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Carte Syllogistic Logic and Mathematical Proof Mancosu

Syllogistic Logic and Mathematical Proof

Autor: Mancosu, Prof Paolo (University of California, Berkeley), Massimo (Scuola Normale Superiore) Mugnai
Limbă: engleză
Legare: Copertă tare
Editura: Oxford University Press
Disponibilitate: În depozitul extern
Expediem în 14-21 zile
517.96 lei
Does syllogistic logic have the resources to capture mathematical proof? This volume provides the fi...

Informații despre carte

Autor
Mancosu, Prof Paolo (University of California, Berkeley), Massimo (Scuola Normale Superiore) Mugnai
Limbă
engleză
Legare
Carte - Copertă tare
Publicat
2023
Pagini
256
EAN
9780198876922
ISBN
0198876920
Enbook ID
42412442
Editura
Oxford University Press
Greutate
494
Dimensiuni
153 x 234

Descriere completă

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. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.

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