Monday, October 20, 2008

Possible Worlds

by Hanno

On the way out of last weeks meeting, Robert asked me about possible worlds. Todd, Lord Matt and I were using the notion of a possible world in the previous weeks discussion, but we did not say much about them. So here goes:

A possible world is a complete way the world might have been. Suppose you could have been a rock star. Then there is a possible world at which you are in fact a rock star. That part is easy, and gives us a way to think about what might have been. But what are possible worlds?

The first philosopher to use possible worlds was Leibniz, long ago. He used them in part to answer the problem of evil: This is "the best of all possible worlds" and hence a good God would naturally chose this one to being into existence. For Leibniz, possible worlds were ideas in the mind of God. Imagine Him going through each of the ways the world might have been. When he finally reaches the best of all of them, he chooses to make that one real. Philosophers call that "actualizing" or "instantiating" that world. So this is the only real world, but the others exist as ideas in the mind of God. When you say "I could have been a rock star" you are saying that there is an idea in the mind of God, and in that idea, you are a rock star. Unfortunately, that world was not the best of all possible worlds, and hence you are actually stuck with only dreams.

Possible worlds lay dormant as a philosophical tool until revived by Saul Kripke in the 1950's and 60's. In order to deal with a difficult problem in Modal Logic (defining validity, and hence providing a semantics, for those curious), he reintroduced the notion of a possible world. Pressed later on their metaphysical stauts, Kripke said that a possible world simply was a counterfactual situation. A counterfactual is a conditional (if-then claim) where the antecedent is false. Example: If Germany had won the war, blah blah blah. That stipulates a possible world where Germany did win the war. On his view, these do not exist as ideas in the mind of God, or any where else. However, if possible worlds do not exist, in what way do they make modal claims true?

Enter David Lewis. Lewis (and I'm not making this up) was reading a work of science fiction in which someone creates a new invention which allows people to travel to other possible worlds. Inspired by this, Lewis defends what he calls "Modal Realism," the view that other possible worlds exist exactly like this one, just in a different space-time. Real people, real situations. What happens in those other worlds makes our claim about what might have been true. Our world is the actual world for us, but our world is a possible world for them, and their world is their actual world. For anything that you think might have been, there is a world, which exists just like this one, where that actually happened.

Actualism is the view that the only thing that exists is the actual world, and actualists reject Lewis's views. More next week, if there is any interest.


ce said...

There is interest, if you're wanting verification of that fact.

Hanno said...

I do, I do!

Anonymous said...

there is a world in which I am interested, is it this one?

Hanno said...

Could be.

Anonymous said...

There must there be a possible world in which it is possible that it is necessary that I am interested, right? And if it is possible that it is necessary that I am interested, then I am interested. Therefore, I am interested.

Anonymous said...

Are there any limits on "the way the world might have been" in God's mind? That is, are ALL worlds possible? Or, are some possible worlds not possible? If not, why not? I think L would say that not all possible worlds are possible, right?

Hanno said...

All possible worlds are possible, by definition. Now, there is a notion important in modal logic and modal discourse called "relative possibility." A possible world is relative to another possible world, and not to others. For a sentence "possibly P" to be true at a world A, P must be true not merely in a possible world, but in a possible world relative to A. So once Aristotle is part of this world, the only possible worlds relative to this one are ones that contain Aristotle, since give that Aristotle exists, it is impossible for him not to exist. That is true despite the existence of possible worlds where there is no Aristotle.

That does not go to the heart of your question. They typical limit that everyone agrees with on possibility is consistency, though that will be spelled out in different ways. Technically, if a world is made up not of sentences but of say states of affairs, then consistency (a property of sets of sentences) does not apply, but informally, inconsistent states of affairs are not acceptable candidates for possible worlds. Other philosophers add more criteria to this.

Lewis, however, always reverses this: it is possible worlds that defines every notion of what is possible.

ce said...

But isn't it possible to use other aspects that are relevant in discussing possible worlds? That is, Aristotle had jack all to do with the Peloponesian War ('twas before his time anyway), and so he does not seem relevant is discussing how the war played out in a possible world.

Thus, "what if" questions in regards to the Peloponnesian War, do not seem bound by any concern for Aristotle. So is Aristotle important when making "what if" claims about the Peloponnesian War? It seems that we could discuss a lot of non-Aristotelian worlds, and make perfect sense of the scenarios presented, provided Aristotle just isn't essential to those events.

As such, I'm not sure why we'd consider such a non-Aristotelian world non-relative to our own, provided all relevant (perhaps read as essential/necessary) factors are present. And so, could you elucidate on the importance of "relative" as you're using it?

Hanno said...

My response was long and got eaten up. grrrrr

Hanno said...

There are possible worlds in which the Peloponnesian War (why did you pick such a big word? And it wasn't so much before his time.) happened and there is an Aristotle, and ones in which it happened and there is no Aristotle. When considering the possibilities, the worlds in which there is or is not an Aristotle make no difference, you are correct. But how will we know this? Because whatever claims we make about what might have been with regards to the Peloponnesian War will have the exact same thing happen wither or not there is an Aristotle, which shows Aristotle's irrelevance to the question.

This has little to do with the relative notion of possibility, which is a logically technical device to handle certain features of the semantics for modal logic, as I will try to explain, though a blog is perhaps not the best place for this.