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.
Evgenii
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