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  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 , 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.  > > > > 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 ] > > 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  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”! > > > > Friendly greetings > > Krassimir > > > > References > >  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. 272. ISBN > > https://en.wikipedia.org/wiki/International_Standard_Book_Number > > 0805074562 https://en.wikipedia.org/wiki/Special:BookSources/0805074562 . > >  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. > > http://www.foibg.com/ijita/vol20/ijita20-01-p01.pdf > >  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 > > > > > > _______________________________________________ > Fis mailing list > Fis@listas.unizar.es > http://listas.unizar.es/cgi-bin/mailman/listinfo/fis > 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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