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  1. Grounding and the indispensability argument.David Liggins - 2016 - Synthese 193 (2):531-548.
    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 (...)
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  • Can the constructive empiricist be a nominalist? Quasi-truth, commitment and consistency.Paul Dicken - 2006 - Studies in History and Philosophy of Science Part A 37 (2):191-209.
    In this paper, I explore Rosen’s ‘transcendental’ objection to constructive empiricism—the argument that in order to be a constructive empiricist, one must be ontologically committed to just the sort of abstract, mathematical objects constructive empiricism seems committed to denying. In particular, I assess Bueno’s ‘partial structures’ response to Rosen, and argue that such a strategy cannot succeed, on the grounds that it cannot provide an adequate metalogic for our scientific discourse. I conclude by arguing that this result provides some interesting (...)
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