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Structuralism and meta-mathematics

Friederich, S. (2010) Structuralism and meta-mathematics. Erkenntnis, 73 (1). pp. 67-81.

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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 Stewart Shapiro in (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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Item Type: Published Article or Volume
Keywords: structuralism, meta-mathematics, mathematical symbols, quasi-concreteness, type-token distinction
Subjects: Specific Sciences > Mathematics
Depositing User: Dr. Simon Friederich
Date Deposited: 03 Nov 2015 16:10
Last Modified: 03 Nov 2015 16:10
Item ID: 11747
Journal or Publication Title: Erkenntnis
Publisher: Springer
Official URL:
DOI or Unique Handle:
Subjects: Specific Sciences > Mathematics
Date: 2010
Page Range: pp. 67-81
Volume: 73
Number: 1

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