In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> > > > Not in the article to which I responded. > > But frequently I made use of what you call quatifier exchange and what > is allowed in case of complete linear sets.
You must prove it is allowed for the special case of what you call "complete linear sets" as it is invalid in general.
> > > > > You said [*] is not true, but [**] is true. > > > > That is not what I said. > > You said: > The only thing that can be stated is (symbolically): > E n A m P(m, n) -> A m E n P(m, n) > not the reverse, this is just basic logic. > > > I said that for the case involved you have to > > *prove* that it is true, because it is not generally true. > > It is generally true for complete linear sets.
Not until you prove it to be so, which you have not done.
You have not even given an adequate definition of what you mean by "complete linear sets", unless you mean only sets for which what you claim is true.
> > > > > Weyl said: Classical logic was obtained from finite sets. > > > > Right. > > > > > Therefore I asked you: Show me a linear complete finite set, that > > > makes your claim [**] right and my claim [*] wrong. > > > > But now you include the word "linear". Where did "Weyl" include the > > word "linear"? > > I did never claim that quantifier exchange is allowed in case of non- > linear sets, like cyclic sets as, for instance, your dice. That would > be nonsense. A simple example: Every country has a country that lies > west of it. But there is no country that lies west of all countries.
If you concede that something does not hold for arbitrary cases and you claim it does holds for certain special cases, then it is your obligation to prove it for those special cases.
Which anyone competent in pure mathematics would have known, but which such professors of impure math as WM does not know.