*Dear Arturo,
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:

Dear Mark,

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 scritto:

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 information.
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:

Dear Colleagues,

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 [1] 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 ).


Figure 1

After creating the mental model it may be reflected by other levels of consciousness. In literature several such levels are described. For instance, in [2], 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. [2]

This means that the mental models are on different consciousness levels and different types (for instance - touch, audition, vision).

In [2], 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” [2].

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 ] <http://www.ithea.org/pipermail/ithea-iss/2018-March/subject.html>. We may sort by [ Thread ] <http://www.ithea.org/pipermail/ithea-iss/2018-March/thread.html> [ Subject ] <http://www.ithea.org/pipermail/ithea-iss/2018-March/subject.html> [ Author ] <http://www.ithea.org/pipermail/ithea-iss/2018-March/author.html> [ 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 [3] we had introduced the new concept “Knowledge marked”. It is remembered in [4] 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” [5] 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”!

Friendly greetings



[1] Kr. Markov, Kr. Ivanova, I. Mitov. Basic Structure of the General Information Theory. IJ ITA, Vol.14, No.: 1, 2007. pp. 5-19.

[2] Hawkins, Jeff (2004). On Intelligence (1st ed.). Times Books. p. 272. ISBN <https://en.wikipedia.org/wiki/International_Standard_Book_Number>0805074562 <https://en.wikipedia.org/wiki/Special:BookSources/0805074562>.

[3] 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.

[4] 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.


[5] 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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*Arturo Tozzi*

AA Professor Physics, University North Texas

Pediatrician ASL Na2Nord, Italy

Comput Intell Lab, University Manitoba


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