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