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November 2020 Mirroring Theorems in Free Logic
Ethan Brauer
Notre Dame J. Formal Logic 61(4): 561-572 (November 2020). DOI: 10.1215/00294527-2020-0020

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

Information

Received: 5 February 2019; Accepted: 8 June 2020; Published: November 2020
First available in Project Euclid: 23 December 2020

Digital Object Identifier: 10.1215/00294527-2020-0020

Subjects:
Primary: 03B45
Secondary: 00A30

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 4 • November 2020
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