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 entail just in case entail 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.
"Mirroring Theorems in Free Logic." Notre Dame J. Formal Logic 61 (4) 561 - 572, November 2020. https://doi.org/10.1215/00294527-2020-0020