This post continues my examination of Peter van Inwagen's "Being, Existence, and Ontological Commitment." The first post in this series is here. There you will find the bibliographical details.
We saw that van Inwagen gives something like the following argument for the univocity of 'exists':
1. Number-words are univocal
2*. 'Exist(s)' is a number-word
3*. 'Exist(s)' is univocal.
The second premise is pure Frege. The question arises: is van Inwagen committed to the Fregean doctrine that 'exists(s)' is a second-level predicate? He says he isn't. (484)
How should we understand a general existential such as 'Horses exist'? Frege famously maintained that 'exist(s)' is a second-level predicate: it is never a predicate of objects, but always only a predicate of concepts. What the sample sentence says is that the concept horse has instances. Despite appearances, the sentence is not about horses, but about a non-horse, the concept horse. The concept horse is not a horse! (Frege also famously and perplexingly maintains that the concept horse is not a concept, but let's leave that for another occasion.) And what our general existential says about the concept horse is not that it exists (as we ordinarily understand 'exists') but that it is instantiated. Van Inwagen, though endorsing Frege's key notion that (as PvI puts it) "existence is closely allied to number" (482) does not follow Frege is in holding that 'exists' is a second-level predicate.
Van Inwagen thus appears to be staking out a middle position between the following extremes:
A. 'Horses exist' predicates existence of individual horses.
B. 'Horses exist' predicates instantiation of the concept horse.
Van Inwagen's view is that 'Horses exist' says that horses, taken plurally, number more than zero. So 'Horses exist,' contra Frege, is about horses, but not about individually specified horses such as Secretariat and Mr Ed. 'Horses exist' is not about the concept horse or any other abstract object such as a property or a set: it is about concrete horses, but taken plurally.
I am trying to understand this, but I find it obscure. One thing I do understand is that there are predicates that hold plurally (collectively) but not distributively, but are not, for all that, second-level. Van Inwagen gives the example:
1. Horses have an interesting evolutionary history.
Obviously, the predicate in (1) is not true of each individual horse. No individual horse evolves in the sense pertinent to evolutionary theory. But the predicate is also not true of the concept horse or the set of horses or the property of being a horse or any other abstract object. No concept, set, or property evolves in any sense. So what is the logical subject of (1)? Horses in the plural, or horses taken collectively. Or suppose the cops have a building surrounded. No individual cop has the building surrounded, and of course no abstract object has the building surrounded. Cops have the building surrounded. Suppose Manny is one of the cops. Then the following argument would commit the fallacy of division: (a) The cops have the building surrounded; (b) Manny is one of the cops; ergo (c) Manny has the building surrounded. What is true of cops in the plural is not true of any cop in the singular.
If I have understood PvI, he is saying that 'exists' functions like the predicate in (1), and like the predicate in 'The cops have the building surrounded.' But this strikes me as problematic. Consider these two arguments:
Horses have evolved
Secretariat is a horse
Secretariat has evolved.
Secretariat is a horse
The first argument is invalid, committing as it does the fallacy of division. The second argument is perfectly in order.
So it seems, contra Van Iwagen, that 'Horses exist' is importantly disanalogous to 'Horses have evolved' and 'The cops have the building surrounded.' 'Exists' is predicable of specified individuals, individuals in the singular. 'Evolved' is not predicable of specified individuals, individuals in the singular, but only of individuals in the plural.
I take van Inwagen to be saying that the logical subject of 'Horses exist' is not the concept horse, but horses, horses in the plural, and what it says of them is that they number more than zero. What I am having trouble understanding is how 'more than zero' can attach to a plurality as a plurality, as opposed to a one-over-many such as a concept (which has an extension) or a set (which has a membership).
A plurality as a plurality is not one item, but a mere manifold of items: there is simply nothing there to serve as logical subject of the predicate 'more than zero.'
"But look, Bill, it is the horses that are more than zero; so there is a logical subject of the predicate."
Response: You can't say what you want to say grammatically. If there IS a logical subject of the predicate, then it is not a mere manyness. But if there ARE many subjects of predication, then 'more than zero' applies to each horse which is not what you want to say. There must be something that makes the particulars you are calling horses horses, and that would have to be something like the concept horse; otherwise you have an unintelligible plurality of bare particulars. But then when you say that the horses are more than zero you are saying that the concept horse has more than one instance, and number-words become second-level predicates.
My suspicion is that van Inwagen's middle path is unviable and that his position collapses into the full-throated Fregean position according to which (a) "existence is allied to number" and (b) number-words are second-level predicates.