On 19 Jan 2014, at 00:33, Russell Standish wrote:
On Tue, Jan 14, 2014 at 10:11:50AM +0100, Bruno Marchal wrote:
Comp does not need actual infinities, but it still needs the
potential infinity of all finite things (integers, or something).
But finitist physicalism
Oops! I meant "ultrafinistism". The idea that the big thing is a
finite thing, like in step seven, or apparently in Edgar's ontology.
is indeed a way out of comp. But then your
theory is non-computationalist. Do you say "no" to the doctor. You
have already answer "no", and later "yes", so I am not sure. Which
is it?
I would agree that finitism contradicts comp, because it contradicts
arithmetic realism
Ultrafinitism, yes.
(some numbers are not as real as others), but why
do you suggest that finitism contradicts "Yes doctor"?
Ultrafinitist physicalism is handled by step 8 (MGA).
It can be handled by a stronger use of Occam razor already in step
seven, instead.
(To be sure I don't like the idea that the infinitely many creatures
which provably exist and have "life" in arithmetic would be zombie.
(but that's between us)).
In a sense, those creatures are sort of zombies, because from their
own first personal views, they exist on the limit measure on
infinitely many computations, and that's something nobody can see.
Yet, it has a complex mathematics of its own, whose propositional part
is given by the variants of G and G* (assuming classical standard
definitions of belief and knowledge). (for the ideally correct machine).
Bruno
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Principal, High Performance Coders
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