On Tuesday, 18 June 2013 20:46:40 UTC+2, Zeit Geist wrote: > 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,
> > 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.
Not at all. Both are completely useless. And that which says the reals can be well-ordered is especially useless because, nevertheless, the reals cannot be wel-ordered.
> 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.
In order to have faith, we have to drop theories which predict false results. Wee-orderability of the reals is such a false 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.
That does not touch my example of common arithmetics and does not help to excuse the false results of set theory.