On 19 May 2012, at 19:17, Stephen P. King wrote:
On 5/19/2012 4:06 AM, Bruno Marchal wrote:
I presented an argument. Whatever you read, if it casts a doubt on
the validity of the argument, you have to use what you read
to find the invalid step.
If not, you act like so many papers pretending that cannabis is a
dangerous, but which are only speculation on plausible
danger, not proof.
A proof, both in math and in applied math in some theoretical
framework does not depend on any further research, by construction.
If you doubt about immaterialism, by reading on Markow (say), then
you might find a way to use Markov against computationalism, or you
must make precise which step in the reasoning you are doubting and
why, and this without doing interpretation or using philosophy.
If not, you confuse science and philosophy, which is easy when the
scientific method tackle a problem easily randed in philosophy, or
at the intersection of philosophy and science.
Now, I don't see why the work you mention has anything to do with
the immaterialism derived from comp. You might elaborate a lot.
I finally found a good and accessible paper that discusses my
bone of contention. To quote from it:
"A theorem proved by Markov on the non-classifiability of
the 4-manifolds implies
that, given some comprehensive specification for the topology
of a manifold (such as
its triangulation, a la Regge calculus, or instructions for
constructing it via cutting
and gluing simpler spaces) there exists no general
algorithm to decide whether the
manifold is homeomorphic to some other manifold [l]. The
impossibility of classifying
the 4-manifolds is a well-known topological result, the proof of
which, however, may
not be well known in the physics community. It is
potentially a result of profound
physical implications, as the universe certainly appears to
be a manifold of at least
The reference to the proof by Markov is:
Markov A. A. 1960 Proceedings of the International Congress of
Mathematicians, Edinburgh 1958
(edited by J. Todd Cambridge University Press, Cambridge) p 300
The point of this is that if the relation between a pair of 4-
manifolds is not related by a general algorithm, how then is it
coherent to say that our observed physical universe is the result of
But comp explained why it has to be like that. The observable universe
cannot be the result of general algorithm, given that it results from
a first person plural indeterminacy on infinite set of possible
By "computation" I mean a set of states together with an universal
number relating them.
The only thing proved by Markov here is that the homeomorphism
relation is not Turing decidable. It suggests that 4-manifold +
homeomorphism is Turing universal (as proved for braids). Any
intensional identity, for any Turing complete system is as well not
Turing decidable. There is no general algorithm saying that two
programs compute the same functions, or even run the "same" computation.
It is a well known result for logicians.
You don't give a clue what it has to do with immateriality. To be
franc, I doubt that there is any.
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