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.)
Antimeta 
Quine accepts the reading of the existential quantifer to carry existential import but the interpretation originated from Boole in the late 1800s. The reasoning is this: (Ex)F is defined in terms of its dual ~(x)~F. Classically the domain is non-empty, so there must be a falsifier to (x)~F to make ~(x)~F true–i.e. for some object k of the domain, ~F(k/x) must be true. But clearly this implies (Ex)~F.
One of the simplest solutions to the problem you raise is substitutional quantification! We want it to come out true that
1. Pegasus has wings.
And from (1) we can infer that
2. Ex(x has wings).
But (2) has no existential import if we read it as ‘Some substitution instance of ‘x has wings’ is true’. And that is true when x=Pegasus–i.e. as in (1). At the same time it is not true that ‘Pegasus is a cow’ and so from this we cannot infer Ex(x is a cow).
Whoops, I meant the falsifier to be F(k/x) for some object k in D, which implies (Ex)F.
Azzouni mentions the substitutional approach. However, he dismisses it because of examples like “some fictional characters have no names”, like most of the people that die in War and Peace, and the crowds in many movies. In this case there is no name to substitute in to make the sentence true. I suppose there might be a definite description available though. However, mathematical examples will work too – “some real numbers can’t be described in any natural language”. That sentence is surely true, because there are uncountably many real numbers and only countably many descriptions in all natural languages put together. But there’s no substitution instance one can make, unless one allows substitutions that aren’t in any language, which then leads me to ask just what these entities you’re substituting in are.
If they are fictional then, as you said, we would use description theory since they have no names. Or we might say they have no name in the movie (though they do within the formal language and interpretation in which we are working).
“Some real numbers can’t be described in any natural langauge” is exactly like the transfinite ordinals paradox. Suppose there is such a class of real indefinable reals, then there is a least (maybe?). Then we have just defined it (as the last indefinable real)–contradiction. These sorts of problems/paradoxes seem to dissolve in a theory of types (which could be outfitted with a substitution interpretation of the quantifiers since there is no restriction that the substitution class be names for individuals).
But there is no definable well-ordering of the reals, the way there is for the natural numbers or ordinals. Thus, although we can define the class of undefinable reals, this class has no least member, no greatest member, and in fact no member that can be picked out by a description in any way. Even if we add more symbols to the language, we can only pick out countably many of these reals, so some of them are always going to remain undefinable.
Well that’s why I threw in “maybe” but plugged-in ‘reals’ for ‘ordinals’ anyway to draw the analogy. In any case, you need to quantify over *all* descriptions of a language, which, in type theory, you cannot do unless the descriptions are all of the same type. So again the paradox cannot arise.
Coincidentally, I just came across this argument against substitutional quantification in Quine’s “Ontological Relativity”, The Journal of Philosophy, vol.65, no.7, 185-212 and it made me think why it should be important at all if, by the Lowenheim-Skolem theorem, we may discount all but denumerably many elements of the domain anyway.
I suppose the Henkin construction gives us a model of a language with countably many extra constants, such that every object is named by some term in the language (because every object is a term in that language). In that model and language, the substitutional interpretation of the quantifiers works just fine. But that model isn’t the actual universe, and that language isn’t the language we actually use. Because that model is entirely made up out of terms in our language, we’re already committed to the existence of all those objects anyway (assuming we’re committed to linguistic entities), so taking the quantifiers to be substitutional there doesn’t reduce our commitments. But again, this isn’t the real model, and to make our sentences come out true in the real world we have to use objectual quantifiers, because we don’t necessarily have a name for every object.
I have a short historical piece on existential commitment here http://uk.geocities.com/frege@btinternet.com/cantor/Eximport.htm. Note that the “reading of the existential quantifer to carry existential import” did not originate with Boole, but with Brentano in 1874. And note that they wouldn’t have called it an “existential quantifier” in those days because they didn’t have one. They had what was called a “particular proposition”, i.e. of the form “some A is B”. Brentano was the first to call this an “existential proposition”. I don’t know who came up with the idea of calling the “existential quantifier” by that name. Anyway, the idea of “existential propositions” and the idea of writing “some A is B” as “for some x A(x) and B(x)” historically came about at the same time. So the question of whether we should “read the existential quantifer to carry existential import” seems pretty odd, historically at least.
What does “ontological commitment” actually mean? It occurs about five times in your posting.
Regards, Edward Buckner
Well, just what exactly “ontological commitment” means is somewhat up for debate. Basically, ontological commitments are the things that a theory says exists (which is why we tend to read them off the quantifiers). But more precisely, it’s what must be among the basic furniture of the universe in order for the theory to be true. Or something like that. When the general notion of ontology fell into disrepute in the early part of the 20th century, Quine revived it by pointing out basically that we can get a sense of the ontological commitments of our best theory of the world, and then suggesting that this is really what we should be doing when we say we’re doing ontology. But this is contentious.
Anyway, I’ll have to check out your piece when I have some free time. Though the idea of using existential quantifiers to convey existential import is not that old, as you point out, it’s also just about as old as existential quantifiers, as you also point out. So one might argue that we just didn’t have the proper framework for discussing the questions before then.
But basically, Azzouni wants to restart the debate about whether existence is better captured with the quantifiers or by a predicate like any other.
Thanks for the reply. You say
1. “Ontological commitments are the things that a theory says exists (which is why we tend to read them off the quantifiers). ”
But then what does “exist” mean?
2. “More precisely, it’s what must be among the basic furniture of the universe in order for the theory to be true. ”
Do I read “be among the basic furniture of the universe” as synonymous with “exist”? Or is the former expression intended to clarify the meaning of “exist”?
3. “Though the idea of using existential quantifiers to convey existential import is not that old, as you point out, it’s also just about as old as existential quantifiers, as you also point out. ”
This was not what I said! I said that nineteenth century logicians did not use the term “existential quantifier”. They recognised what we now call existentially quantified sentences, but they called them “particular propositions”. Brentano (not Boole) introduced the term “existential proposition”. The debate was about whether a particular proposition like “some men are unmarried” implies an existential proposition like “unmarried men exist”.
4. “So one might argue that we just didn’t have the proper framework for discussing the questions before then.”
On the contrary, the innovation of formal sentences like “Ex Fx” obscures, rather than clarifies the whole debate. It confuses the question of whether “Ex man(x) and unmarried(x)” means the same as “some men are unmarried”, with the question whether some “some men are unmarried” means the same as “unmarried men exist”.
When one says “Ex man(x) and unmarried(x)” has “ontological commitment”, does that mean it implies “some men are unmarried”? Or that it implies “unmarried men exist”?
4. “But basically, Azzouni wants to restart the debate about whether existence is better captured with the quantifiers or by a predicate like any other.”
“If the notion of existence is not captured by a quantifier sentence like “something is an F” then someone had better explain what “existence” means. If “F’s exist” means “some things are F”, then of course “existence is better captured with the quantifiers” – how else? If it means something else, then what. Perhaps “F’s are among the basic furniture of the universe”? But what does that mean?”
ROFLMAO
I can’t help to notice that the last questions from Edward Buckner went unanswered.
Could it be that all this philosophizing about “existence” and “ontology” is just vacuous chatter?
I must confess that in this respect I am much worse than even the likes of Azzouni, I don’t think the world “contains” ANY objects, no cats, no water, no triangles, no souls, no bratwursts, zilch, nada, NO objects or concepts.
Such “things” are only names in our discourses which we hope to “handle” not too improperly in order make decisions about the expected future states of the world.
I’m not unsympathetic to the claim that much debate about “existence” and “ontology” might be vacuous. However, you seem to be missing the use/mention distinction when you say that there are no objects, no cats, no triangles, etc. and that these are only names in our discourses. “Cats” is a word of English, but cats are animals. You don’t want to claim that there are no cats (I assume) – you must be just trying to say that the word “cat” is at best an approximation to the things there are. But that isn’t to deny that there are cats, but rather to deny that cats are the sort of thing that we think they are.