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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">cyberspace</journal-id><journal-title-group><journal-title xml:lang="ru">Философские проблемы информационных технологий и киберпространства</journal-title><trans-title-group xml:lang="en"><trans-title>Philosophical Problems of IT &amp; Cyberspace (PhilIT&amp;C)</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">2305-3763</issn><publisher><publisher-name>Пятигорский государственный университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17726/philIT.2024.2.1</article-id><article-id custom-type="elpub" pub-id-type="custom">cyberspace-322</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Концепция рекурсии в когнитивных исследованиях. Часть II: От Тьюринга к Байесу и к сознанию</article-title><trans-title-group xml:lang="en"><trans-title>The Concept of Recursion in Cognitive Studies. Part II: From Turing to Bayes to Consciousness</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Михайлов</surname><given-names>И. Ф.</given-names></name><name name-style="western" xml:lang="en"><surname>Mikhailov</surname><given-names>I. F.</given-names></name></name-alternatives><bio xml:lang="ru"><p>Михайлов Игорь Феликсович, доктор философских наук, ведущий научный сотрудник</p><p>Москва</p></bio><bio xml:lang="en"><p>Mikhailov Igor Felixovich, Doctor of Philosophy, Leading researcher</p><p>Moscow </p></bio><email xlink:type="simple">ifmikhailov@iph.ras.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Институт философии РАН</institution><country>Россия</country></aff><aff xml:lang="en"><institution>Institute of Philosophy of the Russian Academy of Sciences</institution><country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>14</day><month>01</month><year>2025</year></pub-date><volume>0</volume><issue>2</issue><fpage>4</fpage><lpage>22</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Михайлов И.Ф., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Михайлов И.Ф.</copyright-holder><copyright-holder xml:lang="en">Mikhailov I.F.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://cyberspace.pgu.ru/jour/article/view/322">https://cyberspace.pgu.ru/jour/article/view/322</self-uri><abstract><p>В статье обсуждается концепция рекурсии в математике, ИИ, когнитивных исследованиях и ее связь с сознанием. Развитие понятия прослеживается параллельно с историей теории вычислимости, когда были введены концепции машины Тьюринга с оракулом и вероятностной машины Тьюринга. Также рассматриваются такие рекурсивные вычислительные методы, как байесовская рекурсивная оценка и байесовский иерархический вывод. Показано, что с каждым нововведением в рекурсивных методах пределы вычислимости расширялись. Автор утверждает, что рекурсия является жизненно важным аспектом человеческого познания, особенно в разработке и интерпретации сложного языка. В статье также характеризуются проблемы изучения рекурсии и сознания, такие как субъективная природа сознания и сложность нейронных сетей, связанных с сознательным мышлением. Кроме того, анализируются ограничения в понимании рекурсии современных теорий когнитивной обработки, освоения языка и сознания. Делается вывод о том, что исследование связи между рекурсией и сознанием имеет решающее значение для развития более глубокого понимания языка и когнитивной обработки. Автор ожидает, что будущая теория, основанная на рекурсии, поможет решить основные метафизические загадки прошлого и настоящего.</p></abstract><trans-abstract xml:lang="en"><p>This article discusses the concept of recursion in mathematics, AI, cognitive studies and its relationship to consciousness. The development of the notion is followed in parallel with the history of computability theory when concepts of Turing oracle and probabilistic machines were introduced. Also, such recursive computational techniques as Bayesian Recursive Estimation and Bayesian hierarchical inference are reviewed. It is shown that, with each novation in recursive methods, the limits of computability have expanded. The author argues that recursion is a vital aspect of human cognition, particularly in the development and interpretation of complex language. The paper also addresses the challenges of studying recursion and consciousness, such as the subjective nature of consciousness and the complexity of neural networks associated with conscious thought. Additionally, the paper examines the limitations of current theories of cognitive processing and language acquisition in understanding recursion and consciousness. The article concludes that investigating the relationship between recursion and consciousness is critical for developing a deeper understanding of language and cognitive processing. The author anticipates that a future recursionbased theory will help solve principal metaphysical conundrums of the past and the present.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>рекурсия</kwd><kwd>когнитивная обработка</kwd><kwd>сознание</kwd><kwd>усвоение языка</kwd><kwd>нейронные сети</kwd></kwd-group><kwd-group xml:lang="en"><kwd>recursion</kwd><kwd>cognitive processing</kwd><kwd>consciousness</kwd><kwd>language acquisition</kwd><kwd>neural networks</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Mikhailov I. F. The Concept of Recursion in Cognitive Studies. Part I: From Mathematics to Cognition // Philosophical Problems of IT &amp; Cyberspace (PhilIT&amp;C). 2024. № 1. P. 58-76.</mixed-citation><mixed-citation xml:lang="en">Mikhailov I. F. The Concept of Recursion in Cognitive Studies. Part I: From Mathematics to Cognition // Philosophical Problems of IT &amp; Cyberspace (PhilIT&amp;C). 2024. № 1. P. 58-76.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Soare R. I. Computability and Recursion // Bulletin of Symbolic Logic. 1996. Vol. 2, № 3. P. 284-321.</mixed-citation><mixed-citation xml:lang="en">Soare R. I. Computability and Recursion // Bulletin of Symbolic Logic. 1996. Vol. 2, № 3. P. 284-321.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Soare R. I. Turing Computability: Theory and Applications. Berlin Heidelberg: Springer-Verlag, 2016. 289 p.</mixed-citation><mixed-citation xml:lang="en">Soare R. I. Turing Computability: Theory and Applications. Berlin Heidelberg: Springer-Verlag, 2016. 289 p.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Kwisthout J. Motivating explanations in Bayesian networks using MAP-independence // International Journal of Approximate Reasoning. Elsevier Inc., 2023. Vol. 153. P. 18-28.</mixed-citation><mixed-citation xml:lang="en">Kwisthout J. Motivating explanations in Bayesian networks using MAP-independence // International Journal of Approximate Reasoning. Elsevier Inc., 2023. Vol. 153. P. 18-28.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Kato T. et al. Explore/exploit strategic movement of co-occurrence network based on a conscious/subconscious model // 2015 54th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE). IEEE, 2015. P. 301-306.</mixed-citation><mixed-citation xml:lang="en">Kato T. et al. Explore/exploit strategic movement of co-occurrence network based on a conscious/subconscious model // 2015 54th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE). IEEE, 2015. P. 301-306.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Arora S., Barak B. Randomized computation // Computational Complexity. 2012. P. 123-142.</mixed-citation><mixed-citation xml:lang="en">Arora S., Barak B. Randomized computation // Computational Complexity. 2012. P. 123-142.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Antonelli M., Lago U. D., Pistone P. On Randomized Computational Models and Complexity Classes: a Historical Overview, 2024.</mixed-citation><mixed-citation xml:lang="en">Antonelli M., Lago U. D., Pistone P. On Randomized Computational Models and Complexity Classes: a Historical Overview, 2024.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Van Leeuwen J., Wiedermann J. The Turing Machine Paradigm in Contemporary Computing BT — Mathematics Unlimited — 2001 and Beyond / ed. Engquist B., Schmid W. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. P. 1139-1155.</mixed-citation><mixed-citation xml:lang="en">Van Leeuwen J., Wiedermann J. The Turing Machine Paradigm in Contemporary Computing BT — Mathematics Unlimited — 2001 and Beyond / ed. Engquist B., Schmid W. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. P. 1139-1155.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Van Leeuwen J., Wiedermann J. A Theory of Interactive Computation BT — Interactive Computation: The New Paradigm / ed. Goldin D., Smolka S.A., Wegner P. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. P. 119-142.</mixed-citation><mixed-citation xml:lang="en">Van Leeuwen J., Wiedermann J. A Theory of Interactive Computation BT — Interactive Computation: The New Paradigm / ed. Goldin D., Smolka S.A., Wegner P. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. P. 119-142.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Sacks G. E. Metarecursion Theory // Studies in Logic and the Foundations of Mathematics. Elsevier, 1967. Vol. 46, № C. P. 243-263.</mixed-citation><mixed-citation xml:lang="en">Sacks G. E. Metarecursion Theory // Studies in Logic and the Foundations of Mathematics. Elsevier, 1967. Vol. 46, № C. P. 243-263.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Sacks G. E. Higher recursion theory. 2nd ed. Cambridge, UK: Cambridge University Press, 1990.</mixed-citation><mixed-citation xml:lang="en">Sacks G. E. Higher recursion theory. 2nd ed. Cambridge, UK: Cambridge University Press, 1990.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">De Villiers J., Hobbs K., Hollebrandse B. Recursive Complements and Propositional Attitudes // Recursion: Complexity in Cognition. Studies in Theoretical Psycholinguistics, vol. 43 / ed. Roeper T., Speas M. Springer, Cham, 2014. P. 221-242.</mixed-citation><mixed-citation xml:lang="en">De Villiers J., Hobbs K., Hollebrandse B. Recursive Complements and Propositional Attitudes // Recursion: Complexity in Cognition. Studies in Theoretical Psycholinguistics, vol. 43 / ed. Roeper T., Speas M. Springer, Cham, 2014. P. 221-242.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Cabessa J., Villa A. E. P. Recurrent Neural Networks and Super-Turing Interactive Computation // Artificial Neural Networks. Springer Series in Bio-/Neuroinformatics, vol. 4. Springer, Cham., 2015. P. 1-29.</mixed-citation><mixed-citation xml:lang="en">Cabessa J., Villa A. E. P. Recurrent Neural Networks and Super-Turing Interactive Computation // Artificial Neural Networks. Springer Series in Bio-/Neuroinformatics, vol. 4. Springer, Cham., 2015. P. 1-29.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Wen Y. et al. Probabilistic recursive reasoning for multi-agent reinforcement learning // 7th International Conference on Learning Representations, ICLR 2019. 2019. P. 1-20.</mixed-citation><mixed-citation xml:lang="en">Wen Y. et al. Probabilistic recursive reasoning for multi-agent reinforcement learning // 7th International Conference on Learning Representations, ICLR 2019. 2019. P. 1-20.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Corballis M. C. The Recursive Mind. The Origins of Human Language, Thought, and Civilization // The Recursive Mind. Princeton University Press, 2014. 309 p.</mixed-citation><mixed-citation xml:lang="en">Corballis M. C. The Recursive Mind. The Origins of Human Language, Thought, and Civilization // The Recursive Mind. Princeton University Press, 2014. 309 p.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">TECHSLANG. What is Recursive Bayesian Estimation? A short definition of Recursive Bayesian Estimation [Electronic resource]. 2024. P. 1-5. URL: https://www.techslang.com/definition/what-is-recursive-bayesianestimation (accessed: 22.02.2024).</mixed-citation><mixed-citation xml:lang="en">TECHSLANG. What is Recursive Bayesian Estimation? A short definition of Recursive Bayesian Estimation [Electronic resource]. 2024. P. 1-5. URL: https://www.techslang.com/definition/what-is-recursive-bayesianestimation (accessed: 22.02.2024).</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Daunizeau J. The Bayesian Brain: An Evolutionary Approach to Cognition // Encyclopedia of Behavioral Neuroscience: Volumes 1-3, Second edition. 2021. Vol. 1-3. P. V2-202-V2-221.</mixed-citation><mixed-citation xml:lang="en">Daunizeau J. The Bayesian Brain: An Evolutionary Approach to Cognition // Encyclopedia of Behavioral Neuroscience: Volumes 1-3, Second edition. 2021. Vol. 1-3. P. V2-202-V2-221.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Ruffini G.An algorithmic information theory of consciousness // Neurosci Conscious. 2017. Vol. 2017, № 1.</mixed-citation><mixed-citation xml:lang="en">Ruffini G.An algorithmic information theory of consciousness // Neurosci Conscious. 2017. Vol. 2017, № 1.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Vergauwen R. Consciousness, Recursion and Language // Language and Recursion. NY: Springer New York, 2014. Vol. 9781461494. P. 169-179.</mixed-citation><mixed-citation xml:lang="en">Vergauwen R. Consciousness, Recursion and Language // Language and Recursion. NY: Springer New York, 2014. Vol. 9781461494. P. 169-179.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Oizumi M., Albantakis L., Tononi G. From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0 // PLoS Comput Biol / ed. Sporns O. Public Library of Science, 2014. Vol. 10, № 5. P. e1003588.</mixed-citation><mixed-citation xml:lang="en">Oizumi M., Albantakis L., Tononi G. From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0 // PLoS Comput Biol / ed. Sporns O. Public Library of Science, 2014. Vol. 10, № 5. P. e1003588.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Peters F. Consciousness as recursive, spatiotemporal self-location // Psychol Res. 2010. Vol. 74, № 4. P. 407-421.</mixed-citation><mixed-citation xml:lang="en">Peters F. Consciousness as recursive, spatiotemporal self-location // Psychol Res. 2010. Vol. 74, № 4. P. 407-421.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
