Van Inwagen on the Univocity of 'Exists'

In "Being, Existence, and Ontological Commitment" (in Metametaphysics: New Essays on the Foundations of Ontology, eds. Chalmers et al., Oxford 2009, pp. 472-506), Peter van Inwagen argues that 'exists' is univocal: it does not have "different meanings when applied to objects in different categories." (482)  This post will examine one of his arguments, an argument found on p. 482.  All quotations are from this page.

Van Inwagen begins by noting that number words such as 'six' or 'forty-three' do not "mean different things when they are used to count objects of different sorts."  Surely he is correct: "If you have written thirteen epics and I own thirteen cats, the number of your epics is the number of my cats."  So the first premise of the argument is the indisputable:

1. Number-words are univocal in sense: they mean the same regardless of the sorts of object they are used to count.

Van Inwagen takes his second premise straight from Frege:

2. "But existence is closely allied to number."

How so?  Well, to say that unicorns do not exist is equivalent to saying that the number of unicorns is zero, and to say that horses exist is equivalent to saying that the number of horses is one or more.  Surely that is true for both affirmative and negative general existentials.  Whether it is true for singular existentials is a further question.

Van Inwagen proceeds: "The univocacy [univocity] of number and the the intimate connection between number and existence should convince us that existence is univocal."  The conclusion of the argument, then, is:

3. Existence  is univocal.

The first thing to notice about this argument is that it is not even valid.  Trouble is caused by the fudge-phrase 'closely allied to' and van Inwagen's shift from 'exists' to existence.  But repairs are easily made, and charity demands that we make them.  Here is a valid argument that van Inwagen could have given:

1. Number-words are univocal

2*. 'Exist(s)' is a number-word

Therefore

3*. 'Exist(s)' is univocal.

The latter argument is plainly valid in point of logical form: the conclusion follows from the premises.  It is the argument van Inwagen should have given.  Unfortunately the argument is unsound.  Although (1) is indisputably true,  (2*) is false.

Consider my cat Max Black.  I joyously exclaim, 'Max exists!'  My exclamation expresses a truth.  Compare 'Cats exist.'  Now I agree with van Inwagen that the general  'Cats exist' is equivalent to 'The number of cats is one or more.'  But it is perfectly plain that the singular  'Max exists' is not equivalent to  'The number of Max is one or more.'  For the right-hand-side of the equivalence is nonsense, hence necessarily neither true nor false.

This question makes sense: 'How many cats are there in BV's house?'  But this question makes no sense: 'How many Max are there in BV's house?'  Why not?  Well, 'Max' is a proper name (Eigenname in Frege's terminology) not a concept-word (Begriffswort in Frege's terminology).  Of course, I could sensibly ask how many Maxes there are hereabouts, but then 'Max' is not a proper name, but a stand-in for 'person/cat named "Max" .'  The latter phrase is obviously not a proper name.

Van Inwagen's argument strikes me as very bad, and I am puzzled why he is seduced by it.  (Actually, I am not puzzled: van Inwagen is in lock-step with Quine; perhaps the great prestige of the latter has the former mesmerized.)  Here is my counterargument:

4. 'Exists' sometimes functions as a first-level predicate, a predicate of specific (named) individuals.

5. Number-words never function as predicates of specific (named) individuals

Therefore

6. 'Exists' is not a number-word.

Therefore

7. The (obvious) univocity of number-words is not a good reason to think that 'exists' is univocal.

Of course, there is much more to say -- in subsequent posts. For example if you deny (4), why is that denial more reasonable than the denial of (2*)?

Comments

[Andrew]

Here are two problem cases for (5):

a) 'Max is one in number'
b) 'Max and Sam are two in number'

These strike me as sentences that predicate, of specific individuals, number-words. a) says of Max that he is properly counted by the number one; Max is exactly one in number; the number of things that are identical to Max is one. b) says of Max and Sam that they are properly counted by the number two. Both a) and b) strike me as odd, but still perfectly grammatical.

[Casey]

I take it you agree with van Inwagen's conditional that IF "exist" is a number word, then it is a univocal term. But can you elaborate on your defense of why "exist" is not to be applied to individuals as a number word?

I agree that at first blush it sounds absurd to say "How many Max are there in BV's house?" However, what if we alter two aspects of that statement. What if we change "How many" to "Is there at least one," and what if for "Max" we substitute a description that picks out only Max and picks him out necessarily. (I take it that accidental descriptions of Max -- "The cat who drank milk in BV's house at time t" -- might pick out only Max in the actual world but not in every possible world, i.e. might not be essential definitions.) So, what if instead we say, "Is there at least one cat with (say) DNA structure X in BV's house?"

Having thought about this issue for quite some time, I'm very curious as to your view on whether, for individuals as opposed to kinds, there even are any descriptions that essentially pick out an individual and only that individual. You may not think so -- I'm not sure I do, I'm not sure I think Max's DNA (or anything else) is Max's essence, if he has an essence (though it also doesn't sit easy with me thinking that we can change his properties as much as we like, all the while leaving his Max-hood intact. Then individual existence can begin to seem quite untethered and elusive -- Plato's basic intuition?). But if there were, ex hypothesi, descriptions that gave the essences of individuals, could not "exist" be used as a number word when applied to individuals? If we could make "There is at least one Max in BV's house" sensible (via supplying an adequate description of Max), wouldn't "exist" be a number word? Along these lines, might van Inwagen's argument be salvaged by our finding the description that picks out only Max? Perhaps such a description is an El Dorado or a Fountain of Youth.

[Bill Vallicella]

Casey,

Thanks for the very intelligent comment.

Suppose there is a concept or property C which satisfies the following conditions: a) C is possibly uninstantiated; b) if C is instantiated, then C is instantiated by Max alone; c) if C is instantiated, then it is not possible that C be instantiated by any object distinct from Max. We can call C Max's individual concept or haecceity concept or Max's haecceity. We can give C the name 'Maxhood' and we can think of it as the property of being identical to Max. It individuates him (ontologically, not epistemically) across all possible worlsd and somehwo captures his nonqualitative thisness.

I deny that there is such a property as Maxhood. But suppose there is. Then 'Max exists' is equivalent to 'The number of Maxhood is not zero' or less bizarrely 'There is at least one instance of Maxhood.'

I take it that what I have just sketched is equivalent to your suggestion.

I grant that an approach like this would rescue PvI's thin theory of existence -- if there are haecceities. But I deny that there are haecceities. I have some posts explaining why which I will now try to locate.

[Bill Vallicella]

See here: http://maverickphilosopher.typepad.com/maverick_philosopher/2010/06/my-difficulty-with-haecceity-properties.html

for an argument why there can be no haecceity properties.

[Bill Vallicella]

Andrew,

Thanks for the challenging comments.

'Max and Sam are two in number.' But what does the predicate 'two' apply to? Not to Max, and not to Sam. We need some further item, an item distinct from Max and distinct from Sam, to be the subject of the predicate 'two.' But then 'two' is not functioning as a predicate of a specific individual.

'Max is one in number.' I grant that this is a grammatical sentence. But it won't do as an analysis of 'Max exists.' For Max might not have existed. But it is not the case that Max might not have been one in number. 'Possibly, Max is zero in number' and 'Possibly, Max is two in number' are nonsensical.

[Andrew]

Bill,

I agree that 'are two in number' is, in b), not predicated of Sam and is not predicated of Max. But it is predicated of Sam and Max *plurally*. Consider:

c) 'Jim and Jill are surrounding the building'

c) might be true even if it is false that Jim surrounds the building and false that Jill surrounds the building (neither Jim nor Jill are big enough, let us suppose, to individually surround the building). But the two of them, together, *do* surround the building. The same goes for b), I suggest. Neither Sam nor Max are two in number (there is exactly one thing that is Sam and exactly one thing that is Max, after all). But the two of them, together, are two in number. Some predicates are plural. 'are two in number' is one of those predicates. You note correctly that 'are two in number' is not predicated of a specific individual. But it is, I suggest, predicated of specific individuals.

--- --- ---

As for a). Max is a merely contingent being, let us suppose; he might not have existed. And had Max not existed, he wouldn't have been one in number, I'd think. For x to be one in number is for exactly one thing to be identical to x; and if Max were to not exist, nothing would be identical to him. I think we disagree, then, about whether a) expresses a necessary truth. I say that it is not, because Max is a contingent being.

Consider now:

d) 'Possibly, Max is zero in number'
e) 'Possibly, max is two in number'

I don't think d) or e) are nonsensical.

I think that d) does, in fact, express a truth (supposing, as above, that Max is a contingent being). d) says of Max that he could have been zero in number, that it could have been that nothing is identical to max. And were Max to not exist, I'd think that's exactly what would be the case: nothing would be Max.

I think that e), on the other hand, is meaningful but necessarily false. Meaningful: it says of Max that he could have been two in number, that the number two could have correctly counted him. Necessarily false: no one thing could have been two in number; for were that the case a thing would have to part ways with itself, as it were. But nothing can part ways with itself!

That said, here are two reservations:

I. Though I think that a) expresses a proposition that is logically equivalent to (true if and only if) the proposition that Max exists, I'm not sure that it is an adequate *analysis* of that proposition.

II. Though I'm fairly confident that a) and b) are grammatical and that d) and e) are both grammatical, meaningful, and respectively, true and false, I do have reservations about relying on grammatical intuitions to do much philosophical world. There's a not-long-dead tradition in philosophy that deployed intuitions about what sentences ordinary people would use as a guide to all sorts of substantive matters. That tradition died for some very good reasons. I hope to repeat its mistakes.

Cheers!

-Andrew

[Bill Vallicella]

Andrew,

You are right to bring up plural predication since in PvI's paper he fights shy of endorsing (or rather he rejects) Frege's view that 'exists' is a second-level predicate, a predicate of concepts. So while "existence is allied to number," PvI does not take the further step of saying that number-words are predicates of concepts. They are plural predicates.

It is clear that if the cops have the building surrounded, then it is not the case that each cop has the building surrounded. It is also clear that no abstract object such as a property or set has the building surrounded.

PvI gives the example, 'Horses have an interesting evolutionary history.' This is not about any individual horse, nor is it about an abstract object. It's about horses taken plurally.

PvI want to say something similar about 'Horses exist.' The sentence does not predicate of each individual horse that it exists, nor does it a la Frege predicate of the concept *horse* the second-level property of being instantiated. 'Horses exist' is about horses in the plural and says of them thay they are one or more in number.

But I think there is an important disanalogy between 'Horses have an interesting evol. history' and 'Horses exist.' It is nonsense to say that Secretariat has an interesting evol. history, but it is not nonsense to say that Secretariat exists.

PvI attempts to tread a 'middle path' between saying that 'exists' is a predicate of individuals and and 'exists' is a predicate of concepts. He wants to say that it is a predicate of pluralities.

Unfortunately, it is not clear what a plurality is. It seems too obscure and frail a reed to support an attribute.