Syllogistic Logic and Mathematical Proof av Prof Paolo (University of California Berkeley) Mancosu, Prof Massimo (Scuola Normale Superiore) Mugnai

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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, theclaim 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 whethermathematical 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 t