Contemporary platonism has been conditioned in large part by two dogmas. One is the belief in a fundamental cleavage between intelligible but invisible Platonic forms that are real and eternal, and perceptible objects whose confinement to spacetime constitutes an inferior existence and about which knowledge is impossible. The other dogma involves a kind of reductionism: the belief that Plato’s unhypothetical first principle of the all is identical to the form of the good. Both dogmas, I argue, are ill-founded.

Plato seems to countenance both positive and negative Forms, that is to say, both good and bad ones. He may not say so outright, but he invokes both and rejects neither. The apparent finality of this impression creates a lack of direct interest in the subject: Plato scholars do not give negative Forms much thought except as the prospect relates to something else they happen to be doing. Yet when they do give the matter any thought, typically for the sake (...) of a prior concern, they try either to support the textual evidence or to contradict it, indicating that the evidence does not stand on its own. The purpose of this paper is to determine why they tend to affirm or deny the obvious, how they try to confirm or dispute it, and what this says about Plato’s position. The strategic vehicle is a comparative case study. The confirmation comes from Debra Nails (2013), who needs to embrace negative Forms to demonstrate that the unhypothetical first principle of the all is not identical to the Form of the good, something she cannot do unless Plato recognizes negative Forms. The contradiction comes from Holger Thesleff (2013), who needs to reject negative (Ideal) Forms because the defining feature of his (Ideal) Forms is the possession of positive intrinsic value, which cannot be predicated of anything negative. Despite defending opposite views, or perhaps because of this, they jointly make up for any lack of interest in the scholarly community. I appreciate both yet side with Thesleff. (shrink)

This is a study of the correspondence between Forms and particulars in Plato. The aim is to determine whether they exhibit an ontological symmetry, in other words, whether there is always one where there is the other. This points to two questions, one on the existence of things that do not have corresponding Forms, the other on the existence of Forms that do not have corresponding things. Both questions have come up before. But the answers have not been sufficiently sensitive (...) to the intricacies of the questions. Nor have they been adequately resourceful with what little evidence there is in the original sources. The intention here is to make up for that deficiency, not just with better answers but also with better insight into the questions. (shrink)

Theaetetus, asked what knowledge is, replies that geometry and the other mathematical disciplines are knowledge, and so are crafts like cobbling. Socrates points out that it does not help him to be told how many kinds of knowledge there are when his problem is to know what knowledge itself is, what it means to call geometry or a craft knowledge in the first place—he insists on the generality of his question in the way he often does when his interlocutor, asked (...) for a definition, cites instead cases of the concept to be defined. (shrink)

The purpose of this paper is to point out that some mathematical doctrines attributed by Aristotle to Plato find their origin in a threefold order of problems: first, in some allusions contained in the dialogues, which might create ambiguities within the so-called standard model of ideas; second, in the Aristotelian interpretation of ideal entities as universals or predicates, an interpretation in turn partly authorized by Plato himself; third, in the tendency not to emphasize the possibility of understanding participation and the (...) whole-part relationship from a non-quantitative point of view. In this paper I will disregard the complex debate about whether or not to attribute the unwritten doctrines of the Aristotelian account to Plato, but I will appraise in what sense some Aristotelian objections to participation may arise from the fact of conceiving of numbers and magnitudes as ideas. (shrink)

‘The similes of the Sun, Line, and Cave in the Republic remain a reproach to Platonic scholarship because there is no agreement about them, though they are meant to illustrate.’ So wrote A.S. Ferguson in 1934, and so he could write to-day. Four decades have produced at least twenty more substantial contributions to the debate, but no agreement. I shall not attempt to arbitrate between existing interpretations, nor shall I offer an account of the ‘simile of light’ as a whole. (...) I shall confine my attention to a single point: the significance of the shadows in the cave, and of the objects which cast them. The suggestion I shall make seems an obvious one, but I have not found it in the literature. I hope to show at least that it deserves serious consideration. (shrink)

In Plato's Phaedrus, Socrates offers two speeches, the first portraying madness as mere disease, the second celebrating madness as divine inspiration. Each speech is correct, says Socrates, though neither is complete. The two kinds of madness are like the left and right sides of a living body: no account that focuses on just one half can be adequate. In a recent paper, Hugh Benson gives a left-handed speech about a psychic condition endemic among mathematicians: dianoia. Benson acknowledges that his account (...) is one-sided, but only hints at the virtues of right-handed dianoia. This note sketches a somewhat fuller picture. (shrink)

AT the beginning of the third part of the Theaetetus , Socrates entertains an interesting theory of knowledge in the form of a ‘dream’. In Cornford's translation, it reads as follows: I seem to have heard some people say that what might be called the first elements () of which we and all other things consist are such that no account () can be given of them. Each of them just by itself can only be named; we cannot attribute to (...) it anything further or say that it exists or does not exist; for we should at once be attaching to it existence or nonexistence, whereas we ought to add nothing if we are to express just it alone. We ought not even to add ‘just’ or ‘it’ or ‘each’ or ‘alone’ or ‘this’, or any other of a host of such terms. (shrink)

ABSTRACTThis article aims at understanding the functions of the forms of Being and the Other in Plato's Sophist. In contrast with a linguistic interpretation purporting to draw a distinction between uses of the verb “to be,” I shed light on the ontological role ascribed to “the great genus” in the interweaving of forms. Focusing on the vowel analogy, I argue that the roles of Being and the Other respectively are that of a connector and a separator actualizing the participations and (...) the differences between the forms. The outcome of this analysis is to offer an explanation of the dialectical methods described in that dialogue in a rather obscure, abstract way; the much-debated question of self-predication can be settled without recourse to selfparticipation. (shrink)

This article asks the question “Why did Plato not write the ‘unwritten doctrine’?” and answers it by citing a combination of two obstacles. The first derives from the limitations of the episteme available to an embodied soul about the essence of the good. Even if the dialectician has access to some kind of knowledge, the mismatch between the unchanging essence of the good and the precarious logoi which aim to identify it (and allow others some measure of access to it) (...) can never fully be overcome. At best, Socrates (or Plato) can lead souls to an incomplete account of it: It is possible that even the most expert dialectician can only have a claim to knowledge, but no absolute certainty. Another obstacle lies in the audience or readership itself: No shortcut to understanding is possible, and yet a mere written presentation, which is all they have, is just such a shortcut, and so represents an empty promise. In memory of Charles H. Kahn (1928–2023), a letter of his from September 5, 1989, concerning the question “Why did Plato not write the ‘unwritten doctrine’?” is published, along with some comments. (shrink)

The question of ontological commitment in Plato’s Hippias Major has been important in disputes over the dialogue’s place in the corpus, its meaning, and its authenticity. But this question seems to have been settled—the Hippias Major is not committed to the ‘forms.’ Such an ontological conclusion has been vigorously defended, but its defenses rest on a problematic meta-ontological framework. This paper suggests a more adequate framework and brings more evidence to the evaluation of the question of ontological commitment in the (...) Hippias Major. It concludes that the dialogue is indeed committed to some kind of form. (shrink)

Despite the fact that the theory of Forms is regarded as the hallmark of Plato’s philosophy, it has remained remarkably elusive, because it is more hinted at than explained in his dialogues. Given the uncertainty concerning the nature and extension of the Forms, this article makes no pretense to coming up with solutions to all problems that have occupied scholars since antiquity. It aims to elucidate only two aspects of that theory: the indication in certain dialogues that the Forms are (...) what in modern parlance are called functions or purposes, and the indication in other dialogues that such functions rely on harmonious structures. (shrink)

With the late Author’s kind permission, the present text is published here in a somewhat abbreviated and modified translation that has been given appropriate subheadings and supplemented with an extensive bibliography. Its German original from 1996 has been translated into French and English. The purpose of the present translation is to make the Polish reader acquainted with the important and innovative account of Plato’s philosophy that has been put forward by the Tübingen School whose one of the most prominent co-founders (...) was Hans Joachim Krämer. While this text is devoted to Plato’s critique of writing, it also presents Plato’s agrapha dogmata as an important supplement to the written dialogues. A fuller overview of the major assumptions of this new interpretation is to be found in the recently published Gesammelte Ansätze zu Platon. (shrink)

The following article reconstructs Plato’s argument for the existence of god in Laws X. The article starts with interpreting the argument for the priority of soul and continues with a discussion of the argumentation for rationality of the soul in charge of heavens . The view defended here is that Plato first defines the essential characteristics of the divine, namely self-motion and rationality, and then shows that there are entities which possess these characteristics and therefore deserve to be called gods (...) or divine. The article further shows that several sub-arguments mirror the structure of the overall proof. (shrink)

In this article I argue that "Timaeus" 48e-52d, the passage in which Plato introduces the receptacle into his ontology, Contains the material for a satisfactory response to the third man argument. Plato's use of "this" and "such" to distinguish the receptacle, Becoming, And the forms clarifies the nature of his ontology and indicates that the forms are not, In general, self-predicative. This result removes one argument against regarding the "Timaeus" as a late dialogue.

Dans un célèbre ouvrage surContemplation et Vie contemplative selon Platon, A.J. Festugière donnait de la dialectique platonicienne une interprétation selon laquelle celle-ci constituait une véritable expérience mystique possédant presque tous les traits de la contemplation chrétienne. La dialectique platonicienne y était présentée, surtout dans son acte final, comme une sorte d'extase, une union d'ordre mystique, un contact de l'âme perdue dans son objet, contact qui suscite en elle un sentiment qui dépasse tout l'ordre normal de la connaissance. Le Bien ou (...) l'Un en tant qu'objet dernier de l'ascension dialectique y était conçu comme quelque chose d'ineffable et d'indéfinissable. (shrink)

In this paper I show that Aristotle’s widely criticised exclusion of Platonic efficient causes at Metaph. A 6.988a7–17 is defensible as an interpretation of Plato, and that alternative accounts are unpersuasive. I argue that Aristotle is only interested in – what he supposes to be – Plato’s first principles and that the usual candidates that are brought forward in scholarship as possible first principles and efficient causes (e.g. from the Timaeus and the Philebus) all fall short in crucial respects according (...) to Aristotle. This reading has the dual benefit of illuminating Aristotle’s strategy in book A and of letting him appear as a more trustworthy doxographer of his predecessors’ views. (shrink)

In the De Generatione et Corruptione II 9, Aristotle aims to achieve the confirmation of his theory of the necessity of the efficient cause. In this chapter he sets out his criticism on the one hand of those who wrongly attributed the efficient cause to other kinds of causality and on the other, of those who ignored the efficient cause. More specifically Aristotle divides all preceding theories which attempted to explain generation and corruption into two groups: i) those which offered (...) an explanation by using the formal cause ii) those which provided an explanation by using the material or the instrumental causes. According to Philopo­nus, when Aristotle reproaches the other philosophers for adducing no proper notion of the efficient cause he alludes to both Anaxagoras and Plato. Regarding Anaxagoras, in our view this cannot be confirmed by internal textual evidence. In terms of Plato, in this chapter we trace an explicit and an implicit criticism of the Platonic Forms as causes. Aris­totle’s implicit criticism is that the Forms are not at all active causes. We can understand better the grounds for this criticism if we also consider his relevant arguments in Book Lambda of his Metaphysics. His explicit criticism, articulated in two arguments, is formulated in GC 335b18–24. We examine the different lines of its interpretation in the second­ary literature, but primarily we focus on Philoponus’ exegesis, which contributes significantly, not only to the clarification of Aristotle’s thinking, but also to the manifestation of the arguments articulated in defence of the Platonic theory of the Forms. In this paper, through the analysis of Philoponus’ exegesis we set out to prove that Aristotle’s criticism of the Platonic causes can be construed from the perspective of either Aristo­telian theory or the Platonic and Neoplatonic influence. Finally, based on Philoponus’ exegesis, we examine Aristotle’s criticism of those who posited matter or instrumental causes as efficient causes. (shrink)

In what follows I propose to consider the relevance of Plato's early claim that his Forms are explanatory to the structure of, and several of the main arguments of, the Parmenides. The first section of the paper looks into some implications of separate existence, exploring connections between the criticism of separation and the conception of Forms as explanatory principles. I focus attention on what the Forms do not explain, and suggest that the burden of much of Parmenides’ criticism centers on (...) that question. Part two deals with Plato's evidently changing stance on the issue of explaining the Forms themselves. The third section takes up passages from the Parmenides in support of the view that Plato came to believe that his Forms stood in need of the same sort of explanation as he had originally thought was required for sensory particulars. The discussion is largely exploratory, and the connections adumbrated are intended as guidelines for further investigation. (shrink)

The Cratylus begins with a paradox; it ends with a paradox; and it has a paradox in between. But this disturbing characteristic of the dialogue has been overshadowed, not to say ignored, in the literature. For commentators have seen it as their task to discover exactly what theory of language Plato himself, despite his declared perplexity, intends to adopt as he rejects the alternatives of Hermogenes and Cratylus. A common view, then, has been to suppose that the πορίαι of the (...) dialogue are mere camouflage for the hidden dogma, whatever that may be. A favoured candidate, of course, has been the theory of transcendent forms, in some preliminary version. As a consequence, the dialogue has often been seen as a precursor to the great metaphysical works of Plato's middle period such as the Phaedo or the Republic. Not so, I shall argue. My case is that this dialogue centres upon a series of paradoxes which are both powerful and unsettling. Their final effect is to attack the theory of forms, not to defend it. They are, I suggest, genuine proposals of philosophical difficulty, rather than mere artifice to disguise an idealist truth. As such, they belong, and may clearly be seen to belong, with works of the critical period which subject the theory of forms to scrutiny. Thus the πορίαι of the Cratylus have their counterparts in the Parmenides, the Theaetetus and the Sophist. I propose, then, that the dialogue was written during the late, critical period of Plato's philosophical activity. (shrink)

RésuméEn expliquant la relation entre hypothèses et images dans l'analogie de la ligne du livre Vl de laRépubliquede Platon, je m'attarde d'abordsur l'élucidation platonicienne de la nature des mathématiques telle que la conçoit le mathématicien lui-même. Je poursuis avec une critique des interprétations traditionnelles de cette relation, qui partent de l'assomption douteuse que les mathématiques s'occupent des Formes platoniciennes. Pour formuler mon point de vue sur cette relation, j'exploite la notion de «structure». Je montre comment les «hypothèses» comme principes de (...) preuve peuvent déterminer les structures des «images» par lesquelles les structures intelligibles correspondantes des objets mathématiques en viennent à être connues. (shrink)

Aristotle thinks that the Platonic theory of Forms is vulnerable to the Third Man regress. According to Alexander of Aphrodisias, the regress arises from the conjunction of three Platonist claims, which I label ‘Exemplification’, ‘Similarity’, and ‘Distinctness’. It is clear why, taken together, these three claims generate an infinite regress of Forms. What is not clear is why Aristotle thinks that a Platonist should have to accept each of the claims. My answer begins from the fact that, in Metaphysics A (...) and M, Aristotle mentions the Third Man as a consequence, not of positing Forms, but of certain ways of arguing for Forms. By working out what these arguments are likely to have been, we can understand why he took the Platonist to have been committed to all three claims, and thus why he saw the Third Man as a serious difficulty. (shrink)

Towards the close of Book V of theRepublicPlato tells us that the true philosopher has knowledge and that the objects of knowledge are the Forms. By contrast, the ‘lovers of sights and sounds’, he tells us, have no more than belief, the objects of which are physical particulars. He then goes on to present us with some very radical-sounding assertions about the nature of these physical particulars. They are bearers of opposite properties, he says, in so thorough-going a manner that (...) we cannot say of them that they are nor that they are not: they lie somewhere between being and utter non-being.This passage of theRepublic still awaits an agreed interpretation and I want to suggest as a reason for this that it is usually interpreted in isolation. I will argue that it becomes easier to understand when seen against the background of Plato's developing thought. To be more precise, it makes sense when taken as a rejection by Plato of one of his earlier beliefs: namely, a doctrine of essentialism to be found in thePhaedo.The greater part of this paper then will be an attempt to show thatRepublicV is a rejection of thePhaedo'sdoctrine of essences. Its concluding part will try to explain why that doctrine was rejected. (shrink)

Dans la seconde partie de son Prologue au Commentaire du premier livre des Éléments d'Euclide, Proclus, un néo-platonicien du Ve siècle après J.-C., a donné sur Platon un jugement qui semble avoir été accepté d'une façon assez unanime par les anciens, lorsqu'il écrit: «Après eux [Hippocrate de Chios et Théodore de Cyrène] vécut Platon qui fit prendre aux Mathématiques en général, à la Géométrie en particulier, un essor immense, grâce au zèle qu'il déploya pour elles, et dont témoignent assez ses (...) écrits tout remplis de discours mathématiques, et qui, à chaque instant, éveillent l'ardeur pour ces sciences chez ceux qui s'adonnent à la philosophie». Les historiens modernes de la géométrie grecque ont dû nuancer ce jugement de Proclus, allant même jusqu'à parler de légende à propos des prétendues découvertes géométriques de Platonz. De fait, il semble que l'essor des mathématiques et de la géométrie au IVe siècle av. (shrink)

Simplicius reports that Xenocrates and Andronicus reproached Aristotle for positing an excessive number of categories, which can conveniently be reduced to two: τὰ καθ᾽αὑτά and τὰ πρός τι. Simplicius, followed by several modern commentators, interprets this move as being equivalent to a division into substance and accidents. I aim to show that, as far as Xenocrates is concerned, this interpretation is untenable and that the substance-accidents contrast cannot be equivalent to Xenocrates’ per se-relative one. Rather, Xenocrates aimed to stress the (...) primacy of Plato’s binary distinction of beings, as presented at Sophist 255c13–4, over Aristotle’s list of the categories. (shrink)

In his critical study of Speusippus Leonardo Tarán (T.) expounds an interpretation of a considerable part of the controversial books M and N of Aristotle's Metaphysics. In this essay I want to consider three aspects of the interpretation, the account of Plato's ‘ideal numbers’ (section I), the account of Speusippus’ mathematical ontology (section II), and the account of the principles of that ontology (section III). T. builds his interpretation squarely on the work of Harold Cherniss (C.), to whom I will (...) also refer. I concentrate on T. because he has brought the ideas in which I am interested together and given them a concise formulation; he is also meticulous in indicating the secondary sources with which he agrees or disagrees, so that anyone interested in pursuing particular points can do so easily by consulting his book. (shrink)

The present paper deals with eight charges that are frequently leveled against any research that focuses on the agrapha dogmata. The charges are demonstrated to be completely unfounded and, therefore, duly dismissed. In particular, it is argued here that the phrase ta legomena is by no means to be understood as ironic. Consequently, the article rejects the very common picture of Plato as some sort of dogmatist and author of a fixed philosophical system. However, Plato’s philosophy is presented as rather (...) ‘overt’ and ‘straightforward’ in its nature. With the situation being as it is, thorough knowledge of the agrapha dogmata is shown to be an absolute prerequisite for understanding Plato’s dialogues. The paper concludes with an observation that while investigating the issue is completely warranted and does not in any way entail any devaluation of the dialogues, Aristotle’s testimony must also be taken into account. (shrink)

In this paper I wish to argue for a view that, despite its traditional standing, has not yet in any detail been defended. The view is briefly that in the Republic, at the point where Plato is engaged in contrasting the true philosopher with the “lover of sights and sounds”, he characterises sensible particulars — referred to as “the many” — as being bearers of opposite properties in so radical a manner that they can be said neither to be nor (...) not to be: they lie somewhere between being and utter non-being.There are two related reasons why this traditional view should now be closely scrutinised. The first is that, whatever the outcome, the passage of the Republic in question — 475a-480a — is quite crucial to our understanding of the development of Plato's thought about sensible particulars. The second’ is that it has been suggested recently, and ably argued, that Plato is not in fact talking about particulars at all; rather about types or sorts of particulars. (shrink)

This paper argues for two claims. First, that in the Sophist a metaphysical theory of being is constructed from the ground up, largely on the basis of a claim treated as an axiomatic principle, the ‘dunamis proposal’ (247d–e), which, I will argue, ought to be understood as Plato’s own definition of being. Second, once its core is in place, the theory is put to use to provide dialectical arguments against proponents of alternative metaphysical theories for the existence of various entities (...) in the ontology. These include—notably—an argument for the existence of Forms. (shrink)