On 07 Feb 2011, at 20:52, Andrew Soltau wrote:

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How do you define the relative point of view?Do you know Gödel's provability predicate? The points of view aredefined by intensional variants of the current provabilitypredicate of the machine with or without some oracle. There are 8basic points of view p (truth), Bp (provability/believability), Bp& p (knowability), Bp & Dp (observability), Bp & Dp & p(sensibility/feelability). Three of them inherits the G/G*splitting, making a total of 8. It is really 4 + 4*infinity,because the 'material points of view' (with Dp) admits themselvesgraded variants.I know *about* Gödel's provability predicate!

Good.

(Is the 'intensional' referred to here the 'attach' you used inanother email?)

Not really, although it is related.

`"Intensional" refers to the fact that if you define a provable(x) by`

`beweisbar(x) and x', where x' denote the proposition which has x as`

`Gôdel number, you define a probability "predicate", which is not`

`definable by the machine, or in arithmetic, yet proves exactly the`

`same proposition of arithmetic than the one provable. Provable(x) and`

`beweisbar(x) are intensional variant of provability. They are`

`extensionnally equivalent, but intensionnally different, a bit like`

`different algorithm can have the same behavior.`

`More simple beweisbar(x) & ~beweisbar(~x) is an intensional variant`

`of beweisbar(x).`

`Intensional variant of bewesibar(x) have been introduced by Rosser in`

`his elimination of Gödel's assumption of omega-completeness in the`

`proof of incompleteness of formal systems.`

I am still no clearer about how you define the machine, "with orwithout some oracle", and what defines the relative point of view.

`Oracle have been introduced by Turing for the study of the degree of`

`unsolvability. It is a package of usually infinite information,`

`typically not computable. The halting oracle provides the halting`

`information, that no computer can generate. The goal consisted in`

`showing that some problem remains non solvable, and that some function`

`remains uncomputable, even when powerful oracle are added, and this`

`has been used to study the degrees of unsolvability of arithmetical`

`and mathematical problems.`

`The UD generate all the oracles, like it dovetails on all the reals`

`(trivial exercise; yet people are often wrong on this because they`

`confuse the impossibility of enumerating the reals, with the`

`impossibility of generating them). Think about the iterated self-`

`duplication experiment.`

Given that you are defining 8 basic points of view in the abstract,applied to " intensional variants of the current provabilitypredicate of the machine with or without some oracle", it sounds abit, well, abstract. Could you be a bit more specific?

`I try to be more specific in sane04. May be we should start from that.`

`Or search hypostasis or hypostases in the archive, or "guardian`

`angel", etc.`

Read the book by Smullyan, and Boolos 1979 (simpler than Boolos 1993). Read perhaps the Theaetetus by Plato.

`In short you can say that I model "belief" or "opinion" by "formal`

`probability" (Bp). I define then knowledge, following Theaetetus by`

`the true opinion (Bp & p), observation by the consistent opinion (Bp &`

`Dp), and sensibility by the true consistent opinion (Bp & Dp & p).`

`Incompleteness motivates the initial model, even if it leads to a`

`restriction on the ideally correct machine. The whole thing provides`

`an arithmetical interpretation of Plotinus theory of the one, the`

`intellect and the soul + his double (intelligible and sensible) matter`

`theory. The arithmetical matter theory has been compared to the`

`current inferred theory of matter, and it looks, up to now, that`

`Nature is correct :)`

(correct with respect to comp and its neoplatonist rendering, for sure). 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 everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.