Le 18-nov.-05, à 20:39, Stephen Paul King a écrit :
> Dear Bruno,
>
> Are you claiming that the communicable part is to the
> non-communicable
> part as the classical is to the quantum?
Oops, no, sorry. My fault. I was trying to be short. You can see Godel,
Lob, Solovay discovery as the discovery that the *classical* logic of
self-reference is (already) divided into two parts, corresponding to
the provable and the unprovable. At their propositional levels,
Solovay, in 1975, showed that the modal logics G and G* capture soundly
and even completely the *provable* part of the logic of self-reference
and the *true* part, respectively. The purely unprovable (but true)
part is then given by G* \ G (the set difference of the theories).
"Provable" means provable by some fixed sufficiently rich machine, or
theory.
Now observation and knowledge are defined in the logics of
self-reference, i.e. by transformation of G and G*, and so are each
multiplied by two. Actually and amazingly for the knower (the first
person) G and G* give the same logic, like if the first person
conflates truth and provability. But for the notion of observation, G
and G* give again different logics, so that the observer can
distinguish communicable observations ("physical facts") and non
communicable observations (sensations, I would argue). But to be
honest, the quanta (or the shadows of the quanta) seems to appear at
the G* level, confirming "quantum physics" is a first person plural
notion, i.e. based on bets made by multiplication/differentiation of
populations of individuals; like in Everett (QM without collapse) where
superpositions are contagious to the observers.
To sum up, the difference provable/unprovable or
communicable/incommunicable is inherited by all the transformations of
G, except the one which gives the stronger notion of the first person.
(I guess this one *is* the solipsist who lives in each of us, the one
who needs some education or encouragement for learning to listen to the
"solipsist" living in the others).
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Sat Nov 19 2005 - 10:25:34 PST