Abstract
In a 2005 paper, John Burgess and Gideon Rosen offer a new argument against nominalism in the philosophy of mathematics. The argument proceeds from the thesis that mathematics is part of science, and that core existence theorems in mathematics are both accepted by mathematicians and acceptable by mathematical standards. David Liggins (2007) criticizes the argument on the grounds that no adequate interpretation of “acceptable by mathematical standards” can be given which preserves the soundness of the overall argument. In this discussion I offer a defense of the Burgess-Rosen argument against Liggins’s objection. I show how plausible versions of the argument can be constructed based on either of two interpretations of mathematical acceptability, and I locate the argument in the space of contemporary anti-nominalist views.
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References
Burgess, John, and Gideon Rosen, ‘Nominalism reconsidered’, in S. Shapiro (ed.), The Oxford Handbook of the Philosophy of Mathematics and Logic, Oxford University Press, 2005, pp. 515–535.
Chihara Charles (2007) ‘The Burgess-Rosen critique of nominalistic reconstructions’. Philosophia Mathematica (III) 15, 54–78
Corfield, David : ‘Mathematical blogging’. The Reasoner 1 3, 6–7 (2007)
Liggins, David : ‘Anti-nominalism reconsidered’. Philosophical Quarterly 57, 104–111 (2007)
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Baker, A. No Reservations Required? Defending Anti-Nominalism. Stud Logica 96, 127–139 (2010). https://doi.org/10.1007/s11225-010-9277-z
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DOI: https://doi.org/10.1007/s11225-010-9277-z