The making of mathematics : heuristic philosophy of mathematics

著者

• Cellucci, Carlo

書誌事項

The making of mathematics : heuristic philosophy of mathematics

Carlo Cellucci

（Synthese library, v. 448）

Springer, c2022

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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 Goedel'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.

目次

1. Introduction Part I. Heuristic vs. Mainstream2. Mainstream Philosophy of Mathematics3. Heuristic Philosophy of Mathematics Part II. Discourse on Method4. The Question of Method5. Analytic Method6. Analytic-Synthetic Method and Axiomatic Method7. Rules of Discovery8. Theories Part III. The Mathematical Process9. Objects10. Demonstrations11. Definitions12. Diagrams13. Notations Part IV. The Functionality of Mathematics14. Explanations15. Beauty16. Applicability Part V. Conclusion17. Knowledge, Mathematics, and Naturalism18. Concluding Remarks Index

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詳細情報

• NII書誌ID(NCID): BC14132518
• ISBN:
  • 9783030897307
• 出版国コード: sz
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: [Cham]
• ページ数/冊数: xx, 450 p.
• 大きさ: 25 cm
• 分類:
  • DC23 : 510.1
• 件名:
  • LCSH : Mathematics -- Philosophy
  • LCSH : Heuristic
• 親書誌ID:
  • BA00017801