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Dossier : Les Formes platoniciennes dans l'Antiquité tardive

Proclus and the Third Man

Lloyd P. Gerson
p. 105-118

Texte intégral

  • 1 It is fair to say that modern discussion of this argument begins from an article more than fifty ye (...)

1The so-called Third Man Argument (hereafter TMA) in Plato’s Parmenides (132A-B) continues to rivet the attention of Plato’s friends and foes alike.1 In this paper, I focus on Proclus’ treatment of the TMA in his Commentary on Plato’s Parmenides. I do so to repay a debt of piety, offered in a spirit I would like to think Proclus would understand perfectly. For though prior to having read Proclus, I arrived at an analysis of this argument essentially identical to his, it was my encounter with the Proclean text along with my reading of Plotinus that completely reoriented my approach to ancient Greek philosophy. I came to appreciate that the pejorative and anachronistic term ‘Neoplatonism’ was actually an impediment to understanding Plato and even Aristotle as well. I also became acutely aware that philosophical sophistication in the interpretation of Platonic texts does not date from the appearance of Anglo-American scholarship in the latter half of the 20th century.

The TMA in Plato’s Parmenides

2Let us begin by briefly reviewing the argument and the explicit problem it is supposed to throw up for Socrates’ hypothesis about Forms :

  • 2 Parm. 132A1-B2 : Οἶµαί σε ἐκ τοῦ τοιοῦδε ἓν ἕκαστον εἶδος οἴεσθαι εἶναι· ὅταν πόλλ᾽ ἄττα µεγάλα σοι (...)

“I think you think that each Form is one for this reason : whenever it seems to you that some things are large, there seems to be, I guess, when you look at all of them, some one self-identical Idea, for which reason you think that Largeness is one.”
“That is true,” he said.
“What happens if you take Largeness itself and the other large things and look at all of them in this way in your soul ? Will there not appear some one large thing by which all these appear to be large ?”
“It seems so.”
“Then, another Form of Largeness will appear, besides Largeness and the things that partake of it. And in addition to all these, yet another, by which all these will be large. And then no longer will each Form be one, but it will be unlimited in plurality.”2

  • 3 The word ὅµοιον is usually translated as ‘like’ or ‘similar’ in English, semblable in French. In no (...)

3Parmenides is here summarizing for Socrates the hypothesis about Forms that he has been assuming in his arguments with Zeno’s defense of Parmenides’ One. Whenever Socrates believes that many things are large, he then infers that there is an Idea of Largeness ‘over and above’ (ἐπί). Although the text is not explicit on this point, this Idea is presumably intended to explain the existence of a phenomenon, namely, that there can be ‘many large things’. How is it supposed to do this ? Again, presumably, it is somehow the supposition that if there is one Largeness, then there can be many large things. That is, there can be many things that are the same (ὅµοιον) insofar as they are large.3 This one Largeness is what we find in each large thing ; but its nature is such that its presence in one large thing does not preclude its presence in another. This is by contrast with other ‘things’ whose presence ‘here’ precludes their presence ‘there’. Socrates believes that the only way that the hypothesized Idea of Largeness can serve its proposed function is if it is ‘over and above’ the instances of largeness, that is, over and above the large things. For now, I shall just mention that ‘over and above’ must at least mean ‘other than’, that is, ‘distinct from’ the instances of largeness that constitute our initial datum. What more it may mean remains to be determined.

4Parmenides, in reply to Socrates’ agreement that this is a fair way to express his theory, asks him to look at this Idea or Form and the ‘other large things’ ‘in his soul’ and to consider if, as in the previous case, he will need to hypothesize another Form ‘over and above’ in order to account for the sameness found in the original Form and in the ‘other large things’. With this concession on Socrates’ part, we can easily see the start of the infinite regress. But it is extremely important to understand why this is a vicious infinite regress. The original hypothesis as articulated by Parmenides is that there is one Idea or Form ‘over and above’ that is needed to account for the cases of sameness found among things. But the Form that is ‘over and above’ the original Form of Largeness and the original many cases of largeness is, by the logic of the argument, both ‘over and above’ the original Form and, evidently, identical with it. For it, too, is the Form of the original many cases of largeness. So, the original Form is both one and infinitely many, which is as much as to say that it is not simply or unequivocally one. Its identity is, as it were, infinitely exploded. But since the hypothesis of the Form was the hypothesis of a unique Form, a Form that is simply one, then that original hypothesis cannot stand.

  • 4 See G. Fine, On Ideas. Aristotle’s Criticism of Plato’s Theory of Forms, Clarendon Press, Oxford, 1 (...)
  • 5 See Tht. 186A-D where the refutation of the definition of knowledge as perception depends on showin (...)

5It has frequently been maintained in the literature that Socrates should not have conceded that the original many cases of largeness and the original Form of Largeness constitute a legitimate many, that is, the sort of many that requires hypothesizing a Form over and above it to explain the sameness among this many.4 When we turn to Proclus in a moment, we shall see that he clearly understood that this is a superficial response to the TMA. For when Socrates is asked to consider the original many cases of largeness and the Form of Largeness, he is asked to ‘look at them in the soul’. I take it that this qualification ‘in the soul’ is not gratuitous ; it is meant to indicate a contrast with looking at them in another way, presumably, with his eyes. Of course, one cannot look at the Form of Largeness with one’s eyes. So, what would it mean to look at the many cases of largeness other than with one’s eyes, that is, with one’s soul ? Surely, the largeness of large things is not visible either.5 What Socrates is being asked to do is consider the largeness of large things and the largeness of the Form of Largeness. This is something he can do with his soul, that is, with his intellect. But when he does this, he is already committed to allowing that the largeness of the Form of Largeness is ‘over and above’ the ‘largeness’ of the cases of largeness that he is considering. He is also implicitly constrained to admit that, though it is the case that the largeness of the Form of Largeness is no larger than is the largeness in any one case of largeness, it does nevertheless have largeness in it. Those who think that the TMA is defeated by insisting that the Form of Largeness is not large are off the mark. That is true but irrelevant. For the original phenomenon of sameness is among the cases of largeness in large things, not the things that are large themselves. That is why one can ‘look at them with one’s soul’ ; one cannot look at, say, a large building with one’s soul, whereas that is exactly what one can do with the largeness of a large building. So, Socrates is not in a position to complain that the grouping of the original Form and the original cases of largeness into a new group requiring a Form ‘over and above’ is illegitimate. The reason for positing a Form ‘over and above’ in the first place seems to apply with equal force to the positing of a Form ‘over and above’ the original Form and the original many cases of largeness.

6Nor is Socrates obviously in a position to claim that the largeness that is the Form of Largeness or rather is what the nature of the Form of Largeness is and the largeness in large things are somehow different such that they cannot be grouped together as the same requiring a Form ‘over and above’. He does try this approach in what has come to be called the TMA 2 :

  • 6 Parm. 132C12-D4 : Ἀλλ᾽ οὐδὲ τοῦτο, φάναι, ἔχει λόγον, ἀλλ᾽, ὦ Παρµενίδη, µάλιστα ἔµοιγε καταφαίνετα (...)

“Alright, Parmenides, matters really seem to me to be like this : the Forms are just like models standing in nature, and these other things are images and likenesses of them, and participation itself by these others in the Forms comes about in no other way than by being made images of them.”6

7Socrates is here suggesting that we stipulate the Form as a model (παράδειγµα) and the instance as an image (εἰκών) or a likeness (ὁµοίωµα). This likeness amounts to something being ‘imaged’ in relation to the model or paradigm. We have already seen that the ground for hypothesizing a Form in the first place is sameness, that is, ὁµοιώτης, the identical word being used here and which I render as ‘likeness’. The point is surely that a ὁµοίωµα of a Form might be thought not to be ὁµοίον that Form – and so paving the way for the vicious infinite regress – provided that it is made in that Form’s image. But Parmenides quickly disabuses Socrates of this conceit.

  • 7 Parm. 132D5-133A4 : Εἰ οὖν τι, ἔφη, ἔοικεν τῷ εἴδει, οἷόν τε ἐκεῖνο τὸ εἶδος µὴ ὅµοιον εἶναι τῷ εἰκ (...)

“If, then, something is an image of a Form, can that Form not be like that which was made as an image of it, just insofar as it was made the same as that Form ? Or is there some way in which that which is the same as something is not the same as that which is the same as it ?”
“There is not.”
“And must not the thing which is the same as that which is large share with the thing that is the same as it the same thing ?”
“Necessarily.”
“And will not that in which the same things share be the Form itself ?”
“Absolutely.”
“If so, then, it is not possible for something to be the same as the Form or for the Form to be the same as anything else ; otherwise, a second form will always appear, and if that Form is the same as anything, then another one will appear, and there will never stop being a new Form coming to be, if the Form is to be the same as the thing that partakes in it.”
“Most true.”7

8Granted the fact that the instance of a Form is an image of it, this does not preclude the sameness of the image and that which is imaged. This is so because sameness is a reciprocal relation : if A is the same as B, then B is the same as A. The fact that A is made in the image of B is neither here nor there with respect to their sameness. Specifically, if an image is truly an image, then we can consider it ‘just insofar as’ it is the same as that of which it is an image. Consider, for example, the sameness of the proportions of a blueprint and the house that is built according to that blueprint. This sameness is not negated by the fact that the house and the blueprint each have, as it were, a different ontological status. If it were not possible to consider the original just insofar as it is the same as its image or copy, in what sense would it be an image ? Stated otherwise, if A is not the same as B, what does it mean to call it an image of B as opposed to an image of C ? And given this sameness, the original infinite vicious regress arises again.

  • 8 See H. Cherniss, “The Relation of the Timaeus to Plato’s Later Dialogues”, originally in American J (...)

9Parmenides’ argument is not sophistical, as some scholars maintain.8 Nor, as we have seen, is it answered by insisting that the Forms are not self-predicative. If, though, some sort of theory of Forms is to be retained, the argument has to be answered. This answer requires us to probe a bit more deeply into the ontology of the intelligible world than contemporary scholars are inclined to do. Of course, this probing, that is, the exploration of the implications of the existence of intelligible entities in the first place, is the stock in trade of Platonism in late antiquity. To that we now turn.

Proclus and the TMA

  • 9 See Proclus, In Tim. I. 13.14-19, who seems to identify Iamblichus as the first to order the study (...)
  • 10 See In Parm. 630, 15 - 645, 8.

10The importance of Plato’s Parmenides to late Platonism is well known. Along with Timaeus, this dialogue was studied as the culmination of one’s philosophical education.9 Consequently, Proclus takes great pains to offer an exposition and criticisms of various interpretations of the dialogue, in particular the relation of the second part to the first.10 Proclus’ own interpretation, of course, aims to show that in the second part of the dialogue, the correct responses to Parmenides’ challenges to Socrates are found.

  • 11 See In Tim. II. 313, 15ff.

11The essence of Proclus’ solution to the TMA­­ – a solution that may well have originated in Iamblichus11 – is that a real distinction must be recognized within the Form such that we can distinguish that in it which is participated and that in it which is not.

  • 12 In Parm. 890, 1-14 : Ὥσπερ οὖν ἐπὶ τῆς προτέρας ἀπορίας ἐλέγοµεν, ὅτι τὰ εἴδη καὶ πάρεστι τοῖς µετέ (...)

“As we said, then, in connection with the previous problem that the Forms both are present to their participants through imparting a share in themselves, and are not present by reason of their transcendent essence, even so in the case of the second problem we shall say that the Forms both commune with their participants and do not commune with them ; to the extent that they illuminate them from their own essence, they commune with them, but to the extent that they are unmixed with what they illuminate, they do not commune ; so that it is not for themselves, but for the things derived from them, that they have generated a certain degree of likeness. For this reason, indeed, it may be said that they commune in some way through these means with those entities which receive them, but this communion is not that of synonyms, but rather of primary and secondary participants in a term.” (Morrow/Dillon trans.)12

  • 13 El. theol. §23.
  • 14 In Parm. 887, 29-35 : ... ἵνα δὲ µένῃ τὰ µετέχοντα τῆς ἰδέας ἀεὶ καὶ µηδέποτε ἐκλείπῃ, δεῖ τινος ἄλ (...)

12This solution here clearly consists of a distinction within a Form according to which there can be µεταδόσις of a Form at the same time that the Form is separate. That which the Forms give – the nature that its name names – is distinct from that which is not given. This is, of course, not a mere conceptual distinction ; it is, in the useful Scholastic jargon, a real minor distinction. A real minor distinction is a distinction within one entity as opposed to a real major distinction, which is a distinction among different entities. The realness of a real distinction, as opposed to a conceptual distinction, is that it is prior to and independent of our language or concepts. It is the distinction that in the Elements of Theology is designated to be the distinction between the unparticipated (τὸ ἀµέθεκτον) and the participated (τὸ µετεχόµενον).13 With this distinction, we can reply to Parmenides that participation in a Form is more precisely participation in the nature that the Form’s name names, not participation in the Form itself, which is really distinct from that nature. Consequently, though the largeness in the Form of Largeness is the same as the largeness in large things, the Form that accounts for this sameness is not another Form ‘over and above’, but the original unparticipated Form.14

13Τhe crucial question, then, is what is the justification for such a distinction ? After all, it might be maintained that a real minor distinction is possible only within or for a body, not for a bodiless entity like a Form. One might want to argue that bodiless or immaterial entities are essentially simple and that even if there are Forms, there is no real distinction within it between it and its nature. One might maintain that it is arbitrary to insist that participation in a Form can in any way leave the Form unparticipated.

  • 15 Εἰ ἔστιν, ἆρα οἷόν τε αὐτὸ εἶναι µέν, οὐσίας δὲ µὴ µετεχειν; Οὐχ οἷόν τε.

14The Platonic text to which all Platonists will recur in justifying the above distinction is Parmenides 142B5-6 : “Is it, then, possible for it [the One] to be, and for it not to partake of being ? It is not possible.”15 For anything that has being or οὐσία, there is a real minor distinction between it and its being. The precise argument for this claim is found in Plotinus.

  • 16 The possibility of real distinctiveness within one thing follows from a denial of nominalism, which (...)

15In Ennead V, 4 [7] 1, Plotinus, explicating the Platonic position, argues that : (1) every composite must be accounted for by that which is incomposite or absolutely simple and (2) there can be only one absolutely simple thing. We can better understand the reasoning for (1) if we concentrate first on the reasoning for (2). Assume that there is more than one absolutely simple thing. Then, there would have to be something that each one had that made it at least numerically different from the other, say, for example, a unique position. But that which made it different would have to be really (not merely conceptually) distinct from that which made it to be the one thing it is.16 That which had the position would be really distinct from the position itself. But then something which had a position and so was distinct from it would not be absolutely simple. So, that which is absolutely simple must be absolutely unique. Only the first principle of all is unqualifiedly self-identical ; the self-identity had by anything else is necessarily qualified. This argument suggests the meaning of ‘composite’ that Plotinus has in mind when he argues for (1). A composite is anything that is distinct from any property it has. What we might call a ‘minimally composite individual’ is one with one and only one property from which it is itself distinct. Compositeness is, then, equivalent to qualified self-identity. Anything with οὐσία is at least minimally composite.

  • 17 See In Parm 879, 11-12.

16If, in a Form, it and its οὐσία were not really distinct, then either the Form would not have an οὐσία or else it would be nothing but οὐσία. In the former case, there would, of course, be no reason to posit a Form to account for one sort of sameness rather than another ; the Form would be a completely empty explanans. In the latter case, the Form would become nothing more than a common nature, that is, what all things that are the same have. But the common nature as such does not explain anything. This is so because the common nature is in itself neither one nor many ; in itself it has no existence as one or as many. The common nature as such is posterior, not prior, to that of which it is the common nature. Hence, it cannot explain the existence of anything. To recognize its existence is to recognize it as really distinct from its οὐσία. So, we can conclude that it is the οὐσία of the Form, not the Form itself, that is participated in, whereas the Form itself is unparticipated. Proclus refers to the οὐσία that is participated in as φύσις and the οὐσία as participating, φυσικὸς λόγος.17 The latter is the expression of the φύσις in what is ontologically posterior.

  • 18 In Parm., 880, 8-11 : οὔτε συνώνυµον εἶναι χρὴ τὸ ἐν τοῖς ὑφ᾽ ἑαυτὸ πολλοῖς, ἵνα µὴ πάλιν εἷς ὢν ἀµ (...)

17Even if the vicious infinite regress argument is stopped by the above strategy, one might still want to contend that there is a synonymy between the nature that the Form is and the ‘physical’ λόγος. This Proclus decisively rejects ; the relation between the former and the latter is ἀφ᾽ἑνὸς καὶ πρὸς ἕν18 Proclus evinces no discomfort in recognizing the πρὸς ἕν relation as Platonic, which is to say that its fundamental use by Aristotle is not viewed as an anti-Platonic move. How are we to understand the claim that there is no synonymy between the nature that the Form is and that nature in its instances, even though there is sameness ? Stated otherwise, how are we to understand the claim that a man is unequivocally said to be large, even though his largeness is not synonymous with the largeness of the Form of Largeness ?

  • 19 See El. theol. §30. Cf. Plotinus, Enn. V, 2 [11] 2.

18There is scarcely anything more central to Platonism than the explication and defence of this claim. Proclus’ general defence is presented in his Elements of Theology.19 The gist of the defence relies on the distinction, drawn from Plato’s Parmenides, and echoed in Aristotle’s Metaphysics, between sameness (ἡ ὁµοιώτης) and identity (ἡ ταυτότης). The Form cannot be identical with its instance ; if it were, then there could not be multiple instances, which is as much as to say that there could not be many things that are the same. Yet it is the identical or, better, self-identical nature that is present in the Form and the instance. That nature is present in the Form as cause, and present in the instance as effect. The reason that the cause is not synonymous with the effect even though it is the same as it is that a true cause is such that its entire nature is to be that cause. That is, for example, the Form of Largeness as cause is nothing but largeness, whereas the effect is, say, the largeness of the man or the building. There is less being or derivative being in the latter in the precise sense that the largeness in each, though it is largeness, is occluded or ‘compromised’ largeness. Thus, the only way that the man can be large is by being of a certain size, whereas the nature of largeness has nothing to do with being of a certain size. That precise size, of course, could also constitute the man’s smallness.

  • 20 See In Parm. 885, 1-6 : Ἄλλο ἄρα δεῖ πρὸ τῶν ὁµοίων εἶναι τὸ τῶν ὁµοίων αἴτιον, καὶ δεῖ διὰ ταῦτα ἀ (...)

19The Form is thus a formal cause or explanation (τὸ αἴτιον). In what sense, then, is the instance an effect ? It would be more accurate to say that the nature of the Form is the formal cause and that the Form itself is a productive cause of which the instance is an effect.20 The Form is a productive cause owing to the fact that it is the perfect exemplar of the nature it is, and everything perfect produces. The Form produces according to its nature that which it is capable of producing. The general principle that explains this production is, of course, bonum est diffusivum sui. That which is essentially good of a certain kind necessarily produces according to its nature. The evidence for this bold assertion is simply the very existence of the variegated universe.

  • 21 In Parm. 886, 40-1.

20The Form is self-caused or self-explaining as well as being the cause of its instances.21 This is perhaps the clearest way to explain the transcendence of the Form. In general, if X is self-caused and the cause of Y, then X transcends Y, that is, it is not identical with Y and can exist even if Y does not. As we know, for Plotinus, only the One is self-caused. For Proclus, the self-causality of the Forms is a sort of relative self-causality. That is, it is self-caused only within its own ‘line of causality’. For example, the only explanation for the being of Largeness is the Form of Largeness itself. What this means, I take it, is that the being or existence of any Form does not have an explanation outside of it and independent of the explanation (or non-explanation) for its nature.

  • 22 See In Parm. 885, 26ff.
  • 23 The central passage on the range of Forms is In Parm. 815, 15ff.
  • 24 See In Parm. 796, 24 ; 978, 30 ; 978, 34, et cet.
  • 25 In Parm. 831, 27.
  • 26 See In Parm. 880, 30-6 : Ὅθεν καὶ ὁ ἐν τῷ Φιλήβῳ Σωκράτης ποτὲ µὲν ἑνάδας καλεῖ τὰς ἰδέας, ποτὲ δὲ (...)

21The fact that the Form is not synonymous with its instances entails that the Form is not to be identified with that which is common (τὸ κοινόν) among particulars. Thus, insofar as a universal is taken to be that which is common, the Form is not a universal. The point here is, I think, that any two or more things can be seen to have something in common. But this commonality is not what requires the hypothesizing of a Form. For example, two things can have in common the fact that they are owned by me. That is why we cannot suppose that the commonality among non-existent things forces us to hypothesize Forms for them.22 Mere commonality differs from the sameness that does require the hypothesizing of a Form in this way. A genuine case of sameness is a case where there is a single nature, hence a single Form whose nature that nature is. Commonality does not entail such a single nature, though it seems that it does not exclude that possibility. So, commonality is a broader notion than sameness, though it includes it.23 It is apparently for this reason that Proclus­ – unhelpfully in my view – does say that the Form is a universal.24 He also says that Forms are of universal substances (τῶν καθολικῶν οὐσιῶν).25 I take it that what Proclus is here trying to convey is that the nature that a Form has is universal ; thus, there are no Forms of particulars as such. But the Form itself cannot be a universal because a Form is one – a henad with respect to its instances and a monad with respect to the One.26

  • 27 See Metaph. VII 13, 1038b35-1039a3 ; VII 16, 1040b25-30 ; XIII 9, 1086a32-5.
  • 28 Cf. In Parm. 881, 27-33 ; 888, 2-4 ; Syrianus, In Metaph. 106, 26-107, 1.

22The point is of some importance since Aristotle’s principle objection to the theory of Forms he considers in his Metaphysics is that Forms must be substances because they are separate, but they must also be universals because they are predicated of many things.27 It seems that the absence of synonymy precludes the predication. That is, a predicate is univocally said of its instances. The Form of course cannot be predicated of its instances because in itself it is unparticipated. The nature of a Form is participated, so it would seem to be univocally predicable of its instances. But neither is it a universal ; in itself it is neither one nor many. This nature, only as it exists in an intellect, is universal. Perhaps the sense in which the Form is a universal refers, then, to its existence as intelligible object for the Intellect.28

Forms as ‘paradigms standing in nature’

23Commenting on Socrates’ suggestion that Forms are ‘paradigms standing in nature’, Proclus identifies Socrates’ error as thinking that the Forms are ‘static’ and therefore not active causes. But if this were the case, then there would be more activity in the instances than in the Forms, which is absurd. Therefore, the causality of the Forms is indeed active or efficient causality :

  • 29 In Parm. 908, 28-909, 12 : Ἕκαστον γὰρ εἶδος οὐ παράδειγµα µόνον ἐστὶ τῶν αἰσθητῶν, ἀλλὰ καὶ ὑποστα (...)

“Each Form is not only a pattern to sensible objects, but is also the cause of their being ; for they do not require any other force to produce things in their own image and to assimilate to themselves the things of this realm, while remaining themselves inactive and motionless and without any productive capacity, like wax moulds in this realm, but rather they themselves produce and generate their own images. It would be absurd, after all, if the reason-principles in nature were to possess a certain creative power, while the intelligible Forms should be devoid of any causal role in creation. So, then, every divine Form has not only a paradigmatic aspect, but a paternal one as well, and by virtue of its very being is a generative cause of the many particulars ; and not only this, but is a cause of completion to them ; for it possesses the faculty of leading the things of this realm from an incomplete state to completion and of conferring goodness upon them, and of filling out their lack, and leading matter, which is all things potentially, to being actually all that it was potentially before the creative onset of the Forms. The Forms, you see, have also this perfective faculty within them.” (Morrow/Dillon trans.)29

  • 30 In Parm. 909, 22-9.
  • 31 Cf. Tim. 29D, 30E. Cf. In Parm. 911, 1-7 : ἐν Τιµαίῳ δὲ τὸ παράδειγµα εἰκόνος εἶναι παράδειγµά τινο (...)

24As Proclus goes on to claim, not only is the Form generative and perfective, but it is also preservative (φρουρητική), cohesive (συνεκτικός), and unitative (ἑνωτικός).30 In making this claim, Proclus is taking to its logical conclusion the standard Platonic understanding of the identity of Intellect and intelligible, that is, of the Demiurge and the Forms or, as Proclus puts it, the creative and the paradigmatic causes. He refuses to see the Demiurge as active and the Forms as static patterns ‘observed’ by the Demiurge prior to his imposition of intelligibility on the sensible world. Proclus here seems to be thinking of the passages in Timaeus in which the Demiurge is said to want the cosmos both to resemble the Forms and to resemble himself.31 This only makes sense if there is an extensional equivalence between the Demiurge and the Living Animal to which he looks.

  • 32 In Parm. 913, 14.
  • 33 See In Parm. 886.4ff. Vlastos, art. cit., identified ‘the self-predication assumption’, along with (...)

25Proclus repeats the point about the non-synonymous sameness of Form and instance, but adds an additional crucial consideration. Forms do not have properties (οὐδὲν πέπονθε).32 Thus, the real distinction between a Form and its nature is not a distinction between a substance and its properties, as is, for example, in a sensible substance and its properties. How, if the largeness of the large building, which is a property of that building, is the same as the largeness in the Form of Largeness is the latter not a property of that Form ? The general answer to this question seems to be that the compositeness of an intellectual and intelligible entity is not the sort of compositeness that allows the specific real minor distinction that exists between a substance and its properties. I speculate that this has something to do with the fact that sensible substances are extensive magnitudes and the real distinctiveness within them depends upon this. In any case, since largeness is not a property of the Form of Largeness, the Form is not self-predicative. Whether or not Proclus is correct in thinking that Parmenides is being made to raise a problem for the theory of Forms to which he already knows the correct solution, it is clear enough that, according to Proclus’ understanding, those scholars who think that Plato is wedded to the so-called self-predicative assumption are simply mistaken.33

26At the conclusion of Parmenides’ refutation of Socrates’ suggestion that the Form is a paradigm fixed in nature, Parmenides appears to make a specific point :

  • 34 Parm. 133A5-7 : Οὐκ ἄρα ὁµοιότητι τἆλλα τῶν εἰδῶν µεταλαµβάνει, ἀλλά τι ἄλλο δεῖ ζητεῖν ᾧ µεταλαµβά (...)

“Then, it is not by sameness that other things share in Forms, but one must seek some other way by which they share.”34

  • 35 See In Parm. 915, 32ff.

27Are we supposed to take from this the conclusion that instances of Forms are not the same as the Forms, a conclusion that would go beyond the one already reached to the effect that the instances are not synonymous with the Forms ? Proclus’ reply to this question is not altogether clear ; he does appear somewhat puzzled by the relation between, say, the Form of Man and the Form of Sameness.35 But his somewhat tentative answer provides further insight into his understanding of the metaphysics of the intelligible world.

  • 36 In Parm. 916, 15-23 : ἆρα ὁ ἄνθρωπος ποιεῖ τὸν τῇδε ἄνθρωπον µόνον, ἢ καὶ ὅµοιον ἑαυτῷ ποιεῖ, καὶ π (...)

28Proclus proposes the following dilemma : does the Form of Man make a man the same as the Form or not ? If it does, then the work of the Form of Sameness is duplicated or eliminated for that Form ; if it does not, then the Form of Man is not producing a man, that is, something with the same nature as the Form.36 The solution that Proclus wants to provide to this dilemma is that Forms work together (πάντα µετ᾽ ἀλλήλων ἐνέργεῖ καὶ γεννᾷ). It is wrong to suppose that their work is dispersed (διασπᾷν), that is, that their works are not necessarily connected. So, the man is a man by the Form of Man and he is the same as that Form by the Form of Sameness.

29This proposal faces the difficulty that the cooperation of the Forms or their lack of dispersion threatens the integrity of each. For instance, if the Form of Man is not in some way dispersed from the Form of Sameness in producing the man, presumably, the same can be said for the Form of Dog in producing the dog. That is, it, too, is not dispersed from the Form of Sameness. But the Form of Man does not thereby produce a dog nor does the Form of Dog produce a man even though neither of them is dispersed from the Form of Sameness.

  • 37 See Soph. 254D-255C.
  • 38 Soph. 255E3-6.
  • 39 Cf. In Parm. 973, 1-3.
  • 40 Cf. In Parm. 974, 7-14 : Τὸ δέ γέ τι προσκείµενον δηλοῖ τὸ µοναδικὸν αὐτοῦ καὶ τὸ ἐν ἀρχῆς λόγῳ προ (...)

30It will be noticed that this problem is analogous to the problem in Plato’s Sophist where it is shown that the Form of Self-Identity (τὸ ταὐτόν) is different from the Form of Being (τὸ ὄν) and the Form of Difference (τὸ θάτερον).37 Plato’s argument works for self-identity, difference, and being because he says that each of these Forms partakes of each other, that is, Being is different from Self-Identity owing to its partaking in the Form of Difference, and Difference is different from Self-Identity owing to its partaking in itself.38 If, however, Proclus accepts this solution, it would seem that he would have to allow that the unparticipated Form does participate. In the case of the above example, the Form of Man will participate in the Form of Sameness. Strictly speaking, there is no contradiction in maintaining that a Form that is unparticipated in relation to that which participates in its nature nevertheless does participate. But, of course, it must participate in the nature of another Form, not in that Form insofar as it is unparticipated. So, we have unparticipated Forms ‘communing’ among themselves, in Plato’s words, while each is distinct from the other. Apart from the obvious problem that the Form’s nature as participated is supposed to be on a higher ontological level that that which participates in it, if the Intellect is cognitively identical with all that is intelligible, it would seem to follow that the array of unparticipated Forms is actually nothing but this Intellect.39 We have already seen that Proclus tends towards this position in his discussion of the Demiurge. But if this is the case, then the Demiurge is actually the henad that previously each Form was supposed to be.40

Conclusion

  • 41 In Parm. 888, 17-19.

31Perhaps it is a good time to conclude. It is certainly a relief to conclude by merely mentioning a puzzle about the henadic character of Forms. It is, I hope, clear that Proclus’ solution to the problem posed by the TMA – whether the core of that solution is original to Proclus or not – is superior to any alternative solution on offer today. I shall end by offering the following consideration. The Xenocratean definition of a Form, quoted by Proclus, namely, that the Form is “the paradigmatic cause of whatever is composed continually according to nature” should not be taken as a principle from which we are supposed to derive directly the range of Forms.41 According to this definition, Proclus can leave as a scientific research project the question of exactly what is produced continually according to nature. If, for example, advances in science lead to the discovery that the elements hitherto thought to be four in number are in fact more than 30 times that number, and that the original elements are in fact natural compounds or, indeed, that they are not single compounds, nothing changes for the theory of Forms. If – and this is a more provocative and far reaching point – it should turn out that the paradigms of things that are produced by nature are in fact mathematical, we would still require these paradigms in order to account for the intelligibility of nature. In this case, however, there would be somewhat less motivation to distinguish the henadic character of one ideal mathematical ratio from another.

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Notes

1 It is fair to say that modern discussion of this argument begins from an article more than fifty years ago by Gregory Vlastos. See “The Third Man Argument in Plato’s Parmenides”, Philosophical Review, 63, 1954, pp. 319-49. This article continues to dominate the discussion of the argument. Here, I limit my references to (a) works in English, (b) works written in the last twenty years, and (c) works that focus on the TMA. See D. Bailey, “The Third Man Argument”, Philosophy Compass, 4, 2009, pp. 666–681 and S. Rickless, Plato’s Forms in Transition, Cambridge University Press, Cambridge, 2006, for the most recent detailed examination of the argument. Some other notable recent detailed discussions of the argument and surrounding issues are : R. Dancy, Plato’s Introduction of Forms, Cambridge University Press, Cambridge, 2004 ; G. Fine, Plato on Knowledge and Forms, Clarendon Press, Oxford, 2003 ; S. Scolnicov, Plato’s Parmenides. Translation with Introduction and Commentary, University of California Press, Berkeley, 2003 ; A. Silverman, The Dialectic of Essence, Princeton University Press, Princeton, 2002 ; V. Harte, Plato on Parts and Wholes, Clarendon Press, Oxford, 2002 ; R. Patterson, “Forms, Fallacies, and the Functions of Plato’s Parmenides”, Apeiron, 32, 1999, pp. 89–106 ; R. Turnbull, The Parmenides and Plato’s Later Philosophy, University of Toronto Press, Toronto, 1998 ; S. Rickless, “How Parmenides Saved the Theory of Forms”, Philosophical Review, 107, 1998, pp. 501–554 ; D. Hunt, “How (not) to Exempt Platonic Forms from Parmenides’ Third Man”, Phronesis, 42, 1997, pp. 1–20 ; K. Sayre, Parmenides’ Lesson : Translation and Explication of Plato’s Parmenides, University of Notre Dame Press, South Bend, IN, 1996 ; C. Meinwald, Plato’s Parmenides, Oxford University Press, New York,1991.

2 Parm. 132A1-B2 : Οἶµαί σε ἐκ τοῦ τοιοῦδε ἓν ἕκαστον εἶδος οἴεσθαι εἶναι· ὅταν πόλλ᾽ ἄττα µεγάλα σοι δόξῃ εἶναι, µία τις ἴσως δοκεῖ ἰδέα ἡ αὐτὴ εἶναι ἐπὶ πάντα ἰδόντι, ὅθεν ἓν τὸ µέγα ἡγῇ εἶναι. Ἀληθῆ λέγεις, φάναι. Τί δ᾽ αὐτὸ τὸ µέγα καὶ τἆλλα τὰ µεγάλα, ἐὰν ὡσαύτως τῇ ψυχῇ ἐπὶ πάντα ἴδῃς, οὐχὶ ἕν τι αὖ µέγα φανεῖται, ᾧ ταῦτα πάντα µεγάλα φαίνεσθαι; Ἔοικεν. Ἄλλο ἄρα εἶδος µεγέθους ἀναφανήσεται, παρ᾽ αὐτό τε τὸ µέγεθος γεγονὸς καὶ τὰ µετέχοντα αὐτοῦ· καὶ ἐπὶ τούτοις αὖ πᾶσιν ἕτερον, ᾧ ταῦτα πάντα µεγάλα ἔσται· καὶ οὐκέτι δὴ ἓν ἕκαστόν σοι τῶν εἰδῶν ἔσται, ἀλλὰ ἄπειρα τὸ πλῆθος. Translations are the author’s except where noted.

3 The word ὅµοιον is usually translated as ‘like’ or ‘similar’ in English, semblable in French. In non-philosophical Greek, this translation is relatively harmless. For translating philosophical Greek, and Plato in particular, it is at best misleading. Anything can be held to be like or similar to anything else. It is not likeness or similarity that leads to the postulation of Forms, but sameness. This is because likeness or similarity is not a relation ; it is likeness or similarity in some respect, that is, sameness, that is the relevant relation. Because two things are the same (e.g., tall or equal or blue), they are indeed like or similar. But it is the sameness that generates a self-identical (ταὐτόν) Form, not the likeness.

4 See G. Fine, On Ideas. Aristotle’s Criticism of Plato’s Theory of Forms, Clarendon Press, Oxford, 1993, chs. 4 and 15 for a careful analysis of the various senses in which the one-over-many principle might or might not lead to the TMA. The point is not that Plato could not simply limit legitimate ‘manies’ to the sensible world, but that it might be arbitrary to do so.

5 See Tht. 186A-D where the refutation of the definition of knowledge as perception depends on showing that we cannot see with our eyes the properties of sensible things.

6 Parm. 132C12-D4 : Ἀλλ᾽ οὐδὲ τοῦτο, φάναι, ἔχει λόγον, ἀλλ᾽, ὦ Παρµενίδη, µάλιστα ἔµοιγε καταφαίνεται ὧδε ἔχειν· τὰ µὲν εἴδη ταῦτα ὥσπερ παραδείγµατα ἑστάναι ἐν τῇ φύσει, τὰ δὲ ἄλλα τούτοις ἐοικέναι καὶ εἶναι ὁµοιώµατα, καὶ ἡ µέθεξις αὕτη τοῖς ἄλλοις γίγνεσθαι τῶν εἰδῶν οὐκ ἄλλη τις ἢ εἰκασθῆναι αὐτοῖς.

7 Parm. 132D5-133A4 : Εἰ οὖν τι, ἔφη, ἔοικεν τῷ εἴδει, οἷόν τε ἐκεῖνο τὸ εἶδος µὴ ὅµοιον εἶναι τῷ εἰκασθέντι, καθ᾽ ὅσον αὐτῷ ἀφωµοιώθη; ἢ ἔστι τις µηχανὴ τὸ ὅµοιον µὴ ὁµοίῳ ὅµοιον εἶναι; Οὐκ ἔστι. Τὸ δὲ ὅµοιον τῷ ὁµοίῳ ἆρ᾽ οὐ µεγάλη ἀνάγκη ἑνὸς τοῦ αὐτοῦ [εἴδους] µετέχειν; Ἀνάγκη. Οὗ δ᾽ ἂν τὰ ὅµοια µετέχοντα ὅµοια ᾖ, οὐκ ἐκεῖνο ἔσται αὐτὸ τὸ εἶδος; Παντάπασι µὲν οὖν. Οὐκ ἄρα οἷόν τέ τι τῷ εἴδει ὅµοιον εἶναι, οὐδὲ τὸ εἶδος ἄλλῳ· εἰ δὲ µή, παρὰ τὸ εἶδος ἀεὶ ἄλλο ἀναφανήσεται εἶδος, καὶ ἂν ἐκεῖνό τῳ ὅµοιον ᾖ, ἕτερον αὖ, καὶ οὐδέποτε παύσεται ἀεὶ καινὸν εἶδος γιγνόµενον, ἐὰν τὸ εἶδος τῷ ἑαυτοῦ µετέχοντι ὅµοιον γίγνηται. Ἀληθέστατα λέγεις.

8 See H. Cherniss, “The Relation of the Timaeus to Plato’s Later Dialogues”, originally in American Journal of Philology, 1957, reprinted in R.E. Allen (ed.), Studies in Plato’s Metaphysics, Routledge, & Kegan Paul, London, 1965, pp. 338-78. The discussion of the import of Parmenides’ criticisms is found at 364ff.

9 See Proclus, In Tim. I. 13.14-19, who seems to identify Iamblichus as the first to order the study of the dialogues in this way. Cf. Theol. Plat I 8, 32.15-18.

10 See In Parm. 630, 15 - 645, 8.

11 See In Tim. II. 313, 15ff.

12 In Parm. 890, 1-14 : Ὥσπερ οὖν ἐπὶ τῆς προτέρας ἀπορίας ἐλέγοµεν, ὅτι τὰ εἴδη καὶ πάρεστι τοῖς µετέχουσιν αὑτῶν διὰ τῆς µεταδόσεως, καὶ οὐ πάρεστι διὰ τῆς χωριστῆς ὑποστάσεως, οὕτω καὶ ἐπὶ τῆς δευτέρας ἐροῦµεν καὶ κοινωνεῖν τὰ εἴδη τοῖς µετέχουσι, καὶ µὴ κοινωνεῖν· τῷ µὲν ἀφ᾽ ἑαυτῶν ἐλλάµπειν αὐτὰ, κοινωνεῖν, τῷ δὲ ἀµιγῶς εἶναι πρὸς τὰ ἐλλαµπόµενα, µὴ κοινωνεῖν· ὥστε οὐχ ἑαυτοῖς, ἀλλὰ τοῖς ἀπ᾽ αὐτῶν παρεσπάσατό τινα ὁµοιότητα πρὸς αὐτά· διὰ δὴ τοῦτο λέγεσθαι κἀκεῖνα τοῖς ταῦτα δεξαµένοις διὰ τούτων τρόπον τινὰ κοινωνεῖν, καὶ εἶναι τὴν κοινωνίαν, οὐχ ὡς ἐν συνωνύµοις, ἀλλ᾽ ὡς δευτέροις καὶ πρώτοις.

13 El. theol. §23.

14 In Parm. 887, 29-35 : ... ἵνα δὲ µένῃ τὰ µετέχοντα τῆς ἰδέας ἀεὶ καὶ µηδέποτε ἐκλείπῃ, δεῖ τινος ἄλλης αἰτίας, οὐκ ἐν αὐτοῖς οὔσης ἢ κινουµένης, ἀλλ᾽ ἐφ᾽ ἑαυτῆς ἱδρυµένης, πρὸ τῶν κινουµένων ἀκινήτου, καὶ διὰ τὴν οἰκείαν σταθερότητα προξενούσης καὶ τοῖς κινουµένοις τὴν ἀνέκλειπτον µετοχήν.

15 Εἰ ἔστιν, ἆρα οἷόν τε αὐτὸ εἶναι µέν, οὐσίας δὲ µὴ µετεχειν; Οὐχ οἷόν τε.

16 The possibility of real distinctiveness within one thing follows from a denial of nominalism, which is the view that all self-identity is unqualified self-identity. To claim, for example, that x is f, is for Platonists to acknowledge that f somehow identifies that which is nevertheless distinct from the identifying property.

17 See In Parm 879, 11-12.

18 In Parm., 880, 8-11 : οὔτε συνώνυµον εἶναι χρὴ τὸ ἐν τοῖς ὑφ᾽ ἑαυτὸ πολλοῖς, ἵνα µὴ πάλιν εἷς ὢν ἀµφοτέρων λόγος ἕτερον ἀπαιτῇ τι κοινὸν ἐπ᾽ αὐτοῖς· ἀλλ᾽ ὡς εἴρηται πολλάκις, ἀφ᾽ ἑνὸς καὶ πρὸς ἕν. See below and 912 ff.

19 See El. theol. §30. Cf. Plotinus, Enn. V, 2 [11] 2.

20 See In Parm. 885, 1-6 : Ἄλλο ἄρα δεῖ πρὸ τῶν ὁµοίων εἶναι τὸ τῶν ὁµοίων αἴτιον, καὶ δεῖ διὰ ταῦτα ἀπὸ τῶν καθέκαστα κοινῶν ἐπὶ τοῦτο ἀνατρέχειν τὸ ἕν, τὸ προσεχῶς ὑποστατικὸν τῶν αἰσθητῶν, ἐφ᾽ ὃ καὶ αὐτὸς ὁ Παρµενίδης ἡµᾶς ἀνήγαγεν. Cf. El. theol. § 25ff.

21 In Parm. 886, 40-1.

22 See In Parm. 885, 26ff.

23 The central passage on the range of Forms is In Parm. 815, 15ff.

24 See In Parm. 796, 24 ; 978, 30 ; 978, 34, et cet.

25 In Parm. 831, 27.

26 See In Parm. 880, 30-6 : Ὅθεν καὶ ὁ ἐν τῷ Φιλήβῳ Σωκράτης ποτὲ µὲν ἑνάδας καλεῖ τὰς ἰδέας, ποτὲ δὲ µονάδας· εἰσὶ γὰρ ὡς µὲν πρὸς αὐτὸ τὸ ἓν µονάδες, διότι καὶ πλῆθός ἐστιν ἑκάστη καὶ ὄν τι οὖσα καὶ ζωὴ καὶ εἶδος νοερόν· ὡς δὲ πρὸς τὰ ἀπ᾽ αὐτῶν παραγόµενα καὶ τὰς σειρὰς ἃς ὑφεστᾶσιν, ἑνάδες. Cf. In Eucl. 1, 50, 16-51, 13 ; Simplicius, In. Cat. 69, 19-71, 2.

27 See Metaph. VII 13, 1038b35-1039a3 ; VII 16, 1040b25-30 ; XIII 9, 1086a32-5.

28 Cf. In Parm. 881, 27-33 ; 888, 2-4 ; Syrianus, In Metaph. 106, 26-107, 1.

29 In Parm. 908, 28-909, 12 : Ἕκαστον γὰρ εἶδος οὐ παράδειγµα µόνον ἐστὶ τῶν αἰσθητῶν, ἀλλὰ καὶ ὑποστατικὸν αὐτῶν· οὐ γὰρ ἄλλου δεῖται τοῦ παράγοντος πρὸς αὑτὰ καὶ ἀφοµοιώσαντος αὑτοῖς τὰ τῇδε, µένοντα αὐτὰ ἀργὰ καὶ ἀκίνητα καὶ δραστηρίαν οὐδεµίαν ἔχοντα δύναµιν, ἀλλ᾽ ἐοικότα τοῖς ἐνταῦθα κηροπλαστικοῖς τύποις, ἀλλὰ καὶ αὐτὰ παράγει καὶ ἀπογεννᾷ τὰς ἑαυτῶν εἰκόνας· καὶ γὰρ ἄτοπον, εἰ οἱ µὲν ἐν τῇ φύσει λόγοι ποιητικὴν ἔχοιέν τινα δύναµιν, τὰ δὲ νοητὰ εἴδη τῆς τοῦ ποιεῖν αἰτίας παρῃρηµένα τυγχάνοι. Οὐ µόνον ἄρα παραδειγµατικόν ἐστι πᾶν τὸ θεῖον εἶδος, ἀλλὰ καὶ πατρικόν, καὶ αὐτῷ τῷ εἶναι γεννητικὸν αἴτιον τῶν πολλῶν· καὶ οὐ µόνον ταῦτα, ἀλλὰ καὶ τελεσιουργόν· αὐτὸ γὰρ τὸ ἐκ τοῦ ἀτελοῦς ἐπὶ τὸ τέλειον τὰ τῇδε περιάγον καὶ τὸ εὖ περιποιοῦν ἑκάστοις, καὶ τὸ τὴν ἔνδειαν αὐτῶν ἀποπληροῦν, καὶ τὴν ὕλην δυνάµει πάντα οὖσαν ἄγον εἰς τὸ κατ᾽ ἐνέργειαν γίνεσθαι ὁπόσον ἦν δυνάµει πρὸ τῆς εἰδοποιΐας· ἔχει ἄρα καὶ ταύτην τὴν τελεσιουργὸν ἐν ἑαυτοῖς τὰ εἴδη δύναµιν.

30 In Parm. 909, 22-9.

31 Cf. Tim. 29D, 30E. Cf. In Parm. 911, 1-7 : ἐν Τιµαίῳ δὲ τὸ παράδειγµα εἰκόνος εἶναι παράδειγµά τινος· πρός τι γὰρ ἑκάτερον, τὸ µὲν πρὸς γένεσιν, τὸ δὲ πρὸς εἰκόνα λέγεται· ἔστι δὲ ὅµως ἐν ἑκατέρῳ τὸ λοιπόν, παραδειγµατικῶς µὲν ἐν τῷ παραδείγµατι τὸ ποιοῦν, ποιητικῶς δὲ τὸ παράδειγµα ἐν τῷ ποιοῦντι συνειληµµένον.

32 In Parm. 913, 14.

33 See In Parm. 886.4ff. Vlastos, art. cit., identified ‘the self-predication assumption’, along with the ‘non-identity assumption’ as generating the TMA and, as far as Plato could see, unavoidable. See supra n.7, for the article by H. Cherniss which challenged the claim that Plato is committed to self-predication, though Cherniss thought that because self-predication is prima facie absurd, not only could Plato not have held it but that his theory of Forms could not even be susceptible to it, malgré lui.

34 Parm. 133A5-7 : Οὐκ ἄρα ὁµοιότητι τἆλλα τῶν εἰδῶν µεταλαµβάνει, ἀλλά τι ἄλλο δεῖ ζητεῖν ᾧ µεταλαµβάνει.

35 See In Parm. 915, 32ff.

36 In Parm. 916, 15-23 : ἆρα ὁ ἄνθρωπος ποιεῖ τὸν τῇδε ἄνθρωπον µόνον, ἢ καὶ ὅµοιον ἑαυτῷ ποιεῖ, καὶ πότερον τὴν οὐσίαν αὐτῷ δίδωσι µόνην, ἢ καὶ τὴν πρὸς αὑτὸν ἀφοµοίωσιν; εἴτε γὰρ τὴν οὐσίαν δίδωσι µόνην, οὐ ποιεῖ ἑαυτοῦ εἰκόνα, µὴ ποιῶν ἑαυτῷ ὅµοιον· εἴτε καὶ τὴν ἀφοµοίωσιν, τί λοιπὸν ἔτι τῆς ὁµοιώσεως ἔργον, ἀρκοῦντος ἑκάστου τῶν εἰδῶν ἑαυτῷ παραπλήσιον ἀποτελέσαι τὸ γινόµενον;

37 See Soph. 254D-255C.

38 Soph. 255E3-6.

39 Cf. In Parm. 973, 1-3.

40 Cf. In Parm. 974, 7-14 : Τὸ δέ γέ τι προσκείµενον δηλοῖ τὸ µοναδικὸν αὐτοῦ καὶ τὸ ἐν ἀρχῆς λόγῳ προϋπάρχον· οὐ γὰρ οὕτως ἐπὶ τῶν εἰδῶν τό τι προστιθέµενον ὡς ἐπὶ τῶν ἐνύλων καὶ ἀτόµων, ἀλλ᾽ ὡς τῆς ἑνότητος καὶ τοῦ πέρατος σύµβολον· καὶ ὡς µερικὸν δὲ ὂν τὸ εἶδος, εἰ περιβάλλοιτο πρὸς αὐτὸ τὸ ἓν ὄν, εἰκότως ἄν τι ἐπονοµάζοιτο.

41 In Parm. 888, 17-19.

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