On 05 Sep 2011, at 21:02, Evgenii Rudnyi wrote:

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


Well, he has not discussed what idealism has to do with universals. Please have a look. If I understand your argument correctly, according to it the universals do exist literally.

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.



On 05.09.2011 18:59 Bruno Marchal said the following:
Hi Evgenii,

On 04 Sep 2011, at 18:30, Evgenii Rudnyi wrote:
A short remark. I have decided start with philosophy, as it is more
entertaining as mathematical logic.

I'm afraid you are wrong on this, with all my respect. Mathematical
logic is the most entertaining thing in the world (except perhaps
salvia divinorum). Of course ML asks for some work, and the initial
work is a bit boring, and is the hardest part of logic (you have to
understand that at some point you are asked to NOT understand or even
interpret the symbols).

About "philosophy" I have no general opinion. The word has a
different meaning according to places and universities. When I was
young, the prerequisite for studying philosophy consists in showing
veneration and adoration for Marx. I made myself a lot of enemies by
daring to be just a little bit skeptical, if only on materialism.
They have never forgive me. In the country nearby, philosophy is
literature, with an emphasis of being vague, non understandable, and
"authoritative". To get good note, you need to leak the shoes of the
teacher. It is "religion" in disguise (pseudo-religion).

So, I don't believe in philosophy, per se. I don't take people like
Putnam or Maudlin, or Barnes, as philosopher, but as scientist.
because they are clear and refutable. Yet in the USA it is called
"philosophy", but it is not: it is just fundamental serious inquiry.
There is no difference between "philosophy of mind" and fundamental
cognitive science.

I don't really believe in science either. I believe in the scientific
attitude, which is just an attempt toward clarity and modesty. A
scientific theory is just a torch lighter on the unknown. Many
confuse the torch and the unknown, or the shadows brought by the
torch and reality.

Right now I listen to lectures of Maarten J.F.M. Hoenen (in


His title "Controversy in philosophy" took my attention first but he
has some more offers. Say now I listen to "What is philosophy". He
speaks a bit too much but I have already got used to him.

The half of his series on controversies has been devoted to realism
vs. nominalism. If I understand correctly, your theorem proves
that comp implies realism

Could you define realism? For some weak-materialist (believer in
primitive matter), realism is physical realism.

Comp proves nothing on that, but it assumes arithmetical realism,
which is believed by all mathematicians and scientists (except some
of them when they do Sunday philosophy (that is non

Arithmetical realism is the belief that a number is either prime or
is not prime. It is the belief that the excluded middle principle can
be applied for close arithmetical statement (close = without having a
variable which is not in the scope of a quantifier).

and in my view your argument is a mathematical model for realism.

My argument is just a proof that you cannot be rational, consistent,
mechanist and weakly materialist. It is a constructive proof that if
we are machine, physics cannot be the fundamental science, but that
is is derivable from number theory. With the nice surprise, when we
do the math, that we get a theory of qualia extending naturally a
theory of quanta.

It is interesting to note that Ockam was a nominalist and with his
razor he wanted to strip realism away.

Could you define 'nominalism'. I think nominalism needs arithmetical
realism. Mechanism needs arithmetical realism (only to define what
is a machine, really), but can be said to lead to some form of
epistemological realism. The physical universe is an illusion, but
that illusion is real, in some sense. Comp makes it 'more real' and
more 'solid' than what can be brought by any observation.

By the way, in the middle ages realism was quite popular as it was
easier to solve some theological problems this way. At some time,
one philosophy department had even two different chairs, one for
realism, another for nominalism. Hence Plato's ideas have not
disappeared during Christianity completely.

This is true. Christians do even reject some typical point of
Aristotle theology (like the mortality of the soul), and embrace a
lot in Platonism. Unfortunately they have taken Aristotle doctrine of
primary matter (which is certainly a quite good simplifying
methodological assumption, but is just basically wrong in case we are

Prof Hoenen specializes in the middle ages and it gives some charm
to his lectures.

I might try to understand when I got more time. Although I talked
German up to the age of 6, I have not practice it a lot since, and
German philosophers can do very long complex sentences.


On 03.09.2011 19:41 Bruno Marchal said the following:
Hi Evgenii,

On 02 Sep 2011, at 21:12, Evgenii Rudnyi wrote:


Thanks a lot for your answers. I have said Bruno's theory just
to keep it short, nothing more, sorry.

No problem. But logicians knows the devil is in the details,
and, frankly, "theorem" is just one letter longer than theory, so
I don't ask for so much. If you are skeptical it is a theorem,
just say "argument".

Your theorem is on my list but presumably I will try to think
it over in some time, not right now. At the moment I just
follow your answers to others, in other words I am at the stage
of gathering information. I should say the list was so far very
helpful to learn many things.

Just one thing now. Do I understand correctly that your
theorem says that the 1st person view is uncomputable?

You are right. This follows already from UDA 1-6. No need of
anything except a rough idea of how most machines works (by
obeying simple computable laws).

The first person view is indeterminate, and non local. To predict
the precise result of a physical experience, you have to take
into account that you don't know, and cannot know, which
universal (or not) machine(s) execute(s) you (even just in the
physical universe, if that exists). When a physicist uses a
physical law, to predict a first person experience (like seeing
an eclipse, or a needle pointing on a number), he uses implicitly
an identity thesis between his body/neighborhood and its
experience. A logician would say that the physicist use an
inductive close, like saying that my equation predicts I will see
an eclipse, and no other laws or history is playing that role.
But when we assume comp, such identity thesis cannot work (this
subtle point *is* the main UDA point: basically you can still
escape, at step 6 and 7, such conclusion by assuming that the
universe is little (finite and not too big).

If you are a machine, you are duplicable. And if you are
duplicated, iteratively, you (most of the resulting "you"s) can
correctly bet that the outcome of the duplication(s) cannot been
predicted in advance. Children get the UDA 1-6 point without
problem. OK, for "UDA step 6" they have to be a little bit older
and capable to understand the plot in "the prestige" or in
"simulacron 3". No need of math, or even of technical or
theoretical computer science.

Now, In AUDA, the first person appears also to be "a non
machine", from the machine's point of view. This is due to the
Theaetetus' connection between belief and truth, to define a
knower. That is *much more* technical (to see that we stay *in*
the arithmetical, to study an internal vision which escapes
completely the arithmetical).

But you don't need this to understand that if we are machine
weak materialism becomes a sort of vitalism. We don't need it,
and it can only prevent the DM solution of the mind-body problem
(the 'solution' being a pure body-appearance problem in

Comp, alias DM, can lead toward a contradiction, but up to now,
it leads to a quantum like reality. It leads to a many-words, or
better many (shared) dreams, internal interpretations of
elementary arithmetic (notably).



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