In article <fccf2aaf-c674-4114-aded-fdbd4aa16af6@q2g2000vbv.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 25 Mai, 16:06, Shmuel (Seymour J.) Metz > <spamt...@library.lspace.org.invalid> wrote: > > In <20120524213225.934...@newsreader.com>, on 05/25/2012 > > at 01:32 AM, c...@kcwc.com (Curt Welch) said: > > > > >But it seems to me, that once you do that, you have stepped > > >outside of reality and created endless self contradictions in > > >your system > > > > How it seems to you is irrelevant. Violating your aesthetics and > > prejudices does not prove a self contradiction. Showing that it is > > incompatible with some other system that you prefer is not good > > enough. You won't be taken seriously until you produce an actual proof > > of a contradiction. > > Here is a proof of a contradiction. > > Ordering objects is impossible without identifying them as distinct. > Reason: Unless you can identify objects as distinct, you cannot be > sure to have more than one (or even to have any). > ZFC "proves" that the set of real numbers is uncountable and can be > well-ordered.
I was under the impression that ZFC merely assumed that well-orderability.
> Mathematics proves that only countably many objects can > be distinguished and identified.
What you miscall mathematics merely assumes it, but never proves it based only on assumptions that do not presume it. > > This is a contradiction in any theory that does not preclude the > existence of contradictions
According to Godel, there are no such theories sufficient to produce arithmetic.
