PLATO'S LATER PLATONISM

WILLIAM CHARLTON

QuJN E defines Platonism as the doctrine that there are ab tract ob­jects, that 'abstract entities have being independently of the mind' .• As typical abstract objects he offers us 'classes, attributes, proper­ties, numbers, relations and functions', 2 and he equates holding that 'there are' entities of a specified kind with admitting them as values of bound variables.

Readers of the Phaedo (e.g. 76 D-77 A), the Republic (e.g. 479), and the Phaedrus (e.g. 247 D-E) can find in them a richer Platonism than this. Plato says not only that 'there are' certain Forms, but that they enjoy a changeless existence 'beyond the heavens'. But in some supposedly later dialogues it may be wondered if Plato is even a Quinean Platonist. At Philebus 15 B 1-2 he says it is 'a big problem whether we ought to understand that there really are certain mon­ads' such as a one ox and a one beautiful 'really existing'. On the face of it, the second part of the Parmenides is a serious and, in the end, inconclusive attempt to tackle this question. And although on some interpretations the analyses of negation and false statement in the Sophist call precisely for quantification over abstract objects, those passages have also been interpreted as requiring quantification over concrete objects like Theaetetu .

Particularly since Owen and Frede,' studies of the Sophist pas­sage have accumulated at an exponential rate: and Pelletier dis-

C William Charlton 1995

A first version of this paper was read at the University of Pittsburgh in September 1992. I am grateful to the audience on that occasion, and also, for comments on a later ver ion, to Paolo rivell i.

' W. V. . Quine, From a Logical Point of View (Cambridge, Mass., 1964), 14. ' ld., Word and Objtct (Cambridge, Mass. , 196o), :ZJJ . ' G. E. L . wen, 'Plato on Not-being', in G. VIa tos (ed.), Plato, i ( ew York,

1971), 223-67; M . Frede, 'Pradikation und Existenzau sage', Hypomnemata, 18 (1967). 1-99·

• There are useful bibliographies in P. Criv IIi, ll 'Sofista' di Platone (Florence, 1990). and G. Movia, Apparen:u, tsstre e veritO (Milan , 1991).

I 14 William Charlton

tinguishes no fewer than thirteen interpretations of them.' But the passages themselves are brief and the issue clear. In what follows I first explain (Section I} why I prefer a Platonizing interpretation, and (Section II} question whether Plato is willing to quantify over concrete objects at all. I then ( ection III} con ider how he would wish us to understand existential claims to the effect that 'there is' something or that something 'shares in being'. ext (Section IV} I show how, using quantification over abstract but not ·over concrete objects, and al o using the five Greatest Kinds mentioned in the Sophist, Plato could analyse various kinds of statement. He did not, of course, have the concept of quantification logicians have today. But he had strong logical instincts, and the suggestions he throws out lend themselves to development with the aid of quan­tifiers in a perspicuous and intriguing way. Finally (Section V) , I suggest that his analysis of negation in terms of otherness reveals a sort of Platonism that is itself other than that defined by Quine: he believes that the difference between being and not being is in­dependent of our thought in a way it would not be on an analysis similar to that proposed for change in Section IV.

I

At Sophist 257 B the Stranger introduces a new point:

'When we say "not civ" we do not say omething the contrary of civ, but only something other. '

'How do you mean?' 'For instance, when we say something is not large, do you think we make

out by our speech that it is mall any more than equal?' 'No.'

' o when negation is aid to signify a contrary we shall not agree, but concede only this, that negative particles intimate something other than the word they are placed before, or rather than the things for which the words spoken after them are e tablished.' (257 B 3-<: 3)

The opening ntence is obscure indeed. 'Small', however, signifies the contrary of larg , so the example shows that the analysis the

tranger reject is that 'A is not f' means 'A is the contrary off'. And since 'equal' (equal, pre umably, to that which large exceeds

' F.]. Pell tier, Parmmidts, Plato and tht Semantics of Not-btitllf (Chicago, 1990), ch. 4 ·

Plato's Later Platonism 115

and small falls short of) signifies omething other than large, we are led to expect that the preferred analysis will be that saying 'A is not/' is saying that A is something other than what is signified by the expression following the negative particle. That is precisely the natural way of understanding the lines B ro-c 3· If we use quantifiers, and/ range over Forms, 'A is not large' appears as:

(3/)(A isf&f*large)

This analysis requires quantification over abstract objects. Unfortunately, as an analy is of negation it will not do. To say 'A

is large' is not to say that largeness is the only property A ha , and hence 'A is not large' is not equivalent to 'There is some property other than largeness that A ha '. Accordingly, modern readers of Plato mostly think the natural construal of B 1 o-c 3 must be wrong, and propose alternatives.

One alternative (advocated by Bostock)6 i this: 'When we use "not" we mean, not that the subject is the contrary [sc. of what is signified by the following words], but that it is other than all the objects to which the following words apply.' On this analysis 'A is not large' becomes:

('Vx) (xis large-+A*x)

and Plato needs to quantify only over concrete objects. There are two difficulties about obtaining this from B xo-c 3·

First, we have to take 'the things for which the words spoken are establi hed' (1TEpt a-r-r' civ KIT}Tat) to be the object to which the words apply. In 'A is not seated' 'seated' is 'established' for Zeno, Socrates, and any other seated objects. But it is much more natural (a Bostock perhaps senses) to uppos that 'seated' is established for the position, the di position of limbs, that seated people exhibit. Secondly, according to this interpretation the erroneous analysis is still (B 9) that using 'not' is predicating of something the contrary of what is signified by the expression that follow ; but the correct ana­lysi i now, not that using 'not' is predicating something different, but that it is saying that the subject is non-identical with certain things. In 'When we u e "not" we mean, not that the subject is the contrary, but that it is other than ... ' the fir t 'i ' is predicative and the second the 'i ' of identity. The erroneous analy is is erroneous

• D. Bostock, 'Plato on "i not"', Oxford Studies in Ancient Philosophy, 2 (1984), 89-119 at us, following Frede, 'Priidikation und Existenzau age', 86~.

JI6 William Charlton

not because it misidentifies what is predicated but because it takes as predicative an utterance which is not predicative at all. If Plato really means this he has expressed himself very awkwardly. (We may also doubt if he would wish to analyse 'Phaedo is large' as 'Phaedo is identical with one of the things for which "large" is established'.)

Of interpretations that require quantification over abstract ob­jects and avoid the objection I made just now to what I called the 'natural' reading, the simplest is probably this: 'When we use "not" we mean, not that the subject is the contrary [of what is signified by the following words], but that everything it is is other than the things the following words signify' .1 'A is not large' then becomes:

('Vf) (A isf~f*large).

I readily concede that this is even harder to obtain from B 9-c 3 than the account that requires quantification over concrete objects. But it is far from clear that those lines are intended as a formal account of negation, much less as Plato's last word. We can read them in the natural way as a first approximation which, because of the defect we have noted, Plato will later wish to refine. But how would he refine it? On the natural reading, he wants to be able to quantify over ab tract objects. Will he drop that requirement and settle for an analysis that calls for quantification only over concrete objects, or keep it and amend the analysis in some way like that just described? Since his purpose in considering negation is to explain how we can speak falsely-this being to say 'what is not'-we can answer this question only by examining the account of falsehood he eventually produces at 263 A-D.

The utterances 'Theaetetus is sitting' and 'Theaetetus is flying', it is agreed, belong to or 'are concerning' Theaetetus (A 4-5, c 7). The second says 'things other than the things that are' (B 7), 'things that are not, therefore, as being' (B 9), 'things that are other than things that are concerning you (sc. Theaetetus: -rr£p~ uov}. For we aid that many things are with regard to each thing (7r£p~ lKo.u-rov}

and many are not' (B I I-I 2). The 'things' here are abstract, not con­crete; they are things predicable of concrete objects like Theaetetus. That is confirmed, if confirmation is needed, by the back-reference of B J I-12. That is to 256 E s-6, a passage concerned solely with Forms: ' o concerning each of the Forms, that which is is much,

1 o D. Wiggins, ' ntence Meaning, Negation and Plato's Problem of Not­being', in Vlastos (ed.), Plato, i. a68-303 at 294.

Plato's Later Platonism I I7

and that which is not is unlimited in multitude.' We may notice that Plato in these passages uses 7T£pt with the accusative for the claim 'concerning', i.e. with regard to, a Form that it is not, i.e. that it is other than another Form, whereas he uses it with the genitive for the claim that a Form 'is concerning', i.e. is had by, a concrete object.

According, then, to B 4-1 I, in a false utterance we predicate, as belonging to an object, things other than the things that belong, and in a true utterance we predicate the things that in fact belong, that is, we say that they belong (B 4; cf. Rep. 477 B 10-1 I, 478 A 6). The formal account of D 1-4 is fully in line with this: 'When things are said concerning you, things that are other, however, as the same and things that are not as things that are, that sort of combination of verbs and nouns seems to be really and truly false statement.' The suggestion is that in 'Theaetetus is flying' a certain doing (7rpii~'s, z6z B 6) is said as being the arne as a doing of Theaetetus, that is, the utterance has the form: 'There is a doing that is the same as one in which Theaetetus shares.' If that is how we should analyse 'Theaetetus is flying', we must think that in 'Theaetetus is not sitting' (for negative false statements see 241 A I) sitting is said to be other than any doing in which Theaetetus shares. We obtain the simple analysis involving quantification over abstract objects:

(Vf) (Theaetetus is f -+!*sitting)

II

It is one thing to say Plato does not require quantification over concrete objects for his analysis of negation or falsity, another to say he does not want it at all. If by 'quantifying over concrete objects' we mean no more than using words like 'all', 'some', and 'three' with nouns like 'ox' and 'finger', of course he does that. But do we ourselves have to quantify over concrete objects to make any of hi analyses perspicuous? If the analyses of negation and falsity do not require thi it will be hard to find any others that do.

Cornford1 thought it wa an integral part of the Stranger's solu­tion to the problem of false statement to point out that a remark like 'Theaetetu is flying' i about something that exists. That shows

• F. M. Comford, Plato's Theory of KN)W/tdge (London, 1935), 314, 317.

IJ8 William Charlton

a misunderstanding of the problem. On a natural view, to speak falsely is to say something that 'is not' (i.e. that is not the case). It looks, then, as if Epimenide ays omething false only if there is something which both is not and is said by Epimenide . But then we wonder: how can something that is not nevertheles be and be said? The dilliculty is not that a false statement is about something non­existent but that its content is non-existent (Soph. 237 E, Theaet.

I89A-B). 'In his concluding speeches', says Corn ford, 'the Stranger em­

phasises once more that the false statement, Theaetetus flies, is a statement, not "about nothing", but about the Theaetetu who ex­ists here and now ... The name Theaetetus stands for a "thing that is" in the sense of an element of an existing fact.' 9 By the Stranger' 'concluding speeches' Cornford means tho e of 263 c 5-11. The point there, however, is that the sentences in uttering which we say omething true or false have subject-predicate form, not that the subject is an existent thing. The Stranger does not say that Theaetetus is a 'thing that is', an ov. Neither does he say of any concrete object what he says at 256 D-E of every Form, that it 'shares in being'.

But surely, it may be protested, Plato did conceive concrete ob­jects a existent things. Two passages from the Sophist might be cited to how thi . First, there is the difficult sentence 262 c 3-5. Cornford translates this: 'neither in this example [Lion, stag, horse] nor in the other [Walks, runs, sleeps] do the sounds uttered signify any action performed or not performed or nature of anything that exists or does not exist, unless you combine verbs with names.' 10 I do not think, however, that in the words he translates 'or nature of anything that exists or does not exist' the participle of the Greek verb 'to be' is used existentially. Cornford thinks Plato's point is that the string of names 'Lion, tag, horse' 'does not state that there exi t or does not exist anything with the nature expressed by the name'. Rath r it is that the string does not say, either that anything is, or that anything is not, a Lion, stag, or horse. A better translation would be: 'Neither in this example nor in the other do the sounds uttered show a doing or a staying inactive or a being of a thing that

• Comford, Plato's Thtory of Knowltdge, 317; similarly I. M. Crombie, An Ex­amiMtion of Plato's Doctrims [Examination], ii (London, 1963), 497: 'The realities ar Theaet tu and flying.'

•• Comford, Plato's Thtory of Knowltdgt, 305.

Plato's Later Platonism 119

is [sc. walking, sleeping, a lion] or of a thing that is not [walking, sleeping, a lion]'; we have here an elliptical predicative use of 'to be', not an existential u e.

Secondly, at 249 D we are told that what is, n~ ov, must include both unchanging and changing things, and the latter, surely, are ma­terial objects. We have just been warned, however, that the Friends of Forms do not accept that having a power to act or be acted upon is sufficient for coming within the bound of what is (248 c). They think that things with this power rather become than are (c 7-8), and the only change they allow into the sphere of being is change within the soul (249 A-B).

The distinction between being and becoming to which the Friends appeal is probably that of Republic 476-80 (Timaeus 48-52 contains a different use of the di tinction, though one equally derogatory to material objects). Somewhat as Cambridge change i being/ at one time and not at another, so Platonic becoming seems to be being/ in relation to one thing and not to another. Things that rather become than are will in Jude acts like returning a sword that are just in some circum tances and unjust in others (Rep. 479 A; cf. 33 I B), materials that are beautiful in one artefact and ugly in an­other (cf. H.Ma. 289 E-290 D), stones that are equal to some stones and unequal to others, and large compared with some of the latter and small compared with others (Rep. 479 B; cf. Phaedo 74 B), and objects that 'become' on or three according as we think of them as fingers or joints (cf. Rep. 523 c-525 A). No doubt a finger is always a finger and gold is always gold: that stops them from being enti­ties that 'in no way are' (cf. Soph. 237 B). But a Friend of Forms might well feel that entities which share in contrary properties have insufficient 'clarity and truth' (Rep. 509 D, 51 I E) to be values of a bound variable.

Of course, if Plato is unwilling to quantify over material objects, that disastrously limits his philo ophy of language. It looks as if he will be unable to analyse such elementary sentences as 'All birds fly' and 'Some birds do not fly'. Pelletier•• offers highly ingenious translations of such sentences into what he calls 'th philosopher's language', but he as umes (104) that the philosopher can quantify over harer in Forms.

In fact, Plato has at his di posal a way of dealing with universal statements. In modern logic we use the principle that if all objects

11 Parm~des, Plato and the Semantics of ot-being, 141-4.

120 William Charlton

in a given domain have a certain property, an arbitrarily selected object has it. At several places in the Parmenides(145 B-B, 157 C-B,

158 E) Plato develops an argument (not, of course, a proof in logic) by making an arbitrary selection. He could analyse 'All birds fly' as 'There is a Form which is bird and a Form which is flying, and if any arbitrarily chosen object {or organism) X shares in bird it shares in flying':

(3/) (3g) (j= bird &g =flying& (X isf-+X is g))

'No bird flies' says that if X shares in bird then every Form in which X shares is other than flying:

(3/) (3g} (j =bird &g =flying & (X is/ -+(Vh)(X is h-+h'l:g)))

But Plato could not deal like this with 'Some birds fly' or 'Some birds do not fly'. Indeed, his philosophy of language will not allow them to be genuine statements. 'It is necessary', says the Stranger, 'that any statement should be concerning something (nvo!>') (262 B s-6); 'for there to be a statement that is not a statement concerning something is impossible' (263 c 10-11 }. If xis a genuine statement, there is a definite y that it 'concerns' or 'belongs to'. It might be argued (though the argument is finely spun) that since Plato thinks 'Theaetetus is sitting' is a genuine statement this second-order generalization requires him to hold that Theaetetus is a thing that is; but however that may be, there is nothing that 'Some birds fly' belongs to or concerns.

III

It is now time to consider what, in Plato's view, we claim when we say that 'there is' a certain thing, or that that thing 'shares in being'. Many of Plato's readers have thought that phrases like 'shares in being' are used by him (consciously or unconsciously) to pick out an existential use of the verb 'to be', a use of it to express existence. They a sume, if not that existence really is one thing among others in which something might share, at least that it would be natural for Plato to uppo e it is. This is doubtful. The Greek verbs ~:Tva' and y{yv~:a8a,, 'to be' and 'to come to be', can be used both abso­lut ly and with a complement, as Aristotle (SE 167•1-2, Post. An. 90"2-5, Phys. 190"31-2) and Plato (Parm. 163 c) are aware. But as

Plato's Later Platonism 121

Charles Kahn has argued forcefully, 11 from this grammatical fact it does not follow that when used absolutely it expresses something it does not express when used with a complement. Kahn also ques­tions whether the Greeks had a concept of exi tence as something expressible. It is not, in fact, at all natural to imagine that existing is like breathing only quieter. Nobody is likely to think there is such a thing as existence before it has been noticed that besides words like 'ox' and 'holy' language contains words like 'is' and inflexions of tense.

Plato was perhaps the .first person to enquire into such fancy linguistic items (see 'Theaet . 202 A, zos c, Parm. 147 o, 151 B-I 52 A, 152B, 1550,1560, 160A, I64A},andatSoph.243B3-']ando8-Bz he asks what we say of a thing when we say it is. He argues that those who say that there are two things that are, hot and cold, will not want to say that being is a third (243 B); neither will those who say there is only one thing want 'is' to signify something other than what 'one' signifies (244 B-e). Since he recalls these arguments at the beginning of the discussion of change, staying unchanged, and being in 250 A-c, we should be on our guard against a simplistic reading of the conclusion that being is a 'third' thing over and above change and staying unchanged ( c I); if being were one Form among others in which things can share, it would hardly be as puzzling as he insists it is at zso B 1-2.

But if sharing in being is not sharing in one Form among others, what, in Plato's view, i it? In our own times it has been suggested that to say 'Tame tigers exist' is to say that the number of tame tigers is not zero, but this approach to existence would not commend itself to Plato. If tame tigers are not none in number, they are one or several. Plato is emphatic that each Form is one and not many (Parm. I 32 A-B); 'Largeness exists' does not mean 'Largenesses are many'. But he also tells us that to say 'One [i.e. the Form of one) is' is not the same as to say 'One is one' (Parm. 142 s-c). Moreover, it would be odd if Plato did think that being is being one or several in number, since at Soph. 238 A-B he seems to be taking the intuitively piau ible line that in order to have a number, things must already be. (Thi n d not commit him to holding that concrete objects are, since he thinks numbers do not attach to them unambiguously: Rep. 525 A, Parm. 129 c.) If having a number presupposes being,

" e.g. C. Kahn , 'The Greek V rb "To Be" and the Concept of Being', Foundntions of Langua~, :z (1¢6). :l4s-s6.

IZ2 William Charlton

it cannot constitute it. David Wiggins suggests: 'Flying is because, although it does not qualify Theaetetus, it does qualify other things, birds, insects, etc.' 13 I am not sure whether he means to attribute this view to Plato or simply to offer it as the truth. It is, of course, pure Aristotelianism. But l think that far from Plato's being, in his later years, an Aristotelian, Aristotle preserves a Platonic theory of the nature of being.

Aristotle's discussion of Eleatic Monism in Phys. 1. 2-3 could contain material dating back to his time at the Academy, and I hear echoes in it of discussions attested by the Theaetetus, Parmenides, and Sophist (compare 185bi 1-16, for example, with Theaet. zo3 B-205 B, Parm. 157 c-B, 145 B-E). At I 86"34-b6 he argues roughly as follows. If ov means some one thing, either it signifies something that can supervene on things that are not already things that are (as education supervenes on uneducated people), or it can apply only to precisely what is, TO OTT€p ov, i.e. to being itself. But the first is absurd. And if ov applies only to being itself, why say that it means 'thing that is' rather than 'thing that is not'? What is ov will have no other positive nature at all. This argument i.s akin to those of Soph. 243-5 and z38 A, and if it succeeds, it shows that sharing in being is not sharing in some one definite thing. The critique of the Eleatics ends (187"8-9) with the slightly cryptic rhetorical question which I translate: 'Who understands by "that which is, itself" (atho TO ov) anything but precisely what is something definite?' I suggest that it was Academy orthodoxy in Plato's later years that to be was to be something definite. It is evidence for this that Plato sometimes, when he is writing with special care, replaces the absolute use of 'to be' by 'to be something', £lvat TL: Phaedo 102 B 1-2, Soph. 247 A 8-<).

But perhaps the best argument comes from more general con­siderations. What is the point of saying that Forms of just, equal, etc. are? Whatever else they may be, these are objectivity-claims. They say that whether this stone is equal to that, whether this penalty is just for that offence, are questions of fact that have an answer independently of our feelings. Nothing is gained by adding that Forms of equality and justice have a non-physical location 'above the Heavens' . But if it is pointed out that the stone, though equal to one stone, is unequal to another, or that the penalty of

u ':"i~gins, 'Sentence Meaning, Negation and Plato's Problem of Not-being', 287; B1m1larly Owen, 'Plato on Not-being', 255, 259.

Plato's Later Platonism 123

30 minae, though just for corrupting the Athenian youth, is unjust for parking on a yellow line, the Platonic counter is 'But the equal itself is always equal', 'Justice itself i never unjust'. The existential claims and the self-predications are two sides of the same coin. Plato distinguishes sharply between sharing in a Form/ and being f . At Parm. 158 A, for instance, he says that what shares in one is other than one: 'One itself (i.e. the Form of one) would not share in one but be one. ' In general, the many f things share in f, but the Form is f. The 'clarity and truth' of Forms consist in their each being, in this non-participatory way, non-relatively even to time (Tim. 37 B-

38 A) , the definite thing it is; and my suggestion is that this, rather th.an sharing in some further Form, is what it is for them to share in being.

Plato is exercised over what it is for things to be throughout his lat r work, and this by no means exhausts his conclusions. I make a further suggestion below about how he thought that being is a 'vowel' Form. But if he thought, not only that each Form is something definite in this pecial way, but that this is what it is for it to be, we can understand his reluctance to quantify over concrete objects.

IV

Perhaps there are signs that he is overcoming his squeamishness in hi later work, not only in the Sophist but also, for instance, at Parm. I 52 B-e, where he says that a changing thing desists from becoming and achieves being 'in the now time'. But in any case we may wonder how far the analytical tools he does allow himself will ta ke him. To determine this I shall use and expand the symbolism already introduced. J, g, and h are Form variables and F and G Form constants. A is a concrete-object constant and X an arbitrarily chosen concret object. m (from 1Ln£xn) is a symbol for 'sharing in ' .

On the face of it, 'Theaetetus is flying' has the form:

mFA

and 'Theaetetus is not flying', I have argued, has the form :

(Vj)(mfA -+f~F)

124 William Charlton

The utterance , however, do not look a different in form as this sugge t . Plato invokes a Form of same co-ordinate with the Form of other, and 263 o suggests that he thinks 'Theaetetus is flying' has the form:

(3/) (mfA &f =F)

i.e. 'Flying is the same as some Form in which Theaetetus shares.' Same and other are only two out of five Kinds which Plato singles

out in the Sophist for special study. The others are being, change, and staying unchanged. How do they fit into analyses? Wiggins says that change and staying unchanged 'are surely just examples or specimen predicates' ,•• i.e. ordinary Forms in which concrete objects share, and those who think that Plato distinguishes an ex­istential use of flvo.t take being as the particular Form sharing in which is existing. I have already made some objections to this view of being, and I do not think we should acquiesce in Wiggins's rather banal view of change and staying unchanged until we have seen if there is not omething worthier of Plato's genius in the analogy with vowels and consonants at Soph. 253 A.

Ryle claims (plausibly, despit David Gallop's observations in the Philosophical Review) 15 that Plato is thinking here rather of phonemes than of letters, and suggests that vowels are counted as bonds becau e 'A vowel supplies a syllable in which it occurs with its breath and o coli cts the consonants with itself into a unitary utterance.'' 6 What stands, he thinks, to an utterance as a vowel to a syllable is a verb. There does seem to be something in this analogy. I am not completely happy with Ryle' statement that the verb 'supplie the sentence in which it occurs with its assertive force': what about th verbs in 'Is Theaetetus sitting?' and 'Theaetetus, sit down'? But in the way in which you can have a syllable consisting simply of one vowel, like 'I', o you can have a entence consisting of one verb, like 'Go' (or 'I' again, if you speak Latin). Developing thi line of thought, Ryle suggests that Plato's five greatest Kinds are 'ba ic verb forms, or summa genera of what is a ertible about subject terms':

Kinesis i the generic verbaJ noun for all live verb and verb inflections

•• ' ntence Meaning, egation and Plato's Problem of Not-being', 290. " . Gallop, 'Plato and the Alphabet', PmlosophUal Rtview, 72 (1C}6J), 364--76. " 'Letters and Syllables in Plato', in olltctul Pa~rs (2 vo!s.; London, 1971), i.

54-'7' at 64.

Plato's Later Platonism 125

of happening, doing, beginning, stopping and the like. Stasis is the verbal noun for all verbs and verb inflections of continuing and remaining. 'Being' is the verbal noun for existing and for being so and so. 'Identity' is the abstract noun for 'is' where this is the 'is' of identity. 'Otherness' is the abstract noun for the phrase 'is not' where this is the 'is not' of non-identity. (Collected Pa~rs, i. 67)

On this view objects share in change in walking, Hying, cutting, or engaging in any 1rpii[,s like that. They share in staying unchanged, perhaps, if they wait about, are becalmed, or sleep: Ryle does not work out any examples for us, but Plato might consider sleeping an example of cl1rpo.fto. (Soph. :z.62 B-e). And they share in being, not only if they exist, but if they are lions or are spherical. In ef­fect, Ryle is construing Plato's greatest Kind as a classification of things signified by predicate-expressions, and hence as a forerunner of Aristotle's Categories. This interpretation, however, really fits only change and staying unchanged. Ryle's treatment of identity and otherness is weak, and what he says about being is at best programmatic. Does Plato, in his view, think that existence is a Form in which tame tigers share, or that their being existent is logically similar to their being stripy?

For Ryle, being is co-ordinate with the other four Kinds. Wig­gins, in contrast, 11 suggests that change, staying put, sameness, and otherness are so many 'specific determinations' of being: a thing's being consists in or comprises changing, staying unchanged, being the same, and being other. Wiggins does not link this suggestion with the idea that the greatest Kinds stand to other Forms as vow­els to consonants, but if he did the result would be a theory with a Spino zan flavour. Spinoza hold that change and staying unchanged are among the 'infinite and eternal modes' of substance (Letter 64), i.e. that they are ternal ways in which extended substance exi ts. For Wiggins's Plato, being would be ubstantial being, and the other Form ways in which thi is modified; and it could be said that the only true ontological vowel is being.

Crombie argues that if vowel-Forms are connectors between other Form as vowels are between con onants (cf. Soph. 253 A

s), the only genuine ontological vowel is samen

It is by participation in difference that A is different from B. It i therefore difficult to resist the su picion that difference (or the partS of difference)

" 'Sentence Meaning, egation and Plato's Problem of ot-be.ing', ot88-91.

126 William Charlton

[Crombie alludes to 257 c ff.] are the disrupters. But since the disrupters are paired with the vowels, and since difference is paired with sameness, it is natural to go on to the further inference that sameness (or the parts of sameness) are the vowels. (Examination, ii. 414)

This argument goes too fast. As Frege points out, 11 connection and disruption are not on all fours. AJI speech depends on connection, and to say that A is other than B is still to connect them in a certain way. Plato seems to be clear about this. He does not, like the later writers whom Frege has in his sights, say that language proceeds componendo et dividendo, but simply that it depends on interweaving, avp:rrAoK~. (Neither, as a reader of Crombie might suppose, does he postulate any such phonetic items as counter­vowels.)

It would be most satisfact~ry if we could offer an interpretation on which all five greatest Kinds are analogous to vowels, but clearly we must first decide what the analogy is meant to be. On Ryle's interpretation, vowels sound and consonants modify the sound. Ryle was reluctant to think that any consonant is a component of a spoken syllable; he preferred to think that syllables which differ in their consonants, like 'cat', and 'pan', are like objects that differ in their properties or 'features'. 19

Crombie, in contrast, focuses his attention on Plato's calling a vowel a 'connection' or 'bond' (8w~6s'). This suggests a different idea about vowels, that they are that in virtue of which consonants can be combined into syllables. I think Ryle would have liked to attribute to Plato the idea that a vowel-Form is one the concept of which is the concept of something in virtue of which other Forms are combined in thought and speech-combined either with one another or with object . But he did not see how this account would fit all five Greatest Kinds. I have already shown how it fits sameness and otherness. They appear as connectors in the analysis of the simplest affirmative and negative statements. How is it best to deal with the other three?

Change and staying unchanged can be presented as connectors in two ways. Con ider the difference between 'Theaetetus is in the proce s of sitting down' and 'Theaetetus is in a state of being

•• G. Frege,' egation' (1919), ln P. Geach and M. Black (eds.), Translations from tlu Philosophical Writings of Gottlob Frege (Oxford, 1952), 117-35 at 122-4.

" See G. Ryle, 'Logical Atomism in Plato's Theaetetus', Phrorusis, 35 (1990), 21-46 at 4o-4.

Plato's Later Platonism 127

seated' --or, if you prefer, 'Theaetetus' limbs are taking a share in the seated position' and 'Theaetetus' limbs have a share in the seated position'. We could say that the first asserts that there is a change in which Theaetetus shares, and which is the same as becoming seated. Using k (K{V1Ja's) as a variable ranging over changes, that gives us the form:

(3k) (mkA & k = K)

Similarly, using s as a variable ranging over stayings unchanged, we may say 'Theaetetus is in a state of being seated' has the form:

(3s) (msA & s = S)

(There is a staying unchanged in which he shares and which is being seated.) This retains Ryle's idea that change and staying unchanged are genera of predicates. The difference between the utterances is formal but only in the way 'Theaetetus is pale' is different from 'Theaetetus is six feet tall' .10

Alternatively we could say that the first utterance has the form:

(3f) (kfA &j= F)

while the second has the form:

(3f) (sfA &f =F)

where in both cases F is the Form sitting. On this second view, change and staying unchanged are two modes of sharing: an ob­ject can share in a Form by having it (staying unchanged) or by acquiring or losing it (change).

Which view is more Platonic? Some modern philosophers of events11 want becoming/ and being/ to be different things that can be predicated of an object, different properties. It seems to me more realistic to view them as different ways in which a single property can be related to an object, and I find Plato so viewing them in the Parmenides. He is careful to distinguish (e.g. I 55 E-I 56 A, I 58 B,

163 D) between, on the one hand, being, having, and having a share (lx£,v, p.£TExnv), and, on the other, taking a share in, letting go, losing {juTa.Aap.fJavnv, cbrillaTT£a8a~). Under pain of a regress he cannot allow lxnv and f'£TEXEW to signify Forms in which a thing can share;

•• Ryle maintain the formal character of these category-differences in his paper 'Categories', in Collected Papers, ii. 17o-84 at 17H.

" So A. Goldman, 'The Individuation of Action', Jourrtal of Philosophy, 68 (1971), 761-?4·

IJO William Charlton

say 'He did not assert, but denied, that Theaetetus was seated' and 'He did not assert of Theaetetus, but denied of him, that he was seated'. This suggests that we have two ways of making a tatement and two ways of predicating. In each case Frege allows only one. We may assert that Theaetetus is seated or assert the negation of that, and we may assert of him that he is seated or that he is not seated. Wiggins takes a different line, at least about predication. He calls for 'the notion of withholding x from a class' and says: 'Af­firmation or placing is unintelligible without a twin notion of denial or exclusion.'11 I do not think he means that in 'Theaetetus is not sitting' we hold the seated position and Theaetetus apart from each other. That is the error that Frege rightly condemns. But whereas for Frege subject and predicate are connected in the same way here as in 'Theaetetus is sitting', and the difference is that in the negative sentence either the predicate is negative or negation is performed on the whole complex of subject and predicate, Wiggins locates the difference precisely in the way subject and predicate are connected. This makes it like the difference I said Plato might wish to find between 'Theaetetus is becoming seated' and 'Theaetetus is seated'. I brought that difference out by introducing the symbols k and s to replace m. In the same way (taking i from 'is' and n from 'not') we could say that 'Theaetetus is flying' has the form:

(3f) (ijA &f=F)

and 'Theaetetus is not flying' has the form:

(3f) (nfA &f = F)

If Plato thought that being had and being acquired are two ways in which a Form may be related to a concrete object, why should he not think the same about being had and being lacked? It would not stop him quantifying over Forms or force him to quantify over concrete objects. As it is, by explaining negation in terms of otherness he puts himself on the same side as Frege. He recognizes only an af­firmative mode of predication, and hence he could hardly have a negative mode of making statements even if he wanted it.

Thi is surpri ing, and not ju t because of the indications as to how he wants to treat the difference between being and becoming. It i not ea y to show that Wiggins's view is correct, but one line of thought t~t leads to it i precisely the argument of the Sophist.

" 'Sentence Meaning, egation and Plato's Problem of Not-being' , JOO.

Plato's Later Platonism IJI

On the Fregean view, a true statement says something that is the case; there is something that is both stated in it and is (or is said to be so and is so); and a false statement says something that is not: something is said in it, and at best its negation is. Many philoso­phers think that this is pretty clear, and that the difficulties involved are purely technical: we mustn't make the howler of hypostatizing negations, it is too bad that English doesn't have the expressions 'somewhether' and 'thether' and so forth. But the thrust of the Sophist is that we shall never account for truth and falsity in this way. There is nothing that in the one case is said and is, and in the other is said and is not. Saying is not a simple exhibiting of a complex unity. It is a complex affair of exhibiting one thing as being or not being concerning a second. And we can do it in two ways. We can (1) say things that are as being and things that are not as not being; or (2) we can say things that are as not being and things that are not as being. These two modes of speaking are called 'speaking truly' and 'speaking falsely'. So while there is nothing that is said and true or said and false, there is such a thing as saying-something-true and such a thing as saying-something­false. 'A certain sort of putting together of verbs and nouns is really and truly false statement' (263 D; the same idea appears at Crat. 430E-431 B).

If this is Plato's theory of how truth and falsity get into language he ought to say that 'Theaetetus is not seated' has the form nFA or

(3f) (nja &f =F)

The symbols i and n are perfectly combinable, of course, with k and s. 'Theaetetus is not seated' is strictly speaking of the form:

(3j) (nsf A &j = F)

and 'Theaetetus is not flying to America' of the form:

(3f) (nkfA &f =F)

(where F is being, thanks to an aeroplane, in America; not, perhaps, a Form for which the author of the Timaeus would much care).

What keeps Plato from this analysi is, I suspect, a strand in his Platonism not captured by Quine's definition. If the concepts of being and not being are concepts of ways in which Forms are related to objects in our thought and speech, the difference between being and not being is not independent of us. Sameness and otherness are

!28 William Charlton

neither, then, can p.€-raAap.{JavfLV or d1TI:w\&.-r-r€a8at. At 163 c-o the difference between being and becoming is explained in term of the difference between having and taking a share, and at 152 C-D

it is explained in terms of relations to time: when something in its progress from 'formerly' to 'hereafter' light on 'now' it desists from becoming and then is. Plato is clearly thinking that there are things an object may either become or be, not that becoming, changing, or staying unchanged are themselves things it may be.

Equipped with the second symbolism, the dialectician can pro­ceed to formulate such plausible theorems as:

('Vf) (kjX ~('Vg) (sgX ~g~f))

-in common parlance, 'If an object is acquiring a property it does not already have it', and

('Vf) (kjX ~(3g) (sgX))

'Extreme Heracliteanism (cf. Theaet. 181 E) is false'. If we adopt the former, Rylean way of treating change and staying unchanged, this will be impossible.

Our last great Kind is being: how can the concept of this be seen as a concept, not of a Form in which things can share, but of a way in which other Forms are related to each other and to objects? The answer is obvious. It is the concept of a quantifier, of what is signified in our symbolism by 3. It enters into the form of a simple declaration like 'Theaetetus is sitting' and probably into the form of every speech; for every speech must contain (at least implicitly) a Form-expression and Plato seems to think that all such expression have existential import. It is significant that two of the clearest examples of an ab olute use of ffvat in Plato's later dialogues occur when he is bringing out existential import. At Soph. 243 D-E

the people who say that 'all thing are hot and cold or some such pair' are told that they are declaring 'each or both of the pair to be'. At Parm. 149 E, having argued that things must have largeness and mallness, Parmenid say : 'So there are such Forms as these, largeness and smaJJness? For surely if they were not, they would not be opposite or come to be in things that are.'

All five Kind , then, can be seen as vowel-Forms. On my inter­pretation, however, they do not connect in the same way. Change and staying unchanged are forms of connection between material objects and Forms; sam ne and otherness connect Forms; and as

Plato's Later Platonism 129

a quantifier, being is part of the form of a thought or speech with­out itself connecting a Form to anything. This diversity of role is a strength rather than a weakness in the interpretation.

Does Plato, it may be wondered, think that there are other vowel­Forms besides these five? They are often grouped with like and unlike, equal and large and small, and one and many. Of these, however, some are reducible to others. From Parm. 139 E we can see how we could deal with claims of likeness. 'Socrates is like T heaetetus' is of the form:

(3/) (mfA & mfB)

'Socrates is like a torpedo-fish' is of the more complex form:

(3/) ((mF X ~mfX) & mfA)

(That is, there is a property that any arbitrarily chosen torpedo-fish has and that Socrates has.) Equality too can probably be accommo­dated without the need for additional symbols. As for one and many, they are clearly related to being (on our interpretation of being in Plato), and Plato might wish to treat them as forms of quantifica­tion. From the Sophist we cannot say how the art of dialectic would have developed, but we can say that it need not have run out of steam at its inception.

v

It is uncontroversial that we have concepts of some sort of change, staying unchanged, being, sameness, and otherness, and there is a good case to be made for analysing them as syncategorematic concepts, concepts of how other things are related in speech and thought. But philosophers have not generally followed Plato in his account of negation. Today we should say that 'Theaetetus is not flying' has the form:

- mFA

We symbolize negation by a truth-functional entential operator. Frege goes further. He thinks negation is an operation carried out on a declarative sentence that yields a second sentence expressing the truth function -p of what is ex pre sed by the first. In ordinary speech we u e 'deny' and 'a ert' as alternative in two ways. We

IJ2 William Charlton

independent of us. The Plough is other than Orion and the same as the Bear independently of us (though the names, of course, are imposed by us) and, what is of greater interest to Plato, two is other than three and the same as half of six independently of us. Plato, I suggest, felt that the difference between being and not being must be mind- and language-independent. He felt, if you like, that not being must be real. He can protect these intuitions, and at the same time avoid the difficulties of supposing there can be something that is both said and true or false, by explaining negation in terms of otherness.

I call Plato's realism here 'Platonism' because it seems to me excessive. We need to distinguish two ways in which something can be dependent on our thought. Something is dependent in one way if thinking makes it so: perhaps whether pineapples are pleasing to us is like this, but any realist would say that whether Theaetetus is seated is not. It is not sufficient for his not being seated that we think he is not. But suppose that he is not, in fact, sitting. That he is not seated is not a thing that is true of him independently of us: not being seated is not a feature he has in addition to being snub-nosed, pop-eyed, and knowledgeable about mathematics.

We might try to retain the mind-independence of not-being by connecting it with incompatibility. Theaetetus is in fact, perhaps, standing, and the standing position is incompatible with the seated po ition. Still, the standing position does not make him objectively non-sitting. At most it stops him from objectively sitting. And it does this rather as a formal than as an efficient cause. In 'He is not sitting becau e he is standing' 'because' introduces a justification for saying 'He i not sitting', not a piece of preventive causal action (contrast '1 cannot ee the stage because he is standing'). Standing does not make it a fact that he is not sitting, but non-causally prevents it from being a fact that he is.

For Plato, in contrast, there are countless negative truths about Theaetetus. We may assert that he is not sitting, and also that he is not swimming, and not in London, and not knowledgeable about Old Icelandic, and infinitely many other things. Surely this is for him to prout, if not a beard, at least some other bushy Platonic growth.

University of Edinburgh

Plato's Later Platonism

APPENDIX Summary of propositional forms proposed for

Plato's later Platonism

IJJ

f, g, hare Form variables and F, G Form constants. xis an object variable, A an object constant, X an arbitrarily selected object.

Theaetetus is sitting: (3/) (mfA &f= F) Theaetetus is not sitting: not: (3/) (mfA &f,;.F)

or: (Vx) (mfx-tx,;.A) but: ('if) (mfA -t f ,;.F)

or: (3/) (j = F & (Vg)(mgA -.g,;.f)) Theaetetus is becoming seated: not: (3k) (mkA & k =F)

but: (3/) (kfA &f =F) Theaetetus is in a state of being seated: (3/) (sf A & f =F) All birds fly: (3f)(3g)(/= F &g= G&(mfX-tmgX)) No birds fly: (3/) (3g) (/= F &g= G &(mfX-t("'h)(mhX -th~g)))

With quantification over objects

Some birds fly: (3x) (mFx & mGx) Some birds do not fly: (3x) (mFx & ('if) (mfx-tf,;.G))

With affirmation and denial as forms of predication

Theaetetus is sitting: (3f) (if A &f =F) Theaetetus is not sitting: (3f) (nfA &f =F) Theaetetus is not coming to be seated: (3f) (nkfA &f =F)

Reduction of likeness (Parm. 139 B)

Socrates is like a torpedo-fish: (3f) ((mtorpedo-fishX -tmfX) & mfSoc­rates)