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The Making of Mathematics = Heuristic Philosophy of Mathematics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The Making of Mathematics/ by Carlo Cellucci.
其他題名:	Heuristic Philosophy of Mathematics /
作者:	Cellucci, Carlo.
面頁冊數:	XX, 450 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	History of Mathematical Sciences. -
電子資源:	https://doi.org/10.1007/978-3-030-89731-4
ISBN:	9783030897314

The Making of Mathematics = Heuristic Philosophy of Mathematics /
Cellucci, Carlo.

The Making of MathematicsHeuristic Philosophy of Mathematics /[electronic resource] :by Carlo Cellucci. - 1st ed. 2022. - XX, 450 p. 1 illus.online resource. - Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,4482542-8292 ;. - Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,359.

1. Introduction -- Part I. Heuristic vs. Mainstream. 2. Mainstream Philosophy of Mathematics -- 3. Heuristic Philosophy of Mathematics -- Part II. Discourse on Method. 4. The Question of Method -- 5. Analytic Method -- 6. Analytic-Synthetic Method and Axiomatic Method -- 7. Rules of Discovery -- 8. Theories -- Part III. The Mathematical Process. 9. Objects -- 10. Demonstrations -- 11. Definitions -- 12. Diagrams -- 13. Notations -- Part IV. The Functionality of Mathematics. 14. Explanations -- 15. Beauty -- 16. Applicability -- Part V. Conclusion. 17. Knowledge, Mathematics, and Naturalism -- 18. Concluding Remarks -- Index.

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.

ISBN: 9783030897314

Standard No.: 10.1007/978-3-030-89731-4doiSubjects--Topical Terms:

785417
History of Mathematical Sciences.

LC Class. No.: QA8-10.4

Dewey Class. No.: 510.1

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