9 found
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  1. Deep Fried Logic.Shay Allen Logan - 2022 - Erkenntnis 87 (1):257-286.
    There is a natural story about what logic is that sees it as tied up with two operations: a ‘throw things into a bag’ operation and a ‘closure’ operation. In a pair of recent papers, Jc Beall has fleshed out the account of logic this leaves us with in more detail. Using Beall’s exposition as a guide, this paper points out some problems with taking the second operation to be closure in the usual sense. After pointing out these problems, I (...)
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  2. Depth Relevance and Hyperformalism.Shay Allen Logan - 2022 - Journal of Philosophical Logic 51 (4):721-737.
    Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result (...)
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  3.  65
    Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.
    Relevant logics infamously have the property that they only validate a conditional when some propositional variable is shared between its antecedent and consequent. This property has been strengthened in a variety of ways over the last half-century. Two of the more famous of these strengthenings are the strong variable sharing property and the depth relevance property. In this paper I demonstrate that an appropriate class of relevant logics has a property that might naturally be characterized as the supremum of these (...)
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  4. Putting the Stars in their Places.Shay Allen Logan - 2020 - Thought: A Journal of Philosophy 9 (3):188-197.
    This paper presents a new semantics for the weak relevant logic DW that makes the role of the infamous Routley star more explicable. Central to this rewriting is combining aspects of both the American and Australian plan for understanding negations in relevance logics.
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  5.  47
    Categories for the Neologicist.Shay Allen Logan - 2017 - Philosophia Mathematica 25 (1):26-44.
    Abstraction principles provide implicit definitions of mathematical objects. In this paper, an abstraction principle defining categories is proposed. It is unsatisfiable and inconsistent in the expected ways. Two restricted versions of the principle which are consistent are presented.
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  6.  77
    The semantics of social constructivism.Shay Allen Logan - 2015 - Synthese 192 (8):2577-2598.
    This essay will examine some rather serious trouble confronting claims that mathematicalia might be social constructs. Because of the clarity with which he makes the case and the philosophical rigor he applies to his analysis, our exemplar of a social constructivist in this sense is Julian Cole, especially the work in his 2009 and 2013 papers on the topic. In a 2010 paper, Jill Dieterle criticized the view in Cole’s 2009 paper for being unable to account for the atemporality of (...)
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    Abstractionist categories of categories.Shay Allen Logan - 2015 - Review of Symbolic Logic 8 (4):705-721.
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  8.  3
    On Not Saying What We Shouldn't Have to Say.Shay Allen Logan & Graham Leach-Krouse - unknown
    In this paper we introduce a novel way of building arithmetics whose background logic is R. The purpose of doing this is to point in the direction of a novel family of systems that could be candidates for being the infamous R#1/2 that Meyer suggested we look for.
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  9.  28
    A comprehensive study of abstractionism: Philip A. Ebert and Marcus Rossberg : Abstractionism: Essays in philosophy of mathematics. Oxford University Press, 2016, 360pp, $85.00HB.Shay Allen Logan - 2018 - Metascience 27 (2):327-329.
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