On 26 May 2012, at 16:48, Evgenii Rudnyi wrote:

On 26.05.2012 11:30 Bruno Marchal said the following:

On 26 May 2012, at 08:47, Evgenii Rudnyi wrote:

...

In my view, it would be nicer to treat such a question
historically. Your position based on your theorem, after all, is
one of possible positions.

What do you mean by "my position"? I don't think I defend a position.
I do study the consequence of comp, if only to give a chance to a
real non-comp theory.

A position that the natural numbers are the foundation of the world.

I don't defend that position. I show it to be a consequence of the comp hypothesis + occam razor.



I agree that you often repeat the assumption for your theorem but I believe that your answers to my question have been answered exactly from such a position.

That is possible, that is why I repeat ad nauseam that I assume comp, not that I defend that theory, only that that it is testable. It gives also a rational alternative with less magic notion, like primitive matter, or consciousness.

UDA is an argument showing that if the brain (in a large sense) is a machine at some level, then the natural numbers, or their universal cousins, are the foundation of the web of interfering computations on worlds supervenes.






In your paper to express your position you employ a normal human
language. Hence I believe that that the question about general
terms in the human language is the same as about the natural
numbers.

? (I can agree and disagree, it is too vague)

When we talk with each other and make proofs we use a human language. Hence to make sure that we can make universal proofs by means of a human language, it might be good to reach an agreement on what it is.

This is an impossible task. That is why I use the semi-axiomatic method (in UDA), and math in AUDA. If you disagree with a method of reasoning, you have to explain why. In english, no problem.




Again, the ideal world of Plato was not designed for natural
numbers only.

Sure. Although it begins with "natural numbers only", and it ended on
this, somehow, because the neoplatonists were aware of the
importance of numbers and were coming back to Pythagorean form of
platonism.

Now, with comp, or just with Church thesis, there is a sort of
rehabilitation of the Pythagorean view, for the "non natural numbers"
reappears in the natural number realm as unavoidable epistemic tools
for the natural numbers to understand themselves, and anymore than
numbers (and their basic laws) is not just unnecessary, it is that it
cannot work without adding some explicit non-comp magic.

I am not against non-comp, but I am against any gap-theory, where we
introduce something in the ontology to make a problem unsolvable
leading to "don't ask" policy.

We are back to a human language. It seems that you mean that some constructions expressed by it do not make sense. It well might be but again we have to discuss the language then.

I don't see why we have to discuss language, apart from the machines and their languages.



As for comp, I have written once

Simulation Hypothesis and Simulation Technology
http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html

that practically speaking it just does not work. I understand that you talk in principle but how could we know if comp in principle is true if we cannot check it in practice?

The whole point is that we can check it, at least if you accept the classical theory of knowledge. Physics arise from number self- reference in a precise constrained way, and the logic of observable already give rise to quantum-like logic. If mechanism is false, we can know it. If it is true we can only bet on it, and the bet or not on some level of substitution. The facts (Everett QM) gives evidence that our first person plural is given by the electronic orbital, our stories does not depend on the precise position of electron in those orbitals.



I personally find an extrapolation of a working model outside of its scope that has been researched pretty dangerous.

I am just showing that computationalism (widespread) and materialism (widespread) are incompatible. I reason only, and I extrapolate less than Aristotelians.

Bruno


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



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