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Varieties of Pluralism and Relativism for Logic

In Steven D. Hales (ed.), A Companion to Relativism. Malden, MA: Wiley-Blackwell. pp. 526–552 (2010)

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  1. Structures and Logics: A Case for (a) Relativism.Stewart Shapiro - 2014 - Erkenntnis 79 (2):309-329.
    In this paper, I use the cases of intuitionistic arithmetic with Church’s thesis, intuitionistic analysis, and smooth infinitesimal analysis to argue for a sort of pluralism or relativism about logic. The thesis is that logic is relative to a structure. There are classical structures, intuitionistic structures, and (possibly) paraconsistent structures. Each such structure is a legitimate branch of mathematics, and there does not seem to be an interesting logic that is common to all of them. One main theme of my (...)
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  • Translating Logical Terms.Stewart Shapiro - 2019 - Topoi 38 (2):291-303.
    The is an old question over whether there is a substantial disagreement between advocates of different logics, as they simply attach different meanings to the crucial logical terminology. The purpose of this article is to revisit this old question in light a pluralism/relativism that regards the various logics as equally legitimate, in their own contexts. We thereby address the vexed notion of translation, as it occurs between mathematical theories. We articulate and defend a thesis that the notion of “same meaning” (...)
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  • Synonymy and Intra-Theoretical Pluralism.Patrick Allo - 2015 - Australasian Journal of Philosophy 93 (1):77-91.
    The starting point of this paper is a version of intra-theoretical pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second (...)
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