Novosibirsk State Pedagogical University Bulletin, 2018, No.4, pp.141-157
159.955; 165.0; 51-77; 7.013

What is the exact knowledge and how it is prodused in the cognitive processes

Trofimov V. M. 1 (Krasnodar, Russian Federation)
1 Kuban State Technological University

Introduction. According to recent studies the images of numbers and sets are present in the neural networks of humans and animals. It is experimentally confirmed that animals, unlike humans, are not able to perform accurate calculations. There is a problem of determining the nature of exact knowledge, necessary criteria of its existence. The role of exact knowledge in cognitive processes and the conditions of its storage and accumulation remain unclear. When considering the exact knowledge as a subject of study should take not only the exact calculations, but also the exact line of the artist, the exact poetic image, the expression of accurate thought. The purpose of the work is to identify mathematically correct conditions for providing exact knowledge in cognitive processes.
Materials and Methods. The concepts of a number and a set allow us to get closer to the accurate description of facts and processes using the language of set theory. Application of this method to consider the features of human perception and information processing is justified by known data on the "sense of numbers" in humans and animals. The same method allows us to design the structure of the object of cognitive activity. The method of the theory of dimensions and similarity allows us to clarify the conditions of economical memory.
Results. The author has identified some apparently key conditions to ensure accurate knowledge in the daily activities of people associated with the development and storage of knowledge, in particular, the stability of the language. The author considers the concepts of number and set in application to the object of cognitive activity and reveals the embodiment of the set-theoretic interpretation of the object not only in scientific research, but also in everyday life. The author raises the question whether it is possible to know exactly in the changing paradigm of knowledge and how if it is possible. Equally important is the question of the dynamics of accurate knowledge storage in the conditions of its growth.
Conclusions. The author proposed the concept of exact knowledge, produced by man in any form of knowledge, and gave its justification by means of a set-theoretical method, as well as links to known experimental data of related sciences.


Cognitive activity of the person; Exact knowledge; Concept of exact knowledge; Changing paradigms of knowledge; Stability of language; Interpretation of the cognizable object

  1. Ivlev V. Y., Ivleva M. L., Inozemtsev V. A. Ccognitive revolution as a factor in the formation of a new epistemological paradigm and methodology of the study of knowledge in modern science. Izvestiya MGTU MAMI, 2013, vol. 6, no. 1, pp. 91–99. URL:
  2. Isaeva V. V. Fractal and chaotic patterns in animal morphology. Proceedings of the Zoological Institute RAS, 2009, vol. 313, no. S1, pp. 199–218. URL:
  3. Trofimov V. M. Service and educational activity in ontological aspect. Monograph. Novosibirsk, Novosibirsk State Pedagogical University Publ., 2012, 184 p. URL:
  4. Birch S. A. J., Brosseau-Liard P. E., Haddock T., Ghrear S. E. A ‘curse of knowledge’ in the absence of knowledge? People misattribute fluency when judging how common knowledge is among their peers. Cognition, 2017, vol. 166, pp. 447–458. DOI:
  5. Borgianni Y., Matt D. T. Ideality in Axiomatic Design and beyond. Procedia CIRP, 2016, vol. 53, pp. 95–100. DOI: 10.1016/j.procir.2016.07.029
  6. Briglia J., Servajean P., Michalland A.-H., Brunel L., Brouillet D. Modeling an enactivist multiple-trace memory. ATHENA: A fractal model of human memory. Journal of Mathematical Psychology, 2018, vol. 82, pp. 97–110. DOI:
  7. Nieder A., Dehaene S. Representation of number in the brain. Annual Review of Neuroscience, 2009, vol. 32, pp. 185–208. DOI: 
  8. Franklin D. R. J., Mewhort D. J. K. Memory as a hologram: an analysis of learning and recall. Canadian Journal of Experimental Psychology / Revue Canadienne de Psychologie Expérimentale, 2015, vol. 69 (1), pp. 115–135. DOI:
  9. Friston K., Kilner J., Harrison L. A Free energy principle for the brain. Journal of Physiology-Paris, 2006, vol. 100, issue 1-3, pp. 70–87. DOI:
  10. Friston K. The free-energy principle: a unified brain theory? Nature Reviews Neuroscience, 2010, vol. 11, pp. 127–138. DOI:
  11. Grigorescu D. The discussion between Heisenberg and Dirac regarding the nature and meaning of scientific knowledge. Procedia – Social and Behavioral Sciences, 2015, vol. 203, pp. 400–404. DOI:
  12. Howard M. W. Memory as Perception of the Past: Compressed Time in Mind and Brain. Trends in Cognitive Sciences, 2018, vol. 22, issue 2, pp. 124–136. DOI:
  13. Li J., Wang F., Shen M., Fan G. The tendency of unconscious thought toward global processing style. Consciousness and Cognition, 2017, vol. 53, pp. 14–22. DOI:
  14. Longo G. From exact sciences to life phenomena: Following Schrödinger and Turing on Programs, Life and Causality. Information and Computation, 2009, vol. 207, issue 5, pp. 545–558. DOI:
  15. Mikolajczyk T., Moldovan F., Ciobanu I., Chalupczak A., Marin A. G. Brain research using computer test. Procedia Technology, 2016, vol. 22, pp. 1113–1120. DOI:
  16. Pinker S. So How Does the Mind Work?. Mind & Language, 2005, vol. 20, issue 1, pp. 1–24. DOI:
  17. Brugger P. The Tell-Tale Brain: Unlocking the Mystery of Human Nature. Cognitive Neuropsychiatry, 2012, vol. 17, issue 4, pp. 351–358. DOI:
  18. Richmond L. L., Gold D. A., Zacks J. M. Event Perception: Translations and Applications. Journal of Applied Research in Memory and Cognition, 2017, vol. 6, issue 2, pp. 111–120. DOI:
  19. Roediger H. L., Rajaram S., Srinivas K. Specifying criteria for postulating memory systems. Annals of the New York Academy of Sciences, 1990, vol. 608, issue 1, pp. 572–595. DOI:
  20. Ruigendijk E., Friedmann N., Novogrodsky R., Balaban N. Symmetry in comprehension and production of pronouns: A comparison of German and Hebrew. Lingua, 2010, vol. 120, issue 8, pp. 1991–2005. DOI: 
  21. Tulving E. Episodic Memory: From Mind to Brain. Annual Review of Psychology, 2002, vol. 53, pp. 1–25. DOI: 
  22. Velichkovsky B. M. Cognitive science: The art and its implications. Psychology in Russia: State of the Art, 2017, vol. 10 (3), pp. 2–7. DOI:
  23. Versace R., Labeye E., Badard G., Rose M. The contents of long-term memory and the emergence of knowledge. European Journal of Cognitive Psychology, 2009, vol. 21, issue 4, pp. 522–560. DOI:
  24. Versace R., Vallet G. T., Riou B., Lesourd M., Labeye É., Brunel L. Act-In: An integrated view of memory mechanisms.Journal of Cognitive Psychology, 2014, vol. 26, issue 3, pp. 280–306. DOI:
  25. Xiaofan Xu, Yu Chen, Yufang Zhao, Juan Yang. The neural evidence of the reflected appraisal process as a main path for learning about one's self-knowledge of personality. Biological Psychology, 2015, vol. 110, pp. 85–90. DOI:
  26. Erlich J. The Shape of Inner Space: String Theory and the Geometry of the Universe`s Dimensions. American Journal of Physics, 2011, vol. 79, issue 5, pp. 559. DOI:   
Date of the publication 31.08.2018