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The Making of Mathematics
Heuristic Philosophy of Mathematics
Taschenbuch von Carlo Cellucci
Sprache: Englisch

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Beschreibung
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 provingby 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.
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 provingby 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.
Über den Autor

Carlo Cellucci is emeritus professor of logic at Sapienza University of Rome. He is the author of seven books: Teoria della dimostrazione (Boringhieri, 1978); Le ragioni della logica (Laterza, 1998); Filosofia e matematica (Laterza, 2003); Perché ancora la filosofia (Laterza, 2008); Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer, 2013); Breve storia della logica: Dall'Umanesimo al primo Rinascimento (with Mirella Capozzi, Lulu Press, 2014); Rethinking Knowledge: The Heuristic View (Springer, 2017).

Zusammenfassung

Provides an alternative to current philosophy of mathematics; heuristic philosophy of mathematics

Shows that mathematics is not merely theorem proving by the axiomatic method

Of interest to both graduate students and scholars working in philosophy of mathematics

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Genre: Geisteswissenschaften, Kunst, Musik, Philosophie
Rubrik: Geisteswissenschaften
Medium: Taschenbuch
Inhalt: xx
450 S.
1 s/w Illustr.
450 p. 1 illus.
ISBN-13: 9783030897338
ISBN-10: 3030897338
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Cellucci, Carlo
Auflage: 1st edition 2022
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 26 mm
Von/Mit: Carlo Cellucci
Erscheinungsdatum: 09.03.2023
Gewicht: 0,709 kg
Artikel-ID: 126637492
Über den Autor

Carlo Cellucci is emeritus professor of logic at Sapienza University of Rome. He is the author of seven books: Teoria della dimostrazione (Boringhieri, 1978); Le ragioni della logica (Laterza, 1998); Filosofia e matematica (Laterza, 2003); Perché ancora la filosofia (Laterza, 2008); Rethinking Logic: Logic in Relation to Mathematics, Evolution, and Method (Springer, 2013); Breve storia della logica: Dall'Umanesimo al primo Rinascimento (with Mirella Capozzi, Lulu Press, 2014); Rethinking Knowledge: The Heuristic View (Springer, 2017).

Zusammenfassung

Provides an alternative to current philosophy of mathematics; heuristic philosophy of mathematics

Shows that mathematics is not merely theorem proving by the axiomatic method

Of interest to both graduate students and scholars working in philosophy of mathematics

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Genre: Geisteswissenschaften, Kunst, Musik, Philosophie
Rubrik: Geisteswissenschaften
Medium: Taschenbuch
Inhalt: xx
450 S.
1 s/w Illustr.
450 p. 1 illus.
ISBN-13: 9783030897338
ISBN-10: 3030897338
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Cellucci, Carlo
Auflage: 1st edition 2022
Hersteller: Springer International Publishing
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 235 x 155 x 26 mm
Von/Mit: Carlo Cellucci
Erscheinungsdatum: 09.03.2023
Gewicht: 0,709 kg
Artikel-ID: 126637492
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