Plato: One and Many

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 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 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. (shrink)

Plato’s invention of the metaphor of carving the world by the joints (Phaedrus 265d-66c) gives him a privileged place in the history of natural kind theory in philosophy and science; he is often understood to present a paradigmatic but antiquated view of natural kinds as possessing eternal, immutable, necessary essences. Yet, I highlight that, as a point of distinction from contemporary views about natural kinds, Plato subscribes to an intelligent-design, teleological framework, in which the natural world is the product of (...) craft and, as a result, is structured such that it is good for it to be that way. In Plato’s Philebus, the character Socrates introduces a method of inquiry whose articulation of natural kinds enables it to confer expert knowledge, such as literacy. My paper contributes to an understanding of Plato’s view of natural kinds by interpreting this method in light of Plato’s teleological conception of nature. I argue that a human inquirer who uses the method identifies kinds with relational essences within a system causally related to the production of some unique craft-object, such as writing. As a result, I recast Plato’s place in the history of philosophy, including Plato’s view of the relation between the kinds according to the natural and social sciences. Whereas some are inclined to separate natural from social kinds, Plato holds the unique view that all naturalness is a social feature of kinds reflecting the role of intelligent agency. (shrink)

Empleando procedimientos de la lógica simbólica, se intenta contribuir a una mejor comprensión del ejercicio dialéctico llevado a cabo en el Parménides. La interpretación de las formas del ser y el no ser a partir de la oposición entre el objeto de conocimiento y el pensamiento acerca del mismo, abre la puerta a una manera original de enfocar el problema de la verdad en Platón. Puede resultar interesante, asimismo, la solución que se propone a la aporía planteada en Parménides 132b-c, (...) relativa a la confusión del pensamiento o el no ser con otras formas. (shrink)

This paper provides a rational reconstruction of a Platonic trope bundle theory that is a live alternative to contemporary bundle theories. According to the theory, Platonic particulars are composed of what Plato calls images of Forms; contemporary metaphysicians call these tropes. Tropes are dependent on Forms and the Receptacle, while trope bundles are structured by natural kinds using the Phaedo's principles of inclusion and exclusion and the Timaeus’ geometrised elements, as well as by co-location in the Receptacle. Key elements of (...) discussion include persistence and abundance of Plato's tropes. The resulting theory is compared with contemporary trope bundle theories. (shrink)

Republic 596a introduces a One over Many principle that has traditionally been considered as an argument for the existence of Forms, according to which, one Form should be posited for each like-named plurality. This interpretation was challenged by (Smith, J. A. 1917. “General Relative Clauses in Greek.” Classical Review 31: 69–71.), who interpreted it rather as a statement that each Form is unique and correlated to a plurality of things that have the same name as it. (Sedley, D. 2013. “Plato (...) and the One-over-Many Principle”, in Chiaradonna & Galluzzo 2013, 113–37.) has offered a forceful defence of Smith’s interpretation. I argue that Sedley’s defence fails and that the traditional interpretation should be preferred. (shrink)

Este trabajo pretende ser una referencia útil para los estudiosos de la filosofía de Platón. Aporta un enfoque original a la investigación de los procesos lógicos que condicionan que unas formas participen de otras. Con la introducción del concepto de participación relacional, abre una posible vía de solución a las distintas versiones del argumento del «tercer hombre». Puede resultar de interés asimismo el método de generación de los números a partir de lo par y lo impar, propuesto en la interpretación (...) de Parménides 143e-144a. El escrito tiene continuidad en un segundo artículo acerca del ser y la verdad en Platón. (shrink)

I discuss Aristotle’s opening argument against Platonic Forms in _Metaphysics_ A.9, ‘the Razor’, which criticizes the introduction of Forms on the basis of an analogy with a hypothetical case of counting things. I argue for a new interpretation of this argument, and show that it involves two interesting objections against the introduction of Forms as formal causes: one concerns the completeness and the other the adequacy of such an explanatory project.

In this essay, we consider the formal and ontological implications of one specific and intensely contested dialectical context from which Deleuze’s thinking about structural ideal genesis visibly arises. This is the formal/ontological dualism between the principles, ἀρχαί, of the One (ἕν) and the Indefinite/Unlimited Dyad (ἀόριστος δυάς), which is arguably the culminating achievement of the later Plato’s development of a mathematical dialectic.3 Following commentators including Lautman, Oskar Becker, and Kenneth M. Sayre, we argue that the duality of the One and (...) the Indefinite Dyad provides, in the later Plato, a unitary theoretical formalism accounting, by means of an iterated mixing without synthesis, for the structural origin and genesis of both supersensible Ideas and the sensible particulars which participate in them. As these commentators also argue, this duality furthermore provides a maximally general answer to the problem of temporal becoming that runs through Plato’s corpus: that of the relationship of the flux of sensory experiences to the fixity and order of what is thinkable in itself. Additionally, it provides a basis for understanding some of the famously puzzling claims about forms, numbers, and the principled genesis of both attributed to Plato by Aristotle in the Metaphysics, and plausibly underlies the late Plato’s deep considerations of the structural paradoxes of temporal change and becoming in the Parmenides, the Sophist, and the Philebus. After extracting this structure of duality and developing some of its formal, ontological, and metalogical features, we consider some of its specific implications for a thinking of time and ideality that follows Deleuze in a formally unitary genetic understanding of structural difference. These implications of Plato’s duality include not only those of the constitution of specific theoretical domains and problematics, but also implicate the reflexive problematic of the ideal determinants of the form of a unitary theory as such. We argue that the consequences of the underlying duality on the level of content are ultimately such as to raise, on the level of form, the broader reflexive problem of the basis for its own formal or meta-theoretical employment. We conclude by arguing for the decisive and substantive presence of a proper “Platonism” of the Idea in Deleuze, and weighing the potential for a substantive recuperation of Plato’s duality in the context of a dialectical affirmation of what Deleuze recognizes as the “only” ontological proposition that has ever been uttered. This is the proposition of the univocity of Being, whereby “being is said in the same sense, everywhere and always,” but is said (both problematically and decisively) of difference itself. (shrink)

A quotation from the early Platonic dialogue Hippias Major is used as an epigraph to Concluding Unscientific Postscript. Apart from this paratextual (and liminal) presence of the Platonic text, “the Hippias as an introduction to the beautiful” could serve, according to Climacus’ words, “as a kind of analogy to an introduction such as that” his own book aims to be; that is, an introduction which will throw light “on what Christianity is” but make “it difficult to become a Christian”. The (...) aim of the present paper is to investigate whether the above claim of Climacus could be attested in the Postscript and how the Platonic dialogue helps him reiterate a “new approach” to the problem of the Crumbs and orient his reader to the particularity of the Crumbs’ crumb philosophy. (shrink)

One of the questions regarding the Parmenides is whether Plato was committed to any of the arguments developed in the second part of the dialogue. This paper argues for considering at least one of the arguments from the second part of the Parmenides, namely the argument of the generation of numbers, as being platonically genuine. I argue that the argument at 142b-144b, which discusses the generation of numbers, is not deployed for the sake of dialectical argumentation alone, but it rather (...) demonstrates key platonic features, such as the use of the greatest kinds and the generation principle. The connection between the argument for the generation of numbers and Plato’s philosophy of mathematics is strengthened by the exploration of a possible reference in Aristotle’s Metaphysics A6. Taken as a genuine platonic theory, the argument could have significant impact on how we understand Plato’s philosophy of mathematics in particular, and the ontology of the late dialogues in general – that numbers can be reduced to more basic entities, i.e the greatest kinds, in a way similar to the role the greatest kinds are assigned in the Sophist. (shrink)

This paper discusses Aristotle’s statement (Metaph. A 9, 991a8-9) that both Anaxagoras and Eudoxus claimed that things are the result of a mixture of original elements, in relation to Plato’s metaphysics. Eudoxus used this immanentistic thesis to reform one central component of Plato’s Theory of Form, that is the “participation”. The first part of the paper analyzes some Anaxagorean aspects in Plato’s metaphysics, showing that Plato shares with Anaxagoras the “Transmission Theory of Causality” (as called by Dancy), but he refuses (...) its immanentistic version. The second part interprets Hip. Maj. 301b2-301c2 as a refusal of a immantestic interpretation of verbs like prosgivgnomai and kosmei'tai. It is also rejected Morgan’s thesis according to which Hippias supports an aware mereological metaphysical theory. The third part contests that Phaed. 100-106 is a defense of an immanentistic metaphysics abandoned by Plato in his later works. The meaning of the expression to; ejn hJmi'n does not include a mereological approach to the causality. In Plato’s metaphysics there is no strong contradiction between transcendence and immanence. The fourth part shows that the Parmenides refuses any immanentistic version of the relationship between Forms and things. Lastly, I will argue that from a Platonic point of view the only acceptable version is the separated interpretation of Transmission Theory of Causality. (shrink)

Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals (...) along with a new concept to abstractly model the functions of a brain. (shrink)

Few arguments from the past have stirred up as much interest as Aristotle’s “Third man” and not so many texts have received as much attention as its account in chapter 22 of the Sophistici elenchi. And yet, several issues about both remain highly controversial, starting from the very nature of the argument at stake and the exact signification of some of its features. The essay provides a close commentary of the text, dealing with its main difficulties and suggesting an overall (...) interpretation of Aristotle’s discussion of the “Third Man” argument. (shrink)

Exegetical work on philosophical systems requires not only that one give an account of the structure of a system’s assumptions and arguments, but also of its forms, such as the form of expression (or genre: dialogue, poem, aphorisms, and so on), or its form of argumentation (clear cut dis- cursive exposition, logical formalization, metaphorical, allegorical discourse, and so forth). These formal considerations may seem to be secondary, merely ornamental issues, but they can raise unexpected questions. The literal reading of a (...) text has its counter-part in allegorical interpretation. This way of reading, which must have started with the first readers of Homer and found a fertile ground in Philo’s allegorical commentaries on the Bible, was amazingly natural for Proclus (c. 411– 485), whose writings and commentaries represent the last phases of late antique philosophy, and particularly of the relation between philosophy and rhetoric. (shrink)

This paper examines the relationship between participation and motion with respect to the natural philosophy of the "Phaedo". Aristotle’s criticism of participation and its failure to account for motion shows the relevance of the dialogue to this problem. Challenging Aristotle’s critique, I interpret the "Phaedo" as offering a possible solution to the question of how forms cause motion in material beings. The verb ὀρέγεσθαι at 65c8, 75a2, and 75b1, together with the active ὀρέγειν at 117b2, ground an account of ontological (...) striving as a solution to the difficulties inherent in participation within the literary context of the dialogue. (shrink)

Plato's account of the tripartite soul is a memorable feature of dialogues like the Republic, Phaedrus and Timaeus: it is one of his most famous and influential yet least understood theories. It presents human nature as both essentially multiple and diverse - and yet somehow also one - divided into a fully human 'rational' part, a lion-like 'spirited part' and an 'appetitive' part likened to a many-headed beast. How these parts interact, how exactly each shapes our agency and how they (...) are affected by phenomena like erôs and education is complicated and controversial. The essays in this book investigate how the theory evolves over the whole of Plato's work, including the Republic, Phaedrus and Timaeus, and how it was developed further by important Platonists such as Galen, Plutarch and Plotinus. They will be of interest to a wide audience in philosophy and classics. (shrink)

Luc Brisson’s translation and challenging interpretation of the Parmenides stands out as one of the most influential contributions to contemporary exegesis of Plato’s arguably most controversial dialogue. While acknowledging its many virtues, the essay rejects Brisson’s understanding of the text’s focus and purpose. Brisson’s methodological assumptions are especially discussed and proven to be highly questionable on account of a rather straightforward transfer of the doxographical concerns which Plato is supposed to share with contemporary historians of Parmenides’ philosophy.

Studies of Plato’s metaphysics have tended to emphasise either the radical change between the early Theory of Forms and the late doctrines of the Timaeus and the Sophist, or to insist on a unity of approach that is unchanged throughout Plato’s career. The author lays out an alternative approach. Focussing on two metaphysical doctrines of central importance to Plato’s thought – the Theory of Forms and the doctrine of Being and Becoming – he suggests a continuous progress can be traced (...) through Plato’s works. He presents his argument through an examination of the metaphysical sections of six of the dialogues: the Euthyphro, Phaedo, Republic, Parmenides, Timaeus, and Sophist. (shrink)

Na controvérsia da relação entre os diálogos platônicos e as doutrinas não escritas, o Filebo ocupa um lugar privilegiado. O artigo quer mostrar que a recusa de dar uma definição do Bem e alguns aspectos da doutrina dos quatro gêneros são indícios que podem ser remetidos ao ensinamento oral de Platão.

Do Ideas exist and can we prove it ? Do proofs of their existence have all the same value or not ? Aristotle addresses these issues in two famous documents of the controversy that pitted supporters of the theory of Forms against its opponents within Plato’s Academy : his lost work, quoted by Alexander of Aphrodisias by the title of Peri Ideon, and the lengthy thrust against Ideas that can be read, with some minor variations, in books A, chapter 9, (...) and M, chapter 4, of his Metaphysics. As we only have fragments of the first, the second being laconic and little more than a summary, there has been much speculation about the exact number and nature of the arguments for and against the Forms. Since the pioneering works of Léon Robin, Paul Wilpert et Harold Cherniss, one problem in particular has attracted the attention of specialists : what arguments does Aristotle accuse of either producing Ideas on relatives for one or of dragging in the « Third Man » for another ? Why does he consider these arguments to be more rigorous than the others ? If we are not dealing with the same arguments, how can these be more or better argued than those mentioned by Aristotle in the same breath, namely the arguments Plato’s followers took from the sciences, the one over many and the thought about things that have perished ? Through detailed analysis of texts from the Corpus Aristotelicum and Alexander’s commentary on Aristotle’s Metaphysics, Rationes ex machina develops a new interpretation of the controversial file of the akribesteroi tôn logôn as well as a micrological solution to the puzzle that has come to be a sort of compulsory figure of the exegesis of the Aristotelian criticism of « Plato’s Ideas ». (shrink)

The paper will study an unpublished 1930–31 seminar where Heidegger reads Plato’s Parmenides, showing that in spite of his much-criticized habit of dismissing Plato as the progenitor of “idealist” metaphysics, Heidegger was quite aware of the radical potential of his later dialogues. Through a temporal account of the notion of oneness (to hen), the Parmenides attempts to reconcile the plurality of beings with the unity of Being. In Heidegger’s reading, the dialogue culminates in the notion of the “instant” (to exaiphnēs, (...) Augenblick)—a high point in the entire metaphysical tradition—where the temporal plurality of presence and un-presence converges into a unified disclosure. (shrink)

The aim of the work is to preent the connection between the conception of One - έν and the Good - τάγαθόν in Plato's late writings , in the fragments of writings of the members of the First Plato Academy: Philip of Opus , Eudoxos of Knidos, Speusippus, Xenocrates and the chosen Aristotle's writings . In the analysis of the texts all the derivatives of the conception of One and the Good are taken into account. As a research hypothesis the (...) distinction between έν and τό έν is introduced. This distinction can be seen in comprehending έν as One and τό έν as the One . The One is, first of all, a simple and indivisible being.The work consists of two main parts. The first one is devoted to the analysis of the conception of One - έν and the second contains the analysis of the conception of the Good - τάγαθόν. Each part is made up of two chapters, the first of which illustrates the researched conceptions in the chosen Plato's dialogues, his Unwritten Teaching and the fragments of writings of the members of First Plato Academy, and the second shows these conceptions in Aristotle's philosophy. There is a connection between researched conceptions in Plato's philosophy, what is clearly illustrated in the dialogues the Philebus and the Laws. In the Philebus the Good is One, although it consists of many elements, but Plato does not give a reason for that. In the Laws every watchman must be aware that the good is the one, although it is manifested in many different ways. The One principle is identified with the Good in Plato's Unwritten Teaching. The connection can be also noticed in Aristotle's conception of First Mover , which is the God, the highest Good and the One , because it is, as a pure act, the simple and indivisible being. (shrink)

Anyone who has read Plato’s Republic knows it has a lot to say about mathematics. But why? I shall not be satisfied with the answer that the future rulers of the ideal city are to be educated in mathematics, so Plato is bound to give some space to the subject. I want to know why the rulers are to be educated in mathematics. More pointedly, why are they required to study so much mathematics, for so long?

One of the main problems of Plato's unwritten doctrine has to do with whether his theory of principles has a strictly dualistic or rather a more monistic character. The thesis of this essay is that Plato combines monism and dualism in a particular fashion. Both the dialogues and the testimony of the unwritten doctrine reveal that in Plato's metaphysics the One is the genuinely absolute principle; Plato's second principle, the Many, is not a second absolute - otherwise it would dissolve (...) the very concept of the absolute. Instead, Plato conceives the principle of multiplicity itself as a unity, therefore as in some - in any event ineffable - way as being derived or having emanated from the absolute One. The One itself is wholly transcendent and thus ineffable, knowable neither by reason nor by intellective intuition. Nonetheless, being and knowledge are constituted by the coordination of the One and the Many, for which reason the latter is a principle. Hence, Plato's metaphysics combine a monistic ascent to the absolute with a dualistic derivation of being, a combination made necessary because the One transcends not only all being, but also all knowledge. (shrink)

As a means of overcoming the "Third Man" argument, several commentators have developed an influential theory of the relationship between Platonic Forms and particulars based on Plato's use of "image" analogies. This essay explores the viability of this "image-analogy" hypothesis and, in particular, examines an important, but neglected, argument advanced by R. E. Allen intent on establishing an ontological distinction between an image and its object-source.

An interpretation of the “Parmenides” is proposed in base to the Plato’s “unwritten doctrines”. The greek author demonstrates in this dialogue that with the One only is impossible to think (hypothesis I), and this is why a principle of difference is required; that with the ontological conception of this difference neither, because contradictory conclusions would be followed (hypothesis II); and that without the One isimpossible to think, too (hypothesis III). These conclusions suggest the reader that the One is necessary to (...) think, but another or other principles must be searched to stablish a dialectic. Plato confirms this way the parenetic character of his dialogues respecting at the same time the selfconstrained taboo of the “unwritten doctrines” (he doesn’t mention the undefinite dyad). To come to these conclusions the author ofthis paper proposes a plan of the second part of this work, that divides it in three hypothesis, not in eight, like is usual today, and analyzes the categories that sustain the argumentatives subdivisions of each one of the hypotheses: the structure of all the hypotheses is the same. All this in critical discussion with the actual bibliography about the topics. (shrink)

In Republic VI 508e-9b Plato has Socrates claim that the Good is the cause (αίτίαν) of truth and knowledge as well as the very being of the Forms. Consequently, as causes must be distinct from and superior to their effects, the Good is neither truth nor knowledge nor even being, but exceeds them all in beauty (509a), as well as in honour and power (509b). No other passage in Plato has had a more intoxicating effect on its readers. To take (...) just one example, James Adam was moved to quote St. Paul when he remarked about this passage that, 'it is highly characteristic of Plato's whole attitude that he finds the true keystone of the Universe — the ultimate fountain from which both Knowledge and Existence flow — in no cold and colourless ontological abstraction, like Being, but in that for which "all creation groans and labours". (shrink)

A close reading of the presentation of the method of dialectic at Philebus 16c-18d and, I argue, of its display in the account of the kinds of art necessary for a good city at Statesman 287c-290a and 303d-305e.

There are a variety of puzzling features about this argument. One of them—questions of validity apart—is its apparent redundancy. Parmenides’ initial division provided him with an infinite plurality of parts. He might therefore have given an existence proof of infinitely many numbers, conceived as pluralities of units, by means of this division. Instead, he introduces a new principle of division for the purpose. Again, he derives the conclusion that Unity has infinitely many parts from the infinity of number; but he (...) has already shown that Unity is infinitely divisible into parts consisting of being and unity. In short, the new principle of division introduced for number seems unnecessary, and Parmenides has twice shown that Unity has infinitely many parts. (shrink)

The main lines of interpretation offered to date of the Third Man Argument in Plato's Parmenides (132a1-b2) are considered and rejected. A new, set-theoretic, reconstruction of the argument is offered. It is concluded that the philosophical point of the argument is different from what it has been generally supposed to be: Plato is pointing out the logical shortcomings in his earlier formulated principle of One-Over-Many.