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  • © 2018

The Philosophers and Mathematics

Festschrift for Roshdi Rashed

Editors:

  • Clarifies the nature of the relationship between mathematics and philosophy throughout history

  • Examines the ways philosophy and mathematics helped each other expand and transform

  • Features historical examples throughout to vividly illustrate important points

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

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eBook USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-93733-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 119.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xliii
  2. Scientific Philosophy and Philosophical Science

    • Hourya Benis Sinaceur
    Pages 25-66
  3. Avicenna and Number Theory

    • Pascal Crozet
    Pages 67-80
  4. Zigzag and Fregean Arithmetic

    • Fernando Ferreira
    Pages 81-100
  5. M      

    • Reinhard Kahle
    Pages 117-126
  6. Enthymemathical Proofs and Canonical Proofs in Euclid’s Plane Geometry

    • Abel Lassalle-Casanave, Marco Panza
    Pages 127-144
  7. Mathematics and the Physical World in Aristotle

    • Pierre Pellegrin
    Pages 189-199
  8. Avicenna: Mathematics and Philosophy

    • Roshdi Rashed
    Pages 249-262
  9. For a Continued Revival of the Philosophy of Mathematics

    • Jean-Jacques Szczeciniarz
    Pages 263-295
  10. The Foundations of Arithmetic in Ibn Sīnā

    • Hassan Tahiri
    Pages 297-314
  11. Back Matter

    Pages 315-320

About this book

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.

Keywords

  • 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

Editors and Affiliations

  • Center for Philosophy of Science, University of Lisbon, Lisbon, Portugal

    Hassan Tahiri

About the editor

Hassan Tahiri is a fellow researcher at the Centre for Philosophy of Science of the University of Lisbon (CFCUL) and the University of Charles de Gaulle Lille 3 (MSH, Nord-Pad-de Calais). His research interests focus on the history and philosophy of mathematics, logic and argumentation. Some of his main publications include Mathematics and the Mind. An introduction into Ibn Sīnā’s Theory of Knowledge (Springer Brief Series in Philosophy, 2016) and The Unity of Science in the Arabic Tradition. Science, Logic, Epistemology and their Interactions (Springer, 2008).

Bibliographic Information

Buying options

eBook USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-93733-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 119.99
Price excludes VAT (USA)
Hardcover Book USD 119.99
Price excludes VAT (USA)