FOM: Re: Plural Quantification and Comprehension

[Roger Bishop Jones]

In response to charles silver Friday, September 15, 2000 12:19 AM

>     I think it's unfortunate that Quine's famous essay "On What There
> Is" exerts such a powerful influence on philosophers today.   In the
> essay, Quine misleadingly suggests that acceptance of a theory with an
> abundance of entities is tantamount to overpopulating the
> world with them--creating an "ontological slum," in his words.   (Set
> theorists take note.)   This seems like a category mistake.  A
> theory with excessive baggage could only be a "theoretical slum,"
> not an ontological one.

I agree with this.
Though it was a slick idea, the idea that "ontological" committment can be
read off the range of quantifiers is basically wrong, if ontological
committment is to be taken in any absolute sense.
Of course, it does tell us what is in the domain of discourse of the
language under consideration (or one type of that language), but this is a
trivial rather than a profound observation.

Apart from the possibility that a language might be exclusively about
abstract or fictitious objects to which we need make no absolute ontological
commitment, it may also be the case that a language is really "about" things
which are not in the range of quantifiers at all, as may be argued for first
order logic, a major part of which is propositional logic which is expressed
without the use of quantifiers at all.

As I have mentioned in a previous posting, my view is that neither logic nor
mathematics need or can make any absolute ontological commitments, and I
doubt that a worthwhile distinction between logic and mathematics can be
founded on ontology.

What "exists in the real world" is a question for empirical science.
What exists in abstract mathematics depends upon our choice of subject
matter.

Roger Jones