Dialectica 59 (2):265–282 (2005)
The aim of the present paper is twofold. One task is to argue that our use of the numerical vocabulary in theory and applications determines the reference of the numerical terms more precisely than up to isomorphism. In particular our use of the numerical vocabulary in modal and counterfactual contexts of application excludes contingent existents as candidate referents for the numerical terms. The second task is to explore the impact of this conclusion on what I call semantic nominalism, which is the view that ordinary physical objects and other contingent existents are eligible to be the referents of numerical terms. I suggest that for semantic nominalism to have a chance we must reform our usage of the numerical vocabulary in modal and counterfactual contexts. I tentatively explore some ways in which this might be done and call attention to some of their costs.
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References found in this work BETA
The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Bob Hale (ed.) - 2001 - Oxford University Press.
Recantation or Any Old W-Sequence Would Do After All.Paul Benacerraf - 1996 - Philosophia Mathematica 4 (2):184-189.
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