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The Third Man Argument (Parm.132a1-b2)-a 'Purely' Metaphysical Exercise?

 

Marcus Nabielek

 

Recibido: 10-05-2010.
Aceptado: 24-06-10.

 

Abstract

All commentators of the 'Parmenides' agree that the Third Man argument, 132a-b2, raises a difficulty for Plato's theory of forms. Many commentators, following Vlastos, hold that the argument's infinite regress is vicious for epistemic reasons. Rickless contends that the infinite regress is vicious for exclusively metaphysical reasons. This essay intends to show that Rickless' interpretation is inadequate, as well as to vindicate Vlastos' interpretation.

 

Resumen

Todos los comentaristas del 'Parménides' están de acuerdo en que el argumento del 'Tercer Hombre', 132a1-b2, ofrece una dificultad a la teoría de las formas de Platón. Muchos comentaristas, siguiendo a Vlastos, creen que el regreso al infinito del argumento es vicioso por razones epistemológicas. Rickless sostiene que el regreso al infinito es vicioso por razónes únicamente metafísicas. Este trabajo quiere mostrar que la interpretación dada por Rickless es insuficiente. Quiere tambien confirmar la interpretación de Vlastos.

 

1.

Commentators on the Third Man argument (TMA) tend to agree that Plato intended the argument to be a vicious infinite regress argument, the regress' viciousness pointing to a problem for the theory of forms.¹ One group of interpreters holds,² following Vlastos, that the viciousness is epistemic in kind.

Rickless has challenged the traditional epistemic reading by proposing a metaphysical reading.³ In 2) I will present the text and in 3) I will delineate the argumentative ground shared by Rickless and the epistemic group. In 4) I will provide an outline of TMA's basic structure accepted by Rickless and the epistemic group, as well as an outline of the epistemic group's interpretation. I will present Rickless' interpretation in 5), and offer a criticism in 6). In 7) and 8) I will suggest that Rickless himself can and should accept the epistemic reading.

 

2.

Rickless' discussion of TMA relies on Gill and Ryan's translation of Parm.132a1-b2:⁴

(132a1) P: 'I suppose you think each form is one on the following ground: whenever some number of things seem to you to be large, perhaps there seems to be some one character, the same as you look at them all, and from that you conclude that the large is one.'

(132a5) S: 'That's true', he said.

P: 'What about the large itself and the other large things? If you look at them all in the same way with the mind's eye, again won't some one thing appear large, by which all these appear large?'

S: 'It seems so.'

(132a10) 'So another form of largeness will make its appearance, which has emerged alongside largeness itself and the things that par- (132b1) take of it, and in turn another over all these, by which all of them will be large. Each of your forms will no longer be one,but unlimited in multitude.'

 

3.

Rickless shares considerable philosophical ground with the epistemic interpreters of TMA, such as Vlastos.⁵ First of all, Rickless and the epistemic interpreters agree on a fundamental metaphysical divide between the world of sensible things and the world of forms. Rickless calls it 'Radical Distinctness', RD,⁶ which signifies the claim that no form is identical to any sensible thing. Sensible particulars like Simmias or the football on the pitch have general characters or properties they can share with other sensible particulars: Simmias is large, and so is Cebes. They are both large things, which makes for their largeness. The football is white, and so are the two other footballs on the pitch. They are all white things, which makes for their whiteness. In general, if a is a particular and F a property then the expressions 'a is F', 'a is an F-thing' or 'a is an instance of F-ness' are used synonymously.

Forms are agreed to exist,⁷ corresponding to properties, with the proviso that not to every property there has to correspond a form, Parm.130a-c.⁸ In general, if there is a form corresponding to property F then it is denoted by the expression 'the form of F-ness'. Forms are entities in their own right, having their own identity.⁹ In this uncontroversial sense Rickless understands Plato's otherwise much debated claim that forms are 'themselves by themselves', and refers to it as principle I.¹⁰ Rickless and the epistemic group specify what kind of entity forms are by way of the forms' causal, explanatory function:¹¹ forms are those entities that are responsible for (sensible) things having the properties they have.¹² The causal relation is that of partaking of or sharing in a form. In the case that there is a form corresponding to property F, then particular a is F in virtue of partaking of the form of F-ness. Rickless himself formulates the epistemic interpretation's main tenet as follows:¹³ '...the primary function of the F is to explain the F-ness of F-things and hence to make it possible for humans to apprehend and know things as F.' Rickless' use of 'the F' to denote a form is slightly problematic, for it seems to signal the form's uniqueness, the claim that there is exactly one form for every property to which there corresponds a form, Rickless' principle U.¹⁴ This ambiguity carries over into Rickless' formulations of his own principle of 'Causality', that if a form corresponds to property F and a has F then a has F in virtue of partaking of 'the F',¹⁵ or in virtue of 'a'¹⁶ form of F-ness, that is not necessarily exactly one form. In his more extensive treatment of TMA Rickless opts for the weaker formulation.¹⁷

Rickless accepts the major assumptions that epistemic interpreters, following Vlastos, consider to be crucially involved in generating TMA's infinite regress, notably 'One-over-Many', OM,¹⁸ 'Self-Predication', SP,¹⁹ and 'NonIdentity', NI.²⁰ According to OM, for a plurality of things that all have property F, there is a form of F-ness 'above' the property, by virtue of partaking of which each member of the plurality is F Vlastos sharpens OM by importing U into OM, maintaining that there is exactly one form of F-ness above the property F.²¹ Other epistemic interpreters do not follow Vlastos in this.²² Rickless agrees that U is a tenet of the theory of forms,²³ and concedes that it might be implicated in TMA, but eventually considers it irrelevant for TMA.²⁴ He regards U as a principle independent from OM, evinced by his assertion that U together with OM entails 'Causality':²⁵ if for a plurality of F-things there is a form of F-ness over them, in virtue of which the F-things are F, OM, and if for every property F to which there corresponds a form there is exactly one form of F-ness,U, then things that are F are F in virtue of partaking of 'the' form of F-ness, 'Causality'. So while Rickless understands 'Causality' here in terms of U he does not read U into OM. The derivation of TMA's regress can proceed without a sharpening of OM by way of U.²⁶

SP is the claim that every form of F-ness is itself F²⁷ Rickless holds that Plato's adoption of SP is implied by his adoption of the principle of 'Transmission-Causation'.²⁸ He points out that SP is implied by 'Causality' and 'Transmission-Causation':²⁹ if particular a is F by virtue of partaking of the form of F-ness, ('Causality'), and whatever causes something to be F must itself be F, ('Transmission-Causation'), then the form of F-ness must itself be F. Rickless agrees with Vlastos that the statement 'the form of F-ness is F' is an ordinary predication, in the sense that the form of F-ness has the property F.³⁰ The statement does not assert that the form of F-ness 'is' the property F in the sense of being identical to it. It should be added that Rickless also accepts the principle that if x causes y to be F then x cannot be F's contrary,³¹ 'No Causation by Contraries', NCC,³² implied by 'Transmission Causation'.³³

Finally, NI in Vlastos' formulation is the principle that no F-thing is identical with the form in virtue of which it is F³⁴ Rickless formulates NI differently and offers three versions of NI. First, by 'NI' he refers to the claim that no form is identical to any sensible thing,³⁵ that is RD. Secondly, he takes NI to be the claim that no form is identical to anything that partakes of it.³⁶ Thirdly, he formulates NI as the principle NSE, 'Non-Self-Explanation', the claim that no form of F-ness is F by virtue of partaking of itself.³⁷ The first formulation is confusing and I shall henceforth ignore it. As to the second and third formulations Rickless does not offer a justification for them. Causal-explanatory considerations readily furnish such a justification. Given the ancient principle of causation that a cause is an entity always distinct from its effect,³⁸ then if x partakes of y, y is always a distinct entity from x. It follows that an entity that is F cannot be identical to the form in virtue of partaking of which it is F, (Vlastos's formulation), nor can a form be identical to any entity partaking of it, (Rickless' second formulation), nor can a form partake of itself, (Rickless' third formulation). In Rickless' more extensive treatment of TMA he uses NSE.³⁹ Since a form of F-ness cannot be F by partaking of itself, NSE, and, by 'Causality', must partake of some form in order to be F, it follows that it must partake of something different from itself, which is an instance of Vlastos' formulation. Since Rickless endorses NSE and 'Causality' he should accept Vlastos' formulation of NI as well.

 

4.

Rickless not only accepts the epistemic interpretation's basic assumptions, OM, SP, and NI, but also agrees with the epistemic interpreters on TMA's basic structure. Rickless agrees⁴⁰ that the argument proceeds basically as follows: given a plurality A,B,C of large things, then, by OM, there is a form of Largeness L1, in virtue of partaking of which A,B,C are all large. By SP, L1 is itself large. Added to A,B,C, to form the new plurality of large things, A,B,C,L1, by OM, there is another form of Largeness, L2, in virtue of which A,B,C,L1 are all large. By NI, L2 is different from L1, and, by SP, it is itself large, and can be added to A,B,C,L1 to form a new plurality of large things. The steps are iterable indefinitely, yielding infinitely many forms of Largeness. The argument is generalizable to any property to which there corresponds a form.

The epistemic reading, to account for the regress' viciousness, also goes back to Vlastos.⁴¹ Vlastos claims that '...we apprehend particulars as F through F-ness', since the function of forms is to '...enable us to discern the relevant characters in the particulars and then in the first of the corresponding forms.'⁴² He argues that the series of forms' infinity would not be vicious, if the first form, L1, fulfilled this function satisfactorily, with the remaining forms being superfluous. But the infinite regress is vicious, he contends, for TMA shows that apprehending that A is large not only requires apprehending L1 as large, but that apprehending L1 as large requires apprehending L2 as large, and so on ad infinitum. To summarize Vlastos' reasoning, apprehending particular a as having discernible character F requires apprehending infinitely many forms as F, and thus apprehending infinitely many forms. Since apprehending infinitely many forms is humanly difficult or impossible, it is humanly difficult or impossible to apprehend a as F.

Vlastos' statement of the epistemic reading needs to be qualified. First, 'apprehending' a as F should involve knowledge. For Plato knowledge is explanatory knowledge, namely to know why a is F, and to know that involves knowing causes of a being F he associates with forms.⁴³ Secondly, these causes operate regardless of human apprehension, and thus independently of what is humanly difficult or impossible: a is F in virtue of the form of F-ness causing it to be F. Vlastos contends that an infinite series of such forms is unacceptable for Plato, relying on Rep.597c,d:⁴⁴ 'if, per impossibile, there were two Forms of anything, there would have to be a third, which would be 'the' Form of that thing.' In an infinite series of forms of F-ness there is no last member, and thus no such form. So if there was such a series then it is not just due to a human limitation that an attempt to know, why a is F, remains thwarted. In this sense, '... the boundless multitude, however, in any and every subject leaves you in boundless ignorance',Phil.17e3-5.⁴⁵ Thirdly, Vlastos concedes that Plato does not admit that F-ness must be apprehended as F, but implies this via SP.⁴⁶ The implication is plausible, when adoption of SP is motivated by 'Transmission Causation'.⁴⁷ If for the form of F-ness to cause particular a to have property F it must itself have property F, then it is reasonable to assume that property F is the form of F-ness' causally relevant property. Knowing why a is F thus requires apprehending the form of F-ness as F. Finally, Vlastos's sharpening of OM by way of U is not strictly necessary in order to be able to apply the epistemic reading. As long as the causal-explanatory series of forms 'above' a property is finite, there is a last member in the series, and thus a definite cause or explanation of a particular having that property. It is the series' infinity that introduces the causal-explanatory indeterminacy which is at the heart of the epistemic interpretation. Some epistemic interpreters do not follow Vlastos in adopting U.⁴⁸ So the epistemic interpretation can be formulated in two versions, one adopting U, the other not adopting U.

 

5.

Rickless rejects the epistemic interpretation, in favour of a more metaphysical one. He believes that TMA brings into critical focus Socrates' belief that no form can have contrary properties, 'Radical Purity', RP.⁴⁹ For Rickless adoption of RP, the keystone of his interpretation, is legitimised by the great metaphysical divide between sensible particulars and forms generally attributed to Plato.⁵⁰ As Socrates sets out in the 'Phaedo', forms, as opposed to sensible particulars are pure, 'katharon', Ph.67b2, and unmixed, 'eilikrines', Ph.66a2,3. Rickless accounts for purity and impurity in terms of contrary properties:⁵¹ Simmias is large, and the football is white, but not purely so. Compared to Socrates Simmias is large, and compared to Phaedo he is also small, Ph.102b,c. The football, when looked at closely, contains brown pigments and is thus also brown, and when thrown into the dust it certainly becomes also brown. But for Plato, so Rickless, the form of Largeness, in virtue of partaking of which Simmias is large, and the form of Whiteness, in virtue of partaking of which the football is white, cannot also be small or brown, respectively, and can never become also small or brown, respectively.⁵² According to Rickless it is plausible to assume that every sensible particular has or can have contrary properties to which forms correspond.⁵³ This claim together with the claim that no form can have contrary properties, RP, entails RD, the claim that no form is identical to any sensible thing.⁵⁴

How his own reading of TMA brings RP into focus Rickless attempts to show as follows: he objects to the epistemic interpretation on two grounds.⁵⁵ First, it does not make sense of TMA's set up, with OM entailing 'Oneness', O, the claim that each form is one, whence 'the large is one',132a3. Secondly, it does not make sense of this entailment's conflict with TMA's conclusion that each form '...will no longer be one, but unlimited in multitude',132b2.

Rickless concedes that if the epistemic interpretation understands OM in terms of U, and as entailing that there is exactly one form of Largeness, the conclusion, if understood as '...there are infinitely many forms of Largeness', does conflict with this entailment.⁵⁶ But he believes that, at 132a1-3, Parmenides is thinking not of U, but of O alone, where 'being one' is an ordinary predication.⁵⁷ He points to 129b-d, where 'being one' is taken to mean 'being something that can be counted', treated on a par with 'being large.' Socrates' being one is claimed to follow from his being one amongst a group of several people,129c-d. In addition, 'being many' and 'being one' are assumed to be contrary properties,129b-c. 'Being many' is also treated as an ordinary predication: Socrates' being many is taken to follow from his having many parts,129c, or having many properties, Phil. 14c-d.

More specifically, Rickless argues as follows:⁵⁸ Since O is intended at 132a1ff, 'the large is one', 132a3, as an instance of O, is not equivalent to 'there is exactly one form of Largeness.' In this case the epistemic reading's 'there are infinitely many forms of Largeness' of TMA's conclusion does not conflict with 'the large is one', since each of the infinitely many forms of Largeness is something that can be counted. Similarly, since 'being many' is also an ordinary predication, 'each form of Largeness is unlimited in multitude', is not equivalent to 'there are infinitely many forms of Largeness.' With the ordinary predicates, 'being one' and 'being many' being contraries, the former, but not the latter conflicts with 'the large is one.' If the epistemic interpreters were to uphold the latter reading, they would have to show that it implies the former.

Rickless offers a reading of TMA which allows for just this implication:⁵⁹ given a group of large things, A,B,C, by OM, there is a form L1 'over' them in virtue of partaking of which they are all large. Just as Socrates' being one follows from his being one 'among' a group of people, L1's being one follows from its being one form 'over' many large things. By SP, L1 is itself large. Forming a new group of large things, A,B,C,L1, by OM, there is a form L2 'over' this group. By NI, L2 is different from L1 L2 is also 'one' in the sense of an ordinary predication and L1 partakes of L2. By SP, L2 is itself large. Forming a new group, A,B,C,L1,L2, application of OM, SP and NI produces yet another form of Largeness L3, different from both L1, and L2, which is 'one' and of which both L1,L2 partake. The procedure can be iterated ad infinitum, yielding an infinite hierarchy of forms of Largeness, where each form partakes of the infinitely many forms above it. Where there is a form of F-ness corresponding to a property F, an F-thing is F by partaking in that form, and an F-thing partaking in the form implies its having that property.⁶⁰ So each form in the hierarchy, in virtue of partaking in (infinitely) many forms above it, has (infinitely) many properties. Since having many properties implies being many in the sense of an ordinary predication, each form is (infinitely) many. Now RP comes into play. By RP no form can have contrary properties. Since 'being many' and 'being one' are contraries, it follows that no form of Largeness is one, which does indeed conflict with 'the large is one' at 132a3, which is an instance of O.

 

6.

Acceptance of Rickless' reading is questionable for three reasons. First, Rickless acknowledges '...the epistemic language that Plato sprinkles throughout the Third Man passage', but holds that '...it is unlikely that the epistemic reading is what Plato had in mind,' because, to recall, it does not make sense of TMA's set up with OM entailing O, and hence that L1 is large.⁶¹ Epistemic vocabulary, indeed, abounds in the passage:⁶² 'ek tou toioude...oiesthai',132a1, 'doxê(i)',132a2, 'dokei',132a2, 'idonti',132a3, 'hothen...hêgê(i),132a3, 'tê(i) psyche(i) epi panta idê(i)s,132a6, phaneitai, 132a7, 'phainesthai', 132a8, 'anaphanêsetai',132a10. The 'hô(i) at 132a5,b12 is a causal dative.⁶³ If TMA is conspicuously formulated in epistemic terms then it is likely, instead, that Plato had the epistemic reading in mind.

Secondly, the epistemic reading can make sense of OM entailing O. To recall,⁶⁴ Rickless accepts 'Transmission-Causation', which implies NCC, also accepted by him. OM assumes that a plurality of particulars share a single, discernible character F, and it is in virtue of partaking of a form corresponding to that character that they share this single character. Agreeing with Rickless on the ordinary predication account of 'being one' at 129c,d, F is one, for the same plurality might also share character G, and another plurality character H. So F is one discernible character of many that pluralities of particulars can share. By NCC, the form causing the plurality's members to share F, F being one, cannot itself be many, 'being many' being the contrary property of 'being one.' By 'Transmission-Causation' the form of F-ness must itself be one. Hence, Rickless is wrong to assume that the epistemic reading cannot make sense of OM entailing O.

Finally, Rickless confronts the problem, why the regress' infinity should play a significant role in its viciousness. Supposing that the hierarchy of forms of Largeness is finite, L1,...,Ln, then, by SP, all these forms are large, and all of L1,...,Ln-2 partake of two or more than two forms above them, while Ln-1 partakes of Ln, and Ln partakes of no form in the hierarchy. All of L1,...,Ln-2 are many. So, by RP, they cannot be one, and thus falsify O. L1 already falsifies O in a hierarchy of only three forms, L1,L2,L3, where L1 partakes of L2 and LB. For Rickless the regress' infinity ensures that each form in the hierarchy is (infinitely) many, since each partakes of infinitely many forms above it. Given TMA's generalizability to all forms corresponding to a discernible property, TMA's conclusion then implies that, without exception, no form is one. Hence the theorist of forms retaining both O and RP will find no form satisfying both principles. For Rickless then the regress' infinitude is not strictly necessary to account for its viciousness, but is only necessary to account for a viciousness of greater metaphysical generality!

 

7.

Despite these three weaknesses Rickless' account might still be a viable interpretation of TMA when compared to the epistemic reading. In 4) two versions of the epistemic reading were pointed out, one that adopts U, and one that does not adopt U. I also pointed out in 3) that Rickless is somewhat undecided about adopting U. The epistemic reading adopting or not adopting U can thus be compared to Rickless' reading adopting or not adopting.

For the epistemic reading adopting U a finite series of forms suffices to falsify U. A series of two forms, L1,L2, already falsifies the claim that there is uniquely one form L1, in virtue of which A,B,C are all large. For the epistemic reading not adopting U a conflict with U obviously does not arise. But for both versions a merely finite series of forms does not suffice to imply the epistemic reading's characteristic causal-explanatory problem of A,B,C's being large having no determinate cause or explanation and remaining unknowable.⁶⁵ In a finite series there is an ultimate form and thus a definite cause or explanation. Both versions of the epistemic reading thus require the regress' infinity to account for the regress' viciousness.

For the sake of argument, if Rickless adopts U, then also for his reading a finite series of forms suffices to falsify U. In addition, as just seen at the end of 6), a finite series of forms suffices to falsify O, and reveals the interpretation's characteristic conflict between O and RP. If Rickless does not adopt U, then, obviously, a conflict with U does not arise, but again a finite series of forms suffices to falsify O and reveals a conflict between O and RP.

Both Rickless and the epistemic interpreters agree that TMA is a vicious infinite regress argument. They thus agree that a satisfactory reading of TMA must show that the regress' infinity is relevant to the regress' viciousness. In both versions of the epistemic reading the regress' infinity is necessary to account for its viciousness, while in both versions of Rickless' reading it is not necessary to account for its viciousness. As just seen at the end of 6), the regress' infinity is necessary only to reveal a conflict between O and RP of greater generality. The epistemic reading is thus a serious alternative to Rickless' reading, which, so far, derives its plausibility only from a greater metaphysical generality or elegance.

The epistemic reading is not only an alternative to Rickless' reading. Rickless should also consider its adoption, based on two observations. First, as just seen, Rickless overtly ignores the significance of the TMA-passage's epistemic language. Without indicating his neglect he also takes no account of the reference of 'poll'atta megala',132a2, and 't'alla ta megala',132a6, to sensible particulars only, indicating a distinction in TMA between sensible particulars and forms. Textual evidence supports this interpretation. The use of the soul,⁶⁶ 'tê psyche(i)', in surveying a plurality of large things is indicated at 132a6,7, when a form is first added to the initial plurality, description of whose survey at 132a2,3 does not refer to the soul. Parmenides himself claims that apprehension of forms as opposed to sensible particulars requires reason,135e4,5, and reason, for Plato, is in the soul.⁶⁷ 'Poll'atta megala' at 132a2 is thus likely to refer to sensible particulars only. Furthermore, both Parmenides and Socrates retain the distinction between forms and sensibles, invoked by Socrates at 128e5ff to give, contra Zeno, a consistent account of sensibles⁶⁸ having contrary properties, at various places:⁶⁹ '...there are certain forms which these other things, by getting a share of them...',130e5,6; 'so other things don't get a share of the forms by likeness',133a5. Hence, 't'alla ta megala' at 132a6 is also likely to refer to sensibles only. Rickless himself regards RD, 'Radical Distinctness', the claim that no form is identical to any sensible thing, as a central tenet of the theory of forms in the 'Parmenides', implied by the claim that all sensible things have contrary properties together with RP.⁷⁰ So, by his own interpretation, there is no reason to ignore textual evidence for RD in the TMA-passage. His ignorance of the distinctness' possible significance in the passage is evinced by his failure to mention, in his exposition of TMA, the fact that A,B,C form part of all the new pluralities generated.⁷¹ But the lack of an explanation of and failure to know why sensibles A,B,C are all large is just what the viciousness of the regress of forms' infinity is based on according to the epistemic reading.

The second observation is that, as seen in 3), Rickless' reading incorporates causal principles central to the epistemic reading, such as 'Causality', 'Transmission-Causation', and NCC. Rickless concedes that OM, which is essential for the regress' derivation, implies, in conjunction with U, the principle of 'Causality'.⁷² Rickless even motivates the adoption of SP and NI, crucial to his reading of TMA, with considerations conforming to the epistemic reading. He holds that SP is implied by 'Causality' and 'Transmission-Causation',⁷³ and formulates NI as a principle of 'Non-Self-Explanation ', (NSE), the principle that no form of F-ness is F by virtue of partaking of itself.⁷⁴ Rickless fails to provide a justification for NSE. Yet, for a causal-explanatory principle like NSE it is reasonable to expect a justification in causal-explanatory terms. As set out already in 3), such a justification is available. NSE is a consequence of the ancient conviction that a cause is always an entity distinct from its effect.⁷⁵

Since there is no reason for Rickless to ignore the epistemic language and the distinction of sensibles and forms in the TMA-passage, both pointing to the epistemic reading, and since for Rickless TMA's main assumptions are motivated by the epistemic reading's central tenets, he should consider adopting the epistemic reading, which would run as follows: the fact that A,B,C are all large is explained by L1 in virtue of being large itself. By NSE, L1 cannot explain itself its being large. By OM and NSE a form L2, distinct from L1 explains why A,B,C,L1 are all large, in virtue of being large itself, but without being able to explain itself its being large, and so on. An infinite explanatory regress ensues. A,B,C's being large remains unexplained and an attempt to know why A,B,C are large remains thwarted.

 

8.

In order to commend his own reading Rickless could still point out its metaphysical generality and elegant simplicity: TMA brings into critical focus only one principle, RP, by way of a conflict with one other principle, O. RP, so Rickless, is also what Socrates focuses on when introducing the forms at 128e5ff, at the dialogue's beginning, and rejecting RP is what Parmenides, at the dialogue's first part's end, suggests Socrates should do to save the theory forms, 135d-e, and thus dialectic, 135b-c.⁷⁶ But in this respect the epistemic reading need not be at a disadvantage.

What assumption, according to the epistemic reading does the regress bring into critical focus? The regress would stop if L1 could explain A,B,C's being large in virtue of its being large, as well as its being large itself, which, by NSE, it cannot do. Right at the beginning,129al, Socrates introduces forms as being 'themselves by themselves', what he refers to as principle I.⁷⁷ As said in 3), Rickless accepts an uncontroversial reading of I, namely that forms are entities in their own right. Rickless believes that I is irrelevant for TMA, but amongst the stronger interpretations of I he favours the traditional one of existential independence.⁷⁸ So Rickless himself would probably not object to 'itself by itself ' being rendered as '...itself responsible for its own proper being, independently of other things.'⁷⁹ If L1's 'own proper being' is being large, NSE is incompatible with L1 explaining its being large independently of L2,L3,.... Denying NSE thus contributes to maintaining that forms are themselves by themselves. But denying NSE requires only that some, not that all forms corresponding to a property are self-explanatory with regard to that property. This is compatible with forms partaking of other forms, namely forms corresponding to one property partaking of a form corresponding to another- for Plato, after all, all forms partake in the form of Goodness, Rep.509a,b. This is also compatible with there being a hierarchy of 'intermediate' forms corresponding to one property, which must be finite and end in a self-explanatory one, in the way Plato conceives dialectic science.⁸⁰

So the epistemic reading as well brings into critical focus one central assumption, I, by way of a conflict with one other assumption, NSE. In addition, I is at least as important for Socrates and Parmenides as RP. Socrates introduces I at the first part's beginning, 129a1, and Parmenides refers back to it at its end, 135a1-3, speaking of a form as 'something itself '. Finally, saving I, by restricting NSE is very much in accord with Plato's conception of dialectic science, which both Parmenides and Socrates intend to save, 135b,c.

Rickless offers no reason whatsoever as to why I is irrelevant for TMA.⁸¹ He thus seems to believe that the simplicity of his reading centred on RP justifies this neglect. He also offers no reason as to why U is irrelevant for TMA.⁸² Again he seems to believe that the simplicity of his reading centred on RP outweighs any possible relevance. In the case of U Rickless' neglect is surprising, since he certainly acknowledges U as a tenet of the theory of forms,⁸³ and concedes that TMA is partly directed against it.⁸⁴ Even if one agrees with Rickless that Parm.129c-d favours O,⁸⁵ one need not accept that U is out of play at 132a,b. Rickless himself accepts that OM together with U entails 'Causality.'⁸⁶ Rickless also agrees that Parmenides appeals to 'Causality' in the argument preceding TMA,⁸⁷ and clearly accepts OM as a premise of TMA. So Rickless should accept U as well.

The only way Rickless could, with some plausibility, discard without justification central assumptions as irrelevant for TMA, is by maintaining that RP is such a fundamental principle for the entire dialogue that its relevance for TMA does not allow other principles to have any relevance. This is indeed Rickless' strategy. He points out that four of the dialogue's first part's six arguments⁸⁸ question RP,⁸⁹ and that the second part's deductions suggest that rejecting RP, U, and NCC would save the theory of forms.⁹⁰ Yet, if RP, U, and NCC must be rejected, then it is more reasonable to assume that all these principles, and not just RP, are in critical focus in the dialogue's first part, including TMA. It is thus worth reconsidering these three principles' involvement in TMA .

First, U is just the principle whose adoption makes for one version of the epistemic reading. Rickless himself admits that 'perhaps'⁹¹ U is in play in TMA and must be rejected to save the theory of forms.

Secondly, NSE, an assumption that TMA, according to the epistemic reading, brings into critical focus, together with 'Synonymy-Causation' entails NCC: by NSE for x to explain y's being F x must partake of something else z, which, by 'Synonymy Causation', must itself be F. So z cannot be not-F, and thus cannot be F's contrary, NCC. Rejecting NCC thus permits to reject NSE, and thus permits to save the forms in the way the epistemic reading would suggest.

Finally, what about RP? If U, despite Rickless' qualms, is in play in TMA, then so is O. Since the claim 'there is exactly one form' characterises a group with one member, the claim implies that the form is a countable thing. U entails O, but not vice versa. A thing's being countable does not entail there being only one such thing. Suppose then that U entails O, and the infinite regress ensues. According to the epistemic reading the infinite regress is vicious because it implies explanatory indeterminacy via NSE. But it can, in addition, be interpreted in Rickless' way, as implying a general conflict between O and RP. Alternatively suppose that, as Rickless prefers, U is not at play in TMA and that the infinite regress ensues. According to Rickless' reading the infinite regress is vicious because of a general conflict between O and RP. But, as shown in 6), the epistemic reading can support the implication of O by OM without any recourse to U. So the epistemic reading is also applicable: in addition to a general conflict between O and RP according to Rickless' reading, the infinite regress also implies explanatory indeterminacy via NSE.

In sum, if U is in play in TMA, the regress shows a conflict with U and NSE according to the epistemic reading adopting U, as well as a conflict with U and RP according to Rickless' reading adopting U, that is with all three principles to be rejected according to Rickless' interpretation of the dialogue's second part. If U is not in play, the regress shows a conflict only with NSE, according to the epistemic reading not adopting U, and with RP according to Rickless' reading not adopting U, that is with two of the three principles to be rejected according to Rickless' interpretation of the dialogue's second part. So, regardless of whether U is adopted or not, Rickless' reading is not even an alternative reading to the epistemic reading in the sense of being logically incompatible with it. The two readings are consistent, and Rickless can adopt the epistemic reading while retaining his own reading. In 7) I also pointed out reasons why he should adopt the epistemic reading. Even if, despite these reasons, Rickless does not adopt the epistemic reading, by realizing that he can adopt it without inconsistency, he should realize that TMA neither needs to be nor should be a 'purely' metaphysical exercise.

 

Bibliografía

BURNET, J. (1991): Platonis Opera. Tomus II. Oxford.         [ Links ]

FINE, G. (1993): On Ideas: Aristotle's criticism of Plato's theory of forms. Oxford.         [ Links ]

FREDE, D. (1993): Plato: Philebus. Indianapolis.         [ Links ]

GILL, M. L., RYAN, P. (eds.) (1996): Plato: Parmenides. Indianapolis.         [ Links ]

GOLDSTEIN, L., MANNIC K, P. (1978): 'The Form of the Third Man Argument'. Apeiron, 12, 6-13.         [ Links ]

PANAGIOTOU, S. (1971): 'Vlastos on Parmenides 132a1-b2: some of his text and logic'. Philosophical Quarterly, 21, 255-259.         [ Links ]

RICKLESS, S. C. (1998): 'How Parmenides saved the theory of forms'. Philosophical Review, 107, 4, 501-54.         [ Links ]

----------, (2007): 'Plato's Parmenides'. In: Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/plato-parmenides/        [ Links ]

SEDLEY, D. M. (1998): 'Platonic Causes'. Phronesis, 43, 2, 114-132.         [ Links ]

TELOH, H., LOUZECKY, D. (1972): 'Plato's Third Man Argument'. Phronesis, 17, 1, 80-94.         [ Links ]

VLASTO S, G. (1954): 'The Third Man Argument in the Parmenides'. Philosophical Review, 54, 319-349.         [ Links ]

----------, (1969): 'Plato's Third Man Argument (Parm.132a1-b2): Text and Logic'. Philosophical Quarterly, 19/1, 283-301.         [ Links ]

 

Notes

¹ Rickless (2007:11).

² Vlastos (1954); Goldstein,Mannick (1978); Fine (1993); see Rickless (2007:11,12) for an overview.

³ Rickless (1998),(2007).

⁴ Gill,Ryan (1996).

⁵ Rickless (2007:10-12); Vlastos (1954:320-322); Vlastos (1969:290,291).

⁶ Rickless (1998:512).

⁷ Rickless (1998:503)

⁸ Rickless (2007:6,7).

⁹ Rickless (1998:508).

¹⁰ Rickless (507, 508, &.13).

¹¹ Vlastos (1954:320,328); Rickless (1998:503); Rickless (2007:4).

¹² I have bracketed 'sensible' here to leave open the possibility that forms can have properties in virtue of other forms, which is one of the key issues raised by TMA.

¹³ Rickless (2007:12).

¹⁴ Rickless (2007:5).

¹⁵ Rickless (2007:4).

¹⁶ Rickless (1998:503).

¹⁷ Rickless (1998:503,518-525).

¹⁸ Vlastos (1954:320); Rickless (2007:5).

¹⁹ Vlastos (1954:324); Rickless (2007:5).

²⁰ Vlastos (1954:325); Rickless (2007:11).

²¹ Vlastos (1954:320).

²² Goldstein,Mannick (1978:6,7).

²³ Rickless (2007:5).

²⁴ Rickless (2007:13).

²⁵ Rickless (2007:5).

²⁶ See 4) below.

²⁷ Rickless (1998:507); Rickless (2007:5).

²⁸ Rickless (2007:5,6); Sedley (1998:123,129).

²⁹ Rickless (1998:508,510).

³⁰ Rickless (1998:507,508,fn.13).

³¹ Rickless (2007:10).

³² My shorthand.

³³ If for x to cause y's being F x must be F, then x cannot be not-F, and thus cannot be F's contrary. Rickless (1998:511, 512).

³⁴ Vlastos (1954:325).

³⁵ Rickless (2007:5).

³⁶ Rickless (2007:11).

³⁷ Rickless (1998:520).

³⁸ Sedley (1998:121,131).

³⁹ Rickless (1998:518-525).

⁴⁰ Rickless (1998:520).

⁴¹ Vlastos (1954).

⁴² Vlastos (1954:328.&12).

⁴³ Phaedo 96-102.

⁴⁴ Vlastos (1954:328.&12).

⁴⁵ Frede,D. (1993:10,11).

⁴⁶ Vlastos (1954:328.&12).

⁴⁷ See 3) above.

⁴⁸ Goldstein and Mannick, for example, reject U, (Goldstein,Mannick (1978:6,7)).

⁴⁹ Rickless (2007:12,13).

⁵⁰ Rickless (1998:511,512).

⁵¹ Rickless (1998:505-507); Rickless (2007:4,5).

⁵² Parm.129b,c,129e-130a; Rickless (1998:506,511).

⁵³ Rickless (1998:505,511).

⁵⁴ Rickless (1998:512).

⁵⁵ Rickless (1998:520-522).

⁵⁶ Rickless (1998:521).

⁵⁷ Rickless (1998:513).

⁵⁸ Rickless (1998:520-522).

⁵⁹ Rickless (1998:522,523); Rickless (2007:12,13).

⁶⁰ Rickless (1998:503).

⁶¹ Rickless (2007:12).

⁶² Burnet's edition, (Burnet: 1991), of the Greek text is used.

⁶³ Sedley (1998:130).

⁶⁴ 3) above.

⁶⁵ 4) above.

⁶⁶ A divergence from Gill, Ryan's translation as 'mind's eye'; 2) above.

⁶⁷ Teloh,Louzecky (1972:84).

⁶⁸ 'you and I',129a2; 'stones and sticks',129d3; 'visible things',129e7.

⁶⁹ 131a8,9;131b1;131c12-d1;131e3,4;132d1-4; Panagiotou (1971:257,258), (contra Vlastos (1996:298.fn.11).

⁷⁰ Rickless (1998:511,512).

⁷¹ Rickless (1998:522,523).

⁷² Rickless (2007:5). See also 3) above.

⁷³ See 3) above.

⁷⁴ Rickless (1998:520).

⁷⁵ Sedley (1998:131).

⁷⁶ Rickless (1998:537,538).

⁷⁷ Rickless (1998:508)

⁷⁸ Rickless (1998:508,509, fn.14).

⁷⁹ Gill,Ryan (1996:128.fn5).

⁸⁰ Rep.597c,d;Phil.16d-17a,17e; Plato imagines the finite web of interconnected forms, all subjugated to 'Goodness' as dialectic science's outcome, (Goldstein,Mannick (1978:9,10)).

⁸¹ Rickless (1998:509,fn.14).

⁸² Rickless (2007:12,13).

⁸³ Rickless (2007:5).

⁸⁴ Rickless (2007:13).

⁸⁵ Rickless (i998:513).

⁸⁶ Rickless (2007:5). See 3) above.

⁸⁷ Rickless (2007:8).

⁸⁸ 130a-e;130e-131e;132a,-b;132b-c;132c-133a;133a-134a.

⁸⁹ Rickless (1998:537,538). For Rickless 130a-e does not involve RP, while the 'Greatest Difficulty'-argument, 133a-134a, involves RP, but rejecting it does not resolve the 'Difficulty'; (Rickless (2007:33)).

⁹⁰ Rickless (2007:33).

⁹¹ Rickless (2007:13).