Syllogistic Logic and Mathematical Proof

Syllogistic logic has been debated as to whether it has the resources to capture mathematical proof. This volume provides an account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the debate is a fascinating and crucial insight into the relationship between philosophy and mathematics.

Format: Hardback
Length: 240 pages
Publication date: 18 May 2023
Publisher: Oxford University Press

This comprehensive volume explores the historical endeavors to address the central question of whether syllogistic logic possesses the capacity to capture mathematical proof. It delves into the reasoning behind the diverse positions taken on this matter, as well as the profound implications of these positions. Aristotle, renowned for his influential contributions to philosophy and science, asserted that scientific knowledge, encompassing mathematics, is derived from a distinct type of syllogism known as scientific (demonstrative) syllogisms. Throughout ancient Greece and the Middle Ages, the notion that Euclid's theorems could be recast syllogistically was widely accepted without much scrutiny. However, as early as Galen, the significance of relational reasoning in mathematics was recognized. Over the ensuing centuries, the question of whether mathematical proofs could be recast syllogistically gained increased attention, with critical voices emerging in the Renaissance. Supported by more detailed analyses of Euclidean theorems, these efforts led to attempts to extend logical theory to encompass relational reasoning and arguments purporting to reduce relational reasoning to a syllogistic form.

Philosophers such as Kant made influential defenses of the view that mathematical reasoning is heterogeneous with respect to logical proofs. Kant's account of synthetic a priori judgments is deeply rooted in the debate about the adequacy of syllogistic logic for mathematics. While it is now widely acknowledged that syllogistic logic alone cannot fully account for the logic of mathematical proof, the historical and analytical exploration of this debate, spanning from Aristotle to de Morgan and beyond, offers a fascinating and essential insight into the intricate relationship between philosophy and mathematics.

Weight: 500g
Dimension: 161 x 242 x 20 (mm)
ISBN-13: 9780198876922