Aristotle's Syllogism and the Creation of Modern Logic

Between Tradition and Innovation, 1820s-1930s

Lukas M. Verburgt, Matteo Cosci

• Publisher: Bloomsbury Academic
• Year: 2023
• Print ISBN: 9781350228849
• eBook ISBN: 9781350228863
• Edition: 1
• Topic: Philosophy
• Subtopic: History & Philosophy of Mathematics

Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.

Table of contents

• Cover
• Halftitle Page
• Title Page
• Dedication Page
• Contents
• List of figures and tables
• List of contributors
• Acknowledgements
• Introduction: History of modern logic in a new key
• 1 Richard Whately’s revitalization of syllogistic logic
• 2 Mill and the British tradition of inductive logic: The role of syllogism
• 3 The Aristotelian roots of Bolzano’s logic
• 4 George Boole and the ‘pure analysis’ of the syllogism
• 5 Logic of relations by De Morgan and Peirce: A case study for the refinement of syllogism
• 6 Ernst Schröder’s algebra of logic and the ‘logic of the ancient’
• 7 Brentano and Hillebrand on syllogism: Development and reception of the ‘idiogenetic’ theory
• 8 Hugh MacColl: Never twist the syllogism again
• 9 Frege’s relation to Aristotle and the emergence of modern logic
• 10 Christine Ladd-Franklin’s antilogism
• 11 Syllogism and beyond in the Peano School
• 12 Hilbert’s use of the syllogism
• 13 The role of syllogistic logic in early set theory
• 14 The fate of the syllogism in the Göttingen school
• Index
• Imprint