Kant: “Existence” is not a predicate

Kant's objection to the ontological argument was grounded in a log­ical point about the idea of existence. He argued that “existence” wasn't really a predicate at all, certainly not a predicate like “being red” or “weighing 200 pounds.” For one thing, something can't be red or weigh 200 pounds unless it exists.

Both Anselm's and Descartes' arguments effectively proceed by saying something like this:

It follows from the conception of God that he has (the property) existence.

Kant was arguing that, while it could be part of the conception of a thing that it was red or heavy, it couldn't be part of the conception of an individual thing that it had Existence, for there is no such property for individual things to have.

This claim is bound to seem paradoxical, since we do say that individual things exist. Didn't I say, in 3.5, that a predicate corre­sponded to an open sentence with one blank? And isn't “ 

exists” a perfectly good open sentence that is satisfied by you, me, and the postman? Indeed, didn't we discuss in Chapter 2, an argu­ment of Descartes' whose conclusion was “I exist”?

You can see what is going on here more clearly if you recall the idea of the existential quantifier that I introduced in Chapter 3. I said there that “There exists an X such that X F” means something satisfies the open sentence “------------------------------- F.” Now we can see the force of

Kant's objection.

ANSELM: If there is an X and a Y such that X and Y have the same properties except that X has Existence and Y doesn't, then X is greater than Y.

size=2 color=black face="Times New Roman">DESCARTES: If there is an X such that X is perfect, then X has Existence.

But Existence isn't something that you have: rather, to exist is to sat­isfy some open sentence. So these premises of the two versions of the ontological argument aren't true. And so, the argument, even if it were valid, isn't sound.

Frege, who invented the modern treatment of the existential quantifier, put this by saying that “Existence” wasn't a first-order predicate—that is, one expressing a property of things—but rather a second-order predicate, that is, one expressing a property of first- order properties. (Thus “is red” is a first-order predicate, and “is common” is acting as a second-order predicate when we say, “Redness is common.”)

To say that something exists, on this view, is to say that some first- order properties, such as redness, have instances—that is, to claim that an open sentence, such as “———is red,” is satisfied. You can't just be, in other words; you have to be something or other. “X exists” isn't, strictly speaking, meaningful. As we saw with Mary (of the sad story in 8.3), when we say someone exists, what we're really saying is that some individuating description is satisfied.

There are some significant reasons for wanting to avoid treating “Existence” as a first-order predicate. One I have already mentioned. It just doesn't seem right to say that an object has the property of exist­ing (the property I have been calling “Existence,” with a capital “E”) in the way in which it can have the property of being red or heavy.

A second problem comes when we think about nonexistence.

The argument has two premises. The first is an assumption about the relationship between properties and their “opposites.” Ordinarily, when something has a property, it makes sense to sup­pose that there might have been something that didn't have the property. Ordinarily, that is, if being-F is a property, then not-being- F is a property, too. So our first assumption is:

E: If Existence is a property, Nonexistence is a property.

The second assumption is that when a sentence of the form

A has the property F

is true, then we may infer

There exists something that has F.

This assumption is the logical principle of existential generaliza­tion. Now, given E, we suppose that when we say, “Romeo doesn't exist,” what we're saying is equivalent to:

Romeo has the property of Nonexistence.

By existential generalization we get:

C: There exists something that has the property of Nonexistence.

But this just looks contradictory: how can there exist something that doesn't exist?

If C isn't a contradiction, then “exists” must have two different meanings: one in the existential quantifier, and another one when we say Romeo does or doesn't exist. Casting about among the options, you might, for example, propose that the first “exists,” the one in the existential quantifier, means exists in some possible world or other. Then if Romeo exists in a possible world—one of the worlds in which the story of Shakespeare's Romeo and Juliet is not a fiction but truth—we can say that C means:

There is something in some possible world that has the property of Nonexistence in the actual world.

But that interpretation doesn't go with the logical principle of exis­tential generalization.

There exists something that has F

from “John has F,” we mean that something in the actual world has F (namely, of course, John). While it is certainly also true that some­thing in some possible world has F—because the actual world is a possible world, too—that is a much less interesting claim. So that can't be what we ordinarily mean by the existential quantifier.

Yet this does suggest a more serious possibility. When somebody talks about Romeo or Juliet, he or she does so in a way that you only really understand if you recognize that the person is talking about characters in a story. Suppose to each story there corresponds a set of possible worlds, the ones where the story is not fiction but truth. We can call these the “story worlds” of that fiction. Then we can think of people who say

Romeo loves Juliet

as wanting us to take them as having said

In the story worlds of Shakespeare's Romeo and Juliet, Romeo loves Juliet.

Now, in those story worlds Romeo has lots of properties and satis­fies lots of predicates. Someone who said in one of those story worlds “Romeo exists” could be taken to be saying, as we saw ear­lier, that someone in that world satisfies some of the individuating descriptions of Romeo. In that sense, Romeo exists in the story worlds of Shakespeare's Romeo and Juliet. But in the actual world nobody satisfies the individuating descriptions that are true of Romeo in all the story worlds of Romeo and Juliet. And so when we say “Romeo doesn't exist,” we're essentially pointing to that fact.

If Frege is right and we don't, strictly speaking, ever ascribe the property of Existence to an individual thing, then we need to explain why we say things like “Dorothy exists.” (So Frege would agree with Wittgenstein's suggestion, which I discussed in 3.3, that sometimes the superficial grammar of a sentence can be misleading.) If we can give an explanation of such sentences that is consistent with Frege's treatment, like the sketch I just gave for claims about Romeo's exis­tence, then we will, indeed, have reason to reject the ontological argument.

Now, “exists” is something of a philosopher's word.

One uncontroversial use of “exists,” the one that Frege permits, is when we say something like “Purple marigolds exist.” Here what we're saying is that something satisfies both the predicate “is pur­ple” and the predicate “is a marigold.” When we say things like “Merlin exists,” there are at least two possibilities. One is that we are affirming that someone who used to exist still exists. Here there's no problem about existence being a property. It's just a way of referring to the property of being alive. The other is that, as in the sad story of Mary I mentioned earlier, what we're saying is that a name that we took to be a fictional name is in fact a real name. Here, the func­tion of saying that someone exists is to communicate the status of the name: it's not assigning a property to a person, it's clarifying the status of a word. Here “exists” is equivalent to “is not fictional” or “is not imaginary” and “does not exist” is equivalent to “is fictional” or “is imaginary.” Our ordinary ways of speaking, then, are ontologi­cally misleading.

If we accept Frege's account, we must suppose either that there are no other uses of “exists” to apply to individual things or that they can be similarly explained away. Whether or not that is so is still a topic of controversy.

8.7