Possible Worlds II

We were talking about possible worlds being relative to other possible worlds, not relevant, and this is a technical term.

First, for most philosophers, all possible worlds are relative to all possible worlds. This has a consequence that it is governed by a formal logical system called S-5. If not all worlds are possible to all possible worlds, then weaker systems of logic govern our inferences. This is precisely what Kripke showed in his published work in the 1950's, when he was 18(!).

It follows in S-5 that anything which is possibly necessary is actually necessary. this has been used to prove God's existence in a version of the Ontological argument. God, if he exists, has the property of being a necessary being. It is possible that there is a God. Therefore, it is possible that a necessary being exists. By S-5, God is actually necessary, and and since anything which is necessary is true, God exists in this world, too.

Other philosophers deny that all possible worlds are possible relative to all possible worlds. Aristotle might not have existed. So there is a world at which there is no Aristotle. At that world, is it possible that Aristotle's son existed? What does it mean to say that some non-existent thing might have existed? In response to these kinds of questions, they deny the universal connection between possible worlds. Worlds in which Aristotle exists are not possible from worlds in which Aristotle does not exist, though the reverse does not hold. If that is right, the logic of modality is not S-5, but something weaker (S-4, for those who are counting) and it no longer follows that just because something is possible that it is necessarily possible, nor does it follow that something that is possibly necessary is actually necessary.

I am looking at my car. It is possible for it to start. But is it necessarily possible for it to start? On one way of looking at things, no, because it is possible for the engine block to be totally ruined. Spelling that out in possible worlds means some possible worlds are not possible from all possible worlds. It is possible that Aristotle exists. But is it necessarily possible? What if human beings never develop? What if the world blew up before humans ever appear on the world stage? Then there would still be a possible world in which Aristotle exists ("Aristotle might have existed" is true), but that world would not be relatively possible from worlds where the world blows up before humans arrive on the scene. Hence we can say Aristotle could not exist if the world blew up before humans arrive on the scene, even though he might exist in other circumstances.

Hope that helps.

I was going to post more on the metaphysics of modality, but ce side tracked me. Blame him. Will try to do that Monday.