In article <firstname.lastname@example.org> WM <email@example.com> writes: > On 11 Jun., 15:07, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: ... > > > > 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?
My question still stands and I see no answer.
> > > > > 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,
That is not an answer to my question.
> > > > > 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.
Yes, I know you do not like logic.
> There is > one Fool Of Matheology, for instance, who thinks that the cartesian > product of the set of finite alphabets is uncountable.
What is "the cartesion product of the set of finite alphabets"? The only definition I know is that "the cartesion product of a set" is "the cartesian square of a set", i.e. the set of pairs (x, y) where both x and y come from the set. Apparently you mean something else. Can you properly state what you *do* mean?
> Better stop > recommending or even using that nonsense.
So you think I should follow nonsense where many things are not properly defined and only follow intuition?
> > > > > 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.
No. There are two statements: (1) What is valid for finite things is also valid for infinite things. The contrary of that is: (2) What is not valid for infinite things is also not valid for finite things. But neither is true. But you intend the reverse: (3) What is valid for infinite things is also valid for finite things. Which is also false.
So, which of (2) or (3) do I believe according to you?
> > > > > 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.
What has *that* to do with logical reasoning? Logical reasoning is able to come up with algorithms like APR-CL that decide whether a number is prime or not. What is the relation with "action and reaction of physical subjects"? How does "action and reaction of physical subjects" relate to the logic that constructed algorithms (like NSF) to factorise numbers? What are the "actions and reactions of physival subjects" involved in taking the union of FISONs? -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/