Grounding and the indispensability argument

Synthese 193 (2):531-548 (2016)
Authors
David Liggins
University of Manchester
Abstract
There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses.
Keywords indispensability argument  grounding  fictionalism  hard road nominalism
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DOI 10.1007/s11229-014-0478-2
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References found in this work BETA

Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109-36.
The Things We Mean.Stephen Schiffer - 2003 - Oxford University Press.
There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.

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