Does the phrase " Russell's paradox " should be replaced with another phrase?

[vldm10]

On December 5, 2012, I wrote on this user group the following:
“ I distinguish real objects from abstract objects. I defined
abstract objects and the identification of each of these objects.
See (3.3.3), section 3.3, from the above mentioned paper
“Database design and data model founded on concept and
knowledge constructs”, (at http://www.dbdesign11.com )
In my paper only the "m-attributes" are determined with
our perceptual abilities. All other (more complex) objects are
defined recursively, according to their complexity
(see m-entities, m-relationships and m-states).
The complex objects are determined by our mental activities.

We can notice that E. Codd not distinguish these objects.
He did not even notice these objects.

On the other hand, we can notice that (3.3.3) is important because
it defines the relationship between concepts and identification,
that is, it determines the relationship between the relation of satisfy
and the corresponding identification. “

So, (3.3.3) means that there is another mind-world link.
This link is the identification.
Because of this, there are two mind-world links; these two links
are the concept and identification. Thus, the "identification" is
what is missing in Frege's theory.

My conclusion is as follows:

1. Gottlob Frege was right. He has not made a mistake.
But what is missing in his theory, it is the identification.

2. Bertrand Russell's paradox is not paradox. This is not
a matter which is about the using of classical logic, nor matter
which is about logical tricks. This is not matter about a proof.
This is a matter which is about the effective semantic
procedure.
This procedure is presented in my (here mantioned) paper.
Note that, G. Frege introduced and defined semantics
and concepts.
So Russell was wrong.

In my opinion, (3.3.3) gives the answers to other questions.
One such question is the following: Does the "identification"
is a non-conceptual representation?
My answer is: It depends on how you are looking at things that are
related to "identification".

(3.3.3) gives the answers also to the following question:
For example, some subject (a person) is not capable to identify
some three numbers from a finite set of natural numbers.
Is it possible to set a concept on this set of natural numbers for
this subject (person)?
The answer is no. (See universal attributes at my paper “Database design
and data model founded on concept and knowledge constructs”, section 3.3.
Note that I use term “matching” instead of “identification”, because
sometimes the identification is not direct. )

Vladimir Odrljin

[vldm10]

Here are some additional explanations regarding this post.

Notice that there is no concept, so that none of the objects can satisfy this concept. And this means, that we cannot identify an object which satisfy this concept.
Notice that only objects which are identified by subject can satisfy the corresponding concept. In other words, the unidentified objects can not satisfy the subject's concept.

So, before one checks whether a particular object satisfies certain concept, he needs to identify the object. In another words, only "known" objects can satisfy certain concept. Therefore, Russell's paradox makes no sense, because there is no object that satisfies a concept that is defined by Russell. In other words, no one can identify an object that satisfies Russell's concept.
So B. Russell was overlooked the identification of objects (individuals). But the identification of an object is the simplest way of the introducing the object.

In my paper “Database design and data model founded on concept and knowledge constructs”, at http://www.dbdesign11.com section 5.3 ” I introduced the following definition:
5.3 Definition of Concept
A concept is a construct which determines one or both of the following:
(i) A plurality of things in which all the things satisfy the concept;
(ii) A particular thing from the plurality determined by (i).

In order to identify an entity we use the following procedures:
Procedure1: Identifying the plurality.
Procedure2: Identifying individuals.

Procedure2 is not effective without Procedure1.
Note that Procedure1 is related to the concepts, because concepts define extension (plurality), while Procedure2 is related to “identification” of objects.

There is a special case "learning about an entity", see my paper “Semantic databases and semantic machines”, section 5.12 at http://www.dbdesign11.com . Here, I presented process of learning about an entity as the database structure.

When we talk about abstract objects, we can notice that people are starting to identify the natural numbers at the age of three or four years. However, mathematicians gain knowledge about the real numbers, throughout their lives.

Vladimir Odrljin

[vldm10]

Dana subota, 22. prosinca 2012. 10:41:27 UTC+1, korisnik vldm10 napisao je:
> Here are some additional explanations regarding this post. Notice that there >is no concept, so that none of the objects can satisfy this concept. And this >means, that we cannot identify an object which satisfy this concept. Notice >that only objects which are identified by subject can satisfy the >corresponding concept. In other words, the unidentified objects can not >satisfy the subject's concept. So, before one checks whether a particular >object satisfies certain concept, he needs to identify the object. In another >words, only "known" objects can satisfy certain concept. Therefore, Russell's >paradox makes no sense, because there is no object that satisfies a concept >that is defined by Russell. In other words, no one can identify an object that >satisfies Russell's concept. So B. Russell was overlooked the identification >of objects (individuals). But the identification of an object is the simplest >way of the introducing the object.

When I speak here about objects and sets, I mean the following:
1. The set has the elements.
2. These elements are names that denote objects.
3. I use Frege’s definition of the objects

>In my paper “Database design and data model founded on concept and knowledge >constructs”, at http://www.dbdesign11.com section 5.3 ” I introduced the >following definition: 5.3 Definition of Concept A concept is a construct which >determines one or both of the following: (i) A plurality of things in which >all the things satisfy the concept; (ii) A particular thing from the plurality >determined by (i). In order to identify an entity we use the following >procedures: Procedure1: Identifying the plurality. Procedure2: Identifying >individuals. Procedure2 is not effective without Procedure1. Note that >Procedure1 is related to the concepts, because concepts define extension
>(plurality), while Procedure2 is related to “identification” of objects.

Notice that Procedure2 in this definition can be based on the concept or identification.
If we apply (3.3.3) to Procedure2, Procedure2 then becomes a process of identification.

The subject that performs the identification “knows” the corresponding objects or he “knows” the identifiers of these objects.

Notice that here we have two constructs; one is the set, the other is an element of this set.
Here is one really trivial example, which may give a clearer picture about the concepts.
There are persons who can see only black and white; there are persons who can not see any color.

It is now evident that the universal attributes strongly influence the functional capabilities of a subject. It is also evident that different subjects can identify different numbers of universal attributes from the same property (here we have the concept of color).
By this trivial example I want to present the complexity of the concepts, as well as the importance of concepts as the mind-world link. This is not just a matter of concepts, this is also a matter of objects that satisfy this property (concept) and this is a matter of the identification of these objects.
These examples from the real world show that Russell approach leaves out imortant parts and simplify concepts (properties) so much that a distorted impression of it is given. This oversimplification has far-reaching consequences.

In my opinion G. Frege was right. He understood that this is a matter of semantic procedure (not logic). Therefore, we can fix Frege’s theory by adding the process of identification of the objects which satisfy the corresponding concept.

Vladimir Odrljin

[vldm10]

My solution, introduces two semantic procedures in working with concepts, say
ProcedureA and ProcedureB. ProcedureA uses "the relation of satisfaction", which
checks whether a particular attribute satisfies the given concept. ProcedureB
performs the identification of the attribute for which we want to determine
whether it satisfies the given concept. Obviously B. Russell did not use
ProcedureB, Russell only used ProcedureA. Generally, the existing theory only
uses ProcedureA, that is, it checks only a concept, and does not check the
elements that are the input into the concept.
The work of these two procedures is formally presented in my paper "Database
design and data model founded on concept and knowledge constructs“, from 2008,
at http://www.dbdesign11.com , by using the following formula:

=========================
S (the m-attribute, the concept of the property) = T
iff the m-attribute matches the entity’s attribute. … (3.3.3)
=========================

Later in mentioned paper, the formula (3.3.3) in addition to attributes is used
also for the entities, relationships and m-states. Thus, the concepts of
attributes, entities, relationships and states have been introduced recursively.
Note that in this hierarchy attributes are atomic; they are indivisible objects
when they are in the concept and when they are elements of the corresponding
extension. In my papers, I defined that factual sentences are also atomic
sentences. This was based on the decomposition into the binary data structures.
These sentences are atomic in terms of their meaning and their truth-value.
Sometimes, factual sentences are atomic because they are facts about the
attributes.

1. Russell’s Paradox
With regard to Russell's Paradox, I would like to point out that Frege made
clear distinction between a concept and its extension. In my post from December
14, 2013, in my critique of Peter Chen's theory of conceptual model, I showed
how to construct the corresponding set from a concept. Note that in Chen's
paper, it is not known what it is a concept. A similar situation exists in the
current database theory, concepts are not defined. I also wrote that the
predicate denotes concept and the predicate gets the meaning, using the concept
(according to Frege). Note also that Frege distinguishes "logical axioms" from
the axioms of Set Theory.

In my post from September 24, 2013 I presented a schema of predicates of
unsaturated expressions. This schema shows that the concepts can be very
complex. The complexity of predicates enables that the theory of databases (and
the modern mathematics) formalizes the very complex objects and their whole
world, and not only numbers.
Frege's concepts are usually represented through properties. Usually concepts
are represented in the following way: that for given property P there exists a
set consisting of those and only those objects that have the property P. The
usual notation has the following form: {x|P(x)}.

For the construction of his paradox, Russell applied: “x not belong x“
property. This is a property that set x is not a member of itself. So we form a
set S = {x | x not belong x}. This formula can be written in the following way:
For every set x we have: (x belongs S) ≡ (x not belong x)
Since this is true for every x, we can take S for x, then we have contradiction
(S belongs S) ≡ (S not belongs S)
==================================
Where did Russell make a mistake in this proof? The mistake is that Russell puts
in the concept, objects that can not be identify. He could not identify the
above-mentioned set S. Set S does not actually exist, and therefore it can not
satisfy the concept.
My formula, labeled by (3.3.3), argues that the inputs in concepts are only
those elements that we can identify. (Note that subject also must exist for a
concept). Thus Frege did not make a mistake with the concepts. In his theory
lacks the part that relates to the identification of the elements, which are
input into the procedure for the concept. So Frege was on the right track, but
did not realize the importance of identifying elements that are input into a
concept's. In contrast to Frege, Russell doubted in concepts.
================================

2. Identification
As I have already noted, the identification in my model is mostly determined by
formula (3.3.3). In my solution I use m-attributes, m-entities, m-relationships
and m-states. The prefix "m" is placed to suggest that these objects are stored
in memory. m-objects that are stored in the computer's memory are modeled so
that they comply with the man's image of the corresponding real object. Thus,
the meaning has a great importance in the identification of real objects. In
addition to m-attributes, in my paper, I've also defined a universal attributes
and particular attributes. Particular attribute is defined as an attribute of
the particular entity. For example, it may be the red color of a particular car.
Universal attribute is man's innate ability to perceive certain attributes. For
example, one can determine whether two cars have the same color. The main
purpose of the universal attributes is to identify the corresponding particular
attribute of a real entity. Of course, these attributes can be abstract, for
example, one can identify a number.
In my conceptual model, in addition to concepts, identification plays a vital
role.

In my data model, with respect to the identification, all the objects are
divided into the following groups:

(i) Attributes. Attributes are atomic objects, and each attribute is an
identifier. Formula (3.3.3) defines the attribute as an identifier and specifies
the procedure for identifying of attributes.
(ii) Complex objects. Entities, relationships and states are complex objects in
my data model. They are defined recursively, according to the complexity of
these objects. Each complex object has an identifier that is constructed
according to identifiers of its parts. For example, an entity consists of
attributes, each of these attribute is an identifier. A set of these attributes
(identifiers) specifies the entity identifier.
A Relationship is constructed from the entities. These entities determine the
identifier of the relationship.
At the end, the identifier of a state is constructed of elements that determine
the state.

Frege's idea about the concept and extension, allows a significant expansion of
mathematics. In addition to the numbers, we can now introduce the various
properties and their corresponding extensions with objects that belong to these
extensions. For example, we can work with the concept of color or a concept of
car.
In the equivalence (3.3.3), there are four possible cases in the analysis of
truth-values of the equivalence. In the real life, this equivalence will only
work when both of its sentences are true. So if m-attribute satisfies the
concept, and m-attribute is identified, then the whole semantics works OK. So
here we have a connecting between what is imagined and what is real.
Let's imagine that we have to construct a semantic machine that has these two
semantic procedures. Then the concept, roughly speaking, constructs a set and
the procedure for the identification must know (identify) the elements of the
set. So, in addition to the set, we need to know the elements that are input
into the concept. If we exclude some elements (attributes), then the
functionality of this semantic machine can change dramatically, no matter what
the concept remained the same. Suppose now, that the semantic machine can have
thousands of concepts, and that there is no identification of attributes, which
are input into these concepts – it will be very bad.
Let's take one example that might be naive, but that is an example from real
life. It is known that various beings see the world in different ways. Some
insects can see maybe a thousand different colors. Man can see maybe a hundred.
Leo sees mainly two colors, black and White. (Maybe that's reasons why they have
problems with zebras). So, all these beings have the same concept of color, but
different elements that satisfy the concept of color. These small differences in
attributes cause huge differences in the real life.
==========================
Conclusion: The concept and procedures that are associated with the concept, we
need to understand as one totality (a whole), and not as one procedure. These
procedures refer to the following link: Subject - The real World.
==========================

3. The construction of the numbers
Peano's axioms did not give the construction of natural numbers, but they
defined axioms, the natural numbers must satisfy. G. Frege made the first
construction of natural numbers. He did it in the following way:
==================================
0 = {Ø}. Representation of 0 is the set of all sets containing 0 elements. Only
such set is empty set.
The set n is representation of the natural number n and n consists of all sets
with n elements.
--

Today, the natural number is constructed by using successor function. Given a
set x, the successor of x is the set x+ = x U {x}.
Note that (x belongs x U{x}) < = > (x belongs x) OR (x = x). Thus x+
contains x as a subset and contains x as element.
Note that for this element x, must be satisfied the following:
(x not belong x).
==================================

How did Frege came to this construction of natural numbers? I will show it on
the example of the number 3. On some building we can notice certain group of 3
windows. So, 3 denotes these windows. Note, that according to Frege theory the
name denotes the corresponding real world object and give the sense of it. Note
that the name 3 can denote any three windows on this building. The name 3 can
denote any three windows on the world. The name three can denote any 3 doors,
cars etc. B. Russell wrote that "Frege identified with number 3-s a plurality of
pluralities, and number in general, of which 3 is an instance, is a plurality of
pluralities of pluralities. The elementary grammatical mistake of confounding
this with the simple plurality of a given triad made the whole philosophy of
number, before Frege, a tissue of nonsense in strictest sense of term
"nonsense". "

Thus, this explanation suggests why Frege represents a natural number N as "all
sets with n elements." With examples about colors and numbers, I wanted to show
that the concept and identification of attributes are strongly associated with
the real world. They are semantic procedures.

I think my solution of Russell's Paradox is essential. It is not on the formal
level. In contrast, my solution is at the level of important semantic
procedures, which are the important link mind-the real world.

In the current Set theory (say Zermelo-Fraenkel) there are formulas that are not
of a "set type". For formula, namely for property p (x) is said to be "set type"
if there is a set whom belong all sets with the property p (x).

In Set theory can be proved the following two theorems:
Formulas (x not belongs x) and (x = x) are not “set type”.

4. Some historical facts about Russell's Paradox
When he submit his capital work to printing, in the late evening of the day,
Frege received a letter from Russell in which Russell briefly informs Frege that
he had found a paradox in Frege’s work. The paradox refers to the main axiom in
Frege's theory. Here is what Frege wrote about this event: “Hardly anything more
unfortunate can befall a scientific writer than to have one of the 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 ... I should gladly have dispensed with this
foundation if I had known of any substitute for it. And even now I do not see
how arithmetic can be scientifically established; how numbers can be apprehended
as logical objects, and brought under review; unless we are permitted – at least
conditionally – to pass from a concept to its extension. ....“

From this Frege's text two things are clear: First, Frege kept his ideas on
concepts and extensions. Second, Frege predicted certain restrictions on the
level of concept / extension, as Zermelo later did with axioms of set theory.

After the happenings of Russell’s Paradox, Frege abandoned completion of what
was to have been his greatest achievement and his work of large scale. He
produced no work for next seven years. He spent his last years as broken and
bitter man, without scientific interest as he had before.

In the spring of 1908th, director of Universities of Jena, Mr. Dr. von Eggeling,
in charge of awarding medals and awards in such circumstances, announced the
following: “Mr Frege does not belong any of medals, since his scholarly
activities are of the lower level and the University has no specific benefits of
them.” In 1908 Frege was 60 years old.

In one period Frege has held lectures at Jena University. Rudolf Carnap and a
retired colonel, who was involved in contemporary logical theory as a hobby,
were the only students at these lectures. Carnap described Gottlob Fregea as a
professor who was a great mathematician and philosopher. Note that R. Carnap is
recognized as a great logician. Many scientists put Carnap on the second place
at the list of great logician, behind Frege.

If anyone has any criticism regarding this post, then feel free to post it. For
me this is a very important topic.

Vladimir Odrljin

[vldm10]

Recently, I presented my solution of Russell's paradox in the Mathematical
Institute of the Serbian Academy of Sciences. Abstract of the presentation
can be found at the address:
http://www.mi.sanu.ac.rs/seminars/programs/seminar1.nov2014.htm

I would like to make a few comments related to my solution of the Russell's
paradox, after this event.
My solution contains the following two types of sets:
- Sets whose elements denote objects
- Classic mathematical sets, which have arbitrary elements. So, these are
the sets that belong to the current set theory

==================================
(i) Sets whose elements denote objects
==================================
This kind of sets is typical in databases and I consider them as a specific
type of mathematical sets.
For these sets I have developed a theory of states, theory of
identification, and the theory of decomposition of structures into atomic
structures that are presented on this group.
I took Entity / Relationship philosophy and mathematics, as it is described
by Kurt Gödel in his work from the 1944, as the foundation for this type of
sets.
This paper clearly confirms that the priority of ideas for Entity /
Relationship model does not belong to Peter Chen. Entity / Relationship
philosophy and mathematics belong to Kurt Gödel and probably to some other
mathematicians and philosophers. Kurt Gödel published this work, before the
theory of databases was created and before the occurrence of computers.
We can say that Peter Chen applied these ideas in databases. Because of the
great importance of this work and regarding the priority of the idea, I'll
quote greater part of this Gödel's work:
“By the theory of simple types I mean the doctrine which says that the
objects of thought (or, in another interpretation, the symbolic expressions)
are divided into types, namely: individuals, properties of individuals,
relations between individuals, properties of such relations, etc. (with a
similar hierarchy for extensions), and that sentences of the form: " a has
the property φ ", " b bears the relation R to c ", etc. are meaningless, if
a, b, c, R, φ are not of types fitting together. Mixed types (such as
classes containing individuals and classes as elements) and therefore also
transfinite types (such as the class of all classes of finite types) are
excluded. That the theory of simple types suffices for avoiding also the
epistemological paradoxes is shown by a closer analysis of these.”
-------
This Godel’s paper is from: Kurt Gödel: Collected Works: Volume II, Oxford
University Press, 1990
-------
Note that K. Godel called objects, properties and relationships as "the
object of thought". In my paper from 2008, I introduced m-attributes, m-
entities, m-relationships and m-states, where m is the shortcut for a
memory. Here the suffix “m” is in accordance with my definition of abstract
objects.
In my opinion, these sets whose members denote objects actually form part of
a new theory. More precisely this part of today's database theory is part of
a new mathematical theory.
In my solution, serious and unresolved problems related to the
identification of objects are precisely represented and their solution is
given.
On this user group, for the first time, the wrong solutions, related to the
identification of objects in RM / T, Anchor Modeling and OO databases are
precisely explained and solved. In all these three approaches, it was used
so-called surrogate key.

Leibniz’s Law enables work on the identification of entities. By using this
law we assure that identification of objects is a mathematical discipline.
Properties in Leibniz's Law, I have divided into two types: intrinsic and
extrinsic properties.

==============================
(ii) Sets that are classic mathematical sets.
==============================
The members of these sets do not denote objects, that is, these members are
arbitrary. Elements of sets are objects. Since the set can be an element of
a set, then sets are also objects. Now in (3.3.3) we have to use m-entity
instead of m-attribute. Note that I am using two semantic procedures.

========================
The axioms of set theory
========================
Note that if Russell's Paradox is solved, then the axioms of set theory must
be changed.

Note that from Frege's definition of the concept and extension; we can
derive “comprehension” and “extensionality” for sets. For example, this can
be seen in the excellent and beautiful work about Frege, from John Burgess,
Princeton University.
On the other hand I also use my theory of identification, in the
construction of a set.

================================
About some inaccuracy in Russell's paradox
================================
In the example by which Russell presented a paradox in Frege's theory, in my
opinion Russell used imprecise assertions. In Russell's paradox is not
defined which concept he used.

It is often used example of a set of all sets. This set comes down to the
example that is used in Russell's paradox. But we can set the question -
what is the concept that determines the set of all sets and what is the
appropriate extension. Whether in this example, Russell thought about the
concept of all concepts? By the way it seems that such concept is nonsense.
In order to better illustrate this lack of clarity, regarding to Russell's
paradox, let's take an example that can be found in the English textbooks.
Frege has defined construction of natural numbers. Now I will focus on the
natural number 1. Frege defined the natural number 1 as:
{x: x is a set and x has one element}
Let us denote by [1] set of all one-element sets. Then {[1]} belongs [1].
Thus, we have that [1] belongs {[1]} belongs [1]
and this is not “nice”.
However, if we use precisely Frege's notation, we must determine which
concept we use in these two cases.
For example, if we use my definition for concepts, then we can see that:
In first case we can identify one simple element, which belongs to
one-element set…(1)
In second case we can identify set as element of one-element set…(2)
Now we can see that (1) has the object which is simple element and that (2)
has set as element. Is the concept for (1) same as concept for (2).
Obviously, these are two different concepts.
In Russell’s papers, it is not clear distinction between concepts and
extensions. Later Russell tried to solve this matter by using hierarchy of
types?
In my opinion there is no good definition about types. However, if somebody
thinks that Russell has good definition of type, I would have been grateful
to the person who can present such definition of the type on this user
group.

Vladimir Odrljin

[Ed Prochak]

While I found this message interesting, I think think you will get more feedback by posting in the sci.math group.

[vldm10]

Dana subota, 6. prosinca 2014. 16:32:11 UTC+1, korisnik Ed Prochak napisao je:
> While I found this message interesting, I think think you will get more feedback by posting in the sci.math group.

This my post, is very related to the theory databases and I think it speaks
about things that are more important than Russell's Paradox. I will mention
just two of the many reasons that this post is placed on group for the
theory of databases:

1. Here are introduced sets whose elements denote objects. Such sets are
typical for databases. However Set Theory is about arbitrary sets. These
sets, whose elements denote some objects are associated with complex issues.
For example, on this user group for the first time was shown why a surrogate
key is a bad solution. Let me mention that two well-known theories - RM / T
and object oriented approach - use surogatte key.
2. Notice that I am using two semantic procedures, which are presented in
this thread. Although I do not use the axioms of set theory, I have pointed
out, the fact that some important axioms may be constructed from Frege's
definitions of concepts and extensions. Also identification could be
presented by axioms. After such axiomatization, we could build the data
model that is based on sets.

--
However I agree with you, that I should present this solution of Russell's
Paradox at (international) mathematical community. Maybe later I will do
that, but now in this moment I am very busy.

Vladimir Odrljin

[vldm10]

1.Division of set theory into two parts
============================
In my previous post, in this thread, I have introduced the division of set
theory into two theories:
(i) The existing mathematical set theory.
(ii) Sets whose elements denote objects. An important feature of these sets
is that by using them we introduce semantics.

In both types of these sets, we introduce axioms. The axioms can be viewed
as constraints. But we can, if necessary, introduce other types of
constraints.
Given that the number of objects (real and abstract) is large, then this
second type of sets is very large.

Notice that in connection with the above-mentioned set, authors of "Anchor
Modeling" have a lack of understanding of the basic ideas of set theory.
These authors in "Anchor Modeling" introduced "set of actors." Of course
such a set does not exist.

2. New results on the identification from my papers
=====================================
In my procedures for the identification, for the first time are introduced
the following:
(i)
I introduced the subject which "execute" identification. In my paper
"Database design and data model founded on the concept and knowledge
constructs", in section 3, I have defined important constraint on the
subject, with the following title:
Limitation of Interpretation. Our assumption related to real world objects
is that we can recognize or match those objects for which we have
perceptual, inferential or rational abilities.
(ii)
I have defined that attributes are identifiers. Attributes are defined by
the formula (3.3.3), see my article from 2008. So, these attributes are
defined with the subject's ability to identify these attributes.
Please note that in my model I have properties (of entities and
relationships). Attributes are instances of properties. In some of my posts
I wrote that concepts depend on the subject's ability to identify
identifiers.
(iii)
Identifiers of entities are constructed using identifiers of the
corresponding attributes. Then I apply formula (3.3.3) to the m-entity.
Procedures for identification of relationships and states are similar. So
for the first time, procedures of complex objects are derived (recursively)
from simpler objects. For example in my post to Derek I explained that
identifiers of states are defined by identifiers of entities and by general
knowledge related to the corresponding entity. Derek noticed that
identifiers of states are similar to surrogates. But I explained that the
construction of identifiers of states is more complex.
Identifiers for attributes are not derived. They are given (they depend on
subject's abilities).
(iv)
For the first time it was explained, what are the identifiers of entities,
and what they are not. In my opinion these are the three important types of
identifiers.
a) the surrogate key
b) the locally defined identifier
c) the industry-standard identifier

For example the anchor key is not surrogate key as it is presented in
"Anchor Modeling". If you have the number of invoice, which is written on
the invoice, then that number is not a surrogate, this number is real
because it is on the real invoice, in the real world.
I explained in my posts to Derek, that identifiers of entities are related
to subject's operations with a memory; how to store an identifier of m-
entity into a memory and how to recall it from the memory. I explained that
surrogates are related to a subject and a memory (the memory where
surrogates and the corresponding m-attributes are stored).
I also explained that the industry-standard identifiers can be used to
explain how thoughts and semantic content are conveyed between two subjects.

My procedures for identification are introduced in (3.3.3). In (3.3.3) I
also use term "matching" because sometimes the procedure of identification
is more like matching.
The mentioned identifiers I explained in thread "some information about
anchor modeling".
In mentioned thread I showed that "Anchor Key" and "Surrogate key" are
special cases of the identifier of an entity, which is presented in my
Simple Form. As I already wrote a surrogate is not a surrogate if it belongs
to a real object. This is also serious nosense in "Anchor Modeling".
(v)
I introduced General Form in 2005 for general databases, that is for
databases that maintain "history". In April 2006 I introduced Simple Form,
for simple databases, that is databases that maintain current state. I wrote
in details about these forms on this user group. General and Simple Form
enable the decomposition of database's structures into atomic structures.

Note that atomic structures and the corresponding atomic sentences can be
identified by the corresponding identifier of the state. Every complex
sentence also can be identified by using the identifier of the corresponding
state. Note that sentences express thoughts.
The atomic structures enable huge advantage for the identification
procedures.
(vi)
My definition of the identifier of an entity, procedures for identifiers of
entities as well as atomic structures, enable to store an entity ( to store
one thing) in database. Please note that Internet of Things (IoT) are
becoming very popular. There is prediction that IoT will become the biggest
part of businesses in the near future.

3. Some big drawbacks in RM, ERM and "Anchor Modeling" at the level of the
db design
=========================================================================
a) These models do not explain and do not prove, on which they base the
claim that objects are made of attributes.
b) These data models do not provide proof that the identification of the
entity is determined by the identification of the corresponding attributes.

Example: Honda dealer received 200 new Honda Civic cars, which all have the
same attributes. Imagine now that someone has wiped out all the VIN numbers
from these Honda Civic. Then we get 200 cars that have all the attributes
the same. So we made a counterexample. Obviously the authors of these three
data models are not noticed this kind of problems.

In my data model I use Leibniz's Law and my generalization of Leibniz's Law
(In my paper I named it - the General Law).

In his paper RM/T, section 3, E. Codd wrote: "A database so structured will
then consist of two parts: a regular part consisting of a collection of
time-varying relations of assorted degree (this is sometimes called the
extension) and an irregular part consisting of predicate logic formulas that
are relatively stable over time (this is sometimes called the intention,
although it may not be what the logicians Russell and Whitehead originally
intended by this word)"

It seems to me that Codd, here in this text, attempts to attribute one of
the greatest discoveries in the history of science to his countrymen B.
Russell and A. Whitehead. This is about logic, predicate calculus, meaning,
relations ...
I have already pointed to this user group that Codd's Relational Model is
just application of Frege's theory to databases. See my post in the
following thread "Sensible and NonsenSQL Aspects of the NoSQL Hoopla" posted
on 24.9.2013. at
https://groups.google.com/forum/?fromgroups=#!msg/comp.databases.theory/IfFnvnKoP4w/KkqT0DFeEzQJ
Note that some well known scientists proclaimed Frege for one of the
greatest mathematicians and philosophers so far.

E. Codd shows a serious misunderstanding of semantics. For example, Codd is
mostly linked to the "meaning" when he talks about the names of attributes.
As I already pointed out, Frege introduced "meaning".
Note that in RM, attributes are basic thing. Attributes are important for
identification and that is related to Leibniz's Law, rather then to Frege's
theory about meaning.

Note that in RM, in a crucial stage of building a database, that is in phase
of DB Design, db designer is often forced to do the wrong design, in order
to be able to correct it by applying the normal forms. In other words, in RM
has not been resolved the following fundamental problem: How to design the
correct basic structures, in the first step at the level of db design.

Note also that in the RM / T Codd introduced entities, but he did not even
mentioned mapping between ERM and RM. The mapping between data models is
huge and serious theory, obviously Codd did not notice this whole area.

Vladimir Odrljin

[Eric]

On 2015-02-25, vldm10 <vld...@yahoo.com> wrote:
8>< --------

> In his paper RM/T, section 3, E. Codd wrote: "A database so structured
> will then consist of two parts: a regular part consisting of a collection
> of time-varying relations of assorted degree (this is sometimes called
> the extension) and an irregular part consisting of predicate logic
> formulas that are relatively stable over time (this is sometimes called
> the intention, although it may not be what the logicians Russell and
> Whitehead originally intended by this word)"

That should be "intension", not intention.

Eric
--
ms fnd in a lbry

[vldm10]

Dana srijeda, 25. veljače 2015. u 17:57:40 UTC+1, korisnik vldm10 napisao je:

> In my data model I use Leibniz's Law and my generalization of Leibniz's Law
> (In my paper I named it - the General Law).

I think I need further clarification in relation to this above text:
I introduced the following theories:

1.
In my data model, the entity is determined, by using above-mentioned laws.
So, in my data model, entities are constructed of attributes (intrinsic and
extrinsic).

2.
However I also construct states of entities. In my data model, states of an entity
are determined with the general knowledge of one or more subjects about the entity.
An entity is the best determined by its states. So, when we use the states of an
entity, then we have the best identification of the entity.
Thus, states are not determined by using Leibniz's Law or by using General Law.
=============================================================
I have introduced two kinds of history of events.
(i) The history of events from the past.
(ii) The history of events from the future.


Vladimir Odrljin