On 7/18/2011 2:48 AM, Bruno Marchal wrote:
On 17 Jul 2011, at 20:28, meekerdb wrote:
On 7/17/2011 10:11 AM, Bruno Marchal wrote:
On 15 Jul 2011, at 18:41, meekerdb wrote:
On 7/15/2011 2:15 AM, Bruno Marchal wrote:
Numerology is poetry. Can be very cute, but should not be taken
too much seriously. Are you saying that you disagree with the fact
that math is about immaterial relation between non material
beings. Could you give me an explanation that 34 is less than 36
by using a physics which does not presuppose implicitly the numbers.
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Nice, indeed. We do agree that 34 is less than 36, and what that means.
I am not sure your proof is physical thought. Physics has been very
useful to convey the idea, and I thank God for not having made my
computer crashed when reading your post, but I see you only
teleporting information. That fact that you are using the physical
reality to convey an idea does not make that idea physical.
I was expecting a physical definition of the numbers.
Of course there is no physical definition of the numbers because the
usual definition includes the axiom of infinity.
You don't need the axiom of infinity for axiomatizing the numbers. The
axiom of infinity is typical for set theories, not natural number
theories. You need it to have OMEGA and others infinite ordinals and
cardinals.
As finite beings we can hypothesize infinities.
Yes, but we don't need this for numbers. On the contrary, the
induction axioms are limitation axioms to prevent the rising of
infinite numbers.
By thinking that I can understand your proof, you are presupposing
many things, including the numbers, and the way to compare them.
On the contrary I think you (and Peano) conceived of numbers by
considering such such examples. The examples presuppose very little
- probably just the perceptual power the evolution endowed us with.
That is provably impossible. No machine can infer numbers from
examples, without having them preprogrammed at the start. You need the
truth on number to make sense on any inference of any notion.
Nothing can be proven that is not implicit in the axioms and rules of
inference. So I doubt the significance of this proven impossibility.
So it is a funny answer, which did surprise me, but which avoids the
difficulty of defining what (finite) numbers are.
It *is* a theorem in logic, that we can't define them "univocally"
in first order logical system. We can define them in second order
logic, but this one use the intuition of number.
If you agree that physics is well described by QM, an explanation of
34 < 36 should be a theorem in quantum physics,
I'm sure it is. If you add 34 electrons to 36 positrons you get two
positrons left over.
Physics is not an axiomatic system.
That is the main defect of physics. But things evolve. Without making
physics into an axiomatic, the whole intepretation problem of the
physical laws will remain sunday philosophy handwaving. Physicists are
just very naïve on what can be an interpretation. The reason is they
"religious" view of the universe. They take it for granted, which is
problematic, because that is not a scientific attitude.
Accepting what you can feel and see and test is the antithesis of taking
it for granted and the epitome of the scientific attitude. The trouble
with axiomatic methods is that they prove what you put into them. They
make no provision for what may loosely be called "boundary conditions".
Physics is successful because it doesn't try to explain everything.
Religions fall into dogma because they do.
Physicists use mathematics (in preference to other languages) in
order to be precise and to avoid self-contradiction.
That is the main error of the physicists. They confuse mathematics
with a language.
And the main error of mathematicians is they confuse proof with truth.
Brent
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