Important typo error in my reply to John (Mikes):
On 12 Jul 2014, at 10:08, Bruno Marchal wrote, notably in reply to
John M when he wrote:
> Please add to every one of my sentences in ( - ) "I dunno".
Instead of:
That is wise, but by asking more than arithmetic (the reality, not
the theories), you seem to miss a "I dunno". Keep in mind that
before Gödel, we thought that arithmetic was computable, but now, we
know that only a tiny part is computable. That part is enough (when
we postulate comp), but for the internal epistemologies, we need the
"complete" arithmetical reality which is PROBABLY beyond all
theories, made by humans or aliens, or even a vast variety of divine
entities (divine here means "non-machine emulable"). The
arithmetical truth is inexhaustible. It is far beyond us.
Read:
"That is wise, but by asking more than arithmetic (the reality, not
the theories), you seem to miss a "I dunno". Keep in mind that before
Gödel, we thought that arithmetic was computable, but now, we know
that only a tiny part is computable. That part is enough (when we
postulate comp), but for the internal epistemologies, we need the
"complete" arithmetical reality which is PROVABLY beyond all theories,
made by humans or aliens, or even a vast variety of divine entities
(divine here means "non-machine emulable"). The arithmetical truth is
inexhaustible. It is far beyond us."
The "V" is too close to the "B" on the keyboard!
It is the beauty and importance of Löbianity: Lôbian machines are
clever enough to *prove* that they have intrinsic limitation with
respect to truth, notably about the truth concerning themselves, they
understand "agnostic", and the wiser *are* agnostic and can even
explain why. (using just the arithmetical interpretation of the
classical definition of the field).
Bruno
http://iridia.ulb.ac.be/~marchal/
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