Erkenntnis 73 (1):67 - 81 (2010)
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|
|Categories||categorize this paper)|
References found in this work BETA
Mathematics Without Numbers: Towards a Modal-Structural Interpretation.Geoffrey Hellman - 1989 - Oxford University Press.
Criteria of Identity and Structuralist Ontology.Hannes Leitgeb & James Ladyman - 2007 - Philosophia Mathematica 16 (3):388-396.
Thinking About Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2000 - Oxford University Press.
Citations of this work BETA
Mathematical Intuition and Natural Numbers: A Critical Discussion.Felix Mühlhölzer - 2010 - Erkenntnis 73 (2):265-292.
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