Le 14-juin-05, ā 00:35, George Levy a écrit :

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Bruno Marchal wrote:Godel's theorem: ~Bf -> ~B(~Bf), which is equivalent to B(Bf -> f) -> Bf,Just a little aside a la Descartes + Godel: (assume that "think" and"believe" are synonymous and that f = "you are")

`All right. Of course this follows that for any p in the language of the`

`machine, we have indeed that the machine can prove`

B(Bp -> p) -> Bp

`That is: the machine does prove its Lob's theorem. (in my post to`

`Brent f was the constant "FALSE").`

B(Bf -> f) -> Bf can be rendered as:If you believe that "if you think that you are therefore you are",then you think you are.

`Nice! This makes a relation between Lob's theorem (which generalizes`

`Godel's second incompleteness theorem) and Descartes systematic`

`doubting procedure. The link exists already with Godel's theorem. If`

`you look at the "arithmetical placebo phenomenon" (in my SANE paper),`

`you are relating Descartes and the Placebo. Quite cute!`

That's what Descartes thought!

`I agree essentially. See Slezak for a pionering and readable paper`

`relating Godel and Descartes:`

`SLEZAK P., 1983, Descartes 's Diagonal Deduction, Brit. J. Phil.`

`Sci. 34, pp. 13-36.`

`And this is related also with the debate on Godel and Mechanism`

`(against Penrose and Lucas), on which Slezak wrote a paper, which could`

`be needed for the reading of its Godelian reading of Descartes.`

`SLEZAK P., 1982, Gödel's Theorem and the Mind, Brit. J. Phil. Sci.`

`33, pp. 41-52.`

Bruno http://iridia.ulb.ac.be/~marchal/