Re: Is Russell's paradox in fact fraud?

At the end, it is necessary bring a conclusion because I think this area remains with incomplete solutions in some its parts. According to the above mentioned facts, Ernst Zermelo was the first to discover this paradox and the first to solve this paradox.

In the above-mentioned work written by Nicole Fillion, the following facts  are particularly emphasized:
„The point of talking about this dispute here is not so much to establish who discovered the paradox first, but only to show that the mathematicians of the group of Gottingen were aware of such paradoxes in set theory, and surely worked actively to solve the problem.“ As far as I know, E. Husserl and Hilbert were mathematicians who belonged to Gottingen's group. At that time, most mathematicians have had opinion that Hibert was the best mathematician. So, this powerful group knew for this paradox and worked on it before Russell. It should be noted that Frege just started to print three books in which he wanted to show that mathematics can be completely constructed on the basis of logic. At a time when Frege received a letter from Russell, the printing of second volume was near completion. After that Frege remained with the paradox and a bunch of printed books. So, Russell sent his letter right at the time Frege had printed his three books. After that, Russell wrote a book "Principia Mathematica" in which he also tried to build mathematics that was built on the basis of logic. But in 2005 there appeared the book with the name Fixing Frege written by John Burgess, who, with some corrections, succeeded in realizing Frege's great idea - mathematics can be built on the basis of logic. In my opinion, this Frege project is the largest and most significant project in the history of mathematics and probably in the history of science.

Here's how Frege reacted when he received Russell's letter and when he finished printing his two books:
„Hardly anything more unfortunate can befall a scientific writer than to have one of foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion. ... “

After Russell's letter, Frege did not publish scientific papers for six years.

Nowadays, more and more facts reveal that Frege had, in terms of volume, a large correspondence with the most prominent mathematicians of his time, using long, detailed and carefully written letters. Unfortunately, during the bombing in 1945, most of Frege's correspondence was lost.

At the end I will give my opinion about this paradox. Frege did not make any mistake related to concepts. He defined the concepts well. The concept does not construct elements of a set, but checks whether an object satisfies or does not satisfies the concept. One concept generates a plurality of objects.
In my opinion, Frege, Russell and Zermelo did not focus on the identification of objects. It was a failure, because of which there was the paradox and why they did not find the real reason for this paradox.

We notice the following:
- elements of a set are objects

• a set is an object
• a concept defines the plurality of objects that meet that concept.

We need to identify objects for several reasons. I will list only the two most important ones:
(i) the concepts are the capital part of the semantics. (ii) Memory is important for working with objects. I will mention only three basic things in the work with every memory:
- The object must be stored in a memory. (Write)

• The object must be found in the memory. (Read)
• The object must be written in a language. Entering an object in some memory allows the permanence of this object.

Databases work with real-world objects. But the database does not contain real objects, but the names of real objects are stored. The same goes for abstract objects and fictitious objects. Still, in real-world practice, professionals usually say that objects are stored in a database, which is a deep misunderstanding of databases and memories.

Today, real-life data has reached enormous size and become global. Because of this, the sets that contain data about real objects become an important part of the applied and theoretical mathematics. These data are from the real world. But databases also contain data that are about abstract objects ...
Today, at the global level there is an identification for each car (VIN number). Identification for each book (ISBN number). Identification of every person (passport, social security number, memberships in any organization - school, library, tax, medical numbers, telephone numbers ...), address system, owners, bar-codes etc.
In short, a proper mathematical theory is required for the identification of objects.

Vladimir Odrljin Received on Sun Oct 01 2017 - 01:34:44 CEST