On 19 May 2012, at 19:17, Stephen P. King wrote:

On 5/19/2012 4:06 AM, Bruno Marchal wrote:

Stephen,

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.

Bruno


 Dear Bruno,

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
four  dimensions."

    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 general algorithms?


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 computations.

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.


Bruno


http://iridia.ulb.ac.be/~marchal/



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