Modality and Ontology
Shapiro (Stewart)
Source: Mind 102.407, July 1993, pp. 455-481
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Philosophers Index Abstract

    This paper concerns the relationship between ideology and ontology. The starting point is a series of recent programs whose strategy is to reduce ontology in mathematics by invoking some ideology, typically a modal1 operator. In each case, there are straightforward, often trivial, translations from the set-theoretic language of the realist to the proposed language with added ideology, and vice-versa. The contention is that, because of these translations, neither system can claim a major epistemological advantage over the other. The prima facie intractability of knowledge of abstract objects indicates an intractability concerning knowledge of the "new" notions. The prevailing criterion of ontological commitment, due to Quine, is that the ontology of a theory is the range of its bound variables; but recall that Quine insists on a fixed, and very austere ideology. It is proposed here that, when this constraint is relaxed, the Quinean criterion is flawed, and an alternative, in structuralist terms, is developed.

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