Syllogistic Logic and Mathematical Proof Mancosu Paolo
Syllogistic Logic and Mathematical Proof Mancosu Paolo Does syllogistic logic have the resources to capture mathematical proof? Aristotle had claimed that scientific knowledge, which includes…
Specifikacia Syllogistic Logic and Mathematical Proof Mancosu Paolo
Syllogistic Logic and Mathematical Proof Mancosu Paolo
Does syllogistic logic have the resources to capture mathematical proof? Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. 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.
Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. 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.