Mind 121 (484):1007-1029 (2012)

Stephen Yablo
Massachusetts Institute of Technology
Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains
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DOI 10.1093/mind/fzs120
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References found in this work BETA

There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
The Explanatory Power of Phase Spaces.Aidan Lyon & Mark Colyvan - 2008 - Philosophia Mathematica 16 (2):227-243.
Models and Fictions in Science.Peter Godfrey-Smith - 2009 - Philosophical Studies 143 (1):101 - 116.
Non-Catastrophic Presupposition Failure.Stephen Yablo - 2006 - In Judith Jarvis Thomson & Alex Byrne (eds.), Content and Modality: Themes From the Philosophy of Robert Stalnaker. Oxford University Press.

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