The making of mathematics [electronic resource] : heuristic philosophy of mathematics / Carlo Cellucci.
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 presente...
Saved in:
| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham, Switzerland :
Springer,
2022.
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| Series: | Synthese library ;
v. 448. |
| Subjects: |
MARC
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| 245 | 1 | 4 | |a The making of mathematics |h [electronic resource] : |b heuristic philosophy of mathematics / |c Carlo Cellucci. |
| 260 | |a Cham, Switzerland : |b Springer, |c 2022. | ||
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| 490 | 1 | |a Synthese Library ; |v v.448. | |
| 505 | 0 | |a 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. | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a 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. | ||
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| 776 | 0 | 8 | |i Print version: |a Cellucci, Carlo |t The Making of Mathematics |d Cham : Springer International Publishing AG,c2022 |z 9783030897307. |
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