Institute of Philosophy
Russian Academy of Sciences

  Alexander S. Karpenko
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Alexander S. Karpenko



Alexander S. Karpenko      

 Alexander S. Karpenko was born on 7 April, 1946, in the city of Kuibyshev (now Samara, Russia). In the same year, his parents returned to their home town of Mogilyev in Byelorussia. After graduating, in 1965, from Mogilyev polytech, he served in the army. After the army, studied philosophy at the Moscow State University as an undergraduate and then a postgraduate student specializing in logic. In 1979, he got a degree PhD and, in 1991, a degree D.Sci with the thesis Fatalism and Contingency of the Future: a Logical Analysi. Since 1977, A. S. Karpenko has been doing research at Institute for Philosophy of Russian Academy of Sciences, where he has been the head of Department of Logic since 2000. Alexander Karpenko is also a professor of the Moscow State University and a member of Russian Academy of Natural Sciences. Editor-in-chief of the annual almanach Logical Investigations published in Russian and English.




Academic interests

  • Early publications are devoted to a new type of  semantics for many-valued logics, which have been called  "factor-semantics".  The most important result contained in this body  of work is the Boolean algebras can be used to interpret a wide class  of many-valued logics, and the truth-values themselves can be  understood as certain subsets of the set of Boolean-valued vectors.
  • By use of the logical matrices to prove the independence of axioms were constructed the different finite Boolean lattices of implicative and implicative-negative logics. The main result of this work is a construction of a "maximal" lattice that includes most important implicative logics.
  • A number of  publications is devoted to a radically new outlook on the nature of  prime  numbers and their logical properties. As a  result,  prime numbers were structured in the form of rotted trees and an  algorithm of building such trees out of each of the prime  numbers has been  developed.  Also the Sheffer stroke operator for prime numbers is constructed. A combination of various algebro-logical definitions of  prime numbers led to the law of generation of the classes of prime numbers.
  • As the final result of the research in the field of multi-valued logics the monograph " The Development of Many-valued Logic" has been published (M., 2010) where the development of multi-valued logic is traced from Aritotle to the modern day. The special attention is paid to the results obtained by Russian logicians.
  • From 2000, the scientific interests have started to take a new direction. As well as the problem of the foundations of mathematics has risen hundred years ago, now there is the problem of the foundations of logic itself. It has been shown that at the end of the XX century the question "What is logic" has become actively discussed. This question itself points at the crisis of the foundations of logic, which has led to the complete reevaluation of the status of logic and its purpose.
  • Apart from  purely logical, wider philosophical topics have also been developed, such as the various fatalistic arguments. The main thesis of this line work is that the phenomenon of the free will is intimately connected with a very difficult problem of the changeability of the past. Recently have been analyzed the theories which require the realization to the actuality of all the physical possibilities and in addition to that – all of which is being thought of as possible. This signifies the transition from the substantial thinking to the modal thinking. This way the philosophical paradigm emerges with the completely new range of problems, which  is supported by the modern development of cosmology in the form of the various theories of the multiverse.
  • In a series of works pen-named A. Belovezhski the problem of K-totalitarianism has been developed.
  • Under the pen-name A. Chakha poetry and short stories are published.



I. Academic publications


  • Łukasiewicz J. On Aristotle's principle of contradiction. Critical Investigation (trans. from Polish to Russian). Ed. A.S. Karpenko with introductory article and comments. — М. – SPb: CGI, 2012. — 256 p. — ISBN 978-5-98712-038-5 (Abstract in English, full text in Russian).
  • Karpenko A. S. The Development of Many-valued Logic. Moscow: LKI Publishers, 2010 (stereotype edition in 2014). (Preface, contents, references (in Russian)). Review by A. Schumann: Voprosy Filosofii, 3: 184-185, 2012 (in Russian).
  • Karpenko A. S. Łukasiewicz Logics and Prime Numbers. Luniver Press, Beckington, 2006 (Introduction, contents, full text).
  • Karpenko A. S. Many-valued Logics. Moscow: Nauka, 1997 (in Russian).
  • Karpenko A. S. Fatalism and Contingency of Future: a Logical Analysis. Moscow: Nauka, 1990 (in Russian). Moscow.: LKI/URSS, 2008, 2nd edition.

Representative papers

  • Bochvar's three-valued logic and literal paralogics: Their lattice and functional equivalence // Logic and Logical Philosphy. 2016.
  • Modal Propositional Truth Logic Tr and its Completeness // Logical Investigations. 2016. Vol. 22. № 1, P. 13-31 (PDF).
  • Giperrealizm [Hyperrealism], Part I, II // Filosofskii zhurnal [Philosophical journal]. 2016. Vol. 9(2), P. 5-23; Vol 9(3), P. 5-24 (Abstract in English).
  • Predislovie. Mnogoobrazie trekhznachnosti [Foreword. The variety of three-valuedness] / Devyatkin L.Yu., Prelovskii N.N., Tomova N.E. V granitsakh trekhznachnosti [Within the boundaries of three-valuedness]. M.: IF RAN, 2015, S. 9-33.
  • Toska po filosofii. [Yearning for Philosophy], Paper I, II // Voprosy filosofii [Problems of Philosophy]. 2015. № 10. P. 133–149; 2016. №2. P. 137-147. (Abstract in English).
  • V poiskakh real'nosti: Ischeznovenie [In search of reality: the disappearance] // Filosofiya nauki [Philosophy of science]. V. 20. 2015. P. 36-72 (Abstract in English, full text in Russian).
  • Reshetki chetyrekhznachnykh modal'nykh logik [Lattices of Four-valued Modal Logics] // Logicheskie issledovaniya [Logical Investigations]. 2015. № 21(1). P. 122-134 (PDF).
  • The Basic Question of Metaphysics // Philosophical Journal. 2014. № 2(13). P. 51-73 (Abstract in English, full text in Russian).
  • Many-valued logic in Poland: The golden age // The History and Philosophy of Polish Logic. Essays in Honour of Jan Woleński / Eds. K. Mulligan, K. Kijania-Placek and T. Placek. PALGRAVE MACMILLAN, 2014, P. 13-48.
  • Philosophical problems of foundations of logic // Studia Humana, 3(1): 13-26. 2014 (PDF).
  • Philosophical principle of fullness (extended and revised (in Russian)) // Philosophy and Culture, Vol. 11-12, 2013. (Abstractp in English, full text in Russian: Part I, Part II).
  • Philosophical principle of fullness, Part I, II // Voprosy Filosofii. 2013. № 6. P. 58-70; № 7. P. 95-108.
  • Von Wright’s truth logic and around // Logical Investigations (Special Issue), 19: 39-50, 2013.
  • Preface. The History of Finish-Soviet Logic Colloquium // Logical Investigations (Special Issue), 19: 5-9, 2013.
  • Moscow logical schools (Period of ideology 1917 – 1991), in A. Schumann (ed.), Logic in Central and Eastern Europe: History, Science and Discourse, University Press of America, 2013, pp. 317-380.
  • Aristoteles and Łukasiewicz on the law of contradiction (In favor of publishing of Jan Łukasiewicz's book "On Aristotle's principle of contradiction. A critical study") // Voprosy Filosofii, 8: 154-165, 2012.
  • Logic in Russia, in New Russian Encyclopedia. M., 2012. pp. 498-500. (in Russian).
  • Towards protologic. Logical investigations, 17: 152-166, 2011. (in Russian).
  • Continuity of three-valued logic: problems and hypotheses. Logical investigations, 16:  127-133, 2010. (in Russian).
  • Modern study in philosophical logic: worldwide level and Russian science. Studies in Logic, Grammar and Rhetoric, 14 (27): 35-71, 2008.
  • Application of logic in computer science, in Logic: Perspectives of Development. Kiev: Kiev University, 2006, 35-41. (in Russian).
  • Non-classical logics versus classical. Logico-Philosophical Studies, 3: 48-73, 2005 (in Russian).
  • The subject of logic in the light of the main trends of its development. Logical investigations, 11: 149-171, 2004 (in Russian).
  • Contemporary research in philosophical logic. Voprosy philosophii, 9: 54-75. 2003 (in Russian).
  • Atomic and molecular paraconsistent logics. Logique et Analyse, 177-178: 31-35, 2002.
  • Three-valued paraconsistent logics. Multiple-Valued Logic, 5: 117-123, 2000.
  • A maximal paraconsistent logic: The combination of two three-valued isomorphs of classical propositional logic, in Frontiers of Paraconsistent Logic. Baldock, 2000, 181-187.
  • The classification of propositional calculi (Finite Boolean lattices for implicational logics). Studia Logica, 66: 253-271, 2000. (PDF)
  • Logic at the turn of the millennium. Logical investigations, 7: 7-60, 2000 (in Russian). (Abstract in english, MS Word)
  • The class of precomplete Łukasiewicz's many-valued logics and the law of prime number generation. Bulletin of the Section of Logic, 25: 52-57, 1996.
  • A logic without fixed points, in Philosophical Logic and Logical Philosophy. Dordrecht: Kluwer, 1996, 213-219.
  • Logic, determinism and the past. Voprosy philosophii, 5: 72-81, 1995 (in Russian).
  • Characterization of prime numbers in Łukasiewicz's logical matrix. Studia Logica, 48(4): 465-478, 1989.
  • Truth-values. What are those? In Investigations on Non-Classical Logics. Moscow: Nauka, 1989, 38-53 (in Russian).
  • From factor-semantics to a calculus of algebras, in Sintactic and Semantic Analysis Non-Extensional Logics. Moscow: Nauka, 1989, 93-100 (in Russian).
  • T-F-sequences and their sets as truth-values, in Intensional Logic, History of Philosophy and Methodology. Budapest, 1988, 109-119.
  • Paraconsistent structure inside of many-valued logic. Synthese, 66: 63-69, 1986.
  • Factor-semantics for n-valued logics. Studia Logica, 42: 179-185, 1983.
  • Aristotle, Łukasiewicz and factor-semantics. Acta Philosophica Fennica, 35: 7-21, 1982.

II. Political commentary, poetry, prose

  • Pen-names / Alexander Belovezhsky, Alexander Karpenko, Alexander Chakha, Shura Belochkin, Alex Zero. M. – S.-Pb.: C.G.I., 2011. — 224 p. — ISBN 978-5-98712-072-9 (Annotation in English, Full text in Russian).
  • Alexander Chakha. White Cardinal (PDF (in Russian)).