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GENERALITY AND EXISTENCE 1: QUANTIFICATION AND FREE LOGIC

Published online by Cambridge University Press:  18 December 2018

GREG RESTALL
GREG RESTALL*
Affiliation:
School of Historical and Philosophical Studies, University of Melbourne
*
*SCHOOL OF HISTORICAL AND PHILOSOPHICAL STUDIES THE UNIVERSITY OF MELBOURNE PARKVILLE, VIC 3010, AUSTRALIA E-mail: [email protected]URL: http://consequently.org
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Abstract

In this paper, I motivate a cut free sequent calculus for classical logic with first order quantification, allowing for singular terms free of existential import. Along the way, I motivate a criterion for rules designed to answer Prior’s question about what distinguishes rules for logical concepts, like conjunction from apparently similar rules for putative concepts like Prior’s tonk, and I show that the rules for the quantifiers—and the existence predicate—satisfy that condition.

Keywords

03A0503F03free logicproof theorysequent calculusgenerality
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 1 , March 2019 , pp. 1 - 29
Copyright
Copyright © Association for Symbolic Logic 2018 

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