Re: modal logic and possible worlds

From: Wei Dai <weidai.domain.name.hidden>
Date: Mon, 12 Aug 2002 23:18:13 -0700

Tim, I'm afraid I still don't understand you.

On Mon, Aug 12, 2002 at 06:00:26PM -0700, Tim May wrote:
> It is possible that WWIII will happen before the end of this year. In
> one possible world, A, many things are one way...burned, melted,
> destroyed, etc. In another possible world, B, things are dramatically
> different.

Ok, but what about my point that you can state this by explicit
quantification over possible worlds rather than using modal operators?
I.e., "There exist a world accessible from this one where WWIII happens
before the end of this year." instead of "It is possible that WWIII will
happen before the end of this year."?

> There can be no implication from one world to the other. That is, we
> can't say "A implies B" or "B implies A."

What does that have to do with my question? Anyway A and B are supposed to
be worlds here, not propositions, so of course you can't say "A implies
B". I don't know what point you're trying to make here.

> This branching future is exactly what I was talking about a week or so
> ago in terms of "partially ordered sets." If the order relationship is
> "occurs before or at the same time as," which is equivalent to "less
> than or equal to," A and B cannot be linearly ordered. In fact, since
> both A and B are completely different states, neither can be said to be
> a predecessor or parent of the other. In fact, A and B are not
> comparable.

I'm with you so far in this paragraph.

> We cannot say "A or not-A."

Now I'm lost again. Again A is a world not a proposition so what would "A
or not-A" mean even if A and B are comparable?

If anyone else understand the point Tim is making please help me out...
Received on Mon Aug 12 2002 - 23:19:54 PDT