Bruno,

Thanks for your comments. You are right. It is necessary to be more accurate with terms. I have read about physicalism on SEP and I see that I do not need mechanism right now. By the way, where I can read about mechanism? I see nothing on SEP.

Below is a new version of the problem. I have left Pi though.

Evgenii

P.S. I like a lot this quote about physicalism from SEP

"The first thing to say when considering the truth of physicalism is that we live in an overwhelmingly physicalist or materialist intellectual culture. The result is that, as things currently stand, the standards of argumentation required to persuade someone of the truth of physicalism are much lower than the standards required to persuade someone of its negation. (The point here is a perfectly general one: if you already believe or want something to be true, you are likely to accept fairly low standards of argumentation for its truth.)"

I should confess that it describes my personal feeling very well. Cheers to philosophers.

----------------------------------------------------------------
An experiment to perform in order to find experimentally what is the meaning of Pi under the physicalism hypothesis

Version 2.0

*Assumptions*
-------------
I assume physicalism. From SEP

http://plato.stanford.edu/entries/physicalism/

"Physicalism is the thesis that everything is physical, or as contemporary philosophers sometimes put it, that everything supervenes on, or is necessitated by, the physical."

"The general idea is that the nature of the actual world (i.e. the universe and everything in it) conforms to a certain condition, the condition of being physical. Of course, physicalists don't deny that the world might contain many items that at first glance don't seem physical — items of a biological, or psychological, or moral, or social nature. But they insist nevertheless that at the end of the day such items are either physical or supervene on the physical."

"Physicalism is sometimes known as ‘materialism’; indeed, on one strand to contemporary usage, the terms ‘physicalism’ and ‘materialism’ are interchangeable."

*Problem*
---------
The Pi number enjoys extensive use in physics. This raises the question what Pi means under the physicalism hypothesis.

*Experiment*
------------

Below there is a description of the experiment that one could think of to check the relationships between Pi and physicalism.

Let us take a completely isolated bunker where the experiment begins. There are two mathematicians in the bunker and the initial conditions are enough so that mathematicians can comfortably work for awhile and prove the existence of Pi on a paper. Eventually the oxygen in the bunker will run over and both mathematicians die.

From a physicalism viewpoint, we have a dynamical system that eventually comes to the equilibrium state. Because of experimental settings, we can neglect the interaction with environment and I hope that this could be done even for the quantum mechanics treatment.

The experiment takes an operational approach to what Pi means. During the initial stage of the experiment mathematicians prove the existence of Pi. This should be enough to claim that Pi is present in the bunker at least for some moments.

*Questions to discuss*
----------------------

How Pi supervenes to the physical states of the bunker with mathematicians?

Is Pi invariant in respect to states of the dynamical system in question or not?



On 04.03.2012 18:48 Bruno Marchal said the following:

On 04 Mar 2012, at 17:12, Evgenii Rudnyi wrote:

Bruno,

Actually it is not a joke. I guess it is my first step toward
Platonia. As I am a chemist by background, the problem might be not
 mathematically correct indeed. Yet, if you could help, we could
improve it in this respect.

The background is as follows. I am a chemist and I am still at the
 level of what you refer to as physicalism or mechanism.

Hmm... You should read more carefully the post. On the contrary I
claim, and explain, that mechanism and physicalism are incompatible.

I am aware that physicalist, naturalist and materialist tend to use
mechanism as a sort of modern way to put the mind under the rug.

You can see all what I am talking about as an explanation that not
only mechanism does not solve the mind-body problem, but on the
contrary, it leads to the falsity of physicalism and the necessity to
explain where the physical (and physicalist) *belief* come from.

Mechanism entails the negation of physicalism. That's what the UDA is
 all about.

The physical reality is not the fundamental reality. The physical
reality will reappear as the way the border of the mathematical
reality looks when seen form inside, from some points of view
(actually the points of view of predicting measurement values).

I can argue that with comp, concerning the basic ontological level,
it is absolutely undecidable if there is anything more than the
numbers, that is 0, the successor of zero, the successor of the
successor of zero, ...

And every lawful thing is deducible from the laws of addition and
multiplication (that you have learn is school, and certainly apply in
 chemistry).

So, with mechanism, physics is not the fundamental science. Physics
has to be reduced to digital machine (number) biology, psychology,
theology (given that non provable truth have a big role in the origin
of matter).




Before I consider your theorem, first I would like to understand
better in my own terms what physicalsim and mechanism mean and what
 are the limits. When you talk about this, it is too fast for me.

You have to do the thought experiment. You have to admit the
hypothesis, if only for the sake of the argument.



According to a common view in natural sciences, a human being (and
 hence mind) has been created during evolution.

Something like that might be locally correct, but appears to be wrong
in the comp (digital mechanist) theory.



Right now however, after following discussion here, I have a
problem with mathematics along this way. Science has been pretty
successful with mathematical models in physics, chemistry and even
in biology. Yet, according to my current view, mathematics has been
created by the mankind. Thereafter I have got suddenly a question,
why mathematical models (physical laws) are working at all to
describe the Universe when there was no mind. The mathematics, it
seems, was not there at the times of Big Bang.

You might confuse mathematics, branch of human science, and the
possible mathematical reality.

The mathematical reality does not depend on the physical reality, and
a large part of it might no depend on the human mind.

For example the fact that 17 is prime, is a mathematical fact which
does not depend on the presence of human. It is just the fact that a
line of 17 distinguishable objects cannot be cut in a finite of part
to be reassembled into a rectangle different from the line itself.
For example 8 is not prime because the line

. . . . . . . .

can be cut and become

. . . . . . . .

You might convince you experimentally that 17 is prime in this way,
but you can also prove it entirely as a consequence of the laws of
addition and multiplication. No concept of physics enter in this at
all. You might *apparently* need a physical reality to convince a
human being that 17 is prime, but you don't need to refer to it to
transmit the concept of prime number, despite it can helps for the
intuition, like above.






We cannot repeat Big Bang to understand this.

Remember that we (try) to be scientist, meaning that we cannot commit
 ourself ontologically, except by making clear our postulate. The
big-bang theory is a theory, an hypothesis, which usually assume an
ontological (primitively existing) universe.

With mechanism, that theory is already refuted by UDA+MGA.

What is the big bang, then. Open problem. Most plausibly a first
person plural sharable computational state of some universal number.





According to the current economic situation, it is highly unlikely
 that taxpayers are ready to spend money on bigger and bigger
particle accelerators. Hence my proposal. If we cannot repeat Big
Bang, then for a relatively small budget we could make easily a
local heat death of a small Universe with two mathematicians and
see what happens with mathematics there. In a way, we repeat
evolution in the reverse direction.

I can see you don't like mathematician! :)




It would be nice to exclude mind out of consideration at all but as
 this is impossible my goal was to reduce its role as possible. We
know that mathematics is what mathematicians do.

Some constructivist mathematicians might agree, but most
mathematicians consider that they explore territories. They consider
that they make discoveries. Most discoveries are unexpected.
especially after Gödel, it is hard to defend a conventionalist
philosophy of math. And the, just to define what could mean
"mechanism", you need to assume that the arithmetical truth is more
primary than the mathematicians, if only to model mechanist
mathematicians by (Löbian) numbers. The you can distinguish the math
produce by the number, and the math of the number.



Pi is a nice number


But it is a real number. I prefer to exclude them of the ontology,
because they have the same fate as matter. If they have an
ontological existence, it will not change anything in the machine
(number) epistemology. So they are like invisible horses, and with
occam, you can exclude them. Natural numbers will belief in real
number, independently of any of their ontological status.


and most of taxpayers have heard about it. In the experiment we
could allow mathematicians to write the prove that Pi exists on a
paper, it would be even simpler. If you think that some other
mathematical object would be nicer, please make your suggestion.

It is very weird, here.




So, at the beginning of the experiment we have mind (two working
brains of mathematicians) and they prove on the paper that a given
 mathematical object exists. An open question to discuss is what
happens with this mathematical object at the end of the
experiment.

Mathematical objects are invariant. Nothing happens to them. Things
can happen to them, in a relative sense, by the intermediate of true
 relation bearing on them.

If you divide 8 by 4, this gives 2. But 8 remains untouched by that
operation. It is just that it is true that there exist a number which
 multiplied by 4 gives 8, and that such a number is 2 (the nickname
for the successor of the successor of 0).

Mathematical object are structured only by their relations, and this
in a way which does not depend on time, space, animals, humans, or
whatever. Indeed, that is why math is useful to describe atemporally
 even temporal relation, by a function of the type y = f(t).

But all questions require a precise theory in the background, and if
 what I say don't help, you might think about formalizing a bit more
the background you are using.

Bruno



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