The Philosophers and Mathematics

1. Front Matter

   Pages i-xliii

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2. Analogy and Invention Some Remarks on Poincaré’s Analysis Situs Papers

   • Claudio Bartocci

   Pages 1-23

3. Scientific Philosophy and Philosophical Science

   • Hourya Benis Sinaceur

   Pages 25-66

4. Avicenna and Number Theory

   • Pascal Crozet

   Pages 67-80

5. Zigzag and Fregean Arithmetic

   • Fernando Ferreira

   Pages 81-100

6. The Foundations of Geometry by Peano’s School and Some Epistemological Considerations

   • Paolo Freguglia

   Pages 101-116

7. M     

   • Reinhard Kahle

   Pages 117-126

8. Enthymemathical Proofs and Canonical Proofs in Euclid’s Plane Geometry

   • Abel Lassalle-Casanave, Marco Panza

   Pages 127-144

9. Some Reasons to Reopen the Question of the Foundations of Probability Theory Following Gian-Carlo Rota

   • Carlos Lobo

   Pages 145-187

10. Mathematics and the Physical World in Aristotle

    • Pierre Pellegrin

    Pages 189-199

11. The Axiom of Choice as Interaction Brief Remarks on the Principle of Dependent Choices in a Dialogical Setting

    • Shahid Rahman

    Pages 201-248

12. Avicenna: Mathematics and Philosophy

    • Roshdi Rashed

    Pages 249-262

13. For a Continued Revival of the Philosophy of Mathematics

    • Jean-Jacques Szczeciniarz

    Pages 263-295

14. The Foundations of Arithmetic in Ibn Sīnā

    • Hassan Tahiri

    Pages 297-314

15. Back Matter

    Pages 315-320

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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

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

  Hassan Tahiri

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).

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