# The Philosophers and Mathematics

## Festschrift for Roshdi Rashed

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Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 43)

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Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 43)

This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements.

The essays offer insight into the role that mathematics played in the formation of each included philosopher’s doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way.

Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.

Abstract Algebra Analogy in Poincaré’s Mathematical Practice Aristotle’s Philosophy of Nature Avicenna’s Analytical Philosophy Avicenna’s Theory of Knowledge Axiom of Choice The Comprehension Principle and Predicativity Constructive Type Theory Hilbert and Husserl on Critical Thinking Dialogical Logic The Foundations of Geometry: Gassmann Peano Hilbert Frege’s Logicism and Russell’s Paradox Hilbert’s Axiomatic Method and Proof Theory Husserl’s Phenomenology Kant’s Transcendatenlism Kolmogorov’s Axiomatization of Probability Gian-Carlo Rota’s Algebraization of Probability Russell’s Zigzag Theory Theory and Practice in Mathematics Jules Vuillemin’s Systematic Philosophy

- DOI https://doi.org/10.1007/978-3-319-93733-5
- Copyright Information Springer International Publishing AG, part of Springer Nature 2018
- Publisher Name Springer, Cham
- eBook Packages Religion and Philosophy
- Print ISBN 978-3-319-93732-8
- Online ISBN 978-3-319-93733-5
- Series Print ISSN 2214-9775
- Series Online ISSN 2214-9783
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