Le 23-févr.-06, à 07:32, Kim Jones a écrit :

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The Loebian machine only believes the truth, yes? Not a pack ofBiblical lies, surely?

`Not necessarily, or ... Well, not so easy to describe in few words. The`

`sound loebian machine believes the truth. True. But then the *sound*`

`<any-entity> only believes the truth, by definition. And then the`

`loebian machine is modest in the sense that she believes she is`

`accurate (true, correct) with respect to some proposition only when she`

`actually prove that proposition.`

Christians have to get their heads sorted out on what is real and whatis not real. This is what the book deals with largely.

`But who are we to pretend being able to sort out what is real and what`

`is not real? Certainly not a sound loebian machine, which can guess`

`somehow how far the real can be from her ratiocination. Better, the`

`sound loebian machine knows that if she takes the real from granted`

`then she is provably going into the false.`

`The loebian machine knows that there are some truth which would be`

`wrong once she takes it as axiom. "comp" belongs to that type, and that`

`is why I insist that "comp" is more than just an hypothesis. It needs`

`some "act of faith".`

`There is nothing magical. The phenomenon results from the fact that the`

`machine or the theory (or the entity) has some third person`

`description. To take a trivial example, consider the theory which has`

`as unique axiom:`

"1 + 1 = 2"

`Now that theory has only one axiom, OK? So it is true that that theory`

`has only one axiom, OK? Let us add the true formula "the theory has`

`only one axiom" to the theory. This gives a new theory saying:`

"1 + 1 = 2" "The theory has only one axiom" Now the second axiom is plainly false.

`You can see G*, the "divine intellect" as an exhaustive catalog of true`

`propositions, which, if added without caution to the entity's`

`collection of beliefs, would make the entity inconsistent.`

`The loebian machine can learn to guess that not all truth can be taken`

`freely as axiom. Some truth remains forever undecided. Those truth can`

`be hoped for, but should never be taken as granted, because if they`

`are, they become false. Self-consistency (~Bf), and soundness (Bp -> p)`

`are of that type. Those proposition are true ... as far as we doubt`

`them.`

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