Re: modal logic and possible worlds

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 13 Aug 2002 20:47:02 -0700

On Tue, Aug 13, 2002 at 03:51:49PM -0700, Tim May wrote:
> I also don't know what your goals are, despite reading many of your
> posts. If, for example, you are looking for tools to understand a
> possible multiverse, or how multiverses in general might be constructed,
> I'm not at all sure any such tools have ever existed or _will_ ever
> exist, except insofar as tools for understanding toposes, lattices, etc.
> exist.

I think the theory of everything is a multiverse theory. So I want to
understand the implications that following from the idea that multiple
universes exist. These include philosophical, practical, and scientific
implications. Right now I really want to know the answers to these
questions:

1. What do probabilities mean? 2. How should one reason and make
decisions? 3. What is the structure of the multiverse? Which class of
universes does it contain? For example does it contain non-computable
universes?

1 and 2 are philosophical questions, but clearly very practically
relevant. For 3, I'm only interested in the coarsest level of detail for
now. It needs to be answered because the answer makes a difference for
question 2.

> The MWI/Tegmark/Egan stuff is very far out on the fringes, as we know,
> and there is unlikely to be anything one can do calculations of. Still,
> it seems likely that a _lot_ of mathematics is needed...a lot more math
> than physics, almost certainly.

I think there are a lot of philosophical and practical questions that
can be answered without detailed investigation into the fine structure of
the multiverse. Certainly understanding the fine structure, including the
structure of all of the universes that it contains, requires a lot of math
(in fact it requires ALL of math if Tegmark is correct), but I'll leave
that to the future.

> Modal logic seems to me to be _exactly_ the right logic for talking
> about possible states of existence, for talking about possible worlds,
> for talking about branching universes. So the issue is not "But can't I
> find a way to do everything in ordinary logic?" but is, rather, to think
> in terms of modal logic offering a more efficient "basis" (in the
> conceptual vector space), a basis with a smaller semantic gap between
> the formalism and the hypothesized world.

I don't know. When I hear a modal sentence, I have to interpret it in
terms of possible worlds. It seems easier to just talk directly about
possible worlds. I haven't seen where the efficiency comes from. I'm sure
it is more efficient for some purposes, but I'm not convinced that it is
for mine.

> Seen this way, category and topos theory are worth studying for their
> own sake. I don't think it is likely that "every conceivable universe
> with consistent laws of mathematics has actual existence" (to nutshell
> my understanding of Tegmark's theory) is actually true (whatever that
> means). Nor do I take Schmidhuber's "all running programs" notion very
> seriously. Interesting ideas to play with, and to use some tools on.

Well why don't you take these ideas seriously?
Received on Tue Aug 13 2002 - 20:48:19 PDT