Overview
- Provides an alternative to current philosophy of mathematics; heuristic philosophy of mathematics
- Shows that mathematics is not merely theorem proving by the axiomatic method
- Of interest to both graduate students and scholars working in philosophy of mathematics
Part of the book series: Synthese Library (SYLI, volume 448)
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Table of contents (18 chapters)
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Front Matter
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Heuristic vs. Mainstream
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Front Matter
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Discourse on Method
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Front Matter
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The Mathematical Process
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Front Matter
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The Functionality of Mathematics
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Front Matter
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Keywords
About this book
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics.
By using the heuristic approach, this book argues that mathematics is not theorem provingby the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.
Reviews
“The book is extensive and circumstantial. … The book is well written, based upon sources … with a clear intention to advance the case of ‘heuristic’ philosophy of mathematics. … the book is a valuable position which could start a debate and possible revision of modern philosophy of mathematics.” (Roman Duda, zbMATH 1497.00010, 2022)
“The book is an interesting contribution to the new trend in the philosophy of mathematics, the trend in which the attention is paid mainly to the mathematical practice, to making of mathematics and not to mathematics as a finished structure of theorems and proofs.” (Roman Murawski, Mathematical Reviews, November, 2022)
Authors and Affiliations
About the author
Carlo Cellucci is emeritus professor of logic at Sapienza University of Rome. He is the author of seven books: Teoria della dimostrazione (Boringhieri, 1978); Le ragioni della logica (Laterza, 1998); Filosofia e matematica (Laterza, 2003); Perché ancora la filosofia (Laterza, 2008); Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer, 2013); Breve storia della logica: Dall’Umanesimo al primo Rinascimento (with Mirella Capozzi, Lulu Press, 2014); Rethinking Knowledge: The Heuristic View (Springer, 2017).
Bibliographic Information
Book Title: The Making of Mathematics
Book Subtitle: Heuristic Philosophy of Mathematics
Authors: Carlo Cellucci
Series Title: Synthese Library
DOI: https://doi.org/10.1007/978-3-030-89731-4
Publisher: Springer Cham
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-030-89730-7Published: 08 March 2022
Softcover ISBN: 978-3-030-89733-8Published: 09 March 2023
eBook ISBN: 978-3-030-89731-4Published: 07 March 2022
Series ISSN: 0166-6991
Series E-ISSN: 2542-8292
Edition Number: 1
Number of Pages: XX, 450
Number of Illustrations: 1 b/w illustrations
Topics: Philosophy of Mathematics, History of Mathematical Sciences