Existence and Contingency

Let us return to the problem of contingency that I was belaboring in my last existence post.  Consider this reasoning:

1. (x)(x = x).  Principle of Identity: everything is self-identical
2. Venus = Venus.  From (1) by Universal Instantiation (UI)
3. (∃x)(x = Venus).  From (2) by Existential Generalization (EG)
4. (1) is logically true, hence necessarily true.
5. If p is necessary, and p entails q, then q is necessary.  (Principle of Modal Logic)
6. (3) is necessarily true.  The necessity of (1) is transmitted via the Modal Principle to (2), and then to (3)
7. 'Venus exists' is contingent.
8. If sentence s1 adequately translates sentence s2, then s1 preserves both the truth and the modal status of s2.  (Translation Principle)
Therefore
9. (3) is not an adequate translation of 'Venus exists': it preserves truth but not modal status.

And of course this result is generalizable:  'x exists' cannot be adequately translated as '(∃y)(x = y).'  But that is the canonical translation on the Quinean version of the thin theory.  So the Quinean version is untenable.

If you don't accept this argument, which premise or inference will you reject and why?

If Venus exists, then of course it is identical to something.  But surely it is not contingent that Venus  is identical to something.  It is contingent, however, that Venus exists.  Therefore, the existence of Venus is not its identity to something.  Once again we see that the thin theory is false. 

Comments

[Andrew]

I deny that 1 entails 2. For 1 might be true though 2 is false. Consider a situation where there is exactly one thing, Mars; and suppose that Mars is not Venus. In that situation, 1 holds; everything (that is, Mars) is self-identical. But Venus is not self-identical in that situation. Venus is not *anything* in that situation. There is nothing that is Venus, after all; and so it is not the case that Venus is Venus.

You say: "surely it is not contingent that Venus is identical to something". And I reply in two ways. First, don't call me Shirley. Second, it seems to me that since Venus is a contingent being (Venus could have failed to exist) it is indeed contingent that Venus is identical to something. For in situations where Venus does not exist, Venus is not anything. And if Venus is not anything, then Venus is not even Venus. So it is, after all, contingent, that Venus is Venus.

[Elliott]

Dr. V,

Your argument seems to rest on the contradictory relationship between premises four and seven. I agree with your reasoning because I think that the principles of logic, such as the laws of identity and non-contradiction, are necessarily true. However, if one were inclined to disagree, then challenging premises one and four would be a start.

One might claim that that the principles of logic are not necessarily true. One might hold that God created such principles (e.g., the so-called doctrine of created eternal truths). One might hold that the principles of logic merely reflect the thought patterns of the human mind (e.g., psychologism) or that truth itself is relative (e.g., cognitive relativism). On these accounts, the principles of logic are contingently true; they are contingent upon God, or the human mind, or human culture, etc.

If one can make the case that the principle of identity is contingently true, then one might hold: (a) that it is contingent that Venus is identical to something; and (b) that it is contingent that Venus exists. One could then argue that the examples of contingent existence in these two propositions are somehow compatible. Hence, one could say that your argument is not convincing, and that the theory of existence as self-identity survives by virtue of some version of the effort to reject the necessary truth of the principles of logic.

[Bill Vallicella]

Andrew,

Shirley was a girlfriend I borrowed from Plantinga. (You are right, though, that 'surely' involves an element of bluster.)

Note first that all these recent posts on existence presuppose standard first-order predicate logic with identity. So we have the built-in assumption that names such as 'Venus' are nonempty. On this assumption, 'surely' (2) follows from (1).

Are you denying the validity of UI in standard logic?

We agree that Venus is contingent. And I think you will agree that there is no possible world in which Venus exists in which he is not identical to something.

Your point is that in those worlds in which Venus does not exist, Venus does not have the property of identity-with-something: he is not there to have that property. So it is not true that in every world Venus = Venus.

My claim was a conditional one: given that Venus exists, Venus cannot fail to be identical to something. Perhaps the point could be put by saying that identity with something is an essential, though not a necessary, property of Venus.

But if existence is the property of identity with something, and Venus exists (as is in fact the case), then how could there be any world in which Venus does not exist?

Tricky stuff!

[Andrew]

Bill,

I am unsure how to answer your first question. Maybe this will help: I am less concerned with the validity of an inference from 1 to 2 *in some formal system or other* than I am with the question of whether 1 entails 2. One way to test whether x entails y is to see if there's a possible situation where x is true and y is false. I suggested that there is, with respect to 1 and 2, just such a situation. The Situation (as we might call it) is one in which Mars exists but Venus does not. Everything is, in The Situation, self-identical (so 1 is true). But it is not the case that Venus is, in The Situation, self-identical (2 is false); Venus isn't around and so has no properties, much less the property of self-identity. Perhaps we make our disagreement more precise. I hold to all three of the following, which together imply that 1 does not entail 2:

a) The Situation is possible.
b) In The Situation, 1 is true.
c) In The Situation, 2 is false.

We disagree about whether 1 entails 2, and so must disagree about a, b, or c. Which of a, b, or c do you deny?

You say: "given that Venus exists, Venus cannot fail to be identical to something". But this doesn't seem right. For Venus does in fact exist, and Venus might be (and indeed, is!) a contingent being. Venus could have failed to exist, that is; and in situations where Venus does not exist, Venus is not identical to anything. So it is, after all, possible for Venus to fail to be identical to something (even though Venus in fact exists).

You end with a question: "how could there be any world in which Venus does not exist?" This is, I take it, equivalent to the question of how it could be that Venus is a contingent being. I do not have an answer to that; but I take it we agree that Venus *is* contingent. And so this question doesn't seem to get at our disagreement.

Cheers,

-Andrew

[Bill Vallicella]

Elliot,

If God creates a truth of logic such as (1) it doesn't follow that it is contingently true. It doesn't even follow that it is contingently existent.

One could maintain the following. Propositions are necessary beings. They depend for their existence on God. (Everything depends for its existence on God except God.) To paraphrase Aquinas, God has his necessity from himself; other necessary beings have their necessity from another, namely, God. Some of these propositions are true and some of the true ones are necessarily true. And among the latter are the truths of logic.

[Bill Vallicella]

Andrew,

My concern in this series of posts is to assess the thin theory of existence or being. (I take PvI to be the most articulate defender of this theory.) In particular, I am now concerned to assess the thin theory in its Quinean variant (as opposed to its Frege-Russell 'second-level predicate' variant), the former being the variant that PvI expounds. The thin theory, however, is tied to standard logic, MPL. It is the theory that MPL's treatment of exstence is entirely adequate and that "Existence is what existential quantification expresses." (Quine)

So I am working within and presupposing a well-defined and widely accepted formal system, MPL. That is not to say that your broadening of the question is not also legitimate.

More later.

[Bill Vallicella]

Andrew,

Note that (1) and (2) are unmodalized. I cannot see how you can resist the inference from (1) to (2) given the tacit assumption (built into MPL) that substituends for variables in applications of UI cannot be vacuous names.

But this leaves open the question whether (1) entails (2). Entailment is a modal notion: p entails q =df there is no possible world in which p is true and q false.

On this understanding of 'entails,' you will maintain that (1) does not entail (2). And this for the reason that in worlds in which Venus does not exist, it is not self-identical.

I grant that I need to be able to say that (1) entails (2) if I am to apply the Modal Principle I mention in (5). It is not enough that the move from (1) to (2) be 'kosher' by the strictures of MPL -- which it is.

Well, what if I said this: in every world in which Venus does not exist, it has a representative: a qualitative essence QEV (not to be confused with a nonqualitative thisness) which is a conjunction of all the qualitative properties Venus has in the actual world.

When we say that, necessarily, Venus = Venus, what we are saying is that every world w is such that if anything instantiates QEV in w, then that thing is self-identical.

[Elliott]

I agree with your reply. The objections from psychologism and relativism remain. But to close the loop, I think they ultimately fall. It seems to me that logical psychologism can be reduced to some form of cognitive relativism, and that cognitive relativism is self-refuting. Of course, the loop is still open, so to speak, if you have further insight.

Thanks,

Elliott

[Bill Vallicella]

For an argument against psychologism, see here: http://maverickphilosopher.typepad.com/maverick_philosopher/2012/06/are-the-laws-of-logic-empirical-generalizations.html

In the relativism category there are many argments against cog. relativism.

[Edward Ockham]

Late to the discussion again. One point: classic MPL (i.e. without free logic) assumes direct reference, as I have pointed out. In the formula 'Fa' the constant (or 'proper name') must always refer to something - even if it is something in a possible world. So if existence reduces merely to being something, then of course any singular existential existential is necessarily true. So your objection that singular existential statements are contingent boils down to an objection to direct reference. As I have always argued.