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Record Nr. |
UNINA9910552711503321 |
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Autore |
Cellucci Carlo |
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Titolo |
The Making of Mathematics : Heuristic Philosophy of Mathematics / / by Carlo Cellucci |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2022 |
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ISBN |
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9783030897314 |
9783030897307 |
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Edizione |
[1st ed. 2022.] |
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Descrizione fisica |
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1 online resource (457 pages) |
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Collana |
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Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, , 2542-8292 ; ; 448 |
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Disciplina |
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Soggetti |
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Mathematics - Philosophy |
Mathematics |
History |
Philosophy of Mathematics |
History of Mathematical Sciences |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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 |
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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. |
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