Strongly Millian second-order modal logics

Bruno Jacinto*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)397-454
Number of pages58
JournalReview of Symbolic Logic
Volume10
Issue number3
Early online date19 Jun 2017
DOIs
Publication statusPublished - Sept 2017

Keywords

  • Actuality
  • Comprehension principles
  • Modality
  • Phrases necessitism
  • Second-order modal logic

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