Title: Re: modal logic and possible
worlds
George Levy wrote:
I have been following the latest
very scholarly exchange involving different logical models in relation
to the MWI, however I fail to see how it relates to my own perception
of the world and my own consciousness unless I think
Wei Dai wrote:
Thank you for the explanation on S4, IL, and CL. I'm interested in
more details, but rather than bombarding you with endless questions, can
you suggest a book on this topic? Something that talks about
what you just did, but in more detail?
BM:
Try perhaps the book by Van Dalen
- Original Message -
From:
George Levy
To: [EMAIL PROTECTED]
Sent: Friday, August 16, 2002 7:39
PM
Subject: Re: modal logic and possible
worlds
I have been following the latest very scholarly exchange
involving different logical models in relation to the MWI, however I fail
Thank you for the explanation on S4, IL, and CL. I'm interested in
more details, but rather than bombarding you with endless questions, can
you suggest a book on this topic? Something that talks about
what you just did, but in more detail?
Unfortunately I'm still not able to understand much
pecially when
even newer ideas coincide).
I agree with you here. I have been somewhat imprecise.
George
007f01c24609$8a1cfa00$5e76d03f@default">
- Original Message -
From:George
Levy
To:
[EMAIL PROTECTED]
On Saturday, August 17, 2002, at 08:06 PM, George Levy wrote:
The arbitrariness of my, your or anybody's own mind point to the
need for the relativistic approach which I have been advocating. The
frame of reference here is the logical system residing in the
observer's mind. It may not be
At 10:29 -0700 13/08/2002, Wei Dai wrote:
Does it mean anything that S4 and intuitionistic propositional
calculus (= 0-order intutionistic logic, right?) ...
Right.
have the same kind of models, or is
it just a coincidence? I guess Tim is saying that it does mean something,
but I
At 10:11 -0700 14/08/2002, Wei Dai wrote:
Let me generalize my question then. Is it true that for any modal logic
that has a semantics, any sentence in that logic has a corresponding
sentence in non-modal quantificational logic with the same meaning?
It depends of the semantics. It depends of
I have been following the latest very scholarly exchange involving different
logical models in relation to the MWI, however I fail to see how it relates
to my own perception of the world and my own consciousness unless I think
according to those formal systems which I think is unlikely.
Using
Wei Dai wrote:
Thanks for your answers. They are very helpful.
Y're welcome. I want just add something.
Your general question was Why using modal logic when
quantifying on worlds is enough. My basic answer was
that Kripke's possible world semantics works only on a
subset of the possible
Hi Tim, just some quick comments.
On Tue, Aug 13, 2002 at 10:08:50AM -0700, Tim May wrote:
* Because toposes are essentially mathematical universes in which
various bits and pieces of mathematics can be assumed. A topos in which
Euclid's Fifth Postulate is true, and many in which it is
On Wed, Aug 14, 2002 at 04:38:45PM +0200, Bruno Marchal wrote:
Your general question was Why using modal logic when
quantifying on worlds is enough. My basic answer was
that Kripke's possible world semantics works only on a
subset of the possible modal logics.
Let me generalize my question
Bruno probably does, but I'll put my spin on it. Each distinguishable
world is a description*, which is a conjunction of propositions I
have green eyes _and_ I live in Sydney _and_ the twin towers were
destroyed by airliners on 11/9/2002 _and_ ..., and as such is a
proposition. I'm not completely
Wei Dai wrote:
According to possible world semantics, it's necessary that P means that
P is true in all worlds accessible from this one. Different modal logics
correspond to different restrictions on the accessibility relation. Before
the invention of possible world semantics, people argued
On Monday, August 12, 2002, at 11:41 PM, Russell Standish wrote:
Bruno probably does, but I'll put my spin on it. Each distinguishable
world is a description*, which is a conjunction of propositions I
have green eyes _and_ I live in Sydney _and_ the twin towers were
destroyed by airliners
On Tuesday, August 13, 2002, at 10:08 AM, Tim May wrote:
This graph, this set of vertices and edges, is a per-ordered set.
More than just a set, any category with the property that between any
two objects p and q there is AT MOST one arrow p -- q is said to
be pre-ordered.
I meant to
On Monday, August 12, 2002, at 11:18 PM, Wei Dai wrote:
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,
Tim, I think I'm starting to understand what you're saying. However, it
still seems that anything you can do with intuitionistic logic, toposes,
etc., can also be done with classical logic and set theory. (I'm not
confident about this, but see my previous post in reponse to Bruno.) Maybe
it's not
On Tuesday, August 13, 2002, at 02:34 PM, Wei Dai wrote:
Tim, I think I'm starting to understand what you're saying. However, it
still seems that anything you can do with intuitionistic logic, toposes,
etc., can also be done with classical logic and set theory. (I'm not
confident about
On Tue, Aug 13, 2002 at 10:08:50AM -0700, Tim May wrote:
* Because toposes are essentially mathematical universes in which
various bits and pieces of mathematics can be assumed. A topos in which
Euclid's Fifth Postulate is true, and many in which it is not. A topos
where all functions are
On Tuesday, August 13, 2002, at 06:16 PM, Wei Dai wrote:
On Tue, Aug 13, 2002 at 10:08:50AM -0700, Tim May wrote:
* Because toposes are essentially mathematical universes in which
various bits and pieces of mathematics can be assumed. A topos in which
Euclid's Fifth Postulate is true, and
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
On Tuesday, August 13, 2002, at 08:47 PM, Wei Dai wrote:
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
On Monday, August 12, 2002, at 12:07 PM, Wei Dai wrote:
According to possible world semantics, it's necessary that P means
that
P is true in all worlds accessible from this one. Different modal logics
correspond to different restrictions on the accessibility relation.
Before
the
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
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