In article <firstname.lastname@example.org> WM <email@example.com> writes: > On 12 Jun., 04:15, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: > > In article <102f1c16-0ef5-4189-aea6-bcccf7729...@z19g2000vbz.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes: ... > > > > > > 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 question: Does what Weyl wrote a long time ago still have > > > validity now? > > > > My question still stands and I see no answer. > > Then take my answer: Yes.
Interesting: Q: What is the relevance? A: Yes. You state that what Weyl wrote still has validity, I doubt that. Then you reply that it is 50 years younger than Cantors writing, and I ask what the relevance is. I still have doubts about the validity of what Weyl wrote, and I still do not see the relevance of what he wrote being 50 years younger than Cantors writings.
> > > > > 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. > > That answer is: Logic is obtained from the behaviour of things.
Still no answer to my question. Where in logic is it stated that the union of a *complete* set of finite linear sets is a finite linear set.
> > > > > 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. > > I like logic, but not nonsense.
Well, I see, you think mathematical logic is nonsense.
> > > 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. > > No. I mean exactly that: The set of finite words over a finite > alphabet is countable.
> The set of meanings of these words, i.e., the > set of languages, is countable.
Is it? I would state that the set of meanings of each of those words can indeed be countable (I do not know), nothing more.
> The set of finite alphabets is > countable.
Is it? I would state that a finite alphabet consists of a finite number of disctinct symbols. Now you are actually stating that the number of symbols is countable.
> > > > 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? > > The logic is obtained from physical objects. How else should it have > come into being? Remember, even brains are physical objects.
Yeah, I know that you have a verr liberal view on what is part of physics and what not. As you once wrote: that we use computers to do cryptography means that we use physical objects to do cryptography, and so it is part of physics... -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/