At Tractatus Logico-Philosophicus 4.1271 we read: "So one cannot say, for example, 'There are objects', as one might say, 'There are books'."
In endnote 9, p. 194, of "The Number of Things," Peter van Inwagen (Phil. Issues 12, 2002) writes:
Wittgenstein says that one cannot say " 'There are objects', as one might say, 'There are books'." I have no idea what the words 'as one might say' ['wie man etwa sagt'] could mean so I will ignore them.
Is van Inwagen simply feigning incomprehension here? How could he fail to understand what those words mean? Wittgenstein's point is that object is a formal concept, unlike book. One can say, meaningfully, that there are books. One cannot say, meaningfully, that there are objects. Whether Wittgenstein is right is a further question. But what he is saying strikes me as clear enough, clear enough so that one ought to have some idea of what he is saying rather than no idea. By the way, van Inwagen is here engaging in a ploy of too many analytic philosophers. In a situation in which it is tolerably, but not totally, clear what is being said, they say, 'I have no idea what you mean' when, to avoid churlishness, they ought to say, 'Would you please clarify exactly what you mean?'
Be this as it may. Philosophers are a strange, in-bred breed of cat, and they acquire some strange tics. My present topic is not the tics of philosophers, nor formal concepts either.
According to Wittgenstein, one cannot say (meaningfully) that there are objects. Van Inwagen responds:
Why can one not say that there are objects? Why not say it this way: '(Ex)(x = x)'? (p. 180)
Without endorsing Wittgenstein's claim, or trying to determine what exactly it means, my thesis is that van Inwagen's translation of 'There are objects' as 'Something is self-identical' is hopeless.
I do not deny the logical equivalence of the two sentences. I do not claim that there are self-identical items that do not exist. Everything exists. My claim is that to exist is not to be self-identical. They are not the very same 'property.' If they were, then van Inwagen's translation would be unexceptionable. But they are not. Here is a reductio ad absurdum argument to show that existence and self-identity are distinct, that existence cannot be reduced to self-identity.
0. Existence and self-identity are the very same property. (Assumption for reductio)
1. If existence and self-identity are the very same property, then nonexistence and self-diversity are the very same property, and conversely. (Self-evident logical equivalence.)
2. Possibly, I do not exist. (Self-evident premise: I am a contingent being.)
3. Possibly, I am not self-identical. (From 1, 2)
4. What is not self-identical is self-diverse. (True by definition)
5. Possibly, I am self-diverse. (From 3, 4)
6. (5) is necessarily false.
7. (0) is false. Q.E.D.
The thin theory of existence is the theory that existence is exhaustively explicable in terms of the purely logical concepts of standard first-order predicate logic with identity. Identity and quantification are such concepts. Now the only way within this logic to translate 'There are objects' or 'Something exists' is the way van Inwagen suggests. But what I have just shown is that 'Something is self-identical' does not say what 'Something exists' says.
If things exist, then of course they are self-identical. What else would they be? Self-diverse? But their existence is not their self-identity. Their existence is their being there, their not being nothing, their reality -- however you want to put it. If something is self-identical, it cannot be such unless it first exists. It astonishes me that there are people, very intelligent people, who cannot see that. What should we call this fallacy? The essentialist fallacy? The fallacy of thinking that being = what-being? Or maybe it is not a fallacy of thinking, but a kind of blindness. Some people are color-blind, some morally blind, some modally blind. And others existence-blind.