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.
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.
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. Even Einstein was wrong on this. Wheeler, Deutsch and
Penrose are already far less wrong on this. Mathematics is independent
of language. We can be wrong on this because mathematics is highly
dependent on language when we want to *communicate* mathematical
facts. Logic can help to make this precise. But when logic is studied
superficially, it can aggravate the confusion, due to the role of the
formal languages.
That doesn't mean that physics is mathematics.
A good point. Even with comp, physics is not mathematics, nor is
theology pure mathematics. But with comp, math plays a more
fundamental role, and in a sense, theology (of a provably correct
machine) is a branch of arithmetic. But it happens we cannot know that
for ourselves. This is coherent with the fact that the proposition "I
am conscious" cannot be made mathematical. The first person is, from
its point of view, beyond math (and physics).
That |||||| is fewer than ||||||| is a fact about the world,
... about reality. OK. The word "world" is ambiguous.
that 5<7 is a theorem in mathematics which may be interpreted as a
description of that fact.
I would say that it is a justification, or explanation of that fact.
The description is still another thing.
But when talking philosophy we should be careful to distinguish
facts from descriptions of the facts.
And to distinguish description and justification-proof, which can
themselves be described, like in logic-metamathematics.
but the problem here is that quantum physics assumes real numbers
and waves (trigonometrical functions), and that reintroduce the
numbers at the base.
If it were an axiomatic system it would have lots of axioms
(probably including Peano's) but it isn't. I'm not sure axioms are
"assumptions" though.
I use assumption in the sense that we cannot prove them (in the theory
under consideration).
Bruno
http://iridia.ulb.ac.be/~marchal/
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