parmenides on separation and the knowability of the forms: plato parmenides 133a ff

Parmenides on Separation and the Knowability of the Forms: Plato Parmenides 133a ffAuthor(s): Frank A. LewisSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 35, No. 2 (Feb., 1979), pp. 105-127Published by: SpringerStable URL: http://www.jstor.org/stable/4319277 .

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FRANK A. LEWIS

PARMENIDES ON SEPARATION AND THE KNOWABILITY

OF THE FORMS:

Plato Parmenides 1 33a ff.

(Received 14 April, 1978)

At Parmenides 133a ff., Parmenides presents the last of his arguments critical of the theory of forms.' He is careful to emphasize that the argument holds good against the view that forms are separate from sensibles; indeed, he says that his argument presents the greatest of the difficulties that await such a view. Now Parmenides has already called our attention to separation as a crucial feature of the theory of forms (1 29d, 130b), but his previous arguments pay more attention to other assumptions of the theory, whose relation to separation he neglects to explain (in the immediately preceding argument, for example, he repeats the reference to separation [133a8-10], but in virtually the same breath tells us he is attacking the doctrine that things participate in forms by a principle of likeness [a5-7] ). But it will be worthwhile not to ignore his suggestion here that his present argument focusses especially on separation: there is, I will suggest, some plausibility to thinking that separation is the key theme that runs throughout the argument.

The principal conclusion Parmenides offers is that we in this world cannot have knowledge of forms: forms are unknowable by us.2 In arguing for this conclusion, Parmenides rests heavily on some principles which he links directly to the declaration of separation at the head of the argument. Our main business in interpreting the argument will be to make sense of these principles: to ask in what way, if in any, they develop the notion of separation, and to see also if they provide the support Parmenides needs for his sceptical conclusion. My procedure will be to consider first (I) the principles on which Parmenides rests his argument, beginning with his first remarks about separation. I will then comment (II) on how well these principles support the conclusion about knowledge which he builds upon them. Next (III), I make some remarks on the general significance of Parmenides' argument. In an Appendix, finally, I consider his argument for the complementary conclusion, that god cannot know sensibles.

Philosophical Studies 35 (1979) 105-127. 0031-8116/79/0352-0105$02.30 Copyright ? 1979 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.



106 FRANK A. LEWIS

I. THE PRINCIPLES OF SEPARATION

1. 'Simple' Separation of Forms from Sensibles

The language of separation is prominent in Parmenides' opening remarks:

You see how great the difficulty is if someone marks them off as forms themselves by themselves3 (1 33a8-9, referring to the preceding argument)

...You have, so to speak, by no means yet grasped the perplexity itself, how great it is,4 if you are going to set up each as a single form, always separating it off as something from among the things that are5 ... (alI-b2)

...whoever posits the being of each thing to be something itself by itself (c3-4).

This last phrase, 'itself by itself', also appears with the same use at c5-6: no form could be present in us, for as Socrates argues, it could not then be 'itself by itself'.

Parmenides is drawing attention in these passages to the thesis that a form is not identical with any sensible. Forms are 'by themselves' because they are differentiated from the many sensibles that fall under each. Although Parmenides offers no further elaboration, it is worth noting here that the non- identity of forms with sensibles is reinforced for Plato by the claim that forms have categorial properties in common which are shared by no sensible. All forms are eternal, immutable, intelligible, and the rest: sensibles are none of these.6

In the sense of 'separation' relevant here, I shall also speak of the 'simple' separation of forms from sensibles. As we shall see, there are other ways in which forms and sensibles are separate.

2. 'Proper Separation' of Forms from Sensibles

The next four lines of Parmenides' remarks run as follows:

So as many too of the forms which are which they are with respect to one another - these have their being themselves with respect to themselves, but not with respect to the things among us, whether likenesses or however one is to regard them, possessing which we are called each thing (c8-d2).

For example:

...mastery itself is what it is of slavery itself, and likewise slavery itself is slavery of mastery itself (e3 4).

In these lines, Parmenides introduces a quite different notion of separation, which I shall call 'proper separation'. But before I argue for this reading,



PLATO Parmenides 133a ff. 107

three preliminary points must be made. It is clear first (i), that Parmenides regards the claim he is about to make as in some sense an application of his preceding remarks about simple separation (oVKoV-v, c8). Secondly (ii), it seems equally clear that he has now passed from generalizing about all forms in his previous remarks (simple separation is observed by all forms with respect to sensibles), to dealing with only a proper subset of all forms (Kai ouat rwv cc6Eo&v..., c8). So the characterization by which he refers to this restricted set of forms (they "are which they are with respect to one another") cannot be true of all forms whatever. What is less clear thirdly (iii), is the nature of what he goes on to assert about this new set of forms. According to one reading, what is said of them (that they "have their being themselves with respect to themselves", and so forth) is exactly what was said of all forms in assertions of simple separation in the first group of passages at 133a8-c7 above. The form of the inference referred to in (i) will then be that of simple instantiation: since all forms obey simple separation, so too will any proper subset of forms. In fact, I think this is not the correct account of the text: 7 what Parmenides is asserting here of a limited class Qf forms is that they obey a related but still new principle of proper separation. To explain this notion, we must begin with the difference between the categorial and proper properties of a form.

The principle of the simple separation of forms from sensibles, as we have seen, is bound up with the categorial properties of forms: what it is to be a form as such. When we list the categorial properties of a given form, therefore, we do not succeed in distinguishing it from any other form. The categorial properties of forms are properties that all (and only) forms have. If we want to distinguish a form x from other forms, we must give properties of it not qua form, but qua x. That is, we will give proper properties of it, as opposed to its formal or categorial properties. We say, for example, that the form man is rational, or mortal, and so distinguish that form from others, as we do not do if we say that the form man is eternal, immutable, and the rest. The proper properties of a form, then, focus on what it is to be this form, rather than what it is to be a form simpliciter.

In the passage at hand, Parmenides is dealing with a particular -subset of forms - those which "are which they are with respect to one another". His initial examples are the forms slavery and mastery. Parmenides will here say what it is to be each of these forms by way of saying what it is to be a form of this particular logical type. 8 The primary fact in Parmenides' mind is that



108 FRANK A. LEWIS

mastery and slavery are relational forms. We can bring out their relational character by indicating, for example, that something belongs (or can belong) in the range of the relation. Or, as Parmenides does here, we may specify the appropriate converse relation. Thus by the claim, for example, that mastery is what it is of slavery, I take Parmenides to mean just that mastery is a relation, and has as its converse the form slavery. His assertion, therefore, gives a proper property of its subject.

Parmenides hangs a good deal of his subsequent argument on the principles illustrated by this and similar assertions. It is worth making two points about those assertions here.

(1) Above all, the assertions, "Mastery is what it is with respect to slavery", or "Mastery is mastery of slavery", are not to be confused with the claim that mastery is a master of anything. In Parmenides' jargon, the connectives, '...is what it [mastery] is with respect to...', or '...is mastery of ...', are not used to assert that mastery is instantiated by anything (for example, by mastery with respect to slavery). Rather, he uses them to make a point about the logical relation of the two concepts concerned, namely, that the one concept is the converse of the other.

How then is Parmenides' sentence, 'Mastery is mastery of slavery', related to the issue of self-predication? In its broadest use, the term 'self-predication' can be applied to any sentence of the form rThe A is (an) A7. This defines a purely syntactical notion of self-predication.9 Other uses of the term vary with the interpretation we give to sentences whose surface structure satisfies our syntactical definition. Some instances of syntactical self-predication in Plato must be interpreted in a way that makes them logically vicious; others presumably need not. It has often been supposed that Parmenides' sentence here is logically vicious, involving the claim that mastery is an instance of itself with respect to slavery.'0 On the interpretation offered here, however, Parmenides' sentence is an instance of syntactical self-predication, but is harmless.

(2) Given the interpretation of Parmenides' sentence proposed, it follows that mastery is not mastery of anything other than slavery, that is, of anything which is not in fact its converse (133c9-d2, e5). In particular, it would be a gross mistake to suppose that the converse of a relation R is not the relation R-1, but some member of the domain of R-1. Mastery, for example, is mastery of slavery, but not of any particular slave.

It is now easy to see why Parmenides regards his present point as logical-




ly connected with his earlier principle of simple separation. No form should be confused with what falls under it, and a converse form should not be confused with the members of its domain. It follows that a relational form does not have as its converse some member of the domain of the converse relation. In short, if certain forms have their being with respect to each other, then by simple separation they have their being with respect to no sensible.

By proper separation, accordingly, Parmenides requires that the converse of a relational form is another relational form. He adds the warning that we must not confuse the converse of a relation with the entities in the domain of that converse.

3. 'Factual Separation'

Proper separation has an immediate corollary. If by proper separation the converse of a relation is another relation, then by a complementary principle the entities in the domain of a relation bear that relation not to the converse relation, but to the entities in the domain of the converse relation. I shall call this new principle the principle of the factual separation of sensibles from forms. Parmenides' formal statement of this principle is as follows:

But the things among us, which are the namesakes of those [the forms mentioned], are again themselves with respect to themselves but not with respect to the forms, and (they are) of themselves but not of those, as many again as are called in that way (d2-5).

He goes on to give some examples:

...if one of us is master or slave of something, what he is slave of is not master itself, which is master, and the master is master not of slave itself, which is slave. Rather, being a man, he is each of these [slave or masteri of a man (d7-e3).

The two principles of proper and factual separation are in an easy way the complements of one another. It is also important to see that a statement observing the proper separation of forms from sensibles entails a statement which observes the factual separation of sensibles from forms. Thus, for example, the statement, 'Mastery is mastery of slavery', which observes proper separation, entails the statement, 'Masters are masters of slaves', which obeys factual separation.

This entailment is an instance of the general point that any statement of proper properties of a form entails a corresponding statement about sensibles. Thus the sentence, 'The lion is tawny', which for Plato asserts a proper



110 FRANK A. LEWIS

property of the form lion, entails the sentence, 'All lions are tawny', which is a generalization over sensible lions. The entailment can also be seen as a consequence of principles connecting statements about relations and statements about the entities in the fields of those relations.

4. Parmenides'Strategy

It will be useful at this point to consider the use Parmenides plans to make of the various principles of separation he has put forward. Parmenides first lays down a principle of the simple separation of forms from sensibles. Given this variety of separation, he is able to argue for the two further principles of proper and factual separation. The last step in Parmenides' argument is now this. As we have seen, any statement of proper separation entails some statement about sensibles observing factual separation. Is there then a statement observing proper separation regarding knowledge, which has as a consequence a statement of factual separation to the effect that a sensible, for example, Jones, may know only sensibles? Parmenides' final move will be to put forward a statement about forms which observes proper separation, and which apparently entails that human knowers can know only non-forms, that is, can know only sensibles.

It is important here to see that Parmenides is not advancing a general policy that non-forms can bear relations only to non-forms. Factual separation counsels us only that, in saying of a given relation R what bears R to what, we must not confuse the entities in the range of R with the converse relation R 1 itself. Thus, where R is a relational form, nothing can bear R to R -'. Again, proper separation requires only that a relational form may not have as its converse any member of the domain of that converse. It follows that a converse relational form may not itself be a member of its own domain, and again, for any relational form R, nothing can bear R to R -' . These warnings by no means add up to a general prohibition against relations between forms and sensibles.

Despite this, Parmenides has almost universally been taken as arguing that all relations between forms and sensibles are impossible. The comment by Matthews is representative: "...if forms are totally different from perceptible things, and there is a great gap fixed, then there may be relations between them, but not between them and us"."1 These and similar remarks about the argument rest in part on a false interpretation of separation. Separation as



PLATO Parmnenides 133a ff. 111

such - that is, simple separation - is only the doctrine that forms and sensibles are non-identical, and very different kinds of thing. (The sense in wilich they are different is made more precise by the notion of the categorial properties of the forms.) Perhaps they are different enough that it is hard to see how there can be relations between them (cf. Section III below). But separation as such is not the view that there cannot be any relations between forms and sensibles, nor in fact does Parmenides' argument urge any such conclusion.

A second source for attributing to the argument a general prohibition on relations between forms and sensibles may be a misreading of part of Plato's text. Having sketched the different kinds of separation and applied them to the mastery example, Parmenides goes on to summarize his results so far:

But the things in us do not have their power with respect to them nor they with respect to us, but as I say, they on the one hand are themselves of themselves and with respect to themselves, and the things among us on the other hand likewise (have their power) with respect to themselves. (133e4-134al)

Does this deny the possibility of relations between any form and any sensible? Not if it is a fair summary of what Parmenides has already shown. Parmenides has been discussing relational forms; he has in mind in particular his exarnples of mastery and slavery introduced just above. So in the sentence, 'The things among us do not have their power with respect to them', Parmenides' word 'them' cannot refer tor all forms whatever, but only to relational forms and their converses. Thus, sensibles that bear R to something do not bear R to the converse relation, but only to the entities in the domain of that converse. Sensible masters, for example, are masters of slaves, not of slavery. So Parmenides has shown at most that some sensibles cannot stand in some relations to some forms: sensibles in the domain of a relation R cannot bear R to the converse form R-1 .

We can now return to the main thread of Parmenides' argument. Parmenides' strategy is to show that there is some statement observing proper separation, which entails a statement which itself observes factual separation, such that it is correct to say of Jones that he knows sensibles, but never correct to say that he knows any form. Similarly, Parmenides might have defended the claim that human masters are masters only of human slaves by pointing to the statement observing proper separation that mastery is mastery of slavery. We must not confuse slavery with its instances; accordingly, the converse of the relation mastery is the relation slavery, while



112 FRANK A. LEWIS

what sensible masters bear the relation mastery to must be sensible slaves. Can Parmenides use an analogous argument to show that what persons can know must likewise be only sensible objects of knowledge, and never forms?

It is easily shown, following Forrester,'2 that such an argument cannot succeed. By analogy with the mastery example, knowledge is knowledge of its converse, namely the relation (being-an-) object-of-knowledge (-to). By the same analogy, any entity in the domain of knowledge - for example, any human knower - can never have knowledge of the converse form, that is, of the form object-of-knowledge. But we may still know entities in the domain of that form, whether forms or sensibles. So we may know any instance of the form object-of-knowledge - form or sensible - and we may not know only the form object-of-knowledge itself. So Parmenides' argument fails.1 3

This point does not hit home directly against Parmenides in our text. Forrester's argument shows that Parmenides' strategy cannot succeed: but Parmenides' actual procedure makes a rather different use of the mastery example, and so his argument too fails for rather different reasons. To see this, we must consider the application Parmenides makes of his principles of separation, and examine the statements about knowledge which he offers with their aid as counterparts to his statements about mastery.

II. SEPARATION AND KNOWLEDGE

1. Some Points About Knowledge

If knowledge is to be sufficiently like Parmenides' earlier examples of mastery and slavery, Parmenides must be treating it as a relation.'4 His first remark about knowledge establishes this common feature:

So too therefore for knowledge - that very thing which is knowledge is knowledge of this very thing which is truth (134a3-4).15

More simply:

(1) Knowledge is knowledge of the forms.

Contrast with knowledge in (1) the concept, say, geometry or geometrical knowledge. Parmenides says:

Again, each of the knowledges, which is, would be knowledge of each of the things-that- are, which is (a6-7).



PLATO Parnenides 133a ff. 113

Thus of geometry Parmenides would say:

(2) Geometry (geometrical knowledge) is knowledge of the form figure.

The contrast between knowledge and 'each of the knowledges' is roughly that between the genus, knowledge, and its various species.16 But there is an important and unorthodox difference here between the genus and its species. Although geometry, for example, is called knowledge of something, geometry is not, as knowledge is, itself a relation: it is not called geometry of something (cf. Aristotle Categories 1 la23ff.).1 7

This last fact introducts a point of major importance about the relation of the genus knowledge to its various species."8 In the usual case, we move from the genus to one of its species by introducing a restriction on the members of the genus via the differentia. This cannot be exactly the paradigm for knowledge and its species. The genus knowledge is a relation, holding between knowers and the objects of their knowledge, that is, facts'about the forms. Its species, however, are classes but not relations: geometry, for example, is the class of truths known about geometrical forms. So the differentia introduces a restriction on the range of the relation, picking out as members of the species the members of a subclass of the range of the genus. The species geometry, for example, is a body of knowledge consisting of facts known about the form square, facts known about the form triangle, and so on. It is obtained by a restriction on the range of the generic relation to facts about geometrical forms.

Parmenides invites us to compare sentence (2) about knowledge and its species, geometry, with his earlier examples of mastery and slavery, in particular with the statement,

(3) Mastery is mastery of slavery.

As we have seen, saying what the extensional consequences are of (3) gives the crucial move from a sentence of proper separation to one of factual separation. Parmenides' whole argument now depends on obtaining an analogous move in the case of (2) concerning geometrical knowledge.

What, then, are the extensional consequences of (2)? (2) defines geometry by means of its genus and differentia. The relevant differentia is concerned with figure, or some such. Sc we must look first to those ordered pairs making up the genus knowledge whose second member is a fact about some



114 FRANK A. LEWIS

geometrical form. Accordingly, as we have seen, the instances of geometrical knowledge are just those facts known about geometrical forms. That is, the two concepts geometry and knowledge of figure are coextensive.

A second extensional consequence concerns the concepts geometry and knowledge. According to (2), the relation between these is that of species to genus. It also follows from (2), therefore, that an instance of geometrical knowledge is at the same time a member of the range of the relation knowledge. Thus, geometrical knowledge is the class of facts known about some or other geometrical form.

Given these facts about (2) and its extensional consequences, what follows for what sensibles can know? Suppose Jones something - that is, he is a member of the domain of the relation knowledge. Then for all we have seen so far, what he knows may well be some member of that subclass of the range of knowledge that constitutes geometrical knowledge. That is to say, he may know a fact about some geometrical form. This result is flatly inconsistent with the conclusion Parmenides wishes to urge upon us. For Parmenides, any instance of geometrical knowledge must be a member of the class of facts about instances of geometrical forms. It is time, then, to see how Parmenides himself completes his argument for this conclusion.

2. The Completion of Parmenides 'Argument

...So too therefore for knowledge - that very thing which is knowledge is knowledge of this very thing which is truth (134a3-4) ...Again, each of the knowledges, which is, would be knowledge of each of the things-that-are, which is (a6-7)

But

...wouldn't knowledge among us be of truth among us? and again wouldn't each knowledge among us turn out to be knowledge of each of the things-that-are among us? (a9-bl)

...But yet we do not have the forms themselves, and they cannot be among us (b3-4).

...But supposedly the forms themselves each of which is are known by the form itself of knowledge (b6-7).

...We do not have it [the form of knowledge] (b9);...So no form is known by us, since we do not partake of knowledge itself (bI 1-12). So the beautiful itself, which is, and the good, and all that we suppose to be forms themselves, are unknowable to us (b 14-c2).

a3-4 and 6--7 are statements about knowledge itself and 'each of the knowledges'. They are intended to be analogous to the earlier statement that mastery is mastery of slavery, and like it to observe proper separation.



PLATO Parmenides l33a ff. 115

a9-bl is a statement regarding 'knowledge among us' that is meant to observe the complementary principle of factual separation: compare the claim above that masters are masters of slaves, not of slavery.

b3-4 is a generalization about all forms, asserting their simple separation from sensibles: compare in particular 133c3-6 above (no form could be present in us, for it could not then be separate from us). With this remark, Parmenides has now recalled all three varieties of separation to the argument.

b6-7 needs more extended comment. It is, on the face of it, a remarkable sentence. The claim that the forms are known by the form of knowledge appears to be a passive transformation of the sentence, 'The form of knowledge knows the forms'. b6-7 is thus a thinly-disguised instance of syntactical self-predication; and it has been interpreted by most commentators as an instance of vicious self-predication as well.19 If this is the correct interpretation of the text here, then we are surely forced to read back a notion of vicious self-predication into Parmenides' earlier discussion of mastery and slavery. If we do not restructure the earlier parts of Parmenides' argument in this way, what possible relevance could a notion of vicious self-predication have at this late point in the argument?

I owe to Sandra Peterson the idea that the sentence at b6-7 need not be taken as introducing a vicious notion of self-predication. Parmenides' sentence is in fact an alternative way of stating his earlier and unproblematical claim that knowledge is knowledge of truth: that is, knowledge is knowledge of the forms.

This interpretation of Parmenides' sentence may seem tenuous. But the case for the alternative reading of the sentence, on examination, rests on surprisingly weak foundations. The argument is this. One might expect that Plato would distinguish the two locutions ' is (a) knowledge of - - -' and

_ knows - - -'. The claim, 'Geometry is (a) knowledge of figure', for example, seems unexceptionable, while the sentence 'Geometry knows figure' appears to suggest that geometry stands to figure in the same relation in which any knowing subject stands to the object of his knowledge. Both sentences are, nearly enough, instances of syntactical self-predication (recall that by 'geometry' Parmenides means simply 'geometrical knowledge'). But the second sentence also seems to introduce a vicious notion of self-predication, and the same is not obviously true of the first. Correspondingly, then, we might expect that Plato would also distinguish between the passive forms of our original locutions: thus between '--- is an object of knowledge to



116 FRANK A. LEWIS

' and '--- is known by ' (for example, 'Figure is an object of knowledge to geometry' and 'Figure is known by geometry'). In fact, these assumptions about Plato's usage are false. There is ample evidence in the Charmides that Plato is not sensitive to any difference between the two active locutions (with for example 165d7-8, el, 166a4, b5, cl-3, e5-6 etc., compare 169el, e6-7), so it is unreasonable to expect him to observe any distinction on the passive side. Thus by his sentence 'The forms are known by the form of knowledge' at b6-7, he can be taken to mean no more than what we would ordinarily express by saying that various forms are objects of knowledge to the form of knowledge. That is, Parmenides is merely repeating the point from a3-4 (and by implication, a6-7 as well) that knowledge is knowledge of something (that is, of the forms), and that the various branches of knowledge are each knowledge of some particular subject-matter.

We may now proceed with the remainder of Parmenides' argument. He has so far recalled the three varieties of separation introduced at the beginning of the argument, and renminded us that knowledge is of the forms, while the branches of knowledge are concerned with various particular forms. b9 now instantiates from b3-4: given simple separation for all forms, the form of knowledge too is not present in us (the same by implication is true of the various forms of knowledge, knowledge of figure, knowledge of odd and even, and the like, as well).

bl 1-c2 repeats the point from b9, that the form knowledge is not present in us, and concludes from this that no form can be known by us.20

In this half of the argument, Parmenides first completes his strategy of identifying a statement apparently observing proper separation, which entails as the corresponding statement apparently observing factual separation, the claim that knowledge among us is only of the things-that-are among us. The rest of the passage repeats this same material. Knowledge itself is not among us. But if knowledge itself is not among us, we cannot know the entities which knowledge itself is knowledge of; that is, we cannot know the forms.

In this summary, Parmenides attempts to weave together once more the three principles of simple, proper, and factual separation. Among us we find only instances of knowledge, or of the various branches of knowledge: Jones, say, who has geometrical knowledge, or the geometrical facts which he knows, or finally Jones' geometrical knowledge, which is perhaps a relation between the two.2" Here, Parmenides is enforcing an uncontroversial consequence



P LA TO Parmenides 133a ff. 117

of simple separation: neither we nor our knowledge are to be confused with knowledge itself, or with any of the kinds of knowledge. But consider what knowledge, or its kinds, are knowledge of. By proper separation, apparently, we know that, for example,

(2) Geometry is knowledge of figure.

Parmenides plainly believes that if (2) is true, then by factual separation, our geometrical knowledge - 'geometrical knowledge among us' - can only be of 'the things that are among us': of sensible instances of figure, but never of figure itself, or of the forms for the various kinds of figure, the square, the triangle, and so on.

3. Some Difficulties with the Argument

Parmenides' argument does not succeed. His strategy is to establish various principles of separation for his examples of mastery and slavery, and then apply those principles to statements about knowledge. But the two sets of statements are not sufficiently alike for this move to have any hope of success.

Consider again the two statements

(2) Geometry is knowledge of figure

and

(3) Mastery is mastery of slavery.

Knowledge, like mastery, is a relation. More than this, the names of each appear in (2) and (3) in superficially similar grammatical contexts: 'Mastery is mastery of...', 'Geometrical knowledge is knowledge of...'. Thus both setences are, nearly enough, instances of syntactical self-predication (but of nothing worse than that). Despite these similarities, however, the discrepancies between the two are more than enough to undermine Parmenides' strategy. (i) 'knowledge of figure' in (2) gives the genus and differentia respectively of the species geometrical knowledge. The differentia here is, in full, 'concerned with figure'. So the expression 'figure', by itself, has no important logical role in the sentence. It is quite otherwise with the last word, 'slavery', in (3), for it denotes the converse relation whose instances form the range of the original relation, mastery. These facts are reflected in the different extensional consequences of the two sentences. It follows from (3) that



118 FRANK A. LEWIS

instances of mastery are so-called with respect to instances of slavery. But 'figure' does not have the same logical role in (2) that 'slavery' has in (3), and there is no support for the analogous conclusion that, given (2), instances of geometrical knowledge are such with respect to instances of figure. (ii) There is also the difference that, unlike (3), Parrnenides' (2) does not obey the principle of proper separation. According to the mastery example, a statement observes proper separation insofar as it associates a relational form with its converse. But Parmenides' sentence (2) only connects a relational form with the class of things that make up its range. So the sentence observes separation of a sort, since it contains designations only for forms, but it is not a sentence of proper separation. And if (2) is not a statement of proper separation, there is no reason to suppose that it will imply a corresponding statement of factual separation. Accordingly, Parmenides' further claim,

(4) Knowledge among us is of only the things-that-are among us,

is not plausibly an instance of factual separation, since he has failed to point to any statement observing proper separation that entails (4). There is no reason, therefore, to think that (4) succeeds in specifying all and only the entities that humans can know.

III. CONCLUSION

Does Parmenides' argument touch any issue of substantive philosophical interest for Plato? The fallacy the argument commits is perhaps of some interest in the theory of relations, or in deciding the logical form of certain sentences - but intrinsically it has little bearing on questions in epistemology. It is useful to recall, however, as Parmenides himself emphasizes, that his argument is addressed particularly to the idea that sensibles and forms are in some sense separate each from the other. Roughly put, forms and sensibles are so different, that it may seem a puzzle how there could be a relation that holds between entities of these two kinds. And so it may also seem a puzzle, supposing knowledge to be a relation between entities, how a sensible can have knowledge of forms (or god have knowledge of sensibles).

It is often suggested that the problem of how sensibles can know the forms is solved for Plato by the view of the soul as an intermediary between the sensible world and the forms, in combination with the doctrine of recollec-




tion.22 But this seems a temporary answer at best. For if the soul is sufficiently like the forms to be able to know them, it is sufficiently unlike sensibles for it to be a puzzle how the knowing soul can ever be related to a human body. Recall for example the list of disparate properties of soul and body that Socrates reels off at Phaedo 80b, where the differences that divide soul and body are, by design, precisely those that set apart sensibles and the forms.

Traces of these difficulties are evident also in the Phaedrus. Here, Plato distinguishes two kinds of knowledge. The one, true knowledge, has its character in common with its own, special objects: it is "the veritable knowledge of being that veritably is". As such, therefore, it is all too different from the "knowledge that is neighbour to becoming, and varies with the various objects to which we commonly ascribe being" (Phaedrus 247d-e, Hackforth's translation). More than this, however, true knowledge also calls for a special kind of knower: either god or a discarnate soul. With this last step, Plato comes perilously close to saying that the difference between forms and the sensible world is so great that incarnate souls can have only the inferior kind of knowledge that is of "that to which we commonly ascribe being", while only gods and souls in the discarnate state can have true knowledge, which is of the forms.

Plato's own remarks elsewhere, then, suggest that forms and sensibles are so different that it may be a puzzle how a sensible can know the forms. How can this puzzle be made more precise? What is needed is an exact statement of the difference between forms and sensibles, that makes us doubt that there could be relations between them. Parmenides' argument does appear to speak to this question. For a large part of the argument, Parmenides is trying to spell out the various kinds of separation, and so give content to the idea that forms and sensibles fall into different 'worlds'. Officially, the argument leads to the conclusion that, given the various kinds of separation, knowledge relations between sensibles and forms are impossible. In fact, however, the argument depends on fallacies that make its conclusion moot. But the purpose of the argument is not trivial. Indeed, in the Sophist Plato finds a better argument, again with separation as a premise (xcoptis, 248a7), to show that there is after all a categorial property of forms - namely, their im- mutability - that may be incompatible with their knowability.3



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APPENDIX: THE 'MORE TERRIBLE CONSEQUENCE'

Parmenides has argued that any instance of knowledge can be knowledge only of instances of forms; no sensible, then, can know the forms. At 1 34c4ff., he proceeds to sketch what he calls a "still more terrible consequence". There are two possible accounts of this new conclusion. If we take Parmenides exactly at his word, then his conclusion is that if someone, say god, has knowledge itself, he cannot know sensibles. It is easily assumed, however, that Parmenides is offering a different conclusion: that god knows the forms, and only them, and can know no sensible. The difficulty with this latter version of Parmenides' conclusion is that it is not obviously consistent with his previous proof that any instance of knowledge is knowledge only of instances of forms. For it would seem to follow that the forms themselves are not known by anything, god or sensible. The only way Parmenides might argue that this does not follow is by insisting that god's knowledge is not an instance of knowledge. This is not a very pronising line of thought, although as we shall see, Parmenides is perhaps tempted by it. Provisionally, then, Parmenides' conclusion can be represented as follows. He is arguing at least that if god has knowledge, he cannot know sensibles. He may also mean to argue that god does know the forms: if so, however, he must be able to show how this is not inconsistent with his earlier argument.

Parmenides' argument for his conclusion rests in part on some new ideas, and in part, as he suggests, on some principles carried over from his earlier argument. As with any form, the form itself of knowledge is "far more perfect" than knowledge among us. And the most perfect knowledge is most fittingly had by god. But if god has knowledge itself, then by earlier principles he can know no sensible. I will look first (1) at the new ideas in this argument, and secondly (2) at the assumptions it claims to have in common with its predecessor.

(1) The major new idea in this argument concerns the theory of predication. Parmenides suggests that we will need two different theories of predication: one for sentences with certain sensibles as subjects, and aw.new theory for certain non-sensibles as subjects. The theory for sensibles as subjects has already been in force in the earlier argument. It is this:

For at least some sensibles x, if x is F, then x possesses (metechein) a likeness of the F, "or whatever one should call it" (133c9-d2).




Note that this account cannot hold for all sensibles F if a likeness of the F is itself a sensible and is F: cf. 1 33d3.

Parmenides here relies on the point, which he repeats a number of times, that we do not have the F itself (134b3, b9), that is, the F itself is never present in any sensible (133c5, 134b4, b12). This is part of the thesis of simple separation, as noted above. Despite his uncertainty on details, Parmenides is emphatic that predication of sensibles is to be analyzed as an immanence relation not between a form and a sensible, but between, for example, a likeness of a form and a sensible.

For non-sensible- as subjects, the theory that now emerges is this:

For at least some non-sensible x, if x is F, then x has the F itself (134cl1, d2), or x possesses (metechein) the F itself (I 34c1 0).

This principle cannot hold for all non-sensibles that are F, for the F itself is a non-sensible, and we know from 133d3 that the F itself is F (6,io'wa ... eKeLVOt1q, 133d3). In the account Parmenides gives, the principle is applied only to the single non-sensible, god.

Parmenides has an argument to persuade us that it is plausible to adopt this new account of predication where god is the subject. Knowledge itself, he suggests, is 'more perfect' than knowledge-among-us, and so it is appropriate that god (himself presumably perfect) should have knowledge itself, rather than mere knowledge-among-us.

(It is very often thought that a vicious notion of self-predication is implicit in the argument at this point. Thus, the form of knowledge is 'the most perfect knowledge' because it is its own best instance. Weak though Parmenides' argument is, however, it does not require a reading of this sort. For example, Parmenides may think knowledge is 'most perfect' only because it is a form, and so shares the honorific status Plato accords to all forms. If so, then the argument rests on a principle of the affinity between god and the forms: compare the similar principle of the affinity between the forms and the soul, again independent of any notion that the forms are self-exemplifying, at Phaedo 78b ff.)

Parmenides' theory for predicating things of god may be useful to him in two ways. First (i), if we say thlat god knows something, we assert a relation between god and knowledge itself, not between god and knowledge-in-us. Given this result, Parmenides may feel able to argue that although our knowledge can be knowledge only of instances of forms, not forms themselves, the knowledge god has is not limited in this way. For, simple separation does not



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separate god, as it does sensibles, from the forms. If, then, god knows something, he has not the immanent form but knowledge itself. And unlike knowledge-in-us, knowledge itself can be knowledge of forms. This suggestion is not in fact cogent. Parmenides' new theory for how things are predicated of god requires that god has knowledge itself, not the immanent form, knowledge-in-us. But this fact makes no difference to the point that even god's knowledge can be only an instance of knowledge. As such, god's knowledge too is bound by the results of the previous argument. God's knowledge can be knowledge only of instances of forms, and no one, not even god, knows the forms.

Accordingly, we will understand Parmenides in the present argument to be arguing for exactly the conclusion he states: if god has knowledge, he cannot know sensibles. This is consistent with the conclusion to his earlier argument and together with it produces the result that - since god cannot know sensibles, while the forms are not known by anything - god in fact knows nothing.24

(ii) Parmenides new theory of predication may, however, serve a different purpose. Parmenides will want to borrow from his first argument the principle of proper separation, in order to show that god's knowledge cannot be knowledge of sensibles. But proper separation is a principle about relational forms, and does not govern 'the things among us', where this phrase seems to cover any sensible whatever, including immanent characters. So proper separation cannot apply to god's knowledge unless it too is a form, and not a mere immanent character. Parmenides' theory for how things are predicated of god thus smooths the way for his later appeal to the principle of the separation of forms from sensibles.

(2) Parmenides, then, also claims support for his conclusion that god cannot know sensibles from the principles of separation presented in his earlier argument. Thus, 134d5-7 is verbally an echo of 133e4-134al. According to proper separation, forms are what they are, or have their power,

with respect to one another. This was explained as the principle that the converse of a relational form is another relational form. In accordance with this principle, knowledge itself has its power with respect to no non-form. That is, the converse of the form knowledge, like the converse of any relational form, is itself a relational form, not a sensible.

This is not the interpretation Parmenides now gives to proper separation. He now takes the principle to imply that if anything, say god, has knowl-




edge itself, then he cannot know any non-form. Parmenides has here exploited an ambiguity in the expression '...has its power with respect to -- -2

between (i) '...has as its converse - - - and (ii) '...has instances which bear that relation to -- -'. These two readings are redically different in intent. Mastery, for example, has as its converse the relation slavery, but it is not true to say that mastery has instances which are masters of slavery. Cor- rectly understood, proper separation stipulates that a relation R has as its converse another relational form, and not any sensible. For his present purposes, however, Parmenides takes the principle to imply that instances of R cannot bear R to any non-forms. For example, since knowledge is a relation that has its power with respect to forms, god cannot stand in that relation to any non-forms. This conclusion is not legitimately obtained by means of Parmenides' earlier principles. So as Parmenides himself predicts, neither of his arguments - the argument that we cannot know the forms, or that god cannot know sensibles - can stand close examination.25

University of Arizona

NOTES

Recent printed treatments of this argument include James Wm. Forrester, 'Arguments An Able Man Could Refute: Parmenides 133b-134e',Phronesis XIX (1974), 233-237; briefer accounts are by Rudolph H. Weingartner, 7he Unity of the Platonic Dialogue, Indianapolis 1973, pp. 183ff, Norio Fujisawa, "'EXewv, MeTE'XEV, and Idioms of "Para- deigmatism" in Plato's Theory of Forms', Phronesis XIX (1974), 30-58, and Charlotte Stough, 'Explanation and the Parmenides', Canadian Journal of Philosophy VI (1976), 379-401. I have learned most, however, from an unpublished paper by Sandra Peterson: 'The Greatest Difficulty for the Theory of Forms: the Unknowability Argument of Parmenides 133c-134c'.

The title of Forrester's paper is an unfortunate one, since it advertizes a misreading of 133b (cf. also Forrester p. 233; the same mistake appears in Weingartner, op. cit., p. 183). As Heindorf noted long ago, 6 appta,3qrCwv, 133b8, the man of whom ability is required, is the objector, if he is to be convinced of the flaws in his objection (cf. 135a3ff), not the defender of the knowability of the forms - the latter must be Too eV66IKVVI1AoV, b9, where the reference is back to 8Aeitaatat, b7. 2 He also argues at 134c4ff for the complementary conclusion (the 'more terrible' consequence, c4) that god can know no sensible: see Appendix below. Parmenides' two arguments together attempt to show that we can know nothing of the divine world, while god can know nothing of us. 3 CS el'6& dvra a?aT Ka9' a-ia' 6op'flTat. Readers of Cornford's translation may not catch the reference to separation here: a&rTa KaO' av'& 6topLr?7TaL is weakened to 'asserting their existence as forms just by themselves' (my italics), while de TL oplp6giO-'o (b2 below) is unrecognizable in Cornford's version, see n. 5 below.

4o654irw &rrT abrti' o6an CaTlv Iu aropta, presumably a parody of a typical formula



124 FRANK A. LEWIS

for referring to separate forms: see among other examples, Symposium 211c8-dl, Kat 'yvcy -reXeTvrWv o' east KaXd l.

SEi YJJ 6,O J EKaaTOV rC.V 6VrWVr d aEL TL a PLpto6,evoc t5r aev, bI -2. I take rCv 6v'rwv as genitive after &dOPL.'11EVOq ('von den Dingen getrennten ... Wesenheiten', Apelt, cf. Parmenides 158a2, although I take the genitive to be closest to that at Hippias Major 298d6-8 and Sophist 257e2, cf. Campbell ad loc.). Cornford and others construe the words with the preceding g`Kaorov ('for every distinction you make among things', Cornford, presumably understanding CeKaaTov TCwv 6vrwv as the combined object of aopltoipevoq). On the reading I recommend, eKaaTov here distinguishes one form from all the remaining forms (cf. Parmenides 158al-3); TCZv 6vrwv ... hpopto0'evoq indicates its separation from the sensibles that fall under it. 6 Cf. Vlastos pp. 245ff for the interpretation of separation via the categorial properties of forms (Gregory Vlastos, 'The Third Man Argument in the Parmenides', reprinted in R. E. Allen (ed.), Studies in Plato's Metaphysics, New York 1965, pp. 231-- 261). This provides the link between separation and Parmenides' other arguments against the theory of forms (see p. 105 above): for as Vlastos suggests, the assumptions operating in those arguments can be regarded as explications of separation in terms of various categorial properties of forms.

On 133c5-6, note that not being 'in' any sensible appears among the categorial properties of forms at Timaeus 5 2a, cf. Symposium 21 la. 7 When Parmenides says that they "have their being themselves with respect to themselves", I take him to be speaking collectively of the members of the relevant proper subset of forms, and to mean that the being of each is specified by reference to some other form in that set (but not that each has its being with reference to itself). Cf. Heindorf ad loc. and Parmenides' own example at e3--4. The contrary view appears for example in Weingartner: his gloss is "that forms do not obtain their being by virtue of standing in relation to particulars, is precisely what has been meant all along by the absolute and independent character of the forms" (Weingartner, op. cit., p. 185). By missing the restriction to relational forms, Weingartner is forced to suppose that Parmenides' argument hinges on an exaggerated notion of separation that prohibits all relations between sensibles and forms; against this, see pp. 110-111 below. 8 The predicates he asserts of these forms then count as B1-predicates in Owen's clas- sification: G. E. L. Owen, 'Dialectic and Eristic in the Forms', pp. 108ff, in Owen (ed.), Aristotle on Dialectic, Oxford 1968, pp. 103-125. (But simple separation is a matter of A-predicates.) For other discussion of the distinctions among predicates of forms referred to here, see Michael Frede, Pradikation und Existenzaussage. Hypom- nemata, Heft 18, Gottingen 1967, pp. 33f and David Keyt, 'Plato's Paradox that the Immutable is Unknowable', Philosophical Quarterly 19 (1969), pp. 1 ff. 9 The purely syntactical definition of self-predication is wider that that given by Vlastos, who reserves the term for cases of the instantiation of a form or concept by itself, or the sentences in which such cases are expressed (Gregory Vlastos, 'The Unity of the Virtues in the Protagoras', reprinted in his Platonic Studies, Princeton 1973, n. 97). 10 Vlastos, for example, explains the claim that mastery is mastery only of slavery by suggesting that only mastery is exactly a master, and only slavery exactly a slave, so that only slavery can be an appropriate object of mastery's mastery (Vlastos, op. cit., p. 258). Others who have found a vicious form of self-predication at work at this point in the argument include Cornford (F. M. Cornford, Plato and Parmenides, London 1939, pp. 98f), Runciman (W. G. Runciman, 'Plato's Parmenides', in Allen, op. cit., p. 159), Suhr (Martin Suhr, Platons Kritik an der Eleaten, Hamburg 1969, p. 109), Weingartner, op. cit., pp. 186, 189, Forrester, op. cit., p. 234, and Stough, op. cit., pp. 397-398. Curiously, Cornford does briefly concede a harmlessly self-predicational interpretation of Parmenides' premisses: "Mastership, the Form, has as its correlate, the Form Slavery;




and we may say, in that sense, that is is 'Mastership of Slavery itself', as Parmenides does say at 133e" (Cornford, op. cit., p. 98; the second set of italics are mine). There are also some suggestive remarks on Parmenides' premisses in P. T. Geach, 'The Third Man Again', in Allen, op. cit., pp. 268f, cf. Vlastos, 'Postscript to the Third Man: A Reply to Mr. Geach', in Allen p. 289. The presence of vicious self-predication in the argument is outright denied by Fujisawa, op. cit., p. 31, n. 1: he does not explain what he takes to be the correct reading of the premisses. There is an excellent discussion of the general issue of self-predication in the argument in Peterson, op. cit. Other places in the argument at which self-predication in a logically vicious sense is frequently seen are at 134b6-7 and c6-11: see pp. 115-116 and 121 below. " Gwynneth Matthews, Plato's Epistemology, London 1972, p. 121. Cf. Auguste Dies, Parmenide (= Platon, Oeuvres Compltes, Vol. VIII, part 1), Paris 1923, p. 27, A. J. Festugiere, Contemplation et Vie Contemplative Selon Platon, 2nd. ed., Paris 1950, p, 189, n. 2, Harold Cherniss, Aristotle's Criticism of Plato and the Academy, Baltimore 1944, pp. 282ff esp. n. 19 1, Gilbert Ryle, 'Plato's Parmenides', in Allen, op. cit., pp. 108f, Runciman, op. cit., p. 159, Edith Watson Schipper, Forms in Plato's Later Dialogues, The Hague, 1965, p. 15, Weingartner, op. cit., pp. 185-187, and Fujisawa, op. cit., pp. 30ff. The contrary view is argued well by Peterson and Forrester, op. cit., p. 236. 1 2Forrester, op. cit., pp. 234ff. 13 No doubt the conclusion that there is any form that is unknowable will be sufficiently distasteful for Plato. But Parmenides' announced conclusion is that all forms are unknowable, and this conclusion cannot be obtained by the analogy with mastery and slavery.

There is also some question whether the mastery-slavery example can establish even that the single form object-of-knowledge cannot be an object of knowledge. No master is a master of slavery, and no slave is a slave of mastery: so in each of these cases, the converse form is not a member of its own domain. But does this principle hold for all relational forms and their converses? And more generally, can no form be an instance of itself? The same, for example, is a relational form that apparently falls both in its own domain and in its own range, while the form the one appears to be an instance of itself. So the examples of mastery and slavery do not by themselves show even that the form object-of-knowledge cannot be a member of its own domain. '4 The Greek 'epistemd' is ambiguous between a name for (i) the relation knowing and (ii) a body of facts known, which is a class and not a relation. 'Episteme' in the first sense is perhaps better translated 'knowing': but I will retain the conventional translation, 'knowledge', for both senses of the word. ' The grammar of Ti,r 6 E"artv dXiAOeta is puzzling: I take 6 e`artv dxtoeca as an indeclinable noun, getting its gender from its constituent noun detxeta. Possibly abri o eart cnrrWTrg17 in the same sentence at a3 should be explained in the same way; o eart 6earn6rrs, 133d8, may also be an indeclinable noun in apposition with avTov 6eardrov, cf. el, abrob 6ovJXo5,6` ea-r 6oOXos. For possible parallels elsewhere in Plato, see oi5rwc CroL7'juev giav ovZOlv avTrwv EKeW'lV7l 0 EUTLV KXW'V?, Republic 597c3, EKEOV TEr

opeycraL TOo O c6rtv 'aov ,Phaedo 75b1 -2,andr'v T1 v rCO 6 UTWv dv 06Vrwq f7LaTpnrm.V ovuav, Phaedrus 247el --2.

I do not have any firm view of the internal grammar of such indeclinable nouns: in my translation I take 6' as subject and axfi'eta, 6eanroTrn, and the rest as predicate, but without much confidence. For different treatments, see Loriaux (R. Loriaux, L' Etre et La Forme Selon Platon, Bruges 1955, pp. 117ff), who takes the relative pronoun 6 as subject with Wd7e&La etc. as its antecedent ('truth which is', where he interprets the 'is' as existential), and Mills (K. W. Mills, review of Loriaux, Gnomon xxix, 5 (1957), 328), who would identify dXi69eta etc. as subject of C6Urt, with 6' as its predicate ('what truth (really) is': see his sample translation of 1 34a6-7: "Again, each of the knowledges, i.e. that which each of them really is [the Form of each knowledge] , will be the knowledge



126 FRANK A. LEWIS

of each of the things that are, i.e. of that which each of them really is [of the Form of each of the things that are] "). On yet another view, the distinction between subject and predicate becomes irrelevant, since the ealrtv expresses an identity: d eirt x on this view means 'what is identical with x' (H. F. Cherniss, 'The Relation of the Timaeus to Plato's Later Dialogues', reprinted in Allen, op. cit., p. 372). 16 Cf. Charmides 171a5-7, Republic 438c6-e9, Sophist 257c7-d3, and Aristotle Categories 1 a24ff. 17 Knowledge (episteme) is most clearly a relation in those passages where it is pictured as a dynamis or power (Republic 477d, cf. 477bl0-1 1: e1rWT7f.l ...dretCT b'VTL lreIpVKE,

'yoc'aiW' c. Car TO 6'v, 508e3, cf. eS [and e6, 509a6]: WTt7uLr ... Kat LX7Eac, __vWae__ TE KaL adXs?eiac..., Charmides 165c4-6: et -y&p 6ih -(Lyv(h)aKeLv ye Ti caTW

o aW poatiV7, S&io'V bTi naLTajpn TrS n V ETh Ka 7L rWo [ri here is object of 7Lyvw' aKEW,

not nominative singular in agreement with it, as Jowett 3 takes it] . Parmenides 134a3-4 indicates the relational character of knowledge by citing the

class of objects in its range: knowledge itself is of truth itself - that is, of the forms - while the various branches of knowledge are of some particular form or other. Cf. Republic 438c6ff: EILaT'fl.n Ae'v a&rT 4ad5,uaToc aiuroo 67r=Tfll EaTTWv ti orov 6b'i 66 9ewvaL T7lIv i7LaT7;S7V, WMT97A7 6Tf' TL' iaL notodT 7rOLOVL TLOc Kal TLWdL (cf. Charmides

168a6-8), Republic 477b1O-1 1 (cited above), Aristotle Categories 6b32ff: ...' 6wrLor g?rtuT71TOV XS-yeTat UwT?7 Kal TO f lTOV 8lruT7 l 8LaTUUTdJv, and Proclus, In Parm.

Comm., p. 933 Cousin: T7l)v AV' darTX C LaT7nI.7ta irpbv TO c 0urXc) wT71Tov,Trv 66 swa 7 rWTaI- 1.1Wvp TO T 67rtarTnTOV.

Geometry (geometrical episteme), by contrast, is not a relation: it is one of the many technai or epistemai (Sophist 257dl-2) - that is, it is a body of knowledge. Cf. Charmides 171a5-7, Republic 438c6-e9. This fits well with Aristotle's view in the Categories that the species of the genus knowledge are not themselves relations (but contrast Topics 145al3-18, cf. J. L. Ackrill,Aristotle's CategoriesandDe Interpretatione, Oxford 1963, p. 108). The general ambiguity of the Greek 'episteme' (Note 14 above) is in this case resolved by Parmenides' phrase 'each of the epistemai' at 134a3: for 'episteme' in the plural must refer to bodies of knowledge. " The point will be clearest if we borrow a set-theoretic account of genus and species. Although this is almost certainly a distortion of Plato's general views on division (cf. J. M. E. Moravcsik, 'The Anatomy of Plato's Divisions', in Exegesis and Argument: Studies in Greek Philosophy Presented to Gregory Vlastos, ed. by E. N. Lee, A. P. D. Mourelatos, and R. M. Rorty, Phronesis suppl. vol. 1 (Van Gorcum, Assen, 1973), pp. 324--348), it will not materially affect anything at issue here. '9 Add here to the references in n. 10 above, Sir David Ross, Plato's Theory of Ideas, Oxford 1951, p. 90, Gilbert Ryle, 'Plato's Parmenides', reprinted in Allen, op. cit., p. 109, and I. M. Crombie, An Examination of Plato's Doctrines, London 1963, Volume II, p. 333. Reservations about this reading of the lines appear in Stough, op. cit., n. 29. 20 Contrary to Cornford, op. cit., p. 99, I take Parmenides' claims that we do not lhave the form of knowledge (i.e. the form of knowledge is not 'in' us) at b9 and that we do not partake of the form knowledge at bl 1-12 to be equivalent. All that Parmenides needs for his argument is to repeat the point that among us we find only instances of knowledge, not knowledge itself (nor even any of the many forms of knowledge: the forms knowledge of figure, knowledge of odd and even, and so on). For 'partake' at bi 2, cf. 133dl-2 (on which see Cornford p. 96, n. 1, cf. p. 84, n. 3 and p. 85, n. 2), and Fujisawa, op. cit., pp. 31ff. Plato's sentence at I 34b1 2 is discussed in some detail by Peterson, op. cit. 21 Jones' geometrical knowledge might also be understood non-relationally, as the class of geometrical facts Jones knows. This is, as often, the effect of the ambiguity of 'knowledge', translating the Greek 'episteme', between knowledge in the proper sense (a body of knowledge), 'nd the relation knowing: cf. Note 14 above.




22 So for example Cornford, op. cit., p. 99, Festugiere, op. cit., p. 189, n. 2, and cf. Timaeus 35a, and Symposium 20leff on the nature of eros as an intermediary. 23 Sophist 248aff. (On this argument, see David Keyt, op. cit.). 24 Parmenides has now shown that god can know neither sensibles nor forms, while sensibles cannot know forms. Although he does not notice the point, it follows that unless sensibles can know sensibles, both the domain and the range of the relation knowledge are necessarily the empty set. This is an intriguing consequence, for - if Parmenides' arguments stand - Plato must defend the possibility that sensibles can have knowledge of the sensible world, else it becomes problematical in what sense knowledge (episteme: 'knowing') is a relation at all. (I am indebted to Merrilee Salmon for pointing out to me the difficulties of a relation whose domain and range must be null.) 25 1 am grateful to James W. Forrester, Keith Lehrer, Ronald D. Milo, and Merrilee Salmon for helpful discussion and criticism.



parmenides on separation and the knowability of the forms: plato parmenides 133a ff

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