Structuralism and Meta-Mathematics

Erkenntnis 73 (1):67 - 81 (2010)
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Abstract

The debate on structuralism in the philosophy of mathematics has brought into focus a question about the status of meta-mathematics. It has been raised by Shapiro (2005), where he compares the ongoing discussion on structuralism in category theory to the Frege-Hilbert controversy on axiomatic systems. Shapiro outlines an answer according to which meta-mathematics is understood in structural terms and one according to which it is not. He finds both options viable and does not seem to prefer one over the other. The present paper reconsiders the nature of the formulae and symbols meta-mathematics is about and finds that, contrary to Charles Parsons' influential view, meta-mathematical objects are not "quasi-concrete". It is argued that, consequently, structuralists should extend their account of mathematics to meta-mathematics

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Simon Friederich
University of Groningen

References found in this work

Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
The Blue and Brown Books.Ludwig Wittgenstein - 1958 - Philosophy 34 (131):367-368.
Mathematical Thought and its Objects.Charles Parsons - 2007 - New York: Cambridge University Press.

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