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)

This book is a quest for the real Plato, forever hiding behind the veil of drama. The quest, as the subtitle indicates, is Cartesian in that it looks for Plato independently of the prevailing paradigms on where we are supposed to find him. The result of the quest is a complete pedagogical platform on Plato. This does not mean that the book leaves nothing out, covering all the dialogues and all the themes, but that it provides the full intellectual apparatus (...) for doing just that. It consists of two parts. The first is a general orientation in three chapters, one each pertaining to the life, thought, and works of Plato. The second is a dialogic companion covering the four dialogues built around the last days of Socrates, with a separate chapter devoted to each: Euthyphro, Apology, Crito, and Phaedo. (shrink)

The idea of negative Platonism, first formulated by Jan Patočka in the early 1950s, can be understood as an interpretation of the history of philosophy, with particular reference to its Greek beginnings, as well as a strategy for critical engagement with the metaphysical tradition and a reformulation of central phenomenological themes. Patočka reconstructs the Greek road to metaphysics as a shift from a non-objectifying comprehension of the world as a totality to a quest for systematic knowledge of ultimate reality. In (...) light of this reclaimed background, he then proposes a new reading of Plato: the realm of ideas, separate from empirical reality, becomes a symbol of human freedom, understood as an ability to transcend the world and in so doing grasp it as a totalizing horizon. The concept of freedom thus links a submerged theme of metaphysics to more explicit concerns of contemporary thought. (shrink)

We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in a decimal (...) system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers. (shrink)

This article offers a Polish translation of Aristotle’s treatise, On Philosophy, of which only certain fragments and testimonies have been preserved. The translation is supplied with an introduction presenting the history of various interpretations and reconstructions of Aristotle’s work.

The present article offers the first Polish translation of Theodore Metochites’ important essay on the philosophers’ use and abuse of irony. The translation is preceded by an introduction which briefly presents the author of the Miscellanea philosophica et historica, upon which it reconstructs the argument of essay 8 and provides an assessment of Metochites’ account of irony.

El presente artículo pretende, tras pasar revista a la bibliografía existente y al estado de la cuestión sobre el mito delPolítico de Platón, proponer en primer lugar una nueva lectura de este a la luz de la tradición religiosa griega y, concretamente, del Leitmotiv hesiódico del mito de las edades del hombre. En segundo lugar, la comparación de este mito y su trasfondo religioso con otros diálogos políticos del filósofo ateniense, notablemente con las Leyes, revela a nuestro ver a una (...) insistencia en las nociones de la edad de oro y del gobierno divino como ideal político. Considerar este pasaje del Político como un fundamento en el nivel mítico y alusivo para estas nociones en otros diálogos de Platón permitiría, si nuestra hipótesis de trabajo se confirma, ilustrar la interacción del proyecto político global del filósofo con el recurso a la tradición religiosa y con los ejemplos míticos de otros diálogos políticos. (shrink)

This paper is an attempt to clarify the ontological status of Platonic ideas. My considerations are based on the example of mathematical ideas and their relation to the subjects of mathematics and phenomena, since such modes of existence are distinguished in the philosophy of Plato.