Carlo Cellucci

eBook, PDF

The Making of Mathematics (eBook, PDF)

Heuristic Philosophy of Mathematics

Beschreibung

Mainstream philosophy of mathematics, namely the philosophy of mathematics that has prevailed for the past century, claims that the philosophy of mathematics cannot concern itself with the making of mathematics, in particular discovery, but only with finished mathematics, namely mathematics presented in finished form. On this basis, mainstream philosophy of mathematics argues that mathematics is theorem proving by the axiomatic method. This, however, is untenable because it is incompatible with Gödel's incompleteness theorems, and cannot account for many features of mathematics.

This book offers an alternative approach, heuristic philosophy of mathematics, according to which the philosophy of mathematics can concern itself with the making of mathematics, in particular discovery. On this basis, the book argues that mathematics is problem solving by the analytic method, and that this can account for all the main features of mathematics: mathematical method, objects, demonstrations,definitions, diagrams, notations, explanations, beauty, applicability, and knowledge.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 8.24MB

Barrierefreiheit

• Text-to-Speech

Autor

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).

Produktdetails

• Verlag: Springer International Publishing
• Seitenzahl: 450
• Erscheinungstermin: 7. März 2022
• Englisch
• ISBN-13: 9783030897314
• Artikelnr.: 63570193

Rezensionen

"Carlo Cellucci ... published what can be understood to be one of the most significant books in the philosophy and pedagogy of mathematics in the past century. His erudition and explication are evident on every page, but what makes it most valuable for an understanding and presentation of mathematics is the clarity he brings to the argument ... . Such an understanding could transform the way mathematics is presented in journals, textbooks, and classrooms." (Marshall Gordon, Philosophy of Mathematics Education Journal, Issue 1, February, 2024)

"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)