Arbitrary reference, numbers, and propositions

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 Melia 1992, King, Soames and Speaks 2014). 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 two. First: we do not know which objects are the referents of proposition and numerical terms since their reference is fixed arbitrarily. Secondly: 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.