Re: modal logic and possible worlds

2002-08-19 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-19 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-17 Thread jamikes
- 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

Re: modal logic and possible worlds

2002-08-17 Thread Wei Dai
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

Re: modal logic and possible worlds

2002-08-17 Thread George Levy
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]

Re: modal logic and possible worlds

2002-08-17 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-16 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-16 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-16 Thread George Levy
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

Re: modal logic and possible worlds

2002-08-14 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-14 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-14 Thread Wei Dai
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

Re: modal logic and possible worlds

2002-08-13 Thread Russell Standish
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

Re: modal logic and possible worlds

2002-08-13 Thread Bruno Marchal
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

Re: modal logic and possible worlds

2002-08-13 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-13 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-13 Thread Tim May
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,

Re: modal logic and possible worlds

2002-08-13 Thread Wei Dai
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

Re: modal logic and possible worlds

2002-08-13 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-13 Thread Wei Dai
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

Re: modal logic and possible worlds

2002-08-13 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-13 Thread Wei Dai
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

Re: modal logic and possible worlds

2002-08-13 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-12 Thread Tim May
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

Re: modal logic and possible worlds

2002-08-12 Thread Wei Dai
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