Syllogistic logic and mathematical proof / Paolo Mancosu and Massimo Mugnai.

Format:

Book

Author/Creator:

Mancosu, Paolo, author.

Mugnai, Massimo, 1947- author.

Series:

Oxford scholarship online.

Oxford scholarship online

Language:

English

Subjects (All):

Syllogism--Mathematics.

Syllogism.

Logic--Mathematics.

Logic.

Proof theory.

Physical Description:

1 online resource (238 pages)

Place of Publication:

Oxford : Oxford University Press, 2023.

Summary:

A unified account of the history of attempts to convert mathematical proof to a syllogistic form of reasoning, from Aristotle to major advances in logic in the nineteenth century. The analysis of the debate provides insights into the relationship between philosophy and mathematics.

Contents:

Cover

Syllogistic Logic and Mathematical Proof

Copyright

Contents

Acknowledgments

Dedication

Introduction

1. Aristotelian Syllogism and Mathematics in Antiquity and the Medieval Period

2. Extensions of the Syllogism in Medieval Logic

2.1 Oblique Terms and Relational Sentences in Late Medieval Logic: John Buridan, William of Ockham, and Albert of Saxony

2.2 Expository Syllogism: Identity and Singular Terms

3. Syllogistic and Mathematics: The Case of Piccolomini

3.1 Piccolomini's Syllogistic Reconstruction of Euclid's Elements I.1

First Syllogism

Second Syllogism

Third Syllogism

Fourth Syllogism

3.2 A Critical Analysis of Piccolomini's Reconstruction

4. Obliquities and Mathematics in the Seventeenth and Eighteenth Centuries: From Jungius to Saccheri

4.1 Johannes Vagetius (1633-1691)

4.2 Gottfried Wilhelm Leibniz (1646-1714)

4.3 Juan Caramuel Lobkowitz (1606-1682)

4.4 Gerolamo Saccheri (1667-1733)

4.5 A First Conclusion

5. The Extent of Syllogistic Reasoning: From Rüdiger to Wolff

5.1 Andreas Rüdiger (1673-1731) and His School on Oblique Inferences

5.2 Christian Wolff on Oblique Inferences

5.3 Mathematics, Philosophy, and Syllogistic Inferences in Wolff, Rüdiger, Müller, Hoffmann, and Crusius

5.3.1 Wolff: Every Mathematical Demonstration Is a Chain of Syllogisms

5.3.2 Rüdiger and His School on the Non-Syllogistic Nature of Mathematics

5.3.2.1 Andreas Rüdiger on the Non-Syllogistic Nature of Mathematics

5.3.2.2 Syllogism and Mathematical Reasoning in Müller, Hoffmann, and Crusius

5.3.2.3 Appendix: Note (d) in Rüdiger's De Sensu Veri et Falsi (1722)

6. Lambert and Kant

6.1 Johann Heinrich Lambert (1728-1777) and the Treatment of Relations in His Logical Calculus.

6.2 Kant and Traditional Logic

6.3 Kant on Syllogistic Proofs and Mathematics

7. Bernard Bolzano on Non-Syllogistic Reasoning

8. Thomas Reid, William Hamilton, and Augustus De Morgan

Conclusion

References

Index of Names.

Notes:

Also issued in print: 2023.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (viewed on May 22, 2023).

Other Format:

Print version: Mancosu, Paolo Syllogistic Logic and Mathematical Proof

ISBN:

0-19-198805-7

0-19-887693-9

0-19-887694-7

OCLC:

1378393639