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The making of mathematics : heuristic philosophy of mathematics / Carlo Cellucci.

9783030897314 (electronic bk.)
3030897311 (electronic bk.)
9783030897307
3030897303

Cham, Switzerland : Springer, 2022.

English

1 online resource (457 pages)

10.1007/978-3-030-89731-4 doi

QA8.4

510.1

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 Godels 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.

Includes bibliographical references and index.

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