I haven’t yet finished reading Jody Azzouni’s Deflating Existential Consequence, but I have been enjoying it quite a bit so far. An important thesis of the book is that existential quantifiers don’t automatically come with ontological commitment.
He’s completely right to point out that this is basically an unjustified assumption in Quine. Just as it’s reasonable for intuitionists and classical logicians to debate whether the classical negation symbol really captures the intuitive notion of negation, and most people rightly believe that the conditional symbol of classical logic certainly does not capture the ordinary sense of conditionals, it’s reasonable to ask whether the existential quantifier of classical logic captures the ordinary notion of existence. The simple argument that it does is basically that the semantics for the existential quantifier require there to be something that satisfies the formula. But Azzouni points out that this is just trading an object language quantifier for a metalanguage quantifier – what reason do we have to believe that the metalanguage quantifier has anything to do with ontological commitment either?
Azzouni then goes through a range of possible interpretations for ordinary language locutions like “there are some fictional mice that talk”, which seem to be intuitively true, though they really seem like they shouldn’t have ontological commitment. He suggests that none of the attempted strategies to account for this distinction by paraphrase, cancellation of commitment, or ambiguity in the quantifier will work. Instead, he argues that we just have to accept that the existential quantifier doesn’t automatically carry with it ontological commitment.
Instead, he argues, the criterion for existence is society-relative, and our society has chosen something like “ontological independence” to be our criterion of existence. That is, in order for something to exist, it can’t just be totally made up.
He says that no rational argument can be made for one criterion rather than another, so our ontological commitments are purely relative in this sense. But this seems to me to raise the question of why we should adopt something so relative as playing the role of the important concept of existence? The quantifier commitments of our best regimented theories can be made sense of, but for Azzouni they do no important work whatsoever. The work of existence is done by this other notion, to which many alternatives would work just as well. So I propose the Quinean alternative – ontological commitment to all and only the quantifier commitments of our best regimented theory. We will need to do more work to deal with sentences like “there are some fictional mice that talk”, but I think the paraphrase option is more promising than Azzouni gives it credit for. (I agree with him that the other five or so options are generally less palatable.)