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 ϕ 1 , … , ϕ n 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.
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