Synthese Library : Heuristic Philosophy of Mathematics - Carlo Cellucci

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Synthese Library

Heuristic Philosophy of Mathematics

By: Carlo Cellucci

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Hardcover | 9 March 2023

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Hardcover
472 Pages

Dimensions(cm)
23.5 x 15.5 x 2.41

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$179.00

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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 G¶del'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 proving by 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.

Industry 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)

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