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THE LOGIC OF LEIBNIZ’S GENERALES INQUISITIONES DE ANALYSI NOTIONUM ET VERITATUM

Published online by Cambridge University Press:  18 July 2016

MARKO MALINK  and
ANUBAV VASUDEVAN
MARKO MALINK*
Affiliation:
New York University
ANUBAV VASUDEVAN*
Affiliation:
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

The Generales Inquisitiones de Analysi Notionum et Veritatum is Leibniz’s most substantive work in the area of logic. Leibniz’s central aim in this treatise is to develop a symbolic calculus of terms that is capable of underwriting all valid modes of syllogistic and propositional reasoning. The present paper provides a systematic reconstruction of the calculus developed by Leibniz in the Generales Inquisitiones. We investigate the most significant logical features of this calculus and prove that it is both sound and complete with respect to a simple class of enriched Boolean algebras which we call auto-Boolean algebras. Moreover, we show that Leibniz’s calculus can reproduce all the laws of classical propositional logic, thus allowing Leibniz to achieve his goal of reducing propositional reasoning to algebraic reasoning about terms.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 4 , December 2016 , pp. 686 - 751
Copyright
Copyright © Association for Symbolic Logic 2016 

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