Le 18-nov.-05, à 20:39, Stephen Paul King a écrit :

Dear Bruno,Are you claiming that the communicable part is to thenon-communicablepart 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/