Re: Is Russell's paradox in fact fraud?
Date: Sat, 27 Jan 2018 16:58:55 -0800 (PST)
Message-ID: <90ee74bf-1e73-4fcb-864a-c8ea3990df3f_at_googlegroups.com>
[Quoted] I would like to emphasize that Zermelo-Fraenkel Aksioms (ZFC) are
constructed as follows:
They disable examples of paradoxes that Russell used as the main and only
arguments.
The axiom of separation and the axiom of well-foundedness created by
Zermelo, forbid the sets presented by B. Russell . B. Russell used the
following two examples, with which he tried to bring down the entire Frege's
theory:
- Russell“s example: R = {x : x is a set and x not belongs x}
- Russell“s example Set of all sets:
Did Zermelo have any reason to ban these two Russell examples? Yes, Zermelo had solid reasons to ban Russell's examples. These reasons are as follows:
S belong S also S not belongs S are not well-grounded as the set is always
more complex than its elements. For this reason the set can not belong to
itself.
Note that the condition "x is a set" means "set of all sets" (at example 1).
If a set of all sets are marked with V then V belongs V. We have already
explained that this is not a well-founded statement.
I would now conclude this section with the following conclusions: 1. Russell's paradox is unfounded and is therefore erroneous. 2. Frege did not go wrong with his concepts, that is, with his predicates.
But in Frege's theory there is one missing part.
3. Zermelo found where the fault was in Russell's thinking. This is what I
have already explained in this message.
4. As I have claimed in this group, I have a solution to this problem
and I have published it in my papers, you can see it at www.dbdesign10.com
and at www.dbdesign11.com
My basic idea is that there are two procedures. It is a procedure that determines the plurality and the procedure that determines the individual. Frege solution for the procedure for plurality was well done. However neither Frege, nor Zermelo nor Russell realized that the elements of the set had to be identified. There are many other parts in my solution. I've written all this on this user group since 2005, when I started to publish my solutions. For example, I have a solved the construction of the atomic structures for entities, relationships events, predicates, propositions and concepts.
Set theory is fundamental for databases, especially for the Relational Model. I would mention that the relation is defined as a set.
Vladimir Odrljin Received on Sun Jan 28 2018 - 01:58:55 CET