In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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: > > > 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 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.
Then what Euclid wrote about the need for axioms should still be valid as well.
> > > > > > > > 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.
On the contrary, logic is obtained from the behavior of minds. > > > > > > > > > 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. > > I like logic, but not nonsense.
On the contrary, you seem enamored by nonsense. Otherwise you would not produce anywhere near as much of it. > > > > > 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. The set of finite alphabets is > countable. The cartesian product of these, and possibly some further > features, is countable.
Since one can have a Cartesian product of any set with itself countably many times, if that set contains more than one element, one can inject the set of paths of a maximal infinite binary tree into such a product, proving the product to be uncountable.
So it depends on the sort of Cartesian product one considers whether it is uncountable or not. > > > > > I still do not see the logic through which you obtain it. > > > > > > It is obtained from the action and reaction of physical subjects.
Mathematics is not constrained by physics, except in the minds of those physicists who are not mathematicians.
> The logic is obtained from physical objects.
Logic is derived from mental objects, not physical ones.
> How else should it have > come into being? Remember, even brains are physical objects.
Even though embedded in a physical world, minds are not. They are metaphysical. Minds are not constrained to think only of things existing in WM's physics. If they were, there would be no theist religions, no fairy tales, no novels, no art, no music.