Abstract
In his work The Moscow Philosophic-Mathematical School and Its Founders (1904), P. A. Nekrasov presented mathematics as fundamental to the whole body of knowledge, including philosophy, theology and political theory.
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Notes
According to Belyĭ, Bugaev was not particularly fond of his pupil. See Andreĭ Belyĭ, Na rubezhe dvukh stoletiĭ (Moskva: Khudozhestvennaîa literatura, 1989), 73; id., Moskva (Moskva: Sovetskaîa Rossiîa, 1989), 36–37; Nekrasov is there called “Blagolepov”.
Among numerous articles written on Nekrasov, the following were particularly useful to me: Eugene Seneta, “Statistical Regularity and Free Will: L.A.J. Quetelet and P.A. Nekrasov,” International Statistical Review 71: 2 (2003), 319–334;
Oscar B. Sheynin, “Nekrasov’s Work on Probability: The Background,” Archive for History of Exact Sciences 57 (2003), 337–353.
P.A. Nekrasov, “Moskovskaîa filosofsko-matematicheskaîa shkola i ee osnovateli,” MS 25: 1 (1904), 3–4.
Written later than Nekrasov’s work, E.V. Spektorskiĭ’s Problema sotsial’noĭ fiziki v XVII stoletii ([The problem of social physics in the seventeenth century], 1910–1917) allows one to see what somebody interested in the tradition of mathesis universalis, could have known about it at that time. Spectorskiĭ’s study started the history of sociology not from Comte, but from the then largely forgotten thinkers of the seventeenth century whose sociological theories were integrated into the framework of mathesis universalis. Spectorskiî’s view of them as more profound and scientific than current positivism coincided with that of the Moscow “school.” His survey of seventeenth century thought included interesting and sympathetic pages on theology. It was perhaps not an accident that Spektorskiĭ, who was one of the favorite pupils of A.L. Blok (the notable professor of law and the father of the poet) in Warsaw, defended the first volume of this work as his MA thesis in 1911 at ÎUr’ev (Dorpat) University: rector of the University at that time was the member of the Moscow “school” V.G. Alekseev (more on him see Chapter 4, Section “V.G. Alekseev”). On Spektorskiî, see A.A. Ermichev, “E.V. Spektorskiĭ (1875–1951). Biobibliographicheskaîa spravka,” in E. Spektorskiĭ’s Problema sotsial’noĭ fiziki v XVII stoletii, T. II (Sankt-Peterburg: Nauka, 2006), 506–523.
Nekrasov was the member of the Moscow Psychological Society. The journal of the society Voprosy filosofii i psikhologii regularly published materials related to Kantianism. Nekrasov’s sources on the philosophy of geometry included G.I. Chelpanov’s Predstavlenie prostranstva s tochki zreniîa gnoseologii ([The Notion of Space from the Point of View of Epistemology], 1904; Nekrasov, “Moskovskaîa filosofsko-matematicheskaîa shkola,” 13 n.)
M.V. Chirikov and O.B. Sheĭnin, “Perepiska P.A. Nekrasova i K.A. Andreeva,” IMI 35 (1994), 124; http://www.sheynin.de/download/2_Russian%20Papers%20History.pdf, 70.
See L. Zhmud, The Origin of the History of Science in Classical Antiquity, trans. Alexander Chernoglazov (Berlin — New York: Walter de Gruyter, 2006), 82–83.
P.A. Nekrasov, Nikolaĭ Pavlovich Bogolepov (Moskva, 1901).
P.A. Nekrasov, “Predislovie,” MS 25: 1 (1904), XII.
It was originally a paper read at the mathematical congress in Zürich, in French, in 1897. See N. Bougaïev, “Les mathématiques et la conception du monde au point de vue de la philosophie scientifique,” in Verhandlungen des ersten internationalen Mathematiker-Kongresses in Zürich vom 9 bis 11 August 1897 (Leipzig: Teubner, 1898), 206–223. The following year it was read at the Psychological Society in Moscow. See N.V. Bugaev, Matematika i nauchno-filosofskoe mirosozertsanie (Moskva, 1899).
It seems to have been introduced into the Russian scientific language via French: “Arithmology <…>. This is the name which Ampère gave to pure mathematics in his ‘Essai sur la philosophie des sciences’ <…>” (F.A. Brokhaus and I.A. Efron, eds, Èntsiklopedicheskiĭ slovar,’ T. II (S.-Petersburg, 1890), 100). This definition echoed French dictionaries which referred to Ampère’s classification of sciences proposed in the cited essay, as the source of the term “arithmology”: “Arithmologie <…> (mot créé par Ampère). Science générale des nombres et de la mesure des grandeurs quelles qu’elles soient”
(Paul Guérin, ed., Supplément illustré du Dictionnaire des dictionnaires. Lettres, sciences, arts, encyclopédie universelle, T. 7 (Paris: Libraires-imprimeries réunies, 1895), 91). Bugaev’s use of “arithmology” was different from that in Ampère who divided mathematics into “arithmologie” and geometry, the former embracing, among other branches of mathematics, mathematical analysis which Bugaev opposed to “arithmology.”
See André-Marie Ampère, Essai sur la philosophie des sciences, ou exposition analytique d’une classification naturelle de toutes les connaissances humaines (Paris: Chez Bachelier, Imprimeur-Libraire pour les Sciences, 1834), 40–42, 274.
Andreĭ Belyĭ, Na rubezhe dvukh stoletiĭ (Moskva: Khudozhestvennaîa literatura, 1989), 61.
Cf.: “The new theory of numbers is a return to Pythagoreanism; and my father knew this” (Andreĭ Belyĭ and Aleksandr Blok, Perepiska, 1903–1919 (Moskva: Progress-Pleîada, 2001), 435).
The fullest account of Bugaev’s “arithmology” is a contemporary one, written by one of the members of the Moscow “school”: W.G. Alexejeff, “Über die Entwickelung des Begriffes der höheren arithmologischen Gezetsmässigkeit in Natur- und Geisteswissenschaften,” Vierteljahrsschrift für wissenschaftliche Philosophie u. Soziologie 3: 1 (1904), 73–92.
P.A. Florenskiĭ suggested that the contemporary intellectual trends dealing with discontinuity and thus destroying the modern scientific outlook, arithmology being one of them, foreshadow the proximity of Apocalypse. See his Stolp i utverzhdenie istiny, T. 1 (I) (Moskva: Pravda, 1990), 127. A train of thought behind such expectations could be the following: a scientific grasp of phenomena escaping immutable physical laws might usher in a period when these very laws will cease to exist. See also Avril Pyman, Pavel Florensky: A Quiet Genius. The Tragic and Extraordinary Life of Russia’s Unkown Da Vinci (New York — London: Continuum, 2010), 77, 277 n. 41. According to S.M. Solov’ev, Bugaev “plunged into the theory of numbers” would “fall into a sort of mystical frenzy” over the Apocalypse.
See S. Solov’ev, Vospominaniîa (Moskva: Novoe literaturnoe obozrenie, 2003), 170.
It was not, however, a complete oblivion. Süssmilch was not absent from books on the history of statistics. At the time of Bugaev’s youth readers of Otechestvennye zapiski, which regularly printed materials on statistics, could find a sympathetic account of Süssmilch’s ideas: A. Korsak, “Statisticheskie vyvody ob obshchikh zakonakh narodonaseleniîa i ego zhizni,” OZ 139 (1861), 2–3.
Ad. Quételet, Du Système social et des lois qui le régissent (Paris: Guillaumin et Cie, Libraires, 1848), 103.
P.A. Nekrasov, “Logika mudrykh lîudeĭ i moral.” (Otvet V.A. Gol’tsevu); VFiP 70: 5 (1903), 926. This work was in many ways a preliminary to the Moscow Philosophic-Mathematical School.
One may refer to one of Bugaev’s favorite authors, Camille Flammarion (1842–1925; by the moment of drawing up the catalog of his library he had three books by Flammarion: Les mondes imaginaires et les mondes réels, ed. 1868; Contemplations scientifiques, ed. 1870; Vie de Copernic et histoire de la découverte du système du monde, ed. 1872; ORK i R NB MGU, f. 41, op.1, ed. khr. 252, L. 78 ob., 8). His later work L’inconnu et les problèmes psychiques (1900) must have been known in Bugaev’s circle. Like most of Flammarion’s books it was translated into Russian;
see a very favorable review of the book in Bogoslovskit vestnik, which was also favorable to Nekrasov’s ideas: Sergei Kulîukin, “ÎAvleniîa telepatii i znachenie ikh v oblasti osnovnykh psikhologicheskikh voprosov,” Bogoslovskiĭ vestnik 2: 5 (1901), 200–227. The chapter entitled “L’action psychiques d’un esprit sur un autre” presents the same notion, widespread at that time, of how the knowledge of things distant or past could be obtained, massively using the comparisons of rays, currents, inductions etc.
“Istinno” seems to have become especially frequent during the reign of Nicholas II, who was addicted to this word, and this, according to S.ÎU. Witte, was at the root of its popularity at that time. See S.ÎU. Witte, Vospominaniîa, T. 2 (Moskva: Izd. sotsial’no-èkonomicheskoĭ literatury, 1960), 306, 501.
The resemblance of Nekrasov’s language and ideology to those of the Soviet times was pointed out in M.A. Prasolov, “‘Tsifra poluchaet osobuîu silu’ (Sotsial’naîa utopiîa Moskovskoĭ filosofsko-matematicheskoĭ shkoly),” Zhurnal sotsiologii i sotsial’noĭ antropologii 10: 1 (2007), 46–47.
[G.B.] Nikol’skiĭ, Slovo o pol’ze matematiki ([Kazan’, 1816]), 42. I found this tiny brochure following a reference in Alexandre Koyré’s early book La philosophie et le problème national en Russie au début du XIXe siècle (Paris: Librairie ancienne Honoré Champion, 1929), 74–75. Let us note that Nikol’skiĭ had the opportunity to realize the notions which he formulated. Under the notorious Mikhail Leont’evich Magnitskiĭ (1778–1844) charged with functions of warden of Kazan School District, he became rector of Kazan University. It will be remembered that Magnitskiĭ almost succeeded in destroying this university by trying to turn all the disciplines into religious and loyal ones (Koyré, La philosophie et le problème, 70–76). This attempt somewhat resembles what the Moscow “school” would try to do, the more so since the head of Kazan University was a mathematician embracing the same beliefs in the ideological utility of his subject. Nekrasov almost certainly knew about Nikol’skiĭ; he could hardly have missed a brief account of his ideas in VFiP. See Al.V. Vvedenskiĭ, “Sud’by filosofii v Rossii,” 42: 2 (1898), 331.
For the contemporary interest towards discrete functions, see S.S. Demidov, “N.V. Bugaev i vozniknovenie moskovskoĭ shkoly teorii funktsiĭ deĭstvitel’nogo peremennogo,” IMI 29 (1985), 120.
Leo Tolstoy, War and Peace, trans. Louise and Aylmer Maude, Vol. III (London: Humphrey Milford, Oxford University Press, 1932), 3–4.
An interesting contemporary parallel to Tolstoĭ’s reasoning on continuity and history is to be found in the preface of Jacob Burckhardt’s Die Kultur der Renaissance in Italien (1860). Burckhardt was also concerned with the contrast between the “continuity” of history and the “discreteness” of its representation by historians: “Es ist die wesentlichste Schwierigkeit der Kulturgeschichte, daß sie ein grosses, geistiges Kontinuum in einzelne scheinbar oft willkürliche Kategorien zerlegen muß, um es nur irgendwie zur Darstellung zu bringen” (Berlin: Verlag von Th. Knaur Nachf., 1928, 1–2). From this follows that Burckhardt regarded this problem as the one inherent in a historical narrative to be partly overcome by the proper selection of “discrete” elements. Whereas for the writer the dilemma of continuity/discreteness in history offered an incentive for envisaging a fantastical project of historical research, the historian confined himself to a brief formulation of this dilemma. Interestingly, though, the function of this formulation was in part similar, that is, rhetorical: it was not only a statement of a certain real difficulty, but also an excuse of an essential imperfection of historical narrative.
“‘There is no arbitrariness in nature’ [‘Proizvola net v prirode’]. As soon as this thought had grown into a conviction, all the sorcerers, shamans, magicians were rendered impossible; all the gods of the antiquity became nothing <…>. All this scaffolding, with which man had been erecting the temple of the understanding of nature, could be destructed at once, when the cupola of the immutable law emerged before the eyes of humankind <…>” (P. Lavrov, “Mekhanicheskaîa teoriîa mira,” OZ 123 (1859), 457).
Mikh. Ferd. Taube, Sovremennyĭ spiritizm i mistitsizm (Petrograd, 1909), 40–41. In particular, Taube argued against the deterministic nature of the conceptions of spiritists and insisted on the Creator “being free to work miracles” (Sovremennyĭ spiritizm i mistitsizm, 24). He identified the “discreteness and freedom of the creation [preryvnost’ tvoreniîa i ego svobodu]” with the “miracle in nature [chudo v prirode]” (Taube, Sovremennyĭ spiritizm i mistitsizm, 41; italics are by Taube), and presented arithmology as, among other things, aimed at the mathematical explication of theological notions (Taube, Sovremennyĭ spiritizm i mistitsizm, 218). Cf. Nekrasov, “Moskovskaîa filosofsko-matematicheskaîa shkola,” 70;
V.A. Kozhevnikov, Sovremennoe nauchnoe neverie. Ego rost, vliîanie i peremena otnosheniĭ k nemu (Sergiev Posad, 1912), 122, 129.
Lev Tolstoĭ, Polnoe sobranie sochineniĭ, T. 49 (Moskva: GIKhL, 1952), 94; cf. Kolîagin and Savvina, Matematiki-pedagogi Rossii, 58.
The letter was addressed to V.G. Chertkov (Lev Tolstoĭ, Polnoe sobranie sochineniĭ, T. 85 (Moskva: GIKhL, 1935), 60–61).
P.A. Nekrasov, “Filosofiîa i logika nauki o massovykh proîavleniîakh chelovecheskoĭ deîatel’nosti (Peresmotr osnovaniĭ sotsial’noĭ fiziki Quetelet),” MS 23: 3 (1902) 554–556.
Leo Tolstoy, War and Peace, Vol. II (London: Humphrey Milford, Oxford University Press, 1931), 258.
See R.Sh. Ganelin, Rossiĭskoe samoderzhavie v 190,5 g. Reformy i revolîutsiîa (Sankt-Peterburg: Nauka, S.-Peterburgskoe otdelenie, 1991), 5–6.
N.V. Bugaev, O svobode voli (Moskva, 1889), 19. For the context of this work, see Shaposhnikov, “Filosofskie vzglîady N.V. Bugaeva,” 67.
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Svetlikova, I. (2013). The Moscow “School”: P. A. Nekrasov. In: The Moscow Pythagoreans: Mathematics, Mysticism, and Anti-Semitism in Russian Symbolism. Palgrave Pivot, New York. https://doi.org/10.1057/9781137338280_3
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