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Statistical regularity and free will: L.A.J. Quetelet and P.A. Nekrasov. (English) Zbl 1114.62302

Summary: In the 19th century, causes of empirically observed stability of averages in settings relating to human behaviour were a topic of intense discussion in western Europe. This followed an extensive study of empirical stability by the founder of modern statistics (and of the International Statistical Institute) L.A.J. Quetelet, published in 1835, in what he called ”Social Physics”. The eminent mathematician of strong probabilistic and philosophical inclination and Russian Orthodox religious belief, P.A. Nekrasov, took up and modified Quetelet’s Social Physics in 1902, with (social) independence seen as prime cause of statistical regularity. Our paper focuses on the role free will plays in the statistical writings of Quetelet and of Nekrasov. The work of the latter has remained little known in general, mainly for politico-ideological reasons.

MSC:

62-03 History of statistics
91-03 History of game theory, economics, and finance
01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
03A05 Philosophical and critical aspects of logic and foundations
91E99 Mathematical psychology
91D99 Mathematical sociology (including anthropology)

Biographic References:

Quetelet, L. A. J.; Nekrasov, P. A.
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References:

[1] Alexejeff, Die Mathematik als Grundlage der Kritik wissenschaftlichphilosophischer Weltanschauung: (nach Untersuchungen von N.W. Bugajew und P.A. Nekrassow in Zusammenhang mit meinen Untersuchungen über formale Chemie) pp 48– (1903)
[2] Andreev , A.V. 1999 Theoretical foundations of confidence (strokes for a sketch of P.A. Nekrasov) [in Russian.] Istoriko-Matematicheskie Issledovania
[3] Anon, Nekrasov, Pavel Alekseevich, Novyi Entsiklopedicheskii Slovar 28 (1916)
[4] Buckingham, Mathematics as a Tool for Economic and Cultural Development: The Philosophical Views of the Leaders of the Moscow Mathematical Society, 1867-1905., Michigan Academician 31 pp 33– (1999)
[5] Buniakovsky, Osnovania Matematicheskoi Teorii Veroiatnostei. [Foundations of the Mathematical Theory of Probabilities.] (1846)
[6] Droesbeke , J.-J. Jongmans , F. 2001 Adolphe Quetelet In Heyde and Seneta 127 131
[7] Ford, Dmitrii Egorov: Mathematics and religion in Moscow., Mathematical Intelligencer 13 pp 24– (1991)
[8] Franklin, The Science of Conjecture: Evidence and Probability Before Pascal (2001) · Zbl 0996.01001
[9] Gol’tsev , V.A. 1903 Vozrazhenie P.A. Nekrasovu. [Response to P.A.Nekrasov] Voprosy Filosofii i Psikhologii 754 755
[10] Hankins, Adolphe Quetelet as Statistician. (1908)
[11] Heyde, I.-J. Bienaymé: Statistical Theory Anticipated. (1977)
[12] Statisticians of the Centuries (2001) · Zbl 1016.01025
[13] Kant, Kritika chistago razuma Kant. [Critique of Pure Reason of Kant.] (1907)
[14] Koblitz, A Convergence of Lives. Sofia Kovalevskaia: Scientist, Writer, Revolutionary. (1983) · Zbl 0527.01009
[15] Kolman, My ne dolzhni byli tak zhit’.[We should not have lived that way.] (1982)
[16] Lottin, Quetelet, Statisticien et Sociologue. (1912)
[17] Lyusternik, The early days of the Moscow Mathematical School., Russian Mathematical Surveys 22 (1967) · Zbl 0156.00203
[18] Mlodzeiowski, Zamechanie professora B.K. Mlodzeiowskago. [Remarks by Professor B.K. Mlodzeiowski]., Voprosy Filosofii i Psikhologii 14 pp 558– (1903)
[19] Nekrasov, General properties of numerous independent events in connection with approximative calculation of functions of very large numbers. [in Russian]., Matematicheskii Sbornik 20 pp 431– (1898)
[20] Nekrasov, Filosofiia i Logika Nauki o Massovikh Proiavleniiakh Chelovecheskoi Deiatelnosti (Peresmotr osnovanii sotsialnoi fiziki Ketle) (1902)
[21] Nekrasov , P.A. 1912a Teoriia Veroiatnostei. Dopolnennoe Statisticheskoi Teoriei Veroiatnostei i Elementarnoi Nomografii [Theory of Probabilities. Supplemented by the Statistical Theory of Probabilities and Elementary Nomography.] Izd. 2e [2nd edn.] Sankt Peterburg: K.L. Rikker [532pp.]
[22] Nekrasov, Viera, Znanie, Opyt. Osnovnoi Metod Obschestvennikh i Estestvennikh Nauk. [Faith, Knowledge, Experiment. The Fundamental Method of Social and Natural Sciences]. (1912b)
[23] Orlov , M. 1933 Matematyka i Religia. [Mathematics and Religion.] Partvydav ”Proletar
[24] Petrova , S.S. 1994 P.A. Nekrasov i metod perevala Voprosy Istorii Estestvoznaniia i Tekhniki 107 109
[25] Petrova, The origin of the method of steepest descent., Historia Mathematica 24 pp 361– (1997) · Zbl 0894.01006
[26] Polovinkin , S.M. 1991 Moskovskaia filosofsko-matematicheskai shkola Obschestvennie Nauki v SSSR.
[27] Polovinkin , S.M. 1994 Psikho-aritmo-mekhanik. (Filosofskie cherti portreta P.A. Nekrasova) Voprosy Istorii Estestvoznaniia i Tekhniki 109 113
[28] Porter, The Rise of Statistical Thinking. 1820-1900. (1986)
[29] Quetelet, Sur l’homme et le développement de ses facultés, ou Essai de physique sociale. 2 vols (1835)
[30] Quetelet, A Treatise on Man and the Development of his Faculties (1842)
[31] Quetelet, Lettres à S.A.R. le duc régnant de Saxe-Cobourg et Gotha, sur le théorie des probabilités, appliquée aux sciences morales et politiques. (1846)
[32] Quetelet , A. 1847 Statistique morale. De l’influence du libre arbitre de l’homme sur les faits sociaux, et particulièrement sur le nombre des mariages Royaume de Belgique. Ministère de l’Intérieure. Bulletin de la Commission centrale de statistique
[33] Quetelet, Sur la statistique morale et les principes qui doivent en former la base., Mémoires de l’Académie royale des sciences et belles-lettres de Bruxelles 21 (1848)
[34] Quetelet, Physique sociale, au Essai sur le développement des facultés de l’homme. 2 vols (1869)
[35] Reichesberg, Die Statistik und die Gesellschaftswirtswissenschaft. (1893) · JFM 27.0016.02
[36] Reichesberg, Der berühmte Statistiker Adolf Quetelet. Sein Leben und sein Wirken. Eine biographische Skizze. Stümpfli et Cie (1896) · JFM 27.0016.02
[37] Rümelin, Reden und Aufsätze. pp 370– (1875)
[38] Seneta, The central limit problem and linear least squares in pre-revolutionary Russia. The background., Mathematical Scientist 9 pp 37– (1984) · Zbl 0542.01003
[39] Seneta, A sketch of the history of survey sampling in Russia., Journal of the Royal Statistical Society, Series A 148 pp 118– (1985) · Zbl 0606.62001
[40] Seneta, Encyclopedia of Statistical Sciences 9 pp 658– (1988)
[41] Seneta, Markov and the birth of chain dependence theory., International Statistical Review 64 pp 255– (1996) · Zbl 0918.60008
[42] Seneta , E. 2001 Fedor Andreevich Schcherbina Heyde and Seneta (2001) 239 242
[43] Sheynin, A. Quetelet as a Statistician., Archive for History of Exact Sciences 36 pp 281– (1986) · Zbl 0605.01002
[44] Sheynin, Perepiska P.A. Nekrasova i A.I. Chuprova, Istoriko-Matematicheskie Issledovania. (36) pp 159– (1995)
[45] Sintzow [Sintsov], Review of Nekrasov (1902)., Fortschritte der Mathematik 33 pp 236– (1903) · JFM 33.0597.01
[46] Sluginov, P.A. Nekrasov., Trudy Matematicheskogo Seminaria Permskogo Universiteta, Perm 1 pp 37– (1927)
[47] Solov’ev , A.D. 1997 P.A. Nekrasov and the central limit theorem of probability theory. [in Russian.] Istoriko-Matematicheskie Issledovania. 9 22 · Zbl 0916.03031
[48] Stigler, The transition from point to distribution estimation., Bull. International Statistical Institute 46 pp 332– (1975) · Zbl 0351.62005
[49] Stigler, Statistics on the Table: The History of Statistical Concepts and Methods. (1999) · Zbl 0997.62506
[50] Uritsky , S. 1924 Prof. Pavel Alekseevich Nekrasov Izvestia, 24 December 7
[51] Istoria i teoria statistiki v monografiakh Wagner’a, Rümelin’a, Oettinger’a i Schwabe. [The history and theory of statistics in the monographs of Wagner, Rümelin, Oettingen and Schwabe.] (1879)
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