A Second Van Inwagen Argument for the Univocity of 'Exists'

I discussed one of the Peter van Inwagen's arguments here and found it wanting.  He has a second argument:  ". . . 'exists' is univocal owing to the interdefinability of 'there exists'  and the obviously univocal 'all.'  But this is a powerful argument, for, surely, 'all' means the same in 'All natural numbers have a successor' and 'All Greeks are mortal'?" (484).  The argument could be put as follows:

'Every' is univocal.

'Exist(s)' and 'every' are interdefinable:  'Fs exist' is equivalent to 'It is not the case that everything is not an F.'

Therefore

'Exist(s)' is univocal.

I accept this crisp little argument -- but with a restriction: 'exist(s)' is univocal across all affirmative and negative general existential sentences.  But what about a singular existential such as 'Peter exists'?  Does 'exist' in the latter have the same sense that it has in 'Rabbits exist'?  I say it doesn't:  'exist(s)' is not univocal across all existence sentences, general and singular.

To warm up, what are we saying when we say that rabbits exist? On Frege's approach, we are saying that the concept rabbit is instantiated.  So 'exist(s)' in general existentials means 'is instantiated.'  But 'Peter exists' does not say that Peter is instantiated.  So is it not spectacularly obvious that 'exist(s)' is not univocal across singular and general existentials? 

But we needn't follow Frege is holding that 'exist(s)' is a second-level predicate.  And van Inwagen does not follow him in this.  Perhaps it would not be unfair to characterize van Inwagen as a half-way Fregean: he likes the notion that "existence is allied to number" but he does not take that characteristic Fregean thesis to entail that 'exist(s)' is a second-level predicate, i.e., a predicate of concepts, not objects.  Van Inwagen could and would say something along these lines:

1. Rabbits exist:  It is not the case that everything is not a rabbit.  ~(x)~Rx.

2. Peter exists:  It is not the case that everything is not identical to Peter.  ~(x)~(x = Peter)

I will now try to show that, even on van Inwagen's preferred translations, there is still equivocity as between general and singular existentials. (1) and (2) are equivalent to

1*. Rabbits exist: Something is a rabbit. (Ex)Rx.

and

2*. Peter exists:  Something is (identically) Peter. (Ex)(x = Peter).

Now it seems to me that we are still stuck with equivocation.  The predicate in (1*) is 'something is (predicatively) ___.'   The predicate in (2*) is 'something is (identically) ___.'  Now the 'is' of predication is not the 'is' of identity.  So the equivocation on 'exist(s)' remains in the form of an equivocation on 'is' as between the 'is' of predication and the 'is' of identity.

The equivocation ought to be obvious from the notation alone.  The immediate juxtaposition of 'R' and 'x' in '(Ex)Rx' signifies that x is (predicatively) R.  But in '(Ex)(x = Peter)' we find no such juxtaposition but a new sign, '=.'  

My thesis, then, is that while 'exist(s)' is univocal across all general existentials, it is not univocal across all existentials.  This reflects that fact that -- to switch over to material mode -- existence cannot be reduced to or eliminated in favor of any thin logical notion or combination of such notions.

Comments

[Willie]

These are intriguing thoughts to me. Bill, would you consider perhaps that the "is" of predication and the "is" of identity are the sole "forms" that "is" can take (two forms of “existence/exists” if you will, presuming no semantic difference between the terms "existence" and "exists") or do you consider other forms viable? Furthermore, do you perhaps consider these two forms of "is" to be opposites of sorts, perhaps in the sense that one deals with the "particular" and the other deals with the "universal"? Your insight into this is appreciated.

[Edward Ockham]

I agree that in 'rabbits exist' and 'Flopsy exists' the word 'exist' has the same meaning.

[Alfredo]

Dr. Vallicella: Couldn't Van Inwagen make the same move Quine makes in "On What There Is" and treat '= Peter' as a single-place predicate? Let this be the predicate 'P'. The extension of this predicate is just Peter. Then 2' will be ~(x)~Px. So on the face of it there is no apparent distinction between the logical form of 1 and 2'.

[Alfredo]

I would accuse Van Inwagen's argument of being a 'non sequitur', at least if we construe it in a non-question begging way. You state the argument thus:

(1) 'Every' is univocal.

(2) 'Exist(s)' and 'every' are interdefinable: 'Fs exist' is equivalent to 'It is not the case that everything is not an F.'

Therefore

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

Clearly, as is, this argument is not valid. To make it valid we need some further premise. I'm not sure what sort of plausible premise he is using to get to his conclusion, but maybe it is something like:

(2.5) If two terms are interdefinable then each of the terms' uses have the same sense relation.

(Just a clarificatory point: Sense relations are things like 'univocity' or 'equivocity', and Van Inwagen thinks that all the uses of 'exists' are univocal.) How are we to understand interdefinable here? Surely not as meaning 'semantically equivalent', for that would be utterly question-begging. We must construe it then as something like 'logically equivalent'. The problem is that (2.5) is not obviously true on this interpretation. I'll explain.

I think we can admit that 'some' and 'every' are univocal, that these two are interdefinable in the sense of logically equivalent, but still say that 'some' doesn't fully capture the *meaning* of 'exists', so neither does 'every'. Of course, every 'some' statement is logically equivalent to another 'there exists' statement, but that does not imply they are semantically equivalent.

The natural language quantifier 'there exists' has many senses, but all beings have one of its senses; thus the range of this quantifier includes all beings. And since there are no non-existent beings, the range of the quantifier 'some' is over all beings. So the two quantifiers range over the same domain of discourse; and since any 'some' and 'there are' statement is logically equivalent, this is why we can translate statements involving either of them with the same symbol in predicate-logic, '(Ex)'. This is also why they are each logically equivalent to at least one 'all' statement. But it simply doesn't follow that they have the same meaning. It is true that our 'some' quantifier ranges over only and all beings, but it ranges over them regardless as to which of the many analogous senses of 'being' they exist in.

Let me know if that makes any sense.

[Bill Vallicella]

Alfredo,

As for your first comment, that is a possible move to make. We take 'x = Peter' and split it into 'x' and '= Peter.' The latter becomes the sign for the property of identity-with-Peter or Peterhood. Then we rewrite '(Ex)(x = Peter)' as '(Ex)Px.'

But then you have to take on board haecceity properties with all the problems they have. I have discussed this in my book and in a number of posts.

Futhermore, the distinction between the 'is' of identity and the 'is' of predication cannot be ignored. But that is what you are doing if you say that 1* and 2* have the same logical form.

[Bill Vallicella]

Alfredo,

Excellent comments. You are right: van I. needs an auxiliary premise to make his argument valid. Your (2.5) would do the trick. If two terms are interdefinable, then if one is univocal(equivocal)then so is the other.

I agree that logical equivalence is not the same as what you are calling semantic equivalence, except that I would not use 'semantically equivalent' but 'semantically identical.' Equivalence is an extensional notion. But we are concerned with the intensions (senses) of 'Every' and 'exists.' You and I agree that they cannot have exactly the same sense. But it is surely true that a general existential of the form *Fs exist* is logically equivalent to a sentence of the form *It is not the case that everything is not an F.*

You and I are on the same page. But I would quibble with your last sentence: >>but it ranges over them regardless as to which of the many analogous senses of 'being' they exist in.<<

The exist in different modes (ways) not different senses. We have to distinguish between senses and modes. The first term is semantic, the second ontological. Consider 'There are substances' and 'There are accidents.' 'There are' has the same sense in both sentences, but substances exist in a different way than accidents do. They differ in their mode of existence.

I say that it is intelligible that there be different modes of existence. Van I. strenuously denies this and he thinks that people like me are making a crude mistake. More on this later. Do you have van I's paper at your disposal?

[Alfredo]

Thanks for those necessary corrections. I was just re-reading my last comment and I felt it was sloppy in some parts and I noticed some of the same problems you did. I'd generally stand by the substance of what I've said though.

With regard to your first reply, I think this would explain why Edward Ockham would think that in 'rabbits exist' and 'Flopsy exists' the term 'exists' has the same sense in each.

With regard to the second comment, I agree, we must distinguish between modes and senses. Still, I think that it's not obviously correct that something like (2.5) is true and that PvI's conclusion follows; someone who believes the semantic thesis that 'exists' is said analogically could reasonably deny it. Maybe someone like Aristotle ('being is said in many ways'). To more accurately express this I think I might re-write my last paragraph as follows:

"On the idea that 'exists' is analogical, the natural language quantifier 'there exists' has many senses, but all beings can be said to exist in one of its senses; thus the range of this quantifier includes all beings (regardless as to which sense of 'being' can be said of them). And since there are no non-existent beings, the range of the quantifier 'some' is over only and all beings. So the two quantifiers range over the same domain of discourse; and since for any 'some' statement there is a logically equivalent 'there exists' statement, it follows that we can translate logically equivalent statements involving either of them with the same symbol in predicate-logic, '(Ex)'. This is also why they are each logically equivalent to at least one 'all' statement. But it simply doesn't follow that they have the same meaning. It is true that our 'some' quantifier ranges over only and all beings, but it ranges over them regardless as to which of the many analogous senses of 'being' is said of them. So it's consistent with both 'some' and 'all' being univocal that 'being' or 'exists' are not."

I should be clear that I'm not here *defending* the doctrine of the analogy of the term 'being'. I'm only saying that someone could provide a picture according to which it's true and consistent with Van Inwagen's two premises.

I do have the paper in question at hand. Did you want to recommend I look at a particular section? I actually defended his and Ted Sider's views in a term-paper this past Winter!

[Edward Ockham]

>>But then you have to take on board haecceity properties with all the problems they have.

Just a quibble, but the predicate '--- is identical with Peter' does not of itself require haecceity properties. A haecceity property, as I understand it, is a singular property that exists in the absence of its bearer. But, in standard (modern) logic, the proper name 'Peter' is not intelligible without a referent. Therefore the predicate '--- is identical with Peter' is not intelligible without a such a referent. Therefore the modern theory does not require haecceity properties, in your sense.

In scholastic logic, by contrast, proper names themselves are predicates, and we dispense with the identity sign (you remember we discussed Fred Sommers' excellent point about this. Then perhaps we do need haecceity properties. (Perhaps).

[Bill Vallicella]

That's a good point, Ed.

But then I would argue that there is a deep logical difference between names and predicates, and that no name can be transmogrified into a predicate. The identity sentence 'Peter is Peter' cannot be parsed as the predication 'Peter/ is Peter.'

I would argue that there is no predicate '___ is Peter' and no property corresponding to it, whether the property can exist unexemplified or not.

If you deny that, are you not eliding the distinction between the 'is' of identity and the 'is' of predication as that distinction is understood by most analytic philosophers incl. van Inwagen?

Isn't it highly counterintuitive to maintain that particulars such as Peter can be predicated? That which is predicable must be at least possibly such as to apply to more than one thing.

[Bill Vallicella]

Alfredo,

I take it you have the Metametaphysics volume. I need to get totally clear about the PvI paper, so I need to write some more posts on it, one about his thesis that Being is not an activity. So maybe you could look at that section. I haven't carefully studied Sider's paper, so we could discuss that as well.

I have a paper coming out, "Existence" Two Dogmas of Analysis." There is still time to make improvements. This is why I am studying these recent articles. The one dogma is that existence is instantiation, the other is that there are no modes of existence.

[Bill Vallicella]

Alfredo,

If we stick to gen'l existentials, then I see only univocity. That is why I think PvI's argument above is cogent if restricted to gen'l existentials. There are: dogs, numbers, accidents, substances, holes, surfaces, thoughts, . . . . 'There are' has the same sense for each corresponding sentence. I think that is obvious if existernce is instantiation. There aren't different senses of 'instantiate.'

Equivocity and analogicity shows up, if at all, at the level of singulars.

I would insist that God and Socrates do not exist in the same way. But does it follow that 'exists' as applied to God and as applied to Socrates have different senses?

As for the analogia entis I don't want to talk about that just yet.

[Alfredo]

I will look over that part of the PvI paper. I'm not sure that Ted Sider's article is particularly relevant to the two dogmas of analysis you are up against, though there is certainly much interesting material worthy of discussion in his work and I'd be happy to talk about it in further posts. Sider is a Quinean about ontological commitment and also defends a "Quinean methodology" about metaphysics, but Quine's views on ontological commitment aren't really all that problematic so far as I can tell (sure, quantifying over x commits you to x's existence). The "methodology" I may take issue with.

Would it be okay if I saw a draft of your paper at some point? Is that allowed?

[Bill Vallicella]

Alfredo,

I'll send you a draft of the paper, but first I should add some improvements.

Next on the agenda is a discussion of wherther Being is an activity. This part of PvI's paper I find bizarre.