In article <2056d314-cabe-420c-a859-1b0d95e69fe6@i6g2000yqj.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 28 Mai, 05:21, Virgil <virg...@nowhere.com> wrote: > > > > > The problem boils down to the following: > > > > > > > En Am: m =< n <==> Am En m =< n [*] > > > > > En Am: m =< n ==> Am En m =< n [**] > > > > > > > You know: Classical logic was obtained from finite sets ... > > > > > Show me a finite set that obeys [**] but not [*]. > > > > I said: For complete linear sets [*] is true. > > > You said [*] is not true, but [**] is true. > > > Weyl said: Classical logic was obtained from finite sets. > > > Therefore I asked you: Show me a linear complete finite set, that > > > makes your claim [**] right and my claim [*] wrong. > > > > What Weyl may have said in no way limits logic, classical or otherwise, > > to finite sets. Or does WM claim that Weyl was speaking ex cathedra? > > Weyl has recognized, by the end of his life (when obtaining his > doctorate under Hilbert he was preoccupied with Hilbert's opinion), > that logic is not included into the 10 commandments, but has to be > constructed or obtained as an abstraction from the reality. Therefore > we have no guarantee that it is suitable for sets that cannot belong > to reality. And I added: We cannot use logical theorems that are > counterfactual, i.e., contrary to what we obtained from reality.
WM presumes that everything true can be, and must be, obtained only from reality, but the laws of logic are derived from thoughts of an ideal world and such thoughts are not obtained solely reality, but from largely from an unreal vision of the ideal.
There > is no model of a complete linear set in reality that makes [*] false > and [**] true. But there are many models showing that [*] is true > whenever [**] is true.
And many models for which "ExAy P(x,y) ==> AyEx P(x,y)" is false. > > > > > No. I do not use the implication only, I use the full equivalence. Of > > > course the equivalence includes the implication [***] as well as the > > > implication [**] > > > > Then WM is not operating in the same world as everyone else. > > Most of your ilk intermingle the worlds in which they work. They work > in potential infinity if the question is put whether there is a > largest natural number. But they work in actual infinity if the Cantor- > diagonal or any other irrational number is concerned. Only the > possibility to complete it by a limit process, leads to the erroneous > assumption of uncountability.
Then WM better confine his attentions to areas in which no limiting processes are wanted and no infinite sets are wanted, which excludes him from all calculus.
> > This had already been recognized by the late Alexander Zenkin, one of > the brave scientists who dared to condemn this hypocritical behaviour
Scientists may mess with physics to their hearts content, but as scientists, have no business messing with pure mathematics.
So if anyone introduced any "false logic", it would be physicists rather than mathematicians.
