Saibal wrote:

>An interesting article by Ken Olum can be obtained from:
>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)).


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.

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