Saturday, November 12, 2011

Question about Possible Worlds

I need some help with possible worlds . . . .
An atheist . . . [said] recently that existence itself is necessary because:

The proposition "this world exists" is necessarily true in all possible worlds.
The proposition "this world does not exist" cannot be true in any world.
The proposition "existence exists" is an a priori analytic truth.

I'll be happy to see if I can help! Let's examine the first claim.

The proposition “this world exists” is necessarily true in all possible worlds.

First, we need to understand what is meant here. The word “this” is used as an indexical pointing to some world. “World” is denoting a completely consistent set of propositions including the affirmation of every proposition or its negation. “Exists” seems to refer either to the longer clause “is actual” or simply as a manner of speaking for “there is” (as in, “there is a possible world X” where all we mean is to say such a world entails a complete set and is possible).

Now it becomes apparent the proposition is woefully underdeveloped. For what is meant by “this world?” It seems he can mean either one of a few major things. Perhaps he means (1) “The actual world is actually in existence” is necessarily true in all possible worlds. If this is what is meant, I don’t see the harm. For it seems tautologically true, like saying “it is what it is,” “whatever will be, will be,” etc. Perhaps then he means (2) “The world we are in now [call it W1 for the actual world we are actually in] exists as the actual world” is necessarily true in all possible worlds. This again has difficulty escaping the tautology.

Perhaps then he really means (3) “This world exists,” where “this” refers to whichever world one is referring. But this isn’t quite right, unless existence simply means “there is a possible world such as this one.” Such a claim is quite uninteresting. So perhaps he then means to say (4) “W1 [the actual world] is the actual world” is true in all possible worlds. It then follows that proposition is necessary, and hence the actual world we have now is necessary.

There seems to be a bit of a problem with (4), however. It seems to smuggle in what it seeks to prove. For instance, consider the very intuitive idea that W2 could have been the actual world. W2 is identical to W1 in every respect but one—and that difference is miniscule and incidental (by definition, it affects nothing else). It’s extremely important to note that if (4) is taken to mean “W1 is the actual world,” then there just are no other possible worlds. But I suspect we arrive at “W1 is the actual world” being true in all other worlds as an a posteriori justification. That is to say, we think “W1 is the actual world” is true in all other possible worlds only because it turned out that W1 is the actual world—not because, as a metaphysical feature, all other possible worlds contain the proposition “W1 is the actual world.” In that latter case, it doesn’t even make sense to speak of other possible worlds!

But further, there is the problem of necessity de dicto vs. necessity de re. Suppose that in this world (W1), I throw a green ball. So then, in every possible world, it is true that “in W1, Randy throws a green ball.” This is true even in worlds where I throw no balls, much less green ones. But in that case, the aforementioned proposition becomes necessarily true. So I guess that means I had no choice in throwing the ball, right? Wrong. One of the issues at play is the necessity de dicto, or of a statement itself (rather than the metaphysical ontology of me performing the act). Another issue at play is temporal becoming. We can see it would be truly bizarre for us to argue that because we performed any act, that act was therefore necessary! Only the truth of the statement itself is necessary. I don’t see any reason to think this is not the case with the issue of “W1 is actual” being true in every possible world. Why would this not be a case of de dicto necessity, as opposed to de re?

To illustrate the difference even more, consider the following two propositions. Taken de dicto, (4) would be: (5) Necessarily, if W1 is the actual world, then it actually exists. If taken de re, (4) would be: (6) W1 is necessarily the actual world. The argument needs something very much like (6) to be true in order to get off the ground. However, we can’t just assume (6) is true over and against (5)—if we do, this would be question-begging. Moreover, it seems whatever plausibility the argument has actually derives from an acceptance of (5), not (6).

Of course, I suppose one could assume that de re is in view because there just is nothing, on atheistic naturalism, to “get the world going,” so to speak. Hence, logical necessity is all that could have brought the world into existence. Interestingly, I may agree—God is such a being!

His second contention, that “this world does not exist cannot be true in any world” is an entailment of the first contention. The third just looks like an argument from contingency for a necessarily-existing being. This looks exactly like a theistic argument to me! I hope this helps somewhat, and possibly clears up confusion.
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  1. I wonder if the atheist is confused about what is meant by a "world". It does not mean planet or even physical reality, but merely, as you say, a consistent set of true and false propositions. Unless the atheist proposes that propositions actually exist like abstract objects, then what is to stop us from asserting that there is a possible world in which the proposition "Nothingness is here instantiated"? If there is such a possible world, then the atheist has by no means shown existence to be necessary.

    But suppose he does succeed in showing “existence itself” to be in some sense necessary. To whose existence does he refer? All that follows from this is that something exists necessarily, which is what the theist has always maintained. I don’t see that this could be constructed as an argument for atheist unless it begs the question, in which case it is just a bad argument for atheism.

  2. Hi Daniel thanks for the comments! I agree with your take concerning nothingness being instantiated.

    I am also not aware of the full context of the atheist's proffered argument, so I admit I am being speculative here. But I think the argument is offered in an attempt to avoid God. Like saying, "the universe is necessary because this actual world is necessary." But that's just a guess, and as you rightfully point out, the only valid conclusion from the argument proffered is that something necessarily exists (that is, at best, something holds its existence in a necessary mode, not contingent), which is what the theist holds. But I'm not even sure we can be that generous for his argument, as it may only be the case that his valid conclusion is "necessarily, something exists" (again, as a de dicto statement).

  3. I agree with treating 'this' in this case like an indexical. That seems to be exactly what's happening to me as well. I think the more interesting case would use something like David Lewis's modal realism. Then, you could probably say that any particular thing would exist necessarily (in some sense) in virtue of being a possible thing. It's hard to see where that atheist would have been going with this, though.

  4. Hey Dr. Mike! :)

    I agree. I also wish to reiterate that this was a question posed to me by a Christian and I did not get a chance to see the full context. It's why I tried to explore the various alternatives of meaning.


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