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THE PERIPATETIC PROGRAM IN CATEGORICAL LOGIC: LEIBNIZ ON PROPOSITIONAL TERMS

Published online by Cambridge University Press:  06 November 2018

MARKO MALINK  and
ANUBAV VASUDEVAN
MARKO MALINK*
Affiliation:
Department of Philosophy, New York University
ANUBAV VASUDEVAN*
Affiliation:
Department of Philosophy, University of Chicago
*
*DEPARTMENT OF PHILOSOPHY NEW YORK UNIVERSITY 5 WASHINGTON PLACE NEW YORK, NY 10003, USA E-mail: [email protected]
†DEPARTMENT OF PHILOSOPHY UNIVERSITY OF CHICAGO 1115 EAST 58th STREET CHICAGO, IL 60637, USA E-mail: [email protected]
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Abstract

Greek antiquity saw the development of two distinct systems of logic: Aristotle’s theory of the categorical syllogism and the Stoic theory of the hypothetical syllogism. Some ancient logicians argued that hypothetical syllogistic is more fundamental than categorical syllogistic on the grounds that the latter relies on modes of propositional reasoning such as reductio ad absurdum. Peripatetic logicians, by contrast, sought to establish the priority of categorical over hypothetical syllogistic by reducing various modes of propositional reasoning to categorical form. In the 17th century, this Peripatetic program of reducing hypothetical to categorical logic was championed by Gottfried Wilhelm Leibniz. In an essay titled Specimina calculi rationalis, Leibniz develops a theory of propositional terms that allows him to derive the rule of reductio ad absurdum in a purely categorical calculus in which every proposition is of the form A is B. We reconstruct Leibniz’s categorical calculus and show that it is strong enough to establish not only the rule of reductio ad absurdum, but all the laws of classical propositional logic. Moreover, we show that the propositional logic generated by the nonmonotonic variant of Leibniz’s categorical calculus is a natural system of relevance logic known as RMI$_{{}_ \to ^\neg }$.

Keywords

01A2001A4503A0503B0503B47LeibnizAristotlecategorical syllogismhypothetical syllogismreductio ad absurdumrelevance logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 1 , March 2020 , pp. 141 - 205
Copyright
Copyright © Association for Symbolic Logic 2018 

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