(Ebook PDF) Syllogistic Logic and Mathematical Proof 1st edition by Mugnai Mancosu, Massimo Mugnai 0198876947 9780198876946 full chapters

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ISBN-10 :  0198876947 

ISBN-13 :  9780198876946

Author:  Mugnai Mancosu, Massimo Mugnai 

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: ‘scientific’ (‘demonstrative’) syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid’s theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form.

Syllogistic Logic and Mathematical Proof 1st Table of contents:

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
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
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

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Syllogistic Logic,Mathematical Proof,Mugnai Mancosu,Massimo Mugnai