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Reconstructing Hilbert to Construct Category Theoretic Structuralism

Landry, Elaine (2009) Reconstructing Hilbert to Construct Category Theoretic Structuralism. In: [2009] EPSA09: 2nd Conference of the European Philosophy of Science Association (Amsterdam, 21-24 October, 2009) > EPSA 2009 Contributed Papers.

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    Abstract

    This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to mathematical structuralism. My aim is to show that category theory has as much to say about an algebraic consideration of meta-mathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or meta-mathematical background theory as a “foundation”, or turning meta-mathematical analyses of logical concepts into “philosophical” ones. Thus, we can use category theory to frame an interpretation of mathematics according to which we can be algebraic structuralists all the way down.


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    Item Type: Conference or Workshop Item (UNSPECIFIED)
    Keywords: Category theory; mathematical structuralism; Hilbert; Shapiro.
    Subjects: Specific Sciences > Mathematics
    Conferences and Volumes: [2009] EPSA09: 2nd Conference of the European Philosophy of Science Association (Amsterdam, 21-24 October, 2009) > EPSA 2009 Contributed Papers
    Depositing User: Elaine Landry
    Date Deposited: 01 Sep 2009
    Last Modified: 07 Oct 2010 11:18
    Item ID: 4857
    URI: http://philsci-archive.pitt.edu/id/eprint/4857

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