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Publisher’s description: 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.
The articles of this volume will be reviewed individually.
Indexed articles:
Bartocci, Claudio, Analogy and invention some remarks on Poincaré’s analysis situs papers, 1-23 [Zbl 1445.01010]
Benis Sinaceur, Hourya, Scientific philosophy and philosophical science, 25-66 [Zbl 1436.00031]
Crozet, Pascal, Avicenna and number theory, 67-80 [Zbl 1453.01007]
Ferreira, Fernando, Zigzag and Fregean arithmetic, 81-100 [Zbl 1436.03035]
Freguglia, Paolo, The foundations of geometry by Peano’s school and some epistemological considerations, 101-116 [Zbl 1436.51002]
Kahle, Reinhard, Let none but geometers enter here, 117-126 [Zbl 1436.03043]
Lassalle-Casanave, Abel; Panza, Marco, Enthymemathical proofs and canonical proofs in Euclid’s plane geometry, 127-144 [Zbl 1436.51003]
Lobo, Carlos, Some reasons to reopen the question of the foundations of probability theory following Gian-Carlo Rota, 145-187 [Zbl 1436.60005]
Pellegrin, Pierre, Mathematics and the physical world in Aristotle, 189-199 [Zbl 1444.01007]
Rahman, Shahid, The axiom of choice as interaction brief remarks on the principle of dependent choices in a dialogical setting, 201-248 [Zbl 1436.03071]
Rashed, Roshdi, Avicenna: mathematics and philosophy, 249-262 [Zbl 1457.01004]
Szczeciniarz, Jean-Jacques, For a continued revival of the philosophy of mathematics, 263-295 [Zbl 1436.00040]
Tahiri, Hassan, The foundations of arithmetic in Ibn Sīnā, 297-314 [Zbl 07219626]