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STRONGLY MILLIAN SECOND-ORDER MODAL LOGICS

Published online by Cambridge University Press:  19 June 2017

BRUNO JACINTO
BRUNO JACINTO*
Affiliation:
Centre of Philosophy of the University of Lisbon
*
*CENTRE OF PHILOSOPHY FACULTY OF LETTERS OF THE UNIVERSITY OF LISBON ALAMEDA DA UNIVERSIDADE, 1600-214 LISBON, PORTUGAL E-mail: [email protected]
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Abstract

The most common first- and second-order modal logics either have as theorems every instance of the Barcan and Converse Barcan formulae and of their second-order analogues, or else fail to capture the actual truth of every theorem of classical first- and second-order logic. In this paper we characterise and motivate sound and complete first- and second-order modal logics that successfully capture the actual truth of every theorem of classical first- and second-order logic and yet do not possess controversial instances of the Barcan and Converse Barcan formulae as theorems, nor of their second-order analogues. What makes possible these results is an understanding of the individual constants and predicates of the target languages as strongly Millian expressions, where a strongly Millian expression is one that has an actually existing entity as its semantic value. For this reason these logics are called ‘strongly Millian’. It is shown that the strength of the strongly Millian second-order modal logics here characterised afford the means to resist an argument by Timothy Williamson for the truth of the claim that necessarily, every property necessarily exists.

Keywords

03B45necessitismsecond-order modal logicmodalitycomprehension principlesactuality
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 3 , September 2017 , pp. 397 - 454
Copyright
Copyright © Association for Symbolic Logic 2017 

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