Arbitrary reference, numbers, and propositions

European Journal of Philosophy 26 (3):1069-1085 (2018)
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Abstract

Reductionist realist accounts of certain entities, such as the natural numbers and propositions, have been taken to be fatally undermined by what we may call the problem of arbitrary identification. The problem is that there are multiple and equally adequate reductions of the natural numbers to sets (see Benacerraf, 1965), as well as of propositions to unstructured or structured entities (see, e.g., Bealer, 1998; King, Soames, & Speaks, 2014; Melia, 1992). This paper sets out to solve the problem by canvassing what we may call the arbitrary reference strategy. The main claims of such strategy are 2. First, we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Second, our ignorance of which object is picked out as the referent does not entail that no object is referred to by the relevant expression. Different articulations of the strategy are assessed, and a new one is defended.

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Michele Palmira
Complutense University of Madrid

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References found in this work

New Work for a Theory of Universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
What Good Are Counterexamples?Brian Weatherson - 2003 - Philosophical Studies 115 (1):1-31.
Possible Worlds.Robert Stalnaker - 1976 - Noûs 10 (1):65-75.
Semantics and the Objects of Assertion.Dilip Ninan - 2010 - Linguistics and Philosophy 33 (5):355-380.

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