Saibal wrote:
>An interesting article by Ken Olum can be obtained from:
>
>http://xxx.lanl.gov/abs/gr-qc/0009081
>
>In short you don't get any information by observing your age, because you
>made two observations:
>
>1) I exist
>
>2) I am one year old
>
>When you compute your updated probability distribution according to Bayes'
>theorem by taking into account 1) and 2), you find that the updated
>probability distribution is the same as the original one.
>
>The mistake is to use 2) and omit 1).
>
>Nick Bostrom has argued against including 1) (Self Indicating Axiom) in
>Bayesan reasoning. This leads to all sorts of nonsensical results. E.g.:
> [...]
Interesting paper, thanks. I appreciate very much the idea to
put "existing" and possible on the same setting. It is that very
idea that I translate in arithmetic,
when I go from the thaetetus idea of 1-knowledge, where p is known if p
is provable and true:
provable(p) & p ([]p & p)
toward the 1-plural measure:
provable(p) & consistent(p) ([]p & <>p)
Consistency is the arithmetical version of possibility.
Note that G* can prove that provable(p) entails p, and provable(p)
entails consistent(p). But G, which represents the machine from its
own perspective cannot. (ex: The machine cannot prove
provable(f) -> f
because this is equivalent to "not provable(f)" which is equivalent to
its consistency, which is unprovable (by the consistent machine)).
Bruno
PS I hope everyone can verify with truth table that (p -> f) is
equivalent with (not p). I recall f is the constant false, and t
is the constant true.
Received on Sat Sep 15 2001 - 09:52:09 PDT