The making of mathematics heuristic philosophy of mathematics / [electronic resource] :
- 作者： Cellucci, Carlo.
- 其他作者：
- 其他題名：
- Synthese library, studies in epistemology, logic, methodology, and philosophy of science ;
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Synthese library, studies in epistemology, logic, methodology, and philosophy of science,v. 448
- 主題： Mathematics--Philosophy. , Philosophy of Mathematics. , History of Mathematical Sciences.
- ISBN： 9783030897314 (electronic bk.) 、 9783030897307 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: 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.
- 摘要註: 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 Godel'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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讀者標籤：
- 系統號： 005513686 | 機讀編目格式
館藏資訊
This book offers an alternative to current philosophy of mathematics: heuristic philosophy of mathematics. In accordance with the heuristic approach, the philosophy of mathematics must concern itself with the making of mathematics and in particular with mathematical discovery. In the past century, mainstream philosophy of mathematics has claimed that the philosophy of mathematics cannot concern itself with the making of mathematics but only with finished mathematics, namely mathematics as presented in published works. On this basis, mainstream philosophy of mathematics has maintained that mathematics is theorem proving by the axiomatic method. This view has turned out to be untenable because of Gödel’s incompleteness theorems, which have shown that the view that mathematics is theorem proving by the axiomatic method does not account for a large number of basic features of mathematics. By using the heuristic approach, this book argues that mathematics is not theorem proving by the axiomatic method, but is rather problem solving by the analytic method. The author argues that this view can account for the main items of the mathematical process, those being: mathematical objects, demonstrations, definitions, diagrams, notations, explanations, applicability, beauty, and the role of mathematical knowledge.