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)

Gilles Deleuze (January 18, 1925–November 4, 1995) was one of the most influential and prolific French philosophers of the second half of the twentieth century. Deleuze conceived of philosophy as the production of concepts, and he characterized himself as a “pure metaphysician.” In his magnum opus Difference and Repetition , he tries to develop a metaphysics adequate to contemporary mathematics and science—a metaphysics in which the concept of multiplicity replaces that of substance, event replaces essence and virtuality replaces possibility. Deleuze (...) was also well-known for a number of important monographs he published in the history of philosophy (on Hume, Nietzsche, Kant, Bergson, Spinoza, Foucault, and Leibniz), as well as for his writings on the various arts, which include a two- volume study of the cinema, books on Proust and Sacher-Masoch, a monograph on the painter Francis Bacon, and a collection of essays on literature. Deleuze considered these latter works as pure philosophy, and not criticism, since he sought to create the concepts that correspond to the artistic practices of painters, filmmakers, and writers. In 1968, he met Félix Guattari, a political activist and radical psychoanalyst, with whom he wrote several works, among them the two-volume Capitalism and Schizophrenia , comprised of Anti-Oedipus (1972) and A Thousand Plateaus (1980). Their final collaboration was What is Philosophy? (1991). (shrink)

While many of the most important figures in the history of philosophy have employed the concept of the simulacrum in one way or another, a detailed study of this usage has yet to be written. In this essay, I will attempt to tell the story of a sequence in that history of that usage, by focusing on one of Deleuze's case studies of the concept of the simulacrum. To do so, I will focus primarily on one the appendices to The (...) Logic of Sense: ‘Lucretius and the Simulacrum’. In order to understand what I will call the Deleuze–Lucretius encounter, I will proceed as follows. After a few initial guiding remarks regarding the general project of the ‘inversion of Platonism’, we will outline some of the most fundamental features of atomistic physics. This will allow us to discuss Lucretius’ thoughts on the clinamen, the swerve. This, in turn, leads directly to the concept of the simulacrum. With such a picture of Lucretian physics in hand, I will pivot to a discussion of Lucretius’ ethics. The ethics consists of a critique of superstition in terms of a general project of demystification. Although this sequence will concentrate mostly on what became one of the appendices to The Logic of Sense, I will end by looking at the more general usage of Lucretian atomism, especially as it functions in Difference and Repetition and The Logic of Sense. (shrink)

The Heidegger–Deleuze relationship has attracted significant attention of late. This paper contributes to this line of research by examining Deleuze’s claim, recently reiterated and developed by Philip Tonner, that Heidegger offers a univocal conception of Being where there is one sense of Being that is said throughout all entities. Although these authors maintain that this claim holds across Heidegger’s oeuvre, I purposefully adopt a conservative hermeneutical strategy that focuses on two writings from the 1927–1928 period—Being and Time and the following (...) year’s lecture course translated as The Metaphysical Foundations of Logic—and emphasize the lesson of the ontological difference that Being is always the Being of an entity, to argue that with regards to these texts, at least, an alternative equivocal interpretation is possible in which Being is always said differently. The conclusion draws out the implications of this for the relationship between Heidegger’s fundamental ontology and Deleuze’s differential ontology. (shrink)