My solution for the Russell's paradox
Date: Mon, 15 Oct 2018 02:24:16 -0700 (PDT)
Message-ID: <4c12e837-85d4-436e-8b75-3e7965c99116_at_googlegroups.com>
[Quoted] I presented my solution of "Russell's Paradox" at this user group. At that time, I did not know that Zermelo was the first who discovered this paradox and the first who solved it.
In my thread about Russell paradox, I have underlined that Zermelo's solution is given within the set theory by using axioms. My solution is of a general nature. It is at Logic and Semantics level. Before presenting my main ideas in solving this paradox, I will present what other scientists have rightly solved in this paradox. After reading Russell's letter, Frege realized that there were some mistakes in his work. In Frege's response to Russell's letter, he wrote the following: „ ... Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic ...“.
However, no one has specified exactly where the mistake is. In the first post in my thread about R. paradox I wrote that Russell did not understand the basic things of paradox. By the end of his life, Frege remained convinced that he well defined the concept. Zermelo introduced a kind of constrain but did not explain the essence of the problem.
When I talk about "Russell Paradox", then my mathematical solution to this paradox is based on the following:
The identifier of an element of a set can not have the same identifier as the identifier of the set to whom this element belongs.
Russell's paradox does not comply with above rule, that is Russell uses in fact the same identifier for a set and for one element of this set. This is wrong.
Note that concepts (predicates) determine plurality, that is a set. In the
set theory, the basic concept is an object(entity). Elements of a set are
objects. Since a set can be an element of another set, then a set is also an
object.
In my solution, I assume that elements of the set are names of objects
rather than objects. In section 2.1 authors of „anchor modeling“ put
physical objects into sets?! Their main structure is described in section
2.1 as "An anchor is a set of entities, such as a set of actors or events".
From here it is clear that authors of "Anchor modeling" do not understand
the great Frege's semantic theory. They do not know that at mental level we
put „objects“ into concepts. At the linguistic level, man puts the object's
name in the predicate.
Database theory is a kind of semantic theory because every data that belongs
to the database has meaning.
I have built the theory of identification. I have introduced the identification of objects, attributes and relationships. In my opinion there is the identification theory that is closely related to semantics. Regarding set theory and axioms associated with this paradox, I wrote about this topic and also about identifying of elements of a set, in my thread "A new way for the foundation of set theory".
In my paper I presented at this user's group in 2005 the identifier of the entity and the identifier of the state of the entity (relationship) instead of the keys, in order to do the identification. I also introduced the identification of an attribute and identification of a number of other necessary things.
Definition of Identification for Databases In my papers I gradually developed the identification theory and wrote about it on this user group. Now I just want to explain this theory briefly. Identification means determining and identifying the identity of the following:
(i) determining the identity of the attributes (ii) determining the identity of the entities (iii) determining the identity of the relationships (iv) determining the identity of state of attributes, entities orrelationships
In the above definition of identification, two things are the most
important:
1. Identification of names
2. Identification of the construction of what we want to identify.
One of the mathematicians who defined entity-relationship model was K. Godel. He published it in 1944. Frege first defines the "entity-relationship model". In fact Frege's theory is much more general than the Peter-Chen entity-relationship model. According to Frege a predicate determines the following:
(i) one predicate determines one or more attributes of the object
or
(ii) one predicate determines relationships among objects
This definition defines entities and relationships, and links them to the logic of predicates.
I'm writing about Godel and Frege because I believe that Peter Chen must quote these two great scientists in his paper about the entity / relationship model. We can notice that G. Frege had written the entity / relationship theory as a theory about the world almost 100 years before Peter Chen. Frege also introduced objects (entities) into the Predicate logic. Frege established link between entities, concepts and sets. This is why the whole model is named "conceptual model".
As can be seen from this short text, identifiers are very important in my data model. Authors of "Anchor Modeling" published their second paper , a few months after my public critique of their first paper on this user group. Their second paper has title „Anchor modeling - Agile information modeling in evolving data environments“ and was published in 2010, in „Data and Knowledge Engineering“, whose The Editor-in-Chief is Peter P. Chen. Paper „Anchor Modeling“ won the ER 2009 Best Paper Award at the well-known World Congress ER 2009 in Brasil, whose honorary president was Peter Chen.
In their second paper authors of „Anchor modeling“ introduced the identifiers in all their data structures, without any serious explanation. This term „identifier“ is introduced in „Definition 16“ in the second paper of "Anchor Modeling".
As you can see I introduced identifiers in 2005 and presented it in my paper that is presented on this user group in September 2005.
The second important thing in my model are states of entities and states of relationships that I presented on this user group in 2005. The authors of "Anchor modeling" introduced states in above mentioned their second paper from 2010, section 4.5.
Vladimir Odrljin Received on Mon Oct 15 2018 - 11:24:16 CEST