# Re: Realism, nominalism and comp

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On 06 Sep 2011, at 21:23, Evgenii Rudnyi wrote:```
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Let me try it this way. Could we say that universals exist already in the 3d person view and they are independent from the 1st person view?
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I think we can say that.

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With the 'modern logic' approach we can bypass the middle-age "problem of universal".
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For example I would say that "prime number exist", and so, that the notion of "being prime" can exist independently of any first person. But this can be translated in first order logic with the quantification restricted to the natural numbers, for example by
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Ex (x is prime)

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with (x is prime) being an abbreviation of (y divides x -> ((x ≠ 1) & ((y = 1) or (y = x))
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with (y divides x ) being an abbreviation of (Ez (y * z = x))

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So, the existence of universal can be translated into the truth of some (arithmetical) relations. You can do the same with
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Ex (x is a universal number)
Ex(x is a Löbian machine)
Ex (x is a finite computation)
or even
Ex (x is the code of a possibly infinite computation)

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We can probably not say Ex(x is a dog), but we can say Ex(x is very plausibly a dog), without any trouble, so we can have fuzzy universal too. Those are well handled by programming technics and fuzzy set theory, for example.
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Bruno

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Evgenii

On 06.09.2011 09:00 Bruno Marchal said the following:
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On 05 Sep 2011, at 21:02, Evgenii Rudnyi wrote:

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```Realism and nominalism in philosophy are related to universals (I
guess that numbers could be probably considered as universals as
well). 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 then the question would be if something
universal and related to a term "person" exists in A and B.

Realism says that universals do exist independent from the mind (so
in this sense it has nothing to do with the physical realism and
materialism), nominalism that they are just notation and do not
exist as such.

It seems that this page is consistent with what Prof Hoenen says

http://en.wikipedia.org/wiki/Problem_of_universals

Well, he has not discussed what idealism has to do with universals.
according to it the universals do exist literally.
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I am not sure. UDA shows that we can take elementary arithmetic as
theory of everything (or equivalent). In that theory only 0, s(0),
s(s(0)), ... exist primitively (literally?).

Then you can derive existence of objects, among the numbers, which
have special property (like the prime numbers, the universal numbers,
the Löbian Universal numbers). Do they exist literally? I don't know
what that means. Do they exist primitively? That makes sense: s(s(0))
exists primitively and is prime.

Then you have the epistemological existence, defined by the things
the numbers, relatively to each other believes in (this includes the
physical universes, the qualia, persons, etc.). They does not exist
primitively, but their properties are still independent of the mind
of any machines. This is epistemological realism. Pain exists, in
that sense, for example.

All what you have, in the 3-pictures, are the numbers and their
relations and properties. This is enough to explain the "appearances"
of mind and matter, which exist from the number's perspective (which
can be defined by relation between machines' beliefs (defined
axiomatically) and truth (which is assumed, and can be approximated
from inside).

Now with comp, the primitive object are conventional. You can take
combinators, Turing "machines" or java programs instead of the
numbers. That will change nothing in the theory of mind and matter.

Bruno
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