The Making of Mathematics Heuristic Philosophy of Mathematics
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...
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| Format: | eBook |
| Language: | English |
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Cham
Springer International Publishing
2022, 2022
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| Edition: | 1st ed. 2022 |
| Series: | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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