'Something is Self-Identical' Cannot Translate 'There are Objects': Another Argument Against the Thin Theory

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. 

Comments

[Alex Leibowitz]

Does premise 5 mean that you might not have been the same as you are, or that you might not have been the same as you were?

I agree that nothing is (actually) not the same thing as it (actually) is, but I'm not sure if that entails that nothing could have not been what it (actually) is.

So I think it makes a difference whether we read premise 5 to mean that you might not have been the same thing as you might have been, or to mean that you might not have been the same thing as you (actually) are. On the former reading, it goes through, but on the latter reading, I'm not so certain.

The question is whether you could have existed without being the same as yourself -- and I say you might have existed without being the same thing as you actually are, so long as you would not have been a different thing than you would have been (what you would have been would in that case be different a different thing than what you actually are).

Sorry if I'm not putting this very clearly, but I'm confused by the phrase "self-diverse".

[Leo Carton Mollica]

Thanks for the post.

I wonder if you might not run into this difficulty: you are saying that it is not possible that I be not self-identical, which amounts to saying that it is necessary that I am self-identical. But it is possible that I not exist. So at some possible world W, I do not exist, but am self-identical. But, surely, if at W something is identical with Leo, then Leo exists at W. So, it would appear that your assumptions land you in a contradiction (that at some possible world W, I both exist and do not exist).

[William]

OK, so existence is not captured with a equals sign.

What would

(Ex) (x)

mean? Would that work?

[Bill Vallicella]

William,

Identity, not equality.

'(Ex)(x)' does not express a complete thought. 'For some x, x' is neither true nor false. 'For some x, x =x' expresses a complete thought, and is true, but not the same thought expressed by 'Something exists.'

[Bill Vallicella]

Leo,

You are necessarily self-identical, but not a necessary being. In possible worlds jargon: in every world in which you exist, you are self-identical; but you do not exist in every possible world.

I don't see any contradiction.

You are necessarily self-identical but contingently existent. I conclude that existence is not self-identity.

Of course, when I say that you are necessarily self-identical I do not mean that every world W is such that you are in it and self-identical; I mean that every world you are in is a world in which you are self-identical.

[Bill Vallicella]

Alex,

The point I am making is very simple. It is true that I might not have existed; it is not true that I might not have been self-identical. So existence is not self-identity.

[Leo Carton Mollica]

Dr. Vallicella,

But then it seems you're illegitimately shifting the sense of "necessary" and "possible": in (2) you are using "possibly" to mean that there is some accessible possible world in which I do not exist, but in (6) you are using "possibly" to mean that there is some accessible possible world in which I exist and at which I am not self-identical. Surely, "There is an accessible world at which p" and "There is an accessible world at which I exist and p" are not equivalent. If you were to use one sense of "possible" consistently, you would need to reject either (2) or (6).

In other words, if what you mean by "necessarily self-identical" is that "every world you are in is a world in which you are self-identical," then by parity of reasoning "necessarily existent" should be construed as "every world you are in is a world in which you exist," which would render (2) trivially false.

[Bill Vallicella]

Well, in (6) I don't use 'possibly.' Do you mean (5)?

If you don't accept the reasoning, tell me which premise you reject or which inference you consider invald.

[Hrodberht]

Leo,

What's the alternative? That at all worlds where you do not exist, you are not self-identical? (if existence is self-identity, then that seems to follow) Well, at those worlds where you do not exist, what is it that is not self-identical anyway? In a domain with everything but Bill, what is the truth-value of "Bill is self-identical"? "Bill is not self-identical"?

[Bill Vallicella]

Hrod,

The alternative is that in a world in which I do not exist, I am distinct from everything, which does not imply that I am self-diverse in that world, since I don't exist there.

But, as you seem to appreciate, there must be something in those whorlds in which I do not exist that represents me there so that it can be true there that I do not exist. See my latest post for details.

[Edward Ockham]

Again, I am agreeing with you all the way here. Existence is not self-identity. It is, of course, the instantiation of a singular concept. But there we disagree.

[Bill Vallicella]

Ed,

Partial agreement is better than no agreement!