Aristotle’s Modal Syllogistic

Marko Malink

• Publisher: Harvard University Press
• Year: 2013
• Print ISBN: 9780674724549
• eBook ISBN: 9780674727540
• Topic: Philosophy
• Subtopic: Ancient & Classical Philosophy

Aristotle was the founder not only of logic but also of modal logic. In the Prior Analytics he developed a complex system of modal syllogistic which, while influential, has been disputed since antiquity—and is today widely regarded as incoherent. In this meticulously argued new study, Marko Malink presents a major reinterpretation of Aristotle's modal syllogistic. Combining analytic rigor with keen sensitivity to historical context, he makes clear that the modal syllogistic forms a consistent, integrated system of logic, one that is closely related to other areas of Aristotle's philosophy.

Aristotle's modal syllogistic differs significantly from modern modal logic. Malink considers the key to understanding the Aristotelian version to be the notion of predication discussed in the Topics—specifically, its theory of predicables (definition, genus, differentia, proprium, and accident) and the ten categories (substance, quantity, quality, and so on). The predicables introduce a distinction between essential and nonessential predication. In contrast, the categories distinguish between substantial and nonsubstantial predication. Malink builds on these insights in developing a semantics for Aristotle's modal propositions, one that verifies the ancient philosopher's claims of the validity and invalidity of modal inferences.

Malink recognizes some limitations of this reconstruction, acknowledging that his proof of syllogistic consistency depends on introducing certain complexities that Aristotle could not have predicted. Nonetheless, Aristotle's Modal Syllogistic brims with bold ideas, richly supported by close readings of the Greek texts, and offers a fresh perspective on the origins of modal logic.

Appendix B

The Predicable Semantics of the Modal Syllogistic

In this appendix the predicable semantics is proved to be adequate with respect to Aristotle’s modal syllogistic. In other words, it is proved that every mood and conversion rule held to be valid (or invalid) by Aristotle is valid (or invalid) in the predicable semantics, and that every premise pair held to be inconcludent by Aristotle is inconcludent in it. In Appendix A, each of Aristotle’s claims of (in)validity and inconcludence was assigned a number in square brackets. This number refers to the Fact in which the claim is proved to be true within the predicable semantics in the present appendix.

An Overview of the Predicable Semantics

First of all, the predicable semantics is formulated in classical first-order logic without identity, based on three primitive binary relations:

Aab		a is aX-predicated of b		pp. 66–71
Nab		a is a N-predicated of b		pp. 110–131
N̂ab		a is strongly aN-predicated of b		p. 250

These primitive relations are governed by six theses, which are regarded as axioms (see pp. 249–250):¹

(ax1)		Aaa
(ax2)		Aab ∧ Abc ⊃ Aac
(ax3)		Nab ∧ Abc ⊃ Nac
(ax4)		N̂ab ∧ Abc ⊃ N̂ac
(ax5)		Nab ⊃ Aab
(ax6)		N̂ab ⊃ Nab

There are a number of complex notions defined in terms of the three primitive relations. Those req...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright
• Dedication
• Contents
• Acknowledgments
• Abbreviations of Aristotle’s Works
• Introduction
• I. The Assertoric Syllogistic
• II. The Apodeictic Syllogistic
• III. The Problematic Syllogistic
• Appendix A: Aristotle’s Claims of Validity, Invalidity, and Inconcludence
• Appendix B: The Predicable Semantics of the Modal Syllogistic
• Appendix C: Aristotle’s Terms
• Bibliography
• Index of Names
• Index of Passages
• Index of Subjects