Plato's Semantics and Plato's "Parmenides"

Plato's Semantics and Plato's "Parmenides"Author(s): Thomas Wheaton BestorSource: Phronesis, Vol. 25, No. 1 (1980), pp. 38-75Published by: BRILLStable URL: http://www.jstor.org/stable/4182082 .

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Plato's semantics and Plato's "Parmenides" THOMAS WHEATON BESTOR

Plato's self-criticism in the Parmenides has long been a source of perplexity and rage to philosophers. On the one hand, we might suppose Parmenides' arguments at 130b- 135d are telling ones and that Plato realized they were. Fine. But then why didn't he back off from the theory of Forms subsequently? On the other hand, we might suppose the arguments are blatantly and self-consciously fallacious. Fine again, but then why did Plato bother to write them down in the first place?

The perplexity is a simple one to resolve, I believe, as soon as we pay a bit of attention to Plato's theory of Forms as a piece of semantics. In this guise the theory tells us that a general word "f" is predicated of sensible particulars in a distinctively derivative way (marked by saying they must be related to the Form F in order to be f) while the Form F itself has "f" predicated of it in a primary way (marked by saying that the Forms are directly f, f without reference to anything else). We have two different orders of nominata and corresponding to them we have two different modes of predication. Such indeed is precisely the account which Parmenides himself is made to state at the beginning of the whole duck-shoot:

"Well, tell me; do you think that, as you say, there are are ideas, and that these other things which partake of them are named from them (ctv r6t8E 'rt &XXa rnETaXapt- VovTOa T(S t'r,wvvuL(cS aVXTWrV 'LCXEiV), as, for instance, those that partake of likeness

become like, those that partake of greatness great, those that partake of beauty and justice just and beautiful?" "Certainly." (Parm. 130e5- 13 la I: Fowler translation)

Particulars which partake of the Forms are "named from them". That is, particulars come to be called great, just, beautiful and so on just insofar as and because they participate in the Forms named by those words, the Form of Greatness, the Form of Justice, the Form of Beauty and the like.

This clue has been used for over two millenia as a way to defuse one or another of Parmenides' objections. Thus ancient and moderns alike use it to show that the infamous "Third Man" argument is an outright fallacy:

Suppose Socrates is called "man" in a sense neither identical with nor merely different from that in which the Form is so called, but derivative from that sense: then the regress cannot get started. If the existence of a class of X-dependent things entails that of an X-thing, this by no means shows that the existence of a class of X-dependent things and one X-thing entails that of another thing that is X.'

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Other philosophers, ancient and modern again, use the same distinction to stop the imitation or "second Third Man" regress:

If Man-himself is synonymous (avvavupos) with the things in this world ... and all synonymous things become synonymous by participation in some Form, then a third man will appear being predicated of the Idea and phenomena. But this argument is ridiculous, for phenomena are not synonymous with the Idea. Since when do images become synonymous with their own paradigm? And we must not suppose that the Idea participates in anything itself, for the Idea brings everything else into participation, being the primary character.2

All these have been good men and true. But, I think, a bit timid perhaps. At any rate what I want to argue here is that Plato's basic theory of language breaks the back of each and every objection which is put in Parmenides' mouth. There are some seven of them altogether and not one is any good against a metaphysics conditioned by a derivative/primary account of predication. This is a surprising fact and tells us a great deal about why Plato wrote the two parts of the Parmenides. Both are beginning pupils' workbooks in Academic method.

I. The Eponym Theory of General Words

Plato's semantics is summarized in Parmenides' formula: "particulars which partake of the Forms are named from them". Clearly, however, there is much more to be said. In the first place, there are actually two .mportant theses involved in Plato's theory. The first is a naming thesis:

(Tl) All general words (all so-called "universal" terms such as adjectives, common nouns, adverbs and even possibly verbs and prepositions) are really proper names, and proper names of Forms. General words, that is, are naming terms and their primary designata, their true referents or meanings or bearers, are Forms.

For its nutshell effect, and also as a bit of a put-down, some philosopher once dubbed this thesis a "Fido" - Fido theory of words. And it is. General words stand to Forms exactly as "Fido" stands to the dog Fido. Any difference there might be between proper names and general words is not a difference in how they name, in the manner in which they hook up to the world (in the nature of the "sign-relation"). The difference lies solely in what they name, in the entity they hook up to: "Fido" names a medium- sized piece of dry goods in the everyday world, a general word "f" names one of the special inhabitants of the world of Forms.

Plato's assumption here is a perfectly natural one - at least it has seemed so to philosophers right down through the centuries. We assume that to

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every significant bit of language there must correspond some entity "out there"9 which is the meaning of the expression because it is the object which the expression is the name for; that is, we take meaning to be a species of naming, we take the "sign-relation" to be in the last analysis nothing but the name-relation. Accordingly, we assume, despite first appearances, that the functioning of each and every word in a sentence such as "Is Fido a grey dog?" is more or less homogeneous; even the common noun "dog" and the adjective "grey" ultimately hook up to bits of the world in a way not importantly different from the way in which the ordinary proper name "Fido" hooks up. Similarly, we assume that the obvious differences between "f"', "f-es", "f-ness" and "f-er" are mere surface grammatical quirks of no lasting philosophical importance; certainly they involve no new relations between our words and the world (as they did for John Stuart Mill say, System of Logic I.II.4-5,7). Finally, we assume that the case of one single name for each single thing named is the model case of naming; we take the case of an ideal proper name or a "logically proper name" (A la Russell) as our paradigm. Once we do all this - and it is immensely difficult not to do all this - then Plato's account in Parmenides 1 30e follows immediately. What makes a word a proper name is that it picks out one specific thing and can be used as a surrogate in place of that thing for purposes of communication: we don't have to carry a basketful of things around with us for show and tell - just uttering its name will make our hearers think of the thing we want them to. This is what the name "Fido" does for a specific dog. This is what Plato says "beauty" does for a specific Form. When we ask a question like "Who is Fido?" what we want to know is which dog the name "Fido" picks out. So too, Plato says, when we ask "What is beauty?" what we really want to know is which Form it is that the name "beauty" picks out.

Curiously, most philosophers seem to think that Plato's theory of language stops right about here. But there is another crucial thesis yet to come:

(T2) When a general word applies to anything it is not the proper name of, it does so onlv at second-hand. And even then it applies only to those things which have a sufficiently intimate relation to the named Form, in virtue of that relation. and as a means of expressing that relation. Sensibles. for example. are never more than the indirect, derivative designata of general words.

Also for its nutshell effect, this thesis might well be dubbed a "Ford" - Ford theory of words. Henry Ford has given his own personal name to other quite different things too, namely to the zillions of cars and trucks and tractors that his company manufactures. Exactly as the word "Ford" stands

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to the hulk in my driveway, so in general the word "f' stands to f particulars. In both cases the application of the word is transferred from the thing it names to other things as well, but only by picking up the named thing on the way. Any important different there might be is not in the indirectness of the way the words work (in the nature of the "sign-relation" again). It is a difference solely in which specific relation to the named thing is involved: "Ford" involves a company founder and mass production, "f' involves a Form and participation.

Once again the assumption here is a perfectly natural one. We assume that if a word "f requires some sort of hook to the world to make it meaningful, and if that hook is provided by its being the proper name of a special Form, then it must apply to the sensibles it applies to in some other way - or else the only meaning hook would already have been provided. Moreover, we assume that this "other way" must be indirect, of a second- order, and must somehow derive from the primary naming way. Accord- ingly, we assume as our model the perfectly familiar manner in which the proper name of M is also applied to some other N provided N is "related in an appropriate way" to M. In different cases ("Sandwich" - sandwiches, "Beghard" - beggars, "Christ" - christian, "Cognac" - cognac, "Plimsoll" - plimsolls, "Hoover" - hoovers, "Oklahoma" - okies, "Laconia" - laconic, "Boycott" - boycott, "Shem" - semite, etc.) altogether different relations are "appropriate" or "inappropriate" depending on the specific details. However, granted just the assumption that there are appropriate relations in these matters, that there are derivative ways for proper names to apply - again, an assumption that is immensely difficult not to grant - the account in Parmenides 130e follows immediately. Plato's view is simply that "participating in" a Form con- stitutes just such as "appropriate" relationship. It is only because there really does exist a certain man named by "Ford" and there really does exist a relation between him and certain cars that we are able legitimately to extend the application of what is actually a proper name to things it is not the proper name of (some car is a Ford because it is produced by the "real" Ford). So too it is only because there really does exist a Form and a relation between it and sensibles that we can extend the application of the proper name "great" to things it does not strictly name (some particular is a great because it participates in the "real" Great).

Because the key expression "naming after" is iuwvv iia in Plato, from which we get the English noun "eponym" ("one who gives, or is supposed to give his name to a people, place or institution"), I've called the complementary theses (TI) and (T2) Plato's "Eponym Theory". The dis-

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tinctive feature of such a theory is, of course, the dualfunction it gives to general words.3 These sorts of words apply to a multiplicity of different things but, seemingly, only in virtue of one thing which is the same about them all. In Plato's vocabulary, they apply to the Many but seem to require a One over that Many. The Eponym Theory explains all this by attaching such words to the two different kinds of things all right, but in two different, though related, kinds of ways. General words name the One and eponymously designate the Many appropriately related to that One. That is, Forms are eponyms for Plato and particulars are named-after things.

It is worth mentioning here that because of its peculiar double-barrelled function, a word which applies at the same time to a sensible and its Form applies neither purely equivocally nor purely univocally but somehow in-between. Beautiful particulars, for instance, take the Form's name "beauty" in virtue of their participation in it. Letting the symbols "P" stand for "primarily" and "E" for "eponymously", this means that a beautiful particular will be fully described as b(E) and the Form of Beauty as b(P): the "b" records their convergence and the "E" and "P"1 their disparity. However, we don't really have two different "senses" of being beautiful here, nor exactly one and the same sense either. The expression "b(E)" is certainly not a synomyn for "b(P)"; but neither is "b(P)"/"b(E)" any sort of simple "bank"/"bank" type homonym or ambiguity. None of these dichotomies is really felicitous anymore since it is a trichotomy that Plato is trying to bring to view. If akin to any other ancient semantic doctrine, in Aristotle say, Platonic eponymy is probably most like Aristotle's "focal meaning" or predication 1TpOS Ev Xey6[mva, also the third member of deliberate trichotomy:4 a word like "Sexists" or "healthy", according to Aristotle, applies "primarily" (Tp wWS) to things in one metaphysical category but can also apply, albeit "secondarily" (iffo 'vws), to things in some other category if they "depend on" or are "directed towards" that first thing (e.g. "Socrates exists"/"Red exists", "'healthy man"/"healthy exercise").

We should also note that, being a distinctly semantic theory, Plato's dual function view really says nothing at all about what the named things must be like in themselves (whether transcendent or not), nor about what the named-after things must be like (whether sensible or not), nor about what the relation between named thing and named-after thing must be like (whether sharing or imitation or whatever). As a theory about the working of words it requires some ontological account, but it does not require any specific one and, indeed, is perfectly compatible with every model to be found in the dialogues. The Form F can be "responsible for" the f-es

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because it is their primogenitor (Hip.Maj. 297a-b, Tim. 36e, 50c-e, 52d, Pol. 258a); because it is their in-dwelling essence (Euth. 5d, 6d-e, Meno 72a-75a, Rep. 476a); because it is their prototype (Rep. 472b-c, 484c-d, 500d, Tim. 48e); because it is the functional specificiation they embody (Crat. 389a- 390d, Rep. 601c-e, Tim. 28a-29b); because it is what projects them as shadows (Rep. SlOb-e, 515b-d); because ... ad nauseum. From beginning to end, it is by being related to some named Form F "in whatever way the relation comes about" (Phd lOOd, Parm. 133d, Tim. 50c, 5ib) that particulars are ever able to take its name and be called f as well.

II. How Deliberate Was Plato About the Eponym Theory?

It is perfectly obvious that Plato himself never wrote down anything as bald as (TI) and (T2) in his dialogues. And it would be anachronistic to expect that of him, 2500 years ago. But have I just made up the Eponym Theory out of whole cloth? I think not.

The evidence for the naming thesis (TI) is unmistakable. It is true, admittedly, that in ancient Greek Plato's term ovo,a has a wider usage than "proper name" has in modern English; it did duty, for instance, for "word", "noun", and "subject term" as well. But Greek was by no means poor in other usable expressions, e.g. '&ros, xarry6puLa1 XE'tIs, 8pos and ,inua (all of which occur in the dialogues). And Plato's assimilation of 6vo6Rarra to names specifically is quite deliberate:

Wisdom, temperance, courage, justice, and holiness are five terms (6vFuaTa). Do they stand for a single reality, or has each term a particular entity underlying it .. .? Your answer was that they are not names (6v6parot) for the same thing, but that each of these terms applies to its own separate reality, and that all these things are parts of virtue. (Prot. 34.b-c: Guthrie translation)

When you use any word (6voFua), you use it to stand for something. You can use it once or many times, but in either case you are speaking of the thing whose name (ToiVop.a) it is: however many times you utter the same word, you must always mean the same thing. Now "different" is a word that stands for something; so when you utter it, whether once or many times, you are using it to stand for, or naming (6voRu6tets), just that thing whose name ('roivopxa) it is. Hence when we say "the Others are different from the One" and "the One is different from the Others" we used the word "different" twice, but nevertheless we always use it to stand for just that character whose name it is. (Parm. 147d-148a; Cornford translation)

There are three points to be noted about anything. I mean, for one, the reality of the thing, what is is, for another the definition of this reality, for another its name (ovoiux). And thus you see that there are two questions we can ask about everything which is. Sometimes a man propounds the bare name ('roVivo%a) and demands the definition: sometimes, again, he propounds the definition by itself and asks for the

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corresponding name ('roivopA) ... We are denoting the same thing, are we not, in either case, whether we are asked about the definition and reply with the name, or about the name, and reply with the definition? ... Well, then, what is the definition of the thing for which "soul" is the name? (Laws 895d; Taylor translation; cf. Epist. VII 342a-b)

Plato treats 66vo6aja as name-like because, in his view, they are name-like. Some of the most distinctive and characteristically Platonic arguments

about sensibles also presuppose a (TI) thesis in the end. Thus, for example, in the "beautiful maiden" passage of Hippias Major 287e-288e the arguments about definition really boils down to something like this:

(i) For every word that has a clear meaning, there must correspond a thing which is referred to in each and every application of the word.

(ii) The reference of a word cannot be some individual particular exemplar, however, for there is no such exemplar which is referred to in each and every application of the word. ("There are many other things that you will say are beautiful.")

(iii) The referents of words therefore must not be specific particulars themselves but whatever it is that is present to each and every one of them.

So too in the "flux" passage of Cratylus 439e-440b Plato reasons that change as such is a Bad Thing primarily because it provides no fixed term for any name-nominatum relation:

(i) For every word that has a clear meaning, there must correspond an entity which really does exist.

(ii) The referents of words cannot be any individual particulars or any individual set of particulars, however, for all particulars are in a constant state of change. They are continually coming into being and continually passing out of being. Hence, if they really were the ultimate referents of our words, our words would continually be coming to have meaning and continually be ceasing to have meaning. ("How can anything be called by its right name if, while we are speaking, it is all the time slipping away from us in this flux?")

(iii) Therefore the referents of words cannot be changeable particulars themselves but must be whatever abides unchanging behind such change.

In the "bees" passage of Meno 72b-73c we have another undeniably semantic argument, the well-known "One over Many":

(i) For every word that has a clear meaning there must correspond a single referent.

(ii) The referents of words cannot be the different particular things which the word applies to, however, for these constitute a Many and not a One.

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(iii) The referent of a word must therefore be the One "over" the Many. ("sSince it is not in being bees that they are vaiious and different from one another, tell me what is that character in respect of which the various bees don't differ at all but are all the same, bees.")

In the "finger" passage of Republic 523a-524d we have a final in- ference-type:

(i) For every word that has a clear meaning there must correspond a clear and unambiguous referent.

(ii) The referents of words cannot be sensible particulars, however, because all (or most) sensible particulars are confused and ambiguous: if any given sensible x can be said to be f, it can also be said to be contrary- of-f. ("The soul must be at a loss as to understand what the sense of touch means by 'hard' since sensation reports to it that the same thing is both hard and soft").

(iii) If the referent are not sensible particulars, they must be non-sensible particulars.

Tricked out this way, Plato's arguments clearly carry a theory of language on their very face. In all of these texts, and they are by no means unusual,5 the pivotal requirement of step (i) is no requirement except on the supposition that a word becomes meaningful when and only when it manages to name something (T 1); each time it is a requirement binding on proper names specifically. And so it is that "if a man refuses to admit that Forms of things exist or to distinguish a definite Form in each case . . . he will completely destroy the significance of all discourse" (Parm. 135b-c) because "no one supposes a man can understand the name of a thing when he does not know what the thing is" (Theaet. 147b).

As for the naming-after thesis (T2), the evidence is even more compel- ling, though less generally recognized.

(1) For a start, we have the very terminology. 'Effwvvpos and its cognates were common-place in humdrum non-philosophical contexts (e.g. the Statues of the Eponymous Heroes, the Archon Eponymos, the &?rt'VVULOL of the age-groups). They were so used by Plato too (e.g. music after the goddesses who foster it, the Muses).6 But equally often Plato used such terms to state his explicitly philosophical theory: sensible particulars bfio- vophtov,rat the intelligible Form in which they participate. In the Phaedo, for instance, this point is made again and again. So Plato summarizes Socrates' theory of predication:

As I remember it, after all this had been admitted [that nothing can come into existence other than by participating in the proper essence of each thing, beautiful things in Beauty and two things in Duality for example], and they had agreed that

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each of the abstract qualities exists and that other things which participate in these get their names from them (rrwvvupav), then Socrates asked ... (102a-b)

Later similar phrases occur in making the all-important distinction between the world of Forms and the world of particulars:

We said before that in the case of concrete things opposites are generated from opposites; whereas now we say that the abstract concept of an opposite can never become its own opposite . . . Then we were talking about [concrete] things which possess opposite qualities and are called after them (ivovo%xovrrev avcxTx irn ixE'vwv 'iTwvvFu>), but now about those [abstract] opposites the immanence of which gives the things their names (rrwvvpuiav -To 6vopato'eva). (103b; Fowler translations)

Earlier on (78e), Plato had equated a concrete thing's being called beautiful with its "bearing the name of' (6pvi'pwv) the absolute essence Beauty. At 102c Socrates' friend Simmias is said to be called both small and tall "after" (bnwvvRiov) the Forms of Smallness and Tallness that he is between. And at 104a Plato takes the number three and says we are bound to apply not only its own name "three" to it but the name of the Form of Oddness ("odd") as well, since three never occurs in separation from that Form. In these passages the point is plainly not just that the Forms "have the same name as" the particulars which participate in them - as might happen for any number of reasons. The point is that the particulars "take the name of" the Form - the word belongs first to the Form and only subsequently to its participants (if M is either irrwvvtios or 6pw"vvjos N then strictly speaking N is neither bff6vvRos nor 6 'vv,uos M).

There are many other passages, from every period, where Plato is just as explicit. In the Lysis for example (219c-220b), Plato insists it is w-ong to say that those who are friends for the sake of something else "are" friends, they are only "called" friends (we are "uttering a mere phrase"); the real friend is the Form of Friend from which all the others get their name and character ("for whose sake all the other things can be said to be friends"). In the Phaedrus (249b) Plato claims that recollection allows us to pass from a plurality of perceptions to a unity gathered together by the understanding and "called after" the Form for that unity (xar' e18os Xeyo6pevov). Later on (250e), beautiful things in particular are said to be the "namesakes of" (bnwvvupL&v) the Form of Beauty. In the Parmenides not only 130e but also 133d makes the point that concrete particulars take the names of their corresponding Forms (6Fu.vuWa iXECVOLS). In the Sophist (252b) all things that are at rest or are apart and so forth are said to share in the corresponding Form and "come to be called by its name because of that sharing" (xovvCtxOiToa"Tros 1'repov O'repov 'poaayopevtLv). Plato also remarks

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(234b) that an artist's imitations (and presumably god's as well) can sometimes "have the same name" (6RWuvvtLa) as the things they are of. In the Timaeus (41c) Plato says it is only fitting that the part of mortal things which is fashioned by the immortal gods "should share the name (6,u'vv,uov) of the immortals" and hence be called divine as they are called. In fact, he later (52a) insists on the perfectly general principle that all sensible particulars, which are things of the so-called "Second Kind", are "named after" (0*,vV[0ov) nonsensible Forms, things of the "First Kind". Even at the end of his life in the Laws (963a-964a with 965c-d), Plato makes precisely the same moves: there the four qualities courage, temperance, justice and wisdom are said to receive a single designation "virtue" "from the single element named by the word which pervades them all".

(2) Plato's Academy was apparently even more hard-nosed about (T2). In a remarkable proof for the existence of Forms preserved in Aristotle's On Ideas, the key assumption is that sensibles can carry a predicate only derivatively, by virtue of being related to a Form which carries it non- derivatively. The details go roughly like this. A single term can be predicated "unambiguously" ( i1 6vwu.v4s) of several different things (that is, "so as to indicate a single nature") for any one of three reasons. Either (i) because all those things are "strictly" (xvpCws) what the term signifies, as when we predicate "man" of Socrates and Plato. Or (ii) because all are "likenesses" (&6xOvEs) of things that are the true possessors of the term, as when we predicate "man" of a portrait of Socrates and a portrait of Plato. Or (iii) because at least one of the things is the original and the others are likenesses of it, as when we predicate "man" of Socrates and then of a portrait of Socrates. Now it cannot be that the word "equal", for example, is predicated unambiguously of different particulars in this world as in (i): none of them can be strictly or truly or precisely (&xpLI3Js) equal for their dimensions fluctuate continuously. Nor can it be that "equal" is predicated unambiguously as in (iii): no particular is any more of an original or a portrait than any other. So it must be as in (ii) - "the equal things in this world are equal qua likenesses of what is strictly and really equal". Therefore, "there is something absolutely and strictly equal by relation to which things is this world, as being likenesses of it, become and are called equal. And this is an Idea."7 The proof is ingenious in its own right, but the obvious semantic trichotomy (strict/derivative/ambiguous predication) is more to the point here.

(3) Finally, if more evidence is needed, we have the historical testimonies of later commentators. Thus Alexander (200AD) catches a few of the key notions:

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Plato would say that it is by participation that the sensible things which have the same names (avv(xvvusx) as each other have their existence ... Not all sensibles participate in one and the same Form, but as many as do are synonymous with one another ... Insisting that Forms give their names to (o6vv4ovs) the things that arise in reference to them, he says that the Forms are synonymous (avvwvvL1oL) as opposed to homonymous (4"vvoL) with those things. In the matters in which Aristotle uses the homonymous expression Plato would use the synonymous. (Arist. Metaph. Comm., 51.9-15; cf. Asclepius, Arist. Metaph. Comm., 46.11-24).

Diogenes Laertius (250 AD) repeats similar testimony from "Alcimus" (Albinus):

Plato said that, if we wish to take in at one glance the principles underlying the universe, we must first distinguish the ideas by themselves ... [and] assume the existence of beauty, goodness, justice and the like, each existing ill and for itself ... remembering that the things within our experience bear the same names as those ideas because they partake of them (&ix To ,LETiXELV [i.'isV] 4vVV[c iMxVOIS; I mean that things which partake of justice are just, things which partake of beauty are beautiful . .. because they are copies of these archetypes. (Lives, III. 12-13; Hicks translation)

This is also the story about predication told over and over again by Proclus (460 AD):

What we call equal down here is filled with its opposite. How then can that which is not strictly equal have in any strict sense the name of equal? . .. [For the same reason] the word "man" is said properly (XiyrETaL xvpCWs) only of the intelligible Form and applied to a sensible man it is not properly its name nor even completely true (ova xvpiws oV6& 'r&v'rr &Xi90ios). Therefore names, if they are the logical images of things, must be firstly (TrpxTs) the names of immaterial things and only derivatively (8?Tvipws) those of sensible things. This is because it is from the intelligible Forms that things here below take their being (Xxlv ovioiav) and their names (Trrv ?fwvvRotv) . . . Many have believed that Plato gives the same predicates both to intelligible and sensible things, some believing he uses them synonymously (ouvvwvv4s), others homonymously (o ltvi4s). As for me, I think he makes homonyms of them but in quite a different sense from the usual. For "man" is not a homonym so much as a name given to two things but to one primarily (fpcTws) and to the other secondarily (8uVTipws). That is why "man" is not the same thing when we use it of the intelligible and when we use it of the sensible .. . In the same way that the being [of the divine Eros and the erotic desires in us] is not the same, in that same way also the name is not the same. And in the same way that being comes to things that are not truly Beings from those which are truly Beings, in the same way the name comes to the inferior things from those which are anterior and superior to them. (Comm. Plat. Parm. pp. 850. 16-852.20)

These are late sources, of course. Our most contemporary source is Aristotle. Here things are a bit tricky, however, since Aristotle thought his own primary/secondary (nrrps ev) predication worked a bit differently from

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Plato's and so introduced it as an entirely novel doctrine, never ac- knowledging Plato as a predecessor (Metaph. 1030a19-b8, Eud. Eth. 1236a I 3-b27). Still, there are plenty of places left where Aristotle explicitly pronounces as Plato's own account of predication a full-fledged naming/ naming-after story. Thus his summary of what was distinctive about the theory of Forms in the Metaphysics:

Plato followed [Socrates' procedure] and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing. These entities he called "Ideas", and held that all sensible things are named after them and in virtue of their relation to them ('nc Op& T'rna xvi xaT& raxrTa

Xi-yWOU); for the plurality of things which bear the same name as the Forms exist by participation in them (r& 'oXX& Tir)V OVVWV}1WV [Trot Et8EML) ... As to what this "participation" or "imitation" may be, [both Plato and the Pythagoreans] left this an open question. (987b3-15; Tredennick translation)

In the Eudemian Ethics Aristotle finds the same view in Plato's notion of the Good:

Men say that the good per se is the best of all things. the good per se being that whose property is to be the original good and the cause by its presence in other things of their being good; both of which attributes belong to the Idea of good ... for good is predicated of this Idea most truly (other things being good by participation in and likeness to this); and this is the original good, for the destruction of that which is participated in involves also the destruction of that which participates in the Idea, and is named from its participation in it. But this is the relation of the first to the later, so that the Idea of good is the good per se. (1217b 2-15; Ross translation)

Each of the crucial doctrines is here in full view. The relation between the Form and its participants is a relation between what is "primary" (ffpCTov) and what is "subsequent" (iarepov). The particulars are "named from" their participation in the Forms (& XEyvraLr4 l.LEn 'XEXELV kX?VqS). "Good" is predicated "most truly" (XEywFOaL &Xdi8bOs) of the Form. Here this is simply what "they say", but elsewhere Aristotle states that it was Plato specifically who made Forms relevantly "primary" or "prior" (Metaph. 1019a2-4) and that it was the Platonists specifically who said goods must be spoken of in two ways, one a strictly "secondary sense" (Nico. Eth. 1096b7- 16).

All in all, though there may be no single passage in the ancient Platonic literature which expresses (T1) and (T2) beyond any possible shadow of doubt, the general tendency of Plato's thought is tolerably clear. Consid- ered in light of this general tendency the seven so-called "refutations" which Parmenides is made to give in the Parmenides make a very poor showing indeed, as we shall now see.

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III. The Fire and Mud Argument (130b-e)

Parmenides' first move is to extract a confession from Socrates that he is not sure the Forms/sensibles story applies everywhere:

"Do you think there is such a thing as abstract likeness apart from the likeness which we possess, and abstract one and many, and the other abstractions of which you heard Zeno speaking just now?" "Yes." "And also abstract ideas of the just. the beautiful, the good and all such conceptions?" "Yes." "And is there an abstract idea of man, apart from us and all others such as we are, or of fire or water?" "I have often been very much troubled, Parmenides, to decide whether there are ideas of such things, or not." "And are you undecided about certain other things, which you might think rather ridiculous, such as hair, mud, dirt, or anything else particularly vile and worthless?" . .. "I think these things are such as they appear to us, and it would be quite absurd to believe that there is an idea of them; and yet I am sometimes disturbed by the thought that perhaps what is true of one thing is true of all. Then when I have taken up this position, I run away for fear of falling into some abyss of nonsense and perishing. .. ." "Yes, for you are still young and philosophy has not yet taken hold upon you, Socrates, as I think it will later. Then you will not despise them." (130b4-e4; Fowler translation)

Here Socrates agrees that there definitely are Forms for such terms as "likeness", "unlikeness", "unity" and "plurality" (as used in Zeno's arguments at 127e) and for terms of virtue like "rightness", "beauty", "goodness" etc. But he hesitates about Forms for "man", "fire" and "water". Presumably this is because they don't admit of degrees; the water we perceive is just that, water, and perception gives us a case of water as fully water as anything can be, not something only deficiently water and working at being more and more watery. He also hesitates about "hair", "mud" and "dirt" - presumably because none admit of perfections (admirably icky Perfect Dirt seems a contradiction in terms).

If we keep in mind that Plato's theory of Forms is a semantic theory, however, we see that it really does have to apply to every general term - that is, for every Many. What explains how the special terms of logic and virtue work turns out to explain how all terms work: words name Forms and it is because and only because they do this that they can then eponymously designate particulars as well. There are no a priori limits on the scope of the eponym mechanism.

This is exactly the import of the full passage in fact. The reservations over "man" and "mud" etc. do not represent solemn reservations Plato had in his mature years but doubts that the "exceedingly youthful" (130el, e4) Socrates "at times" (130c3, d6) falls prey to. Parmenides does nothing but urge Socrates to go whole hog with his theory (130e2-3) because it obviously applies to "man" and "mud" just as well as it applies to "unity"

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and "beauty" (130d6-7, e4). Plato is well prepared to take this advice everywhere else.8 Indeed, the only terms for which he ever explicitly denies a Form are the explicitly eccentric "barbarian" and "number-other-than- thousand" (Pol. 262d-e). Certainly he believes there are Forms for "man" (Phil. 15a) and "water" (Tim. 5 lb-d) and "fire" (Phd. 103c-e) at least.

IV. The Sail Argument (131a-c)

With this bit of softening up behind him, Parmenides now proceeds to attack the first of Plato's favorite ontological models, the view that Forms are characters or ingredients "in" particulars and that to participate is "to have a share in" or "to possess a part of' something - ,Lve?aXaXla3VeLV (131a4) and LvEEXELV (131c6). The usual references are to Phaedo lOOd- 102e, Anaxagoras and Eudoxus,9 but the clearest expression of this view is undoubtedly in the Hippias Major. There the Form of Beauty is some sort of stuff which can be "added to" particular things (289d, 292c-d) and this addition is what explains why the things are "entitled" to the Form's name (288a, 303e). Parmenides' attack is simple. If Forms are so parceled out between the many particulars they are in, they can no longer be the seamless unities Plato wants:

"Does each participant object partake of the whole idea, or of a part of it? Or could there be some other third kind of participation?" "How could there be?" "Do you think the whole idea, being one, is in each of the many participants, or what?" "Yes. for what prevents it from being in them, Parmenides?" "Then while it is one and the same ('Ev &pa "ov xi Tacvr6v), the whole of it would be in many separate individuals at once, and thus it would itself be separate from itself." "No, for it might be like day (Rikpa), which is one and the same, is in many places at once, and yet is not separated from itself; [in this way] each idea, though one and the same, might be in all its participants at once." "That is very neat, Socrates; you make one to be in many places at once, just as if you should spread a sail over many persons and then should say it was one and all of it was over many. Is not that about what you mean?" "Perhaps it is." "Would the whole sail be over each person, or a particular part over each?" "A part over each." "Then the ideas themselves, Socrates, are divisible into parts, and the objects which partake of them would partake of a part, and in each of them there would be not the whole, but only a part of each idea." "So it appears." "Are you, then, Socrates, willing to assert that the one idea (TO 'rv etbos) is really divided and will still be one?" "By no means." (13 la4-c 1 1: Fowler translation)

Parmenides' first step here is to insist that if some particular "shares in" a Form then it must have either the whole of that Form in it or only a part of that Form in it; there is no third possibility. Of course there is, however, as Socrates himself well knew. A single Form, he suggests, may be in many separate particulars in much the way a single day, Wednesday say, may be

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in many separate locations at once. It is Wednesday in Auckland and Wednesday in Wellington. Both cities share in one and the same day. But we aren't in the least inclined to suppose that Auckland has either the whole of Wednesday or else only a part of Wednesday in it. Wednesdays aren't like that. "Part"/"whole" has no application to them. Parmenides does the only thing he can do with this timely analogue. He distracts Socrates with praise and blandly substitutes his own very different analogue: a single Form, Parmenides says, may be in many separate particulars in much the way a single sail may be over many separate people at once. The cleverness of this move is that a sail is divisible into parts (one part over each distinct person) and so in one sense at least is no longer a simple unity after all. Likewise with Forms, Parmenides insists. A single Form cannot be dispersed in many particulars without becoming divided into parts and hence many itself.

Plato sometimes seems to admit the justice of this objection. Ancient authorities were certainly bothered. And nearly every commentator since has thought it decisive.10 But it isn't. Nor did Plato think it was. Remem- bering the semantic story, the eponym story, it becomes easy to see that division and dispersal won't make for any relevant plurality of Forms because, whatever else they do, division and dispersal never make for plurality with eponyms.

Suppose I print up a one and only roll of wallpaper, keep it in a box, and give it a proper name of its own, "Bestor Twizzy". Now suppose I decide to paper my walls with it. I take the roll from the box, cut off bits of it, and stick them onto the wall. Once I do that I can also use the term "Bestor Twizzy"9 of things other than the real Twizzy. I can use it of walls as well and say, perfectly intelligibly, "The two side walls are Bestor Twizzy, the others are just white gloss". In this way various particulars can come to be named after a single eponym because some of that eponym is "on" each of them. But notice that nothing here makes the eponym multiple. The two walls still have on them some of one eponym and not some of two eponyms. Paper from the special roll is cut up and dispersed on many walls, not on one wall, to be sure; but it is still paper from only the one roll which is on those walls - there aren't many Bestor Twizzy wallpapers. As with eponymous wallpapers, so with eponymous Forms. The Form of F-ness, say, may be "dispersed" into 839 different particulars all over the globe; not just one but 839 particulars may have some of the Form of F-ness in them. Moreover, any one particular may have in it only a "part" of the Form of F-ness; none of the 839 particulars may claim to any more than just a certain proportion of F-ness. As long as it remains clear that the part which

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is in some one of these 839 particulars is a part of the Form of F-ness, however, and not a part of some other Form, the Form of G-ness or the Form of H-ness, say, the unity of the Form of F-ness remains perfectly inviolate. We can still pick out what all the 839 particulars share as one thing and not 839 things - precisely what the theory was intended to ensure.

What has gone wrong with Parmenides' sail is plain. Parmenides insists at 131 c that each person is covered by only a part of the entire sail - so the sail must be divisible into parts and hence not a seamless unity after all. But Plato reminds us, via the Eponym Theory at 130e, that each of the many people is covered by a part of just one sail - and being part of one rather than two makes the sail into a perfectly proper unity all over again. Parmenides' perspective is certainly not negligible. But it depends on obscuring Plato's point in talking about One and Many in the first place. For him the point is to explain why some Many can be grouped together and called by the same name. And on this point it is clearly the sense of being one rather than two, not being a whole rather than with parts, which matters to deciding whether many people are or are not rightly denominated by some unity (a sail or a Form) covering them all.

V. A Grab-bag of Larger/Smaller Puzzles ,(131c-e)

Hardly pausing for breath Parmenides bludgeons home his objection with a series of one-liners:

"Suppose it is Largeness itself that you are going to divide into parts, and that each of the many large things is to be large by virtue of a part of Largeness with is smaller than Largeness itself. Will that not seem unreasonable?" "It will indeed." ( 13 Ic 12- d3)

"And again, if it is Equality that a thing receives some small part of, will that part, which is less than Equality itself, make its possessor equal to something else?" "No, that is impossible." (13 1d4-6)

"Well, take Smallness: is one of us to have a portion of Smallness, and is Smallness to be larger than that portion, which is a part of it? On this supposition ... anything to which the portion taken is added will be smaller, and not larger, than it was before." "That cannot be so." (131d7-e2; cf. 150a-c; Cornford translations)

It is sometimes argued that what carries the weight in all this is some sort of "Causal Principle": "a cause must itself possess the quality which it pro- duces in its effects". Plato made this principle an integral part of the theory of Forms before, it is said, and now he is using it again to abandon participation.1" This just can't be, however, for none of these particular "refutations" are anything but absurd.

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Consider the Empire State Building. It is large. It shares in the Form of Largeness, Plato says; it has a portion of that Form in it. Now consider the portion by itself, says Parmenides. As only a portion or part of the Form it is, of course, smaller than the whole Form itself. Nonetheless it is only by having this portion in it that the Empire State Building can be called large at all. So really the building is being called large "6because of' something much smaller than Largeness in it. "'And that is impossible." Nonsense. What makes the Empire State Building large is not that it has a large-sized portion of something or other in it but that it has a portion of Largeness in it. Once again, the theory of Forms is semantic and therefore specific: particulars get their names and characters from named Forms and from nothing else but named Forms. Once again, Parmenides has been made to grab hold of the wrong end of the stick: we call the Empire State Building large from the name of the specific Form which is in it, not from the name of the size of its portion. The size of a thing's portion of F-ness might, I suppose, determine matters of "f-er than"; Plato rarely discusses compar- atives (cf. Phd. 100e, 102b-d). But it never determines matters of "f (as opposed to g)"; on this Plato is uncompromising (e.g. Rep. 476a, 507b-c, 596a).

Much the same error flaws the other two quickies as well. It is because it has a portion of the specific Form of Equality rather than some other Form that some thing can borrow the Form's name; the size of the portion of Equality isn't what determines the eponymous designation "equal". So too, if we add a quantity, any quantity, of Smallness to a particular, there can be no question that we make it small - for all that we are adding to and not subtracting from it.

VI. The "Third Man" Argument (132a-b)

Changing gears, Parmenides gives up trying to prove that each Form has an unlimited number of parts and tries to prove instead that there is an unlimited number of each type of Form:

"I imagine you think each form is one for the following reason; whenever a number of things seem to you to be large, it seems that perhaps there is a single idea, the same applicable to all the things you see, and you consequently think that largeness is one." "That is true." "But what of largeness itself and other large things? If you consider them in your mind all in the same way, won't you again find one largeness. because of which these all seem large?" "Apparently." "So another form of largeness will be discovered, in addition to what was largeness itself and the things partaking of it: and in addition to all these another again, because of which all these will be large; and so no longer will each of your forms be one, but infinite in number." "Yes." (I 32a 1 -b3; Matthews translation)

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This is the infamous "Third Man" Argument (after Aristotle's test predicate).

The literature on this short passage is mind-boggling, but directly we bring Plato's theory of words to bear, Parmenides' fallacy is surprisingly elementary. The difference between naming a Form (T1) and being named after a Form (T2) means that the Form F is never itself f in the special derivative way which demands something "over" it being f. The f particulars are all f(E). The Form F itself is f(P). The 'ovoiua "f' coincides, to be sure. But the very disparity between "E" and "P" utterly ruins any Third Man, for only with "E" and never with "P" do we have any machinery to push a regress to other Form F's further and further back (cf. footnote 1).

Take an example. Suppose, what is usually supposed, that Parmenides is still hacking away at the old characteristic-in-things model:

(1) How is it possible for us to apply the single word "large" to the wildly disparate things: the Empire State Building, Idi Amin's ego, the free-will problem, my Aunt Maude, and other people, places and things? Grant they all have a "similar nature" in being more or less large, what justifies our saying that?

(2) Our justification is the fact that there is just one self-same ingredient immanent "in" each of them, which each of them "has" a certain quantity of - the ingredient largeness. (The word "large" is like the adjective "alcoholic": "alcohol" is the name of an ingredient mixed in drinks and the drinks which have some alcohol in them, like gin, whisky, rum and so forth, are rightly called alcohol-ic after it.)

(3) Not all particulars are equally large of course, which is just to say that different particulars have different amountts of the ingredient largeness in them. As more and more of the Form of Largeness is added to some particular, obviously a higher and higher percentage of its total substance comes to consist of the very ingredient being added. It comes to be made up more and more of that ingredient itself. Thus the least large particular may consist of only 3% of largeness and 97% of other ingredients. The largest particular may consist 99% of Largeness and only the tiniest fraction of other ingredients. (Just as when we mix more and more alcohol in a drink, the drink comes to consist more and more of nothing but alcohol.)

(4) On the other hand, a clear 100% of the Form of Largeness consists of the large-making ingredient. The Form consists of nothing else. The Form's content of largeness is undiluted and unadulterated.

(5) Now the difference between a particular, 99% of which consists of some ingredient, and the Form, 100% of which consists of that ingredient, is not a Very Big Difference. To be sure, the Form of Largeness is at the

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upper-most end of the scale of larges and every sensible is necessarily lower down in that scale. But still the difference is only in quantity or proportion of largeness, not any difference in kind. (In the same way, distilled alcohol, unmixed and undiluted with anything else, is merely the most alcoholic of beverages.)

(6) Thus the class of large things now properly includes as one of its members the top of the scale, the 100% large thing, the Form of Largeness. In this sense at least, the Empire State Building and company together with the Form all have a "'similar nature" - all consist of some percentage or another of the ingredient largeness.

(7) So step (1) reapplies. If being of a ""similar nature" to each other in being more or less large implies the existence of some separate Form in the case of the 3% or 99% larges, it just as well implies the existence of some separate Form in the case of the 100% large.

(8) Since the ingredient largeness is already accounted for, this ad- ditional ingredient in all the 3%, 99% and 100% larges can only be something like the Form of Large2ness. Back and back we go, ad infinitum.

Razzle dazzle helps obscure the fatal flaw here, but fatal flaw there is. The slide between 99% and 100% in steps (4) and (5) is truly breathtaking when taken in the context of Plato's Eponym Theory. Grant that the Empire State Building may be larger than my Aunt Maude. Grant that, if so, it will be because the building has a higher percentage of the ingredient largeness "in" it than my aunt has. Still, the Form of Largeness isn't larger yet in the sense of having an even higher percentage of largeness in it. "Cakes have sugar in them." Yes. "Sugar has sugar in it." No. Particularly in cases where M is to take N's name, expressions like "N is in M" or "'so and so percent of M is made up ofN" make sense only where M is somehow identifiably different from N. That is, only where we have one set of individuation criteria for M and another set of individuation criteria for N. When we say "The ingredient largeness makes up 99% of the content of this particular", for instance, we presuppose, correctly, that we have one way of picking out the thing with that ingredient in it and quite another way of picking out the ingredient which is in that thing. But when we say "The ingredient largeness makes up 100% of the content of the Form of Large- ness" everything is changed. Whatever they may turn out to be, the individuation criteria for picking out the thing (namely the Form of Large- ness) which has the ingredient are exactly the same as the individuation criteria for picking out the ingredient (namely the Form of Largeness) which is in that thing. However could they be different? The moral is obvious. The Form takes the name "large" for a different reason than any

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particular does. So of course it is "of a similar nature" for a different reason too. The 3% and 99% large particulars are of a similar nature in the sense any two things named after the same eponym are; but the Form itself and those particulars are of a similar nature in the sense that any named after thing and its eponym are. (The Empire State Building and my Aunt Maude are both large because both have some of the same ingredient in them. Largeness and Maude are both large, however, because the first is what is in the other.)

Because the fatal flaw is semantic, we get the same result if we recon- struct Parmenides' Third Man using any ontological model for participation - instantiations, functional specifications, paradigms, proto- types, primogenitors, what have you. The point is a perfectly general one because the motive force for the regress is perfectly general. It is simply the "One over Many" principle reapplied to the One itself:

(A) If any set of x, y, z are f, it must be because there is some Form F separate from them all in which they all participate. (The "One over Many"'.)

(B) The Form F is f as well. (The "self-predication" thesis.) (C) Therefore, since x, y, z, and the Form F are all f, it must be because

there is some Form F2 separate from them all in which they all participate. (The regress.)12

The flaw in Parmenides' argument is that (A) just won't apply to (B) to generate (C). Each and every step here is radically misconceived.

Step (A) can never be applied to the Form F, for instance, because in Plato's hands the "One over Many" is a deliberately restricted principle. Plato worried how one word could legitimately be predicated of the many different things it is not the name of. He got his answer when he noticed that the many could well be related to one and the same named thing and so be lent out its name eponymously. Hence his principle: "x, y, z are f because they participate in the Form F":

The one thing that makes [an] object beautiful is the presence in it or association with it. in whatever way the relation comes about, of absolute beauty. (Phd IOOd).

But hence too an obvious restriction on that principle: the set of x, y, z for which it holds is the set of things which "f" does not name but applies only derivatively to:13

Whatever else is beautiful apart from ('rrwXv) absolute beauty is beautiful because it partakes of that absolute beauty. (Phd. lOOc: Tredennick translations)

In its turn, step (B) doesn't provide even the slightest temptation to apply

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(A) as the explanation of predication since "The Form F is f" there is not a case of predication at all and doesn't pretend to be. Neither the expression "Largeness is large" nor the expression "The Form of Largeness itself possesses the property of largeness" in fact occurs anywhere in Plato's actual text. Both have to be inferred - and inferred from nothing but the fact that the same word "large" is said to apply correctly to the Form as well as to its participants: "what if you consider Largeness itself and other large things in your mind all in the same way ... .?" (132a6-8). It is plain enough that Plato's semantics rules out any property reading of this passage. Since Parmenides has only just finished saying (at 130e6) that the word "f" picks out fsensibles only at second-hand, it is probably right to assume that "The other large things can be considered in your mind as large" does comes roughly to "so and so particulars possess the property f-ness" (i.e. participate in the Form F). But Parmenides has also just finished saying (at 130e6) that "C' picks out the Form F not at second-hand. So the statement "Largeness itself can be considered in your mind as large" must come to something else entirely, presumably to something like "The Form F is the entity which the name 'f' names". Far from attributing the property f-ness to the Form F, then, we have in (B) an expression more on a pattern with the identifying statements "Venus is the Morning Star" or "Samuel Clem- ens is Mark Twain" or "Electrons are beta radiation" or "New York is Fun City" (i.e. "Venus is the real referent of 'Morning Star"', "Samuel Clemens is the man named by 'Mark Twain"', "Electrons are what 'beta radiation' actually stands for", "New York is the city called 'Fun City"').14

Accordingly, any regressive conclusion like (C) is not merely un- necessary, obviously, but downright incoherent. Instead of saying (trivial- ly): "We apply the word 'f' to the majority of members of the class of f things because they participate in the Form named by the word and to the remaining member of that class, the Form F itself, because 'f is simply that Form's name", step (C) climbs out on a limb: "We apply the same word to all fes because all participate in the Form F2 named by the word". Such an answer presupposes that the Form F is at least the sort of thing which might possibly participate in some further f Form. But this isn't possible. "Par- ticipation", after all, is just a fancy word for whatever relation it is that things which are named after named things have to those named things in virtue of which they are rightly named after them. So to say that the Form F could be a participant in some further Form F is really to say that the Form F could be a thing whose proper name is "f " and at the same time take that name after a named thing. This is absurd. A general word applies in

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different ways to different sorts of things; it does not apply in different ways to one and the same thing.

VII. The "Thoughts" Model (132b-c)

Young Socrates, as befits his role, makes none of these protestations. Instead, he tries to avoid Parmenides' objection by proposing a new model altogether - that each Form is really a thought (vo6,gRa) "in" us and never "in" its participants:

"But, Parmenides, each of these ideas may be only a thought, which can exist only in our minds; then each might be one, without being exposed to the consequences you have just mentioned." "But is each thought one, but a thought of nothing?" "That is impossible." "But of somethinge?" "Yes." "Of something that is, or that is not?" "Of something that is." "A thought of some single element which that thought thinks of as appertaining to all and as being one idea?" "Yes." "Then will not this single element, which is thought of as one and as always the same in all, be an idea?" "That, again, seems inevitable." "Well, then, does not the necessity which compels you to say that all other things partake of ideas, oblige you also to believe either that everything is made of thoughts, and all things think, or that, being thoughts, they are without thought?" "That is quite unreasonable too." (132b3-c12; Fowler translation)

The vo6ua proposal put in Socrates' mouth was probably that of Plato's rival Antisthenes and is directly counter to everything else Plato ever wanted to say about Forms. This might suggest that the objection put in Parmenides' mouth is, and is meant to be, a knock-down refutation of any view like conceptualism.15

The suggestion is ludicrous, however. Parmenides' argument is a terrible one and couldn't possibly refute anything, as Plato well knew:

(1) Socrates suggests that a Form is a thought and as such "finds a place" (QyyLyvwEOaL) not in different and scattered physical particulars but "in souls" (,v lkUXQXLS).

(2) Each one of those thoughts is one ('Ev) presumably, Parmenides argues. So, of course, it cannot be of not-one (oviev6s). This means that the thought cannot be a thought of not-one, of no-thing, of nothing, but must be "of something" (TLvoS). It must be of something which "really does exist" (3iVTOS) and of some one determinate something (ivos TLVOS).

(3) Thus for each distinct thought we must postulate a single distinct element which that vo6iwa "apprehends" (voCi) as "covering a whole host of particulars" (E'rbo'v kf'i ?r&oLv) and as being "some one form" (v iaVrwa ovaoav

tWav). This thing which is apprehended by the thought is, naturally, the Form (et0os) we have known from old.

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(4) So what we have really proved is that a Form is a "thought" and that the common element "in" particulars is the Form.

(5) Since the common and peculiar elements in particulars are just the constituents or ingredients out of which they are made, this double nature of Forms implies that what particulars are really made up out of are thoughts. And hence, of course, they themselves must be thoughts.

(6) Anything which "has being as a thought" (ij voaItTa 5vTa) obviously cannot "be without thought" (&vo6Ta eIvaL). So the conclusion that all things are thoughts is simply the conclusion that all things think.

Reductio ad absurdum - so Parmenides says. Now the conclusion is an absurd one certainly. Not, however, because the thoughts proposal of( 1) is fallacious, but because of plain old-fashioned skullduggery at step (4). This becomes clear immediately we realize, once again, that Socrates is offering a partly semantic story, a story about (Tl) and (T2).

Indeed, the story is essentially the story given later on by John Locke as a solution to much the same problem of general words. A general word is the proper name of a mental idea in us, Locke says, of a thought we have in our minds, and applies derivatively to external objects only insofar as and because they all "conform to"9 or "agree with" that idea:

That then which general words signify, is a sort of things: and each of them does that by being a sign of an abstract idea in the mind: to which idea as things existing are found to agree, so they come to be ranked under that name. (Essay Concerning Human Understanding, 111.3.12; cf. 111.3.6)

Here we have a very different kettle of fish than before. It is still a story about how words function in terms of naming something (T 1) and naming other things after it becausse of their relation to that something (T2). But the details are very different indeed. Earlier it was the presence of a named stuff "in" a physical particular which gives that particular the quality and name it has - as alcohol gives a distinctive kick to alcoholic beverages. Now it is the existence of a named mental idea to which the physical particular somehow "agrees" that sorts them out - more or less as our abstract image of a triangle tells us which chicken scratches on the black- board are to count as triangles.

The main thing wrong with Parmenides' argument is just that the two stories do work very differently - and Parmenides, ignoring that work, jams them together into one homogeneous mess. In step (4), in particular, Socrates is invited to agree that the common and peculiar element in things which the Form is the thought of is itself a Form - "as always". In doing this, Parmenides is covertly combining the new story with the superseded

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old story and arguing that the Forms which do duty as eponymous thoughts in us also thereby do duty as eponymous ingredients in things. Rubbish. The mental idea of alcohol in my soul can hardly be added to the ice-cubes in my glass to give me a drink with any kick at all. Conversely, the stuff that does kick derives from the fermentation of a vat of carbohydrates, not from a soul in anticipation. A drink can readily be named after an ingredient in it or after an idea in me, but Forms which are eponyms in one way simply can't be eponyms in the other way as well.

VIII. The Imitation Regress (132d-133a)

Scandalous as Parmenides' "refutation" of voi iTn is, Socrates is buffa- loed and retreats to yet another model of participation, his third and last:

"But, Parmenides, the following seems to me to be most likely to be the case: these forms are fixed, like patterns ('IMpUaM(yprrT) in nature, and other things resemble (6oLxivaL) or are likenesses (pL.ouL4a'r) of them; and this participation in the forms is, for these other things, simply being made in their image (eixaxovaL)." "Then if anything resembles the form ('?o01ErX? 6t8EL), can that form avoid being like (6Potov) that which is made in its image, to the extent to which the latter has been made like it? Or is there any way in which what is like can be unlike what is like it?" "No there isn't." "And isn't it absolutely necessary that what is like (6ptoLov) should partake of one and the same thing as that which is like it?" "That is necessary." "And will not that in which like things partake so as to be like be the form itselfr'" "Certainly it will." "Then nothing can be like (8pDov) the form, nor can the forim be like'anythiing else. Otherwise, in addition to the form another form would always be found, and if that were like anything, yet another, and there would be no end to a new form coming into being at every stage, if the form is to be like the thing partaking of it." "That is quite true." "So other things do not come to partake of forms by means of likeness (6 orn), but we must look for some other way in which they participate." "It seems so." (1 32d 1- 133a7; Matthews translation)

This is probably the most interesting argument of the lot and rewards the closest scrutiny. Socrates proposes that the Forms are "patterns" ('rrxpaeL'y[aura) and that participation is properly to be analyzed as "to copy" (koLxEvaL) or "to be made in the image of"' (dxax "vmL). Parmenides speaks of the Forms as "likenesses" (Si.Un) and treats participation as a matter of "being like" (6p4ots). Despite this radical difference in terminology, the objection here is by no means egregious.

For a start, it is not the simple fallacy of treating a non-reciprocal relation as a reciprocal one which so many commentators say it is (cf. footnote 2). True, being like is usually reciprocal for Plato: if M is SB.tos N then generally N in turn is 6IoLos M (e.g. Gorg. 5 lOc, Rep. 349c, Tim. 45c, Epist. VII 335c). True too, copying is usually non-reciprocal: if M is E'CxaawOv to N

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then N is definitely not 'vxaxEv to M (e.g. Crat. 432b, Phdr. 248a, Tim. 52c, Laws 668a-b). Nonetheless, Parmenides never in fact says anything as silly as that copying is in the end reciprocal - that Aunt Maude herself is a copy of my snapshot of her for instance. What he does say is that if my snapshot is a copy, then the original and the snapshot must be like each other and so, on Socrates' hypothesis, they must both be copies of something else.

Against this we might urge the intransitivity of copying: "if M copies N, then N itself cannot be a copy of anything". Parmenides may be right to dispute this principle generally. Ordinary copying often violates it (I have a print of the Mona Lisa but this doesn't mean that da Vinci's original painting wasn't itself a reproduction, of a real lady). Even so, he cannot be right to dispute the principle for Forms, since the copy story there, Plato's semantics tells us, is a story about the derivativeness of (T2) in terms of the directness of (T I). (If the Empire State Building and my Aunt Maude are like in being large, say, it is only because they are both eponymously large, i.e. because there is a Form The Large which they both copy. But The Large itself is not eponymously large, i.e. not large because there is some further Form which it copies.) Though this is probably the right answer in the end, almost certainly it is the easy way out. There is more to Par- menides' attack than transitivity. And there is more to Plato's response too.

Parmenides' attack turns essentially on the assumption that the xEOxao'VaL relation ultimately presupposes the bFoLos relation, at least in the sense that if the higher-order relation holds then the lower-order relation must also hold.16 Socrates' proposal is simply that the lower-order relation of being like can never be fully explained except by assuming that the higher-order copying one obtains. Parmenides' twist is simply that whenever the higher-order relation obtains the lower-order one does too. The repetition of these two principles one after the other generates the regress directly:

(1) Suppose two particulars, the Empire State Building and my Aunt Maude, are like in being large.

(2) By hypothesis, this is so only because both copy a single Form, the Form The Large. The likeness of copies derives from their copying the same thing and the likeness of sensibles derives from their being copies. So

if some particular x is 6boios y that is really because both x and y are E(xaiOv,ra to the same something else, the Form F.

(3) However, in order for x and y to be copies of the Form F they must copy F in some specific respect. If there is no specifiable respect in virtue of which the relation of copying can be said to hold, then there isn't any relation of copying at all. In the case at hand, my Aunt Maude and

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company must copy The Large at least in the respect of largeness as opposed to, say, corporeality or divinity.

(4) Now this is just to say that x and y must be like the Form F in some respect. Aunt Maude and company must be like The Large in respect to largeness. In general: if x is EixaoO'v to F, then x must be Of.LoLos F as well.

(5) Of course, then, the Form F will in turn be like x and y. "Being like", especially "being like in respect of", is certainly a reciprocal relation. (Any two things that are like in some respect must at the very least share that respect in common.) Accordingly, if my Aunt Maude is like The Large, then The Large must be like my Aunt Maude: if x and y are bt,oLot F, then F in turn is 0`uotos x and y.

(6) So we really have not two things which are like each other: x and y, but three things which are like each other: x, y and the Form F. The Empire State Building, my Aunt Maude and the Form The Large are all three like each other.

(7) To explain this we must reapply the hypothesis of step (2). There is no other explanation of likeness available. If Aunt Maude and company can be like each other only insofar as there is some higher thing (The Large) which they copy, then Aunt Maude and company and the Form itself can be like each other only insofar as there is some higher thing (a second The Large) which they all copy: if F is 6polos x and y that must be because F, x and y are all three e';xaU0evTa to the same something else, F2. Such a regress never stops.

Plato's response to this irresistible attack is to resist the assumption which powers it. Though it might seem so at first, copying is not the "higher order" relation which Parmenides says it is in steps (3) and (4). If a copying relation holds between two things it is not in fact the case that a relation of being like must also hold. This is a startling exegesis, perhaps, but not as hard to demonstrate as it is usually made out to be - provided, again, we focus on the semantics of Plato's copy story.

The Official View of copying goes roughly like this. We begin with the perfectly familiar medium-sized pieces of dry goods that make up our everyday sensible world. In addition to them, Plato has discovered, there are certain abstract particulars, Forms, which belong to a different world altogether. Moreover, in comparison with the other things the sensibles are but dummies, simulacra, reproductions. It is rather as if we lived our whole life drinking Nescaf& until someone came along and opened our eyes to a real cup of coffee. In one way nothing is changed about the old world. Cups of instant don't suddenly become metaphysically slippery or diaphanous. We just realize that they are not, as we once thought, the be-all and end-all

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but instead mere imitations. We might call this a "static" reading of copying. (Think of copying by Xerography.) Official as it may be, however, this is not Plato's own view of the matter. What, after all, is the ontological disparity between Plato's new world and our old familiar one? It is, he says, the disparity between the World of Being and the World of Becoming. The Forms are eternal, stable, never coming to be or ceasing to be. Sensible particulars, by contrast, are in constant flux, transient, ceaselessly popping in and out of existence. Now if we have eponyms and named-after things like those, what can the proposal that named-after things "copy" their eponyms possibly mean? It must be the proposal, I think, that particulars are constantly in a process of setting themselves after the Forms (but of course constantly failing to make it). It is because the target of their aspirations, not some plateau at which they have arrived, is this rather than that Form that they can take some Form's name. (Think of copying a master's dance technique.)

The three major texts on copying in Plato's dialogues confirm this dynamic reading. The language of the Phaedo is especially striking:

"Do [equal pieces of wood] seem to us to be equal as abstract equality is equal. or do they somehow fall short (68v&) of being like abstract equality?" "They fall very far short of it." "Do we agree then [with one who] thinks, 'This thing that I see aims at (o06Xe'aL) being like some other thing that exists, but falls short and is unable (oO Uvvaum) to be like that thing, but is inferior to it' . .. [because] all sensible objects strive after (6peyeTa) absolute equality and fall short (h68aeapa) of it. Is that our view?" "Yes." (74d-75b; Fowler translation).

A pair of sticks we call equal are so-called because what they are "striving after" or "aiming at" is the Form of Equality - hence their name. Being particulars, however, all they can do is strive, they "lack the power" to make a success of it but inevitably "fall short" - hence their status as mere copies. In the Timaeus account, dynamism is just as central. There, just because sensibles are ceaselessly in flux, Plato says, we must postulate enduring Forms on top of them which the changes are changes "in the direction of":

"Since no one of [the elements] ever remains identical in appearance. which of them shall a man definitely affirm to be any one particular element and no other without incurring ridicule?" "None such exists. On the contrary, by far the safest plan . . . is this: Whatsoever object we perceive to be constantly changing from one state to another, like fire, that object, be it fire, we must never describe as 'this' (?owro) but as 'suchlike' (? rou)rLorov); nor -should we describe any other element as though it possessed stability .. . but must apply the term 'suchlike' to represent [it as] what is always circling round." (49d-e; Bury translation).

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No sensible ever stands still long enough to have a stable character (to be a "this"). The most that can be said is that when it careens off in the direction of some Form for a time it can, for that time, be dubbed a "such like so and so". The present Parmenides passage is in the same spirit. Socrates in fact does not use copulas in 132d and does not say that Forms "are" fixed patterns and that sensibles "are" likenesses of them (which might possibly allow a static reading). Instead he contrasts Forms and sensibles by con- trasting two verbs: on the one hand the patterns "fix themselves" (ioa?vat) in nature, on the other hand the copies "liken themselves" (oLxEv'aL) to Forms. The name and character of the sensibles thus comes from their likening themselves to some having-fixed-itself thing. And this in explicit contrast to their getting their name and character by fixing themselves in a like rut with some Form."7

Now if this is Plato's story, it is obvious that Parmenides' assumption is illegitimate. M can easily be striving to liken itself to N ("copy") without ever necessarily managing to possess some characteristic which N possesses ("be like"). What Parmenides has really done is freeze a particular on its journey towards a certain destination and then assume that, frozen just there, is must already have reached its destination a bit and so already be in possession of some achieved identity to it. Considering that Socrates' proposal is precisely to explain how it is that unfrozen things can still rightly be grouped together (cf. Theaet. 182d), why suppose this bit of trickery especially worrisome?

IX. The Master-Slave Argument (133b-134e)

The final objection in Parmenides' arsenal is directed not to models for Forms but to the question of knowledge. One way or another, Socrates has made the two orders of sensibles and intelligibles so distinct that it is utterly mysterious how the inhabitants of either one can possibly be known by the inhabitants of the other:

"When ideas are what they are in relation to one another, their essence is determined by a relation among themselves, and has nothing to do with the resemblances, or whatever they are to be termed, which are in our sphere, and from which we receive this or that name when we partake of them. And the things which are within our sphere and have the same names with them, are likewise only relative to one another, and not to the ideas which have the same names with them ... I may illustrate my meaning in this way: A master has a slave; now there is nothing absolute in the relation between them, which is simply a relation of one man to another. But there is also an idea of mastership in the abstract, which is relative to the idea of slavery in the abstract. These natures have nothing to do with us, nor we

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with them; they are concerned with themselves only, and we with ourselves. Do you see my meaning?" "Yes." "And will not knowledge - I mean absolute knowledge - answer to absolute truth?" "Certainly." "And each kind of absolute knowledge will answer to each kind of absolute being?" "Yes". "But the knowledge which we have. will answer to the truth which we have; and, again, each kind of knowledge which we have, will be a knowledge of each kind of being which we have?" "Certainly." "But the ideas themselves, as you admit, we have not, and cannot have?" "No, we cannot." "And the absolute natures or kinds are known severally by the absolute idea of knowledge?" "Yes." "And we have not got the idea of knowledge?" "No." "Then none of the ideas are known to us, because we have no share in absolute knowledge." "I suppose not." (133c7-134bl3; Jowett translation)

It is commonly assumed'8 that Parmenides' objection turns on the old bugbear of "self-predication". For instance, the Form of Mastership must somehow or other be a master of something. What? Certainly not some flesh and blood slave. It must be master of the Form of Slavery. So too with knowledge, Parmenides insists. Knowledge in us can only know things in our world. To suppose we inhabitants of the sensible world could really know the inhabitants of the intelligible world to commit precisely the same error as to suppose flesh and blood could really be slaves of the Form of Master.

Actually, however, Parmenides never says that the Form of Mastership is itself a master of anything, even the master of Slavery. Being Forms, the Slave and the Master are not "relative to" masters and slaves amongst us ('V bi'V4LLV -XEL OV& bXetvx 'rpos ias). Being men, slaves and masters are not "relative to" the Forms Master or Slave (ov' Tr& v fi,v np6s Exeva). The intelligible Master and Slave are "relative to" themselves ('rrp0` xv'Tra kxedv& T?' iUTL) and sensible masters and slaves are "relative to" themselves (sfrap' Lnpiv Woa&trwsp'ps T iavrar). The "self-predication" men read the accusative preposition ffp6s here as essentially the English preposition "of': "Mas- tership is master of Slavery". However, the intention of the text is something very different: "The relative to the Form Master is the Form Slave". "Master", that is, is a "relative" or "incomplete" or "two-place" predicate, so the right name for the Form cannot be simply "the Form of Mastership" but must be something "completed" in the second term, like "the Form of Master-of-Slave". Granting this, the correlative or completing term for "Master-of-" obviously cannot be the word for a sensible slave but must be at least on the Form level; and the completing term in the case of sensible masters-of likewise cannot be a Form name but must be something at least on the sensible level. Parmenides' axiom then is not "self-predication" but the very much more powerful principle that all the (completing) relations of a term used at one level must be strictly with other terms of the same

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level. Applied to knowledge, Parmenides argues, this axiom reveals that "knowledge" too is an incomplete term - it is always knowledge-of- something or other. As such, of course, "knowledge in us" can only have as its correlate something on the same level, namely something sensible. We can't know the Forms.

At first reading this is no mean argument. But in fact Parmenides is made here to contradict precisely the story of eponymous predication which he has spelled out just a few lines before (133d2-4): "the things which are within our sphere and have the same names (6 'vvu,a) with the ideas are likewise only relative to one another and not to those like-named (ovo,u&aeTQL) ideas". In this passage we get the intra-level stuff all right. On the level of Forms, the Form Master-of-Slave and the Form Slave-of- Master are related, as correlative terms at least. On the level of sensibles, masters and slaves are related too, as correlative terms and by some kind of dominance as well. However, that is clearly not the whole story. Perfectly legitimate inter-level relations are also assumed. Between the level of Forms and the level of sensibles, masters are appropriately named after the Form Master-of-Slave because they somehow or other participate in it ("are resemblances or whatever"). Actually, then, we have at least two radically different kinds of "being relative to", one on the same level, one crossing levels:

Form Master-of-Slave correlated Form Slave-of-Master l I with

gives its participates gives its participate: namt to in name to in

a sensible master correlated , a sensible slave with and bosses

It is this story - Plato's full semantic story - which Parmenides immediately goes on to ignore. Of course his axiom is at best only a half truth.

Indeed, it is not even this. The whole purpose of Plato's two-level metaphysics is to make the characters and names on the sensible order entirely derivative from the intelligible order. Strange as it might sound to our ears, a master for Plato really gets his character and name by being "appropriately related" to the Form Master-of-Slave and not by being

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appropriated related to other sensible beings (slaves). True: if I am a master then I must be the master of some slave. False: my being a master derives from my relation to slaves. My being what I am is necessarily cross-categorial for Plato, and no talk of completing incomplete predicates alters the fact one jot.

X. The "Parmenides" and Plato 's A cademy

A certain monotony has been steadily building up over the last few sections I'm sure. The objections which Plato puts in Parmenides' mouth are very varied. But the misunderstandings which they are made to turn on are very repetitious. This is deliberate and, I think, symptomatic. The Parmenides, I want to suggest, was not written for posterity and professionals, neither as an "elaborate jeu d'esprit" against contemporary Eleatic critics A la Taylor, nor as a record of Plato's "own honest perplexity" A la Vlastos. It was written for the Athenian Academy and for students - as an elementary training manual in the method which the Academy specialized in teach- ing.'9

Certainly it is uncontroversial that the Academy was a school with a method, the so-called "aporematic method". And we know a great deal about how the actual details of this training went in the Academy, because of reports by its two greatest teachers and because it is basically the training we provide our own students - training in prising out and evaluating the pivotal assumptions in an argument. In the Academy there seem to have been five distinct stages.

STAGE ONE: The jumping-off point was to find oneself in the special mental state of being stymied (&'ropia, auuXEpeL). There is no work to be done if nothing stands in the way, but insofar as the intellect is stymied,

there is a "knot" in the subject; for in its perplexity [the mind] is in much the same condition as men who are fettered: in both cases it is impossible to make any progress. (Metaph. 995a31-3; Tredennick translation)

(Mark how like being a fly in a fly bottle this all is!) Such is a prerequisite for Plato even as early as the Charmides where Socrates reports himself "at a loss" (&'nopC) and therefore desirous of pursuing the question whether one can know that one knows something (167b). Indeed, making someone mentally "numb" is Socrates' favorite ploy (Meno 80a-b) - and it is a ploy solely to clear the decks and get the real business started (e.g. Euth. 15c-e, Theaet. 15 la). Aristotle is even more explicit. We embark on some inves- tigation, he says, only when everything appears to have equal weight so we

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are "baffled" (&-nopoi)1ev) which course to adopt (Top. 145b16-20); it is only through feeling "wonders" (&ir6pwv) that men have ever philos- ophized (Metaph. 982b12-24); if nothing is "strange" (&'ropiav) then everything is smooth sailing (Phys. 185a8-12).

STAGE TWO: Once at a loss we must then conduct a wide-ranging survey of the difficulties in any given sphere. Aristotle has a technical term for this, 'rrpoaxopedv, "to look over the aporia before the inquiry proper":

One should have surveyed all the difficulties (8vaXepEias) beforehand . . . because people who inquire without first drawing up the aporiae are like those who do not know where they have to go; besides, a man does not otherwise know even whether he has at any given time found what he is looking for or not; for the end is not clear to such a man, while to him who has first drawn up the aporiae ('rproplpcx6'rL) it is clear. (Metaph. 995a33-b4; Owens translation, p. 218)

This means "to go through the difficulties", not in the sense of solving them but in the entirely preliminary sense of finding out what ones there are. This is the stage Plato is going through when he simply lists the problems of fire and the other elements in Timaeus 49b and the questions there seem to be about one and many at Philebus 14c-15b (can I be heavy and light? can Forms be one and divided? etc). Aristotle gives such thumbnail surveys in Metaphysics 995b4-996a 17 and Posterior A nalytics 89b2 1-35.

STAGE THREE: Though sometimes included in the overall survey, we get down to the nitty-gritty only when we go one step further and state a single specific difficulty as exactly and precisely as we can. Aristotle's term for this stage is &cexfopelv and it means to set out some aporiae so the specific knot which makes that particular puzzle distinct from other puzzles is made plain. Aristotle gives some examples concerning time in Physics 21 7b3 1-21 8a3 1. The clearest account of this stage is in Plato, however. The quick introduction of various one-and-many aporiae is immediately followed in the Philebus by a statement of one specific example, a statement which calls not for breadth of vision but the closest attention to precision of expression:

"How are we to conceive that each of [the Forms]. being always one and the same and subject neither to generation nor destruction, nevertheless is, to begin with, most assuredly this single unity and yet subsequently comes to be in the infinite number of things that come into being - an identical unity being thus found simultaneously in unity and in plurality? Is it torn in pieces, or does the whole of it, and this would seem the extreme of impossibility, get apart from itself'?" (1 5b2-c 1; Hackforth translation)

STAGE FOUR: Just as important as being able to state some specific aporia exactly is becoming able to argue on both sides of the question. This

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role-playing sounds a bit alien to our ears, but it is readily accessible if we see it, as the Academy did, in terms of "conversion" (&vTLarpoqp):

For training and practice in this kind of argument one should, in the first place, accustom oneself to converting arguments; for thus we shall be better provided for treating the subject under discussion ... For conversion is the reversing of the conclusion, together with the other questions raised, and the demolition of one of the points conceded; for of necessity, if the conclusion is not true, one of the premises must be demolished, since it was owing to the assumption of all of them that the conclusion necessarily followed. (Top. 163a29-37; Forster translation; cf. Prior A nal. 59b 1-61 a 16)

Against someone who argues "p and q, therefore r", that is, we can just as legitimately argue in reverse "not-r, therefore either not-p or not-q". Being able to do this just is taking now the proponent's part, now the opponent's - arguing "both sides". Fruitful &vrL0TXpO9 obviously requires a "certain genuine natural ability" (Top. 163blO-18) and clumsiness with it quickly causes one to "stammer and become ridiculous" (Theaet. 175d).

STAGE FIVE: Conversion is so powerful and useful because it helps focus on the premises of an argument in a rather special way: "If you grant so and so premise then you get such and such fallacious conclusion. If you do not grant that premise, however, you do not get that conclusion." Put like that, the pre-eminence given this tool fits in well with the fact that the declared end result of applying the Academic method is the isolation of the faulty admission which is the cause of the difficulty:

For those who wish to make a clear passage (riiropiuoaL) it is advantageous to draw up the aporiae properly. For the subsequent clear passage is the solution (X6oLs) of the previous aporiae, and for those who do not know the knot, it is impossible to untie (MifV) it. (Metaph. 995a27-3 1; Owens translation, p. 215)

[About problems like "Can a Form be in many things without becoming many itself?"I it is these sorts of questions concerning the one and many ... Protarchus, which are the cause of much difficulty (&rropias), if you make the wrong admissions (>ui xa)Ks 6boXoyOEvrTa), and the cause of passing through the difficulties (ev'- .nopias) if you make the right admissions (ais xasXs). (Phil. 15b0-c3; Barford translation, p. 89)

Here is no confession, by either Aristotle or Plato, that certain aporiae are intractable and that's all there is to it. There is instead the very different point that whether or not we have an aporia in some case depends entirely on the admissions we make. Apparent difficulties are caused by making the "wrong admission". A "clear passage" is effected immediately this wrong admission is detected and the "right admission" is substituted for it.

Taken against this background of Academic training in aporematic method, the two parts of Plato's Parmenides fall into place very quickly.

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The dramatic situation of the first part (1 26a- 136e) is that Socrates has devised a theory of Forms but doesn't appreciate all the ramifications of that theory. In particular, he doesn't appreciate the ramifications signalled at 130e-131a and 133d that the theory of Forms is as much a theory about how words work as anything else. Thus he constantly makes the "wrong admission" that words work for both Forms and particulars in more or less the same way. The "passage through" the difficulties depends on making the "right admission" - usually that we have a perfectly general theory here or that there is a sharp disparity in function between naming (Tl ) and naming after (T2). In the Fire and Mud objection, for instance, we have a first-class illustration of the whole business. Stage One: Socrates confesses to being "very much troubled" (&-nopia) about the range of Form talk (1 30c3). Stage Two: Parmenides quickly surveys the area of the problem - are there Forms for Zeno's abstractions, for value terms, for man, fire and water, for hair, mud and dirt? (130b3-c6). Stage Three: Parmenides states one of the aporiae exactly and precisely - can there be admirable Forms for sensibles which are vile? (130c6-7). Stage Four: Socrates rehearses both sides of the problem; it seems ridiculous to suppose worthless mud, say, is emulating some perfect thing, the Form; and yet "mud" is a general word like any other so what holds true for one ought to hold true for all (130d3-6). Stage Five: The admission which makes for clear sailing is laid bare - pay attention to what "philosophy" tells us, to treat all general words semantically on a par, and stop considering "ordinary people's opinions" (130el-4). The same five-stage treatment (more or less ab- breviated) is given in the course of Parmenides' other arguments. What we have in the "refutations" of Part One, then, is instruction in technique, nothing more and nothing less.

Such instruction "seems useless and is caalled by most people idle chatter" (I 35d). It is what Socrates desperately needs, however, because he is really "still too young" adequately to defend his thesis (127c, 130e, 135d). When he gets it and so becomes an "able man" (133b, 135a-b) with the "proper training" (133b, 135c-136c), the difficulties will no longer be any trouble but easily "exposed" (133b-c, 135a-d). Accordingly, Plato appends to the first part of the Parmenides a more general workbook (137b-166c) which he probably wrote originally for Aristotle's method class (to accompany the Topics lecture notes). This Part Two contains a much wider variety of "wrong admissions" to practice on. The two workbooks, though perhaps written at different dates (say 362 and 355 BC)20, go together very nicely. Socrates' weakness is due to lack of training in spotting wrong admissions - the moral of Part One. So here is a full-fledged training

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exercise in doing just that - the moral of Part Two. If such is the proper setting for Plato's Parmenides, it is clear that he did

not mean us to come away from the dialogue abandoning the theory of Forms. Plato himself certainly never abandoned that theory.21 And the whole question whether the theory should be abandoned because of the objections there is beside the point if they are expressly due to textbook "wrong admissions" being made. Indeed, if Plato meant us general readers to get anything from the dialogue (which is doubtful in view of his intended audience), it is probably only that we should be wary of making "wrong admissions" about Forms ourselves.

Massey University

NOTES

1 The quote is from G. E. L. Owen, "Logic and Metaphysics in Some Earlier Works of Aristotle', A ristotle and Plato in the Mid-Fourth Centuri'. ed. During and Owen (Almqvist and Wiksel, 1960), pp. 181-2. For others see: Proclus, Commentarium in Platonis Par- menidem ed. Cousin (Durand, 1864), pp. 879.5-880.20, 881.13-23, 886.36-887.23. Asclepius, In Aristotelis Metaphvsicorum Commentaria, ed. Hayduck (Reimer, 1888), p. 75.21-34. Damascius, The Greek Commentaries on Plato's Phaedo, ed. Westerink (North- Holland, 1977), II,p. 326.69. Simplicius, In Aristotelis Categorias Commentarium, ed. Kalbfleisch (Reimer, 1907), p. 77. 21-6. R. E. Allen, "Participation and Predication in Plato's Middle Dialogues", Studies in Plato's Metaphysics, ed. Allen (Routledge and Kegan Paul, 1965), p. 59. M. J. Cresswell, "Participation in Plato's Parmenides': Southern Journal of Philosophy, XIII (Summer, 1975), pp. 163-4. Also worth noting is J. M. E. Moravcsik, "The 'Third Man' Argument and Plato's Theory of Forms", Phronesis. VIII (1963), pp. 51-2, 59-60. 2 The quote is from Syrianus, In Metaphysica Commentaria, ed. Kroll (Reimer, 1902), pp. 11 1.33-112.2. Others include: Proclus, Comm. Plat. Parm., pp. 890. 9-15, 911. 33-912. 38, 913. 41-915. 26. A. E. Taylor, The Parmenides of Plato (Clarendon. 1934), pp. 25-6. F. M. Cornford, Plato and Parmenides (Routledge and Kegan Paul, 1939), pp. 93-4. 3 In characterizing Plato's semantics I have drawn heavily on Allen, "Participation and Predication in Plato's Middle Dialogues", pp. 44-7 and K. W. Mills, "Some Aspects of Plato's Theory of Forms: Timaeus 49c fr", Phronesis, XIII (1968), pp. 145-51. For more details see my "Common Properties and Eponymy in Plato". Philosophical Quarterly, XXVIII (July, 1978). pp. 190-6. Three traditional notices are: Sir David Ross. Aristotle's Metaphysics (Clarendon, 1924), 1, pp. 161-2. A. E. Taylor, A Commentary on Plato's Timaeus (Clarendon, 1928), p. 342. Karl Popper, The Open Society and Its Enemies (Routledge and Kegan Paul) 1, pp. 25-8. 4 Metaph. 1030a 19-b6, Eud. Eth. 1236a 16-b27. For other discussions see: Protrept. frag. 14, Metaph. 1003a33-bl9, 1028alO-30, 1052al5-b24, Eud Eth. 1217b23-41, Nico. Eth. 1096al8-b34, 1157a29-b4. Extra possibilities to mediate between strict synonymy and strict homonymy were not at all uncommon in fourth-century Greece. Aristotle used not only sp&ps '?v XEy6p!vc but at one time or another tried out as well: metaphor (e.g. ends and means to ends, Top. 110b16-18, 139b32-140a17, Poetics 1457b7-16): paronymy

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("grammarian" from "grammar", Cat. la12-15); and analogy (as sight is "good" in the mind so mind is "good" in the soul, Nico. Eth. 1 131a32-b16, Poetics 1457b17-36). Even Speusippus, who was acclaimed for dichotomizing anything he could lay hands on, in fact operated in this territory with a four-fold division: synonymy, homonymy, paronymy and polyonymy (e.g. "sword" and "blade" applied to the same object); see De Speusippi Academici Scriptis, ed. Lang (Georgi, 1911), frag. 32. 5 The "each and every" argument is repeated at: Laches 190e-19le, Euth. 5d-6d, Meno 73d-74e, Prot. 312b-d, Gorg. 449d-451d, 453b-454b. For "really exists" parallels: Hip.Maj. 287c-d, Meno 88a, Prot. 330c-d, Crat. 387c-388c, Theaet. 182d-e, Parm. 142a, Soph. 237c-e, Phil. 59a-b, Tim. 49d-50a, Epist. VII 343b; perhaps even Pol. 262a-263e. The "one and many" figures in: Phd. lOOc-101c, Phdr. 249b-c, 265d, Rep. 596a, 597c-d, Theaet. 146d-e, Parm. 132a, Soph. 232a, 240a, 243d-e, Tim. 83c, Phil. 12c, 15b, 34e. For the "unambiguous" requirement see: Hip. Maj. 289a-d, Phd. 74a-75d, 78d-79a, Rep. 331c-d, 476a-d, 479a-e; but also note Pol. 285e. 6 Alc. I 108c-d. For some other non-philosophical eponyms see: Svmp. 173d, Rep. 580e, 600b. Crat. 393b-395d, 397b-d, 403a, 404b, 409c, 416d, 419b-420b. Phdr. 238a-c, 278d-e, Critias 1 14a, Epin. 987b, Laws 626d. 704a, 713a, 738b, 745d-e, 828c, 878a, 969a. 7 Alexander of Aphrodisias, In Aristotelis Metaphysica Commentaria, ed. Hayduck (Reimer, 1891), pp. 82.11-83.16, quoted by G. E. L. Owen, "A Proof in the Peri Ideon", Studies in Plato's Metaphysics, pp. 294-5. Aristotle himself, it should be mentioned. disagreed with assumption (iii) in the proof and insisted that the same predicate applied to portraits and originals was a case of homonymy pure and simple - "equivocation by chance" (Pt. Anim. 640b36-641a3, Polit. 1253a20-5, Meteor. 389b30-390a 14, Gen. Anim. 726b21-5, Soul 412b2O-2, Cat. Ia 1-4). He never liked (iii)s merely "intriguing metaphor" (Metaph. 991a20-1 = 1079b25-7). This partly explains his scorn for Plato's E'rrfvvllos predication vis-a-vis his own iTp&; ?Ev proposal. It also explains, perhaps, why he occasionally teased Plato with the Third Man (Metaph. 990b27-991a8 = 1079a24-b3) even though he knew if turned on a false dichotomy (1038b34-1039a2 with Soph. EL 178a4-7 and 178b37-179a10, 1059a12-13) and knew that Plato knew it too(104Ob32-5, 1079b3-11, Top. 145a28-32, Lin. Insec. 968a9-14, Eud. Eth. 1217b2-16, 1218a1-8). X Phd. 65d-e, 75c-d, 78d-e, 100b, Rep. 493e, 507b, 596a, Phdr. 249b-c, Parm. 135a-b, Phil. 15d, 16c-d. Tim. 51 b-e. Laws 965b-c, Epist. VII 342d-e. Aristotle, Metaph. 1060a7-18, 1070a18-21, 1078b32-1079a4. ' Aristotle, Metaph. 991a8-19 = 1079b12-23. For Anaxagoras also see Ancilla to the Pre-Socratic Philosophers, ed. Freeman (Blackwell, 1947), frag. 59.4; Aristotle, Phvs. 187a27-b6; John Brentlinger, "Incomplete Predicates and the Two-World Theory of the Phaedo", Phronesis, XVII (1972) pp. 64-9. For Eudoxus: Alexander, Arist. Metaph. Comm., 97.17-98.21; Malcolm Schofield, "Eudoxus in the Parmenides", Museum Helveticum, XXX (1973), pp. 1-2, 15-17. "9 For Plato see Phil. 15b; but compare ? X below. Amoung the ancients are Alexander, Arist. Metaph. Comm., 97.30-98.7, and possibly Plotinus, Enneads, VI.4.5. For moderns note I. M. Crombie, An Examination of Plato's Doctrines (Routledge and Kegan Paul, 1963), 11. pp. 330-1, and M. J. Cresswell, "Is There One or Are There Many One and Many Problems in Plato?", Philosophical Quarterly. XXII (April, 1972), pp. 152-3. 1 For example by Henry Teloh, "Self-predication or Anaxagorean Causation in Plato?", Apeironi, IX (1975), pp. 15-6. 12 This is not in fact an over-simplification; the usual formalizations are over- complicated. For example: Wilfrid Sellars, "Vlastos and 'The Third Man"', Philosophical

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Review. LXIV (July, 1955). p. 419. Peter Geach, "The Third Man Again". Studies in Plato's Metaphysics, pp. 271-4. Colin Strang, "Plato and the Third Man". Plato: Critical Essays, ed. Vlastos (Doubleday, 1971), 1, p. 185. Gregory Vlastos, "Plato's 'Third Man' Argument: Text and Logic", Platonic Studies (Princeton, 1973), pp. 363-5. Marc Cohen, "The Logic of the Third Man", Philosophical Review, LXXX (October, 1971), pp. 463-4, 467. In particular, I am sure that the rhubarb about "self-predication" versus "non- identity" (dating from Vlastos' classic diagnosis in "The Third Man Argument in the Parmenides", Studies in Plato's Metaphysics, pp. 237-41) is an almost total waste of time. The "One over Many" has always been a One over Many principle and so includes "non-identity" right from the start, and with no "hidden inconsistencies" either. "Self- predication" tells us thai the Form F is f. "Non-identity" tells us that the Form F is not one of the things which are f in virtue of their participation in the Form F. "Eponymy" tells us that the Form F is f for another reason entirely. 13 This justifies the still rather ad hoc tradition of limiting the "One over Many" principle: To "things seen with the eyes" by A. L. Peck, "Plato versus Parmenides". Philosophical Review, LXXI (April, 1962). pp. 161, 164-8. To "sensible particulars" by Spiro Panagiatou, "Vlastos on Parmenides 132AI-B2: Some of His Text and Logic", Philosophical Quarterly, XXl (July, 1971), pp. 256-8. To "particulars" full stop by Henry Teloh and David Louzecky, "Plato's Third Man Argument", Phronesis, XVII (1972), pp. 82-4. 14 This is more or less the old-time "identity statement" proposal of Allen, "Participation and Predication in Plato's Middle Dialogues", p. 46, and H. F. Cherniss, "The Relation of the Timaeus to Plato's Later Dialogues", Studies in Plato's Metaphysics, pp. 370-1. Since it reads "The f is f' as the synthetic and significant "The Form F just is itself the character f-ness", this proposal warrants none of the scorn usually heaped on the analytic and empty "F-ness is identical to F-ness" (e.g. by Vlastos in "The Unity of the Virtues in the Protagoras"' Platonic Studies, p. 263 fn. Ill and "A Note on 'Pauline Predications' in Plato", Phronesis, XIX (1974), p. 97 fn. 5). K. W. Mills' proposal "The Form F is the nominatum of 'f" is even more accurate, "Plato's Phaedo, 74b7-c6", Phronesis, 11 (1957), p. 146. 15 For Antisthenes, see Ammonius, In Porphyrii Isagogen, ed. Busse (Reimer. 1891), p. 40.6. The major anti-conceptualist is A. E. Taylor, Plato (Methuen, 1926), pp. 356-7. 16 For defences of this assumption see: Alexander, Arist. Metaph. Comm., pp. 94.15-95.12. Gilbert Ryle, "Plato's Parmenides", Studies In Plato's Metaphysics, pp. 104-5. R. H. Hathaway, "The Second 'Third Man"', Patterns in Plato's Thought. ed. Moravcsik (Reidel, 1973), pp. 85-9. E. W. Van Steenburgh, "On Spiking the Imitation Regress", Apeiron, Vill (May, 1974), pp. 28-9. Roger Shiner's is the most convincing, "Self-predication and the 'Third Man' Argument", Journal of the History of Philosophy, VIII (October, 1970), pp. 372-5. 17 See the excellent discussion by Edward Lee. "The Second 'Third Man': An Interpre- tation", Patterns in Plato's Thought, pp. 103-6, 112-6. 18 For example by James Forrester, "Arguments An Able Man Could Refute: Par- menides 133b- 134e", Phronesis, XIX (1974), pp. 234-6. 19 What follows derives in great part from: Joseph Owens, The Doctrine of Being in the Aristotelian Metaphysics (Toronto, 1951), pp. 211-19. A. L. Peck "'Plato's Alleged Self- Criticism in the Parmenides: Some Recent Views", Cambridge Philological Society Proceedings, CLXXXII (1952-3), pp. 34-6. Robert Barford, The Criticisms of the Theory of Forms in the First Part of Plato's Parmenides (Indiana PhD, 1970). pp. 92-106.

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20 Gilbert Ryle's account in Plato's Progress (Cambridge, 1966), pp. 287-95. 21 Post-Parmenides references to Forms include: Soph, 240a, 247a-b, 248e-249d, 254a, Tim. 29b, 48e, 50c-d, 51a, Pol. 285e-286a, Phil. I5a-b, 59a-c, 61d-62b, Epist. VII 342a-d, 343b-c, 344b, Laws 859e, 965c-d.

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Documents

Plato's Semantics and Plato's "Parmenides"