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  1.  26
    Abstractionist Categories of Categories.Shay Allen Logan - 2015 - Review of Symbolic Logic 8 (4):705-721.
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  2.  7
    Notes on Stratified Semantics.Shay Allen Logan - forthcoming - Journal of Philosophical Logic:1-38.
    In 1988, Kit Fine published a semantic theory for quantified relevant logics. He referred to this theory as stratified semantics. While it has received some attention in the literature, 1–20, 1992; Mares & Goldblatt, Journal of Symbolic Logic 71, 163–187, 2006), stratified semantics has overall received much less attention than it deserves. There are two plausible reasons for this. First, the only two dedicated treatments of stratified semantics available are, 27–59, 1988; Mares, Studia Logica 51, 1–20, 1992), both of which (...)
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  3.  17
    A Comprehensive Study of Abstractionism.Shay Allen Logan - 2018 - Metascience 27 (2):327-329.
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  4.  51
    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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  5.  28
    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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