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Syllogistic logic and mathematical proof /

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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.

Bibliographic Details
Main Authors: Mancosu, Paolo (Author), Mugnai, Massimo, 1947- (Author)
Format: eBook
Language:English
Published: Oxford ; New York : Oxford University Press, [2023]
Subjects:
Syllogism > Mathematics.
Logic > Mathematics.
Proof theory.
Syllogisme > Mathématiques.
Théorie de la preuve.
History & Philosophy.
MATHEMATICS.
PHILOSOPHY.
Proof theory
Philosophy: logic.
Philosophy.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of 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
  • Second Syllogism
  • Third Syllogism
  • Third Syllogism
  • 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