In this paper I present an interpretation of Deleuze's concept of the virtual. I argue that this concept is best understood in relation to the problematic of individuation or differentiation, which Deleuze inherits from Duns Scotus. After analysing Scotus' critique of Aristotelian or hylomorphic approaches to the problem of individuation, I turn to Deleuze's account of differentiation and his interpretation of the calculus in chapter 4 of Difference and Repetition. The paper seeks thereby to explicate Deleuze's dialectics or theory of (...) Ideas, his approach to the principle of sufficient reason, and the concept of the virtual itself. (shrink)

In Différence et répétition, Deleuze's ontology is structured by his theory of dialectical Ideas or problems, which draws features from Plato, Kant, and classical calculus. Deleuze unifies these features through a theory of Ideas/problems developed by the mathematician and philosopher Albert Lautman. Lautman worked to explain the nature of the problems or dialectical Ideas mathematics engages and the solutions or mathematical theories endeavouring to understand them. Lautman drew upon Heidegger to do this. This article clarifies Deleuze's theory of dialectical Ideas/problems (...) by analysing its debts to Lautman and Heidegger and demonstrates a Heideggerian influence on Deleuze via Lautman. (shrink)

Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue that the concept of event—rather than object—better captures the vitality of mathematics, and offers new ways of thinking about mathematics education. In this paper I draw on two different but related (...) theories of event articulated in the philosophies of Alain Badiou and Gilles Deleuze to argue that the central activity of ‘problem solving’ in mathematics education should be recast in terms of a problematic of events. (shrink)

A new ontology that forms the groundwork for ethical practices of resistance What and how should individuals resist in political situations? While these questions recur regularly within Western political philosophy, answers to them have often relied on dogmatically held ideals, such as the distinction between truth and doxa or the privilege of thought over sense. In particular, the strain of idealist political philosophy, inaugurated by Plato and finding contemporary expression in the work of Alain Badiou, employs dualities that reduce the (...) complexities of practices of resistance to concepts of commitment. (shrink)

In this paper I present an interpretation of Deleuze's concept of the virtual. I argue that this concept is best understood in relation to the problematic of individuation or differentiation, which Deleuze inherits from Duns Scotus. After analysing Scotus’ critique of Aristotelian or hylomorphic approaches to the problem of individuation, I turn to Deleuze's account of differentiation and his interpretation of the calculus in chapter 4 of Difference and Repetition. The paper seeks thereby to explicate Deleuze's dialectics or theory of (...) Ideas, his approach to the principle of sufficient reason, and the concept of the virtual itself. (shrink)