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.
>      
>     Sincerely,
>     Mark
> 
>     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: si is a mental model of ri;
> >         - between reality and consciousness: perceiving data and creating 
> > mental models:  triple (si, ei, ri) 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 (si, ei, ri).
> >          
> >          
> >         [clip_image002]
> >         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.
> >          
> >          
> >          
> >          
> >         [image]
> >          
> >         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
> >         Krassimir
> >          
> >         References
> >         [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.
> >         http://www.foibg.com/ijita/vol20/ijita20-01-p01.pdf
> >         [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.
> >         http://www.foibg.com/ijita/vol24/ijita24-04-p01.pdf
> > 
> > 
> > 
> >         _______________________________________________
> >         Fis mailing list
> >         Fis@listas.unizar.es mailto:Fis@listas.unizar.es
> >         http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
> > 
> >     > 
 

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Arturo Tozzi

AA Professor Physics, University North Texas

Pediatrician ASL Na2Nord, Italy

Comput Intell Lab, University Manitoba

http://arturotozzi.webnode.it/ 
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