Substitutional Quantification

Abstract

Suppose that it is accepted that natural language really does quantify over things like times, worlds, possibilities and the like. One way of resisting the conclusion that natural language is therefore ontologically committed to these entities is to insist that the quantification in these cases is to be interpreted substitutionally. On this interpretation

$$ \exists x\phi x $$

would be held to be true in a language ℒ iff there is a singular term a of ℒ for which

$$ \phi a$$

is true. And if we can give the truth conditions for each sentence of the form (2) without assuming an ontology of things which are φ then a subsitutional interpretation of quantifiers shews that (1) makes no extra ontological commitment. Dale Gottlieb, 1980, has argued that this is the case for mathematical statements and would no doubt argue for the same solution in the case of worlds. Gottlieb is however careful to note that certain fairly strict conditions must apply before substitutional quantification can be used for ontological economy, and I shall make similar points by describing first a bogus use of substitutional quantification in order to contrast it with a genuine use so that the case of worlds can then be looked at. The bogus use is this.