Deleuze and the History of Mathematics by Duffy, Simon -- Read -- Imperial Library of Trantor

Index

Cover-Page Half-Title Series Title Copyright Dedication Contents Acknowledgments List of Abbreviations Introduction 1 Leibniz and the Concept of the Infinitesimal

Leibniz’s law of continuity and the infinitesimal calculus Newton’s method of fluxions and infinite series The emergence of the concept of the function Subsequent developments in mathematics: The problem of rigor The theory of singularities The characteristics of a point-fold as reflected in the point of inflection Subsequent developments in mathematics: Weierstrass and Poincaré The development of a differential philosophy The qualitative theory of differential equations Deleuze’s “Leibnizian” interpretation of the theory of compossibility Point of view and the theory of the differential unconscious The mathematical representation of matter, motion, and the continuum The Koch curve and the folded tunic: The fractal nature of motion The metaphysics of monads, and bodies as “well-founded phenomena” Deleuze’s characterization of Leibniz’s account of matter Overcoming the limits of Leibniz’s metaphysics Spinoza and the logic of different/ciation

2 Maimon’s Critique of Kant’s Approach to Mathematics

Kant on the construction of mathematical concepts in pure intuition The concept of the straight line Maimon’s critique of Kant Maimonic reduction The laws of sensibility Noumena, phenomena, and regulative ideas Bordas-Demoulin on the differential relation as “the universal function” Maimon’s infinite intellect is displaced by a theory of problems The rigorous algorithm of Wronski’s transcendental philosophy A “problematic” is “the ensemble of the problem and its conditions” Abel and Galois on the question of the solvability of polynomial equations

3 Bergson and Riemann on Qualitative Multiplicity

The role of judgment in the determination of the idea of an extensive magnitude Mechanical explanation as a method or as a doctrine? Bergson’s problem with the cinematographical method overcome The Riemannian concept of multiplicity and the Dedekind cut Deleuze’s rehabilitation and extension of Bergson’s project

4 Lautman’s Concept of the Mathematical Real

Lautman’s axiomatic structuralism The metaphysics of logic: A philosophy of mathematical genesis Lautman’s Platonism Problematic ideas and the concept of genesis Heidegger and the naive period in the history of mathematical logic The virtual in Lautman Deleuze and the calculus of problems The logic of the calculus of problems

5 Badiou and Contemporary Mathematics

Badiou and the role of mathematics as ontology Orthodox Platonism in mathematics and its problems Badiou’s “modern Platonist” response and its reformulation of the question Cantor’s account of transfinite numbers or ordinals The Platonist implications of axiomatic set theory The model-theoretic implications of Badiou’s “modern Platonism” On the difference between set theory and category theory Mathematics as ontology in Badiou and Deleuze

Conclusion

The “vindication” of Leibniz’s account of the differential The scienticity debate in Deleuze studies Badiou’s relation to Lautman and the mathematical real

Notes

Introduction Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Conclusion

Bibliography Index

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