Mirroring Theorems in Free Logic

Research output: Journal PublicationsJournal Article (refereed)peer-review

Abstract

Linnebo and Shapiro have recently given an analysis of potential infinity using modal logic. A key technical component of their account is to show that under a suitable translation ◊ of nonmodal language into modal language, nonmodal sentences ϕ1,…,ϕn entail ψ just in case ϕ◊1,…,ϕ◊n entail ψ◊ in the modal logic S4.2. Linnebo and Shapiro establish this result in nonfree logic. In this note I argue that their analysis of potential infinity should be carried out in a free logic. I then extend their key theorems to the setting of negative free logic.
Original languageEnglish
Pages (from-to)561-572
Number of pages12
JournalNotre Dame Journal of Formal Logic
Volume61
Issue number4
Early online date23 Dec 2020
DOIs
Publication statusPublished - 2020

Bibliographical note

Thanks to Øystein Linnebo for discussion of these issues and to Stewart Shapiro and an anonymous referee for helpful comments on a draft of this paper.

Keywords

  • potential infinity
  • potentialism
  • modal logic
  • free logic
  • mirroring theorem

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