On 19 Jun., 16:18, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> Well, I see, you think mathematical logic is nonsense.
To great parts, yes.
> > 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. > > > 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.
As a result, the cartesian product of the set of finite alphabets and the set of finite words and the set of languages 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 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..