On 19 Jan 2014, at 21:12, Stephen Paul King wrote:
Dear Bruno,
How do you deal with the fact that there are more than one self-
consistent theory where those theories contradict each other?
That is what explains the consciousness differentiation. Take the WM-
duplication, as basic example.
In Helsinki it is consistent that I will be in W (= <> W)
In Helsinki it is consistent that I will be in Moscow (= <>M)
In helsinki it is not consistent that "I will be in M and I will be in
M" (I = 1-I, of course, and "to be in" means "to be in immediately
after the duplication").
Then after the duplication, my consciousness differentiates into "Oh I
am the one in M" and "Oh, I am the one in W".
So the fact that there are different self-consistent theoretical
extensions can be used to explains what consciousness differentiated
on the many geographies.
The example is where one theory takes the continuum hypothesis as
true and another takes it as false.
This is far way out of comp. You might have taken Bf ([] false). This
and its negation are consistent with PA. But I would not count []f as
available as a world, because I do not identify worlds with model, nor
really with computations. I bypass that problem by using the theory of
knowledge of Theaetetus, invited in arithmetic by the incompleteness
theorem.
Bruno
On Sun, Jan 19, 2014 at 11:44 AM, Bruno Marchal <[email protected]>
wrote:
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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