David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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
W. V. Quine (1969). Ontological Relativity and Other Essays. Columbia University Press.
Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.
Richard Cartwright (1987). Philosophical Essays. The MIT Press.
Neil Tennant (1997). On the Necessary Existence of Numbers. Noûs 31 (3):307-336.
Paul Benacerraf (1996). Recantation or Any Old W-Sequence Would Do After All. Philosophia Mathematica 4 (2):184-189.
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