Set theory is a particular case of named set theory. If s**et theory
solves some problem, then **named set theory solves the same problem.
Use logic and some knowledge and you'll see truth.
On 3/21/2018 11:48 PM, tozziart...@libero.it wrote:
the named set theory does not solve the Russell paradox.
Therefore it would be better to use, in such approaches, the best
theory available, i.e., the Fraenkel-Zermelo sets.
In turn, the latter displays some limits: for example, the need of a
set with infinite elements.
Therefore, set theory is not able to tackle information problems.
You have to go back to other mathematical approaches.
Il 21 marzo 2018 alle 23.42 "Burgin, Mark" <mbur...@math.ucla.edu> ha
Dear Krassimir and other FISers,
After reading the interesting contribution of Krassimir, I would like
to share with you some of my impressions and ideas.
I like very much the term INFOS suggested by Krassimir. It’s possible
to suggest that Krassimir assumed the following definition.
An INFOS is a system functioning (behavior) of which is regulated by
This definition implies that each INFOS has an information processor.
Then it is possible to distinguish different categories and types of
INFOS. For instance:
INFOS only with acceptors/receptors
INFOS only with effectors
INFOS with both acceptors/receptors and effectors
Then it is possible to develop an interesting theory of INFOS.
At the same time, the difference between reality and consciousness
needs improvement because what many people mean using the word
reality is actually only one of the variety of realities, namely, the
physical or material reality, while consciousness is a part of the
mental reality. It is possible to find more information about
different realities and their interaction in the book (Burgin,
Structural Reality, 2012). Please, don’t confuse Structural Reality
with virtual reality.
One more issue from the interesting contribution of Krassimir, which
allows further development, is the structure of a model. Namely, the
relation (s, e, r) between a model s of an entity r forms not simply
a triple but a fundamental triad, which is also called a named set.
Why this is important? The reason to conceive the structure (s, e, r)
as a fundamental triad or a named set is that there is an advanced
mathematical theory of named sets, the most comprehensive exposition
of which is in the book (Burgin, Theory of Named Sets, 2011), and it
is possible to use this mathematical theory for studying and using
models. For instance, the structure from Figure 1 in Krassimir’s
letter is a morphism of named sets. Named set theory describes many
properties of such morphism and categories built of named sets and
their morphism. The structures from Figure 2 in Krassimir’s letter
are chains of named sets, which are also studied in named set theory.
To conclude it is necessary to understand that if we want to apply
mathematics in some area it is necessary to use adequate areas of
mathematics. As Roger Bacon wrote, All science requires mathematics,
but mathematics provides different devices that are suited to
different input. In this respect, when you give good quality grains
to a mathematical mill, it outputs good quality flour, while if you
put the same grains into a mathematical petrol engine, it outputs trash.
The theory of named sets might be very useful for information studies
because named sets and their chains allow adequate reflection of
information and information processes.
On 3/11/2018 3:34 PM, Krassimir Markov wrote:
This letter contains more than one theme, so it is structured as follow:
- next step in “mental model” explanation;
- about “Knowledge market”, FIS letters’ sequences and FIS Sci-coins.
*1. The next step in “mental model” explanation:*
Let remember shortly my letter from 05.03.2018.
To avoid misunderstandings with concepts Subject, agent, animal,
human, society, humanity, living creatures, etc., in  we use the
abstract concept “INFOS” to denote every of them as well as all of
artificial creatures which has features similar to the former ones.
Infos has possibility to reflect the reality via receptors and to
operate with received reflections in its memory. The opposite is
possible - via effectors Infos has possibility to realize in reality
some of its (self-) reflections from its consciousness.
The commutative diagram on Figure 1 represents modeling relations.
In the frame of diagram:
- in reality: real models: s is a model of r,
- in consciousness: mental models: s_i is a mental model of r_i ;
- between reality and consciousness: perceiving data and creating
mental models: triple (s_i , e_i , r_i ) is a mental model of triple
(s, e, r).
It is easy to imagine the case when the Infos realizes its
reflections using its effectors, i.e. relation between consciousness
and reality: realizing mental models and creating data. In this case
the receptors’ arrows should be replaces by opposite effectors’
arrows. In this case triple (s, e, r) is a realization of the mental
model (s_i , e_i , r_i ).
After creating the mental model it may be reflected by other levels
of consciousness. In literature several such levels are described.
For instance, in , six levels are separated for humans (Figure
2). The complexity of Infos determines the levels. For instance, for
societies the levels are much more, for animals with no neo-cortex
the levels a less.
Figure 2. 
This means that the mental models are on different consciousness
levels and different types (for instance - touch, audition, vision).
In , Jeff Hawkins had remarked: “The transformation— from fast
changing to slow changing and from spatially specific to spatially
invariant— is well documented for vision. And although there is a
smaller body of evidence to prove it, many neuroscientists believe
you'd find the same thing happening in all the sensory areas of your
cortex, not just in vision” .
As it is shown on Figure 2 mental models are in very large range
from spatially specific to spatially invariant; from fast changing
to slow changing; from “features” and “details” to objects”.
To be continued...
*2.Aabout “Knowledge market”, FIS letters’ sequences and FIS Sci-coins.*
The block-chain idea is not new. All forums and mailing lists have
the possibility to organize incoming messages in internally
connected sequences. The new is the Bit-coin, i.e. the price for
including a message in the sequence received after successful
solving a difficult task.
What we have in FIS are letters’ sequences already created for many
years. What is needed to start using them is to be strictly when we
answer to any letter not to change the “Subject” of the letter. The
list archive may help us to follow the sequences - only what is
needed to ask sorting by [ Subject ]
We may sort by [ Thread ]
Date ] <http://www.ithea.org/pipermail/ithea-iss/2018-March/date.html>.
This means that the letter corresponds to the block, and the
sequence of letters corresponds to the chain.
What about the currency?
In  we had introduced the new concept “Knowledge marked”. It is
remembered in  where the approach for measuring the scientific
contributions was proposed. It was proposed to use the “paper” as
basic measurement unit. Now I may say, the paper is our “Sci-coin”.
This Sci-coin is convertible to real currencies - it is wide
accepted the price of a paper to be downloaded as pdf-file is about
30-35 EURO or USD.
Finally, the paper “Data versus Information”  is an example of a
FIS Sci-coin mined from the letters’ sequences.
As we had seen, it is not so easy to “mine the Sci-coin”!
 Kr. Markov, Kr. Ivanova, I. Mitov. Basic Structure of the
General Information Theory. IJ ITA, Vol.14, No.: 1, 2007. pp. 5-19.
 Hawkins, Jeff (2004). On Intelligence (1st ed.). Times Books. p.
 K. Markov, K. Ivanova, I. Mitov, N. Ivanova, A. Danilov, K.
Boikatchev. Basic Structure of the Knowledge Market. IJ ITA, 2002,
V.9, No.4, pp. 123-134.
 Kr. Markov, Kr. Ivanova, V. Velychko, “Usefulness of Scientific
Contributions”, International Journal “Information Theories and
Applications”, Vol.20, Number 1, 2013, ISSN 1310-0513 (printed),
ISSN 1313-0463 (online), pp. 4-38.
 Krassimir Markov, Christophe Menant, Stanley N Salthe, Yixin
Zhong, Karl Javorszky, Alex Hankey, Loet Leydesdorff, Guy A Hoelzer,
Jose Javier Blanco Rivero, Robert K. Logan, Sungchul Ji, Mark
Johnson, David Kirkland, Gordana Dodig-Crnkovic. Data versus
Information. International Journal “Information Theories and
Applications”, Vol. 24, Number 4, 2017, ISSN 1310-0513 (printed),
ISSN 1313-0463 (online), pp. 303 -321.
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