar activities is
not to have achieved insight into justice (and such a doxa will be
impotent will "run away" in a novel situation to which no
traditional rules apply). This is so not because Jones should have
acted rather differently, but because "what Jones did" (namely a
debt-paying) is not always just. Token debt-payings may sometimes
be incontrovertibly just. Debt-paying as a type is not always so. 1
This point can be put in a simpler way. I suggest that the phrase ta
polla kala should be translated not only "the multifarious beautifuls"
but also "the multifarious beauties", because I suspect that it con-
noted both of these to Plato. When Socrates asks Theaetetus to
define knowledge, 2 Theaetetus responds by citing many knowledges
of pottery, woodworking and so on; and Socrates comments:
"How generous you are; I asked for one thing and you give me
many/ 5 So the man who, when asked "What is the just?", cites
truth-telling, debt-paying and so on, has given "many justs". If we
translate "the just" in the question into normal English as "justice"
we can similarly express our comment on the answer by saying that
it cites many justices. And each of these many justices will also be
unjust in the sense that it will contain unjust members for example
a token debt-paying which it would not, in the reigning circum-
stances, be just to make. In this way each of the many justices is also
unjust.
(ii) Knowledge and belief in Republic 6 and 1
The main purpose, then, of the discussion in the Fifth Book has been
to contrast the inadequate conception of X-hood which can be
1 A further discussion of this section, including a justification of the point
made in this paragraph, will be found in a later chapter. See below, pp 293-5
3 Theaetetus 146 d 3,
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THEORY OF KNOWLEDGE
derived by identifying X-hood and "the many XV* with the adequate
conception which can only be achieved by what is shortly to be
called dialectic by relentlessly "asking what X-hood is". The con-
trast has been drawn by assigning to an inductively derived concep-
tion of the former kind an ambiguous status (between on and me on) ;
and great stress has been laid on the negative point that an adequate
conception of X-hood cannot be had so long as one identifies X-hood
and the many X's.
When Plato returns to these matters in the passage which begins
towards the end of the Sixth Book and continues through most of
the Seventh, it is not surprising to find that he illustrates his meaning
by making great play with entities of ambiguous status (namely
shadows, reflections, echoes and puppets). At the same time it is not
surprising that the negative emphasis of the Fifth Book is less
prominent. We have been told that no man can govern well unless he
achieves an adequate grasp of beauty, justice and other such entities.
We have also been warned that such a grasp cannot be achieved by
attending to "the many so-and-so's". We want to ask how we can
hope to achieve such a grasp, if we cannot do it inductively, and why
the achieving of it will assist us in practical tasks. In my judgment it
is part of Plato's purpose in the Sixth and Seventh Books to try to
answer these questions, to tell us how we can pass from familiarity
with the natural world to an understanding of the abstract principles
of order, and to explain how it is that such principles are applicable
to the understanding and control of our environment and ourselves.
Obviously some metaphysical doctrine about the relationship
between the forms and the natural world will be involved in any
such explanation.
The passage which we are about to examine is extremely contro-
versial. The controversy may perhaps be said to hinge upon two
questions. First of these is the question how we are to interpret the
entities of ambiguous status, the images as we may collectively call
them, which play such a large part in Plato's exposition. How pre-
cisely is he employing the notion of an image? To put the same
question in a different way, is Plato engaged in stating the meta-
physical doctrine which must, as we said, underlie his attempt to
answer how we can come to know the forms, and turn our knowledge
to practical use, or is he rather expounding an epistemological thesis
and leaving the metaphysics alone? Or is he perhaps doing a little of
both and to some extent confounding the two? When he puts
before us the picture of various layers of objects so arranged that
each layer contains images of the entities which figure in the layer
above, does he want us to believe that there exist in the world various
grades of objects of such a nature that the humbler objects are in
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THEORY OF KNOWLEDGE
some ontological sense images or copies of the superior, or is he
rather telling us that there are various states of mind which are
related to each other in such a way that the content of one of these
states is in some epistemological sense an image of that of the state
above it?
The second question on which the controversy hinges is the
question how positive Plato is really being, to what extent he is
genuinely trying to tell us how true knowledge is after all attainable.
This too could be expressed as a question about how we are to inter-
pret the notion of an image. We can be deceived by images if we
mistake them for originals, but we can use them to tell us something
about the originals if we do not let them take us in. When certain
things (whether entities in the world or conceptions in the mind) are
said to be images, is the primary meaning that they are deceptive or
that they are suggestive? Or (which is perhaps the right answer) does
Plato mean to tell us that they are deceptive in that they take in most
people, but that they can be suggestive to those who treat them
properly? One might I think say that Plato's failure to make clear in
what way he intends the notion of an image to be taken is the main
cause of the difficulty of this passage.
I have already 1 given a sketch of the interpretation which I want
to put upon this passage. Here I shall only recount its barest out-
lines, and then proceed to discuss in more detail various particular
problems.
The passage begins in 505 where Socrates says that the philo-
sopher needs to know what goodness is. This leads him on to the
simile of the Sun in which he tells us that goodness is in the intellig-
ible world what the sun is in the visible world. It is goodness which
provides the light whereby we are enabled to know the other forms,
and goodness is also responsible for their existence. In order, ostens-
ibly, to illustrate what he means by this, Socrates next passes to the
simile of the Line in which he puts before us the contrast between
shadows and reflections on the one hand and originals on the other,
and tells us that the same contrast holds between doxa and episteme,
and that it also holds, "in the intelligible realm", between what he
calls dianoia and what he calls noesis. We took him to mean that if
we liken the man of doxa and also, at a higher level, the man of
dianoia to the man who has before his eyes an image, we may also
liken the man ofepistemg, and in particular the man ofnoests, to the
man who has before his eyes an original.
Socrates next passes to the simile of the Cave, which draws to-
gether the points made in the previous similes and adds to them in
1 In Chapter 3 of Vol. 1.
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THEORY OF KNOWLEDGE
various ways. One of the additional points made by the Cave is that
we are all very inclined to rest content with images, and that the
darker, and therefore the intrinsically less visible, things are, the
easier we find them to look at. In particular although goodness pro-
vides the light by which we do all our abstract thinking, and although
it is, like the sun, supremely visible, it is the last thing that we are able
to see. Another of the additional points made by the Cave is that the
contrast between looking at an image and looking at an original may
also be drawn within the sphere of doxa, and that we need to draw it
if we are to see how truly dreadful is the general intellectual condition
of mankind. Of these three similes, then, the Cave may be said to
apply the implications of the other two to the problem of how we
can get from where we are to where we ought to be, to describe the
resistances which we shall meet with on our journey, and in general
to draw the pedagogic moral from the metaphysical and epistemo-
logical doctrine. Plato's positive point might have emerged more
clearly if he had forced himself to forego the opportunity of being
rude about the mental condition of mankind.
If we could assume the correctness of the interpretation which I
have sketched, it would not take us long to state the contribution
which this part of the Republic makes to Plato's epistemological doc-
trine. But unfortunately there are a number of points which must be
looked into in more detail. Plainly the three similes belong very
intimately to each other and to the educational programme to which
they are prefixed. However, the comparison of the status of goodness
to that of the sun raises problems which belong more to cosmology
than to epistemology, and I shall defer these to the next chapter. I
shall defer also any detailed consideration of the proposed educa-
tional programme. This will leave for immediate attention problems
concerning the similes of the Line and of the Cave.
We can take it that the "simile" of the Line consists of the formula
a:b :: c:d :: a + b: c + d. It says therefore that the relationship
between certain pairs of terms is identical with, or at any rate similar
to, the relationship between certain other pairs. An "analogy" of this
kind is most commonly used when the relationship between one of
the pairs of terms occurring in it is known to the hearer, and the
purpose of the analogy is to acquaint him with the other relationship
by telling him that it is like the known one. It is probable that this is
what Socrates is doing in this case. It should therefore be worth while
asking which of the relationships (that between a and 6, that between
c and dy or that between a -\- b and c + d) Socrates takes to be known
and uses as the base of the analogy. To do this let us see how So-
crates assigns values to his variables.
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THEORY OF KNOWLEDGE
He begins by assigning to d shadows and reflections, and to c the
originals of which these are images. He then however says that b is a
certain mental condition, namely that wherein we have to use hypo-
theses as if they were first principles; and that a is another mental
condition, namely that wherein we use hypotheses as bases from
which to set out in search of first principles. This of course is a
heterogeneous set of values two sorts of visible objects and two
states of mind. Shortly however (511 d-e) he offers a homogeneous
list by assigning to each segment of his line, or to each variable, a
"condition of the mind", a becomes noesis, b dianoia, c pistis and
d eikasia. When he subsequently reverts to the analogy in 533 e-534 a
he gives a slightly modified version of this homogeneous list, and I
think we can assume that these four homogeneous terms are the
terms of the relationships between which the analogy is supposed to
hold. We need not therefore rack our brains to see how noesis could
stand to dianoia in the relationships in which things stand to shadows.
Noesis stands to dianoia in the relationship in which pistis stands to
eikasia, wherep/.s-rms a state of mind correlated with looking at things
and eikasia a state of mind correlated with looking at shadows (etc.).
The analogy says, then, that noesis stands to dianoia as pistis to
eikasia, and as the sum of the first two terms stands to the sum of the
second two, where episteme is taken to be the sum of the first two,
and doxa the sum of the second. 1 On the assumption that one of
these relationships is being used to illuminate the others, which is the
relationship that we are supposed to understand already?
We know roughly by this stage what the words episteme (or
gnosis) and doxa mean. What about the other four words? Eikasia
ought to mean something like "conjecturing" or "representing by a
likeness". Pistis means something like "trust" or "confidence",
though it can be used to mean "proof" or "ground of confidence". 2
There is therefore a clear difference of meaning between these two
terms. The difference between dianoia and noesis is not so clear.
Dianoia ought to mean something like "thinking" and noesis might
well have been used more or less synonymously with it, though evi-
dently that is not the case here. It is fairly clear, then, that we could
not know what the relationship between these two terms is by attend-
ing to the meaning of the words used to name them. When we turn
our attention from the meanings of the words to the natures of the
states that they name, we get a similar result. We have some idea, but
we would like more, of what Socrates takes episteme and doxa to be
and of the relationship between these states. On the other hand it is
1 This is inaccurate as we shall see below (p. 90-101). Doxa is not the sum of c
and d but it is related to c + d.
2 Laws 965 c 7, and perhaps Phaedo 70 b 2.
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THEORY OF KNOWLEDGE
clear that Socrates could not and does not expect us to see at once
what he means when he speaks of the state of mind in which we have
to treat hypotheses as first principles, and contrasts this with the
state of mind in which we use hypotheses as bases from which to seek
for first principles. But we are of course familiar with the difference
between seeing a thing and seeing a shadow or reflection, and we can
use our common sense to work out the epistemological relationship
between these predicaments. Furthermore we are helped by the
application of the two terms pistis and eikasia to these predicaments
in a way in which we are not helped by the term noesis and dianoia 1 .
It is obvious that if I can see something I have grounds for confidence
about it, whereas if I am only looking at a shadow I am reduced to
conjecturing. It is fairly clear therefore that Socrates is intending to
throw light on the relationship between noesis and dianoia, and that
he is getting the light either from the relationship between episteme
and doxa or from that between pistis and eikasia. Since this- last re-
lationship is the only one which is familiar to common sense it is
probable that this is the one which is intended to throw light. This
conclusion is reinforced by the reflection that there is little point in
bringing into the story the intrinsically rather unimportant relation-
ship between seeing things and seeing shadows unless it is brought
in to illuminate the other two, much more interesting, relationships.
The reasonable conclusion seems to be that the analogy is meant to
tell us that the relationship between noSsis and dlanoia and the re-
lationship between episteme and doxa may be likened to the relation-
ship between a man who is looking at a thing and a man who is
looking at an image. A further argument in support of this conclusion
is that throughout this section Plato is using well-known facts about
visual experience to illustrate what he wants to say about thought.
What is not so clear is whether the description eikasia or "con-
jecture" is being used in a subjective or in an objective sense. That is
to say, it is not clear whether the man who has before his eyes an
image is aware of this fact and is using the features of the image as
clues to the nature of the original, or whether on the contrary he is
deceived by the image and assumes that he is looking at a genuine
thing. In the former case he would be conjecturing subjectively; in
the latter case we might say that he was conjecturing objectively., and
say it with pejorative intent. If Plato wanted to speak kindly of doxa
1 Indeed Glaucon seems to imply (511 d 2) that Socrates has chosen the word
dianoia because he wanted a word which could go between doxa and nous (or
noGsis); and in 533 d Socrates seems to say that he chose the word because it
connotes more clarity than doxa and less than epist&m$, and adds that we must
not argue about the choice of a name. This suggests that the choice was, lin-
guistically speaking, somewhat arbitrary.
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THEORY OF KNOWLEDGE
and dianoia he would liken them to the state of mind of a man who
does the best that he can with the kind of indirect information that an
image gives us of its original; if he wanted to speak ill of them he
would liken them to the condition of the man whom the image
deludes. In fact, I think, Plato wants to do both of these things, in
that he wants in particular to tell us that the entities which are studied
at the level of dianoia (namely mathematical entities) can be used as
clues to enable us to grasp the forms, but at the same time that they
are in fact wrongly treated by mathematicians, who do not attempt to
get back behind them. For this reason we probably ought to say that
the condition described as eikasia is neither that of shrewdly con-
jecturing nor that of being deluded, but more generally the condition
of having the kind of second-rate knowledge of a thing which we
have if we can only see an image of it. Pistis by contrast will be the
condition in which we are entitled to be confident because we can
actually see the thing about which we are judging.
This account of the meanings of the terms eikasia and pistis will
have to be revised at a later stage of our discussion, because it is
part of my argument that the meaning of these two terms changes
subtly in the Seventh Book with the complication which is intro-
duced by the subdivision of empirical thought into two grades in the
simile of the Cave. Strictly speaking these two grades are related to
each other as eikasia is related to pistis (in the sense in which these
terms were introduced in the simile of the Line), but Plato speaks as
if the two grades were eikasia and pistis. But this complication must
be deferred until we have looked at the Cave.
Meanwhile so far as the Line is concerned eikasia seems to mean
"having only an image to go on", and pistis seems to mean "having
grounds for confidence because the thing itself is before our eyes".
When he first assigns images to d and their originals to c in 509 d 9,
Socrates says that he is dividing his line in terms of "clarity and un-
clarity" (sapheneia and asapheia), and this surely draws attention to
the difference between the good view that I get of a thing that is
before my eyes and the poor view that I get of a thing of which I
only see a shadow or reflection. This, then, is the fundamental con-
trast, and it is used to illuminate the contrast between noSsis and
dianoia, which two terms, it is clearly implied in 51 1 e 3, also differ in
sapMneia or clarity. 1
Our next question therefore must be that of the identities of
noesis and dianoia. On this topic I shall not say very much in this
chapter. 2 1 take it that the process which Socrates calls no$sis is the
1 1 suspect that sapheneia connotes both goodness of view and directness of
confrontation, the two being thought to amount to the same thing.
2 See Chapter 5, especially pp. 548-62.
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THEORY OF KNOWLEDGE
same as that which he calls dialectic, though the word noesis (which
probably means something like "seeing with the mind") really refers
to success in this process. It is the process whereby we try to "arrive
at just what each thing is" (532 b 1) without the aid of the senses, or
to "grasp the intelligible account (logos) of the essential nature
(ousia) of each thing" (534 b 3). It culminates in the vision of good-
ness, which also provides the light which has been used all along. The
word dianoia is made by Socrates to stand for the mathematical
disciplines which he describes. He does not tell us in so many words
that there is no other branch of thought which deserves the title
dianoia, but he gives no indication of the identity of any other. If
there were any other discipline which could be called dianoia we
would expect it to have the following characteristics, which are
derived from Socrates' and Glaucon's descriptions of dianoia in the
account of the Line. It would be a discipline in which we have to
"seek from hypotheses" (510 b 5), and go not towards an arche
(beginning, first principle or source) but towards a teleute or end. It
would make use of physical things in the manner in which mathe-
maticians talk about the shapes of physical things, such as a drawn
square, although they are not thinking 1 about the drawn square but
about "the square itself" which the drawn square "resembles"
(510 c 5-8). It would be unable to get beyond hypotheses (511 a 5)
and it would not attempt to "give account" of the things that it
hypothesises (510 c6). Its subject matter would consist of things
which are "intelligibles given an arche" (511 d2) and it would
deserve the title dianoia (implying that it comes between doxa and
nous) because although its subject-matter consists of things which
have to be investigated by the mind and not by the senses, it fails to
achieve nous or understanding of them by reason of the fact that,
lacking the arche, it has to use hypotheses (511 c-d).
It is not too difficult to see what this means in terms of mathe-
matics. Mathematicians do not get out their rulers to prove that the
square on the diagonal of a given square is double the area of the
square on whose diagonal it is. They do not do experiments with
bundles of matches to prove that 7 x 7 = 49. They use their minds
and not their senses to prove their theorems. They lay it down that
the units that arithmetic is concerned with are indivisible and equal
each to each (which is true of no ordinary units such as cattle), and
are therefore entities which can be grasped with the mind but not
with the senses (525 d-526 a). In fact, to do mathematics we have to
make an effort of abstraction. But mathematicians do not take this
1 Subjectively or objectively? Does Socrates mean that they know that they are
thinking about "the square itself", or that that is in fact their topic though they do
not fully realise this? In my view the latter is nearer the truth.
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THEORY OF KNOWLEDGE
to its logical conclusion and explicitly allow that they are dealing
with totally abstract entities. In geometry they do not try to ask what
squareness is; they take this to be "evident to all men" (510 d 1), and
therefore their talk has to mention entities which one can only
represent to oneself as shapes of physical things, boundaries of
physical surfaces. Though Plato talks mostly of geometry it is clear
that he thought that something similar applied in the case of arith-
metic. I suppose that what he had in mind must be of the following
kind: we tell ourselves that the units, which can, for example, be
paired off in even but not in odd numbers, are not physical units;
nevertheless, because we have no abstract conception of what unity
is, we have to represent our arithmetical unit to ourselves as some-
thing like a small and featureless pip (the Pythagorean "marbles"),
and no doubt we have to represent the pairing-off as a physical
process of setting side by side. We have no Principia Mathematica to
tell us how to construct arithmetical operations such as division out
of notions which belong to general logic, i.e. have no special appli-
cation to the kind of entities which have to be visualised. Therefore
our mathematical thought has an essential connection with physical
entities, which connection is improper and indeed allowed to be im-
proper by the procedural rules which mathematicians lay down.
Dialectic is the process by which we travel from dianoia, I think, to
noesis. Dialectic "makes its way destroying hypotheses" (533 c 8), or
in other words doing that which the mathematicians leave undone
when they "allow their hypotheses to remain undisturbed, and cannot
give account of them" (ibid, c 2). The feature ofdtanofa which is here
referred to, I believe, is that whereby mathematicians take for
granted such things as the division of numbers into odd and even or
the classification of angles into three kinds as "evident to all men".
Taking such things for granted is objectionable and has to be dis-
turbed, but not primarily because there is any doubt of the truth of
the propositions which are involved in these "hypotheses"* It is
objectionable because the entities which mathematicians take for
granted are "intelligible given an arche". That is to say an oppor-
tunity is missed when we take for granted such a notion as that of an
even number and do not try to give account of it. We can indeed
proceed towards the teleute or end (that is to say, we can deduce the
consequence of our hypotheses, or prove theorems) without giving
account, but we cannot get towards the arche, source or first prin-
ciple. We cannot do so because unless we try to give account of such
notions as even number we cannot discern the source of the division
of numbers into odd and even, the abstract principle which, in its
application to aggregates of units, entails that the number of every
alternate aggregate should be even. We therefore have to accept it as
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THEORY OF KNOWLEDGE
a matter of fact that all numbers are either odd or even, and we lose
the chance of seeing the rationale of this, although it is intelligible
given an arche, i.e. it is the kind of thing whose rationale ought to
be discoverable. It is also the case I think (Plato nowhere explicitly
says this, but it seems to be the natural interpretation of his language
on several occasions) that it is because we do not attempt to seek the
logos or rationale of the things which we take for granted in mathe-
matics that we are forced to represent them to ourselves in sensuous
terms. The thought underlying this, I believe, is that we ought to be
able to achieve an abstract understanding of principles like square-
ness or circularity, and that if we could do so we would not have to
represent such entities to ourselves in terms of the boundaries of
physical surfaces, and that so long as we cannot do so we must think
of them in that way. This is the sense in which dianoia is compelled
(510 b 5) to use hypotheses and to rely on sensibles. The compulsion
is not exercised by the nature of the subject matter of mathematics,
but by the mathematicians' unwillingness to seek to give account.
One might almost say that the compulsion is logical, in that some-
thing which did not rest on hypotheses would no longer be dianoia.
Noesis, being what we attain to when we do dialectic and disturb our
takings-for-granted, will involve understanding the rationale of the
distinctions, classifications and so on which dianoia takes for granted,
it will culminate in the apprehension of the supreme rational prin-
ciple, the nature of goodness, and it will exempt us from all reliance
on sensibles. How it achieves this must be left for another chapter. 1
We can see now that it would not be easy to imagine a subject
other than mathematics which could deserve the title dianoia. To be
dianoia a subject has to be semi-abstract in the way in which mathe-
matics of the kind which Plato is describing is semi-abstract. Mathe-
matics depends upon the act of abstraction whereby we arrive at the
notions of space and quantity, and work out rules of procedure
which enable us to talk about physical things without reference to
any of their physical qualities. It is easy to see that we might be
tempted to say that in mathematics we are talking about physical
entities only in so far as they are ordered (this is a deliberately loose
use of the notion of order), and that we might therefore come to
think that mathematics offers us a unique range of "images'* of the
abstract principles of order whose imposition upon physical things
renders them susceptible to mathematical treatment.
This brings us to the question how it is that dianoia stands to
noesis as eikasia to pistis. The meaning must be that in the state of
dianoia a man has before his mind images of the objects which he
perceives directly in the state of noesis. It is made clear enough that
1 Below, Chapter 5, pp. 548-62,
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THEORY OF KNOWLEDGE
the objects which noesis directly perceives are forms (whatever these
may be); and therefore the proximate objects, as we might call them,
of dianoia must be images of the forms. If dianoia is identical with
mathematics, this ought to mean that the things which mathe-
maticians talk about (squares and circles, perhaps, odd and even
numbers, and similar entities) are images of the forms. He who has
reached the level of abstraction at which he can talk about circles as
opposed to plates, rectangles as opposed to tables, has reached the
level of "conjecturing about the forms", which he perceives indirectly
because he has their images before his mind.
This ought to be what the Line is meant to tell us about the rela-
tionship between dianoia and noesis. What does it mean? Roughly, I
think, the meaning is that which I indicated at the end of the last
paragraph but one. Plato's view was, I believe, that the form, struc-
ture, principle or what you will which constitutes a mathematical
entity such as a circle has no essential application to space. Such
principles can be expressed in spatial embodiments, but in themselves
they are prior to such embodiments and in no way dependent on
them. Furthermore they are capable of other embodiments which are
not spatial in kind. The spatial embodiments of the forms have the
advantage over all other embodiments that they are especially close
to the originals in that the "matter" of the embodiment space is
something abstract, something having no properties of its own which
might compromise the purity of the embodiment or distract attention
from it.
How did Plato come to have such views ? We have already sug-
gested that he might have followed a train of thought similar to that
which, we conjectured, underlay the Pythagorean definition of justice
as the number 4. Justice is reciprocity; 4 is the first square. But in
2x2 the first number treats the second in the same way in which the
second treats the first; each doubles the other. Likewise when you hit
me and I justly retaliate each of us does to the other what the other
does to each. There is therefore an identity of structure between the
arithmetical operation of squaring and the human operation of
retaliation. 1 Incidentally the same structure would presumably be
common also to a geometrical square. Plato stresses that the man
who is to do dialectic must bring his mathematical studies together
and see their kinship (531 d), and it may be that he thought that it
was when we could see the identity of structure between an equal-
sided rectangle and a number whose factors are n x n that we should
be ready to detach the structure from its embodiments and entertain
the notion that it might have other, non-mathematical embodiments,
1 1 am not suggesting that Plato would in fact have thought this an adequate
account of justice. The Pythagoreans chose too simple a mathematical image.
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THEORY OF KNOWLEDGE
There are other instances of principles which have mathematical
and also non-mathematical embodiment. Equality is a mathematical
relationship which exists in two forms, "arithmetical" and "geo-
metrical", and these two forms of equality are also to be found in
human society. The Gorglas, indeed, makes the point that a know-
ledge of mathematics will help the politician to distinguish the two
kinds of equality in society (Gorgias 508 a). There is also the passage
in the Tenth Book of the Laws (Laws 897-8) where the Stranger
speaks of the circle as an image of intelligence; the same principle of
self-consistency which constitutes intelligence also expresses itself in
spatial terms in the form of motion in a circle. There are then
examples such as these of structures or principles which can be
expressed in spatial or numerical terms to give us entities or relation-
ships with which mathematicians are familiar, but which appear to be
capable of non-mathematical embodiment. Such examples might very
well have suggested the thought that wherever we find precise rela-
tionships between spatial or numerical magnitudes we are dealing
with an order which reason has imposed. But reason for Plato is
something which is independent of the existence of space or physical
objects. It might therefore seem that the order v/hich reason can
impose on such entities must also be something which is independent
of them although capable of embodiment in them. But if there appar-
ently exist structures (such as circularity) which are, so to speak,
neutral between their mathematical and their non-mathematical
embodiments, this might be taken to confirm the idea that "in them-
selves" these structures are independent of all embodiment. It is
natural to think that something which can exist either in this form or
in that must also be capable of existing in no form at all, but simply
"in itself. It was entities existing, in this way, "in themselves" which
we were to know at the level ofnoesis, and it was their mathematical
embodiments that we were familiar with at the level ofdfanoia. It was
because the things that we were familiar with at this level are in fact
images of pure principles of reason that students have to do mathe-
matics before they can attempt dialectic.
A modern philosopher might allow that some analogy can perhaps
be detected between equality in mathematics and in political theory,
but he would go on to protest that it would be an idle dream to
suppose that we could ever come to know something called "equal-
ity itself" which is the pure essence of the mathematical and political
embodiments. My suggestion is that Plato did not think this an idle
dream. There are two points which may perhaps make this suggestion
easier to swallow. One is that it may be that Plato primarily wanted
to make a simpler pedagogic point that did not carry with it the
notion of "equality itself" and other such entities. This is the point
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THEORY OF KNOWLEDGE
which is made in effect in the passage in the Gorgias (508 a) cited
above. It is that you can teach a man in the unemotional atmosphere
of mathematics to draw distinctions which excite passion in politics.
A man can learn in mathematics that there are two kinds of equality,
and a man who has thoroughly learnt this will be unable to suppose
that "equality" can have only one meaning in politics. There is
therefore pragmatic value in the proposal to train future rulers in
mathematics. But Plato might have thought that if this was so it must
be due to the fact that the two equalities are embodiments of "equal-
ity itself", and so on with whatever other examples he had in mind.
This pragmatic point might have conspired with his cosmological
belief in a reason independent of the physical world to make him
think it necessary to postulate entities such as equality itself. But the
second point is that it is not certain that Plato did want to postulate
such entities in the most offensive way. He did indeed believe, if I am
right, in the possibility of knowing things like "equality itself", but it
does not fully follow that he thought that this was, so to speak, an
essence which we could extract from its embodiments and put a label
on. That is to say, knowing equality itself according to itself does not
necessarily involve being able to say what it is ; it might be enough to
be able to see the analogy between the embodiments. There does not
necessarily have to be a logos, definition or account, which is the
logos of pure equality. We shall see later in this chapter that at some
stages at any rate Plato may have doubted whether you can always
say what you can be said to know; a certain skill in handling
attempted refutations may perhaps sometimes count as knowledge. 1
He does indeed speak in this passage several times of "giving a logos"
as something that a dialectician must be able to do, and he does
indeed say in one place (534 b 3) that the dialectician grasps the
account of the essence of each thing. But he also says that it is by
trying to give account of the entities which mathematicians hypo-
thesise that we come to know the forms. It is conceivable therefore
that he thought that to come to know a form was to achieve an
understanding that could not be expressed in a formula, and that in
this way "knowing equality itself" was not very different from under-
standing the analogy between its various embodiments. We have to
steer between the twin dangers of taking Plato's language too liter-
ally, thus burdening him with too much ontology, and of bringing
his thoughts too much into line with ours by an over-flexible inter-
pretation.
Whatever exactly the experience of "knowing equality in itself" is
to be thought to consist in, our view is that such an achievement is
what counts as noesis, and that the mathematical embodiment of
1 See below, pp. 122-6.
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THEORY OF KNOWLEDGE
equality which is familiar to us at the level of dianoia is an image of
the form and can be used to "conjecture" it. This is how dianoia
stands to noesis as eikasia to pistis. The question now arises whether
all forms have their images at the level of dianoia. There may be
readers who will agree, more or less, with what has been said so far
but will want to add that of course it is only some of the forms that
have images which we can study at the level of dianoia, at any rate if
mathematics and dianoia are the same thing. It is only "mathe-
matical" forms which can have mathematical images. I think that
this view is wrong, but there are two arguments in its favour. One is
that in the Republic Plato seems to believe in all kinds of forms,
including those of artefacts like beds and tables; and it is absurd to
believe that there are images of bed-hood and tabularity among the
entities of mathematics, as there would be if dianoia involved
familiarity with images of all the forms. The second argument for the
view that it does not involve this is that in the simile of the Cave
there are three sets of simulacra. There are the shadows on the back
wall, which are what the vulgar believe in, there are the reflections in
the pool outside, which are plausibly regarded as the things that
mathematicians talk about, but there are also the puppets that cast
the shadows; and what are these? These could be accommodated if
we thought that whereas forms like squareness and equality had
mathematical images others like justice and bed-hood had less
abstract, more sensuous images, images which were grasped by the
senses and therefore properly located in the cave and represented as
puppets as puppets because these are realities in comparison with
the shadows, as befits the images of forms, but derivative realities, as
befits images.
I shall not attempt to meet this second argument until we have
dealt with the Cave, and I shall only offer a sketch of an answer to
the first. The argument depends, really, on the question how much is
involved in "believing in the existence of a form of so-and-so". There
is no doubt that in the Tenth Book of the Republic Plato evinces
belief, in some sense, in the existence of a form of beds and of tables;
and if this means that in addition to entities such as justice and
circularity he believed also in an independent principle of bed-hood,
then it would be very difficult to suppose that this last could have a
mathematical image. However as we shall see elsewhere 1 Plato had at
least a tendency, at least at some periods, to regard "adjectival"
forms such as equality as more important than "substantival" forms
such as bed-hood. Perhaps he felt that "what it is to be a bed" could
be regarded as a complex function of the properties which beds have
to exhibit. We can after all give some account of what beds ought to
1 See Chapter 3, pp. 353-6.
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THEORY OF KNOWLEDGE
be like by mentioning properties such as rigidity, rectangularity and
so forth. The context in the Tenth Book does not require that bed-
hood should be a totally independent form; it only requires (and the
same is true of the form of a shuttle in the Cratylus) that a principle
of organisation should be prior to the things which are organised in
accordance with it.
However this may be, I should want to urge that in the Sixth and
Seventh Books of the Republic when Plato talks about forms he is not
thinking of particular principles of organisation such as that of beds,
but of altogether more general principles, principles which will be
involved in the organising of anything whatever. I have suggested
that this can be reconciled with what is said of beds in the Tenth
Book. If it cannot, I should prefer to fall back on the hypothesis of
disagreement between the two parts of the Republic, rather than to
allow that it is only mathematical forms whose images the mathe-
maticians are familiar with. For it is clear from the Line, and also
from Plato's educational proposals, that he does intend us to believe
that mathematics is in a unique position, not only with respect to
coming to know mathematical forms, but also with respect to coming
to know what we need to know in order to govern our lives and our
cities. It is therefore a mistake to say that there are mathematical
forms and ethical forms and that only the former have their images
among the proximate objects of the mathematicians. There are not
mathematical forms and ethical forms; there are just forms, or
principles of order, all of which, for all that Plato says to the con-
trary, have their mathematical and also their non-mathematical
embodiments, and may be relevant equally to the study of ordered
quantity and of ordered lives.
It may be retorted that, even if we decide somehow to ignore bed-
hood and tabularity, it is still absurd to say that all the forms have
mathematical embodiments. What is the mathematical embodiment
of that whose presence to something makes that thing beautiful, or
morally good? Shall we be hearing that triangles arc images of
beauty, pentagons of virtue? Half of the answer to this is that it is
not as absurd as it sounds, so long as we do not look too carefully.
We must remember how large a part notions like harmony and pro-
portion played in Plato's ethical, political and aesthetic theories. It is
not difficult to suppose that he might have thought that mathemati-
cians were familiar with harmony and proportion in their mathe-
matical forms. In this way he might have come to think, what he
would anyhow want to think on a priori grounds, that every principle
whose application results in something definite and ordered, is cap-
able of application to space and quantity and therefore has mathe-
matical embodiment. But the second half of the answer to this
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THEORY OF KNOWLEDGE
objection is that we do not need to hit upon a tenable idea in order to
find a correct interpretation of the simile of the Line. For Plato does
not repeat elsewhere the things which he says in this passage about
the special part played by mathematics in the process of coming to
know the forms; and it is at least possible that the reason why he
does not do so is that he had given here an outline sketch of a train of
thought which seemed to him promising, but which he was never able
to make good in detail. It may be that the difficulties which trouble us
also troubled him.
To sum up, then, the interpretation that I am offering of the simile
of the Line is that just as the objects of vision have their shadows
which can on occasion delude us, but which can be used to give us
clues of a kind to the nature of their originals, so the objects of the
mind, the forms or principles of order, have their images with which
we can rest content, but which we also can and should make use of as
clues to the nature of the principles whose images they are; and that
this is so because every principle of order is applicable to the ordering
of space and quantity, and is therefore met with in such applications
in the course of the mathematical sciences. The entities of mathe-
matics are not pure principles; they are embodiments of such prin-
ciples, but abstract embodiments, the discipline of mathematical
study having purged out of them all the material element with the
exception of space and quantity. All that we need therefore, to grasp
the formal element in its purity, is to carry the process further and to
get rid of this residual material element. This is why mathematics
plays a special role in the training of those who need to grasp the
formal element in its purity in order to recognise it in its moral and
political embodiments, and to bring these about.
We pass now to problems connected with the simile of the Cave.
There are two stages within the cave, that of the prisoners who can
see nothing but shadows, and who represent, as Socrates says, "our-
selves", and that of the reluctantly liberated man who is forced to
look at the puppets and recognise that they are the origin of the
shadows. The cave represents the visible world, and this would seem
to mean that whatever happens in it represents some kind of use of
the senses. Any stage of enlightenment which consists in the exercise
of abstract thought is represented by something outside in the day-
light. Therefore if there are two stages within the cave this means that
Plato is distinguishing two grades of empirical thought, the lower of
which is said to be characteristic of "ourselves".
Now the two grades are related precisely as seeing shadows to see-
ing originals ; and since just this relationship has been the motive
power of the Line, it is too much to ask us not to interpret the
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THEORY OF KNOWLEDGE
present passage, a page or so further on, in the light of the earlier.
This has puzzled many people, for they say that Plato cannot seri-
ously mean to tell us that the depth of unenlightenment from which
we all start consists in seeing nothing but shadows and mistaking
them for realities. In our account of this passage we allowed that this
was just, and dealt with the difficulty by saying that Plato is still
analogising. That is to say, just as in the Line he told us that there are
two grades of abstract thought which are related to each other by the
relation which obtains between seeing shadows and seeing things
direct, so here he is to be taken as telling us that there are two grades
of empirical thought between which the same relation holds. What
the prisoners do on their bench stands in the eikasialpistis relation-
ship to what the man does who is forced to look at the puppets. We
decided also to characterise the state of mind of the prisoners on the
bench as that of "the aesthete", that of the man who sees the puppets
as that of "the craftsman". Something must now be said to explain
and justify this.
What primarily requires explanation is Plato's use of phrases like
"the realm which is revealed through the sense of sight" (517 b 2) to
describe that of which the inside of the cave is a likeness. For it is
fairly generally agreed that Plato's primary interest in the prisoners
in the cave is paid to their moral and political and not their visual
illiteracy. There are shadows of justice and so on on the back wall
and it is primarily these that the illuminati^ who have seen the originals
in the outside world, help the prisoners to identify (520 c). It is our
proneness to moral and political, not to optical, illusion that is
relevant. Why then does Plato speak of "the world revealed by
sight"?
The answer is: for no good reason, but from carelessness. Plato
knows quite well that we do not literally see with our eyes that it is
wrong to steal as we see with our eyes that the coffee-pot is empty. I
have complained before of Plato's habit of talking loosely of the
senses when he means something more like common sense; now is an
occasion to justify these complaints. For we can confirm the sus-
picion that Plato is lumping things that are in no sense visual under
"the sense of sight" by looking at the Tenth Book. In the passage in
question (600-4) Plato is talking about painting and poetry. He
refers to the phenomena of illusion, such as the straight stick which
looks bent in water, and he significantly describes them as "shadow-
drawing". He claims that, in painting things as they look, painters
exploit our natural propensity to be deceived by this shadow-draw-
ing; and he tells us that our available defences against this propensity
are such techniques as measuring, counting and weighing. These
techniques are of course those which the craftsman employs, and it is
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THEORY OF KNOWLEDGE
with the craftsman that the painter is contrasted. The painter is con-
cerned to represent what a bed looks like from one angle, and indeed
to paint what the uninstracted vulgar regard as a "beautiful" bed.
The craftsman is concerned to find out from those who use the things
that he makes what they ought to be like, and to make them like that.
For him the kallos, beauty or fineness, of a bed lies in its fitness for its
function; and he wants the bed that he makes to be, and not merely to
look, fit for the job. He is said to be concerned with the aletheia or
truth of beds, and the painter with eiddla or images (600 e etc.). To
this is added the comment that it is the user of an object who has
episteme of what it ought to be like, and that the craftsman, by con-
sulting the user, comes to have pistis orthe or doxa orthe (correct
pistis or doxd). The painter, however, the maker of images, has
neither of these things; he simply imitates whatever the vulgar think
beautiful.
In this discussion Plato seems to bring against the painter two
charges which are distinct but which he does not trouble to distin-
guish. One is that the painter paints (and the poet depicts) appear-
ances, where this means that the work of art has only to look like
that which it represents from a given point of view, in a given light
and so on (and mutatis mutandis for the poet). In this way the artist
is a reproducer of images. This is one charge; it is the charge which
brings the notion of an image into the discussion, and it is the charge
which is connected with the phenomena of optical illusion, but it is
not the main charge. The main charge is that in order to please Ms
clients the painter does not need to know what a bed ought to be like
nor a poet how a battle ought to be fought; they only need to be able
to reproduce something that the vulgar admire. Contrariwise the
craftsman has two distinct virtues; he uses measuring techniques
instead of relying on appearances, and he is concerned with fitness
for function rather than with fashion. On one side of the contrast is
a set of practitioners who are concerned only with how things "look"
(whether literally in the case of painting or metaphorically in the case
of poetry), and who are trying to please those who are concerned
only with how things "look". Such practitioners produce "images",
and to be skilful producers of images they need no accurate ideas
about the nature of what they depict, and they have no technique for
acquiring such ideas. On the other side of the contrast, the craftsmen
(whether they are carpenters making the beds which painters paint,
or generals fighting the battles which poets depict) are concerned with
the aUtheia or reality of things, have to have accurate ideas about
what they ought to be like, and have to learn techniques for making
them so.
We may notice also that although Plato stresses the analogy
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THEORY OF KNOWLEDGE
between painters and poets in that he fits them under a common
formula (they are both "makers of images"), he is also perfectly well
aware that it is only an analogy, that painters and poets do not make
images in quite the same sense (603 b). The images of justice, warfare
and so on in which the poet deals are not the same as images of beds
on canvas, because they do not do the same sort of harm to those who
indulge in them. Poetry hypertrophies the emotions, whereas paint-
ing panders to the tendency to judge by the eyes rather than by the
set square. The two arts are differently damnable, but they can be
attacked together because of the strength of the positive analogy
between them. This lies in the type of person to whom they both
appeal. He is the man who is only interested in how things look, who
is satisfied of the beauty of anything which looks convincing, and
who is to be sharply contrasted with the practical man who demands
good workmanship and who identifies soundness of design with
serviceableness.
It is fairly easy to see the application of this to the parable of the
Cave. We have here a contrast between two levels of empirical
thought. The craftsman, though he "looks towards" the form, does
not know it; that privilege is reserved for the user, who would of
course be the philosopher in the case of the most important kinds of
craftsmanship such as government. The craftsman is still "in the
world revealed by sight" in that he relies on his senses, although he
helps them out with measuring techniques, knowing, as the aesthete
does not know, that things are not always as they seem. Furthermore
it is a common feature of both passages that although Plato does
most of his exposition in terms of the sense of sight he is really more
interested in moral than in optical illusion. We have seen that this is
true of the Cave, and it is also clear that the energy of Plato's attack
in the Tenth Book is directed against poetry and not against painting.
I do not believe that Plato really hoped to convince us that people
who admire pictures are more likely than the rest of us to be taken in
by straight sticks which look bent in water. It is poetry that troubles
him, as the end of the discussion makes clear (605-8), and what
troubles him about poetry is the moral misjudgment that it encour-
ages. In both discussions therefore Plato tells his story in terms of the
sense of sight, but what he is concerned with is the moral blunders to
which a certain class of persons is prone. These persons are those of
whom the man who is interested only in visual appearances is treated
as characteristic. This man is taken as a kind of paradigm of those
who are not concerned with the reality of things. He is described as a
maker or appreciator of "images", a description which is much more
immediately intelligible in its application to him than in its extended
application to the moral sphere. In both passages therefore the
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THEORY OF KNOWLEDGE
notion of images is brought into the story by means of introducing
the visual analogue to moral carelessness, and in both passages the
sense of sight is used to illustrate what Plato wants to say about
morals. He seems to have supposed, quite mistakenly, that he would
thereby make his meaning clearer. Plato's purpose in the Cave is to
castigate the general condition of mankind by attributing to us all a
faith in the reality of "images". This is to attribute to us all the dis-
ease which, in the Tenth Book, he attributes especially to artists and
their public, but which he no doubt supposes to afflict us all to a
greater or lesser extent except in so far as intelligence has effected a
cure by the use of quasi-mathematical techniques. Plainly Plato is
going further than he really means to go when he says that the
prisoners in the cave are "like ourselves", if that implies that none of
us resemble the man who has been made to look at the puppets.
Probably however he intends only to tell us that the condition of the
prisoners is our natural condition, out of which we can be, and many
of us have been, forced to rise by the education which has been given
to us. In so far as we have not risen, our condition is one of being
content with "images", or with the appearances of things, whether
the things in question are objects of vision, objects of moral judg-
ment or something in between.
We can now see that we can say if we wish that the puppets are
images of the forms. This will mean that a well made bed or a well
fought battle will be a genuine embodiment of what it is to be a bed
or a battle, a truly just transaction will be a genuine case of the just.
However it seems to be Plato's purpose to tell us that we ought not
to try to conjecture the forms from images of this kind, but rather
from those which we encounter on the mathematical level. Probably
his reason is that every just act embodies many other principles
besides that of justice. (We remember that in 476 a 6 he tells us that it
is because forms associate with each other in their instances that we
find it difficult to discern their unity). It is because well built beds and
truly just acts can be described as images of the forms that they are
represented by puppets, but they are not the primary images for his
pedagogical purposes, nor are they the only images which some forms
possess, the reflections in the pool being the only images to belong to
others. Both puppets and reflections are replicas of the contents of
the outside world, but replicas of different kinds.
In the simile of the Line there occur two terms, namely doxa and
episteml, to which we have so far paid little attention. It is also the
case that Socrates recapitulates and amplifies the Line in the Seventh
Book (533 d-534 a), and in doing so introduces certain complica-
tions. We must now attend to these matters.
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THEORY OF KNOWLEDGE
The first appearance which the terms doxa and episteme, or rather
guests, make in the simile of the Line is towards the beginning
(510 a 9). Socrates has told Glaucon to remember the distinction
between the visible and the intelligible, has assigned one major part
of his line to the visible and one to the intelligible, has proceeded to
divide the two major parts in terms of sapheneia or clarity and its
opposite, and has progressed with this to the extent of assigning
shadows, etc., to one sub-section of the major part concerned with
the visible, the originals of the shadows to the other. "Would you
agree," he continues, "that the line has been divided, in terms of truth
and not-truth, in such a way that, as the believable is to the know-
able, so the semblance is to that which it resembles ? 5 ' Glaucon accepts
this. Now there are two things which Socrates may intend by his
question, and one that he cannot intend. It is sometimes thought that
he is using the word doxa to refer to the two states which he is about
to name eikasia and pistis, gndsis to refer to the two which are to be
called dianoia and noesis, and that his question means: "Would you
agree that the ratio between the bits of line representing doxa and
gndsis respectively is the same as the ratio between the bit represent-
ing eikasia and the bit representing pistisT* This is what Socrates
cannot mean, and the reason why he cannot mean it is that this
question is not worth asking. For practically all that Socrates has said
so far is that the line is to be divided in such a way that the answer to
this question must be "Obviously yes". It follows from this that we
cannot say that Socrates has so far said that gndsis is equivalent to
nogsis plus dianoia and doxa equivalent to eikasia plus pistis; and it is
a good thing that he has not said this, because it would upset all our
ideas about doxa if we learnt that it comprised nothing but looking
at physical things plus looking at their shadows.
There are two interpretations of Socrates' question which make it
worth asking. What these are we must defer for the moment in order
to look at the complications which Socrates introduces when he
recapitulates and amplifies the Line in the light of the Cave in 533-4.
Having said that the word dianoia will do for the name of the mathe-
matical disciplines, since all that is necessary is to have for the various
states names which indicate their relative status in respect of
sapheneia or clarity, Socrates continues: "It will be good enough,
then, to say what we said before, and call the first segment epistSmS,
the second dianoia,, the third pistis, the fourth eikasia; and the first
two together no$i$ 9 the second two together doxa." There are two
noteworthy points here. The first is that Socrates is not, of course,
saying what he said before, because he earlier called the first segment
nosis. It may be that Plato has deliberately made Socrates commit
this inconsistency in order to underline the point that the names do
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THEORY OF KNOWLEDGE
not matter, or it may be that he has simply forgotten what he said in
Book 6. In either case the inference is that the words noesis and
episteme are more or less interchangeable in Plato's mind. Therefore
the second point about this passage is that Plato does now in effect
say that noesis and dianoia add up to episteme (though he puts it that
episteme and dianoia add up to noesis), and th&tpistis and eikasia add
up to doxa. What this means we shall enquire in a moment. Mean-
while Socrates goes on to say: "Doxa is concerned with genesis
(becoming) and noesis with ousla (reality); and as ousia is to genesis,
so noesis is to doxa, and as noesis is to doxa, so episteme is to pistis
and dianoia to eikasia"*
We must defer for the moment those parts of this which are con-
cerned with the relations between states and objects and consider
what is said about the mutual relations of mental states. This is,
firstly, that a and b together are episteme and c and d together doxa',
and secondly that a+b : c+d : : a : c : : b : d. (The second of these
points follows of course from the original formula). What does all
this mean?
To understand this we have got to allow that the words pistis and
eikasia, as I indicated earlier, have undergone a change of meaning.
They no longer bear the rather restricted sense which they bore when
they were introduced in the simile of the Line, but have taken on a
new sense from the distinction which is drawn between two grades of
empirical thought in the Cave. Pistis now refers to our state of mind
when education forces us to admit the reality of the puppets, or to
care, in the language of the Tenth Book, for the aletheia of things,
eikasia to our state of mind while we are still tolerant of "images".
As we have seen, the relation between these two states is analogous to
the original pistisl eikasia relation. The "aesthete's" conception of a
table or a just action is an "image" of that with whose aWtheia the
"craftsman" is concerned, in that all that the former knows is what
the thing in question "looks" like. Since this is a consequence of what
the thing in question is like, the "aesthete" may be said to perceive a
sort of shadow of that which the "craftsman" perceives direct.
Therefore the craftsman/aesthete contrast is analogous to the
original pistis I eikasia contrast. What has now happened is that, in
the light of this analogy, the words pistis and eikasia have been made
to stand for the two states of mind which are in this way analogous
to the conditions for which the words originally stood.
If this is allowed it can be seen that it is harmless to say (what it
would not have been harmless to say in the Sixth Book) that eikasia
and pistis are collectively doxa. For eikasia and pistis now amount
1 All of this appears to be still within the ambit, strictly speaking, of "it will be
good enough, then, to say what we said before . . . *'.
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THEORY OF KNOWLEDGE
respectively to careless and to careful judgments upon physical
objects, moral actions and the rest of the things which are "revealed
by the sense of sight" ; and it is not grievous to say that these to-
gether constitute doxa. It might be possible to try to drive a wedge
between this use ofdoxa and that which we found in the Fifth Book;
for we thought that in the Fifth Book Plato was primarily thinking of
such things as a doxa or conception of justice, whereas here, it might
be argued, he is primarily thinking of a doxa or judgment on a par-
ticular just act. But I think that we can stop this wedge by reflecting
that though non-theoretical people mainly talk about particular
instances, an observer can nevertheless comment on their concep-
tion of some general term; Jones can have a conception of justice
although his possession of it consists in the particular comments he
makes. This wedge therefore does not drive asunder. Jones is a man
of doxa because he gets his conception from thinking about par-
ticulars only. His doxa will be pistis if he does it well.
The equation of episteme and dianoia with noesis is also harmless;
for these two together constitute the pure activity of the mind, and
that I suppose is what noSsis means here. Had Plato said that noesis,
or the grasp of forms and dianoia, or traffic with their shadows,
together constituted episteme we should have had to say that this was
a rather tolerant use of the word episteme. This perhaps is one reason
why Plato does not in this passage abide by the terminology of the
Sixth Book. He has however just observed before this passage opens
(533 d 4) that the activities comprised under dianoia are often compli-
mented with the title of episteme. The interchange of noesis and
epistem is therefore not essential; and that perhaps is why he did
not think it necessary to alter what he had written in Book 6.
We can now see what Socrates means when he says that as noSsis
is to doxa so episteme is to pistis and dianoia is to eikasia. In each
relationship the second term is inferior to the first, and we are con-
fined to the second term if we do not trouble to seek what is ultimate,
but content ourselves with images. An inductive conception of a
general term is an image of that general term, and we are confined
to the level ofdoxa if we are content with inductive conceptions (our
possession of which will be mainly or wholly manifested, as we saw,
in making particular judgments). Within the level of doxa, or within
the level of mental activity which does not aspire to an abstract grasp
of general terms, we are confined to eikasia if we are content with
images in the sense of the Tenth Book. Within the level ofnoSsis, or
the level which does so aspire, we are confined to dianoia if we do not
attempt to do dialectic.
So far we see that the Line has been mainly concerned to sketch
the part played by mathematics in the work of coming to know the
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THEORY OF KNOWLEDGE
forms, or of achieving an explicit understanding of the source of the
light by which we do our thinking; that the Cave is mainly concerned
to add to this that the base-line from which we all have to start is a
very long way back from the goal; and that in the passage of re-
capitulation which we have just been examining Socrates brings
these two points together explicitly under a common schema. We
must now turn to the question of the "objects" of the mental states
which Plato has distinguished.
We have three passages to consider. The first (510 a 8 sqq.) is
Socrates' question to Glaucon which we have already mentioned:
"Would you agree that the line has been divided, in terms of truth
and not-truth, in such a way that, as the believable is to the know-
able, so the semblance is to that which it resembles ?" The next comes
at the end of Socrates* first account of the Line (51 1 d~e). Here he
allots the four names noesis^ dianoia, pistis, eikasia to the pathemata
or conditions in the mind which are correlated with (epi) the four
segments of the line, and continues (if we accept a standard correc-
tion of the manuscript reading) : "Arrange these four conditions
proportionately, and understand that they partake in sapheneia, in
the way in which the things that they are correlated with (epi) par-
take in aletheia" The next passage comes in the recapitulation of the
Line in the light of the Cave, and consists firstly of that part of what
we have so far quoted which we have not considered, namely that
doxa is concerned with (peri) genesis and noSsts with ousia, and that
as ousia is to genesis, so noesis is to doxa; and secondly of Socrates'
concluding words, that "we must dismiss the question of the pro-
portion which holds between that which these states are correlated
with (epi), and the question of the division of the opinable and the
intelligible (doxastou kainoetou), or we shall involve ourselves in dis-
cussions many times longer than those which we have had" (534 a).
In the earlier chapter summarising the Republic I sat on the fence
with regard to the question whether this part of the dialogue is con-
cerned to grade entities which correspond to the mental states which
it names, or whether it is merely concerned to grade mental states by
grading their "contents". I must now try to justify this posture by
showing that these, which are the crucial passages, are not at all
easy to interpret.
We may begin by noticing that the notion of an object or correlate
is conveyed in these passages in three different ways: (I) by phrases
like "the believable" (to doxaston); (2) by the preposition peri or
"about" used for the relation of noesis to ousia and doxa to genesis;
and (3) by the preposition epi or "in relation to". Of these three
locutions peri is fairly unambiguous; it must I think stand for the
relation which noSsis and doxa have to their subject-matter, and this
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THEORY OF KNOWLEDGE
is confirmed by the fact that the other term of the relation is ousia
and genesis respectively. The meaning must be that you call it
noesis when a man is concerned with eternal truths, doxa when he is
concerned with changeable physical processes. A phrase like to
doxaston however is not so clear. "The believable" might mean "that
about which one can have beliefs", or in other words "the physical
world", or it might mean "that which one can believe", or in other
words "beliefs". Likewise, as we have seen in commenting on Book
5 S the preposition epi might stand for the relation between a mental
state and the objects that it is concerned with, so that dianoia would
be epi circles and pistis epi plates; but it might also stand for the
relation between a mental state and its contents, so that dianoia
would be epi the theorems of mathematics and pistis epi my reports
of what I can see. In the third of our passages epi is used in such close
proximity to peri (they occur two lines apart) that it is difficult to
think that Plato expected us to give each a different meaning; and
the same reasoning would suggest that he expected us more or less to
identify to doxaston with genesis and to nogton, the intelligible, with
ousia. Socrates' meaning would then be : "NoSsis is concerned with
ousia and doxa with genesis., and ousia is to genesis as noGsis is to
doxa; but whether we shall want to sub-divide ousia and genesis, and
what relationships, if so, we shall want to assert between the sub-
divisions are questions we cannot now discuss. Episteme is to pistis as
dianoia is to eikasia and so on, but I am not necessarily saying that
there is a part of ousia which corresponds to episteme, and which
stands to the part of genesis corresponding to pistis in the same
relationship in which the part of ousia which corresponds to dianoia
stands to the part of genesis which corresponds to eikasia. I am not
even necessarily saying that ousia and genesis are to be sub-divided
at all" I think that this is what Socrates means in this place, but it
does not follow from this that we must put an analogous sense on the
phrases to doxaston and to gnoston and on the preposition epi in
Book Six.
It does not follow that we must do this, and it may even seem that
it would be undesirable to do it if we notice that there is an apparent
inconsistency between the present passage and the second of our
three passages. For in the latter Socrates tells us that as his four con-
ditions are arranged in terms of sapheneia so the things which they
are epi are arranged in terms of aletheia. But prima facie this looks
as if Socrates is doing that which he subsequently says it would take
him an impossibly long time to do, namely subdivide that which the
states are epi and say what relationships hold between them. There
are no doubt a good many ways out of this inconsistency. We could
say for example that in the later passage Plato had forgotten that he
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THEORY OF KNOWLEDGE
had written this sentence at the end of the Sixth Book, just as he had
also, perhaps, forgotten how he used the word noesis there; or we
could say that what Plato is now refusing to do is to identify the
parts of ousia and of genesis which correspond to the parts of
noesis and of doxa or to explain what he means by saying that one
part of noesis is superior to another in aletheia just as episteme is
superior to dianola in sapheneia. Too much therefore must not be
made of this inconsistency. Still, such as it is, it exists so long as we
suppose that epi refers to the same relationship in both passages, and
this may make us wonder whether in fact it does, and encourage us to
try to settle the meaning of the earlier passage on its own merits
without reference to that of the later.
What then does Socrates mean in the second of our three passages,
that from the end of the Sixth Book? He says that as the states vary
in possession of sapheneia so the things with which they are correlated
vary in possession of aletheia; and two interpretations of this seem
quite natural. The first interpretation makes the preposition epi refer
to the relationship between a state of mind and its content. Eikasia
would be the state of mind of a man who has before his eyes an
image, and that which this state of mind is epi would be the "con-
jecture" (whether it is a cautious guess or a confident blunder) that
he comes to; pistis likewise would have as its object, or that which it
is epi, a report on something of which I have a clear view, dianoia a
piece of mathematics and noesis an apprehension of a form. A man
who is conjecturing about something is in an unclear cognitive rela-
tionship to it compared with a man who has the thing under his eyes,
and correspondingly a report based on conjecture is rough and
unreliable in comparison with a report based on a clear view. We
can therefore grade the states in terms of sapheneia and we can
correspondingly grade their correlated judgments in terms of a per-
fectly acceptable sense of aletheia. It is not quite so easy to see why
the judgment of a mathematician lacks aletheia in comparison with
the insight of a philosopher, but one feels that it is the sort of thing
that Plato might say. Since we have not been told that pistis and
eikasia together constitute doxa we have not got to grade doxa and
episteme in terms of sapheneia nor their correlates in terms of
aletheia. Nor have we to do this for the terms pistis and dianoia, for
the relationship between the segments c and b corresponding to
these two is not the same as that between d and c and between b and
a. (In fact from the data c and b must be equal). Therefore this
interpretation gives us both of the comparisons in terms of sapheneia
and in terms of aletheia that we have to provide.
The other natural interpretation perhaps deals more satisfactorily
with aletheia. According to this interpretation that which a state is
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THEORY OF KNOWLEDGE
epi is that to which the man in the state is directly related. The man
in a state ofelkasla is directly related to a shadow, the man in a state
ofpistis to a physical thing. Eikasia has less sapheneia th&npistis, not
because one cannot clearly perceive shadows (this would not be
true), but because one cannot clearly perceive things when one can
only see their shadows. 1 Shadows have less aletheia than things in the
sense that they have less genuineness or real existence. (There is an
obvious sense in which this is true enough). When we come to
dianoia the case is a little complicated, because Plato says three times
over (510 b 4; 510 e 2, 511 a 6) that the mathematician is directly
related to physical things. He "uses physical things as images" ; in
fact plates are to him what shadows are to the man who conjectures
from these the nature of their originals. But Plato also makes it
fairly clear that the mathematician ignores in his physical things
everything except their mathematical properties, their shapes and so
on. It seems possible therefore to say that what the mathematician is
directly related to is things like shapes, special mathematicians'
entities which are arrived at by abstraction from physical things.
These could be said to fall short in aletheia in comparison with forms
in roughly the same way in which shadows do so in comparison with
things; or at any rate Plato would presumably be willing to say this,
since it is the theme of the whole passage that the entities that
mathematicians "hypothesise" are as it were images of the forms.
This interpretation also, then, seems to deal satisfactorily with the
necessary gradings of the states and their objects, and it is not easy
to choose between the two. But whichever we choose it seems fairly
clear that Socrates is not here doing that which he refuses to do in his
recapitulation, for neither version provides us with something the
exposition of which would involve a Marathon.
On the whole it is probably best to accept a compromise interpre-
tation of this second passage. I argue elsewhere 2 that Plato tended to
accept a "photographic" conception of thought according to which
the distinction between the content of a thought and its subject-
matter becomes blurred. Probably therefore Plato did not ask him-
self too insistently whether, when he told us that the objects of
eikasia compared ill in point of aletheia with the objects ofpistts, he
meant that the content of an act of eikasia lacked reliability or that
the image that it was based on lacked genuineness. For content and
image, being as alike as sitter and portrait, would share each other's
bad qualities.
1 The fact that eikasia has less sapMneia than pistis makes it fairly clear that
Plato thinks of eikasia primarily as perceiving a thing through an image, and not
as being deluded by an image. For delusion lacks a!@theia rather than sapMneia.
2 See pp. 296 sqq.
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THEORY OF KNOWLEDGE
What then is It that Socrates refuses to do In his recapitulation ?
The probable answer is that he is refusing to be more precise than
he had been at the end of Book Six with regard to the relation
between the objects ofnogsis and ofdtanoia, and also conceivably that
he is refusing to say anything about the relation between the objects
ofpistis and elkasia in the later sense of these terms. For ontological
questions arise at any rate about the first pair. We have been told
that the objects upon which mathematical thought is intended lack
aletheia, and we want to ask, as we have been asking, what these
objects are, in what sense they are "objects", and what kind of
aletheia they lack. It is conceivable that we might want to ask similar
questions about the objects upon which the eikastic thought of the
vulgar is intended, the semblances of justice and so forth. Are the
objects of mathematics entities in the sense in which forms are
entities, or will it do to say that they are images of the forms which
have their existence only in the minds of mathematicians? But it
would not help Plato's exposition if he got involved in these ques-
tions. He wants to explain how we can use mathematics as a base
from which we can conduct our exploration of the rational principles
which are imaged in its concepts; and for this purpose the weaker
thesis will do. It does not matter for the sake of this explanation
whether the entities that the mathematicians hypothesise exist (or
"subsist") as real but low-grade members of the intelligible realm,
nor does it matter what such a question would mean. It is enough
that we know what the rules are which govern talk about triangles,
numbers and similar entities.
The main topic then which is dismissed in the third of our passages
is the topic of mathematika or "mathematicals", the intermediate
entities such as circles, non-physical like forms but plural like things,
in which, as Aristotle tells us, Plato believed, at any rate in later
years. Socrates is not going to tell us whether it is necessary to postu-
late these. It is wrong therefore to say that a belief in mathematical is
taught in the Republic. Indeed one is tempted to say that the whole
tendency of the argument is in the opposite direction from that which
leads to mathematicals. One is tempted to feel that Socrates is telling
us that nouns like "number" and "triangle" are not the names of
entities, and that we shall only suppose that they are if we get stuck
half-way along the path of abstraction which leads from ordered
things to the order which they exhibit. Geometers' objects are spatial,
and yet they lack the physical properties which things need in order
to occupy space; numbers are aggregates of units, but what is a unit
but the ghost of a pebble? Gross minds suppose that talk about
circles is talk about plates, talk about numbers talk about bundles
of matches. The mathematician has got so far as to forbid such
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THEORY OF KNOWLEDGE
grossness, but he has not gone to the logical conclusion and seen that
what he is really talking about is not things at all, whether coarse or
rarefied, but properties which can be embodied in things, principles
of order to which ordered things can conform. Mathematicians*
entities are images in the sense that they are figments which we create
in order to pursue a discipline at a midway level of abstraction. This
is an attractive line of interpretation, but it raises difficulties the chief
of which, perhaps, is to see how, having once pursued such a line of
thought, Plato could ever have relapsed back into a belief in mathe-
maticals. It is safest to say therefore that the Republic neither spon-
sors nor repudiates belief in the "real existence" of such entities, but
refuses to discuss their status.
The remaining question about our third passage is the question
what Socrates means when he says that noesis is concerned with ousia
and doxa with genesis, and that ousia is to genesis as noesis is to doxa.
The first part presumably means that abstract thought is concerned
with the intelligible principles which inform our thinking and under-
lie the world's order, and that no thought which is directly concerned
with what goes on in the world can rise above the level of doxa. I do
not believe that this is primarily intended to forbid us to call an
erroneous statement about justice a doxa, or to call an accurate piece
of empirical observation a piece ofepisteme, though Plato's language
doubtless allows us to deduce these vetoes. Plato is not thinking
about natives who know the way to Larisa nor about eye-witnesses
who saw the assault. He is still thinking primarily about people's
approaches to what are, logically speaking, theoretical questions
such as the nature of justice, and he primarily wants to tell us that in
so far as we achieve any success in understanding abstract principles
we do so by proceeding counter-inductively, and that in so far as our
conceptions are formed inductively they count as doxai, because they
are very indirect and inexplicit apprehensions, whether they are
respectable, as in pistis, or shoddy, as in eikasia. The second of
Socrates' points (that noesis is to doxa as ousia is to genesis) means I
suspect little more than that, for every respect in which the first
member of either pair is superior to the second, there is a corres-
ponding respect in which the same superiority holds within the other
pair. Thus the principles which constitute ousia are changeless
whereas the events which constitute genesis are changeable, and
similarly noSsis is stable while doxa must fluctuate. If we feel that we
must bring the notion of an image into the object side of the analogy,
we can add to this that genesis is an image of ousia in the sense that
the course of nature reflects the principles whose imposition on chaos
renders it nature.
There remains the first of our three passages, that from the begin-
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THEORY OF KNOWLEDGE
ning of Socrates' exposition of the Line. Socrates asks whether the
part of the line corresponding to the visible realm has been so sub-
divided, in terms of aletheia and the absence of aletheia, that as the
believable is to the knowable, so the semblance is to that which It
resembles. There seem to be two feasible interpretations of this.
Which we choose will depend on whether we take the believable and
the knowable to be the same as the visible kind and realm and the
intelligible respectively. If we do make this identification we shall
make Socrates ask the following: "I have divided a line into two
parts; I have assigned one to the visible kind, one to the intelligible;
and I have sub-divided the parts in the same ratio. This means that
the same relation must hold between the two minor parts of either
major part as holds between the two major parts. Now I have
assigned shadows and things respectively to the two minor parts
belonging to the major part which represents the visible kind. Do
you agree that this yields a correct doctrinal interpretation? Do you
agree, that is, that shadows stand to things 1 as the visible kind stands
to the intelligible?"
This interpretation is not identical with that which I earlier said
was untenable. That view (which no one perhaps would explicitly
take, but some seem to assume) says that the entities which Socrates
mentions constitute the whole of the visible kind and that the states
which correspond to them constitute the whole of doxa. The present
view does not say that reflections, shadows, etc., along with animals,
plants and artefacts together constitute the whole of the visible
world, 2 nor that seeing them is the whole of doxa. It says rather that
these two sets of things are the representatives of the visible world in
the simile. In the visible world certain entities (which do not make up
the whole of it, for mountains for example have no place in Socrates'
list) are so related to each other that their relationship, and that of the
cognitive states correlated with them, can be used to illustrate
certain other relationships. On the interpretation which we are con-
sidering the major part which Socrates refers to as "belonging to the
visible" stands for the visible world as a whole, but the values of its
parts belong to the visible world in the sense that they are drawn
from it, not in the sense that they together compose the whole of it,
1 It might be thought that It ought to be "... that eikasia stands topistis . . ."
rather than ". . . that shadows stand to things . . .". The ground for this would be
that Socrates has allotted values to the minor parts in terms of sapMneia, the
relation which holds between mental states. However the values allotted are in
fact objects and not mental states, and I think that we have now crossed to the
object-side. We are talking about relationships in terms ofal&heia.
2 It is pretty clear that "the visible kind" means the visible or physical world.
In 509 d 3 Socrates implies that ouranos or "the heavens" would have done as the
name of the visible kind.
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THEORY OF KNOWLEDGE
This is superficially awkward because the two sub-segments of line
do of course compose the whole of the segment, and it is a little diffi-
cult to use "a + b" as the name of a class of which a and b are not the
only sub-classes. But it can reasonably be said that this is no more
than the sort of difficulty which we run into when we try to make
graphical illustrations of philosophical points, and that nothing
should be hung on it. Socrates' question then, is whether it is true
that the image/thing relationship holds, as his formula makes it
hold, between the visible realm and the intelligible; is the visible
realm an image of the intelligible?
If this interpretation is correct, Glaucon's affirmative answer to
this question presumably carries the same message as Socrates* later
statement, in the third of our three passages, that ousia stands to
genesis as noesis stands to doxa. Such as they are, there are two
difficulties in the way of accepting this interpretation. It is not easy
to see why Socrates changes from "the visible kind*' to "the believ-
able", and one does not feel quite confident that at this stage in the
discussion Plato could have expected his readers to understand "the
believable" to mean "the world about which we can only have doxa"
and to identify this with the visible world. Secondly on this interpre-
tation Socrates* question introduces a complication which is un-
necessary, and which, one would have thought, would have required
more elaboration if it was to be mentioned at all It does not seem to
be essential to Socrates* argument at this point to say that the
physical world is an image of the forms, and if this is to be said it
would come more intelligibly in the place where it probably does
come, namely at the end of the whole passage.
Some might prefer, for these reasons, the second interpretation
that does not so completely identify "the visible kind and place" and
"the believable". According to this view "the believable" means
"that which we can believe", "the knowable" means "that which we
can know". The former will be the class of opinions, bits of informa-
tion and so forth which count as doxa, the latter the intelligible
principles. On this interpretation the point will be as follows.
Socrates has chosen certain sets of entities out of the visible world on
the principle that the cognitive state of a man confronted with one
set is less clear than that of a man confronted with the other. What
he wants to know is whether he has chosen these entities in such a
way that the relationship between them in terms of their aUtheia is
the same as that between that which a man has in his mind in a state
of doxa and that which he apprehends in a state of gndsis; or, in
other words, is a doxa-version of, say, justice, an image of justice
itself?
This interpretation makes superiority in point of aUtheta hold
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between the contents of mental states. It would therefore naturally
go with the interpretation of the second of our three passages (that
from the concluding lines of Book Six) which does the same. The
advantages of this interpretation of the passage we are now consider-
ing are that it does not require that we should understand to doxaston
to mean "the physical world", and that it does not introduce an
unnecessary complication. For the point that is now made is of some
small assistance to the future development of the argument, in that
we really need it if we are to see why the puppets in the Cave are
puppets; but more importantly it ties the present argument on to the
discussion ofdoxa and epistemew, Book Five. Glaucon is being asked
on this view whether being in a condition ofdoxa stands to being in a
condition of episteme in the same way in which being in a state of
eikasia stands to being in a state of pistis; and it is apposite that
Socrates should elicit that this is so before going on to say that the
same relation also holds between dianoia and noesis. However, this
interpretation has two disadvantages. One is that it is perhaps rather
difficult to keep apart the pair: to doxaston and to gnoston, and the
other pair: the visible kind and the intelligible kind, which Glaucon
has just been told to bear in mind. (This of course answers the point
that the reader could hardly be expected to identify to doxaston with
the physical world. The point and the answer seem to me about
equally valid). The second disadvantage is that if we take this
interpretation we deprive Socrates of a chance of explaining why he
has taken one line and divided it into two major parts in the same
proportion in which he has also sub-divided the latter. The reason
will emerge with the shift in the meaning of eikasia and pistis after
the Cave, but it has not emerged yet. For on this interpretation there
is no compelling reason why we should take the relationship between
the two major parts as a symbol of the relationship between doxa
and gndsis. We only get that if we somehow implicate the first of the
major parts with doxa, either by identifying eikasia and pistis with
doxa, or by identifying the visible kind to which shadows and their
originals belong with to doxaston. However it is not difficult to
provide a tolerable answer to this point if we say that the reader will
obviously remember that doxa is bound up with reliance on the
senses and will therefore associate with doxa the major part which
has to do with the senses. The first major part will represent doxa not
in the sense that the two mental states which are on it together com-
pose doxa, nor in the sense that to doxaston is the nickname of the
physical world to which the entities located on it belong, but in the
looser sense that there is an intimate connection between doxa and
relying on one's eyes.
To the question which of these interpretations is right, as to some
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of the other questions which I have mentioned, I do not intend to
try to say which is the right answer. Indeed I think that it might be
wrong in principle to do so. For to do that would be to try to force
from Plato answers to questions which perhaps he had not formu-
lated. Our perplexities take the form of asking: Is this a doctrine
about levels of thought only, or does it also involve a grading of
entities ? In my judgment Plato was not unaware of this point. In
refusing to discuss the inter-relations of the objects of the four
mental states in our third passage he means more, I suspect, than
that he does not intend to get embroiled in the topic of mathe-
maticals. He is showing some awareness of the fact that he has not
given an explicit account of the metaphysical doctrine underlying
the things that he has said; and this, so far as it goes, points in
favour of preferring wherever possible a plain epistemological inter-
pretation, without ontological commitment, of the texts that we
have been examining.
It is time to ask what contribution this whole passage makes to the
epistemology of the Republic. The answer seems to be that what we
get is rather little in comparison with the trouble which it takes to get
it. We learn, from these two books, of the cosmological presupposi-
tion which underlies all Plato's epistemology. This is that the forms
or eternal counterparts of reason are in some way the originals of the
principles which inform our thinking, and also of the order and
distinctness which characterise the physical world, and that it is the
business of philosophy to achieve or "recover" an explicit under-
standing of these principles of order. We learn also that mathematics
has a special part to play in this process, for the reason that the
entities which mathematicians study by abstracting from physical
things all but their spatial and quantitative features are peculiarly
clear images of the forms. Apart from this we can extract from this
passage more clearly than from some of Plato's other writings the
view that the physical world is something of which we cannot have
epist$me. It is of course possible to write this off to a considerable
extent. We can say that what is indisputable is that Plato correlates
doxa with u the world revealed by sight*' and that the world revealed
by sight is not identical with the physical world but only with the
view of the physical world which we get if we look at it but refrain
from thinking about it. "Sight's world", so to speak, can be con-
strued as logically similar to "Sartre's world" or "Proust's world"
not a special world but a special account of it. We can say that Plato
thinks it harmless to hypostatise "sight's world" in this way both
because it is anyhow an intelligible way of talking, and also because
the language proper to the photographic conception of thought
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THEORY OF KNOWLEDGE
happens to have become habitual with him. I have some sympathy
with this line of interpretation and believe that we must rely on it to
some extent when we are wondering how Plato managed to recon-
cile the view that the empirical world is a sphere of doxa with the
view that a rider can know what a bridle ought to be like or an eye-
witness know what the accused did. But I am afraid that we should
be relying on it too far if we said that Plato's thoughts on this topic
were perfectly clear and that it is only his language which is, to us, a
little confusing. He used language appropriate to the photographic
conception of thought not because it had, as it happens, become
congenial to him but because he was not innocent of that conception.
(iii) Knowledge and belief in Republic 10
There are three triads in the tenth book, a triad of makers and a
triad of skills. The triad of makers (596-8) consists of: God who
makes the form of an object (e.g. a bed); the craftsman, who makes
the object, "looking towards the form" ; and the artist who makes an
image of the object. The triad of skills (600-2) consists of: The skill
which consists in using an object; the skill which consists in making
it; and the skill which consists in imitating it. The man who uses an
object has knowledge of its "beauty and Tightness", the man who
makes it acquires right assurance on this point from consulting him,
and the artist is only concerned with what passes for beauty and
Tightness among the vulgar. In a rather similar passage in the
Cratylus (389) the craftsman is said to make objects "looking to-
wards the form", and here the form of the object in question is
identified with "that which is naturally fitted to do the work of the
object". Presumably therefore the form of an X which God creates is
that which an X ought to be like; or the form, we might say, is the
function and the demands which this makes upon whatever is to ful-
fil the function. But this of course is much the same as the "beauty
and Tightness" of an X. Accordingly in this passage we have a some-
what odd situation. Knowledge (the knowledge which e.g. a horse-
man has about bits) is indeed knowledge of a form, but at the same
time it is knowledge of an eminently practical kind, knowledge of the
physical world.
Otherwise the passage is straightforward enough. The subject in
question being: what bits ought to be like, the user, who is directly
acquainted with this, has knowledge. The maker, who is directly
acquainted, not with this but with a representative of it, namely the
user's instructions, has no more than belief. This is familiar enough.
The interest of the passage lies in the licence which it gives us to
evade what appears at first sight to be the plain sense of passages
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THEORY OF KNOWLEDGE
which seem to tell us that knowledge is of the forms and not of the
physical world. For this passage suggests that these are not exclusive
alternatives. It favours indeed something like a view which I explored
earlier and abandoned, 1 namely the view that although we cannot
know things we can know facts about things. That, as we saw before,
is to go too far; but it seems that it is at any rate an over-simplifica-
tion to say that we can divide the world into the two classes of "that
which does not change and can be known" and "that which changes
and cannot be known", with general terms going in the first class
and physical things in the second. For this passage makes it clear
that we can know what bits and shuttles ought to be like, an achieve-
ment which must involve some understanding of the physical world;
and at the same time it is obvious that bits and shuttles themselves
are subject to change. How then are we to classify them? Certainly
as objects which change; but it seems difficult to classify them as
objects which also cannot be known if at least one very important
fact about them, namely what they ought to be like, can be known.
It would seem to follow that we cannot infer from the premise that
bits are subject to change to the conclusion that bits cannot be
known. If we are to talk of "knowing bits" at all, this language could
surely only refer to such achievements as understanding what they
are for, knowing what they ought to be like, and so forth. But these,
apparently, are things which we can know, despite the changeable-
ness of the entities which such knowledge is about.
But of course this passage says nothing about changeableness and
changelessness ; it proceeds along the other road and takes for
granted that direct apprehension is knowledge. It is possible however
that it is easier to take this for granted in a case, like the present,
where what is directly apprehended is something functional. The
reason for this we have already sketched. Essentially the point is that
whatever is knowable must be capable of being absorbed by minds
without remainder. Physical things in their concrete existence are not
so capable ; that anything should be subject to the physical conditions
of change and decay is something which intelligence has to accept as
a brute fact and cannot absorb as something intelligible. Order and
purpose are essentially the concerns of mind; the orderliness and
purposefulness of physical things are therefore absorbable and
knowable, their brute physical existence is not. Along this line of
thought a good deal could be known about the physical world.
However this may be, the present passage at least shows that the
Republic does not single-mindedly support the view that there is no
knowledge of the physical world; for here is a place where the
epfsteme/doxa distinction is drawn, and not drawn in that place.
1 See above, pp. 38-9.
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G. Knowledge and belief in the Theaetetus
Theoretically the second half of the Theaetetus, which discusses
episteme in relation to doxa, ends in failure. The attempt to define
knowledge fails. It had been shown at the end of the first half that
knowledge is to be looked for in the sphere of "properly mental
activity about realities; and this is doxa" (187 a; see above, p. 26).
Yet though knowledge is to be looked for in the sphere of doxa, it is
quickly shown that it is not identical with the latter (201), and the
attempt, which occupies the rest of the dialogue, to identify it with
doxa plus something else fails.
There are various possible views about this negative result. The
simplest is that Plato is as puzzled as he represents Socrates and
Theaetetus as being. Another view holds that he does not allow his
characters to make a serious attempt at defining knowledge. Some
who would agree with this would go on to say that the reason why he
does not is that it ought to stare us in the face that episteme is on a
different level from doxa and cannot possibly be defined as doxa plus
something else; and that this is what Plato is hinting at. Others, who
would agree that he does not make a serious attempt to define know-
ledge, would hold that the reason is not as simple as that, but that
Plato has various doubts and reservations concerning his earlier
accounts of knowledge, that he is not yet in a position to offer a
better account, but that he tries out some of the ideas which are
troubling him. This would incidentally account for the oddly dis-
connected structure of this part of the dialogue.
On the whole the third view seems to me the nearest to the truth,
I would agree that Plato does not make a serious attempt (and does
not therefore fail significantly) to define knowledge as doxa plus
something else. The reason for this is as follows. The formula for
which Socrates and Theaetetus try to find an acceptable meaning is :
Knowledge is right belief plus logos. Now the Meno had said that
belief could be turned into knowledge by logismos aitids, by working
out the explanation. Knowledge is the understanding of what belief
accepts as a brute fact. The phrase logismos aitids is of course
etymologically connected with the word logos, and the notion of
rational insight is commonly part of the meaning of the latter. Yet
when Socrates and Theaetetus try to find senses of logos such that
knowledge may be right belief plus logos they almost ostentatiously
ignore this one. It would be very difficult for any reader who had read
the Meno not to ask himself: "Why do they not try logismos aitidsT*
A possible answer to this question is that given by the second of
the three explanations of the failure to define knowledge which I
quoted, namely that we are meant to recall that knowledge and
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THEORY OF KNOWLEDGE
belief are on different levels, so that the former could not possibly
amount to the latter with the addition of anything. Plato had indeed
said in the Meno, it might be argued, that beliefs can be turned into
knowledge by logismos aitlds\ but even this formula does not imply
that a piece of knowledge is a belief plus something else it merely
lays down how a man may be lifted from the one level to the other.
In the meantime however Plato had come to see that knowledge and
belief result from two quite opposite approaches. Only a philosopher
is potentially capable of knowing anything, and the philosopher
explicitly repudiates the inductive approach which leads to the
formation of beliefs. Therefore the suggestion of Theaetetus that a
man who has acquired a belief can turn it into knowledge by adding
something to it is radically wrong.
This is true enough, but it does not explain the way the Theaetetus
goes. For unless Plato lets Theaetetus try out the interpretation of
logos in terms of logismos altias he cannot expect the reader to con-
clude that the reason why the attempt at defining knowledge as true
belief plus logos has failed is that it could not possibly have suc-
ceeded; for one is bound to feel that its only chance of success has
been wantonly withheld. Furthermore this explanation presupposes
that epistem$ and doxa are being used in the Theaetetus in a strictly
technical sense, derived from the fifth book of the Republic; and it is
far from clear that this is so.
If these arguments are sound one falls back on cither of two ex-
planations of the failure to define knowledge in the Theaetetus. The
first is that Plato is not seriously trying. He has made clear what he
thinks knowledge to be elsewhere; the bulk of the Theaetetus is con-
cerned with the relation of sensation to judgment, and he fills in the
next twenty odd pages by stringing together some thoughts on other
topics more or less connected with his theme. This is not an impos-
sible explanation; but it may seem to do less than justice to the bear-
ing of some of these thoughts. So one comes eventually to the
explanation already mentioned, that Plato has come to have various
more or less specific doubts and reservations about his earlier
account of knowledge. (I mention these two explanations together
because I think they are both tenable, and each blunts the edge of the
other; it is only if the second can establish itself convincingly that the
other is ruled out).
What would these doubts and reservations be? I suggest a rather
mixed bag.
Firstly I have argued that Plato has hitherto conceived of know-
ledge as primarily knowing S and only secondarily knowing that S is
P. The ideal condition is to know (say) triangularity; when that con-
dition is achieved everything that is true about triangularity is
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THEORY OF KNOWLEDGE
synoptically seen. The man therefore who knows a few facts about
triangles has doxa only and not episteme. But now, I suggest, Plato
may have found reason to doubt this. He may have come to feel that
it is necessary to distinguish knowing S (connattre) from knowing
that S is P (savoir\ and that it is an abuse of language to withhold
the title of knowledge from the latter.
Secondly in the Republic it was implied that to know S implies
being able to give a logos of it; and he may have come to feel that he
had made use of the phrase "to be able to give a logos" without
enough hold on its meaning.
Thirdly it may well have struck him that there was something
positively wrong with the notion that to know is to be able to give a
logos, even in the sense he primarily intended. Broadly speaking, I
think, the man who can give a logos of, say, evenness or justice in the
Republic is the man who can "say what the thing in question is".
This means providing a Socratic definition, or resolving the complex
into its elements. It also means (I think) achieving this in such a way
that the logos or account which is offered logon echei or makes sense.
This means both that there is nothing opaque in the definition, and
also that it is impossible to pick holes in it, to show that it leads to
contradictions. There are two troubles here, of either or both of
which Plato may have become conscious. The one (and for myself I
see less evidence that he was troubled by this one) is that it is pre-
sumably not possible to go on resolving complexes into their elements
indefinitely; in the end one must presumably get to elements which
cannot be further analysed. The other trouble, which I think Plato
may have felt, is that it may not, in an indefinite number of cases, be
possible to give a logos which holds water. Parmenides and his
followers had attempted to show that one cannot make sense of any
but a wildly paradoxical account of the world. There is evidence that
Plato became increasingly aware in his later years of the strength of
the Parmenidean criticism of common assumptions, and it is possible
that he was driven by this, not to accept Parmenides' views, but to a
position which held that nothing is incontrovertible and that the
perception of the truth does not therefore depend on argument alone.
To see whether there is any value in these suggestions we must look
at the text of the second part of the Theaetetus. I shall give a rapid
summary of the course of the argument, and then return to comment
upon its significant features.
Summary o/Theaetetus 187-end
A, 1. It having been agreed that knowledge is to be looked for in the
sphere of mental judgment or doxa., Theaetetus suggests that it is true
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THEORY OF KNOWLEDGE
doxa. Socrates does not immediately dispute this, but questions the
division of judgments into true and false. His initial and fundamental
argument against the possibility of false judgment is that you cannot
believe anything about something which you do not know, while you
cannot believe something false about something which you do know.
This is expressed in the form that you cannot confuse two known
terms, nor two unknown terms, nor a known with an unknown
(187-8).
2. This is then developed by briefly advancing the Parmenidean-
Protagorean arguments against the possibility of false belief, and
meetingthemroughlyinthe way whichisto be developed in the Sophist.
The argument is: granted that he who believes what is-not believes
something false, how can one believe what is-not ? For, just as, to see,
one must see something, so, to believe, one must believe something;
and what is-not is nothing. Therefore false belief cannot be believing
what is-not, but believing something other than what is the case ; it
must consist in transposing two realities and accepting the wrong
one (188-9).
3. Against this Socrates develops a rather obscure argument to the
effect that one must entertain at least one of the two transposed
terms and believe something about both of them (viz. about each
that it is the other). But in that case one must be believing something
of whose falsity one is plainly aware as e.g. that the odd is even or
that the cow is a horse. But a man cannot believe anything of the
kind (189-91). (This argument seems to be a development of that in
the first paragraph if S is unknown to me I cannot believe anything
about it, but if it is known I cannot falsely believe that it is P),
4. The argument so far is that false belief can only occur if two
things are transposed in the mind, and that they cannot be trans-
posed. Yet false belief plainly occurs and Socrates proceeds to explain
it by invoking memory. This he does by the image of a wax tablet.
Every experience or thought that we have makes an impression on
the wax, and some of these impressions persist. To judge that this is
Jones is to judge that this present visual impression corresponds to
the memory impression of Jones. But suppose that I either have a
bad view of the man before me or a hazy memory of Jones, then I can
clearly make a mistake. Error can therefore occur through the faulty
fitting of sense-impressions to memory-impressions (191-6),
5. But this does not cope with errors, such as thinking that 7+5
= 11, which do not involve a present sense-impression. To cope with
these within the terms of the rubric that one cannot believe anything,
true or false, about something that one does not know, Socrates
distinguishes between having acquired knowledge, and currently
having it. If I have acquired knowledge of S then I can believe some-
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THEORY OF KNOWLEDGE
thing about it; but in order to be right I must recapture my know-
ledge, and I may make a mistake here and recapture a piece of
ignorance, so to say, instead of a piece of knowledge. This Socrates
expresses in terms of an aviary; everything that I have learnt is a
bird that I have put in my cage; when I want to use something I have
learnt I have to catch it, and I may catch the wrong bird (196-9).
6. But this solution has the paradoxical result that I fail to recog-
nise my bits of knowledge; and how can I be said to know some-
thing if I cannot recognise it? If I mistake a bit of ignorance for a bit
of knowledge, then I am confusing something which I know with
something that I do not know; and this was agreed (A.I) to be
incomprehensible. No explanation of false belief has been found.
B. 1. Socrates then says that they ought to have decided what
knowledge is before they raised the question of false beliefs. (Why?
This rather suggests that to believe is to be relatively successful in the
enterprise complete success in which is knowledge. One should see
what one is trying to do before asking what happens when one fails)
(199-200).
2. It is then shown that knowledge cannot be true belief; for an
advocate can quickly convince a jury of the truth of facts of which
only an eye-witness could have knowledge (200-1),
C. 1. Theaetetus then suggests that knowledge is true belief plus
logos, and mentions a theory that he has heard to the effect that
things which have a logos can be known (201).
2. Socrates' dream. Socrates then suggests that this is the same as
a theory which he has heard in a dream (i.e. it is a post-Socratic
theory and Plato's historical conscience is pricking him). The theory
is to the effect that there are "letters" and "syllables", or elements
and complexes, and that there cannot be a logos (here meaning
"statement") of an element. For a statement is a complex of names,
and mentions (legei) the things whose names it contains. Therefore
a single element cannot have a statement or logos belonging to it.
Elements can be named, but nothing can be said about them and they
cannot be known. Complexes can be both stated and known (201-2).
3. Socrates commends this theory for tying up knowledge with
logos and with right belief, but questions the possibility of making
complexes knowable and elements unknowable (202-3).
4. Of this possibility he gives a neat refutation. Either the "syl-
lable" is the sum of its "letters", in which case if it is knowable they
are also; or the "syllable" is something unitary which results from
the combination of the "letters", in which case, if they are unknow-
able because they are unitary, then it by parity of reasoning must be
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THEORY OF KNOWLEDGE
unknowable also. Elements and complexes can be both knowable or
both unknowable, but the other two combinations are impossible
(203-6).
D. Socrates then points out that logos is ambiguous and offers three
meanings which it might bear in "Knowledge is right belief plus
logos''' (a formula which he had tentatively supported in C.3). These
are:
1. "Plus logos" means that the believer can express his belief. But
belief is silent speech and therefore every belief can be expressed.
"Plus logos" would therefore add nothing (206).
2. "Plus logos" means that the believer can specify the elements of
the thing. But I may correctly specify the elements of something
(e.g. spell a syllable right) by accident and without knowledge, as
may be evinced by my getting it wrong on another occasion. (207-8.
Notice that "dispositionally to be able to specify the elements" would
meet this objection).
3. "Plus logos" means that I can identify the thing its logos is its
differentia. Thus the believer without logos may be able to put a
thing into its right class (he may be right in thinking that Theaetetus
is snub-nosed) but unable to pick it out within its class (to tell
Theaetetus from Socrates). But unless I can identify S I cannot
believe anything about it (for the belief is not about it). Therefore
"plus logos" will again add nothing to "right belief" unless it is
thought that one must have not right belief, but knowledge, about
the differentia. But in that case "To know X is to have right belief
plus logos" becomes a circular definition: "To know X is to have
right belief about it, and to know how it differs from everything
else."
E. At this point Socrates concludes the dialogue by telling Theae-
tetus that it is good for one to have one's bad ideas refuted. It will
improve any subsequent ideas one may have, and if it renders one
sterile for the future, at least it will make one less of a bore.
Discussion of the above summary of Theaetetus 187-end
To see the possible significance of this we shall isolate certain impor-
tant ideas which are canvassed in it.
Reference and identification. The idea of reference is pervasive.
Throughout, the point is made that to state one must refer, and in
D.3 the point is made that to refer to X one must be able to identify
it. The topic of referring can of course be treated as a logical topic,
and Plato's discussion of it in that manner is reserved for another
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THEORY OF KNOWLEDGE
dialogue (the Sophist officially a resumption of the conversation in
the Theaetetus). Here the notion of reference makes itself felt not
explicitly, but in terms of the impossibility of believing anything
about an unknown.
Kinds of knowledge. To make a statement about something, I must
know enough about it to be able to use an expression to refer to it;
to make a mistake about it, I must know less than everything about
it. If the expression "Nehru" means nothing to me (if I am in this
sense totally unacquainted with Mr. Nehru) I cannot wrongly
believe him to be President of the United States; and if I know all
about him I cannot do so either. To believe wrongly that Mr. Nehru
is the American President I must have some correct information
about him, enough to know whose name "Nehru" is, but not enough
to guard me from error. A distinction between being acquainted (in
this sense) with X and being familiar with X would clear away some
of the problems in A.I, A.3, A.5 and D.3, and it is probably fair to
say that Plato is working towards it. The distinction that he actually
introduces in A.5 is the less helpful one between having learnt about
and currently knowing* To see that this is a less helpful distinction
consider the child who says that 7+5=11. One would hesitate to
allow that the child (in Plato's language) "knew 7 and 5" if the child
could not for example count groups of five and seven objects; and a
child in this condition who said "Seven and five make eleven" would
be parrotting and not making a mistake. But a child who satisfies
the tests for "knowing 7 and 5" may still think their sum 11 ; for it
would not be reasonable to include among the tests for the intelli-
gent use of a numerical expression the ability to state correctly the
sum of the number for which it stands and any other number.
(Consider the false belief that 931+127=1,066). Therefore the child
who "knows 7 and 5" may never have known that their sum is 12,
and we do not (as Plato implies) have to choose between the alterna-
tives: that either the child has never known 7 and 5 or he cannot
correctly recapture the knowledge that their sum is 12. It would seem
then that consciousness of the problem of referring has made Plato
aware of the necessity of some distinction within the field of know-
ledge, but he has not got it right (or, if he has, he does not tell us, but
offers us another and shows that it does not work).
Propositions. The idea of a proposition or statement is involved at
various points. It is clearly involved in the passage describing
Socrates' dream (C.2), the discussion of which I shall reserve for the
moment. It is also involved in the demonstration that we cannot
transpose two terms (A.3). The suggestion is that when we make a
mistake we put one thing in the place of another, and Socrates
argues that we cannot do this, because to do this would be to say
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THEORY OF KNOWLEDGE
something like "the odd Is even" and this no one (who knows what
the words mean) ever does. But this of course is wrong. When i
believe that the product of nine and eleven is an even number I do
not say that the odd is even. I say o/something (which is in fact odd)
that it is even. Since the product of nine and eleven is in fact an odd
number there is a sense in which I am committed to believing that
a certain odd number is even, but not in any paradoxical way. For I
refer to this number by using the description "the product of nine
and eleven", and not (for example) the description "the odd number
between 98 and 100". Or, to take a simpler example, when I falsely
believe that Jones has a moustache, I believe of something clean-
shaven that it has a moustache; I am not in the impossible situation
of believing that something clean-shaven has a moustache.
In other words we need three terms and Socrates has only given us
two. The two terms that are transposed are predicates, and we are
able to pick the wrong one because we are not predicating them of
each other but of a third term, the subject. When Socrates goes on to
meet his own difficulties by introducing the image of wax-tablets
(A.4) he implicitly introduces the notion of the subject. For the situa-
tion he is envisaging is something like this: I see a man across the
road. He is in fact Jones, the Labour agent, but I do not know Jones
well (or not at all), and I do not see this man clearly. Accordingly I
take him for Smith, the Conservative candidate, whom I have seen
but do not remember perfectly. What I say is: "That man is
Smith." Here we need three terms the man I see, Jones and Smith;
and I make the mistake by identifying the first with the third instead
of with the second. (It is of course more clearly put in the formal
mode. There are three descriptions, "that man", "Jones" and
"Smith" ; and I wrongly think that the first and the third apply in
this context to the same object).
In this way Socrates implicitly introduces the notion of the subject,
but he cannot be said really to know what he is doing, for the same
point can be made to take care of "7+5=11" (A.5). For this error
can only be made to seem paradoxical if we assume either (as above)
that someone cannot be said to "know" seven, five and eleven unless
he knows that the last is the sum of the other two, or that the child
who says that 7+5=11 is saying that eleven is twelve. Plato could
therefore have dispensed with his aviary if he had been clear that the
correct analysis of the false belief situation is : A believes about S
(which is in fact not-P) that it is P. He was clear about this by the
time he wrote the Sophist, and I think that perhaps it was beginning
to make itself felt at this time. However I shall say some further
tentative things about the aviary in a moment.
Analysts. The idea of resolving complexes into their elements is of
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THEORY OF KNOWLEDGE
course canvassed in Socrates' dream (C.2) and also In the second of
the three meanings of logos (D.2). In the latter place we are apt to
think that Socrates is not being serious when lie suggests that to be
able to give the logos of a thing is to be able to give a list of its com-
ponents, and suggests that a man who can only itemise a thing into
"syllables" is at the level of doxa, a breakdown into "letters" being
necessary for episteme. But on reflection one remembers that In the
Republic knowledge was achieved by dialectic, and that perhaps one
thing that dialectic does (in the Republic) Is to analyse a complex
into its simple parts. In this light It Is Interesting to notice Socrates*
reaction to this sense of "plus logos' 9 . Of the other two senses (D.I
and D.3) he says that the phrase thus interpreted adds nothing. Of
this Interpretation he does not say that, but rather that one can
sometimes correctly perform the feat of analysing a thing into its
elements by accident, and therefore without knowledge. In other
words the ability to "give account" is not sufficient evidence of the
possession of knowledge. It is true that, as Socrates develops his
criticism of this sense, it could be met by arguing that the man who
always spells the syllable "The", or carries out some other itemising
performance, correctly can be said to know. But it Is possible to cap
this retort by arguing that a man might by correct instruction be able
regularly to list (say) the parts of an electric circuit without any
understanding of what he was describing; and that one would hesi-
tate to say of this man that he knew his subject. It is possible there-
fore that the criticism of this sense of "plus logos' 9 may represent
serious doubts about something taken for granted In the Republic.
Knowing Theaetetus and knowing what he is like. It is suggested in
the discussion of the last sense of "plus logos" (D.3) that one cannot
know something or someone (Theaetetus and the sun are examples
taken) unless one can uniquely identify It; and it is possible to think
that it is implied that knowing Theaetetus (in this sense) goes, and
must go, beyond the ability to describe him. True it is suggested that
if you can describe the sun as the brightest of the heavenly bodies,
then you have its logos (and hence ex hypothesi might be said to
know it); but when Socrates is discussing what it is to grasp what
distinguishes Theaetetus from other similar men he uses language
which might be developed into the view that knowledge must always
go beyond the ability to describe. For it is said that to describe
Theaetetus as snub-nosed is only to classify him (and, the implication
is, I can have correct belief of his proper classification without know-
ing him); and I cannot believe anything which is unambiguously
about him until "his particular snub-nosedness has left its own pri-
vate mark on my memory, and all his other components also"
(209 c 5-7). If this language is pressed it could be taken to mean: that
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THEORY OF KNOWLEDGE
nothing prepositional (whether you call it belief or knowledge) can
ever be strictly about X unless the person who makes the proposition
Is directly acquainted with X, and retains in his memory an impres-
sion of X which transcends his ability to describe it. For one can
only describe by attaching predicates, and however many predicates
I string together it is always logically possible that there is some-
thing else, Y, to which they apply equally well.
As this stands it raises the familiar point about reference (that in
order to refer to X I do not need to know it intimately), and unless
that point is made it is intolerably cramping, for it forbids us to say
that anything (for example) that I say can ever be about Julius
Caesar, since I do not know him in the required sense. Let us sup-
pose then that we are meant to make the point, and let us make it;
but the hint of an important position still remains. This is that I can-
not be said to know something unless I am directly acquainted with
it; that therefore, in default of this acquaintance, no truths that I may
utter about it can be said to proceed/rom knowledge*, and knowledge
goes beyond the ability to describe correctly, so that conversely the
ability to describe perfectly correctly is not evidence of knowledge.
Something like this is maintained in the Seventh Letter.
Before leaving this point we must notice that it could be argued
that no great significance should be attached to what Socrates says.
For what he says is said in terms of knowing a man, and is broadly
true of knowing a man, but could not possibly be true of (e.g.) know-
ing triangularity; and that Socrates has not noticed, or has forgotten,
that what applies to knowing men does not apply to "knowing uni-
versals". Indeed it is only Plato's unfortunate tendency to talk about
"knowing triangularity" and so on that has blinded him to the
narrow application of his point. This may be true; I have already
conceded that in looking for doctrinal hints in the second half of the
Theaetetus we may be looking for what is not there. But it could be
retorted that Socrates could hardly be allowed to take the case of
knowing a man as typical of knowledge in general by oversight; for
the oversight is too gross unless it proceeds from a general belief that
knowledge of universals can properly be conceived on the model of
direct acquaintance. (The ambiguities of the know-family might be
responsible for the belief; that is another question).
Socrates' dream. The question what, if any, hints are dropped in
the discussion of Socrates* dream (C.3 and 4) depends on the inter-
pretation of the dream-theory itself (C.2); and of this two opposite
views can be taken.
The dream-theory says that elements have no logos and are un-
knowable whereas complexes have a logos and are knowable.
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THEORY OF KNOWLEDGE
Socrates' refutation shows that you cannot make elements unknow-
able and complexes knowable, but it does not tell us how we are to
resist the arguments of the theory which purports to show that you
must. They can be resisted in two ways. "That X is an element implies
that it has no logos, and that X has no logos implies that it is unknow-
able" can be met by challenging either of the implications by
showing that an element can have a logos or by showing that a thing
which has no logos may yet be knowable. Plato does not tell us which
of these lines of attack we are to take, though he makes it clear that
we must take one of them. By making Socrates in C.3 commend the
theory for tying up knowledge and logos he perhaps indicates a
preference for the former; but if we want a clearer light we shall have
to see what the theory is.
One view holds that the theory is drawing our attention to the fact
that there must be some indefinables. Elsewhere (e.g. in the Sophist
and Statesman) Plato uses the metaphor of letters and syllables in a
certain way. 1 A complex and therefore comparatively specific uni-
versal (such as angling) is said to be a syllable, and the process of
defining it is said to be one of spelling it out into its letters. The
letters will each occur in numerous syllables (as anlmality occurs in
cathood, doghood, etc.) and will therefore be comparatively generic.
Now it seems reasonable to suppose that if the process of spelling
syllables into their letters is continued long enough it will eventually
come to a stop by producing some universals which are letters in an
absolute sense, which can no longer be analysed into their compon-
ents. Unity for example might be such a universal, existence another.
Now since defining is often spoken of as "giving a logos" it is natural
to suppose that when the theory speaks of elements which have no
logos what it has in mind is highly generic and indefinable universals.
Essentially therefore the theory is warning us that it will not always
be possible to "give account" of universals, for some of them must
be too simple to be defined.
It cannot be denied that the theory speaks of its elements as if they
were physical elements (they are said to be sensible 202 b 6); but of
course what applies to physical elements in so far as they are ele-
mentary will apply to any other elements that there may be. On this
view therefore the theory is stated in terms of physical elements, but
intended to apply to elementary universals such as unity. On this
view what Plato has against the theory would be its passage from the
legitimate claim that elements have no logos to the illegitimate claim
that they cannot be known. His view, on this interpretation, is that
knowledge does not always entail the ability to give a logos; that
some knowledge is "intuitive" and not "discursive".
1 See below, pp. 374-88, 41 1-16.
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THEORY OF KNOWLEDGE
This Interpretation is attractive at first sight, and it may be part
of what Plato intended. In refuting the theory by leading it into a
dilemma he of course avoided the necessity of declaring for or
against any particular criticism of the theory. The chief argument, to
my view, for this interpretation Is Plato's use of the letters and
syllables metaphor, which is elsewhere (and, on the whole, subse-
quently) used of universal. But I do not believe that this interpreta-
tion captures what he primarily meant.
On the other view the theory under attack Is essentially a confused
account of the nature of a proposition. What it holds Is as follows:
To know X entails to be able to make a statement about X. Since
every statement contains at least two terms, and is in fact the name of
the complex consisting of these two terms (e.g. "Man is mortal" Is
the name of the complex entity, man's mortality), no statement can
ever be the name of, and we can therefore never make a statement
about, a simple element. Therefore nothing can be said about
elements, and therefore they are unknowable.
But If this is what the theory holds, plainly it is uninstructed on the
subject of reference, or the a^ow^-relationship; and this as we have
seen was one of the topics in Plato's mind at this time. The theory
thinks of a proposition as a complex name of a complex situation,
even such a simple proposition as "X exists" or 'This is X". It is
from this that it infers that nothing can ever be said about an ele-
ment, and that elements can therefore only be named (see especially
202 a 6-8).
It might be thought that the theory as I have described it is too
silly to be seriously held and that this interpretation must be ruled
out on this score. This I think is a mistake. The theory is the natural
result of a tendency which certainly existed to regard the identity-
statement ("A is A") as the type of the true statement. For the only
informative Identity-statement that can be made is about a complex,
and consists of its analysis. "Social democracy is ... (a, b, c)" is the
"private logos' 9 (202 a 7) of social democracy, for it mentions nothing
but social democracy and its components (which add up to it). Given
the tacit assumption that all statements which are not identity-state-
ments are false, then it follows that true statements can only be made
about complexes if we neglect uninformative utterances such as
"Jones is Jones". (It is true that the theory talks about statements and
not about true statements, but of course "the logos of a given situa-
tion" means the true statement of it. Those who regarded statements
as complex names regarded false statements as "non-names" and
could not see how they could signify see Cratylus 429).
If this account of the theory is correct, as I think it Is, then in view
of what happens in the Sophist we might expect Plato to want to say
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THEORY OF KNOWLEDGE
that the theory has not shown that an element cannot have a logos.
To take the metaphor literally, when I say of the letter S that it is a
sibilant I am making a statement about a simple element. This is
something that we would expect Plato to want to say, and I think he
even hints at it by putting into Theaetetus' mouth a patently ridicu-
lous reason for saying that consonants have no logos (viz. that they
have no sound 203 b 5). But he may well have been still far from
clear on this point, and this may be why he avoided a direct attack on
the theory.
We cannot say, then, that the criticism of the dream-theory shows
that Plato was aware that the process of giving a logos would eventu-
ally have to stop when it came up against indefinables. Indeed if it did
show that, I think it would be unique in Plato's writings. Whether or
not Plato ought to have conceded that there are some indefinables, I
know of no place where he did so. I have argued and shall argue
again that there are places which suggest that he thought that the
ability to give a logos is not a sufficient condition of knowledge, but I
suspect that he always held that it is a necessary condition. This is
plainly the case in the Seventh Letter, which is the passage which
provides the proof texts for the view that the ability to give a logos is
not a sufficient condition. This we shall discuss in a moment. Mean-
while we shall have to say that the significance of Plato's criticism of
the dream-theory is uncertain, but that it probably shows once more
that he was already unhappy about the current logic of propositions.
One other interpretation of the dream-theory ought perhaps to be
mentioned, one that gives it a rather Lockeian flavour. This is that
the letters are, or include, "simple qualities" of a sensible kind, and
that the syllables are complexes of simple qualities; and that the
theory is that you can name a simple quality such as greenness, and
can also of course sense it, but cannot give a logos of it; giving a
logos is something which can only be done to a complex entity such
as a horse, and it consists in naming the simple qualities which con-
stitute the complex entity. I do not find this interpretation very con-
vincing. I doubt whether Plato could have expected the metaphor of
letters and syllables to be understood in this way; and this interpre-
tation does not seem to do sufficient justice to the point that a logos is
a complex of names corresponding to a complex of entities (202 b
2-5). In the statement (loc. cit.) that "a logos is essentially a complex
of names" I find it very difficult to resist the view that logos means
"proposition"; and indeed it is largely for this reason that I prefer
the interpretation which I mentioned second. 1
1 Socrates seems to bring forward considerations in favour of the theory
which he heard in his dream ("How could an element have a logos, and how
could that which has no logos be knowable?"), and at the same time he seems to
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THEORY OF KNOWLEDGE
Further reflections about the aviary. The passage about the aviary
(A 5 in the summary above) Is not at all easy to interpret. For one
thing it is not possible to be sure what is represented by the "birds"
(the pieces of knowledge which I have acquired in the past, and which
I am unsuccessfully trying to recapture in the present when I make a
mistake). Are the birds propositions, such as that 7 plus 5 equals 12,
or are they terms such as 12? A possible interpretation however is as
follows. The birds are neither terms nor propositions, but terms
thought of as identical with the true propositions in which they
figure. To be able to make a statement about 12, I must have this
bird in my aviary; that is to say I must at some time have learnt
about it. Now on the assumption that "to know 12" is to know it as
everything that it is (the sum of 7 and 5, the product of 4 and 3 and
so on) I must, if I am to be able to make statements about 12, have
known at some time that it is the sum of 7 and 5 ; and I must still have
this knowledge by me. Now if, when I need the sum of 7 and 5, 1 go
to recapture this knowledge, and lay my hand instead on 1 1, offering
that as the answer, I commit myself to the view that 11 is the sum of
7 and 5. This, as Theaetetus suggests, looks more like a bit of ignor-
ance than a bit of knowledge; so that perhaps we ought to say that
we have bits of ignorance in our heads as well as bits of knowledge.
But the fact remains that, whether we embroider the simile in this
way or not, the use of the simile to explain mistakes runs up against
the difficulty that I cannot really be said to know that it is 12 that is
the sum of 7 and 5 if I assert that this sum is 1 1. Therefore the (valid)
distinction between having acquired information and having it at
one's finger-tips does not help to explain mistakes. I cannot be said to
be recapturing knowledge that I still somehow retain if I fail to
notice that I have captured something else. My failure to notice that
what I have captured is something else shows that I no longer know
what I once knew, and that throws us back on to the other horn of
show that the theory leads to a dilemma which is fatal to it. Presumably therefore
there is something wrong either with the arguments which seem to support the
theory or with those which seem to refute it. My discussion has proceeded on the
assumption that there is something wrong with the arguments which seem to
support the theory, and I hope I have shown what this may be. It is, however,
possible that Plato wanted rather to create doubts in our minds as to the validity
of the dilemma with which Socrates seems to refute the theory. He might for
example have wanted us to argue that a syllable is more than the sum of its
letters (though Socrates does not seem to favour this possibility), but that this
does not make it a further letter; if the syllable is something unitary which re-
sults from the combination of the letters, we cannot reason that, because they
were unknowable because they were unitary, therefore it must be unknowable
also. I believe that Professor Ryle has an interpretation somewhat along these
lines, and it makes Plato make a very good point; but I am not convinced that it
was the one he intended to make.
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THEORY OF KNOWLEDGE
the dilemma. Since the man who says that the sum of 7 and 5 is 1 1
evidently no longer knows either 1 1 or the sum of 7 and 5, how can
anything that he says be intended to refer to either of these entities?
For I cannot refer to that of which I am ignorant.
If this is how we are supposed to understand the passage about the
aviary, what are we meant to learn from it? We have assumed that
the arguments in this part of the dialogue are meant to discredit, or
at least throw doubt on, whatever is responsible for Socrates* in-
ability to see how it is possible to make a mistake. We must ask
therefore what are the presuppositions which make it impossible for
him to get very far with thsprima fade valuable distinction between
having acquired knowledge and currently possessing it. There are
two which obviously suggest themselves. One is the subordination of
savoir to connaitre, the other the view that if I know something I
know it fully. If we subordinate the knowledge of facts to the know-
ledge of individuals we shall tend to think that knowing 12 (for
example) is primary and that knowing truths about 12 is somehow
contained in this. This will make us want to think that a man who
knows 12 will eo ipso know all the true propositions into which 12
enters. (Such an assumption would be more plausible, perhaps, in the
case of "knowing triangularity" than in the case of "knowing 12",
for it might seem that there is only a limited number of a priori truths
about triangles for acquaintance with triangularity to entail. That
perhaps may be the reason why Plato chose an arithmetical example,
by means of which to demonstrate that knowing X cannot be
thought to carry with it knowing all the true propositions, nor even
all the a priori true propositions, into which X enters. An arithmetical
example makes it very clear that there must be something wrong). If
we further suppose that I either know something or am ignorant of
it, and that when I know it the thing itself (in this case 12-as-the-sum-
of-7-and~5, -as-the-product-of-4-and-3, etc., etc.) is in my mind,
whereas when I am ignorant of it the thing is outside my mental
grasp altogether, and all its bag and baggage with it, then it will be
easy to see that either I must be infallible about any given matter, or
else I am unable to refer to it. For either the matter with all its rami-
fications is in my head or I am out of touch with it. 1
We can conjecture then that what creates Socrates* perplexities in
this passage is the two assumptions that what we know are always
terms (the true propositions about these terms being somehow con-
1 Compare Leibniz' doctrine that in a true proposition the predicate is contained
in the subject. This creates analogous difficulties; for if Peter is the sum of his
predicates, then it might be argued that a proposition which ascribes to Peter a
predicate which he does not in fact possess is not in fact a proposition about
Peter.
EPD E 119
THEORY OF KNOWLEDGE
tained in them), and that knowledge and ignorance are related as
black would be to white if there were no shades of grey in between.
We might suggest therefore either that Plato is himself perplexed
about the nature of mistakes of the kind which he discusses because
he is guilty of these assumptions, or of something like them; or else
that he is using Socrates' inability to account for mistakes on a picture
of knowledge which depends on these assumptions to hint that they
cannot be made. Or, between these two extremes, we might suggest
that the truth is that Plato sees the harm that the picture does without
being able to say precisely what is wrong with it.
It may be objected to this account, that Plato could not have
wanted, at this stage, to say that there was something wrong with
treating knowing fully and being totally unacquainted with as exhaus-
tive alternatives, since he had long ago put doxa in between these two
terms. But this is not perhaps so conclusive as it may seem. For on
the view that what we know is terms (entities such as 12, justice and
so on) the insertion of doxa between episteme and agnoia does not
tell us what to do with the principle : either I know X or I do not
at any rate if knowing is thought of as being in touch with. For when
I have a doxa (even a true one) about X, what I have in my mind is
not X, but a doxa of X, an entity between on and me on. In other
words, so long as knowing is thought of as grasping (the entities
grasped being terms) it is impossible to give a satisfactory account of
doxa as that which comes between knowledge and ignorance, for the
reason that the mental content of a doxa is not identical with the
object grasped in episteme. And that a satisfactory account of doxa
requires a re-examination of the nature of episteme is Socrates*
comment on this part of the argument. 1
On what may underlie the second half of the Theaetetus
Let us try to make sense of all this, and let us begin with a simple
point.
Plato was a declared enemy of formulas in philosophy, even if they
came from Socrates or himself. This hostility is re-stated in the last
section of the dialogue (E of my summary). It is very likely that
"knowledge differs from true belief by the presence of logos' 9 had
degenerated into a formula among his followers, and that a prime
purpose of the second half of the Theaetetus was to make trouble for
those who used the formula without knowing what they meant by
logos.
1 1 suspect that I have learnt a lot about this part of the Theaetetus from the
essays of pupils who have attended the lectures of Professor Ryle. How much of
this discussion I owe to him and how much he would repudiate with scorn I do
not know.
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THEORY OF KNOWLEDGE
But perhaps there is more to it than that. We have seen that Plato
was probably dissatisfied with the current prepositional logic, and
that he may have seen (dimly perhaps) that the correct analysis of the
false-belief situation is : A believes about S (which is in fact not-P)
that it is P. To see this is to see that we cannot cope with false belief
in terms of grasp of realities, for false belief is not well described as
grasp of a non-reality. But we saw in discussing Republic 5 that
Plato's vocabulary was modelled on the case of knowledge or true
belief, that is on the case which we can describe as grasp of a reality;
and we saw that his language about states inferior to knowledge was
for this reason awkward. The awkwardness was accepted there, we
thought, because of an instinctive feeling that the language used
about the inferior cases ought to parallel the language used about the
ideal case. Now suppose this feeling to persist, and suppose that
Plato is beginning to see that this language is intolerable in the case of
incomplete or erroneous grasp of facts, that in these cases the notion
of a proposition (of a that-clauso) has to be introduced. In this situa-
tion he might well feel that the notion of a proposition had to be
introduced into true-belief situations as well.
This would not of course necessarily entail anything about the
analysis of knowledge. But if it were combined with doubts about
whether it is reasonable to treat knowing that S is P as a consequence
of knowing S, it might lead to a feeling that there are two different
senses of "knowledge", one for each of these two. Such doubts might
easily have arisen, for example in connection with arithmetic. As we
have seen, if language about "knowing numbers" is adopted, it is
unplausible to say that Jones does not "know" 931 and 127 unless he
knows that their sum is 1058. It is indeed a consequence of what I
have to grasp in order that the expressions "931" and "127" should
have meaning for me that 931 + 127=1058, but I do not have to
know the consequences of everything that I know.
If doubts of this kind had led to the feeling that knowing S is to
be distinguished from knowing that S isP, further doubts might have
been excited. How much, for example, must be included in knowing
SI More perhaps than is needed in order to refer to S (tenuous
acquaintance is enough for this); less perhaps than would be needed
in order to be infallible about S. And if knowing S does not lead
automatically to knowing that S is P, what is the relation between
these two states? Doubts about points such as these might well have
led Plato to discuss the topics raised in the second part of the
Theaetetus.
But there is a further point connected with knowing S where S is a
universal If Plato had come to think that it is not always possible to
give a logos of every universal in such a way that the logos cannot be
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THEORY OF KNOWLEDGE
shown to give rise to contradictions, then he might have come to
have serious doubt about the precise role played in knowledge by the
ability to give a logos. Should we say that the ability is necessary, but
that a correct logos can sometimes be shown to give rise to contra-
dictions ? Should one hold to the view that a correct logos cannot lead
to contradictions and allow that of some universals a logos cannot be
given? Or what should one say? One way or another Plato might
have come to think that there is something in some sense "intuitive"
about the grasp of a universal
That there is some substance in these last suggestions will emerge I
hope from consideration of the Seventh Letter. The conclusion
meanwhile is that the failure of the Theaetetus to define knowledge
may be an indication of certain fairly specific doubts.
H. Knowledge and belief in the Seventh Letter
The passage runs from 341-4. The context is that Plato is protesting
against the alleged publication by Dionysius II of Syracuse of a
treatise expounding Platonism, and Plato is explaining why he has
never published such a treatise himself. To this end he insists that the
intellectual goal is a kind of insight which cannot be communicated
in speech or writing, but can only be brought about in the pupil by
long travail.
What Plato says is this. With respect to any reality (he takes the
circle as his example, but he insists that any other universal would do
as well), there are four things which are concerned with it, but which
must be distinguished from it, and from each other. Firstly there is
"knowledge and right belief and understanding (nous)*\ which exist
in minds and are not to be distinguished for the present purpose.
Then secondly there are the three things through which knowledge
has to be brought about, namely the word ("circle"), the logos or
definition ("the figure all points on whose boundary are equi-distant
from the centre"), and actual physical circles (whether diagrams,
plates or what-not).
What this means so far, I think, is that if a man knows the word
"circle", can give the correct definition of what it stands for, and can
recognise instances, then he must be said to have knowledge, right
belief or understanding of "the circle'* i.e. circularity. But only in a
sense. For Plato goes on to say that without these four (i.e. know-
ledge in this sense and its three components) you cannot achieve
true knowledge of the reality, 1 but that even with them you do not
necessarily achieve the knowledge that you seek. For what these four
1 He says that you cannot achieve the reality. See note at the end of this section,
p. 124.
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THEORY OF KNOWLEDGE
give you (i.e. what knowledge in the inferior sense gives you) is the
answer to the question: "What kind of thing is X?" whereas what
you want is the answer to the question: "What is X?" (343 c 1). To
know the word, to be able to define the thing and to recognise
instances of it is to have knowledge in an inferior sense, and this
knowledge is a necessary but not a sufficient condition of knowledge
in the fullest sense which enables you to grasp the thing.
Plato gives reasons for this. Physical instances are always "full of
the contrary nature" round things for example "touch the straight
at all points" (343 a 7). Words again lack fixity: "circle" could be
used to stand for squares or triangles. And definitions, being Con-
structed out of words, are tarred with the same brash.
To invoke the conventional nature of language at this point seems
to provide a very lame argument. However I daresay that better
arguments could be brought for the view that language cannot
infallibly communicate insight. But perhaps Plato's own arguments
are stronger than they seem, if we interpret them liberally. Because
language is conventional we have to rely in the end on ostensive
definition; we have to learn what "circle" means by reference to
circular objects or diagrams. But if these physical instances are
always "full of the contrary nature", then it is embarrassing to realise
that in the end we have to rely on them.
However good or bad Plato's reasons for saying that words,
definitions and instances cannot communicate insight, what follows
is of the greatest interest. He begins by telling us that whatever we
can say or point to can always be confuted by empirical evidence. He
goes on to say that a man who has not been trained to seek the truth,
but is content with any image of it that he can pick up, can very easily
be made to look a fool by anybody who can handle the four instru-
ments of knowledge that is who knows in the inferior sense "what
sort of thing" something, say a circle, is.
With the well-deserved humiliation of this man Plato seems (he is
too angry to be clear) to contrast the ill-deserved humiliation of
another, namely of the man who really knows in the full sense, and
who is called upon to expound what he knows. For even he has
nothing at his disposal but the four instruments of knowledge he
can only name the thing, give its definition, and point to instances of
it and these are essentially inadequate. This being so he too can
easily be made to seem a fool by anybody who is a skilful picker of
holes. Those who do not realise the inherent limitations of language
and of instances for showing what something is will feel that the
expositor's ignorance has been revealed. But this is a mistake. Words
and instances cannot communicate knowledge; it is only by a
laborious process of taking the pupil through and through these over
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THEORY OF KNOWLEDGE
and over again that knowledge can be brought about, and even then
only in a man who has an affinity to the subject.
This last point Plato develops briefly in terms of moral knowledge,
arguing that this can only come about in a man who has both mental
ability and also an affinity to the subject. For virtue and vice can
only be grasped together, and only together with what is true of
reality as a whole. To understand what is right and wrong, in other
words, is to understand the conditions of human life, and this can
only occur as part of an understanding of the universe as a whole.
This, he continues, can only be brought about by a long and labori-
ous process of "rubbing together" words, definitions and empirical
observations. This "rubbing together" must be accompanied by the
practice of co-operative refutation through the asking and answering
of questions. The end of all this is the sudden shining out of wisdom
and of understanding which strains to the limits of human power.
There is a great deal in all this (343 c-344 c). For our purposes
two things stand out. Firstly, although grasp of the truth has an
intellectual aspect, it is not purely intellectual; for the truth is one and
for certain parts of it at least the right spiritual outlook is required.
Secondly knowledge in the inferior sense cannot communicate
insight, and this is connected with the fact that however skilfully we
try to communicate the truth by language or the use of instances,
what we say or point to is always liable to empirical confutation.
(Note. The account in the Seventh Letter is made the more difficult
to follow by the fact that Plato in some places speaks of: the three
instruments of knowledge, knowledge, and fifthly the thing known;
cp. 342 a 8. Elsewhere however cp. 343 c 1 or d 1-2 he speaks of
the first four of these in a slighting manner and treats the fifth term
as if it were not the thing known but the knowing of it. On the whole
he uses the words phronesis and nous for this ambiguous fifth item. I
have tried to streamline the account by distinguishing "knowledge
in the inferior sense", this being the fourth item, and "true know-
ledge*', this being the fifth).
The passage as a whole seems consonant with passages in Plato's
earlier writings. 1 It is consonant for example with the doctrine of the
Republic that something dramatic, of universal significance, will
happen when we learn what goodness is. It is consonant also with the
passage in the Phaedo (99 e-100 a) where Socrates says that the
accounts we give of things are as much reflections of realities as are
physical instances. Until the goal is reached the forms are only
1 But the manner of argument seems to me very reminiscent of that of the
philosophical passages of the Laws.
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THEORY OF KNOWLEDGE
mirrored in our minds as they are only mirrored in nature. As for the
reaching of the goal, Plato is prepared to insist on the possibility of
insight into the rational order, but he also insists that insight cannot
be infallibly communicated. He is not saying that the truest state-
ments we can make are only partially true, so much as that there is
no true statement but can be misunderstood. The truth is in a sense
ineffable, not in the sense that there is something non-rational about
it, but in that we cannot with certainty communicate it.
Who is the man who knows "what sort of thing a circle is", and
what are the criticisms which seem to make a fool not only of him,
but even of the man who knows "what a circle is"? I suppose that
the first man is one who knows that a circle is an even curve, and
that therefore no part of its circumference can be straight. But when
he says this we can make a fool of him by showing that a straight line
can touch the circumference of a circle. But for one thing to touch
another is for them to have part of their boundaries in common.
Therefore if a tangent can touch a circle, it must be the case that
some part of the circumference is a straight line. (This is apparent
when you lay a straight edge against a physical instance of circular-
ity; ynu see at once that it is "full of the contrary nature"). If our
man tries to defend himself by saying that contact occurs over a
distance less than the smallest finite distance, then (perhaps with
Zeno's aid) we can show him that there is no such thing. Therefore
we have a plain contradiction in the notion of a tangent, a contra-
diction by which the man who knows only "what sort of thing" a
circle is may well be perplexed. From contradictions of this kind an
Eleatic might conclude that there cannot really be such a thing as
circularity, and even perhaps that the whole idea of space is hope-
lessly incoherent.
The condition of knowing "what a circle is", as opposed to "what
sort of thing it is", comes about, I suggest, when we are fully aware
of antinomies of this kind, but remain perfectly convinced that there
is such a thing of circularity; when we, so to speak, acknowledge the
existence of the contradictions, and yet know how to remain un-
perturbed by them. And the point is that this imperturbability is not
achieved by seeing how to resolve the contradictions; for they cannot
be resolved. Rather it comes about when we achieve a kind of direct
acquaintance with the nature of circularity, analogous, mutatis
mutandis, with the direct acquaintance which we can have with an
individual, when we know Theaetetus and do not merely know what
sort of man he is. How this direct acquaintance comes about, Plato
cannot tell us "the light is kindled" is his phrase. When it has come
about we. have, so to speak, got out beyond the antinomies which
are inescapable at the prepositional level. We cannot resolve the
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THEORY OF KNOWLEDGE
antinomies because they arise in some way from the conditions of
language and of the empirical world ; but they cease to trouble us
when our knowledge no longer depends upon language or upon the
production of instances. Teaching must take place through these
media, and therefore to have the correct logos and to be able to
recognise instances are necessary conditions of knowledge and indis-
pensable means of communication. But what teaching seeks to con-
vey must transcend the media, and that is why knowledge cannot be
taught.
It seems to me that something of all this may have been stirring in
Plato's mind when he wrote the Theaetetus, and that it may have
made him feel that the important thing was not to give a correct
statement of what knowledge is, but to make difficulties for those
who suppose that it is an easy matter to characterise the apprehen-
sion of something by the mind.
The Seventh Letter can also be read back with profit into others of
the later dialogues. The Parmenides for example is a sustained con-
frontation of the reader with the antinomies connected with unity;
and perhaps part of the purpose of writing it was to familiarise the
reader with the "refutations" which can be brought against any
account of the nature of unity, so that if he dwelt long enough on its
arguments he would come to see what unity is.
Then again there is the antinomy which Plato mentions in the
Parmenides and again in the Philebus^ the antimony of the unity and
multiplicity of universals. Of these and other antinomies we are
tempted to suppose that Plato must have thought, as we think, that
they are resolvable, that in any contradiction at least one side must
depend on a bad argument. But this is to suppose that Plato was
clearly possessed of the notion of a bad argument, and this may be
wrong. To some extent I believe he thought of arguments not in
logical but in rhetorical terms. An argument is something by which
a hearer is liable to be convinced. We think that the way to defend
oneself against being convinced by the wrong arguments is to make
sure that the arguments one accepts are valid. No doubt Plato
thought this too; he obviously thought that a great many arguments
are not valid. But perhaps he thought that to say that an argument is
not valid is to say that nobody who listens to the argument and to a
criticism of it will be taken in by the argument any more. An invalid
argument would then be one whose persuasive power was feeble
compared with that of the criticism of it. But now suppose an argu-
ment and a counter-argument such that even an intelligent hearer is
convinced by both of them, and cannot develop a convincing
criticism of either* Both arguments will now be valid. If therefore
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THEORY OF KNOWLEDGE
this situation ever arises (and it does seem to arise in connection with
the circle for example) then we can no longer defend ourselves from
error by giving our assent only to valid arguments. In this predica-
ment the only remaining defence, the only way of telling which of the
arguments is right, will be a direct apprehension, transcending argu-
ment, of the subject under discussion. Conceivably this was what
Plato thought.
I. The formal question: "What is knowledge?' 9
I think that we have now looked at all the places where Plato says
something about the formal question: "What is knowledge?". The
answer can be simply given : it is the apprehension by a mind of a
reality, and is to be contrasted with the inferior condition in which
we merely know (in our sense of the word) truths about the thing in
question. Though the answer can be simply given, Plato does not
think that this apprehension can be cheaply bought, nor does he
think that it is easy to answer the question: "But what is it for a
mind to apprehend a reality?". For the obvious answer to this
question is something like: "To have apprehended some reality is to
be able to give correct answers to questions about it, to be able to
point to instances of it and so on." Wanting to say that all this is
something less than knowledge, Plato has left himself with little that
he can do in answer to this question but to make use of metaphors
such as vision and direct acquaintance, and to hope that by use of
such metaphors, and by the continual contrast of knowledge with
the inferior conditions, in the end "the light will break". This is why
he is so consistently enigmatical on this subject.
This account of Plato's answer to the question "What is know-
ledge?" is given of course in terms of the latest of all the relevant
writings, the Seventh Letter. But I do not believe that there is very
much development on this point. Where there is development is in
connection with the inferior state. In the earlier writings (for example
the Timaeus) 1 it is taken for granted that knowledge can be conveyed
by teaching, and the inferior state opposed to knowledge is doxa
which comes about through the uncritical inductive use of the senses.
In the Seventh Letter however Plato is interested in a different con-
trast, that between the kind of knowledge which "plainly arises in
minds and is not identical with the thing known nor with its instru-
ments" on the one hand, and the kind of knowledge which he speaks
of as if it were the thing known on the other; and of the first of these
he says (342 c 5) that that which "plainly arises in minds" is one
1 See Timaeus 51 e 2. It is not, of course, certain that the Timqeus is earlier
than the Seventh Letter.
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THEORY OF KNOWLEDGE
thing, whether you call it epistetne or true doxa. What is new here is
not the importance of the distinction between insight and the ability
to recite the correct formula that was there from the beginning.
What is new is the thought that in comparison with this distinction
the distinction between "knowledge", lying at the end of an a priori,
avenue, and "belief", lying at the end of an empirical avenue,
becomes unimportant. Perhaps even non-existent. For although
Plato obviously never held the absurd view that you can achieve
knowledge without the use of the senses (nobody could hold this
view), he sometimes spoke as if he did. Perhaps to some extent the
hard and fast distinction between the a priori and the empirical
avenues depends on this misleading way of speaking. The distinction,
which he really wanted to draw, between what I have called the
counter-inductive and the inductive approaches, is a matter of
degree with regard to the use of the senses; it is not a question of
whether you use them, but of the point at which you use them, how
critically, and so on. Perhaps this was becoming clear to Plato; and
perhaps, realising that the senses make a contribution to every
degree of enlightenment, however lofty, he saw that the old distinc-
tion between episteme and doxa was not a hard and fast distinction,
and that the important distinction depended simply on whether what
existed in a man's mind was the actual thing which he claimed to
know, or merely a correct account of it in terms of propositions and
the ability to produce instances.
The stress that Plato lays in the Seventh Letter on the part played
by sense-experience in the long process of friendly refutation which
must precede the kindling of the light rather suggests something of
this kind. But it would be a mistake to place too much weight on this
passage. For one thing it is short; and for another Plato is plainly
hurt and angry at the insolence of Dionysius in publishing a hand-
book to the truth, something which "had I thought it possible to
write, I would have been greatly privileged to undertake and more
competent than anyone else" (341 d a rough paraphrase). In this
state of mind he is naturally concentrating his energies on the task of
explaining why he has always thought that the truth cannot be
communicated in handbooks.
J. The material question: "What can we know? 9 *
On the subject of Plato's answer to the material question: "What can
we know?" I have already put the evidence before the reader, and
raised some of the questions* Briefly the position is that there are
places (early and late) where Plato speaks seriously of knowing
matters of physical fact, but that the predominant position (again
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THEORY OF KNOWLEDGE
both early and late) is that we cannot have knowledge of the changing
physical world. I have argued that this position may perhaps be one
that Plato fell into rather than one that he particularly wanted to
take up. This sort of contention cannot of course be made good.
However by reminding ourselves of the considerations which may
perhaps have weighed with Plato in this region we may be able to
form a juster conception of the nature of his beliefs. I shall try to
rough out a list of such considerations in what follows. It will be
found that they constitute a mixed bag. In particular the tendency of
some of them will be to explain how Plato came to think that we can-
not have knowledge of the physical world, whereas the tendency of
others will be to explain away the dicta which suggest that he believed
this.
I. Concentration on general terms. When we discussed the
Republic we saw that Plato was interested in knowledge of universals
or general terms and not (for example) in questions such as whether
we can ever be justified in being certain about matters of empirical
fact. He is not primarily interested in the question whether we can
justly claim to be certain either of a particular matter of fact (what
the defendant said to the plaintiff) or of a general rule (such as the
phases of the moon). He does indeed make observations which seem
to imply that we cannot rightly be said to know things of this kind
(at any rate in the case of general rules), but he is not primarily con-
cerned with such questions. His primary concern is to contrast the
counter-inductive approach to the knowledge of general terms with
the inductive approach. But (as we have seen) he is accustomed to
speak loosely of the counter-inductive approach as if it consisted of
pure thought, and of the inductive approach as if it consisted of
nothing but the use of the senses. Underlying this, perhaps, is the
soul/body contrast of the mystery religions which is to be found in
the Phaedo 1 and which leads Socrates in that dialogue to speak of our
knowledge of empirical matters as if it were one of the tiresome con-
sequences of having a body. However that may be, whatever the
origins of this way of talking, so long as it persisted Plato could say
to himself that we do not acquire knowledge of general terms by the
use of the senses. Now if (his attention being concentrated on the
topic of general terms) the qualification: "of general terms" were to
drop out, he would be left telling himself that we cannot acquire
knowledge by the use of the senses. In this way he could come to say,
and in a sense believe, something which he might not wish to believe
if he thought of it on its own merits.
Yet why might he not wish to believe it? Why should we find it
difficult to allow that Plato thought it impossible to have epistemG
1 cp. Phaedo 65-6, 79-80; discussed above, Vol. 1, pp. 309-15.
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THEORY OF KNOWLEDGE
of matters of empirical fact by the use of the senses? Could it not be
argued that it is only so long as one puts the English word "know-
ledge" in place of the Greek word episteme that difficulty seems to
arise? To some extent it could. Nevertheless we have the following
three points: Firstly that Plato does sometimes allow us to have
episteme of matters of empirical fact. Secondly that if episteme stands
for the optimum mind-thing relationship, it seems odd to deny the
title to direct perception in the case of matters of fact (for what rela-
tion to an empirical fact could be more intimate than direct percep-
tion ?). Thirdly there is the rather obvious consideration that if un-
certainty infects our empirical judgments then it is unreasonable to
suppose that there can be any certainty in our apprehensions of
general terms; for it is undeniable that if I can never be sure that this
is (say) a horse, then I can never be sure that I know what it is to be a
horse. In so far therefore as the reason why Plato withholds the title
episteme from something is that he wishes to say that the state of
mind in question is not one of justified certainty, to that extent to
deny episteme of matters of empirical fact is to make epistemg of
general terms incomprehensible.
So far then we have found in Plato's concentration on the topic of
the knowledge of general terms something which might explain how
he came to conclude that there can be no knowledge of matters of
empirical fact. At the same time we have found three reasons for
wanting to argue that this conclusion must have been inadvertent
rather than deliberate. In the considerations which follow I shall
modify this last point by arguing that on Plato's presuppositions the
second and third of these reasons are less potent than they may seem.
In other words, I have tried to explain away the appearances which
suggest that Plato denied the possibility of empirical knowledge, and
I am now about to try to explain how nevertheless it is possible to
believe that he did deny precisely this, I shall begin by listing four
considerations which undermine the second of the reasons which
make belief in this denial difficult. This was that direct perception is,
in the case of matters of empirical fact, the optimum mind-thing
relationship and that it therefore deserves the title of episteme*.
2. The causal theory of perception. In the Theaetetus, as we have
seen, Plato expresses the belief that we do not in perception get into
direct touch with what is really there. What we experience is sense-
data produced by the interaction between our bodies and the
environment. Perceptual knowledge therefore, even if it is the most
direct relation in which a mind can stand to a physical thing, is still
a gravely indirect relation. We have no resources except conjecture
for getting behind sense-data and arriving at the ultimate facts of the
physical world. There cannot therefore be epist$m$ of physical
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tilings, for the immediate objects of perception are gignomena,
momentary private entities, and not onta or independently existing
things; and the onta in question, or the physical things, can only be
got at by conjecture. Thus so long as Plato held the causal theory of
perception (and it is natural to suppose that his primitive thoughts on
this topic were in line with the developed theory of the Theaetetus),
he would be tempted to say that there cannot be episteme of matters
of empirical fact, whether particular or general. It might however be
retorted to this that it is in the Theaetetus itself just after the exposi-
tion of the causal theory that Plato allows that an eye-witness can
properly be said to know what took place. I have already suggested
that the answer to this may be that there is a relative and an absolute
use of the doxajepistem$ contrast. The best relationship in which I
can stand to a physical occurrence is that of having witnessed it. In
comparison with those whose knowledge of the occurrence is from
hearsay, the eye-witness has episteme. In some contexts however it is
apposite to make the point that knowledge of this kind deserves the
title episteme relatively but not absolutely. The causal theory there-
fore could provide a reason for denying that there can be episteme in
the strictest sense either of particular matters of empirical fact or of
empirical general truths.
3. Cosmological considerations. We shall be discussing Plato's
cosmological views in the next chapter. Meanwhile we all believe it to
be roughly true that Plato thought that the world owes such definite-
ness as it possesses to the ordering work of mind, and that the world
tends to fail to live up to the order which mind has imposed upon it.
This failure would provide a reason for denying that there can be
epistem of natural regularities such as the phases of the moon.
Doubts such as those expressed in the Republic about the capacity of
a heavenly body to run to time would entail the doubt whether there
exists such a regularity to be known. Even however on the hypo-
thesis that the regularity exists Plato might well have doubted
whether our observations could be thought sufficiently reliable to
assure us of its nature. It seems clear that his confidence in the accur-
acy of observations was low (as indeed it was right that it should be
before the development of the experimental method). In this situa-
tion he might well have come to think that in the sphere of natural
science the only things of which we can ever be certain are the con-
siderations which must have weighed with the cosmic reason in the
work of imposing order on the chaos. 1 But these of course are
general terms. Neither the details of the order imposed upon nature
nor the closeness with which things actually conform to it can be
known. There can be no episteme of natural regularities in that there
1 This certainly seems to be the view of the Timaeus.
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THEORY OF KNOWLEDGE
can be no certainty that any regularities are actually conformed to by
physical things, and in that, even if in fact they are, there can be no
certainty about their nature.
4. The fallacy of timeless truths. Reflections on the uncertainties
of scientific conclusions might have been reinforced by confusion
concerning the principle that something which can be known must be
true at all times. From this principle it is possible to conclude
(fallaciously) that it is impossible to know a particular matter of
fact, and that it is impossible to know general truths about things
which change. The point which is made in the Theaetetus, that
describability does not entail complete changelessness, might have
served to indicate that these inferences cannot in fact be drawn, but
we have seen that there are grounds for thinking that neither Plato
nor Aristotle ever got the matter quite straight. Both of them seem to
have thought that the fact that it is now raining is not the sort of fact
that can strictly be known, on the ground that the sentence "It is
now raining" does not always express a truth. That it is now raining,
therefore, lacks the timelessness which one looks for in an object of
knowledge. Likewise that the sun travels in a circle, being a statement
about a changing thing, cannot strictly be known.
5. Form and matter. I considered earlier, and rejected, the sug-
gestion that what Plato meant to tell us is that that which we per-
ceive is physical things and that that which we know includes facts
about physical things. This suggestion stays rejected. Nevertheless
we have seen that in the tenth book of the Republic Socrates was
made to speak as if I can see but not know a bridle, whereas I can
know but not see what a bridle ought to be like; and it is a natural
development of the thoughts described in the last paragraph to say
that when I know something about the physical world what I do is
to pick out a plum of form from the transient pudding of matter.
When I know or understand a tune, what I hear is a changing series
of momentary sounds, what I know or understand is the pattern to
which the sounds conform. 1 In this way what I perceive is not the
same as what I know, and this may have been among the thoughts
which led Plato to say that we cannot know the physical world. If
this point were correctly appreciated it would not amount to the
point that there can be no epist$ml of the physical world, but to the
point that such knowledge should not be called "of the physical
world", but "of a pattern manifested by the physical world". The
suggestion is however that Plato may at times have exaggerated,
rather than correctly appreciated, the significance of this point.
The last four considerations have been such as to undermine the
second of the three reasons of which I said that they ought to make us
1 cp. Theaetetus 163 b-c, mentioned above, p. 8.
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uncomfortable about saying that Plato intended to deny that we can
have episteme of the physical world the reason, namely, that per-
ceptual knowledge, being the optimum cognitive relation to a
physical thing, deserves the title of episteme. I come now to offer
considerations calculated to undermine the third of these three
reasons, namely that which says that if Plato denied that we can
have episteme of particular empirical facts, then he made it incompre-
hensible how we can have episteme of the nature of general terms.
6. Neglect of Cartesian doubts. It may be observed that none of
the above considerations requires us to say that we cannot be certain
of a particular matter of fact as, for example, that this Is a horse.
Those which withhold the title episteme from a judgment of this kind
do not do so on the ground that we ought (always) to have doubts of
its truth. The fact is that Plato was not interested in Cartesian doubt
in asking "Can we ever be really sure that there is a chair in the
room? Or that the litmus paper turned blue?" He was well aware of
perceptual illusion, but he was not unduly perturbed by it. In
Theaetetus 158 b the Cartesian doubt whether we may not now be
dreaming is treated as a commonplace which is of interest only
because the similarity between waking and dream life requires an
explanation; no sceptical capital is made of it. On the whole it is
probably true to say that Plato's view was that measuring and other
techniques can protect us from the effects of perceptual illusion. 1 But
if Plato was not interested in Cartesian scepticism, then in denying
that I can properly be said to have episteme, e.g. that this is a horse,
it would not occur to him that he was telling us that we can never be
certain that we have a horse before us. In that case the question
"How then could we ever come to know what it is to be a horse?"
would not arise.
7. Recollection. We ought however to remember that the question
which we have just mentioned would not have seemed to Plato such
an obvious question as it seems to us. To him the important part of
the achievement described as "knowing what it is to be a horse" is
not accomplished primarily by looking at horses. We do not under-
stand what a horse is until we understand what possibility of animal
existence is represented by this system of organised material known
as the horse. But in the bringing about of this understanding sense-
experience offers no more than cues. What, say, the observation that
horses are fast runners does towards giving us an understanding of
horse-hood is to activate the thought that rapid evasive motion is one
way of preserving life. The observed fact puts us in mind of a possible
sub-division of the general term self-activating physical thing
namely the sub-division self-activating physical thing which preserves
1 cp. Protagoras 356, Republic 602.
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Us life by running away from its enemies. We are able to conceive of
this possibility (and thereby enabled to interpret the fleetness of
horses) because we are able to sub-divide highly generic general
terms by multiplying them, so to speak, by each other (animal by
swift-moving in our example) and thus can conceive, antecedently of
experience, of the relatively specific general terms which are em-
bodied in concrete things. To put the matter more picturesquely,
Plato does not have to believe that we arrive at a knowledge of
general terms by abstraction from particulars, because he believes in
"the homogeneity of mind". Mind is responsible for the order of
nature, and we too, who try to discover that order, are minds; and a
mind is something which can grasp the possible ways of existing.
Inferior minds we may be, and our inferiority is especially due to the
vividness of the impact made upon us by sense-experience, and our
consequent tendency to judge by appearances. This is something
which we must control by getting away from the senses and the
desires that go with them (cp. Phaedo 65-6 and 83). Inferior minds
that we are, if we do try to control the tendency to rely on appear-
ances, and thereby fall back on the citadel of rationality within us,
we are falling back on something which is in sympathy with the
mind responsible for the cosmic order. The eternal intelligence
designed, figuratively speaking, "looking to the intelligible forms";
and what is intelligible to one mind is intelligible to any. The intel-
ligible principles perfectly grasped by the eternal intelligence can
never perhaps be perfectly grasped by us. But since mind is homo-
geneous, in the end what makes sense to any mind must make sense
to any other, so that, if we ruthlessly pursue the policy of discarding
what fails to make sense, we shall get as near as we possibly can get to
discovering the principles underlying the order of nature. This being
so, why waste time on the laborious collection of empirical data? In
the light of this we can see both that Plato would have set a low
value on observations of particular matters of fact or empirical
generalisations (and hence might have been tempted to deny them
the title episteme)', and, more particularly, that he would not have
felt the force of the argument that, if there is no knowledge of par-
ticular matters of fact, there can be no knowledge of general terms.
For our knowledge of general terms is not, for him, built up out of
the knowledge of particulars. The mind is furnished (potentially)
with its store of general terms, out of its own resources.
What is the conclusion of all this? We reminded ourselves in para-
graph 6 that Plato would not have agreed that we acquire a know-
ledge of general terms by abstraction from their instances ; paragraph
5 reminded us that in denying that there is episteme of matters of fact
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THEORY OF KNOWLEDGE
Plato is not committed to denying that we can ever know for certain
the truth of some empirical matter. These two points together under-
mine the contention that Plato cannot have meant to deny that there
is epistemf* of matters of fact on the ground that he would have
thereby made episteme of general terms incomprehensible. Para-
graphs 4-2 meanwhile have suggested reasons why the title
episteme should have been denied to empirical knowledge; roughly
speaking, in empirical knowledge, whether particular or general, we
have not got the fast grip of an ultimate constituent of the world that
episteme connotes either because the grip is not fast or because
what it grips is not ultimate. These points together make it credible
that Plato should have denied that we have episteme of the physical
world; and all that makes us hesitate to say that he did make this
denial is the fact that he did not always do so. The road to Larisa in
the Meno, the eye-witness in the Theaetetus, the user of gadgets in the
Republicthese cannot be ignored. We accommodate them best by
arguing on the one hand that the doxa j episteme contrast can be made
both relatively and absolutely; and by remembering on the other
hand the point made in paragraph 1, namely that Plato's interest was
not in whether there is empirical knowledge of physical fact but in
whether there is empirical knowledge of universals for a negative
answer to the second question may well have expressed itself in
words appropriate to a negative answer to the first.
If the answer is wanted in a nutshell, we must say that Plato often,
but not always, denies that we can have episteme of physical facts;
that in this epistm must be construed as a technical term; and that
Plato has no special desire to tell us that we cannot, in the ordinary
English sense of the words, know matters of empirical fact.
III. THE DOCTRINE OF ANAMNESIS
Everybody who has heard of Plato has heard of the doctrine of
anamnesis or recollection. It is indeed an essential part of Plato's
philosophical outlook. It is however not quite so easy to say what
precisely the doctrine is.
We may observe by way of introduction that the doctrine of
recollection is at any rate a close cousin of some of the things that are
said about goodness in the Republic. It will be remembered that the
culmination of dialectic is the apprehension of the nature of good-
ness, that goodness is the source of the existence and of the intelli-
gibility of the other forms, and that until we apprehend goodness we
cannot be certain of the correctness of any of our earlier dialectical
achievements. It will be remembered also that goodness provides the
light in which we see whatever we are able to see "in the intelligible
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realm", whether at the level of dianoia or at that of noesis. But this
seems to mean that as we make philosophical progress we get nearer
to grasping as a coherent whole the system of universal natures, from
which are in some way derived the conceptions that we use and the
distinctions that we draw in abstract thought. Therefore in doing
dialectic we are advancing towards an explicit grasp of the system of
intelligible natures an implicit awareness of which has guided our
progress. It is easy to see that this might be described in terms of
bringing to the forefront of the mind something which lies at the
back of it, or of recapturing a memory which we hazily retain. We
shall discover that the doctrine of recollection is very much along
these lines. 1
However the Seventh Book of the Republic speaks of using a light
whose source we cannot yet see, and not of recapturing a dimly
retained memory. The passages where the latter notion is expounded
are Meno 80-6, Phaedo 72-7 and Phaedms 247-50.
The passage in the Meno opens significantly, because it shows the
connection between the doctrine of anamnesis and the question:
How do we make philosophical progress ? Socrates has baffled Meno,
and, when Meno protests at this, Socrates says that he is baffled too
and that they must seek the truth together. Meno retorts that seeking
is impossible, because if you knew something you could not seek it,
whereas if you did not know it you would not know when you had
found it. How, in fact, if you are really trying to solve a problem, do
you know that you have got the right answer ?
Socrates says that he has often heard this argument and does not
think much of it. He proceeds to meet it by quoting what he has
heard from "priests . . . who are concerned to be able to give account
of their priesthood, and from inspired poets". Their doctrine is that
the soul is immortal, and goes to Hades and returns to earth, learning
everything in the course of its wanderings. Therefore it is not sur-
prising that it can be reminded of virtue and of other matters, since it
has previously known them. "Since the whole of nature is akin, and
since the soul has learnt everything, there is no reason why we should
not, on being reminded of one thing (or 'learning' it as men say)
rediscover all the rest if we have the strength to persevere" (81 c 9-
d 4). This last sentence needs some comment. By "nature" Socrates
presumably means "the natures of things", or the answers to such
questions as what virtue is. The word for "learn" (manthaneln) can
doubtless be used for learning matters of brute fact, but it also means
"understand", and "come to understand" is probably the best trans-
lation here. Socrates does not want to tell us that we have learnt, at
some time, that Peking is in China or that mules are sterile, but that
1 More of this will be found in a subsequent chapter, pp. 558-61.
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THEORY OF KNOWLEDGE
we have come to understand such things as the rationale of the
division of men into virtuous and vicious. Whether he only wants to
tell us that the things of this kind which constitute "nature** are akin
to each other (c 9-d 1), or whether he also wants to say that they are
all akin to the soul is not clear to me. Nor do I know quite what he
means by saying that if we are reminded of one thing we can by
perseverance re-discover the rest. The sequel suggests that he means
that a man may need help from another in the initial stages to put
him on the right track, but that he can then carry on for himself if he
cares to do so. There does not seem to be any suggestion that there is
some one essential clue which a man has got to be reminded of
before he can begin. At any rate there is no indication what this
essential clue would be unless it were that learning is recollection.
I think however that the point is that we need only to be started off
by another's help.
For in order to convince Meno that to come to understand some-
thing is to recollect it, Socrates takes a slave who has never had any
mathematical teaching, and, roughly speaking, gets the slave to prove
a geometrical theorem. The problem that Socrates sets to the slave
could be put in the following terms: "What is the construction for a
square twice the area of a given square?" In answering this question
the slave has the wherewithal for proving the theorem that the square
on the diagonal is twice the area of the square on whose diagonal it is.
They begin by agreeing on a (rough) definition of a square. Socrates
then shows the slave how to reckon the area of a rectangle, and soon
elicits from him the answer that a square of side 2n will be double the
area of a square of side n. This Socrates refutes by reckoning the area
of two examples, and Socrates and Meno agree that the slave has
benefited by the destruction of this error. The destructive work done,
Socrates now proceeds roughly as follows. He takes four equal
squares and puts them together so that they form one large square.
The resulting figure is a square with a St. George's Cross on it. He
then joins up the tips of the arms of the cross so that it is enclosed in
a diamond. Each side of the diamond is a diagonal of one of the
original squares, and the diamond is composed of four triangles, each
of which is half one of the original squares. Since the diamond con-
tains four of these triangles, and the original squares contain two
each, the diamond (it is taken for granted that its angles are right
angles) is obviously a square double in area to any of the original
squares. All this the slave is made to see, simply by being asked the
appropriate question at the appropriate time. Naturally Socrates*
methods of proof are not rigorous; it is for example accepted as
obvious that all diagonals of squares of equal area are of equal
length. Nor is the slave entirely ignorant of mathematics ; for instance
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THEORY OF KNOWLEDGE
he has learnt to multiply. But of course it would be possible for
Socrates, if time was no object, to prove in the same kind of way the
things that he takes for granted. It is not true, as it is sometimes said,
that Socrates* methods are empirical. He does not, for example, get
out a foot rule. His proof works as mathematical proofs should
work, by extracting the consequences of things previously agreed to,
though some of the steps are omitted.
Socrates' account of what he has done is that the slave, although
untaught, had in him all the right opinions; but since they had to be
elicited (those which tumbled out of their own accord being mostly
wrong ones) he could not be said to know. The asking of the right
question at the right time has activated his true beliefs, and enabled
him to "recover knowledge from his own resources which is what
we call recollecting" (85 d). Since he did not acquire these true
beliefs in his lifetime, he must have got them before he was a man.
Socrates then (86 a 6-b 2) offers a very odd proof of immortality, and
adds that the only part of the argument that he is confident about is
its moral, namely that it is not, as Meno's argument had suggested it
was, a waste of time to pursue the truth.
There seem to be two different strands in this argument, one of
which leads towards religious notions about pre-existence, the other
towards logical notions about the status of necessary truths; and
these strands are difficult to disentangle.
Thus in what I called his "very odd" proof of immortality
Socrates seems to say that true beliefs can at any time be activated in
a soul, whether in or out of the body, by questioning, and that there-
fore the soul must always at all times have learnt all truth (86 a 8),
There is therefore no moment, whether here or in Hades, at which the
act of learning occurs; the soul is always in the condition of having
learnt. (Once again, it seems obvious that by "all truth" Socrates
must mean, not every true statement, but all the truths of philo-
sophy, mathematics and so on, in fact all necessary truths; what he is
telling us is that it is always possible for us to recover a grasp of these
if someone or something will "remind" us of them).
But if we stress the point that a man can always at any time recover
a grasp of intelligible necessities and that therefore he must at all
times be in a condition of having already learnt them, difficulties
arise. For one thing, we wonder what the process of learning is
supposed to be if it is always something that has already occurred*
For another, we wonder how we have a proof of immortality. Pre-
existence is required, and brings with it a proof of immortality, only
if our ability to understand a geometrical theorem depends on actual
geometry lessons which we were given at some time in Hades, and
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which we dimly remember on earth. If we are always in a condition
of having learnt., then there was never a moment at which we did
learn ; and if there was never a moment at which we did learn, what
can be meant by saying that we are always in a condition of having
learnt, except that we are always capable of coming to understand?
But that does not imply that we existed before we were born; to get
that implication we need to say that the time before we were born
was the time at which we did learn.
The idea that necessary truths have to be learnt, but that we are
conveniently taught them before birth, conflicts not only with the
saying that the things that we can know are things that we are at any
moment in the condition of having learnt; it conflicts also with the
example of method which Socrates has given. For what the slave is
made to do is to extract the logical consequences of things which he
has already agreed to, and which are logical consequences of the
initial data or of the constructions which are made, the function of
Socrates being to take the slave step by step, and so prevent him from
confusing himself. There does not therefore seem to be much that the
slave could have been taught in Hades. He does indeed utilise such
facts as that 4 is twice 2 in coming to see the conclusion, but this is
not something that has to be learnt in the way in which we have to
learn that Berlin is in Germany. Socrates could presumably have
brought the slave to see that 4 is twice 2, if it had been necessary, by
his method of questioning. What the slave does is to deduce the con-
sequences of premises, and no additional information is necessary to
perform a valid deduction. Not only is this true, it also looks very
much as if it is the point of Socrates' demonstration. Following this
line of thought one comes to the conclusion that the lesson Plato
means us to derive from this passage is that a soul is at every moment
of its existence capable of reasoning, and thus capable of arriving at
all necessary truths out of its own resources; and that this is figura-
tively called recollection because both this and recollection proper
are cases of bringing something up out of one's hidden resources.
But then one remembers that there is supposed to be some con-
nection with immortality in all this; indeed a proof of immortality.
No doubt we might say that Plato independently believes in im-
mortality; and believes that the soul enjoys the contemplation of the
rational order in the discarnate condition, so that when we discover
and contemplate a rational truth on earth we are enjoying again a
pre-natal experience, and that this is another reason for talking of
recollection. But the fact that Socrates is allowed to talk as if he
were offering a proof, and the fact that the proof would only be a
proof if something like pre-natal instruction were involved, must
make us hesitate to say that all that Plato wants to tell us is that every
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soul is potentially capable of valid reasoning. To say that would be
to over-simplify.
One is tempted to wonder whether, when Socrates says that all
nature is akin, he means to tell us that all universal natures are akin
not only to each other, but also to the soul. This would seem to offer
an answer not only to the question what the learning process is sup-
posed to be like, but also how Plato thought that he had here a proof
of immortality. We should get the answers roughly as follows. That
all universal natures are akin with each other would mean something
to the effect that they all form a coherent system. That they are akin
to the soul would mean that the concepts which we are naturally
prone to form, and the inferences which we are naturally prone to
make with these concepts, correspond to these universal natures and
to the relations between them. The proof of immortality would He
not in the fact that a time has to be found for pre-natal geometry
lessons, but in the presumption (explicitly stated in Phaedo 77-80)
that if the soul is akin to eternal entities such as universal natures it
too must be eternal. To elucidate what I mean when I speak of our
concepts and inferences corresponding to universal natures and the
relations between them, let us take some such notions as squareness
and circularity. We are naturally prone to notice that there is an
important difference between square things and round things; square
and round are headings under which any man will readily classify
objects. We naturally see, also, that round things are more likely to
roll than square things; we can see some of the consequences of
roundness and squareness. We are not likely to see all the conse-
quences; we may, like the slave, think that a square of side 2n will be
double the area of a square of side . Nevertheless, if there is some-
body present to check us, we can see that this is wrong, and we can
eventually work out what is right. We have the ability to discover this
aspect of squareness from our own resources. Our natural tendency
to classify things as round or square corresponds to the difference
which obtains between roundness or squareness as they are in them-
selves; our tendency to infer that a round thing will roll corresponds
to the fact that circularity entails the equidistance of every point on
the circumference from the centre. We are naturally inclined to
classify things into kinds which reason sees to be genuinely distinct,
and we are naturally inclined to see some of the consequences of our
classifications, and able to discover the rest. The way our minds
work corresponds to the way things are, and this is the kinship of the
soul to "universal nature".
However to read all this into the Meno is to import into it what the
text does not plainly contain. It is also, incidentally, to bring the
Meno more into line with the Phaedo. Since the opening of the pas-
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sage in the Phaedo suggests that It is offering an alternative version of
the same doctrine as that in the Meno, this is satisfactory so far as it
goes. It is possible that one cause of the difficulties that we have found
is as follows. In both dialogues anamnesis is supposed to provide an
argument for immortality, and in the Phaedo the argument is pre-
sented as if it were independent of the argument from the souFs
kinship with the forms. To be independent, the argument from
anamnesis must be thought to involve some sort of pre-natal experi-
ence; but as we have seen the Meno makes it difficult to see what
experience this could have been and when it was provided. Might it
not be, then, that Plato intended to impute to Socrates in both places
an argument which did depend on pre-natal experience, but that he
had himself rather more sophisticated ideas than those which he
imputed to Socrates and that he inadvertently spoiled Socrates' case
by making him say things which really only accorded with Plato's?
This seems to be a possible explanation of the fact that the Meno both
insists on pre-natal experiences and also fails to find a place for
them. 1
We come now to the passage in the Phaedo. As we have seen it
begins with what looks like a reference to the Meno (Phaedo 73 a 7).
Kebes suggests that the argument from recollection proves that souls
have discarnate existence, and says that the argument rests on the
fact that if you question people cunningly they give the right answers,
and that this is very clearly seen in geometry. Socrates then offers an
alternative version of the argument, saying that if the one does not
convince, the other may. The new version is as follows.
1. Whenever there is any connection between two objects A and
B (B may be like A, be a picture of A, a familiar piece of A's pro-
perty, and so on) the sight of the one may remind me of the other. If
the connection between A and B is that they are alike, then for B to
remind me of A, I must notice not only the resemblance, but also the
difference (otherwise I should mistake it for A).
2, Now there is such a thing as equality, and we understand what
it is. But where does our knowledge of it come from? In one sense it
must come from experience of equal physical objects; and yet equal-
ity is not the same thing as equal physical objects ; for physical things
can seem equal to one man and unequal to another, whereas "the
1 1 suppose that it is possible that the immortality argument in the Meno is
meant to be simply: "If we at all times have learnt, the learning must have taken
place infinitely long ago. Therefore the soul has existed since that infinitely
distant moment and will presumably exist until an infinitely distant moment in
the future, i.e. for ever," But we should still want an explanation of Plato's
finding this use of the "actual infinite" convincing.
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equals themselves can never seem unequal, nor equality inequality".
There are then two sets of things, equality and equal physical objects, 1
and these are different from each other, whether or not they are
unlike. (In other words the question of the exact relation between
universals and particulars is dismissed; all that is necessary is that
they should not be identified).
3. Now equal physical objects are, and are seen by us to be, less
equal than equality. We have agreed that there is a sense in which we
derive our knowledge of equality from equal physical objects, but
since we realise that equal physical objects fall short, always, of the
standard of equality, we cannot have derived our knowledge of the
standard from things which admittedly always fall short of it. The
natural thing to say therefore is that we have knowledge of equality
independently, and that what equal objects do is to remind us of it.
This is the sense in which our knowledge of equality is derived from
equal objects.
4. Finally the fact that equal physical objects are equal (though
"less equal than equality") is detected by the senses. Since our senses
always tell us that physical instances of equality are imperfect, we
must have become aware of the standard before we came to enjoy
the use of our senses, i.e. before we were born. It cannot be said that
we have retained this knowledge of equality, because a man can give
account of what he knows, and few men can give account of equality
or anything else. Therefore it must be the case that we forget the
knowledge of equality and the other intelligible natures 2 on coming
into the body, and that we are put in mind of them by experience ; and
to be put in mind of one thing by another is recollection.
The general picture presupposed by this argument is familiar to us
from the fifth book of the Republic. There are precise analysable
universals, and there are physical instances which must not be con-
founded with them. The latter do not perfectly exemplify the former,
in the sense that we cannot gather an adequate understanding of the
former from a study of the latter. The reason which is apparently
given for this (para. 2; 74 b 7-8), namely that two physical objects
may seem equal to one man and unequal to another, is a feeble one as
it stands, and I am not sure that this translation is correct. However
we cannot go into this now, 3 so we must leave it that, whatever the
reason, the point is made that universals must not be confounded
1 1 shall not here discuss the question whether "the equals themselves" means
the same as "equality**. See below, pp. 302-3.
a "The things we entitle 'what the thing itself is* in our conversations" Socrates
calls them (75 d 1-3)* He means the things whose definitions he habitually seeks.
a For a detailed discussion of this passage se t>eJow pp, 295-303.
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THEORY OF KNOWLEDGE
with their instances and that the instances do not give us the know-
ledge that we possess of their universals, though they do play some
role in relation to It.
The Republic says, of course, that what the instances do is to give
us a doxa of their universals, an idea of how they seem. To decide
what the present passage says we must clear up an incoherency in the
argument. For it begins by saying that we do of course all know
equality and the other natures "whose definitions we seek", but it
ends by saying that very few people can be said to retain their
pre-natal knowledge, for very few can give account of equality or
whatever it may be. The reason for saying that we know equality is,
roughly speaking, that we know what the word means and can thus
tell that two sticks or stones are not perfect cases of the thing,
whereas the reason for saying that we do not know equality is that
we cannot give account of it.
Looking at these contradictory positions in the light of the reasons
for them and in the light of the Meno, one is inclined to wonder
whether the doctrine is roughly as follows. What we retain is a true
belief concerning the nature of equality. This enables us to see that
these two peas are not a perfect case of it. This is not knowledge, and
it is not a full-blooded revival of the pre-natal vision of equality. For
equality is something that can be grasped abstractly, and of which a
logos or analytic definition can be given; it is thus that the mind
grasped it out of the body, and it is only when this theoretical grasp
is re-activated by the question-and-answer technique of Socratic
definition that full knowledge is achieved. What experience does,
strictly speaking, is to revive not our knowledge of equality, but the
true belief which is all that we retain until it is converted into
knowledge by philosophical methods.
We can see now that there are two prima facie differences between
the accounts in these two dialogues; and on reflection neither of
them is important. The first is that, textually at any rate, what the
Meno makes us remember seems to be propositions, whereas the
Phaedo makes us remember universals. This is not an important
difference, for no doubt Plato would say, along the lines of our
recent discussion, that to remember squareness is to remember the
theorems that flow from it, or the inferences which we can make with
this concept. Indeed we found ourselves wondering whether the
Meno itself did not really intend that what we retain is a grasp of the
universal natures which are, so to speak, the archetypes of the con-
cepts which we find ourselves employing. The second difference is
that the Meno says that we retain true beliefs, in the sense that we
shall tend to give the right answer if a questioner asks questions in the
proper order and thereby saves us from confusing ourselves; and
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THEORY OF KNOWLEDGE
that it is not this implicit retention, but the conversion of it into full
understanding which is to be called "recollection". In the Phaedo on
the other hand "recollection" is not used for the conversion of true
beliefs into knowledge. "Recollection" in the Phaedo is the name for
what happens when our implicitly retained true beliefs about uni-
versals are activated by experience of instances. But this too need
not be an important difference. The Phaedo uses a more "disposi-
tional" or "behaviouristic" sense of the word "recollection" than the
Meno, but this does not imply any doctrinal difference.
It is possible however that there is some doctrinal difference,
though it does not show itself in any positive discrepancy. This is that
the Phaedo insists at one point, as we have seen, that knowledge has
not been regained until one can "give account". This emphasis on the
importance of "giving account" is not to be found in the Meno. In
talking about the process by which beliefs are converted into know-
ledge (the process by which knowledge is recovered out of one's own
resources, the process which it calls recollection) the Meno says:
"and if he is questioned about these same things often enough, and
in enough different ways, in the end he will come to have knowledge
about them as exact as anybody's" (85 c). In other words if you go
over a theorem or group of theorems often enough, taking the steps
in a different order perhaps, and so forth, the result of this repetition
is to confirm your beliefs until they qualify for the status of know-
ledge. It is true that later on in the same dialogue it is said that belief
is turned into knowledge by "the working out of the explanation",
but at this point nothing of this kind is stressed. We are allowed to
get the impression that experience can restore our knowledge to us
provided we are helped by somebody who puts the proper questions
to us in the right order. It is not said, though it is not denied, that
knowledge necessarily involves theoretical insight. This is not a
positive contradiction, but a possible difference of emphasis. When
we were discussing knowledge and belief we found a similar differ-
ence of emphasis between the Meno and the Republic ; and we have
recently seen that the Phaedo seems to be in tune with the Republic on
the subject of this distinction. Since the chronological order plainly is
Meno: Phaedo: Republic, this constitutes a coherent development.
It seems then that the Meno and Phaedo come fairly well into line
with each other, the residual difference being that the Phaedo insists
that to know one must be able to give account. The passage in the
Phaedrus follows the earlier accounts as far as it goes. It is short
however, and it comes in the mythical section of the dialogue, and
therefore we cannot perhaps get very much out of it. It tells us that
all human souls have seen at least some of the intelligible realities,
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THEORY OF KNOWLEDGE
because no soul can become incarnate in a human bod}' unless it can
by reasoning gather together "the so-called form" which is present in
many instances (249 b 6). In other words a human mind must be able
to abstract the common quality in multifarious instances, and this
power depends on recollecting the vision of the forms as they were
seen before birth. It is by virtue of this power of recollection that the
philosophic propensities are powerfully excited in the finer spirits.
Beauty in particular is more luminous in its instances than justice,
and the other things that we revere, and hence it is primarily by
beautiful objects that the soul can be fired to desire to re-possess
itself of the pre-natal vision of reality.
Here evidently what we are put in mind of is universals, and it is
by seeing instances of them that we are put in mind of them. Plato's
purpose at this point is to explain how sexual passion can elevate the
mind: this being so it is probably unwise to try to wring too much
epistemology out of what he says. But if we were to try to do so we
might think that the doctrine of the Phaedrus is simpler and bolder
than that of the Phaedo. For the Phaedrus appears to tell us that the
power of generalising as such is due to the pre-natal vision of the
common natures which we abstract when we generalise; and in the
context of what the Phaedrus says about dialectic, we would expect
these to include such common natures as animality. ThePhaedo does
not go so far as this, in that the Phaedo makes its point in terms of
equality, an example with respect to which it is plausible to say that
we cannot get to know it from its instances. It does not indeed
explicitly allow that there are some general natures (e.g. that of being
a helmet) that we can extract from their instances, but it does not
appear to exclude the possibility as the Phaedrus might be taken to
do. However, the answer to this no doubt is that the account in the
Phaedrus is perfunctory and that Plato is obviously thinking primar-
ily of terms like beauty. Nevertheless it is possible that Plato would
have been prepared seriously to defend the connection between the
power of generalising and that which he calls recollection. We
suggested that the doctrine of recollection can be construed as a way
of putting the point that the fundamental distinctions that common
sense is inclined to draw correspond to real differences which reason
recognises between general terms. Bearing in mind what the Republic
and the Cratylus have to say about forms of artefacts we would
expect Plato to argue that even such a concept as that of a helmet is
a complex function of such fundamental distinctions. For he who
separates off helmets from hats is drawing on notions such as
rigidity, protection and so on. Obviously it would seem possible to
produce a kind of scale of general terms putting at the top those like
equality and justice which it would be plausible to say we "bring to
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THEORY OF KNOWLEDGE
experience" and at the bottom those like concepts of artefacts which
it would be plausible to say we "get from experience"; and Plato
would have to allow that experience plays a larger part in the genesis
of those at the bottom than in that of those at the top. Still, it might
be that he would wish to make the point that all concepts, except
perhaps those of sense-qualities, do depend on the critical use of
experience, or in other words on the application to it of the funda-
mental distinctions, our ability to use which is a "memory" of the forms.
Having looked at the passages in which the doctrine of anamnesis
is put forward we ought to look at one in which it appears to be
denied. This is the passage in which the Theaetetus talks about the
process of learning and compares it to capturing birds and putting
them into an aviary (Theaetetus 196-9). For here Socrates explicitly
says (197 e) that the aviary into which we put the birds that we catch
is empty at birth. Nor is this because he is discussing the learning of
particular matters of fact, for he is not; mathematical facts are
explicitly included among his birds.
This need not amount to a contradiction of the doctrine of
anamnesis. In the language of the Meno we have learnt at all times
that 7+5=12, but we do not fully remember this until we have been
reminded of it, and the Meno also uses "being reminded of" and
"learning" as equivalents. What we recollect in the full sense we can
be said to learn at the moment of recollection, though of course in
another sense of "learn" we had learnt it already, always. But the
child who has not yet "been reminded" that 7+5=12 has not learnt
this fact in the former use of "learnt" and does not yet know it. This
therefore is a bird that the child still has to catch and put into the
aviary. In other words if we suppose that Socrates means the process
of capturing birds to stand for the process of coming consciously to
know something then we should expect the aviary to be empty at
birth; for the doctrine of anamnesis does not require us to possess
any actual as opposed to potential knowledge before we are reminded
of it.
On the other hand if the Theaetetus did intend to deny the doctrine
of anamnesis this would not be surprising in view of what we might
almost call its empiricist theory about the formation of concepts.
This may be illustrated by looking again at the argument in the
Phaedo. Wanting to show that knowledge of equality must have been
acquired before birth, Socrates argues that we have enjoyed the use
of our senses since infancy, and have always been able to sense that
physical equals are not adequate instances of equality. But there is a
serious flaw in this argument. Because we have been able to sense
since birth, it does not follow that we have been able since then to
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THEORY OF KNOWLEDGE
sense that A and B are roughly but imperfectly equal. In the language
of the Theaetetus, we are never able to sense this; we judge it on the
basis of sense-data, and of course infants cannot make such judg-
ments. Once it is admitted that we learn to use such notions as
equality, it is not difficult to go on to see that such notions are of
completely empirical origin. We use "unequal'* to mark gross dis-
crepancies, "equal" where we do not notice discrepancy. Then, hav-
ing said that A, B and C are equal, we notice that there are in fact
discrepancies between them, and so we form the notion of "perfectly
equal" to stand for the postulated case of two entities such that there
is no discrepancy between them. We may or may not believe it
possible to find two such entities, but that is not important. The fact
that a concept is without empirical application ("more beautiful than
Helen", "more tiresome than Jones") does not imply that it is not of
empirical origin.
How far the Theaetetus would be prepared to go in this direction is
uncertain. As we have seen, it insists that whereas the power of
sense-perception is innate, the ability to make judgments has to be
learned. The stress which it lays on similarity as one of the items
contributed by the mind to a judgment, and the things that it says
about comparison of sense-data could be developed into an empiri-
cist theory of the formation of concepts, or at least of empirical
concepts. If the mind is endowed with the power of detecting resemb-
lances it can frame concepts for itself, and this power is all it needs to
bring into the world. I think however that it would be a mistake to
suppose that Plato would ever have been willing to go so far as
Locke and Hume. An empiricist theory of the formation of concepts
leads in the end to the view that reasoning is the manipulation of
material supplied by experience, and this in turn to the view that
reason is inoperative in the absence of material upon which it can be
exercised. It is true that Plato provides the forms to be so to speak
the objects of reason, but an empiricist would want to say that these
are not "objects" in the required sense. You cannot just contemplate
equality, for it is nothing but a relationship which things have to each
other* In so far therefore as Plato wanted the forms to be independ-
ent of things (and this I think is something that he always wanted) he
would have tended to shy away from a full-bloodedly empiricist
theory of the formation of concepts. He would always have wanted
to say that forms can be "known" even without a world of things to
partake in them. But this amounts to saying that entities like equal-
ity have, so to speak, a nature of their own; and so long as you say
this you will be likely to wonder how our concept of equality comes
to conform to the nature of equality; and that is the question to
which the doctrine of anamnesis is an answer.
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THEORY OF KNOWLEDGE
APPENDIX. FURTHER POINTS CONCERNING THE PASSAGE IN THE FIFTH
BOOK OF THE REPUBLIC (see pp. 53-70 above)
I suppose that the standard Interpretation of this passage is that
which takes Plato's meaning to be that the forms are the sphere of
competence of epfstgme, and that they are real ; and that the material
world is the sphere of competence of doxa, and that it is in some
sense only half-real. Leaving aside this use of the notion of "reality",
I have indicated that I do not wish to deny that Plato might, if asked,
have replied that he intended in this passage to tell us that these were
the spheres of competence of these cognitive functions. I certainly
admit that he elsewhere made this allocation. My argument however
is that we get this allocation if we put together what he here says
about the nature of knowledge (viz. that it is the grasp of an on) with
what he is sometimes at any rate willing to say in answer to the
material question: "What can we know?" (viz. that we cannot know
physical things because they are not onto). I contend also that he is
not here primarily concerned with the material question (though how
clearly he disentangled it from the formal question I do not profess to
know) because he is here interested in distinguishing different levels
of apprehension of entities such as justice, and does not want to tell
us that we can never know for certain that this is a just act, but
rather that we shall never see clearly what justice is so long as
we think of it only as the common feature of various (types of)
acts.
Essentially my reason for taking this view is a subjective one, that
I cannot now read the passage and believe that it is saying anything
else. But there is an objective difficulty in the way of any interpreta-
tion which depends (as the spheres-of-competence interpretation
must depend) on making to on mean "the forms". This is that it is
not easy to see how the contemporary reader could have been
expected to understand that "that which is" means "the forms". 1 As a
desperate expedient we could suppose that Republic 5 in the form in
which we have it was published after, say, the Timaeus, though it
seems certain that some version of the Republic must have preceded
the Timaeus. But if the reader of Republic 5 had not read Republic 6
and 7, had not read the Timaeus, and had not read books about
Plato's theory of forms, could Plato have been sure that he would
identify "that which is", or even "that which really is" with the
forms ? To be sure such a reader might have read the Phaedo and
derived such an identification thence. But on the whole Plato does
not write his dialogues as if they were a serial work; there are cross-
1 The reader who understood by to on "that (whatever it is) that Is real" would
get something out of the passage, but he would surely be rather perplexed.
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THEORY OF KNOWLEDGE
references, certainly, but on the whole It is Plato's custom to make
his meaning clear In the current work without depending on some
other. The identification of to on with the forms in the present con-
text, moreover, would have been especially precarious since in con-
texts somewhat like this one it appears to have been common practice
to correlate episteme (or anyhow true belief) with to on in the sense of
"the facts" without any metaphysical preconceptions about what
sort of facts there may ultimately be. (Euthydemus 284 provides a
case in point. Here the Sophist Euthydemus, assuredly no Platonist,
uses on and me on simply to stand for "fact" and "figment" in
developing a form of the Paradox of False Belief; he does this before
an audience who seem to find such language familiar).
It may be retorted that the words episteme and gnosis which
Socrates uses in this passage are solemn words, that the same Is true
of phrases like topantelos on (477 a 3), and that these are indications
from which the reader might have guessed that something was up. 1
I think that he might have guessed that something was up, but the
question is : Could Plato reasonably have expected him to diagnose
what that something was ? Certainly episteme and to on can, but need
not, connote profundity; there is a suggestion that the former delves,
and the latter dwells, beneath appearances* But this is not always so,
as the Euthydemus shows for to on, and as many passages show for
episteme and the verb gigndskein, if not for the (less common) noun
gnosis. And the to on which dwells beneath appearances need not be
Plato's forms, it might be Parmenides* one substance or the water
which some Ionian physicist thought to be the ultimate stuff of
nature. A reader might well have thought that a passage which
correlated epistemS or gnosis with topantelos on was talking about the
ultimate grasp of ultimate realities, and if he remembered his Phaedo
he might have remembered that in the case of the author he was at
present reading ultimate realities were forms; but I do not believe
that Plato would have presumed all this. He knew that people read
Parmenides' writings, and those of the lonians, as well as his own.
I allow then that Plato might have expected the reader of this
passage to conjecture that episteme was not the sort of thing one has
of transient phenomena, being a more penetrating mental function
than that. But I hesitate to allow that he would have expected the
reader to see that episteme is what we have of the forms and that the
forms are what we have episteme of. But I may be told that Socrates
has just been talking of the forms on the previous page (476), speak-
ing of "beauty itself" as something which is "one", and as something
which only philosophers believe in, and that the contrast between
1 But see e.g. Sophist 240 e 5 for almost equally solemn language without
solemn meaning.
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THEORY OF KNOWLEDGE
on the one hand entities like beauty and on the other hand its "par-
ticipants" could not fail to put the reader in mind of the Platonic
theory of forms. I am not so sure of this. What is the theory of forms,
and where do we get it from 7 1 Having found it in later dialogues and
in Aristotle's writings we can detect traces of it in Plato's earlier
works ; and I must allow that there is a good dose of it in the Phaedo
and in Republic 6 and 7. But does what Socrates says about "beauty
itself" in the present passage clearly imply what we mean by the
theory of forms for the present purpose that is to say a doctrine
according to which the forms are the only onta and physical things
cannot be admitted to that status ? I am not sure that it does. Socrates
has drawn a distinction between those who do and those who do not
believe in beauty itself as one unitary thing not unambiguously
detectable in its participants, but this does not require that beauty
should have any special ontological status. It requires that beauty
should be a unitary general term of which a Socratic definition can be
given, and that there should not be as many beauties as there are
types of beautiful things. It requires the doctrine that every genuine
concept corresponds to just one universal common nature. This may
be a view which has seemed obvious from the days of Aristotle until
the other day, but it was certainly not a view which Plato could treat
as obvious. It was therefore a view which non-philosophers could be
quite well represented as denying. But it does not require "the
Platonic theory of forms" if this phrase stands for a view which
asserts the reality of tabularity but denies the reality of this table. It
was, after all, a view that Aristotle would have subscribed to in the
case of most concepts, though it did not in his case carry with it the
view that universals existed otherwise than "in" their instances.
Were it not for the precariousness of taking to on to mean "the
forms" there is another interpretation of this passage that would
seem to me to have merit. It certainly has the merit of not making
Plato impugn the reality of physical things. This is the interpretation
that says that to on stands for the forms, not so much because each
of them really without qualification is 9 as rather because each of
them really without qualification is itself. P-hood is an ontos on not
because it exists without question but because it is without qualifica-
tion P. The forms are those entities each of which is without qualifi-
cation what it is, and this is how they can be collectively referred to
as that which is, Epistem is set over those entities because beauty
and so on are precisely the entities which the mind can grasp. Just as
to on is those entities to each of which there belongs without qualifi-
cation a certain predicate (namely itself), so to m on will be that to
which there belongs no predicate at all This will be something like
1 Serious answers to these questions must be deferred to Chapter 3.
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THEORY OF KNOWLEDGE
the chora or "space" of the Timaeus, the substratum in which pro-
perties inhere, which has no properties of its own, and which cannot be
grasped by the mind except by bastard reasoning. Aristotle tells us
(Physics 192 a 6-16) that Plato called that in which properties exist
to me on ; and Leucippus had used the phrase to refer to empty space,
which he believed to be real but to have no character. It seems pos-
sible then that the phrase could bear this meaning. Since an entity of
this kind can only be grasped by bastard reasoning (i.e. we can see
that it must be postulated but cannot see what it is) agnoia seems an
appropriate cognitive function to correlate with the substratum. 1
Finally ordinary particulars will be between on and me on in that they
consist of the characterless informed by that which is fully character-
ised. Understanding grasps the element of form, agnoia answers to
the element of matter ; judgment, coming between understanding and
agnoia., deals with entities whose definiteness is due to form and
whose changeableness is due to matter. This is an attractive way of
making sense of this passage, but it cannot be its primary meaning
both because of the difficulty already mentioned about the under-
standing of to on> but also and more decisively because of the greater
difficulty over the meaning of to m on which would almost certainly
have beset those who had read neither the Timaeus nor Aristotle.
Lastly, if we accept the spheres-of-competence view, must we say
that Plato here impugns the reality of physical things in a way which
is inconsistent with the rest of his views, for example with the view
that the body is real enough to have disastrous effects on the soul?
The answer to this is a little complicated. Because on this view to me
on has to mean "the non-existent" we shall have to say that in putting
physical things between to on and to me on Plato was logically
committed to impugning their reality in a dangerous way. But we
need not say that he had any intention of honouring this commit-
ment. We can say that he habitually said that physical things were
not onta, meaning thereby not to deny them existence and reality,
but to deny them stability and (in some sense) ultimacy. They were
not onta because they were gignomena, things that "become".
Gignomena are real and exist but they are not onta precisely because
einai 2 and gignesthai are the two poles of a contrast which is drawn
within the class of existent things. But Plato might have failed to see
that it is one thing to contrast einai with gignesthai and another
thing to contrast it with me einai. He saw this in the Sophist in what
some regard as a penitent passage. 3 Here however he could have felt
1 See Cratylus 440 a 3, where it is said that "no knowledge knows what it
knows except as having certain properties".
2 The verb whose participle gives us to on.
* See below, Chapter 3, pp. 419-21.
EPD F 151
THEORY OF KNOWLEDGE
that he was doing no real harm saying that physical things were "not
quite onta" even in a passage in which the contrast was between onto,
and me onta and not between onto, and gignomena. After all me onta
means "not ontd\ and gignomena will seem to be that until you
detect (and Sophist 243 c 2-5 seems to suggest that there Is some
novelty about the detection) that einai is ambiguous.
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COSMOLOGY AND THEORY
OF NATURE
THE topics I shall discuss in this chapter will centre round two ques-
tions: (1) To what extent and in what sense did Plato believe the
natural world to be rationally ordered? and (2) What recommenda-
tions does he offer concerning the proper way of studying the natural
world? The principal documents for these topics will be the Phaedo,
Republic, Timaeus and Laws.
There is a view which holds that Plato thought that the natural
world is a deplorable place, and that the only proper way of treating
it is to ignore it and study "the ideal world" instead. This is an absurd
view, and I shall not waste time disputing it. I hope that its falsity will
sufficiently emerge.
I. THREE PRESUPPOSITIONS
I shall argue that the earlier documents (Phaedo and Republic) can-
not be understood without reading back into them doctrines which
are only explicitly stated in later writings. These doctrines (or
embryonic forms of them) are in my view presupposed in the earlier
writings, and I shall begin by giving a rough statement of these
presuppositions.
Firstly then the natural world is ordered by intelligence; and this
rational ordering consists in the gathering up of disorderly material
into kinds. The state of the natural world without its ordering would
be that of "an infinite sea of dissimilarity" (Statesman 273 d 6) no
definite things, and therefore no likenesses between one part of it and
another, no regularities for science or common sense to observe,
nothing but nothing-in-particular everywhere. The existence of
distinct kinds of things is due to the ordering done by mind; and the
behaviour of the natural woild is due to the natures of the kinds into
which it is ordered.
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COSMOLOGY AND THEORY OF NATURE
Secondly the ordering is rational and not arbitrary. Precisely what
this means Plato may perhaps never have decided, but at least it will
mean something like this: For a thing to be rationally ordered, it
must be possible to see that it had to be ordered like that. If I arrange
things in one way, and they could equally well have been arranged
differently, then my choice of my arrangement is arbitrary and not
rational. Therefore the order which is imposed, the kinds that there
are and the relations between them, is an order which had to be; and
that can only mean that the kinds and the relations between them are
given not products of the ordering mind, or its dispositions would
be arbitrary and not rational, but intelligible necessities, given as
much to the supreme mind which orders as to our minds which try
to understand. Therefore the order which the Craftsman (in the lan-
guage of the Timaeus) imposes is something with which he is already
confronted when he comes, mythically speaking, to the work of
ordering the primal chaos. It is already given by "intelligible neces-
sity" which kinds of things there can be; and the causal relations
which will subsist between the things are given by the necessitation
relations which exist between the kinds.
Ordered existence has from eternity, of rational necessity, its
finite list of kinds; and the act of ordering does not create the kinds,
it creates instances of them. What the kinds of ordered existence are,
and why there are just these and no others, is of course perfectly
known by a perfect divine mind. The kinds of ordered existence are
imperfectly reflected in the products of this mind's ordering, because
these products are physical; and they are imperfectly reflected also
in the minds of human beings, because human minds (until purified
by philosophy) are prevented from becoming pure minds by the
association with the body and by the almost invincible temptation to
identify things as they affect our senses with things as they really are.
But although physical things imperfectly reflect their kinds, none the
less their behaviour, in so far as it is orderly and capable of scientific
study, does depend on the natures of the kinds to which they are
conformed. Therefore in order to understand what really happens in
nature we must purify our minds as best we can by trying to discern
what X-hood really is, and what relations hold between X-hood and
W-hood and Y-hood. This is the only way by which we understand
how W, X and Y things affect each other.
The third presupposition we have already mentioned; it is that the
natural world does not conform perfectly to the order imposed upon
it. This presupposition is evinced in odd phrases in various places;
for example in certain phrases in the Timaeus which we shall en-
counter, or in a phrase in the Phaedo (75) where Socrates speaks of
physical things "trying to be equal and failing". But it comes out
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most clearly in the myth in the Statesman (268-74), and this we shall
briefly look at here. Sometimes, then, the universe rotates one way,
sometimes the other. It goes one way, winding up so to speak, when
God is in charge, and in that period all things are ordered by the
Gods. But then God resigns the helm and lets the universe unwind.
At first, even without divine guidance, all goes moderately well; but
the universe gradually forgets its former state, and unbalance creeps
in. This goes on until the universe has almost sunk into the infinite
sea of dissimilarity, to save it from which God resumes the rudder and
orders things once more. We live in the running down phase, and that
means that the universe as we know it "remembers", but only
imperfectly, the original divine order.
Let us try to sum up these three presuppositions and the lesson
that they involve for the proper study of nature by the scientist in an
allegory which we have used already. Imagine a library and imagine
that the books in it are not only ordered, but rationally ordered.
That is to say, not only does every book have its place, but also the
whole arrangement makes sense; the man who drew up the plan of
classification drew it up with his eye on "intelligible necessities", and
in consequence it is not only a plan, but an excellent plan. Imagine
next that over the years the books have been a little disordered, and
then imagine a man who wants to find his way about it. He will have
to rediscover the original plan, and this is something he will never do
if he simply passively observes where the books now are; for some
of them are in the wrong places. He will have to combine observation
with the presupposition that the library owes such order as it has to
the imposition upon it of a rational plan. He will look at a book and
ask how reason would classify it; not as a red book, nor as a book of
such a size (for a rational librarian does not classify in these ways),
but as a work of seventeenth century ecclesiastical biography for
example. But the section devoted to seventeenth century ecclesi-
astical biography, ought to be a sub-section of the section devoted to
ecclesiastical biography, and that in turn ought to be a sub-section of
the section devoted to biography. Or perhaps this is wrong. Perhaps
the section devoted to seventeenth century ecclesiastical biography
ought to be a sub-section of the section devoted to seventeenth
century church history. Or ... It is only when these questions are
answered that he can decide the significance of the observation that
this biography of Laud is on shelf L.3. For either it ought to be
there, in which case its neighbours ought to be books on ... (what-
ever rational reflection decided to be the proper classification of a
biography of Laud), or else it has got into the wrong place and
should be disregarded as a stray. If its companions turn out to be, in
the main, what reason suggests they should be, then that is evidence
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that it is in the right place and can be used as a clue to the heading of
the section in which it is.
The man who tries to reconstruct the library in this way is reason-
ing as Plato wants the scientist to reason. If this were not ordered (he
is saying to himself) it would be a complete jumble, which it is not. If
it is ordered, the order will be coherent. What order then can we
discern, which, without doing gross violence to the appearances,
shall satisfy the mind as a sensible way (or rather as the rationally
necessary way) of ordering the universe?
Without these presuppositions the things that Plato has to say
about the relations of observation and theory make complete non-
sense; with these presuppositions they make sense. That to my mind
is evidence that he really did presuppose these things.
II. THE PHAEDO
The relevant section of the Phaedo runs from 96 to 107. The context
is this. Kebes concedes to Socrates that there are grounds for think-
ing that the soul is altogether superior to the body, and has the
power to keep the latter alive; but he questions whether this entails
that the soul is immortal. Powerful though it must be, it might
eventually lose its power. Socrates says that this raises the whole
question of the cause (aitiS) of coming into existence and perishing,
and offers to give an autobiographical account of his own attitudes
to the problem.
No doubt the account which follows was believed by Plato to
be a historically accurate account of Socrates' intellectual develop-
ment, but there is also no reason to doubt that Plato believed
that the pilgrimage he described had led Socrates in the right
direction; and therefore I shall take it that, while the episodes are
episodes in the life of Socrates, the conclusions are shared by Plato as
well
It is a complicated passage, raising more hares than it can really
manage. The clue to it is to bear in mind that Socrates is discussing
"the cause of coming into being and perishing**. His problem in other
words is: "What is a cause?" or: "What is an explanation?". It goes
as follows :
1. Socrates begins by confessing his deep interest, in his youth, in
scientific questions. He thought it would be grand to know why
things come into existence and perish, and so he studied scientific
problems of physiology and physics until he became convinced
(this is Socratic irony) of his own incompetence. For things which he
had thought himself to understand perfectly well, he no longer
understood at all e.g. how men grow. Fifth century science, in fact,
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so far from explaining, made things seem more difficult, and there-
fore there must be something wrong with it.
2. He then goes on to describe similar inexplicabilities in the field
of mathematics. How, for instance, when two 1's are added together
can either or both of them become 2? So no more in mathematics
than in science could Socrates understand "the reason why things
come into existence or perish along these lines; and so he muddled
through to the construction of a different method of his own, and
abandoned the other".
3. But then he heard of Anaxagoras, and of his doctrine that mind
ordains, and is the cause of, all things. He was delighted with this,
and took it to mean that Anaxagoras would settle such questions as
the shape and position of the earth by showing the reason why it was
best for it to be as it is. For presumably mind would ordain that
things should be as it is best for them to be.
4. But in fact Anaxagoras let him down, and offered ordinary
causal explanations in terms of efficient causes. This treachery of
Anaxagoras' Socrates characterises as the extremely common failure
to distinguish the aitia (cause or reason) from the conditio sine qua
non, or that without which the cause could not operate. Thus
Socrates would not be sitting in prison unless his legs could bend (the
sine qua non of his sitting there); but he would not be sitting in prison
unless he had thought it wrong to escape (this therefore is the real
reason why he is sitting there, the fact which should be cited in
explanation). It is because of this confusion that scientists postulate
whirlpools and other explanatory devices in order to explain facts
which could be sufficiently explained by demonstrating why it is best
that they should be as they are.
5. Betrayed, then, by Anaxagoras, and unable to discover for him-
self or to learn from anybody else how "the best" serves as the
supreme cause, Socrates evolved for himself a second-best approach
to the search for the aitia. His account of this "second-best" is that
he gave up looking directly at things, and turned to look at their
images in logoi, in the accounts we give of them, or the things we say
of them; "in our concepts of them" might almost hit the mark. At
this point (99 e-100 a) he interpolates the comment, which we have
already noticed, that physical things are just as much images as are
logoi, from which it follows that he was really turning not from
realities to their images, but from one kind of image to another.
(I shall here interject the comment that the charge that physical
occurrences are images surely implies the doctrine that the world is
rationally designed. Why else should they be images ?).
6. Socrates then goes on to make two points somewhat jumbled
together. The first point is that he decided to proceed hypothetically
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in his reasonings. He does not explain until a page or so further
on (101 d) what he means by this. Since the hypothetical method
is not our concern in this chapter we will pursue this no further
here. 1
7. The second of the two points which Socrates jumbles together
is an example of a hypothesis which he provisionally adopted in
accordance with his hypothetical method, namely his provisional
account of what constitutes a cause or explanation. This, Socrates
says, involves something very familiar to his hearers, namely uni-
versal common natures or forms beauty itself according to itself
and so on. Strictly the hypothesis which he adopted concerning what
counts as an aitid is: that there are forms. But this is immediately
taken to entail a rule : that nothing is to count as an explanation of
why S is P, except the presence of P-hood to S, S's participation in
P-hood, or however you like to describe the form-particular relation-
ship. It is not its florid colour, nor its shape, which makes something
beautiful, but only beauty. Socrates goes on to amuse his audience
by working this out further in terms of the arithmetical conundrums
which he had propounded above. Two is not created by addition or
by division (it had seemed queer that the same result a given
number could be produced by these apparently contradictory
methods) but only by the presence of two-ness.
8. This being established, Socrates goes on to his main proof of
immortality which we have already examined. 2 What we must now
notice is that, in order to make his proof, Socrates relaxes his
stringent provisional rule about the nature of an explanation. The
concession is that if there is something, Q, such that the presence of
Q entails the presence of P-hood, then Q can be said to cause S to be
P just as much as P-hood can. We thus get what Socrates calls
bolder answers to the question: "What causes S to be P?" Fire is
now allowed to explain the warmth of things, the unit to explain the
oddness of numbers, soul the activity of bodies.
9. Eventually it is shown that since the soul is that which brings
life, there is just as strong a relation of incompatibility between death
and the soul as there is between death and life. In other words, it has
been shown that something cannot happen, namely that souls
cannot die.
What are the lessons of this long and complicated passage? In
particular what are its criticisms of the current procedure of scientists
and mathematicians, what is the type of explanation recommended,
and what is the attitude here taken up towards teleology, or the view
that physical things are as it is best that they should be?
1 See below, pp. 539-48. VoL I, pp. 318-23.
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a. Socrates' criticisms
Socrates has in fact two complaints against the explanations offered
by his predecessors, and he makes these complaints in two different
contexts, though he neither specifically distinguishes the two com-
plaints nor allots one to the one context, the other to the other. The
first complaint is that the pre-Socratics failed to offer teleological or
for-the-best explanations. This complaint Socrates makes in the
context of cosmology ; and his comment on it is that those who sinned
in this way failed to. distinguish the sine qua non from the cause the
implication being that all true causes are for-the-best causes.
Socrates' second complaint is that the pre-Socratics advanced con-
fused, incoherent, or self-contradictory explanations, and the
examples of this failure are mathematical
Presumably Socrates believed that the provisional rule which he
adopted (para. 7) concerning the nature of a cause would deal with
both of these complaints at once. It is evident that it would get rid of
confused, incoherent and self-contradictory explanations, but it is
startling to find that it is apparently taken for granted that wherever
this is achieved something like a teleological explanation will be
forthcoming. Certainly in the dialogue : "Why is Laura so beautiful ?"
"Because she has beauty", the answer does not strike one as a teleo-
logical explanation.
However that may be, it also seems likely that one criticism that
Socrates is bringing by implication against his predecessors is that of
impetuosity. He is accusing them of jumping to the first conclusion
that came into their heads. Unless this criticism is implied there does
not seem to be any great relevance in Socrates' telling us (para. 6) that
he himself decided to proceed hypothetically. This is surely a method-
ological recommendation designed to avoid the blunders caused by
the impetuosity of his predecessors.
To return to the two complaints which Socrates specifically makes,
let us ask what he means by saying that his predecessors commonly
confused a sine qua non with a cause. The position is probably some-
thing like this. The Ionian scientists asked such questions as: "What
keeps the stars in their courses?" and gave (to Plato) the impression
that they would have been happy if there were visible chains which
stopped the stars escaping from their orbits; there being no chains,
they postulated other physical phenomena, such as whirlpools in
space, to do the work of the chains. This they did because they did
not realise that "it is goodness that must hold the heavens together"
(99 c 5), 1 or in other words that the order of the universe maintains
itself because it is good that it should be as it is. They could not
1 Or perhaps "it is goodness and necessity that holds . . .".
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realise this because they took for granted that such a question as:
"Why doesn't X fall?" must be met with such an answer as: "Well,
look at this bracket that it is resting on." That is, they took for
granted that you explain a physical phenomenon by pointing to
physical apparatus, and for that reason they postulated unnecessary
physical apparatus. To them Socrates retorts the counter-example of
himself remaining in prison a counter-example which is of course
highly tendentious unless it is granted that the physical universe, like
Socrates' body, is operated by mind. This granted, however, the
example shows that another kind of explanation is not only possible
but superior. Physical apparatus explains in some cases how, but in
no case why something happens. (Indeed in the case of the stars there
is no apparatus to explain even how they behave as they do, and this
no doubt is why they are divine; they, like Socrates, behave as they
should simply "under the impulsion of their estimate of what is
best"). Thus when Socrates a little further on (108 e-109 a) comes to
explain why the earth does not fall, he does so by saying that since
the universe is homogeneous there is no reason why it should fall;
i.e. there is no better place for it to move to, and so it stays in the
middle. This is the kind of explanation of a physical fact which
Socrates evidently believes in.
When we turn to Socrates' second complaint (this is the criticism
which is made in the context of mathematics) it is not so clear either
what it is or what he wants. Two lines of criticism suggest themselves.
One is that mathematicians explain mathematical phenomena in
terms of physical operations such as cutting in half and putting side
by side. The other is that in statements such as "2 is produced by
division" (analogous to "Beauty is produced by bright colouring")
one does not get the universal correlation required in an explanation.
Two is not the quotient in every division, nor is division the only way
of arriving at the number 2; some brightly coloured objects are not
beautiful, and some beautiful objects are not brightly coloured.
The only way of ensuring the desired universal correlation is to
say that the only "aitiA of a thing's coming into existence" is its
form: thus 2 is only produced by twoness, beautiful objects only by
beauty.
Putting together these various points, it seems that Socrates is
accusing his predecessors of advancing explanations which have all
or some of the following faults :
They postulate unnecessary physical apparatus in order to explain
physical phenomena.
They confuse the apparatus which explains in some cases how a
thing happens with the reason why it happens.
They neglect teleology.
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They commit "type-transgressions" (as by advancing physical
processes to account for mathematical entities).
They explain, at best, particular cases of a phenomenon, but not
the phenomenon in general.
As his remedy for these defects Socrates seems to offer: first a
general recommendation to proceed tentatively; and then the par-
ticular rule that only the presence of P-hood can explain why S is P.
He seems to suggest that compliance with this advice will avoid all
these defects, and enable us to give satisfactory explanations of how
things come to be and perish ; and (remembering the remoter context)
he seems to suggest that this will enable us to deal with such questions
as whether the soul is immortal.
b. The type of explanation Socrates recommends
This is all very puzzling. With the criticisms of the pre-Socratics we
must feel some sympathy (assuming that the pre-Socratics were as
Socrates describes them); but how on earth are Socrates' recom-
mendations meant to help?
The hypothesis that there are forms, and the "consequence" of it,
that only the presence of P-hood to S can explain why S is P, does not
seem likely to guarantee adequate explanations. Surely if we adhere
to this "safe rule" we shall avoid giving incoherent explanations, if
only because we shall avoid giving any kind of explanations what-
ever. It certainly does not seem at all obvious that we shall arrive at
teleological explanations along this route; and indeed it is often
supposed that Socrates has given up the hope of arriving at such
explanations. He does not however say that he has done so (99 d 1).
He does not say that he has given up seeking for "the best" as aitid,
but that he has adopted a different method of seeking the aitid.
Let us ask then what Socrates is really recommending. At first and
at second glance Socrates* rule is a very stupid one. At first glance we
say something like this: Socrates is frightened out of his wits by the
confused attempts at explanation of his predecessors, and he pre-
scribes the panic remedy of abandoning the attempt to explain. He
justifies to himself the burying of his head in the sand by a fallacious
argument resting on the ambiguity of such words as "makes" in such
questions as: "What makes Laura so beautiful?" In some contexts
we should be seeking for her distinctive kind of beauty, and so the
proper answer would be: "Her delicate colouring." In other contexts
we should be reflecting on the nature of feminine beauty in general,
with Laura merely as an example, and so the proper answer would be
something I shall not try to conjecture. And there are just one or two
contexts (for instance when we are teaching someone the use of
abstract nouns) in which the expected answer to: "What makes
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Laura so beautiful?" would be "Her beauty". So a question begin-
ning "What makes . . . ?" or "Why . . . ?" is ambiguous, and, we may
feel, Socrates has not noticed this fact. In particular he has not
noticed the difference between the gejneral question about feminine
beauty and the particular one about Laura's. And so he feels that
"Her delicate colouring" is simply a wrong answer to the question,
whereas in fact it is a right answer to one interpretation of it. He feels
it is a wrong answer because delicate colouring is not, after all, what
makes Celia so beautiful (for she has black hair and a white com-
plexion); and therefore delicate colouring is not what makes people
beautiful, and therefore it is not what makes Laura beautiful. As we
saw, the idea that Socrates is guilty of this confusion is suggested by
his arithmetical examples. For he objects to the view that 2 is made
by addition on the ground that addition can make other sums, and 2
can be made in other ways. Thinking all this, then, and seeing that it
is the business of scientists to give general explanations, he gives
them a safe rule for general explanation (cite nothing but P-hood in
explanation of the fact that S is P) which loses the baby with the
bath-water; and this is all very reactionary and stupid.
So much for first glance. At second glance a worse thought strikes
us: perhaps Socrates has been misled by his metaphors about par-
ticulars trafficking with universals. Perhaps he is advocating not no
explanation, but a mad kind of explanation. He is attributing to
universals a magic power; what they lay their hands on is conformed
to their likeness ; what beauty touches becomes beautiful, pairs spring
up where two-ness lays its finger.
But if we look again more closely we can perhaps find something
sensible for Socrates to mean. Firstly we must remember that
Socrates* rule does not forbid us to answer the question: "What
makes S P?" by giving the definition of P-hood. If we could answer
the question "What is beauty?" in a way satisfactory to Socrates, we
should have insight into the nature of beauty, because we should
have analysed it into its elements, and that would enable us to see its
connections. Given this insight we could give answers to: "What
makes S P?" which should both remain within the framework of
Socrates* rule and yet also convey information. If one remembers
Socrates' general insistence on the importance of answering such
questions as "What is beauty?" we can see that the effect of his rule
would be to confine explanations within a framework but not to
render them impossible.
But secondly we may observe that Socrates* rule is only provision-
ally put forward, and its rigour is shortly modified. Perhaps then
Socrates does not mean to confine us to saying: "It is beauty that
makes Laura so beautiful", nor even to confine us to saying: "It is a,
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b, c which makes Laura so beautiful" (where "a, b, c" gives the
definition of beauty). This is the incontrovertibly safe form of ex-
planation, and we are allowed to venture a little outside it when we
can see equally safe ways of doing so* The modification which
Socrates in fact makes ("Q may be said to explain why S is P if Q
entails P-hood") is not a very large one, but the reason for this may
be that it is enough to give him all he wants for his proof of im-
mortality. Perhaps he thinks it possible that even more adventurous
steps might be made if each step was tested before it was taken. (This
may be another reason for the mention of hypothetical procedure in
para. 6).
And indeed his modification, small as it seems to us, might have
seemed quite large to Socrates. One is reminded of something that
Aristotle says of Socrates (Metaphysics 1078 b 23-25): "he rightly
sought definitions, for he wanted to syllogise, and a definition is the
starting-point for a syllogism." What Aristotle means by syllogising
in this connection is, I think, the process of drawing the conclusion
that whatever is S must be P, from the premises that S-hood entails
M-hood and M-hood entails P-hood. Aristotle certainly thought, and
Socrates I suggest thought also, that it is possible to arrive at new
truths about "things that cannot be otherwise" by syllogising. We
know that this is wrong, 1 but it is not unplausible After all in
mathematics we find necessary connections between what seem to be
totally distinct natures. To be a three-sided plane figure is not at all
the same, we feel, as to be a plane figure whose internal angles are
equal to two right angles; to be the square of 5 is surely not at all the
same thing as to be the fourth part of 100. Yet in each case wherever
you find the one property you find the other. And indeed it is not
only that the connection is invariant; it is also intelligible. The proof
that establishes the fact also shows why it must be so. Geometry and
arithmetic consist of such intelligible necessities, and yet they seem
to give us vital information about the world. Geometry tells us of the
structure of space, arithmetic of what divisions, combinations and
other arrangements of objects can be made. Is it not then likely (the
ancients may well have thought) that there are other sciences, or
developments of these sciences, which consist of intelligible neces-
sities, and yet give us further information about how things can
behave? If geometry tells us about the structure of space, why should
there not be some other science which teaches us how things can
move about in space? After all geometry itself tells us that a thing
can travel in a straight path, and then in another straight path at
right-angles to its previous path, and then in another straight path at
1 "Wrong" is perhaps too strong. It depends on how you define "new" in "new
truths".
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right angles to each of its previous paths; but that it cannot then
travel in yet another straight path at right angles to all three previous
paths. This may well seem to constitute a restriction upon freedom of
movement imposed by rational necessity and discovered by the study
of rational necessity in geometry.
If we allow that there are necessary connections of this kind, then
we can begin to travel along them; and there was no knowing for
Plato and Aristotle how far we might be able to travel But of course,
as Aristotle says, a definition is the starting-point of a syllogism. You
need to know what S-hood and M-hood are (in the sense of being
able to analyse them) in order to spot the connection which binds
them together. It was not absurd to believe that, if we could fulfil the
Socratic programme of analysing such natures as beauty or justice or
triangularity into their components, we could see what necessary
connections hold; and that, if we could see what necessary connec-
tions hold, we could swing ourselves from branch to branch along
them until we understood the order of nature; and if we did that (to
anticipate) we should see how mind had disposed things "as it was
best for them to be".
Naturally enough there are no very convincing examples of such
journeys from branch to branch in Plato or anywhere else, because
they are not in fact possible. But examples of a kind can be found.
One is under our noses, for Socrates goes on to discover that souls
cannot die. This he does by an implicit analysis of what it is to be a
soul, by which he discovers that the correct answer to "What is a
soul?" is "A bringer of life". This reveals a necessary connection
between souls and life, and the conclusion follows (if we do not look
too closely). In this way analysis shows us what to syllogise, and by
syllogising we discover an important new truth. Or we might think
of the passage at the end of the Philebus (64 onwards), where Socrates
shows that goodness depends on balance, from which he infers that it
is bound up with beauty, and eventually arrives at certain conclusions
about thought and pleasure.
All this has got a good way away from the text of the Phaedo. The
suggestion is that Socrates* rule for explanation is a condensed state-
ment of Plato's methods for constructive philosophising, which are
essentially that you can only establish a conclusion about the rela-
tions of X and Y things by analysing X-hood and Y-hood and seeing
what connections hold between them. Socrates does not tell us
positively that we are to follow this method (probably Plato could
not at this stage state what the method was). He lays down a rule
which prevents us from straying outside the confines of the method,
and he follows the method himself (albeit loosely and informally) in
his proof of immortality. But although Socrates does not delineate
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the method, I think we have to choose between two alternatives.
Either Socrates is telling us that "Opium makes us sleep because it
has a virtus dormitiva" is the model of all valid explanation, or he is
telling us, not how to make sound explanations, but the confines
within which we are to keep if we wish to avoid giving unsound ones,
and arriving at false conclusions. But if he is doing the latter, then
he must have some idea at the oack of his mind about how we are to
move within these confines; and what can this idea be but some
version of the doctrine I have tried to describe?
Assuming that this reasoning is correct we can put Socrates' point
in something like the following way. Kebes had said that, for all he
could see, souls might die. Socrates replies that this raises the whole
question of the aitid of coming into being and perishing. The reason
for this is that Kebes' problem is of the form: "Can X happen to an
A?". And to this Socrates wants to say that those and only those
things can happen to an A which neither are nor entail the contrary
of A-hood. The copper-bottomed rule is that an A thing cannot,
while remaining an A thing, become either non-A or something else
which entails non-A~hood. To decide therefore for certain whether X
can happen to an A it is necessary to analyse X-hood and A-hood in
order to see how they are related to each other. The result of such an
analysis (informally carried out) in the case of death and the soul is
the conclusion that a soul cannot die.
c. Teleology
I have suggested that what Socrates has in mind is the programme of
"syllogising", or of making one's way along a chain of necessary
connections. So far I have argued for this interpretation chiefly by
asking what else Socrates can have had in mind when he advanced
the rule that only the presence of P-hood can explain why S is P (the
rule from which he extracts the principle that an S thing can only
become P if there is no incompatibility between S-hood and P-hood).
We will turn now to the question whether Socrates is abandoning
the hope of teleological explanation which arose in him when he read
of Anaxagoras' doctrine that mind orders all things. I think the
examination of this question will strengthen the view that Socrates
has the programme of syllogising in mind.
The crucial paragraph is 99 d 4-100 a 8 (para. 5 of our summary
above). Just before the paragraph opens Socrates says: "Shall I give
you a demonstration of the second voyage to the search for the aitid
in the way I devised?" The phrase "second voyage" (deuteros pious)
is said to stand for rowing when there is no breeze; in other words for
a more laborious way of getting to one's destination. If Socrates were
using the phrase strictly in this sense here, then he would be telling us
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that the procedure he outlines is a more laborious way of arriving at
teleological explanations than that taken by Anaxagoras. However
one does not always use such metaphorical expressions very strictly,
and there is certainly one place in Plato where this one is used to
mean no more than "next best thing" (Phtlebus 19 c 2). So we cannot
hang anything on this. Socrates may be offering us a less direct
method of reaching teleological explanations, or he may be offering
us a method of explanation which is not so satisfactory as teleo-
logical explanation would be if only teleology were within reach of
our powers.
He then goes on to contrast: looking at things and looking at their
images. He takes the figure of a man blinding himself by staring at
the sun during an eclipse, and compares to the predicament of this
man his own failure to achieve teleological explanations by looking at
realities. With it he contrasts the wiser policy of watching eclipses in
their reflections in water, likening to this his new procedure of look-
ing at things in their logoL So far we are left with the impression that
he has decided to give up science and turn to something else
methodology perhaps or even metaphysics instead. But then we
recall that he tells us that the figure of the sun and its reflection is mis-
leading; for the things he looked at after his change of policy are no
more images than the things he looked at before it, as the figure
implies. At this point we also notice that he employs a different
contrast (99 e) ; no longer between looking at things and looking at
their images, but looking at things with the senses and looking at
them in the logoL
If he simply said: "I turned from things to logoi" we could well
believe that his meaning was that he gave up his interest in the
physical world and went over to logic or some other discipline. But
he does not say this. When he says: "From things, to their images,
namely logoi", he is ironically adopting his opponents' account of
what he did. His own account of it is: "From things through the
senses, to things in logoi" But in this formulation "through the
senses" and "in logoi" are in parallel with each other. It is as if each
of the things he was previously interested in (e.g. the sun) had its
empirical phenomena and also its logos, and that Socrates abandoned
the former for the latter. But if this is right, Socrates is not telling us
that he turned over to logo! in some general sense (this would be
logic or methodology), but to the logoi of whatever things he hap-
pened to be studying; and in this case "the logoi" must mean some-
thing like the accounts, definitions or concepts of the things in
question.
But does the notion of studying the physical world in "accounts,
definitions or concepts" make any sense? One could study the history
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of ideas, surely, in this way, but one could not do science. But yet it
does make sense, on Plato's presuppositions. The idea is that when
one is considering whether, for example, the sun travels in a circle,
or whether the soul is immortal, one does not rely (solely) on observa-
tion. One first tries to find a satisfactory logos of the sun or of the
soul. How the achieving of a logos will settle the question in the case
of the soul we have already seen. In the case of the sun, how about
the following argument: the sun is a self-moving and therefore
spiritual being; but the circle is the motion proper to intelligence;
therefore the sun moves in a circle? 1
I do not think that Socrates means precisely and only this by
"looking at things in logoi". For just after using this phrase he says
(100 a 2): "I always hypothesise what seems to me the strongest
logos", and then goes on to give the hypothesis relevant to the
present discussion which is: that there are forms. And of course
"that there are forms" is not a logos of anything in the sense which
"bringer of life'* is a logos of the soul. I cannot therefore claim that
my interpretation does precise justice to everything that Socrates
says. But it does do justice to the parallelism between "through the
senses" and "in the logo?\ and this is important. For the rest, the
passage is evidently very compressed, and I would argue that
Socrates is passing from one sense to another of logos without notic-
ing the transition. Perhaps he is helped to do this by the fact that the
use which he proposes to make of the hypothetical logos that there
are forms and that only the presence of P-hood can make S P, will,
as we have seen, draw upon the logoi of the entities (life, death and
soul, or whatever it may be) that he is discussing. This logos is a
logos which requires us to study things in their logoi.
Suppose we say then that Socrates is not telling us that he gave up
his interest in questions of physical fact, but that he came to see that
it was at any rate no worse to decide them a priori than to decide
them by relying on observation. The question remains whether this
a priori procedure is a more laborious method of arriving at teleo-
logical explanations, or whether Socrates has given up the hope of
arriving at this goal.
To help us with this question let us ask what Socrates had in mind
when he expected Anaxagoras to decide whether the earth was in the
middle of the universe by demonstrating whether it was better for it
to be there (97 e). Surely he must have envisaged some such argument
as the following: The earth is the noblest of the heavenly bodies
because it is the home of intelligent beings. The place of privilege in
a sphere is the centre. Therefore the proper place for the earth is the
1 This argument is constructed out of something in the Tenth Book of the Laws.
See below, pp. 240-1.
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centre, and for that reason, since there Is no more appropriate place
for it to move to, that is where it will stay (and without the help of
chains, whirlpools or any other physical apparatus). This is the kind
of explanation, surely, that Socrates wanted and Anaxagoras failed
to provide.
But then surely this is precisely the kind of explanation which
Socrates' method of looking at things in their logoi will lead to. If
this is right, then, what Socrates is proposing is not the abandonment
of cosmological and other speculation, but the abandonment of the
idea that questions of this kind can be settled by looking and seeing.
The kind of science which is to result from attention to logoi is the
kind of science which Socrates expected from Anaxagoras, and
which Anaxagoras could not provide, simply because he relied on
observation helped out by wild ad hoc hypotheses (whirlpools and so
forth) instead of asking himself the crucial question, namely what
the entity whose behaviour he is studying really is. Socrates does not
want to abandon science, but to do it in a less empirical way.
But even so, will this bring him teleology? If he is going to do
science by "syllogising", will he thereby discover that things are
arranged as it is best that they should be? If he discovers that it is
impossible that souls should die, will this tell him something about
the cosmic power of good?
The answer to this surely is that the whole programme of syllogis-
ing makes sense only if things are disposed by mind; and clearly "the
best" is identical with that which reason approves of. A common
word in Greek (especially in Aristotle) for logical impossibility is
atopon which properly means "absurd" or "bizarre". An impossible
arrangement is conceived of as an absurd arrangement, such as will
not be allowed to arise in a well-ordered universe. To us it is clear
that there cannot possibly be round squares, and that there should not
be functionless organs in animal bodies, and that what cannot be and
what should not be are two totally different things. But we must get
rid of the idea that Plato would be clear about the gulf between the
two. Rather for him, I think, what cannot be is a gross case of what
should not be. We feel that by "syllogising" one can discover logical
impossibilities, but not teleology. I do not believe that Plato would
draw this line. If we carry out his programme of asking how we
should conceive of the sun, and settle the nature of its orbit in the
light of the answer to this question, then we shall be giving ourselves
a picture of the world in which we see things behaving in the manner
appropriate to their natures; and to see this is to see them behaving
as it is rationally satisfactory that they should; and of course what is
rationally satisfactory is good. This is the kind of teleology which
Socrates wanted of Anaxagoras, and which his own recommenda-
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tions were intended to provide. Socrates has not abandoned Ms hope
of seeing that things are arranged as it is best that they should be; he
has merely abandoned the idea that empirical observation can get us
to this goal.
Some further points about the Phaedo
1 . It is common to feel in Plato's writings that Ms point is better than
his reasons for his point. So here. However true it is that what under-
lies Socrates' rule: "Only the presence of P-faood can make S P" is
the programme of syllogising, it is also true that he is made to argue
for it as if the point were that no other pattern of explanation can
explain every case of something's becoming P. To this argument one
is of course inclined to retort: If you stipulate that the cause of some-
thing, say death, has got to be the same in every case, then of course
you reduce yourself to tautologies of the form "People die because
death is present to them". But the stipulation is quite unreasonable.
There is no doubt that the use of the notion ofaittd in this passage
is very crude, and that quite different topics are jumbled together.
How there can come to be two objects, how one thing can come to be
taller than another, how things can come to be warm or alive there
is no classification of such topics into distinct kinds. Phrases like "the
putting of one alongside one is not the cause of the occurrence of two"
(101 b 9) are used without any clear indication whether the question
is: "Why are there two things here?" (to which an answer in terms
of putting one thing alongside another would be appropriate); or
whether the question is : "How does the number 2 arise ?" TMs failure
to distinguish topics makes it easier to argue that every case of a pheno-
menon must be given the same explanation as every other. For there
is a sense in which one would agree that the number 2 does not some-
times arise by division and sometimes by addition (if only because
the number 2 is not the sort of thing that "arises" at all). But if the
question "How does the number 2 arise?" is thought to be the same
sort of question as "How does life arise ?" or "How do eclipses
happen?", then this will help one to dismiss, as absurd, answers in
terms of anything but "formal causes" ("S becomes P only when
P-hood becomes present to S").
It would be possible to say therefore that this section of the
Phaedo is simply a nest of confusions, and that its only philosophical
interest is to show us what can happen if one-, for example, jumbles
mathematical and non-mathematical topics together, and fails into
the bargain to distinguish different senses of such notions as
"through" and "in virtue of". This is quite true, and it would be a
useful elementary exercise to make a list of such confusions in this
passage. But "one finds bad reasons for what one believes on
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instinct", and the question is, not only what mistakes did Plato make,
but also what ideas had he which made the mistakes seem plausible.
That is the question I have tried to answer.
2. There is something about Socrates' proposals for a priori
science which must strike any modern reader. We might grant that if
a man believes that the universe is a product of intelligent and com-
prehensible planning, then to ask the question: "What sort of entity
is the sun, and what behaviour is proper for an entity of that sort?"
may be a sensible move towards a hypothesis about its behaviour,
but we should insist that a hypothesis arrived at in this a priori
fashion would then have to be tested by observation. But Socrates
only mentions observation to disparage it. The most he can hope for
therefore is to construct for himself a beautiful picture of how things
might be disposed for the best; whether the picture depicts reality he
cannot possibly tell.
To this there are various partial answers. Firstly Socrates has his
eye mainly on questions which cannot be settled by observation, or
which could not be settled by Greek observational technique
questions of cosmology, of the immortality of the soul, and so on.
Secondly Plato is seldom a cautious writer. If his current purpose is
to exalt the role of theory at the expense of observation in the framing
of hypotheses, he is quite capable of exalting the role of theory at the
expense of observation tout court. But thirdly there probably is a
place for observation in Socrates' procedure anyhow. For every
logos which is to be advanced is advanced hypothetically, and its
"consequences" are to be tested before it is taken seriously. Now the
things that Plato says about the testing of "consequences" are
obscure and will have to be examined in a later chapter. 1 Plato
certainly does not say that empirical tests are included, but he does
not say that they are excluded, and I do not think that they are. But
in that case if we take the logos that the sun is an intelligent being,
then it might be a "consequence" of this that it will have the motion
proper to intelligence. But then surely the testing of this logos might
involve ascertaining whether this "consequence" conflicts with
evident facts. There are plenty of examples in the dialogues of a logos
which comes to grief by conflicting with what might easily be called
observed facts. But if Plato is proposing that observation should be
invoked at this stage, then his point about observation is not that it
has no place in science, but that it has negative work to do. He may
well have thought that in the case of the topics he has in mind
observations are ambiguous. The planets appear to move irregularly,
but clearly it is possible that by some system of compound motions
their behaviour can be reduced to order. Our problem therefore is
1 See below, pp. 539-42.
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COSMOLOGY AND THEORY OF NATURE
what to do with observations when we have got them. This being the
case the most that observation can ever do is to show that a theory is
untenable. The choice between theories which clear this hurdle will
have to be made on other grounds; and at this point (at which the
modern scientist invokes such considerations as simplicity) Plato
invokes the presupposition that the world is rationally designed.
III. THE REPUBLIC
We return now to the Republic. The material which concerns our
present purpose is to be found in the Sixth and Seventh Books, but
particularly in the simile of the Sun in Book 6 and in the proposals
for the education of the philosopher-rulers which are made in Book
7. For the general outline of what is said in these places I must refer
the reader to the chapter on the Republic. 1 Here we shall be chiefly
concerned with two questions: (a) whether the Republic believes in
teleology, and (b) what it has to tell us about scientific method. Some
readers may want to say that these questions are inapposite, since the
Republic is not concerned with the material world, but with the forms.
The short answer to such a dismissal of the questions that we want to
ask is that the negative part of this proposition is false and that the
positive part does not entail the desired conclusion. The Republic is
concerned, in the relevant passages, with the material world, for it is
concerned with the question how to train men for government; and,
while the text indeed talks about the structure of the system of forms,
it remains the case that, on almost any view of the relationship
between forms and things, statements about forms must entail
corresponding statements about things. (To give a crude example of
one kind of correspondence, if bee-keeping is a kind of stock-raising,
Jones, being a bee-keeper, must be a member of the class of stock-
raisers). It is indeed often difficult to decide just what statement
about the material world we may infer from some statement about
forms; but it seems obvious that any statement about the relation-
ships of the forms must tell us something about the material world
and about the proper study of it.
a. Teleology in the Republic
The data for considering the question of teleology are mainly to be
deduced from the things that .are said about "the form of the good",
or in other words about goodness. These are to be found in the simile
of the Sun and in its graphic elaboration in the simile of the Cave.
The general outlines of my interpretation of these passages are to be
1 VoL 1, Chapter 3.
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found in the earlier discussion of them; 1 here we shall be concerned
with the more detailed discussion of certain points.
I shall however recapitulate what seems to me to be the essential
point. This is that while all abstract thinking is done (as the Cave
makes clear) in the light shed by goodness, nevertheless (a) goodness
is the last form which we are able to discern, but (b) it is also the first
that we are able to discern with absolute certainty; since it is the
anhupothetos arche of all the others, it is that the discernment of
which is no longer a case of supposing or taking for granted. I have
taken this to mean that an account of the nature of goodness is some-
how presupposed in all the concepts that we form; that in the forma-
tion of concepts we are dimly discerning* or "recollecting" a system
of distinctions or classifications which somehow owes its nature to
goodness. To understand what this might mean I used as a parallel
the principle of classification of a collection such as a library. This
principle, which could be stated in such a phrase as "that the library
should be rationally or properly arranged", is the telos, the end or
good, which gives the classification its point. It is also something of
which any intelligent person can fairly soon get the hang, and of
which anybody must get the hang before he can find his way about
the library. We might also imagine (though here perhaps we are
straining plausibility for the sake of the parallel) that it is impossible
really to understand the principle of classification without first seeing
how it works out that is to say that we have to see what sections
and sub-sections the classification produces before we can fully
grasp the principle of it, and, perhaps, that there is no way of stating
the principle except by stating the arrangement in which it issues. It
would also of course be the case that the principle is responsible for
the existence of the various sections and sub-sections, in that such a
section as, for example, Medieval European Costume would have no
place in a classification whose principle was colour or weight. The
merit which I claim for this parallel is that it gives us some idea of
how Plato might have supposed that goodness was responsible for
the existence and intelligibility of the other forms and of what he
might have meant by telling us that we use all along the light, which
comes from a source the nature of which cannot be discerned until
we have discerned all (or at any rate very many) 
