Philosophical Foundations of Mathematical Conceptualization of Social Phenomena and Phenomena Pertaining to the Humanities
Kushnarenko Sergei Petrovich
Novosibirsk State University of Architecture and Civil Engineering
Submitted: 09.03.2020
Abstract. The article examines the possibility of applying mathematics in the humanities. It sheds light on the reason of "incomprehensible effectiveness of mathematics" in the natural sciences. The author describes a mathematical model (Serre fibration) of relationship between individual acts of consciousness and objective content of these acts in classical rationality. The researcher reveals the productivity source and the implementation scope of a topos model in the sciences about the human. He introduces philosophical-mathematical "logos" as an adequate representation of the humanities objects’ being: it is a "topos of topos" in which its ontological connection with the personality’s act, i.e. its unity with the human’s individual psychic-corporeal apparatus, is explicated.
Key words and phrases: символ, топос, логос, сознание, рациональность, математика, личность, пространство, symbol, topos, logos, consciousness, rationality, mathematics, personality, space
Open the whole article in PDF format. Free PDF-files viewer can be downloaded .
References:
Akchurin I. A. Topologiya i identifikatsiya lichnosti // Voprosy filosofii. 1994. № 5. S. 143-149.
Galilei G. Probirnykh del master. M.: Nauka, 1987. 272 s.
Gobbs T. Izbrannye proizvedeniya: v 2-kh t. M.: Mysl', 1964. T. 1. 582 s.
Grotendik D. Urozhai i posevy. Izhevsk: Regulyarnaya i khaoticheskaya dinamika, 2001. 288 s.
Guts A. K., Pautova L. A. Sotsial'naya topologiya i toposy Grotendika // Matematicheskie struktury i modelirovanie. 2015. № 4 (36). S. 93-109.
Dennett D. Nasosy intuitsii i drugie instrumenty myshleniya. M.: AST; CORPUS, 2019. 576 s.
Zinchenko V. P., Mamardashvili M. K. Izuchenie vysshikh psikhicheskikh funktsii i kategoriya bessoznatel'nogo // Bessoznatel'noe: sb. st. Novocherkassk: Agentstvo SAGUNA, 1994. S. 69-77.
Kant I. Metafizicheskie nachala estestvoznaniya. M.: Mysl', 1999. 1712 s.
Mamardashvili M. K. Strela poznaniya. M.: Shkola "Yazyki russkoi kul'tury", 1997. 304 s.
Serr Zh.-P. Singulyarnye gomologii rassloennykh prostranstv // Rassloennye prostranstva i ikh prilozheniya: sb. perevodov / pod red. V. G. Boltyanskogo. M.: Izd-vo inostrannoi literatury, 1958. S. 9-114.
Spinoza B. Izbrannye proizvedeniya: v 2-kh t. M.: Gospolitizdat, 1957. T. 1. 631 s.
Teleman K. Elementy topologii i differentsiruemye otobrazheniya. M.: Mir, 1967. 390 s.
Awodey S. Type Theory and Homotopy // Epistemology versus Ontology. Dordrecht: Springer, 2012. 415 p.
Русский
