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

Authors
Simon Friederich
University of Groningen
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
Keywords Mathematical structuralism  Meta-mathematics  Quasi-concrete objects  Criteria of identity
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DOI 10.1007/s10670-010-9210-x
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References found in this work BETA

Mathematics as a Science of Patterns.Michael David Resnik - 1997 - Oxford, England: New York ;Oxford University Press.
Mathematical Thought and its Objects.Charles Parsons - 2007 - Cambridge University Press.
Thinking About Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2000 - Oxford, England: Oxford University Press.

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Citations of this work BETA

Philosophy of Science in Germany, 1992–2012: Survey-Based Overview and Quantitative Analysis.Matthias Unterhuber, Alexander Gebharter & Gerhard Schurz - 2014 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):71-160.

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