In article <firstname.lastname@example.org>, email@example.com wrote:
> On Monday, 17 June 2013 07:43:58 UTC+2, Zeit Geist wrote: > > In some systems consisting of ZFC + Some "Large Cardinal Axiom" CH, even > > GHC, can be proved or disproved. Perhaps Godel foresaw the coming power of > > Inner Model Theory and Descriptive Set Theory. > > In some axiom systems it is possible to prove that the reals can be > well-ordered,
Like in WM's pseudo-system, since there every set, thus every ordered set, is finite and thus well-ordered.
> in other axiom-systems it is possible to prove that the reals > cannot be well-ordered.
> This shows that these "proofs" are nonsense
It only proves that different sets of assumptions lead to different conclusions, which, at least outside of WM's wild weird world of WMytheology, is obvious.
And not every system outside of WMytheology fits one and the same set of assumptions.
> The question is simply whether the reals can be well-ordered or not.
Since the form of "the reals" depends on which of many versions of set theory one assumed, as well as one's definition of the set of reals, whether the set of reals can be well ordered depends on which set theory and definition.
Every standard definition for the reals, as a complete Archimedean ordered field, requires it to be uncountably infinite and dense, from which its non-well-ordering easily follows.
We have yet to see any definition by WM of the reals that is compatible with its being a complete Archimedean ordered field.
And WM is certainly totally incapable of providing one. --