Landry, Elaine
(2009)
Reconstructing Hilbert to Construct Category Theoretic Structuralism.
In: UNSPECIFIED.
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 metamathematical analyses of logical structure as it does about mathematical analyses of mathematical structure, without either requiring an assertory mathematical or metamathematical background theory as a “foundation”, or turning metamathematical 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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