Larivée, Annie. 2024. "What Socrates Learned from Parmenides. Part 1. Parmenides’ Gymnasia and Socrates’ Intellectual Virtues." Organon no. 56:89–117.

Abstract: "This is the first of two studies in which I examine Plato’s account of Parmenides’ contribution to Socrates’ education. This account suggests, I argue, that Socrates became a virtuoso of the elenchos and the embodiment of fundamental intellectual virtues thanks to the gymnasia depicted in the Parmenides. I show how Parmenides’ Eighthfold routine is not a method of philosophical investigation strictly speaking; rather, it is a skill-building exercise that relies on memory and whose virtue is partly defensive. My demonstration is based on three sets of distinctions required to do justice to the preparatory character of Parmenides’ gymnasia. The first differentiates three types of intellectual virtues, the second two kinds of training methods, and the third, three telic modes."
———. 2024. "What Socrates Learned from Parmenides. Part 2. Hypothesis, Antilogy, and Philosophical Self-Defense in the Phaedo." Organon no. 56:119–138.

Abstract: "My first study identified the cognitive abilities and argumentative skills developed by the gymnasia presented in Plato’s Parmenides. Since the correspondence with the intellectual virtues Socrates displays in other dialogues is too remarkable to be a coincidence, I concluded that Socrates must have trained with Parmenides’ Eighthfold routine in his youth. My second study supports this conclusion by drawing attention to textual evidence found in the Phaedo. The autobiographical account Socrates shares in that dialogue indicates how the gymnasia impacted his intellectual development, mostly through the action of hypothesizing. This strategic move used by the Eleatics transformed the originally sectarian way So crates related to Forms and enabled him to protect his theory from attacks in a secure yet non-dogmatic way."
Larsen, Jens Kristian. 2019. "Eleaticism and Socratic Dialectic: On Ontology, Philosophical Inquiry, and Estimations of Worth in Plato’s Parmenides, Sophist and Statesman." Études platoniciennes no. 15:1–24.

Abstract: "The Parmenides poses the question for what entities there are Forms, and the criticism of Forms it contains is commonly supposed to document an ontological reorientation in Plato. According to this reading, Forms no longer express the excellence of a given entity and a Socratic, ethical perspective on life, but come to resemble concepts, or what concepts designate, and are meant to explain nature as a whole. Plato’s conception of dialectic, it is further suggested, consequently changes into a value-neutral method directed at tracing the interrelation of such Forms, an outlook supposedly documented in certain passages on method from the Sophist and the Statesman as well.

The article urges that this reading is untenable. For in the Parmenides the question for what entities one should posit Forms is left open, and the passages on method from the Sophist and Statesman neither encourage a non-normative ontology nor a value-neutral method of inquiry. What the three dialogues encourage us to do is rather to set common opinions about the relative worth and value of things aside when conducting ontological inquiries; and this attitude, the article concludes, demonstrates a close kinship, rather than a significant difference, between Plato’s Socrates and his Eleatic philosophers."
———. 2022. "On common forms and dialectical inquiry in Plato’ Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 183–191. Baden-Baden: Academia Verlag.

Abstract: "It is a matter of controversy what message Plato’s Parmenides is meant to convey to its readers as regards the questions what ontological status forms have and for what things we should assume forms. In this article I argue that Parmenides is urging Socrates to posit forms first and foremost for things such as likeness, unity, beauty, and goodness, things that correspond to the forms that Socrates in the Theaetetus designate as common. I further argue that Parmenides encourages Socrates to investigate the interrelation between such forms through the hypothetical method used by Zeno and to use this method to address the question how certain forms are related to other forms, but not the questions for what things there are forms and how sense-perceptible things and forms are related."
Lee, David. 2014. "Zeno’s Puzzle in Plato’s Parmenides." Ancient Philosophy no. 34:255–273.
Lernould, Alain. 2010. "Negative Theology and Radical Conceptual Purification in the Anonymous Commentary on Plato’s Parmenides." In Plato's Parmenides and Its Heritage. Vol. 1: History and Interpretation from the Old Academy to Later Platonism and Gnosticism, edited by Turner, John D. and Corrigan, Kevin, 257–274. Atlanta: Society of Biblical Literature.

£If this reading can be accepted, then our author is closer to Damascius than to an author like Proclus. It is indeed Damascius’s work that, for the purpose of a “radical purification” of our concepts, clearly expresses the idea that the only way of getting close to the One is “to keep quiet, remaining in the secret sanctuary (ἀδύτῳ) of the soul and not leaving it.(65)" (p. 274)

(65) 65. Damascius, Princ. 1:22,14–15 Westerink-Combès. (...)
Lewis, Frank A. 1979. "Parmenides on Separation and the Knowability of the Forms: Plato Parmenides 133a ff." Philosophical Studies no. 35:105–127.

"At Parmenides 133a ff., Parmenides presents the last of his arguments critical of the theory of forms. He is careful to emphasize that the argument holds good against the view that forms are separate from sensibles;indeed, he says that his argument presents the greatest of the difficulties that await such a view. Now Parmenides has already called our attention to separation as a crucial feature of the theory of forms (129d, 130b), but his previous arguments pay more attention to other assumptions of the theory, whose relation to separation he neglects to explain (in the immediately preceding argument, for example, he repeats the reference to separation [133a8-10], but in virtually the same breath tells us he is attacking the doctrine that things participate in forms by a principle of likeness [a5-7]). But it will be worthwhile not to ignore his suggestion here that his present argument focusses especially on separation: there is, I will suggest, some plausibility to thinking that separation is the key theme that runs throughout the argument." (p. 105, a note omitted)
Liu, Kezhou. 2022. "The Problem of Separation in Plato’s Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 287–293. Baden-Baden: Academia Verlag.

Abstract: "In Part I of Plato’s Parmenides, Socrates introduces the theory of separately existing Forms, but this doctrine is severely attacked by Parmenides. In this paper I will argue firstly that Socrates’ thesis of separation is not the same as that which Parmenides paraphrases at the beginning of his speech; secondly, I will show that Plato does not endorse Parmenides’ symmetrical account of separation but would side with the asymmetrical account which stresses the ontological dependence of sensibles on Forms; finally, I will contend that difficulties derived from the symmetrical separation thesis in Part I cannot be thoroughly solved in Part II, for the mechanism of participation needs an efficient cause to bring the formal order to the realm of Becoming."
Liu, Xin. 2024. "How Do the Eighth Hypotheses in Plato’s Parmenides Come to Light? Chiasmus as a Method of Division." Journal of Ancient Philosophy, no. 18:37–66.

Abstract: "In this paper, I aim to explore the structure of the exercise in the second part of the Parmenides. In analyzing the transitional section, I claim that in addition to diairesis, there is another method of division, namely, cross-division, which Porphyry terms chiasmus. On this basis, I explain how Plato uses chiasmus to divide the exercise into Eighth hypotheses, in which the subjects of the paired hypotheses (I–VI, II–V, III–VII, and IV–VIII) are the same and those of the nonpaired hypotheses differ.

In closing, I reconstruct the universal scheme of the exercise on the basis of Plato’s use of chiasmus."
Livingston, Paul M. 2024. "Unity and Predication in Plato’s Parmenides and Nāgārjuna’s Root Verses." In Crossing the Stream, Leaving the Cave: Buddhist-Platonist Philosophical Inquiries, edited by Carpenter, Amber D and Harter, Pierre-Julien, 96–116. New York: Oxford University Press.

Abstract: "This chapter considers in parallel some main argumentative strategies of Nāgārjuna’s Root Verses and the “dialectical exercise” of Plato’s Parmenides. It argues that both can be seen as critically targeting the unity that is attributed to entities as coherent and individual subjects of predication. In particular, both show that it is incoherent to suppose any such subject either has the relevant kind of unity or (lacking such a unity) does not exist at all. This suggests that we may reject familiar analyses of the contradictory or paradoxical conclusions of both arguments as pointing either toward a superior and consistent structure of logical categories or toward a transcendent insight into the ineffable. Instead, we may see both as pointing, rather, to a possible overcoming of the “habit” of reifying conceptualization that is deep-seated in ordinary language and practice, and thereby to the potential soteriological benefits of such an overcoming."
Livov, Gabriel. 2008. "Parmenicide. Political reasons for a platonic crime." Revue de Philosophie Ancienne no. 26:39–73.

"Since it is a topic so widely discussed, it seems necessary to specify the meaning and reach of parricide. What is the philosophical point of this crime hinted at under cover of the image of murdering a father? We suggest understanding the Platonic parricide as a complex act which is made up of three closely related moments: the transgression of a precept, the negation of a concept and the reformulation of a method." (p. 40)
Luchetti, Chiara. 2011. "Nicolai Hartmann’s Plato. A Tribute to the “Power of Dialectics” (Parmenides, 135c 2)." In The Philosophy of Nicolai Hartmann, edited by Poli, Roberto, Scognamiglio, Carlo and Tremblay, Frederic 221–235. Berlin: de Gruyter.

"This contribution is just the beginning of a wider range inquiry into Hartmann’s Platonism and is chiefly aimed at providing a concise overview of Hartmann’s first hermeneutical approach to Plato. Hopefully, it is successful at least insofar as it shows how strongly Hartmann believed in the centrality of dialectics as the privileged way to understand Plato’s thought in general." (pp. 233-234)
Lynch, William. 1959. An Approach to the Metaphysics of Plato through the Parmenides. Washington: Georgetown University Press.

Second edition: Westport, Greenwood Press 1969.

"According to the interpretation of the following pages, Plato in the Parmenides is giving a skeletonized and ordered summary of his views on the essence of the Idea Doctrine, on the basic structure of sensibles and numbers, on the nature of unity, the indeterminate, the relation of the contraries, time, the unmeasurable "instant" in time, motion, the Other, the different forms of non-being, his theory of communication, of participation, the nature of identity, the nature of difference, the possibility and source of predication, the way of opinion versus scientific knowledge, the character of limit and the unlimited, the nature of articulation in any unity, the discrete and the continuous, the possibility of real unity in any one many, the logic of change and transition, of otherness, of relation. Nor are these pieces thrown at us helter-skelter, though some of them are treated indirectly. There are great unifying, ordering, and “enabling” concepts, and I have paid special attention to two of them. They are: (i) Plato’s theory of participation (it is not easy, in the light of this dialogue, to see how Aristotle could ever have regarded it as a passing, ineffective metaphor); and (2) his constant and complicated success in mediating the original Parmenidean dichotomy between being and non-being.

One could say many more things about the content of the Parmenides — but this is only a preface." (Preface, pp. VIII-IX)
MacIsaac, D. Gregory. 2022. "Plato’s Account of Eleaticism: A New Interpretation of Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 67–74. Baden-Baden: Academia Verlag.

Abstract: "I propose a new interpretation of Plato’s Parmenides. I avoid the assumption of Developmentalism, that Plato is criticising his own ‘middle’ theory of forms. Instead, I read the dialogue as Plato’s serious presentation of the Eleatic position. He shows that Eleatics’s counterintuitive thesis follows from the fundamental assumption of qualitative monism. The animating idea of the dialogue is indicated by Zeno. Whereas Parmenides’ critics said many laughable things followed from his thesis of the One, Zeno’s book showed that what follows from the many is more laughable. The dialogue is a step-by-step elimination of the many, so that its readers have no choice but to accept the sole One. Against other interpreters, I argue that the first step in the argument isn’t a survey of the levels of Forms, but a demonstration that Socrates cannot explain how the many material things could possess contradictory characters. I argue that the five problems of participation are not a criticism of Forms, but of participation itself, and are solved by eliminating participants. I argue that the Eighth hypotheses are meant to show that a One without any characteristics is less laughable than a One with a totality of contradictory characteristics, and that only an intelligible world with a single One would yield this more plausible result. The first part of the dialogue, consequently, eliminates the material world and the second part eliminates all Forms but the One. Parmenides, consequently, is not a reductio of Eleaticism, but a presentation of Eleaticism from the inside, as a serious philosophical position. However, having made the best case he can for Eleaticism in Parmenides, Plato will diagnose its mistaken assumption, in Sophist, as the idea that things are ‘one in formula’ and propose the mixing of Forms as its remedy."
Mackenzie [McCabe], Mary Margaret. 1982. "Parmenides' Dilemma." Phronesis no. 27:1–12.

Published under the name ‘Mary Margaret Mackenzie’.

Reprinted in M. M. McCabe, Platonic Conversations, Ne3w York: Oxford University Press 2015, pp. 73-82.

"Parmenides the Eleatic wrote a treatise that intrigued, puzzled, and confounded the later philosophical tradition. In it, he argued for a strong monism: what there is is eternal, complete, immoveable, and unvarying, one and homogeneous (DK 28B 8.3–6).)2) All the rest, the world of perceptible things, is contradictory—or an illusion.

Strong monism is frighteningly radical. So Parmenides left a series of problems in his wake, some of which have proved so recalcitrant as to be dismissed with that counsel of despair ‘it’s a dialectical device’.(3) This chapter addresses two of those problems, and recasts the dialectical device in a mood of optimism." (p. 73, a note omitted)

(2) All references to Diels and Kranz (1968) (DK).

(3) Cf. Owen (1975), 54.

References

Diels, H. and Kranz, W. (1968) eds. Die Fragmente der Vorsokratiker 6th edition (Zurich: Wiedmann)

Owen, G. E. L. (1975) ‘Eleatic Questions’, in R. E. Allen and D. Furley, eds., Studies in Presocratic philosophy vol. 2 (London: Routledge) 48–81.
Makridis, Odysseus. 2016. "The Confusion of Logical Types in Plato's Parmenides." Philosophical Inquiry no. 40:13–29.

"Copious ink has been spilled on the problems, puzzles, and attempted refutations that populate the Platonic dialogue entitled Parmenides." (p. 13)

(...)

"My subject in what follows is to continue this relatively recent tradition of scrutinizing the dialogue’s key claims by bringing advanced logical analysis to bear.

Although a lot has been written on this dialogue over the last century, most of the scholarship applied standard logical apparatus to assess the dialogue’s claims and arguments for such basic features as consistency and validity. The thrust of the case I make is that non-classical logics must be added to the mix if the analysis is to reach sufficient depth." (pp.13-14)
Malatesta, Michele. 1997. "One Instance of Modus Tollendo Tollens in Plato's Parmenides 127 e 1-7?" Metalogicon no. 10:33–40.

"Plato quotes an inference of Zeno of Elea in these terms:

«if the beings are many, they must be both like and unlike; but this is impossible [ ... ] it is impossible that beings are many too». Plat. Parm. 127 e 1-7." (pp. 36-37)

"It is impressive to see that in Plato we find quoted not only an instance of Modus Tollendo Tollens, but, what is even more interesting, such an inference is expressed at the level of the modalized dyadic predicate logic of first order more than two millenniums before the birth of De Morgan, the father of modem logic of relations, and that of Lewis, the father of modem modal logic." (p. 38)
Marion, Florian. 2025. "Plato on Coming-to-Be: A Midway Path between Eleaticism and Creationism." Plato Journal no. 26:1–25.

Abstract: "The Parmenides is the locus of Plato’s theoria motus abstracti (that is, abstract kinematics) for it is here that Plato gives a mereological and locational analysis of motion (First Deduction: 138b7-139b3) and discusses the famous puzzle of the instant of change (Second Deduction: 156c1-157b5). But there is another scholarly very neglected text from this dialogue that provides us with great insights about Plato’s theory of change: the Fifth Deduction (160b3-163b6) and its answer to the Eleatic argument against coming-to-be."
Mársico, Claudia. 2022. "Intra-Socratic polemics. The Parmenides as an element of an anti-Megaric program." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 133–146. Baden-Baden: Academia Verlag.

Abstract: "This paper seeks to show that the consideration of the intra-Socratic discussions between Plato and the Megaric line shed light on the Parmenides regarding three main points. First, as Parmenides constitutes a central figure for the group initiated by Euclid, his influence explains some features of the Platonic recreation in the Parmenides. Then, it will be relevant to dwell on the impact of Eleatism on the Megaric line and its role in the link with Platonism. Second, this approach will identify Megaric elements in the arguments of the first part of the dialogue and their function within the work. Finally, based on the change of attitude of Parmenides’ character, we will suggest an interpretation of the hypotheses of the second section as part of a critical response to the Megaric thesis of the Good-One regarding its method, the nature of the principle, and the relationship between the intelligible and sensible levels. As a result, it will be possible to reach an integral view about the dialogue and its structure."
Matoso, Renato. 2020. "Parmenides’ first and second hypotheses, αὐ τὰ τὰ ὅ μοιά, and Socrates’ astonishment." Filosofia Unisinos. Unisinos Journal of Philosophy no. 21:163–167.

Abstract: "In this paper, I propose a new interpretation for two of the most debated passages of Plato’s Parmenides: Socrates’ long speech (128e5–130a2) and Parmenides’ first antinomy (137c-155e). My aim is to demonstrate: 1) that Socrates’ speech can only make sense if we understand αὐ τὰ τὰ ὅ μοιά as a third kind of entity, the immanent property sensibles have by participating in the form of Likeness; 2) that the first two hypothesis of the second part of the dialogue (137c-155e), together with Parmenides’ criticism in the first part of the dialogue (130b-134e), is an answer to Socrates’ challenge (128e-130a). Parmenides’ arguments aim to show that, according to Socrates’ own premises, it is not possible for forms or immanent properties to be the kind of unity Socrates wants them to be. Finally, 3) I will use these results to suggest an innovative answer to the vexed question about the relation between the first and second parts of the Parmenides. According to my interpretation, the exercise of the second part of the dialogue does not provide the solution to Parmenides’ criticism of the theory of forms, despite what the majority think today. Rather, it radicalizes this criticism by pointing to a fundamental miscomprehension on Socrates’ conception of what it is to be a unity."
McCabe, Mary Margaret. 1996. "Unity in the Parmenides: the Unity of the Parmenides." In Form and Argument in Late Plato, edited by Gill, Christopher and McCabe, Mary Margaret, 5–48. Oxford: Oxford University Press.

Reprinted in M. M. McCabe, Platonic Conversations, New York Oxford University Press 2015, pp. 138-169.

"In what follows, I shall suggest that the reader is put in a specially dialectical position in this dialogue so that the open frame of this dialogue is particularly telling.

The dialogue progresses, I shall argue, from the discussion of views that are particular to the protagonists to a discussion that is entirely general; and it does so in three stages—the Socratic debate of the first part, the discussion of the first hypothesis, ‘if one is’, and the discussion of the second hypothesis, ‘if one is not’. Each stage reflects on the theoretical conditions of its predecessor; each stage of the dialogue is of a higher order of abstraction than its predecessor. Just as the story is narrated by one person who is reporting what was said by another, and he by another, so the arguments of the dialogue are ordered, each reflecting on its predecessor; the frame provides an analogy for the structure of the arguments. The dialogue is then unified by its topic: the whole discussion is an investigation of what there is, demonstrating that any ontology, any account of what there is, counts individuals. The discussion of individuals, of ones, unifies the Parmenides." (p. 140 of the reprint)
McPherran, Mark L. 1983. "Plato's Parmenides Theory of Relations." Canadian Journal of Philosophy no. 13:149–164.

"Hector-Neri Castañeda has argued that in the Phaedo we can find a logically viable Platonic theory of relations.(1) I am in agreement with this view. Furthermore, I find there to be a clarification of Plato's theory in the ‘worst difficulty’ argument of the Parmenides (133a-135a)." (p. 149)

(...)

"1. The Parmenides Theory of Relations

In the course of advancing a general sceptical argument against the classical theory of Forms Parmenides gets Socrates to agree to anumber of general principles:

A. Forms are (categorically) just by themselves (κατ' αυτό; 133a9), and because of this no Form is in us or among us (ἐν ήμιν; 133c2-5), nor do we [particulars] possess (ἔχειν) them (134b3-4).

B. There is a certain class of Forms which ‘are what they are with respect to one another’ and which ‘have their being in such references among themselves’ (133c8-9).

C. The things in us (ἐν ήμιν) which bear the same names as the Forms are related among themselves, not to Forms (133d1-4). This means that, for instance, a particular master cannot master Slavery, nor can Mastery be in reference to a particular slave (133d7-e2).

With this we have the makings of a theory of relations. We then need to see whether it is the theory of the Phaedo." (p. 151)

(1) See H-N. Castañeda, (a) ‘Plato's Relations, Not Essences or Accidents, at Phaedo 102b2-d2,’ Canadian Journal of Philosophy, 8 (1978) 39-53; (b) ‘Plato's Phaedo Theory of Relations,’ Journal of Philosophical Logic, 1 (1972) 467-80; (c) ‘El analisis de Platón de las relaciones y de los hechos relacionales,’ Critica, 14 (1971) 3-18.
———. 1986. "Plato’s Reply to the 'Worst Difficulty’ Argument of the Parmenides: Sophist 248a - 249d." Archiv für Geschichte der Philosophie no. 68:233–252.

"In a previous paper I have argued that the theory of relations Hector-Neri Castañeda has discovered in the Phaedo is clarified and extended in the Parmenides. In particular, the paper contains an Interpretation of the 'worst difficulty' argument (Parm. 133a —135a), an argument purporting to establish that human knowledge of the Forms is impossible2 My Interpretation showed the argument to utilize the extended theory of relations in its premises. I also showed, contrary to previous interpretations, how Plato's argument was logically valid.

One consideration in favor of the Interpretation I offered is that it allows the argument at last to live up to its description as the most formidable challenge to the early theory of Forms (in a long series of tough arguments), requiring a "long and remote train of argument" by "a man of wide experience and natural ability" for its unsoundness to be exposed (Parm. 133b4 c1).

Unfortunately, the Parmenides does not contain such a reply, even though the text at 133b seems to hint that Plato had already formulated one. Did he ever entertain and record a reply, and if so, could that reply rescue some version of the theory of Forms from the devastating consequences of the 'worst difficulty'? In the following, I present my previous reconstruction of that argument and the most plausible lines of response open to a defender of a theory of Forms. In the second section I argue that Plato gives clear recognition to one of those replies in the Sophist, and I show how that reply would save the theory of Forms. Finally, I will contend that this reply is Plato's best line of response, and I will discuss the problem of actually attributing the adoption of this solution to him." (pp. 233-234, notes omitted)
———. 1999. "An Argument 'Too Strange': Parmenides 134c4-e8." Apeiron.A Journal for Ancient Philosophy and Science no. 32:55–71.

"Here, then, I offer an assessment of the second half of the Greatest Aporia that focuses on its unique contribution to the Parmenides' critique of the Theory of Forms.

This account shows, I trust, that this portion of the argument is designed to force on even those students 'of natural ability' who might have found a solution to the Aporia' s first half, the recognition of a potential problem latent in both the metaphysics and epistemology of the Theory of Forms." (p. 57)
Meinwald, Constance C:. 1991. Plato's Parmenides. New York: Oxford University Press.

"In my own interpretation of the exercise, which constitutes the heart of this study, I approach the arguments systematically and read them in the light of Parmenides' methodological remarks. What results is a positive and crucial innovation—a distinction between two kinds of predication— whose application enables us to recognize that the exercise consists of good arguments whose conclusions are not contradictory after all.

Since the point of the exercise is, in large part, to enable us to deal with the problems of the first part of the dialogue, I have placed my analysis of the second part of the Parmenides in its natural context: I precede it with a preliminary discussion of the famous problems, and I return, once I have the results of the second part of the dialogue in hand, to consider how they bear on the problems. By this point, I will have accumulated a body of evidence for my characterization of Plato's position at the moment of writing the Parmenides. An epilogue sets the results of my study in a larger context, namely, our understanding of Plato's development." (p. 4)
Meinwald, Constance C. 2005. "Literary Elements and Dialogue Form in Plato’s Parmenides." In Plato's Parmenides. Proceedings of the Fourth Symposium Platonicum Pragense, edited by Havlícek, Ales and Karfík, Filip, 9–20. Prague: Oikoymenh.
———. 2014. "How Does Plato’s Exercise Work?" Dialogue. Canadian Philosophical Review no. 53:465–494.

Abstract: "I analyse the pros ta alla / pros heauto distinction in Plato’s Parmenides as a contrast between ordinary predication (corresponding to an individual’s display of a feature or, more technically, instantiation) and tree predication (based on a nature X being involved in a nature Y). I engage with my critics and argue that this interpretation vindicates Plato’s methodological remarks and maximizes his argumentative success.

My interpretation shows how the Parmenides bridges the gap between Plato’s Middle Dialogues and the outstanding technical developments of the Late Dialogues."
Meister, Samuel. 2022. "Gunk in the Third Deduction of Plato’s Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 393–400. Baden-Baden: Academia Verlag.

Abstract: "The third deduction in Plato’s Parmenides is often given a constructive reading on which Plato’s Parmenides, or even Plato himself, presents us with a positive account of the relation between parts and wholes. However, I am going to argue that there is a hitch in the third deduction which threatens to undermine the mereology of the third deduction by the lights of the dialogue. Roughly, even if the Others partake of the One, the account of the third deduction leads to an ontology of gunk, that is, an ontology on which there are no mereological atoms (except for the One). Hence, it is unclear whether the participation relation between the Others and the One is sufficient to impose the sort of structure on the Others which, in the context of this deduction, Parmenides (or Plato) seems to hope for.

Instead of the constructive reading of the third deduction, I will therefore offer an aporetic reading on which the third deduction raises further difficulties for the participation relation at the heart of young Socrates’ theory of Forms.."
Mesyats, Svetlana. 2012. "Iamblichus' exegesis of Parmenides hypotheses and his doctrine of divine henads " In Iamblichus and the Foundations of Late Platonism, edited by Afonasin, Eugene V., Dillon, John M. and Finamore, John F., 151–175. Leiden: Brill.

"The doctrine of divine henads was developed in late Neoplatonism in the course of efforts to solve a problem of a transcendent First Principle. In the classical form of this doctrine, which it received from Syrianus and Proclus, henads were thought to be supra-essential unities, proceeding directly from the One and differing from it only by their connection with Being. Due to the connection with something other than themselves henads could not be as much transcendent as the primal One; they came in some relationship with the world and therefore played the role of intermediary substances between the absolutely unparticipated Principle and the plurality of its effects. It seems probable that this theory appeared as a result of exegesis of Plato’s Parmenides and in particular of the idea to consider predicates of the One in the first two hypotheses as the characteristics of the different classes of henads. We suppose that the author of this idea could be Iamblichus, because he was the first to mention divine henads in connection with Parmenides, and to conceive the predicates denied of the One in the 1st hypothesis to be also denied of henads. We have tried to reconstruct Iamblichus’ doctrine of henads, since some previous attempts at reconstruction, where henads were identified with monads of forms and idea-numbers, seem to be unsatisfactory." (p. 173)
Migliori, Maurizio. 2022. "The many meanings of the One in Plato’s Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 299–307. Baden-Baden: Academia Verlag.

Abstract: "The present argument is too complex to be adequately addressed in a few pages. Therefore, this short text only lists the different meanings that Plato conceals behind the word “One”. Plato’s strange behaviour is justified by recalling his very particular conception of philosophical writing. Plato tries to keep the “maieutic” attitude of Socrates in the written text and describes it as an important “game”, because philosophy must be practiced, not passively learned. On this basis it is shown that Parmenides does not respect the proposed argumentation scheme, because he contrasts the One not with the Many but with the Other/the Others. Besides, the first thesis (the One in relation to itself) presents many references to the Others; similarly the second thesis (the One in relation to the Other / the Others) presents a series of characteristics of the One-that-is in relation to itself. Finally, Plato proposes in the first two theses two different ideas of the One, making Parmenides’ scheme – based on a single concept – untenable. The first thesis talks about the One-one that refuses any predicate because it would become two. On the contrary, the One-that-is of the second thesis possesses countless predicates: indeed, it is dual by its very composition (One and Being). Then they are analysed 1) the one-many reality, best expressed by the connection between the One-whole and the One-part, 2) the One that appears only one, regardless of the participation with Being, based on a purely mental operation, 3) the One-number and 4) the One as Principle. The text concludes by showing the coherence of Plato’s dialectical vision and stressing that it expresses a multifocal vision of reality (and requires an analogous attitude of the reader)."
Mignucci, Mario. 2020. "Relatives in Plato." In Ancient Logic, Language, and Metaphysics: Selected Essays by Mario Mignucci, edited by Falcon, Andrea and Giaretta, Pierdaniele, 279–299. New York: Routledge.

"Talking about relations with reference to the ancient world is vaguely provocative. It is enough to peruse any modern manual of the history of logic to find the affirmation that classical antiquity did not work out a theory of relationships. This claim is certainly true if it means that there is no calculus of relations analogous or comparable to what was elaborated by Gottlob Frege in antiquity. But it is false if it means that it is not possible to find a body of reflections, sometimes stimulating and acute, that gives rise to an embryonic theory of relations. Although these reflections are certainly not an alternative to the logic of relations elaborated by Frege, they are of great interest because they allow us to clarify certain philosophical assumptions that are at the root of our modem understanding of the nature of relations. Reflecting on them can help, therefore, to highlight the prerequisites of the Fregean position - prerequisites that are not universally perceived, let alone clearly articulated, by the logicians who have concerned themselves with the theory of relations. In Plato we find, for the first time in the history of Western thought, many of the ideas that will not only constitute the starting point of the subsequent debates on the nature of relations in Greek philosophy but also the main ideas that will be further elaborated in the medieval tradition and in at least a part of the modem one. In this chapter, I will focus on a few texts from the Phaedo, the Symposium, and the Parmenides that can help outline certain aspects of Plato's conception of relations.

Without any pretension of being exhaustive, I set for myself the task of casting some light upon the main lines of Plato's conception of relatives. Needless to say, to fully grasp the complexity of Plato's position a more extensive, and indeed more in-depth, study of the Platonic corpus would be needed." (p. 279?)
Miller, Mitchell H. 1986. Plato's Parmenides: The Conversion of the Soul. Princeton: Princeton University Press.

"Put simply, the project of the present study is to read the Parmenides with unwavering attention to its dramatic wholeness.

Close attention to the dialogical features of the Parmenides will make possible a determinate interpretation of its otherwise indeterminate and riddling content. In particular, it will reveal both the definite range of Parmenides' obscure One and the precise function of his hypotheses, and this, in turn, will permit the intended philosophical significance of the dialogue as a whole to emerge." (p. 6, a note omitted)

(...)

"My orienting question will be: what is the test and provocation Plato intends in devising his hypotheses, and what is the response he seeks to occasion in his hearers? Part One justifies and prepares the question itself. Chapter I discusses the narrative framing, dramatic context, and dramatis personae of the Parmenides, and Chapter II analyzes the elicitative and refutative arguments with which Zeno and Parmenides confront Socrates. A main project in these reflections will be to identify the sort of hearer Plato aims, most of all, to reach(27) and to specify what Plato sees as this hearer's predicament and task. If these reflections succeed, we will have set the stage for the central project of Part Two: the reconstruction of the subsurface significance that Plato intends such a hearer, provoked to a critical rethinking, to find in the hypotheses." (p. 10, a note omitted)
———. 1987. "Aporia and Conversion: A Critical Discussion of R. E. Allen's "Plato's Parmenides"." The Review of Metaphysics no. 41:355–368.

"Every student of the Parmenides will be struck by the substantive richness and close orchestration Allen reveals in Parmenides' criticisms of Socrates' theory of forms and by the sheer elegance of the plan he finds in the hypotheses.

In addition, there are a number of gifts along the way, most notably several illuminating discussions of Greek mathematics and the concept of the infinite, a sustained comparison of Platonic and Aristotelian ontology by way of numerous, surprisingly apt quotations from the Physics and Metaphysics, and a compelling excursus on existence and quantificational logic; all of this expands the context of the hypotheses and allows the specificity and implications of many particular arguments to become evident. In spite of these great merits, however, there are also important limitations to Allen's reading. In part because he does not fully exploit several of his own insights, in part because the remarkable internal coherence of the Platonic plan he sees sometimes distracts him from actualities and possibilities of the text, he stops short of recognizing a still deeper reading that the Parmenides invites." (pp. 369-360)
———. 1995. ""Unwritten Teachings" in the Parmenides." The Review of Metaphysics no. 48:591–633.

"Our path of inquiry shall be as follows. In Parts A and B we will lay out, quite independently of one another, the "unwritten teachings" that Aristotle reports in Metaphysics A6 and the core of the subsurface

argument offered by the Parmenides. In Part C we shall take the first step in bringing these together by noting in the hypotheses the major appearances of the key notions in Aristotle's report, "the One" and "the Great and the Small." But it is not so much in these explicit appearances that the "unwritten teachings" present themselves as it is, rather, in the interplay of "the One" and the dyad that is implied by another passage altogether, the account of participation in hypothesis IIL We must therefore interpret this account and explicate its implications-these will be the projects of Parts D and E, respectively. The result, if these reflections are well taken, will be fresh, mutually supportive interpretations both of the "unwritten teachings" and of parts of the Parmenides. We will also have uncovered the need for several fresh inquiries, which I will title in closing." (p. 594)
———. 2022. "Parmenides 143d–144a and the Pebble-Arithmetical Representation of Number." In Knowing and Being in Ancient Philosophy, edited by Bloom, Daniel, Bloom, Laurence and Byrd, Miriam, 149–165. Cham, Switzerland: Palgrave Macmilllan.

Abstract: "The purpose of this short reflection is to draw on a largely ignored, if not forgotten, ancient resource in order to suggest a fresh reading of a problematic passage in Plato’s Parmenides, Parmenides’ proof for the being of number at 143d–144a. I shall first translate the passage (Sect. 9.1), then note the key problems and explain why I think we should be unsatisfied with the best of the responses that, to my knowledge, have been offered in the secondary literature (Sect. 9.2), and then offer the fresh reading (Sect. 9.3). I shall close with an aside on the possible fit of our passage, under this reading, with one of the otherwise obscure teachings that Aristotle credits to Plato in his report of various unwritten teachings in Metaphysics A6 (Sect. 9.4)."
Moravcsik, Julius. 1982. "Forms and Dialectic in the Second Half of the Parmenides." In Language and Logos: Studies in Ancient Greek Philosophy Presented to G. E. L. Owen, edited by Schofield, Malcolm and Nussbaum, Martha, 135–153. Cambridge: Cambridge University Press.

"The second half of the Parmenides has been a source of puzzlement to generations of scholars, inspiring a wide variety of interpretations. Thanks to the groundbreaking work of Ryle and Owen, one can see this material today as offering serious reflections of conceptual and metaphysical nature. In this chapter I wish to locate the key conceptual problems that Plato addresses in this passage, and argue that Plato is here also defending and revising his theory of Forms." (p. 135, a note omitted)
———. 1992. Plato and Platonism: Plato's Conception of Appearance and Reality in Ontology, Epistemology, and Ethics, and Its Modern Echoes.

See the Chapter 4: The Parmenides: Forms and Participation reconsidered pp. 129-167.

"The interpretation to be presented revolves around three key claims.

First, the key elements of the fundamental realm are the Forms. The conception of these undergoes change in the dialogues, but they remain the basic explanatory entities. Their order is mirrored by whatever else in the world is in some way orderly, and their nature never corresponds to such modern ontological categories as properties or universals. Second, the key Platonic epistemological notions are those of insight and understanding, rather than propositional knowledge. Third, Platonic ethics revolves around the choice of an adequate ideal for individual and communal life. This ideal consists of a worthwhile overall aim for life and a character structure that fits the aim selected." (Preface, pp. VI-VII)

"Many questions can be, and have been, raised about the Parmenides. Here we shall confine ourselves to the following issues: What, if any, conception of the Forms emerges in this dialogue? Does it require changes in the conception examined in chapter 2 [The Forms: Plato’s Discovery]? Does the notion of partaking as presented in the Phaedo require modifications? How do these clarifications help us to assess the explanatory power of the theory of Forms?

Addressing these questions is a formidable task. Thus many other questions — for example, the consequences of the arguments of this dialogue for geometry, the analysis of time, and cosmology — will not be treated, although they have been discussed repeatedly throughout the centuries and in our own time." (p. 132, a note omitted)
Mouroutsou, Georgia. 2022. "A Diagnosis of Dialectic in Parmenides 142b1-144e7." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 193–200. Baden-Baden: Academia Verlag.

Abstract: "In my analysis of the two arguments in Prm. 142b1-144e7, I will follow and modify Owen when he says that Plato introduces the special, as he calls them, syncategorematic terms that will emerge in the Theaetetus and the Sophist. Though I find this true, I think there is something wrong with both arguments that show that the One that is is an unlimited plurality. My hypothesis is that what goes wrong is twofold: (i) The one and the being are not treated as special vowel-connectives and bonds, according to the Sophist’s picture, but like anything whatsoever that is and is one. They are considered component properties (property parts) of one another as any other properties would be in the first argument.

Though the “Anaxagorean holistic model”, as Scolnicov dubs it, might remind us of the complete permeation of being, otherness and sameness in the Sophist, it is problematic in the above respect. (ii) Although the kind of beings that Parmenides alludes to go beyond numbers in the second argument that focuses on instance parts and not property parts instead, we have no question asked about and no theory constructed of a general ontology as formulated in the Sophist. Without such a theory, we are wrong to speak of wholeness and everything in the case of being and the one, given our definition of the whole with which we have operated since the first deduction as what does not lack any part."
Mouzala, Melina G:. 2022. "Proclus on the Forms as Paradigms in Plato’s Parmenides. The Neoplatonic Response to Aristotle and Alexander of Aphrodisias’ Criticisms." Journal of Ancient Philosophy no. 16:115–163.

Abstract: "This paper sets out to analyze Proclus’ exegesis of Socrates’ suggestion in Parmenides 132d1-3 that Forms stand fixed as patterns (παραδείγματα), as it were, in the nature, with the other things being images and likenesses of them. Proclus’ analysis of the notion of being pattern reveals the impact of the Aristotelian conception of the form as paradigm on his views, as we can infer from Alexander of Aphrodisias’ and Simplicius’ explanation of the paradigmatic character of the Aristotelian form. Whereas Aristotle and Alexander of Aphrodisias refute the efficient causality of the Platonic Forms and support that μέθεξις is just a metaphor, Syrianus, Proclus and Asclepius defend the Platonic theory, and specifically Proclus, who brings to the fore the multilateral role of the Forms as patterns with regard to the secondary things of this realm."
———. 2022. "Forms as paradigms in Plato’s Parmenides 132c-d. Proclus’ response to Aristotle and Alexander of Aphrodisias’ attacks on the Forms considered as patterns." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 501–508. Baden-Baden: Academia Verlag.

Abstract: "The aim of this paper is threefold. Firstly, to analyze Proclus’ interpretation of Socrates’ suggestion that “Forms stand fixed as patterns, as it were, in the nature; the other things are made in their image and are likenesses” (Pl. Prm. 132d). This analysis will focus especially on Proclus’ explanation of the quality of being a pattern (paradeigmatikon idiōma) and on his interpretation of the role of Forms as paradigmatic causes. Secondly, to clarify the main point of Aristotle’s criticism of the Forms as paradigms in his Metaphysics (where he seems to discuss the problems of methexis in the order in which they are posed in Parmenides), by investigating Alexander of Aphrodisias’ exegesis of the Aristotelian objections. We will analyze how Alexander explains on the one hand the Platonic Forms as paradigms and on the other the Aristotelian eidos considered as paradigm, both in his Commentary on Aristotle’s Metaphysics as well as in his lost Commentary on Aristotle’s Physics, according to the testimony of Simplicius. Thirdly, to examine in general the Neoplatonic response to the attacks by Aristotle and Alexander of Aphrodisias on the Forms considered as patterns, by comparing the interpretations of Proclus, Syrianus and Asclepius of Tralles of Forms as paradigms (since the latter’s Commentary is highly dependent on the lectures of Ammonius, we can assume that it can be traced within it Ammonius’ view of the notion of paradeigma)."
Mueller, Ian. 1983. "Parmenides 133a-134e. Some Suggestions." Ancient Philosophy no. 3:3–7.
Mulhern, John J. 1971. "Plato, Parmenides 130D3-4 " Apeiron no. 5:17–22.

"It is thought by many scholars that the first part of the Parmenides offers important clues for tracing the development of Plato's Theory of Ideas. This commonly held belief draws support from the fact that three crucial problems for the Theory of Ideas are put forward here: (1) the problem of determining what items the Theory covers--the population of the World of Ideas (130A3-E4); (2) the problem of meeting certain paradoxes connected with the doctrine of participation (130E4-133A7); and (3) the problem of showing that Ideas, if there were such, should fall within the purview of human knowledge (133A8-134~E8).

In recent years, the second of these problems has taken the lion's share of attention. The present note, however, is devoted to the first problem.

I wiah to suggest that, although little seams to have been made of this matter to date, scholars interpret the discussion of the population of the World of Ideas in two fundamentally incompatible ways." (p. 17)
Murphy, N. R. 1937. "Plato, Parmenides 129 and Republic 475–480." The Classical Quarterly no. 31:71–78.

Abstract: "The reply which Socrates makes to Zeno in the Parmenides and that which he makes to the φιλοθμονς in the Republic are perhaps connected chiefly by the fact that a false interpretation of either might prejudice the other, but it seems convenient to take them together for that reason even if they have not much actual connection in themselves. Both are controversial, and in the case of Socrates' reply to Zeno, no re-statement of it could be secure which did not take account of Parmenides' reply to Socrates. For if Parmenides, as is maintained by some, is not attacking the doctrine of forms as such, but only Socratic theories of their relation with particulars, it would be natural to think that these theories about ‘participation’ had been the substance of Socrates' answer to Zeno. So it is impossible to avoid some discussion of the later passage, however cursory, as a preliminary."
Nehamas, Alexander. 1979. "Self-Predication and Plato's Theory of Forms." American Philosophical Quarterly no. 16:93–103.

Reprinted in: A. Nehamas, Virtues of Authenticity. Essays on Plato and Socrates, Princeton: Princeton University Press 1999, pp. 176-195.
———. 2019. "The Academy at Work: The Target of Dialectic in Plato’s Parmenides." Oxford Studies in Ancient Philosophy no. 57:121–152.

Abstract: "Zeno’s argument against plurality in the Parmenides does not support the view that there is only one object in the world—only the view that every object in the world is one. Socrates counters that every sensible object can be many by participating in Forms, but none of the Forms can be many. Parmenides retorts that participation is not consistent with the Forms’ unity. The dialectic Parmenides offers derives a series of contradictions from supposing either that each Form is one or that it is many (that is, qualified by any other feature). The implicit solution is that participation must allow the Forms to participate in one another without losing their essential unity. The net result, central to the Academy’s educational programme, is to articulate, for the first time, the concept of predication as we understand it today. Its results are summarized in the Sophist’s discussion of ‘Greatest Kinds’."
Notomi, Noburu. 2022. "Homonymy and Similarity in Plato’s Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 21–219. Baden-Baden: Academia Verlag.

Abstract: "In this paper, I examine ‘similarity’ (ὅμοιον) as a key to interpret the Parmenides. First, I focus on the backgrounds of the problem and show that, while the earlier thinkers, particularly the Eleatics, used the word ‘ὅμοιον’ in the sense of ‘the same’, Plato was the first philosopher who clearly distinguished between ‘similar’ (ὅμοιον) and ‘the same’ (ταὐτό).

Next, in the theory of transcendent Forms, the relation between Forms and sensible things is explained in terms of ‘similar’ and ‘homonymous’ (ὁμώνυμον). It is worth noting that the concept of ‘the same’ plays a crucial role in introducing Forms, for Forms are grasped by focusing on the same form over many sensible things. The Parmenides introduces the concept of similarity in Zeno’s argument (128e-129b). Against his argument, Socrates suggests that positing the Forms of Similarity and Dissimilarity will solve the difficulty. But the fourth argument of Part 1 (132c–133a) produces an infinite regress in examining the concept of similarity that represents the relation between Forms and sensibles as between models and copies (I follow the interpretation of Schofield 1996). This indicates that the initial introduction of Form of Similarity has raised difficulties. In Part 2 of the Parmenides, similarity is discussed as one feature to examine in relation to the One. There, the concept of similarity is analysed as ‘what is affected in the same way (ταὐτόν που πεπονθός)’ (139e) and is thus defined in terms of Sameness. This seems a crucial step from the vague use of ‘similarity’ towards a new understanding of it in terms of ‘sameness’: the latter is counted among the five Greatest Kinds in the Sophist, whereas the Form of Similarity no longer appeared in the Sophist and later dialogues. This suggests how Plato sorted out the difficulties concerning ‘similarity’."

References

Schofield, M. 1996. ‘Likeness and Likenesses in the Parmenides’. In Form and Argument in Late Plato, edited by C. Gill and M. M. McCabe, 49-77. Oxford: Oxford University Press.
O'Brien, Denis. 2013. "Forms and Concepts." In Plato, Poet and Philosopher: In Memory Of Ioannis N. Theodoracopoulos. Proceedings of the 3rd International Conference of Philosophy, Magoula-Sparta, 26-29 May 2011, edited by Moutsopolos, E. and Protapas-Marneli, M., 193–244. Athens: Academy of Athens.

Summary: "Are Plato’s forms all so many concepts? The question, on the face of it, is a simple one. But even to attempt an answer, we have to tackle two related issues that have been the cause of much misunderstanding in recent scholarly literature, firstly the «existential» use of the verb einai in ancient Greek, and secondly the relation between thought and its object in Plato and his predecessors. Only with at least a preliminary understanding of those two issues can we hope to take the measure of young Socrates’ suggestion, in the Parmenides, that «each of the forms» might be no more than «the thought of these things» (132 b3-4), that the form of largeness, for example, might be no more than the thought of all the many things that we group together as large. Does Plato’s portrayal of young Socrates’ suggestion and of Parmenides’ reply allow us to decide whether, at the time of writing, Plato did, or did not, intend his readers to conclude that the forms are all so many concepts?"
Otto, K. Darcy. 2003. "Solving the Second Horn of the Dilemma of Participation." Apeiron no. 36:25–42.

"The Second Horn of the Dilemma of Participation(1) has caused commentators of the past century a good deal of grief, on two points in particular: first, it is difficult to account for the structure of the argument; and second, it is difficult to provide a consistent interpretation of the paradoxes involving the Large, the Equal and the Small. The main goal of my paper is to solve these two difficulties by offering a new interpretation of the passage. To this end, I shall begin by discussing the argument itself, and then I shall present my interpretation." (p. 25)

(...)

"Conclusion

It should be clear at this point that my interpretation solves both difficulties set out at the beginning of this paper. First, by taking the 'γαρ' at c12 as referring back to Socrates' denial of the Forms being one, I can explain how the Paradoxes are integrated into the structure of the Second Horn. Second, the two-level interpretation allows me to account for Paradoxes consistently: I account for the generality of Parmenides' conclusion (e4-6), while neither supposing that Plato is confused about relations nor orphaning the Third Paradox.

The upshot of this interpretation is that we can read the Second Horn of the Dilemma as a reductio, which means that the Dilemma itself is destructive: participation takes place neither by the whole of the Form being present in the particular, nor by part of the Form being present in the particular. But the argument, as we have construed it, depends upon a number of assumptions; and so Socrates does have a few options. The homoeomereity of a divided Form is difficult to avoid (particularly with respect to function), but he could try to escape the force of the Paradoxes by denying that Forms are divisible: if Forms are indivisible unities, there is no problem with their being one. Nevertheless, such a move would be unproductive unless we have in hand a solution to the First Horn. In any case, it is clear that if Socrates is to give a viable account of participation, he should not begin with the assumption that a part of the Form is present in the particular." (pp. 39-40, a note omitted)

(1) 1 'Dilemma of Participation' is the name R.E. Allen gives to Parmenides 131a9-c3 (1997, 8). I borrow the name, but apply it to 131a9-e8. The Second Horn runs from 131c5-e3.

The translation and line numbers for the Parmenides follow Dies' text (1974). All translations from the Greek are my own unless otherwise noted.

References

Allen, R.E. 1997. Commentary to Plato's Parmenides. New Haven, CT: Yale University Press.

Plato. 1974. Parménide [Parmenides]. CEuvres complètes. Ed. Auguste Dies. Tome VIE, lre Partie. Paris: Les Belles Lettres.
———. 2009. "The logic of the first horn of the dilemma of participation." Ancient Philosophy no. 29:89–105.
———. 2017. "Resemblance and the Regress." Apeiron no. 50:81–101.

Abstract: "This paper examines the second regress argument of the Parmenides (132c12–133a7), and focusses on the question: why is the argument effective?

There is widespread disagreement about how this question should be answered.

Broadly speaking, recent commentators have given three explanations: (i) the regress contradicts the uniqueness of Forms. That is, each Form is unique, and an infinite regress contradicts this uniqueness. (ii) The regress demonstrates that Forms cannot account for why particulars have the characters they do, since the regress prevents the account from ever being complete. (iii) The regress contradicts the unity of the Form, and since each member of the infinite series participates in an infinite number of Forms, each Form has an infinite number of parts. I examine these positions in some detail. While each has its virtues, it is impossible to adjudicate between them without a theoretical framework dedicated to infinite regress arguments. I find a reasonable theoretical framework for infinite regress arguments in a little-known work of T. Roy, “What’s So Bad about Infinite Regress?”. After articulating Roy’s framework, and extending it to make it useful for an analysis of the second regress argument of the Parmenides, I propose three different readings of the regress: Reading A, which supposes that resemblance between particular and Form trigger an infinite number of resemblance relations; Reading B, which supposes that that the regress is ultimately vicious because it fails to account for the F-ness of a given particular, even when that particular participates in an infinite number of Forms; and Reading C, which supposes that there is an inconsistency between the unity of the Form and many particulars participating in the Form. While

none of these readings is absolutely definitive, and Reading B has some significant textual challenges, I argue that Reading B must be the way we are meant to understand Plato’s argument. I then argue that Reading B is the best account of why the second regress is effective."
Palmer, John Anderson. 1999. Plato's Reception of Parmenides. Oxford: Clarendon Press.

"I shall suggest that Plato understood Parmenides as presenting in the deduction that comprises the bulk of B8 a description of the cosmos in its intelligible aspect qua being. This description is compatible with a description of the cosmos considered from another perspective as a differentiated world system. We shall also see that the possibility of considering the cosmos from different perspectives and describing it in its different aspects relates in important ways to the problem of how one thing can have many names." (p. 207)

(...)

"It is a sign of the power of Parmenides' philosophy that it too influenced later thinkers in ways that he himself could never have imagined. Any attempt to describe his influence based on an account of what one presumes he must have meant only betrays his legacy. I hope that the reception-orientated account I have given of a particular chapter in that legacy restores a measure of his true importance in the history of philosophy. I also hope it will point the way to further work on his influence. A properly reception-orientated approach to his influence on Presocratic philosophy, for example, might well lead to significant revisions in our understanding of the history of early Greek thought. Finally, I would like to think that the approach I have taken to this one particular interaction could be extended to other cases of intellectual influence. I will be content, however, if I have achieved the more modest aim of indicating the full complexity of Plato's uses of Parmenides." (p 254)
Palumbo, Lidia, and Reid, Heather L. 2020. "Wrestling with the Eleatics in Plato’s Parmenides." In Athletics, Gymnastics, and Agon in Plato, edited by Reid, Heather L., Ralkowski, Mark and Zoller, Coleen P., 185–198. Fonte Aretusa: Parnassos Press.

"Conclusion.

It has been our purpose to show that Plato’s Parmenides can be interpreted agonistically as a constructive contest between Eleatic and Athenian philosophers. By setting the dialogue at the Panathenaic Games and using athletic language to describe its participants, Plato uses the athletic rivalry between Mainland and Western Greeks to highlight a parallel philosophical rivalry. As a former wrestler, Plato would envision this rivalry as constructive, and imagine the dialectical method, here called gymnasia, as a kind of philosophical training. It is a private, comprehensive, and challenging preparation designed to reveal the weaknesses in hypotheses, but also to develop the kind of “vision” described in Republic V, which distinguishes the philosopher from the mere spectator. This philosophical gymnasia resembles a round-robin training exercise in which the reader is called to participate. In Republic III, Socrates states that gymnastikē primarily benefits the soul (psychē, 410c), while the Parmenides offers a philosophical gymnasium in which all souls are invited to train." (p. 198)
Panagiotou, Spiro. 1969. "The Parmenides is the Philosopher. A reply." Classica et Mediaevalia no. 30:187–210.
———. 1980. "The "Range of Forms" in Plato's Parmenides." Philosophical Inquiry no. 2:420–429.
———. 1981. "The 'Parmenides' and the 'Communion of Kinds' in the 'Sophist'." Hermes no. 109:167–171.

"In Plato's 'Parmenides', Socrates states that he would be indeed amazed if the Forms themselves were shown to be «capable of mingling and separating» (129 D 6- E 3). It seems to be a standing assumption that Socrates' remarks here deny the doctrine of the 'Communion of Kinds' which is put forth and rigorously defended in the 'Sophist' (251 C ff.)(1) I believe that the truth of this assumption is called into question by two different sorts of considerations.

First, it is debatable whether the 'Parmenides' passage has in fact anything to do with the 'mixture' of Forms. Second, even if we suppose that the passage is concerned with the 'mixture' of Forms, it is by no means obvious that it contradicts the position on the 'Communion of Kinds' put forth in the 'Sophist'." (p. 167)

(1) Cf. e. g. W. Lutoslawski, The Origin and Growth of Plato's Logic, 436; F. M. Cornford, Plato's Theory of Knowledge, 11-12, 252-3; W. D. Ross, Plato's Theory of Ideas, 112; W. G. Runciman, Plato's Later Epistemology, 58.
———. 1981. "The Relative Order of Plato's Parmenides and Theaetetus." Classical Philology no. 76:37–39.

"Although stylometric studies generally show that Plato's Parmenides and Theaetetus are adjacent in the order of composition, the exact order of the two dialogues is not at all certain.' In such cases, arguments from internal evidence might prove crucial in tipping the balance one way or the other. There is a longstanding argument from internal evidence according to which one should seriously doubt the posteriority of the Parmenides or even prefer the posteriority of the Theaetetus(1). This argument appears never to have been challenged in print, and the considerations offered below are intended to undermine it by questioning some of its implicit premises," (p. 37)

(1) For the order of composition, cf. D. W. Ross, Plato's Theory of Ideas (Oxford, 1951), p. 2, and L. Brandwood, A Word Index to Plato (Leeds, 1976), pp. xvi-xviii.
———. 1982. "On the date of Plato's Parmenides." Classica et Mediaevalia no. 33:97–117.
———. 1982. "The Consequences of the Divisibility of Forms in Plato's Parmenides." Phoenix no. 36:45–52.

"In this paper I wish to suggest a new interpretation of Parm. 131c12-e2, which is perhaps one of the most puzzling passages in the first part of the dialogue." (p. 45)

(...)

"After remarking to Socrates that one cannot really claim that a Form is both incomposite (one3) and actually divided (131c9-10), Parmenides proceeds to the passage with which I am presently concerned. Parmenides presents three examples, all of which presumably illustrate the same issue. That is, the conclusion in each one of the examples is evidently an instance of a common problem, which arises when one believes that the Forms are divisible or, more generally, when one believes that "participation" is nothing but the presence in sensibles of a part of a Form. It appears, therefore, that we cannot discover the point at issue unless we can discern what, if anything, is common to all three examples. This is in fact the procedure followed by most commentators." (p. 46)
———. 1987. "The Day and Sail Analogies in Plato's Parmenides." Phoenix no. 41:10–24.

"I am here concerned with the following exchange between Parmenides and Socrates in Parm. 131a4-e7" (p.10)

(...)

"My principal claim will be that the two illustrations, the Day and the Sail, are analogous in the relevant respects and that hence Plato takes seriously the considerations adduced by Parmenides. Plato presents Socrates' Day analogy not as a step in the right direction, from which he is "forced," unfairly and wrongly, to retreat, but as a false cast which becomes more obviously such when the Day is replaced by the Sail. If this is so, then Socrates' Day cannot save Plato's middle-period theory of participation." (p. 12)
Parry, Richard. 2022. "The One and Time: Parmenides 151e-153a." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 361–370. Baden-Baden: Academia Verlag.

Abstract: "In the Second Hypothesis, Parmenides draws out the consequences of the one’s partaking of being, where partaking of being implies partaking of time. In an elaborate argument (which I divide into four parts) he draws two conclusions, which contradict one another. First, he concludes that: (III.12) The one always both is and is coming to be older and younger than itself. Second, he concludes that: (IV.4) Since the one is or comes to be for an equal time, i.e., a time equal to itself, it neither is nor comes to be younger or older than itself.

We shall see that the first conclusion, (III.12), is achieved by a conjunction of two previous sub-conclusions but that the conjunction is not logically legitimate. However, the second conclusion, (IV.4), has a better fate, in spite of the apparent incoherence of the phrase ‘a time equal to (the one) itself.’ We will argue that there is a way to make sense of this phrase if we assume that Parmenides’ argument uses Zeno’s paradox, the Flying Arrow: anything occupying a place just its own size is at rest; in the present, what is moving occupies a place just its own size; thus, the arrow is at rest. If we assume that Parmenides models (IV.4) on (a) by making an analogy between movement through space and movement through time, we can rescue (IV.4) from incoherence."
Patterson, Richard. 1999. "Forms, Fallacies, and the Functions of Plato's Parmenides." Apeiron no. 32:89–106.

"Most studies of the Parmenides, ancient or modem, attempt to find in its long and perplexing second part not just a preparatory exercise in 'logic', but positive and even extensive philosophical results. Some very recent studies defend the controversial position that all the arguments of Part II are good ones (sound: valid with true premises) and were meant to establish a series of significant philosophical results."

(...)

"The second approach raises a series of more specific issues: (1) Are there in fact formally or informally defective arguments in Part II? (2) If so, are any of these deliberately bad? (3) Are there any reasonable criteria by which we might identify deliberately bad arguments, or must we rely on a kind of hermeneutic divine madness? (4) Does the presence of deliberately bad arguments prevent our coming away from the Parmenides with some positive results in hand? My answers to these questions will be: (1) yes, (2) yes, (3) yes and no, and (4) no, respectively." (p. 89)
Pavani, Anna. 2025. "The Nun in the Parmenides: Not Another Exaiphnês." Dialogue:1–19.

Abstract: "After some preliminary remarks about Plato’s use of the adverb nun, I explain what the nun is by offering a close textual analysis of the key passage in which it is explicitly addressed (Parm. 151e3–153b7). Its metaxu nature, between duration and limit, requires one to consider another temporal notion of the second part of the Parmenides that is metaxu, namely the exaiphnês. I explain why the nun does not conceptually overlap with the exaiphnês, arguing moreover that there is no model where both notions fit, but rather a model accounting for a switch and another one accounting for continuous change."
Peck, Arthur L. 1953. "Plato's Parmenides: Some Suggestions for Its Interpretation." The Classical Quarterly no. 3:126–150.

Abstract: "In modern work on the Parmenides it is commonly supposed that in the First Part of the dialogue Plato's main concern is criticism of his own doctrine of Forms, or of some formulations of that doctrine, and that the criticisms have some sort of validity and are in some degree ‘damaging’ to the doctrine. It is thus often assumed that Plato's purpose is to make the reader ask himself, ‘Where is Plato wrong? Where is his doctrine of Forms, or his statement of it, inadequate?’ This is no doubt due partly to the fact that no reply is offered to the criticisms, and partly to the fact that they are put into the mouth of Parmenides, for whom Plato had a very great respect. Nevertheless, Plato can hardly have had a greater respect for Parmenides than he had for Socrates; and therefore on general grounds it is at least as likely that he intends us to ask ourselves the question, ‘Where is Parmenides wrong, or inadequate?’ It is, of course, obvious that Socrates is represented as a young man, who, in his enthusiasm for a new doctrine which he has invented himself, has not thought out all the difficulties involved in it or prepared replies to all the possible criticisms. Yet again, on general principles it is not likely that Plato would have written a dialogue primarily to represent Parmenides' position as substantially more satisfactory than that of Socrates. It is therefore of the first importance not merely to have clearly in our minds the nature and purpose of the doctrine of Forms, but also to examine carefully the basis of the criticisms which Parmenides is made to bring against Socrates, and the methods by which Parmenides conducts his arguments."
———. 1953. "Plato's Alleged Self-Criticism in the Parmenides: Some Recent Views." Cambridge Classical Journal no. 2:21–36.

"During the course of some work on the Parmenides(1) I found I was coming to a conclusion about the First Part of the dialogue which was at variance with what I supposed to be the traditional and commonly accepted view. It therefore seemed advisable to ascertain precisely what this traditional view was, and what were the arguments in favour of it; and the contents of this paper represent some part of an attempt to do this. As it happens, they also tend to make the writer appear as one playing the part of a Zeno to his own Parmenides, showing that even stranger results follow from the hypotheses of those from whom he differs than from his own.

As is well known, it is fashionable at the present time to hold that in the First Part of the Parmenides Plato is criticizing himself by the mouth of Parmenides. I do not propose to go into the history of this belief, but merely to examine it as it appears in the works of three well-known commentators, Professor Cornford, Sir W. D. Ross, and Mr. Richard Robinson. All of them are to some extent influenced by it: Cornford,

as we shall see, the least, and Robinson the most." (p. 21)

(1) Classical Quarterly, n.s. III, 1953, I26ff., and IV, 1954, 31 ff.

References

F. M. Cornford, Plato and Parmenides, 1939.

Richard Robinson, Plato's Parmenides, Classical Philology, xxxv, 1942, 51-76 ((reprinted as Chapter XIII in the second edition of his book Plato's Earlier Dialectic, 1953)

W. D. Ross, Plato's Theory of Ideas, 1951.
———. 1954. "Plato's Parmenides: Some Suggestions for Its Interpretation. II." The Classical Quarterly no. 4:31–45.

Abstract: "In the space at my disposal I cannot attempt to deal with all the points which arise in the Second Part of the dialogue, and I therefore confine myself to a few which seem to be of special interest and importance. I hope it may be possible to deal more exhaustively with the dialogue in a fuller commentary. As in the previous part of the article, I have assumed the results of my study of the Sophist already referred to."
———. 1967. "Plato, Parmenides, Block and Exemplification." Mind no. 76:595.

"Students of Plato who have read Professor Irving Block's recent article(1) on Plato's Parmenides may have been surprised at some of the statements in it. I should like to offer some comments on two of these. On page 420 Block twice states that in an article of mine(2) I have' introduced two kinds of forms 'into Plato, forms apprehended by reason (the genuine kind) and forms apprehended by sense (presumably a spurious kind). This statement is incorrect. Only one kind of Platonic form is mentioned or contemplated in my article.

The explanation of Block's mistake is simple. Following Plato's own practice, I used the word 'largeness' of the largeness in particulars as well as of the form largeness. This has led Block to deduce that I consider the largeness in particulars to be a second kind of Platonic form. His criticisms based on this deduction are therefore irrelevant." (p. 595)

(1) " Plato, Parmenides, Ryle, and Exemplification ", Mind, lXXiii (1964), 417-422.

(2) " Plato versus Parmenides ", Philos. Rev. lxxi (1962), 159-184.
Peddle, Francis K. 2022. "Mass, instance, atoms, and the Seventh Hypothesis of Plato's Parmenides." Science et Esprit no. 22:1–16.

Abstract: "The purpose of this essay is to glean some concepts out of the seventh hypothesis of Plato’s Parmenides that can provide a contribution to the often unsatisfying modern debates about the nature of atoms, mass, and what might constitute an instant. The seventh hypothesis (hereafter H7, similarly for the other hypotheses) of Part II of the Parmenides is one of the more neglected of all the hypotheses in the dialogue, despite the fact that it introduces some very novel terms and arguments. A brief overview of Part II of the dialogue is followed by a detailed analysis of the argument in H7. The conclusion brings this essay around to the relevance of H7 for contemporary reflections in theoretical physics and cosmology."
Pelletier, Francis Jeffry. 1983. "Plato on Not-Being: Some Interpretations of the συμπλοκη εἰδῶν (259E) and Their Relation to Parmenides' Problem." Midwest Studies in Philosophy no. 8:35–66.

"In this paper, I am interested in the Platonic response to Parmenides, especially the response that occurs in the middle portion of the Sophist (249-265). Since I am going to evaluate this as a response to the "standard interpretation" of Parmenides, it is clear that I owe a justification for my belief that Plato understood his opponent to be our "standard Parmenides." This issue, too, I will avoid here (further discussion can be found in Pelletier [1990], which discusses the "Parmenidean" arguments of Sophist 237-241, Theaetetus, 188-189, and Cratylus 429-430, with an eye toward showing that Plato was aware of these types of argument.)" (p. 35)

References

Pelletier. Francis Jeffry, Parmenides, Plato, and the Semantics of Not-Being, Chicago: University of Chicago Press 1990.
Pemberton, Harrison J. 1984. Plato's Parmenides: The Critical Moment for Socrates. Norwood: Norwood Editions.

"Our analysis will try to follow the movement of the dialogue as Plato presents it. He designed the dialogue to entice us into considering some fundamental problems by a dramatic and engaging First Part; then in a forbidding Second Part he takes us through a maze of arguments to the unifying recognition at the center of the center of the dialogue. At point what has gone before is cast into a new light, and the problems in the First Part can be seen in a different way. After that point the dialogue continues, in Hypotheses 3-8, to round out the central insight for those who have attained it or merely to continue a tedious discussion for those who have not. The last part is then ironic in a way we are familiar with in Plato's writings. Accordingly, we shall start by examining the First Part in a preliminary way, reading it is an introduction, especially as an indication of how the Second Part is to be regarded. A detailed examination of the Second Part will take us to the end of Hypothesis 2 where the central, unifying point of the dialogues is reached. In light of this we will then have to go back and reconsider the dialogue up to this point, especially the problems in the First Part. Thereafter, we can follow the discussion of the remaining hypotheses with some insight as Socrates could but as Aristoteles does not and come to the eventual but abrupt conclusion." (pp. 8-9)
Peterson, Sandra. 1981. "The Greatest Difficulty for Plato’s Theory of Forms: the Unknowability Argument of Parmenides 133c - 134c." Archiv für Geschichte der Philosophie no. 63:1–16.

"Plato's Parmenides constructs difficulties for the theory of forms. One, called "the greatest" (133b 4), is an argument (133c-134c) which concludes that the forms are unknowable by us.

Plato gives, I think, two routes to the conclusion. The first route, up to 134b 6, achieves the claim that if our knowledge is of something, that something cannot be a form. The second route, after 134b, establishes an equivalent to the achievement of the first: if something is knowledge of a form, that something cannot be knowledge of ours."

(...)

"In giving my reconstruction I have taken seriously Plato's remark that this argument presents the greatest difficulty for the theory of forms."
———. 1996. "Plato's Parmenides: A Principle of Interpretation and Seven Arguments." Journal of the History of Philosophy no. 34:167–192.

"The outcome of Part II of this paper is that it is possible to understand all the results in the final lines of the first of the Parmenides' Eighth sections as true assertions. One can also see how these final results follow from the arguments given. If these results are true, the passage 141-42, given my conviction that it argues from a true hypothesis, confirms the guiding principle that, all arguments of the gymnastic half being valid, all consequents of conditionals under the true hypothesis should be accepted, i.e., taken to be true. The puzzle about 141-42 is solved. The passage no longer seems an exception to Meinwald's interpretation." (è- 192)
———. 2000. "The Language Game in Plato's Parmenides." Ancient Philosophy no. 20:19–51.

"We have been asking how the exercise will help Socrates to mark off kinds properly. Parmenides gave Socrates the advice to exercise at 135c; Socrates had just acknowledged that he did not know what to do about philosophy after Parmenides, questioner, had reduced Socrates, answerer, to absurdity. Parmenides' advice created the impression that Socrates' attempt to 'mark off forms too soon had been displayed in Socrates' conversation with Parmenides. Parmenides, however, also says at 135c that Socrates gave evidence of trying to 'mark off forms too soon when Parmenides was listening to Socrates conversing with the young Aristotle 'the other day' (135dl). Plato does not record that conversation with Aristotle, but we naturally imagine that in that conversation Socrates had his role of questioner familiar to us from other dialogues, and that Aristotle was answerer. Plato is inviting us to imagine some familiar Socratic questioning, and to ask: What indications of a need for exercise might have occurred in such a conversation?" (p. 40)
———. 2003. "New Rounds of the Exercise of Plato's Parmenides." The Modern Schoolman no. 80:245–278.

"Parmenides knows what the young Socrates is interested in, since he has observed that Socrates is trying to define the just and the fine and the good. The Parmenides doesn't give us any evidence that the young Socrates has been looking for such definitions as a means to the goal of living a just life. But the question still naturally arises: if even the young Socrates is asking his questions with the aim of living a just life, and if Parmenides knows that Socrates has the project of living a just life, how exactly does Parmenides intend his recommendations to fit into that project? Does Parmenides think that Socrates can't understand what just is, and can't live a just life, without undertaking these arduous logical exercises? How does the exercise, and its many repetitions, help Socrates to do something "about philosophy," if even the young Socrates understands philosophy as the examined life-i.e. the life in which one has tested oneself to be sure that one is not living the wrong kind of life?

These are further questions to consider." (p. 272, notes omitted)
———. 2008. "The Parmenides." In The Oxford Handbook of Plato, edited by Fine, Gail, 383–410. New York: Oxford University Press.

"Plato's Parmenides contrasts with Plato's other works in several ways. For example, Socrates is depicted as "very young" (127c5), perhaps fifteen or perhaps nineteen. Parmenides questions Socrates, who contradicts himself; in other dialogues of question and answer, Socrates typically questions others, who contradict themselves. Parmenides refutes Socrates on the topic of forms, items such as justice itself and good itself, while the older Socrates of other dialogues presents forms as central to philosophy; the dialogue thus raises the question whether its criticism of forms signals Plato's revision of views expressed in previous writings. The Parmenides is the only dialogue in which forms are the main topic. The dialogue's second part, 137c-166c, is the longest passage of unrelenting argument in Plato's writings. Its arguments are his most puzzling." (p. 383)
———. 2020. "The Argument of Zeno at Parmenides 127e1–7." Platonic Investigations no. 12:11–44.

Abstract: "This essay offers an interpretation of Parmenides 127e1–7. There Socrates reports Zeno’s argument that attacks the thesis that beings are many. The essay’s goal is to understand Zeno’s argument as reported by Socrates. The author first considers he interpretations of J. Barnes, D. El Murr, and R.E. Allen. They propose that Zeno’s target for attack is the thesis that the number of beings is greater than one (“the numerical target”). El Murr also suggests the additional target that each being has many parts. Then the essay considers the interpretations of D. Lee and A. Nehamas. They maintain that Zeno’s target for attack is the thesis that a single being may be many by having multiple attributes (“the multi-attribute target”). This essay makes use of insights from all these interpretations. It also revives a suggestion of P. Curd that Zeno argued against both the numerical target and the multi-attribute target. The author proposes that Zeno argues against a disjunction of (i) the numerical target, (ii) the El Murr addition, and (iii) the multi-attribute target. That is, Zeno argued boldly that beings cannot be many in any imaginable way. This essay calls new attention to the important role in Zeno’s argument of the claim, “for unlikes cannot be likes.”

References

Allen, R.E., tr. (1997), Plato’s Parmenides. Revised edition. New Haven: Yale University Press.

Barnes, J. (1982), The Presocratic Philosophers. New York: Routledge.

Curd, P.K. (1986), “Parmenides 131c–132b: Unity and Participation”, History of Philosophy Quarterly 3.2: 125–136.

Curd, P.K. (1991), “Parmenidean Monism”, Phronesis 36: 241–264.

El Murr, D. (2005), “La critique de la participation en Parménide, 131a–132b: unité, unicité et le paradoxe de Zénon”, in A. Havlíček and F. Karfík (eds.), Plato’s Parmenides: Proceedings of the Fourth Symposium Platonicum Pragens21–57. Praha: ΟΙΚΟΥΜΕΝΗ.

Lee, D. (2014), “Zeno’s Puzzle in Plato’s Parmenides”, Ancient Philosophy 34.2: 255–273.

Nehamas, A. (1982), “Participation and Predication in Plato’s Later Thought”, Review of Metaphysics 36.2: 343–373.

Nehamas, A. (2019), “The Academy at Work: The Target of Dialectic in Plato’s Parmenides”, Oxford Studies in Ancient Philosophy 57: 121–152.
———. 2022. "Socrates Objects to Zeno at 128e-129a in Plato’s Parmenides." In Plato's Parmenides: Selected Papers of the Twelfth Symposium Platonicum, edited by Brisson, Luc, Macé, Arnaud and Renault, Olivier, 83–90. Baden-Baden: Academia Verlag.

Abstract: "This essay newly defends the view that the youthful Socrates of Plato’s Parmenides at 128e1-129a1 makes a decisive objection to Zeno’s argument against plurality at 127e1-4.

That view requires new defense because Alexander Nehamas has recently given several thought-provoking reasons against it. Zeno’s argument is in defense of Parmenides’ thesis that being is one. Socrates’ objection that I believe is decisive consists in the observation that Zeno’s argument presupposes that there are two opposites, likeness and unlikeness.

Nehamas believes (a) that Zeno defends, not the numerical thesis that the number of beings is one, but rather the thesis that each being is predicatively one: it is exactly the one thing that it is. Thus (b) the target that Zeno reduces to absurdity is the thesis that each being has many attributes. And (c) given that target, Socrates’ observation that Zeno’s argument commits Zeno to the presupposition that there are multiple opposite beings shows no incoherence in Zeno’s argument. I here put aside controversy about whether Zeno’s target is numerical or predicative plurality to consider the conditional question: If Zeno’s target is the thesis that beings are predicatively many, then are Nehamas’s considerations sufficient to show that Socrates’ observation does not decisively show a flaw in Zeno’s argument? I discuss here four of Nehamas’s considerations. (I have considered the fifth elsewhere.) I argue that these four considerations fail to show that Plato does not present the youthful Socrates’ objection to Zeno’s argument as decisive. Socrates’ objection against Zeno’s argument is devastating no matter which sort of plurality Zeno targets. I observe some further textual reason to suppose that Plato does present Socrates’ objection as decisive."

References

Nehamas, A. 2019. ‘The Academy at Work: The Target of Dialectic in Plato’s Parmenides’. Oxford Studies in Ancient Philosophy 57: 121-152.

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