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2.4.4. Knowledge and Belief in the Republic
One of Plato's perennial interests is in the distinction between knowing something and merely believing it (albeit truly). The Meno (see Section 2.4.1 above) represents an earlier attempt to come to grips with this distinction, and the Theaetetus (see Section 2.5.3 below) contains a later attempt. In between lies the discussion in Republic, book 5. It is best to enter the argument at 473c where Socrates makes his famous pronouncement that philosophers should rule as kings. This raises the question what constitutes a philosopher. Since knowledge turns out to be distinctive of the philosopher, the argument to establish the nature of knowledge is of the utmost importance for the Republic as a whole.
Plato argues that knowledge is of 'what is', belief of 'what is and is not'. As with Parmenides, we face the problem of what is meant by 'is'. This time the view least likely to be correct is that 'is' means 'exists'. One must not assume Plato is saying 'Knowledge is of what exists' and 'Belief is of what exists and does not exist'. One reason for rejecting this view is that something either exists or it does not: it is not sensible to think existence is a matter of degree.
So what is Plato talking about? Commentators differ over this, but here are two candidate readings. When Plato says 'knowledge is of what is' (or of'something that is'—see 476e-477a) he may mean either (1) knowledge is of something that is true (the so-called veridical reading), or (2) knowledge is of something that is F (the so-called predicative reading). Fhere stands in for some predicate: in other words, on the predicative reading Plato will be saying, 'knowledge is of something that is beautiful, is good, is just, is large, or is some-thing-or-other'. 'Being something-or-other' in this predicative sense is oneway of'being' in Plato's Greek.59
The predicative reading is popular because it allows a link between knowledge and the Forms with which Plato is so preoccupied in the central books of the Republic. This reading fits with a version of the theory of Forms championed by Owen and Vlastos among others.60 In this version a Form, for Plato, is something which strictly and truly is F, in contrast with other things which are only imperfectly or variably F. For more discussion of this, see Section 2.4.5 below, Some would say61 that Plato is not restricting knowledge to Forms in book 5, and at most he is arguing that without knowing Forms someone cannot know anything. (If knowledge of the Form Justice itself is to have any practical application, one would hope that the philosopher could also know that a particular city or person was just, for example.)
59	For a discussion of the different readings, see Gail Fine, 'Knowledge and Belief in Republic V-V1I, in
Everson (ed.), Epistemology, and Annas, An Introduction to Plato's Republic, ch. 8.
60	See Gregory Vlastos, 'Degrees of Reality in Plato', in Platonic Studies, and G. E. L. Owen, 'A Proof in the
Peri Ideon, in R. E. Allen (ed.), Studies in Plato's Metaphysics (London, 1965).
61	Cf. again Fine, 'Knowledge and Belief in Republic V-VII'.

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Plato contrasts philosophers (lovers of wisdom) with other characters whom jje refers to as 'lovers of sights' and 'lovers of sounds'. These people are full of curiosity about the beautiful things to be seen and heard in the cultural sphere, plato says of them that they recognize 'many beautifuls', but not the one Form: 'the Beautiful itself (see 475d-476d). He argues to the conclusion that what these people come into contact with is something that 'is and is not'. Since knowledge is of what is, the lovers of sights and lovers of sounds are excluded from knowledge proper, and have only belief or opinion (see 478d-479d).
There are two crucial questions here: (1) What is 'recognizing many beautifuls' (as opposed to the Form of Beauty itself)? (2) How is it that these 'many beautifuls' both are and are not, and 'are rolling about as intermediates between what is not and what purely is' (479d)?
Consider two possible answers to each. Plato may be thinking of objects—a beautiful statue, a beautiful painting, a beautiful melody—and he may think that each of them is beautiful in a way, and is not beautiful in a way: this answers question 2, understanding 'is' and 'is not' predicatively,
Or he may be thinking of properties—being made of gold, being symmetrical, being in a certain musical key—and he may think that having these properties makes some things beautiful and some not beautiful. In the latter case, the lovers of sights and sounds attempt to answer the question 'What is beauty?' by saying that it is no one thing, because there are many, many properties which count in different circumstances as being beautiful. Question 2 is answered (again adopting the predicative reading) by saying that some things that have these properties are beautiful, but some are not. (Consider especially 479a-d.)62 A final point to note about this argument is that it appears to make the class of things one can know and the class of things one can have beliefs about quite distinct classes. This seems to go against the idea in the Meno that a true belief could be converted into knowledge—with that idea, what you believe and what you know would be the same. Yet in the argument of Republic 476d-478e Plato thinks he can establish that what is knowable must be distinct from what is believable (or opinable).
2.4.5. The Theory of Forms
The theory of Forms has been discussed in English-speaking philosophy probably more than any other topic in Plato over the last forty years. There is much disagreement among scholars in this area, and the debate can become rather abstruse.63
'    H T. H. Irwin, 'Plato's Heracliteanism', Philosophical Quarterly, 27 (1977), 1-13, and/or his Plato's Moral , Ifeiry (Oxford, 1977), 144-52, are of help.
" A newcomer to the topic is advised to consult some of the introductory literature, such as Harold Chemiss, 'The Philosophical Economy of the Theory of Ideas', in Gregory Vlastos (ed.), Plato, i (Garden r.itv

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One point to make is so basic that commentators often take it for granted. Plato's Forms are thought of as part of reality. Each of them eternally exists regardless of changing human conceptions and of changes in the world of ordinary perceptible objects. In other words, Plato believes that Beauty and Justice exist and always will do, even if no one has a correct conception of them, and even if there are no beautiful or just things around in the perceptible world at any given time. (The older translation 'Ideas' instead of'Forms' may encourage the error of thinking Forms exist 'only in our minds'. For Plato they are things the mind may grasp, but not mental entities.)
But what are Forms? An initial thought is that they are what today's philosophers call properties: beauty, or being beautiful, largeness or being large. This distinguishes them from things that have properties: the statue or person that is beautiful, is large, and so on. This is certainly one part of Plato's theory: each single Form is always distinguished from the many things which 'participate' in it. There are many beautiful things, but they all share in the one Form, Beauty. Properties are what are often called universals, as opposed to particulars. (Some of Plato's Forms are rather what we would call relations—Equality, Likeness, Doubleness—but these would also be classed as universals.) Note, however, that Plato does not use the terminology of'property', 'universal', or 'particular'.
A way to approach the theory of Forms is to ask two overall questions: (l) How do Forms differ from the 'other' or 'many' things which Plato says have a share in them? (2) How do these 'other' things relate to a Form in each case?
In answer to question 1, the most obvious points are that 'other' things are many, but a Form is always only one; 'other* things can be perceived by the senses (they are perceptible or sensible), while Forms cannot; 'other' things are subject to various kinds of change and variation while Forms are not.
Forms, unlike the sensible things that share in them, suffer no mixture between being and not being. But what does that mean? Think again of the predicative sense of'being' (introduced in Section 2,4.4). A sensible beautiful thing, Plato claims, is beautiful, but—in different ways—it also is not beautiful, In this sense it 'is and is not'. Forms, as Plato says, simply are, and never are not. They 'truly are'—i.e. whatever they are, they are without any qualification, variation, or imperfection.
NY, 1971) (also in Allen (ed.), Studies in Plato's Metaphysics), and the relevant chapters in Bostock, Plato's Phaedo, or Annas, An Introduction to Plato's Republic, or sections of the general books I. M. Crombie, M Examination of Plato's Doctrines, ii (London, 1963), J. C. B. Gosling, Plato (London, 1973), and Nicholas P. White, Plato on Knowledge and Reality (Indianapolis, 1976); and then the articles Vlastos 'Degrees of Reality in Plato', Irwin, 'Plato's Heracliteanism', and Owen, 'A Proof in the Peri Ideon. Bostock, Plato's Phaedo, 15-31, is also useful. But Plato's own words are best. Here is a list of passages with which one should be reasonably familiar before pursuing more general questions about Plato's Forms: Phaedo 65d-e, 72e-76e, 78c-79a, 95e~107b; Republic 507a-511e, 514a-518d, 523a-525b, 533b-535a, 596a-b; some short passages in dialogues not yet discussed: Symposium 210a-211b, Cratylus 389a-d, 439b-440e; Parmenides 128e-130a, discussed in Section 2.5.2 below.

r	The Pre-Socratics and Plato	3 79
Here many have thought that Plato gets into a serious muddle. If beautiful sensible things are and are not beautiful, and the Form, by contrast, simply is, then do we not have to say that the Form, the Beautiful itself, is beautiful'? This— which is often called the 'self-predication' of Forms—would be a confusion on Plato's part because the property of being beautiful is not itself a beautiful thing, the property of being large is not a large thing, and so on.
Some of the time Plato seems to think of Forms as paradigms. A paradigm of a property is a supreme instance of it which sets a standard for other instances to live up to: something perfectly beautiful would give an absolute standard against which to judge all other beautiful things. Does Plato think of Forms as paradigms, or as properties, or as both? Our answer here (which may not be conclusive) will have repercussions for the general question 2 raised above. If Forms are paradigms, we might expect the relation between them and sensible things to be one of likeness or resemblance; if they are properties, then, whatever the relation is, we would expect it not to be one of resemblance. (Note that Plato is often openly vague about what this relation is: see Phaedo lOOd, Pa.rmenid.es 130e-133a.)
It is clear that Plato in his 'middle' period wants Forms to be things of absolute value. What Justice or Goodness is cannot be relative to different times, people, or places. Justice and Goodness are admirable to contemplate; in the Symposium, and also in the Republic and Phaedo, Plato describes philosophers as passionately loving the Forms. At times he speaks of other things trying or aspiring to be like Forms, but being only an imperfect copy. Plato wants Forms to give an explanation of things' having the characteristics they have—and it may be that he thinks beautiful things can be beautiful only by sharing in something which itself truly is beautiful.64
So a question which must be considered is whether Plato believes in the self-predication of Forms. If so, the easiest verdict is that he is in a muddle. But there may be an alternative verdict: perhaps when Plato thought of the propositions 'Beauty is beautiful' or 'Largeness is large', he was not confusing properties and paradigms. This would be the case if'... is beautiful' or '... is large' were being used in two different ways, one way when applied to Forms, another when applied to other things.65
What were Plato's reasons for believing in Forms? Did he have arguments for them? Answering these questions is not simple. Unfortunately Plato mostly does not argue for the existence of his Forms, but assumes them. However, Aristotle says (Metaphysics M, ch. 4): 'The theory of Forms occurred to the people who stated it because as regards truth they were convinced by the
"" See Phaedo lOOb-lOlc, with the interpretation of Bostock, Plato's Phaedo, ch. 7 (esp. 146-56).
65 Such a line is taken, for example, by R. E. Allen, 'Participation and Predication in Plato's Middle Period Dialogues', in Allen (ed.), Studies in Plato's Metaphysics, and Constance C. Meinwald, 'Good-bye to the Third Man', in Kraut (ed.), The Cambridge Companion to Plato.

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Heraclitean arguments that all perceptible things are always in flux, so that if there is to be knowledge of anything, or understanding, there must be some other, permanent kinds of thing over and above perceptible things, because there is no knowledge of things in flux.' A passage where something approaching this sort of argument occurs is Phaedo 74a-c—though the existence of Forms is not a conclusion of this argument. (Similar trains of thought seem to be at work in Republic 523a-525b and Cratylus 439b-440d.)
Much hangs on what one takes 'in flux' to mean. Often Plato seems less concerned about change over time, more about the simultaneous presence of opposites in things (also a Heraclitean idea, one may recall—see Section 1,3 above)—a ringer may be both large and small, something may be both equal and not equal. The general form of argument seems to be: if we are to know what Fness is, the object of our knowledge cannot be both F and not-F; but sensible things are both F and not-F, so the object of our knowledge (Fness itself) must be other than sensible things. Sometimes Plato may be talking about sensible properties, rather than things (see Section 2.4.4 above).66
This discussion leaves us with a great many problems. Two may be mentioned: (1) Does it make sense to say that, while a finger can be large or small, Largeness itself is just large? Presumably the finger is 'variable' because it is larger than some things, smaller than others: does this mean that Largeness is larger than everything else? Or is it supposed to be large 'absolutely'—i.e. not in relation to anything else? How can this make sense if large' is essentially a relative term? (2) If this kind of argument from 'being and not being' among sen-sibles gives Plato his reason for believing in Forms, will there be a Form for every property? Or will there be only a restricted range of Forms? (In the light of Republic 523a-e, should there be a Form of Finger, for example?)
The latter question is made difficult by the well-known passage in Republic, book 10, where Plato says there are Forms of Bed and Table, and appears to be saying (596a) that whenever we have a collection of particulars to which we 'apply the same name', we may hypothesize a single Form. If there is a Form of Bed, should there not be a Form of Finger?
Interpreting the theory of Forms is thus an enormous challenge. Plato invests great importance in Forms, but does not seem to have a very well worked out theory about them. In the later Parmenides he returns to the topic in more analytical mood, seemingly aware that many crucial questions about Forms still need to be answered (see Section 2.5.2 below).
66 Irwin, 'Plato's Heracliteanism', and Plato's Moral Theory (Oxford, 1977), 144-52, examines dilTnrni ways in which Plato may be taking a 'Heraclitean' view of sensible reality.

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2.5. Problems in Plato's Epistemology and Metaphysics
2J.I- After the Republic
Many of the dialogues which are normally regarded as later than the Republic are philosophically challenging and important. The Phaedrus contains more discussion of Forms, recollection, and the parts of the soul, woven into a brilliant treatment of love, and an exploration of the relationships between philosophy and rhetoric. The Timaeus gives Plato's cosmology, accounting for the creation of the universe by a divine agency who copies the eternal Forms. The Sophist includes an intricate further discussion of Forms, and an attempt to take on Parmenides' claim that you cannot think 'is not'. The Philebus has as its central theme pleasure and its relation to the best human life. Each of these works contains far more than could be discussed in the space available here.
I concentrate here on two works which are often studied for their contribution to Plato's epistemology and metaphysics: Parmenides and Theaetetus.
2.5.2. Criticisms of the Theory of Forms in Plato's Parmenides
The Parmenides is a strange dialogue, whose interpretation is a difficult and contentious matter. It falls into two clear parts, only the first of which appears to concern the theory of Forms directly. Over the last forty years most discussion of the Parmenides in English-speaking philosophy has centred on the first part (126a-136e or thereabouts): anyone wishing to follow the debate should especially attend to it.67
The characters in the first part of the dialogue are Parmenides, Zeno, and Socrates in his youth. It is fairly clear that the young Socrates stands in for Plato himself. Plato is here looking back on his own previous views in a critical spirit. One may ask what Plato's attitude is or should be to the various objections , against the theory of Forms. Does Plato take these arguments seriously? If they are successful, does he need to abandon his theory of Forms—or will some modifications save it? However, the prior task must be to understand each of the main objections to the theory of Forms. After the introductory section 126a-128e, the first part of the Parmenides has the following structure:
(1)	Socrates states the theory of Forms (128e-130a).
(2)	Parmenides  elicits  more  information  from  Socrates  about  Forms
(130a-e):
(a) Separation of Forms themselves from 'the other things that share in them'.
" A recent commentator who regards the mystifying second part as highly important for interpreting the frst is Constance C. Meinwald: Plato's Parmenides (New York, 1991), and/or 'Good-bye to the Third Man'.

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(b) Question: What classes of things have Forms? Socrates' different answers.
(3)	Arguments which reveal problems over the nature of 'participation'
(130e-133a):
(a)	Participation as 'sharing': problems with wholes and parts.
(b)	The so-called 'Third Man' argument: an infinite regress of Forms?
(c)	Could Forms be thoughts? (Two reasons are given why they could
not be.)
(d)	Forms as paradigms or patterns in nature: a regress arises again.

(4)	Final objection: Forms would be unknowable to us if they were com
pletely separate from the sensible world (133a-134e).
(5)	Parmenides'  closing remarks to Socrates: Forms are necessary for
thought and discourse, but Socrates needs to practise dialectical method
(134e-136e).
The Statement of the Theory of Forms (128e-130a and 130a-e) Parmenides asks Socrates whether he himself has drawn the distinction between Forms and other things—he answers yes, but this cannot be taken as a genuine statement of what the historical Socrates believed. The theory is Plato's own. It is usually thought that as stated here it corresponds to the views on Forms put forward in the earlier Phaedo and Republic.
What Classes of Things Have Forms? (130a-e) This is an intriguing section. Note that Parmenides asks about five groups of things that might be thought to have Forms associated with them: (1) likeness, unity, plurality (etc.); (2) Tightness (or justice), beauty, goodness (etc.); (3) man; (4) fire, water; (5) mud, hair, or dirt. Socrates gives one answer for (1) and (2), another for (3) and (4), and a third different answer for (5). Why?
Socrates expresses 'puzzlement'—in some cases he does not know whether there are Forms or not. Finally, Parmenides tells him that his difficulties arise because he is still too young: 'philosophy has not taken hold of you so firmly as I believe it will some day. You will not despise any of these objects then' (130e). It is tempting to view this as the more mature Plato telling his former self that the theory of Forms must in the end have a Form for all the things listed. But why then does he make Socrates give the different answers?
If one thinks of the Forms in the Phaedo, Republic, and Symposium, there are a number of considerations that may be relevant to answering this question. Plato wanted his Forms to be objects of admiration because of their absolute value. He used arguments to do with flux and the unity of opposites in the sensible world and to do with relative terms (see Section 2.4.5 above). On the other hand, in one passage he said there was a Form of Bed, that craftsmen could 'look towards' Forms in making artefacts, and that for any group of things

The Pre-Socratics and Plato	3 83
•which we collect together under the same name there will be a Form. Parmenides 130a-e suggests that Plato is calling not only for a much-needed clarification of the extent of Forms, but also for a thorough examination of the reasons there might be for believing in Forms at all.
participation as Sharing (130e-131e) In this section Parmenides poses a Jilemma. The 'other' things participate in Forms—but does each thing have a •whole or a part of the Form in it? The image of the sail spread over many people is his attempt to illustrate the problem. Is it well chosen? Socrates makes another suggestion: perhaps a Form is present in many things as a single day is present in many places. Is there a way of following up this suggestion which reveals anything relevant to the problem of participation? Is it right to think of a Form being 'divided up' at all?
An overall question about this section (and those following it) is whether Plato means us to make any specific conclusion about what is wrong with Socrates' thinking, or whether he is simply recording a confusion about Forms.
The 'Third Man'Argument (131e~132b and 132d-133a) This is the most discussed of all the arguments in the Parmenides. The argument appears first at 131e-132b, in an extremely short stretch of text.
The argument is called the 'Third Man', though this term does not appear in the text itself. The name arises because Aristotle reports the same argument using the example of 'Man'. The Form Man and any particular man—say, Socrates—appear to have something in common since they are both called 'man'; the theory of Forms (the argument goes) ought therefore to provide for a third 'Man', which both the Form Man and the man Socrates can participate in. Aristotle mentions this as a well-known objection made by his contemporaries to the theory of Forms. It is an objection presumably because the theory wants each Form to be only one. By the 'Third Man' argument we end up with infinite Forms as soon as we have one.
Plato's example is not 'Man', but 'Large' or 'the Large'—by which he means the Form that could otherwise be referred to as 'Largeness'. The conclusion of the argument is that, according to the theory of Forms, each of the Forms will be infinite in number. But where is the argument? In order to reach this con-dusion we need some premisses, but all we have is one premiss: 'When it seems to you that a number of things is large, there seems to be a certain single char-, acter which is the same when you look at them all; hence you think that Largeness is a single thing' (132a).
If the Third Man Argument is to be an objection to the theory of Forms there must be a valid argument which leads to the conclusion: the objection will then be that that conclusion is absurd, so something in the starting-point of the theory is wrong. Analytical philosophers have responded with ingenuity to the

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challenge of reconstructing the argument. But can we find a valid argument here? One positive answer is to be found in Colin Strang's 'Plato and the Third Man',68 where he supplies several unstated or unclear premisses to produce a neat and valid piece of reasoning. Others have concluded that when we attempt to reconstruct the argument, we find there is no valid way to reach the absurd conclusion of an infinity of Forms—hence Vlastos's famous pronouncement69 that this stretch of text is 'a record of honest perplexity' in which Plato realizes something is seriously wrong with his theory, but is not clear what.
Whether or not Plato realizes it, there is one assumption which is needed to make the Third Man Argument intelligible at all, and which is quite questionable. This is the assumption which has been called 'self-predication': the assumption that a Form has predicated of it the property which it names, e.g. that the Form of Largeness is large. Since many discussions of the argument centre around 'self-predication', the reader would be well advised to devote some effort to understanding what it means and why it may be an odd view, then to discover how the Third Man Argument requires the assumption of self-predication, and finally to ask whether the argument is designed to reveal that self-predication is a mistake.
Some more evidence is provided by the second occurrence of an infinite regress of Forms at 133a. This results from Socrates' new suggestion ('the best he can make' of the theory which appears to be falling apart under Parmenides' questioning) that Forms are 'as it were patterns fixed in the nature of things' and that the other things 'are made in their image and are likenesses'. The Greek word translated as 'patterns' is paradeigmata. Here Socrates is trying out the idea of Forms as paradigms (see Section 2.4.5 above).
What one should note here is that the same problem arises as before—a regress of Forms—and that the explicit conclusion is drawn that 'It follows that the other things do not partake of Forms by being like them; we must look for some other means by which they partake.' In other words, the relation between Forms and other things cannot simply be one of resemblance.
The Final Objection: 'Knowledge Itself (133a~134e) This objection is somewhat less discussed, although Parmenides calls it the worst difficulty for the theory of Forms (133b). Immediately afterwards Plato gives a subtle hint, however, that he does not think it ultimately holds water: if someone made this 'worst' objection, he says, one could not convince him that he was mistaken 'unless he chanced to be a man of wide experience and natural ability, and were willing to follow one through a long and remote train of argument'. One might wonder whether this sort of remark applies to all the objections to the theory of Forms:

The Pre-Socmtics and Plato	385
perhaps they are problems only for someone who understands the theory superficially?70
The gist of the final objection is that things in 'our world' are related to one another, while Forms are related to one another in a realm of their own: how can the divide be bridged? In particular, how can our knowing reach across to the Forms?
Parmenides' closing remarks (135a-c) do not suggest that the theory of Forms has to be abandoned because of the objections made. But whether the theory needs to be altered (and if so how), or whether it needs to be thought through more clearly so that its proponent can overcome the objections, are questions of interpretation that are much harder to answer.
2.5.3. The Theaetetus: What is Knowledge?
The Theaetetus, one of Plato's richest works in terms of philosophical argument and insight, was probably written after the Parmenides. (Something which Socrates says at 183e-184a has led people to see an allusion to the Parmenides.) At any rate, the Theaetetus belongs to the same period of Plato's life, after the Republic, when he seems to become more self-critical and not content to accept his earlier central doctrines without a great deal more analysis.
After the Parmenides we may expect the Theaetetus to be concerned with Forms. However, despite the fact that the dialogue pursues the question 'What is knowledge?', there is no explicit discussion of Forms. The easiest way to approach the Theaetetus is as an investigation of the nature of knowledge which holds in abeyance any assumptions about what the objects of knowledge are. Some commentators on this dialogue have, however, found that it implicitly supports the earlier theory of Forms. This is a general issue of interpretation to which the reader should be alert. Sooner or later one will want to ask how Forms might relate to some of the arguments in this dialogue.
In its pursuit of the single central question 'What is knowledge?', the Theaetetus preserves something of the character of a Socratic dialogue. It is also inconclusive: three attempted definitions of knowledge (knowledge as perception, knowledge as true judgement, knowledge as true judgement with an account (logos)') are all refuted. Socrates' methods are also pointed up: he describes himself as like a midwife who can assist others in bringing their philosophical ideas to birth (148e-15ld). It is fairly clear that the reader is to be prompted into active philosophical debate by this dialogue: it will reach its completion when something is brought to birth in each of our minds.

68	In Vlastos (ed.), Plato, i.
69	In 'The Third Man Argument in Plato's Parmenides', in Allen (ed.), Studies in Plato's Metaphysics.

70 See Meinwald, 'Good-bye to the Third Man', who suggests that Socrates falls into this category in the first part of the dialogue.

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Knowledge Prior to the three main definitions of knowledge, there is a discussion in which some examples of knowledge arise (145c-148e). Knowledge covers both craft (tekhne) and mathematics. (Theaetetus, portrayed here in his youth, went on to be a mathematician.) One further feature is worth noting. We may tend to think of knowledge as knowledge that..., where what is known is a proposition. But Plato often talks simply of knowing a tiling. We can say 'I know London' or 'I know Mary'. This prompts the question whether Plato thinks that all knowing can be described in this way. Writers commonly point to the difference in French between connaitre and savoir (or in German between kennen and wissen). Does Plato then think that all knowledge can be described as being acquainted with a thing (connaitre, kennen)'? Or does he vacillate between describing knowledge in this way and in other ways?
If the superficial outcome of the Theaetetus is that we do not yet know what knowledge is (see 210a-d), writers on the dialogue have often come forward with a more positive 'moral' concerning the nature of knowledge which the dialogue supposedly identifies. But such ideas are often only implicit in the text, which presents itself as a series of problems the reader must work through.
Knowledge as Perception (151d-186e)   Theaetetus offers the definition of knowledge as perception by the senses. This definition is eventually rejected, in the course of a discussion whose structure is as intricate as anything Plato wrote. It is as if Plato is using this definition as a way of demonstrating how to follow up all the ramifications a simple statement may produce. One should be prepared for a very challenging, extended argument. The whole section divides into a larger and a smaller part. The smaller (184b-186e) is a direct refutation of the claim that knowledge is perception. Its crucial idea is that knowledge must involve judging, which is distinct from perceiving. Judgements about a thing's being are made by the soul itself, not using any of the particular senses through which it perceives. This powerful objection is a turning-point in the dialogue. One thing that is not questioned from here to the end is that knowledge must at least involve judgement.
The much larger part (151d-184b) is difficult to interpret for two main reasons: (1) its structure is so complicated as to be initially baffling, (2) its purpose maybe in doubt: at 183c it looks as if'knowledge is perception' has already been refuted, so do we have two parallel refutations in the two parts of this section? Or is the refutation really only accomplished in 184b-186e?
In barest outline the structure of 15ld-184b is as follows. Theaetetus defines knowledge as perception. Socrates says that this definition is equivalent (see 151e-152a, 160d-e) to two other philosophical theses: Protagoras' relativist doctrine that 'a man is the measure of all things', and Heraclitus' doctrine that everything is always changing. After argument and counter-argument have

The Pre-Socmtics and Plato	387
been exchanged, both the Protagorean doctrine and the Heraclitean doctrine are refuted.
A neat way to understand the structure of this section is to say that the Heraclitean doctrine leads to absurdity, the Heraclitean doctrine is required by the Protagorean doctrine, and the Protagorean doctrine is required by 'knowledge is perception'—hence this definition is false because it ultimately leads to absurdity (the form of argument known as reductio ad absurdum). But that leaves many questions: Why does Plato spend a long time refuting the Protagorean theory on its own terms? And why does he also need the second chunk of argument to attack 'knowledge is perception'?
There is an alternative reading which sees Plato as on the same ground as he was when he distinguished knowledge from perception in the Republic and Phaedo. This reading says that Plato thinks perception is correctly accounted for by Protagoras and Heraclitus, and that for that reason perception cannot be knowledge.71
Knowledge as True Judgement (187a-c; 200d-201c) 'Judgement' translates doxa, which elsewhere has been translated as 'belief. (Translators who prefer judgement' in the Theaetetus probably do so because of its link with doxazein, which they render as judging' or 'making a judgement'.)
Thinking back to the Meno and the Republic, it would be astounding if Plato were now to say that knowledge is the same as true judgement or belief. The Theaetetus' short discussion of this definition does indeed reject it outright. But, having introduced the definition in 187a-c, Plato postpones the refutation until 200d-201c. The intervening pages concern false judgement—see below.
The brief argument against the definition of knowledge as true judgement seems to reveal some surprising underlying assumptions. On the one hand, Plato is surely right to say that someone can be persuaded into making a true judgement (for example, in a law court) without thereby knowing the truth. On the other hand, why does he think a jury that had been persuaded in a short time would lack knowledge? Is it because they do not have sufficient understanding of the evidence, or (as he seems to imply at 20lb) because they were not present to witness the events they are making a judgement about?72
The Problem of False Judgement (187c-200d) At first sight this section is an island within the dialogue: one can read it on its own as a small masterpiece of argument which sets up a paradox and pursues it with sustained reasoning. However, Plato gives more than a hint that the problems he encounters with false judgement reflect the general inability to understand knowledge (200c-d).
71	See Myles Burnyeat on 'Readings A and B'; his discussion in The Theaetetus of Plato (Indianapolis, 1990),
7-65 is helpful.
72	Burnyeat, ibid. 124-7, and 'Plato and the Jury', draws some interesting conclusions from this passage.

388	Christopher Janaway
The problem is simply how false judgement (or false belief) is possible at all. Plato believes it is possible, but presents a piece of reasoning according to which it is not: hence we have a paradox. The paradox is set up at 187e-188c: this passage should be studied very carefully in its own right before looking at Plato's attempted solutions. Two crucial assumptions are that in order to make a judgement about anything one must know it, and that if one knows something, one cannot make certain kinds of mistake about it. Clearly something must go wrong with the reasoning which sets up the paradox, but it is not entirely straightforward to say what it is. There follow a number of ingenious attempts by Plato to resolve the paradox, including the striking analogies of the wax tablet (or block) and the aviary. No satisfactory resolution is found.
Knowledge as True Judgement with an Account (Logos) (201c~21 Oa) This final section of the dialogue falls into two main parts. The first is a theory which Socrates presents as a 'dream' he has had: the theory says that there are complexes and primary elements, and that an account can be given only of the complexes. This has as a consequence that primary elements are not knowable. It is a theory of considerable abstraction, and has produced much speculation among commentators. (One issue, though perhaps not a central one for the initial reader, is why this theory is put forward as a 'dream' in the first place.) The dream theory is then subjected to two objections: one is based on the idea that a whole is identical with all its parts, another on the idea that elements (such as letters that make up a word or syllable) are knowable.
After the dream theory comes an attempt (206c-210a) to understand what 'knowledge is true judgement plus an account' (logos') might actually mean. Plato considers three senses which logos might have, and decides that none of them will provide a satisfactory definition of knowledge. The first sense of logos is the unpromising 'making one's thought apparent vocally'; the second is the enumeration of the elements of something (seeming to hark back to the concerns of the dream theory); the third, which is perhaps the most promising of the three, is 'telling some mark by which the object you are asked about differs from all other things' (208c): knowledge of X would then be having a true or correct belief about X, while also being able to give an account of what distinguishes X from everything else. However, this definition quickly runs into the problem of circularity. One would have to know that one's account of the thing's differentness was correct: so part of the definition of knowledge is that it involves knowing something, which Socrates describes as just silly'. However, commentators have attempted to draw a number of different 'morals' from the dialogue's inconclusive ending.73

The Pre-Socmtics and Plato	3 89
BIBLIOGRAPHY
, T. H., Classical Thought (Oxford, 1989) is a good, short introduction to the whole of ancient philosophy, covering much wider ground than this chapter.
1. THE PRE-SOCRATIC PHILOSOPHERS
Passages from the Pre-Socratics are quoted in the translation by Jonathan Barnes, Early Greek Philosophy (Harmondsworth, 1987). Passages are also referred to by their standard fragment numbers (B 1 and so on), which relate to their ordering in the collection of the Greek texts made by Diels-Rranz (Die Fragmente der Vorsokratiker, ed. H. Diels and W. Kranz, 10th edn. (Berlin, 1952)). The Diels-Kranz fragment numbers are used here simply for convenience: all recent commentators use them to identify the fragments. Recommended books may arrange fragments in different orders, but all provide an index or concordance which will assist in finding a fragment if one has its Diels-Kranz (DK) number.
ESSENTIAL READING
barnes,]., Early Greek Philosophy (Harmondsworth, 1987). Barnes's introduction, synopsis, and other information are also valuable.
RECOMMENDED READING
barnes,]., The Presocratic Philosophers, Arguments of the Philosophers (London, 1989). The most stimulating philosophical account. Sometimes hard going for a beginner in philosophy, but worth persevering with.
guthrie, W. K. C., A History of Greek Philosophy, i: The Earlier Presocratics and the Pythagoreans (Cambridge, 1962); ii: The Presocratic Tradition from Parmenid.es to Democritus (Cambridge, 1965). Guthrie's two volumes provide a thorough and relatively easy-going account of the whole period.
hussey, E., The Presocratics (London, 1972). Short and introductory.
kirk, G. S., raven, J. E., and schofield, M., The Presocratic Philosophers, 2nd edn. (Cambridge, 1983). Fragments of the Pre-Socratics in translation, with commentary (and Greek text).
ADDITIONAL READING
These items are meant as an additional resource for those engaged in more detailed study of particular topics. Initial reading and further bibliographies are available in each of the books cited under Essential and Recommended Reading. Classic collections of articles often cited (and best used for further work on a specific philosopher) are:
furley, D. J., and allen, R. E., Studies in Presocratic Philosophy, i and ii (London, 1970, 1975).
mourelatos, A. P. D. (ed.), The Pre-Socratics: A Collection of Critical Essays (New York, 1974).

Cf. Bostock, Plato's Theaetetus, 241-67.