On 07 Aug 2015, at 08:26, Evgenii Rudnyi wrote:
Leibniz' note on his Dialogs:
When God calculates and thinks things through, the world is made.
Cum Deus calculat et cogitationem exercet, mundus fit.
I have found it in M. Heller, Ultimate Explanations of the Universe.
OK, but in the universal machine religion this is very close to a
blasphemy, as it tend to associate God with the Computer (RA, the
Universal dovetailler).
But it is true ... if we are self-referentially correct machine. But
this is something we cannot claim, nor even express, and that's why
this talk belongs to G* \ G.
You can see that blasphemy here like deciding that "true = provable",
and that is correct for the comp sigma-1 sentences.
For p sigma_1 you have both:
p -> []p
and
[]p -> p
but if the Löbian machine is indeed able to prove (for p sigma_1) that
p -> []p, the reverse, []p -> p remains true but unprovable by the
self-referentially correct machine, and cannot be claimed true at the
same level of p->[]p.
We do have p <-> []p, which is arguably what Heller said above, but it
would lead to inconsistency or triviality if we forget that []p -> p
can only be true in the eyes of God, and never provable by any finite
creature (when self-referentially correct).
Yes, Leibniz get close to computationalism's consequence, no doubt. he
got close to computationalism itself, but miss the digital machine's
modern definition. he could not seen Church's thesis and the closure
for diagonalization. In a sense, Babbage get closer.
Bruno
Evgenii
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