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/


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