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Gilles Deleuze's engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges are an opportunity to reconfigure particular philosophical problems - for example, the problem of individuation - and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze's philosophy, as well as addressing the undervalued and often neglected question of the mathematical thinkers who influenced his work. Chapter 1: Leibniz and the Concept of the Infinitesimal. Chapter 2: Maimon's Critique of Kant's Approach to Mathematics. Chapter 3: Bergson and Riemann on Qualitative Multiplicity. Chapter 4: Lautman's Concept of the Mathematical Real. Chapter 5: Badiou and Contemporary Mathematics

Discover Spinoza's philosophy of ratio, from geometry and reason to bodies, affects and architectureFrom his geometrical method to his theory of mind and body and from his account of the emotions to his doctrine of how to live well, ratio is of prime importance in Spinoza's philosophy. These essays explore the surprisingly varied dimensions of this unacknowledged keystone of Spinoza's thought. They take you from Spinoza's geometrical diagrams to his concepts of mind, body, the emotions, and the cosmos. It shows how Spinoza's thinking about ratio influences the concept of proportion in Gulliver's Travels, the differential ontology of Deleuze, egalitarian design for wellbeing, and the notion of an affective architecture.Key FeaturesThe first major work to explore ratio as a key concept of Spinoza's thoughtReveals that ratio is a multi-faceted concept that connects geometry, minds, reason, bodies, social relations and the cosmos in Spinoza's philosophyShows how ratio can be used to address enduring questions in Spinoza's thought and take his philosophy in exciting new directionsOffers new applications of Spinoza's thinking to architecture, design and urban studies ContributorsSimon B. Duffy, Yale-NUS College, Singapore. Hélène Frichot, KTH, Stockholm, Sweden.Gökhan Kodalak, Cornell University, USA. Michael LeBuffe, University of Otago, Canada. Beth Lord, University of Aberdeen, UK. Heidi M. Ravven, Hamilton College, New York, USA. Peg Rawes, Bartlett School of Architecture, UCL, UK. Anthony Uhlmann, Western Sydney University, Australia. Valtteri Viljanen, University of Turku, Finland. Stefan White, Manchester School of Architecture, UK.Timothy Yenter, University of Mississippi, USA