On 23 May 2012, at 20:19, Evgenii Rudnyi wrote:

On 23.05.2012 20:01 Bruno Marchal said the following:

On 23 May 2012, at 19:19, Evgenii Rudnyi wrote:


Let us take terms like information, computation, etc. Are they
mental or mathematical?

Information is vague, and can be both.

Computation is mathematical, by using the Church (Turing Kleene Post
Markov) thesis.

But humans, and any universal machine, can mentally handle and reason
on mathematical notions, implementing or representing them locally.

With comp, trivially, the mental is the doing of a universal

It might be good simultaneously to extend this question by
including general terms that people use to describe the word. Are
mathematical objects then are different from them?

I am not sure I understand what you are asking.

I am talking about language that we use to describe the Nature. Information and computation were just an example. We can however find also energy, mass, or animal, human being.

I guess that Plato has not limited the Platonia to the mathematical objects rather it was about ideas. So is my question.

Let me repeat about the fight between realism vs. nominalism. Realism in this context is different from the modern meaning of the word.

Realism and nominalism in philosophy are related to universals. A simple example:

A is a person;
B is a person.

Does A is equal to B? The answer is no, A and B are after all different persons. Yet the question would be if something universal and related to a term “person” exists objectively (say as an objective attribute).

Realism says that universals do exist independent from the mind, nominalism that they are just notation and do not exist as such independently from the mind.

But that distinction is usually made in the aristotelian context, where some concrete physical universe is postulated. With comp we know this is not possible. You can restate it by saying that the natural numbers are concrete, but that a property like 'being prime" is abstract. Then mathematicians are mostly realist, because they believe that "being prime" is an independent property of natural numbers. for a mechanical generable set, like the set of prime numbers, you can come back to nominalism through Gödel numbering, and through the identification of the concept of primes with the number (machine) which generates all and only the prime numbers. But this leads to difficulties for the non mechanically generable sets of numbers, which *do* play a role in the machine/numbers points of view.

To me this difference "realism vs. nominalism" seems to be related to the question whether mathematical objects are mental or not.

But with comp, mental is a number's attributes. And eventually "physical" is a collection of number attribute. If you make mathematical object mental, and *only* mental, you have to tell me what you assume at the start in the theory. If you chose something physical, then you have to abandon comp, and you have to tell how you relate mental and physical, by using provably non Turing emulable components. You will lose also the explanation of why something physical exist, and why it hurts.



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