Le 20-juil.-06, à 13:46, Russell Standish a écrit :
> Bruno, I know in your theory that introspection is a vital component > (the Goedel-like constructions), but I didn't see how this turns back > onto the self-awareness issue. Did you develop this side of the > argument? Yes sure. The Goedel-like construction can handle only a 3-person discursive self-reference. A little like if you where reasoning on some 3-description of your brain or body with your doctor, although it could be also an high level 3-description (like I have a head). The Goedel construction leads to the modal logic G, where the atomic propositions "p" are interpreted by arithmetical sentences, and the modal box "B" by the Goedel provability predicate. So, for example, with f the logical constant FALSE, and "~" = negation, Goedel second incompleteness can be written ~Bf -> ~B ~Bf you can read like the machine says that if the false is provable by er, then that very fact (that the false is not provable) is itself not provable. But "B" is only one among many notion of person, and G corresponds to an intellectual, discursive, 3-describable, scientific if you want, sort of self-referential discourse. G* also, but G* got the whole truth (at this propositional level thanks to Solovay theorem). Consciousness and first person self-awareness will correspond to "theaetetical weakening" of that Goedlian provability notion, besides the arithmetical version of comp. Mainly: Bp & p Bp & ~B~p Bp & ~B~p & p or if you abbreviate ~B~p by the diamond: Dp,: Bp & p Bp & Dp Bp & Dp & p Although G* can prove the arithmetical equivalence of those "provability predicates", G cannot prove them equivalent, and they will give rise to different modal logics corresponding to different internal perception of number-truth. Bp & p gives a temporal knower in an branching multiverse, Bp & Dp gives rise to a quantum sort of sharable credibility or a bottom symmetrical multiverse, etc. Actually, thanks to the nuances you inherit from the corona G* \ G, those "hypostases" are divided into sharable and no sharable part making quanta particular case of qualia. I will come back on the correspondence later. The key point is that the nuance between p, Bp, Bp & p, Bp & Dp, Bp & Dp & p, are imposed by the incompleteness phenomenon, and self-awareness corresponds to the one having " & p" in their definition. It is the umbilical chord between "truth" and intellect of the "reasonable" first person. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
