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. As finite beings we can hypothesize infinities.

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.


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. Physicists use mathematics (in preference to other languages) in order to be precise and to avoid self-contradiction. That doesn't mean that physics is mathematics. That |||||| is fewer than ||||||| is a fact about the world, that 5<7 is a theorem in mathematics which may be interpreted as a description of that fact. But when talking philosophy we should be careful to distinguish facts from descriptions of the facts.

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.

Brent




Bruno




Brent

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