On 11 Jun., 15:07, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > In article <557d4c53-cba7-4fca-aec2-aa6277078...@l32g2000vba.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes: > > On 4 Jun., 04:04, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > > > The word union and the word linear are not mentioned in the quote. > > > > Nevertheless the due logica rules were obtained from unions of finite > > > > sets and linear finite sets. > > > > > > Yes, obtained from. But that does not mean they are identical. Moreover, > > > does what Weyl wrote a long time ago still have validity now? > > > > It is 50 years younger than Canto's writings. > > What is the relevance? > Your questuion: Does what Weyl wrote a long time ago still have validity now?
> > > > But it does rule out theories which are contradicted by the > > > > fundamental logical rules. And one of these rules is that a complete > > > > linear set has a last element. > > > > > > What fundamental rules of logic are you using? I have never seen such a > > > logical rule, because logic does not talk about sets. > > > > Logic states that the union of a *complete* set of finite linear sets > > is a finite linear set > > As I said, logic is not talking about sets. So where in logic is such stated?
Logic is obtained from the behaviour of things. Things can be considered as sets, at least if two things are taken together. Bolzano excused himself for including 2. Later they included 1 and even 0, > > > > > No. I use the fact that for complete linear sets always both > > > > implications are true : > > > > [**] & [***]. This means that [*] is true. > > > > > > You just state so without proof. > > > > A proof is a derivation of theorems from axioms or basic truths by > > means of rules of logical inference. These rules themselves cannot be > > proven but can only be obtained from the behaviour of existing (i.e., > > finite) sets. > > So you are not using mathematical logic?
Nobody should do so. Many "logicians" are below any level. There is one Fool Of Matheology, for instance, who thinks that the cartesian product of the set of finite alphabets is uncountable. Better stop recommending or even using that nonsense.
> > > > > If you disagree, then you should come up with a finite linear set for > > > > which only one implication is true. > > > > > > Why should I show that for a *finite* linear set? Why not for an > > > *infinite* linear set? You are *still* thinking that wat is valid > > > for finite things is also valid for infinite things. > > > > There is no reason to believe that always the contrary is true. > > I do not believe so, so what is the relevance?
You do, because there is no further reason.
> > Potential means not complete. There always appears another number once > > you have found the last one. > > Your definition of complete is not the standard definition. In N there is > always one after the other, but the complete set does exist. > > > > > ZF claims that this denial is correct for complete linear infinite > > > > sets, but this is a wrong claim, as we can obtain from logic. > > > > > > What logic? Not the logic as discussed in sci.logic. > > > > No, I mean the correct logic. > > I still do not see the logic through which you obtain it.
It is obtained from the action and reaction of physical subjects.