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  1.  23
    The Modal Logic of Potential Infinity: Branching Versus Convergent Possibilities.Ethan Brauer - 2020 - Erkenntnis:1-19.
    Modal logic provides an elegant way to understand the notion of potential infinity. This raises the question of what the right modal logic is for reasoning about potential infinity. In this article I identify a choice point in determining the right modal logic: Can a potentially infinite collection ever be expanded in two mutually incompatible ways? If not, then the possible expansions are convergent; if so, then the possible expansions are branching. When possible expansions are convergent, the right modal logic (...)
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  2.  11
    The Dependence of Computability on Numerical Notations.Ethan Brauer - 2020 - Synthese 198 (11):10485-10511.
    Which function is computed by a Turing machine will depend on how the symbols it manipulates are interpreted. Further, by invoking bizarre systems of notation it is easy to define Turing machines that compute textbook examples of uncomputable functions, such as the solution to the decision problem for first-order logic. Thus, the distinction between computable and uncomputable functions depends on the system of notation used. This raises the question: which systems of notation are the relevant ones for determining whether a (...)
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  3.  43
    Relevance for the Classical Logician.Ethan Brauer - 2020 - Review of Symbolic Logic 13 (2):436-457.
    Although much technical and philosophical attention has been given to relevance logics, the notion of relevance itself is generally left at an intuitive level. It is difficult to find in the literature an explicit account of relevance in formal reasoning. In this article I offer a formal explication of the notion of relevance in deductive logic and argue that this notion has an interesting place in the study of classical logic. The main idea is that a premise is relevant to (...)
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  4.  14
    Mirroring Theorems in Free Logic.Ethan Brauer - 2020 - Notre Dame Journal of Formal Logic 61 (4):561-572.
    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 (...)
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  5.  19
    Transmission of Verification.Ethan Brauer & Neil Tennant - forthcoming - Review of Symbolic Logic:1-16.
    This paper clarifies, revises, and extends the account of the transmission of truthmakers by core proofs that was set out in chap. 9 of Tennant. Brauer provided two kinds of example making clear the need for this. Unlike Brouwer’s counterexamples to excluded middle, the examples of Brauer that we are dealing with here establish the need for appeals to excluded middle when applying, to the problem of truthmaker-transmission, the already classical metalinguistic theory of model-relative evaluations.
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  6.  30
    Second-Order Logic and the Power Set.Ethan Brauer - 2018 - Journal of Philosophical Logic 47 (1):123-142.
    Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must (...)
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  7.  31
    Metaphysical Nihilism and Modal Logic.Ethan Brauer - 2022 - Philosophical Studies 179 (9):2751-2763.
    In this paper I argue, that if it is metaphysically possible for it to have been the case that nothing existed, then it follows that the right modal logic cannot extend D, ruling out popular modal logics S4 and S5. I provisionally defend the claim that it is possible for nothing to have existed. I then consider the various ways of resisting the conclusion that the right modal logic is weaker than D.
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  8.  32
    Divergent Potentialism: A Modal Analysis With an Application to Choice Sequences.Ethan Brauer, Øystein Linnebo & Stewart Shapiro - forthcoming - Philosophia Mathematica.
    Modal logic has been used to analyze potential infinity and potentialism more generally. However, the standard analysis breaks down in cases of divergent possibilities, where there are two or more possibilities that can be individually realized but which are jointly incompatible. This paper has three aims. First, using the intuitionistic theory of choice sequences, we motivate the need for a modal analysis of divergent potentialism and explain the challenges this involves. Then, using Beth–Kripke semantics for intuitionistic logic, we overcome those (...)
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  9.  7
    Disagreement, the Independence Thesis, and the Value of Repeated Reasoning.Ethan Brauer - forthcoming - Pacific Philosophical Quarterly.
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  10.  27
    The Metaphysics and Mathematics of Arbitrary Objects.Ethan Brauer - 2021 - Philosophical Review 130 (3):471-474.
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  11.  2
    The Modal Logic of Potential Infinity: Branching Versus Convergent Possibilities.Ethan Brauer - 2022 - Erkenntnis 87 (5):2161-2179.
    Modal logic provides an elegant way to understand the notion of potential infinity. This raises the question of what the right modal logic is for reasoning about potential infinity. In this article I identify a choice point in determining the right modal logic: Can a potentially infinite collection ever be expanded in two mutually incompatible ways? If not, then the possible expansions are convergent; if so, then the possible expansions are branching. When possible expansions are convergent, the right modal logic (...)
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