On Tuesday, June 18, 2013 4:47:47 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > On Monday, 17 June 2013 21:46:17 UTC+2, Virgil wrote: > > > > This shows that these "proofs" are nonsense > > > > > > > It only proves that different sets of assumptions lead to different conclusions, > > > > In this case the question is whether the reals can be well-ordered - and absolutely nothing else! A theory that says yes and no does not contribute soemthing of value. >
Yes, a theory that proves both "yes" and "no" as an answer to that question would be of no value. However, we have a system that proves "yes", and and another that proves "no". The former is invaluable in Real Analysis, whereas the latter is useful in Game Theory. Both of the are useful to the Sciences.
If the Scientist ( you ) wishes only to do his Science, then they need not worry about the Mathematics that produces their formulae. They can just ignore the Mathematical Black Box, and have faith that a formula, when applied correctly, will yield the correct result.
> > Look, when I ask what is 5 + 5? You may answer, depending on the axioms, 10 or not 10, then your answer shows just the same kind of value as matheology. The only empty set that has a right to ebe considered is the story of success of set theory. > In the system of "Rope Arithmetic" or "Gap Arithmetic" we have the true equation, 5 + 5 = 11. This system is a consistent system. Even though it does not work for counting how many stones are in a pile or how many pencil scratches are on a piece of paper, it has real world applications.
And what about Euclidean and Hyperbolic Geometries? Which one is correct? Which on Models "reality"? And, if you an answer, how do prove it is right?
> > Descartes once claimed that the only vacuum existing in the universe, was the brain of Pascal. With respect to modern set theorists, he might have even found some better sites. >
Descartes also claimed a gland in the brain is responsible for bridging the gap between mind and body. More importantly he said Euclidean Geometry is a priori truth. Both of these are completely incorrect.
So, what's your point?
> > Regards, WM
BTW, I thought you wanted to talk about the Continuum Hypothesis. It is much more interesting than the Well-Ordering Principle.