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
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.
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.
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
