On 26.05.2012 21:06 Bruno Marchal said the following:

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

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

I do appreciate the clearness of your position. From this viewpoint, the language of mathematics allows us to remove ambiguities indeed.


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.

I also agree that human language in a way is a mess. Yet, somehow it seems to work and this puzzles my, how it could happen when even mathematicians failed to analyze it.


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.

It seems that there is a gap between the language of mathematics and a human language. It might be interesting to understand it. It might give us a hint on how the Universe is made. You see, we must use a human language to communicate, with the language of mathematics this would not work. I do not know why.

As for comp, I have written once

Simulation Hypothesis and Simulation Technology

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.

I am afraid that reason only is not enough to understand Nature. I am browsing now The Soul of Science: Christian Faith and Natural Philosophy. Let me give a quote that in an enjoyable way expresses my thought above.

p. 19 "In 1277 Etienne Tempier, Bishop of Paris, issued a condemnation of several theses derived from Aristotelianism - that God could not allow any form of planetary motion other than circular, that He could not make a vacuum, and many more. The condemnation of 1277 helped inspire a form of theology known as voluntarism, which admitted no limitations on God’s power. It regarded natural law not as Forms inherent within nature but as divine commands imposed from outside nature. Voluntarism insisted that the structure of the universe - indeed, its very existence - is not rationally necessary but is contingent upon the free and transcendent will of God."

"One of the most important consequences of voluntarist theology for science is that it helped to inspire and justify an experimental methodology. For if God created freely rather than by logical necessity, then we cannot gain knowledge of it by logical deduction (which traces necessary connections). Instead, we have to go out and look, to observe and experiment. As Barbour puts it:

'The world is orderly and dependable because God is trustworthy and not capricious; but the details of the world must be found by observation rather than rational deduction because God is free and did not have to create any particular kind of universe.'"


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