Simon Duffy, 'Deleuze, mathematics and the nature of problems', (23 February 2017)
Channel: Philosophy USM
Date: 2017-03-28

This paper defends a deflationary characterisation of Deleuze’s metaphysics, and the ontological commitments it seems to imply, as a metaphysics of the calculus that draws upon a conception of mathematics that is steeped in the implications of a subject naturalist pragmatist approach to the question of mathematical foundations. In order to make sense of this deflationary metaphysics that I attribute to Deleuze, I argue that it is consonant in useful ways with the subject naturalist pragmatism proposed by Macarthur and Price (2007). One preliminary consonance being that the conception of mathematics that Deleuze develops does not serve the same reductive ends that ‘capital N Naturalism’ requires, but rather it serves as a useful tool for modelling the nature of our relation to the world without the representational presuppositions of the latter. One way of characterising this conception of mathematics that will be explored is the deflationary character of Carnap’s philosophy of mathematics and the principle of tolerance that he advocates with respect to foundational questions in mathematics (Carnap 1937).