Le 12-nov.-05, à 14:53, uv a écrit :
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
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" ?
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
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 & 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
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
the novelty of mathematical logic for the physicists. I know
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.
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!
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?