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