On 19 Nov 2014, at 02:07, LizR wrote:
According to Wikipaedia...
In mathematical logic, Löb's theorem states that in a theory with
Peano arithmetic, for any formula P, if it is provable that "if P is
provable then P is true", then P is provable.
I.e.
where Bew(#P) means that the formula P with Gödel number #P is
provable.
That is correct.
...I have not the remotest idea how one would apply that to a
corporation (or a person, indeed).
It applies to what I call "third person", where the person is
identified with her set of beliefs, and the beliefs are defined by
recursion and extends the belief in the axiom of Robinson
Arithmetic(*). It will apply on all arithmetical en mechanical sound
extension. So if you believe in the axiom of RA (which I hope for
you), and if you are a machine, then assuming you are also
arithmetically sound, it applies to you.
But it does not apply to the first person, defined by the Theaetetus
definition (here: []p = "Bew(#P) & P ").
Indeed, in this case we do have []p -> p, for all p, and if Löb's
theorem was correct for it, all first person would be inconsistent.
Bruno
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
