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Reconstructing Hilbert to Construct Category Theoretic Structuralism

Landry, Elaine (2009) Reconstructing Hilbert to Construct Category Theoretic Structuralism. In: UNSPECIFIED.

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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)
Creators:
CreatorsEmailORCID
Landry, Elaine
Keywords: Category theory; mathematical structuralism; Hilbert; Shapiro.
Subjects: Specific Sciences > Mathematics
Depositing User: Elaine Landry
Date Deposited: 01 Sep 2009
Last Modified: 07 Oct 2010 15:18
Item ID: 4857
URI: http://philsci-archive.pitt.edu/id/eprint/4857

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