Le 12-nov.-05, à 14:53, uv a écrit :
> [bruno]
>> Now, the "real" important things to grasp for
>> making clear the way I use modal logic, consists in understanding
>> the theorem of Solovay. Have you heard about it? It generalizes
>> in some way
>> the theorem of Godel and the theorem of Lob. it makes precise the
>> connection between modal logic and the logic of arithmetical
>> reference.
>
> [uv]
> I understand that "Solovay's theorem is so significant because it
> shows that an interesting fragment of an undecidable formal
> theory like Peano Arithmetic -- namely that which arithmetic
> can express in propositional terms about its own provability
> predicate -- can be studied by means of a decidable modal logic,
> GL, with a perspicuous possible worlds semantics." As such
> it should be very relevant, I most certainly agree
> - but how does it relate to "quantum suicide" ?
>
> [uv]
> I could not work out how it relates to quantum suicide and first
> or third persons in your papers "mechanism and personal
> identity" or "amoeba, planaria and dreaming machines" or
> "Computation,Consciousness and the Quantum" or "The Origin of
> Physical Laws and Sensations" but the logic of the matter has to
> be considered, as you say.
Indeed the link with quantum suicide and comp suicide are in my older
paper "Informatique théorique et philosophie de l'esprit, Toulouse
1988". Also explained in my 1991 paper "Mechanism and personal
identity".
With Kripke, to say Bp is true in the observer moment (OM) alpha means
p is true in each accessible from alpha observer moment beta. The
problem is that with comp, or just with the lobian interview, each OM
can access to a cul-de-sac world (Dt -> DBf). In cul-de-sac worlds, it
follows by elementary classical propositional calculus that Bf is true,
so Bp cannot be taken as the probability of p is one. So we have to
postulated explicitly the consistency of the the proposition we are
proving, and this correspond to the passage from
Bp, to
Bp & Dp
The second Theatetic trick! Define a new bow Cp by Bp & Dp in G.
Now G* (the propositional truth theory on the machine's
provability/consistency) proves that Bp is equivalent with Bp & Dp. But
the machine itself (G) cannot, and this makes the logic of Bp & Dp
quite different of G, and non trivial.
(And then the comp hyp itself can be shown equivalent with adding "p ->
Bp" to G, then if comp is true the logic should give the "propositional
physics", and give indeed already logics belonging to the family of
quantum logics.
>
> [bruno]
>> If you are interested I could try to say more, and that could
>> perhaps helps me to present the result I thjink I got. I do have
>> underestimated
>> the novelty of mathematical logic for the physicists. I know
>> physicists
>> who have a rather good understanding of the incompleteness theorems,
>> but I realize they does not know the completeness theorems, which is
>> indeed the background making what logic really consists in. Other
>> people asks me similar questions so that I will try to post better
>> synthetical summary of what I have try (at least) to communicate.
>>
>> Bruno
>
> [uv]
> Anything you can add on quantum suicide seems interesting to me.
> In particular, where does the difference between death and loss
> of consciousness fit in, for example?
3-death and 3-loss of consciousness are alike, except we can have more
hope in the latter. 1-death and 1-loss-of-consciousness have no
meaning, I would say, although lack of coffee in the morning can create
some trouble which we could easily confuse with some first person
paradoxical apprehension of its own lack of consciousness, like a
zombies complaining nobody want to believe they are zombies!
>
> [uv]
> And does it make all that much difference in that scheme whether
> a person is PERMANENTLY removed from the system or just
> REMOVED FOR A SPACE.
Remember I don't postulate a physical primitive world.
> There are a lot of ways that can
> be done, possibly with very different parameters. (e.g. like in
> Parfit's conjectures, which involved identity in even very
> specific examples like say a long spell in prison). Something like
> 30-40% of people get hypnagogic myoclonus and that is
> another (slightly differing) case.
Could you tell me what is a myoclonus?
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Sat Nov 12 2005 - 10:41:50 PST