In article <351d0bd7-fe7d-4005-a10a-42b63a9037e5@q16g2000yqg.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 26 Mai, 04:07, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > In article > > <15af9b47-eac6-4d22-8720-0d6e7ebba...@e21g2000yqb.googlegroups.com> WM > > <mueck...@rz.fh-augsburg.de> writes: > > > 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 [*]. > > > > The above is not contested: [**] implies > > [*]. > > 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? > > This is so simple that it should be understandable even for someone > who is not "very deep in logic". > > > What is contested is that: > > En Am: m =< n <== Am En m =< n [***] > > implies [*]. And *that* is the form you do use. > > 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. > > > There is a trivial finite > > counter-example. Take three dice where on each of the sides one of the > > numbers one to nine is printed (some of them repeated). Say the set is > > {d1, > > d2, d3}. Define di < dj when the probability to throw a higher number with > > dj than with di is larger than to 1/2. (I would submit that all this is > > quite physical.) There is a set of three dice such that d1 < d2, d2 < d3 > > and > > d3 < d1. > > > > And so we have: > > Am En d_m < d_n (d1 < d2 < d3 < d1) > > but not > > En Am d_m < d_n (there is no best die). > > Of course there is no best die. Therefore this set is not linear. > Every finite set of natural numbers has a "best" number.
It may have a largest, but without a definition of being "better" that is transitive, it need not have a "best". > > Why do you bother with such nonsense examples?
Why does WM bother with his much more nonsensical examples? I doubt that even WM knows.
> But the answer is easy: Because you have no other examples.
We have them, but WM has steadfastly refused to understand them so we are trying to simplify things to a point which WM can understand them. So far we have not been able to get down to his level.
> > > Doesn't it bother you that he gets letters from > > other mathematicians in Germany complaining > > about it, and that he is proud about that fact? > > I have never got a letter from a mathematician complaining about that. > I would never publish a letter of my private correspondence without > consent of the correspondent. My university of applied sciences got a > letter from a greasy informer who may be whatever but certainly is not > a mathematician. > > > Do you not think that it might lower the value of other > > degrees in Germany as well? > > But you think it would increase this value if I taught, as you > propose, that the sum of all natural numbers can be zero?
Considering some of the things you do claim to teach, it would hardly change things.
> Or if I > taught, contrary to fact, Cantor's claim that a real number is the > limit of its finite initial segments but all real numbers are not the > limits of all their finite initial segments?
That may be WM's claim, but it is certainly not Cantor's. Cantor may have viewed reals as equivalence classes of Cauchy seequnces, or, more likely, as Dedekind cuts, but where did WM get his delusion that Cantor ever thought simultaneously that a real was something and at the same time was not that thing?
