Re: Does the phrase " Russell's paradox " should be replaced with another phrase?
Date: Wed, 25 Feb 2015 08:57:39 -0800 (PST)
Message-ID: <0c00ba24-44b2-49be-91bd-668c5e6a7c61_at_googlegroups.com>
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 mentity 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
- These models do not explain and do not prove, on which they base the claim that objects are made of attributes.
- 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).
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 Received on Wed Feb 25 2015 - 17:57:39 CET