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 language | English |
|---|---|
| Pages (from-to) | 561-572 |
| Number of pages | 12 |
| Journal | Notre Dame Journal of Formal Logic |
| Volume | 61 |
| Issue number | 4 |
| Early online date | 23 Dec 2020 |
| DOIs | |
| Publication status | Published - 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