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

The Loebian machine only believes the truth, yes? Not a pack of Biblical 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 what is 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.



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