In article <email@example.com> WM <firstname.lastname@example.org> writes: > On 19 Jun., 16:18, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote: ... > > > No. I mean exactly that: The set of finite words over a finite > > > alphabet is countable. > > > > Right. > > > > > 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. > > Every meaning of every word is defined by a language. > Every language is a finite definition. > The number of finite definitions is countable.
For each word the meaning can indeed be countable. But that does not mean that the set of meanings for all the words in a language is countable.
> > > 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. > > Every symbol is finite and is defined by a finite word. Therefore the > number of symbols and the number of finite sets of symbols is > counatble.
I did not know that every symbol is defined by a finite word. Can you show where I can find that result?
> > > 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 very 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... > > And that answers your question that I snipped above: > Every set of linear sets in physics is finite and has a last element. > Therefore logic, that is obtained from physics, requires for finite > linear sets: > AnEm <==> EmAn..
Yeah, I know that you have a very liberal view on what is part of physics and what not. The mathematicians have a different view. -- dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/