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`

`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.`

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.`

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.`

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?`

`I personally find an extrapolation of a working model outside of its`

`scope that has been researched pretty dangerous.`

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