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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

years with repeated interruptions caused by his innate laziness andworsening **of** health; the book still lacked its most important part, theapplication **of** the art **of** conjecturing to civil life; nevertheless, he, J. B., hadalready shown his brother [Johann] the solution **of** a difficult problem,special in its own way [§ 3.2.3], that justified the applications **of** the art **of**conjecturing.Leibniz, in his own letters to Bernoulli, never agreed that observationscould secure moral certainty but his arguments were hardly convincing.Thus, he in essence repeated Arnauld & Nicole (1662/1992, pp. 304 and317) in that the finite (the mind; therefore, observations) can not alwaysgrasp the infinite (God, but also, as Leibniz stated, any phenomenondepending on innumerable circumstances).He understood randomness as something whose complete pro**of** exceedsany human mind (Leibniz 1686/1960, p. 288) which does not contradict amodern approach to randomness founded on complexity and he was alsoright in the sense that statistical determinations can not definitivelycorroborate a hypothesis. Cf. Cicero (1991, Buch 2, § 17, p. 149): Nothing ismore opposed to calculation and regularity than chance. Leibniz had alsomaintained that the allowance for the circumstances was more importantthan subtle calculations.Gauss (§§ 9.1.3 and 9.1.5) stated that the knowledge **of** the essence **of** thematter was extremely important. Later Mill (1843/1886, p. 353) contrastedthe consideration **of** circumstances with elaborate application **of** probability,but why contrasting rather than supplementing? Anyway, more than a half**of** Chapter 4 **of** Part 4 **of** the AC in essence coincided with passages fromBernoulli’s letters to Leibniz.In 1714, in a letter to one **of** his correspondents, Leibniz (Kohli 1975b, p.512) s**of**tened his doubts about the application **of** statistical probabilities. Forsome reason he added that the late Jakob Bernoulli had cultivated the theory**of** probability in accordance with his, Leibniz’ exhortations.3.2. The Art **of** Conjecturing, Part 43.2.1. Stochastic Assumptions and Arguments. Bernoulli used theaddition and the multiplication theorems for combining various arguments.Unusual was the non-additivity **of** the probabilities. Thus, somethingpossesses 2/3 **of** certainty but its opposite has 3/4 **of** certainty; bothpossibilities are probable and their probabilities are as 8:9. See Shafer(1**978**) and Halperin (1988). Shafer also studied non-additive probabilities inLambert’s Architectonic (1771). Koopman (1940) resumed the study **of** suchprobabilities whose sources can be found in the medieval doctrine **of**probabilism that considered the opinion **of** each theologian as probable.Franklin (2001, p. 83) dated the origin **of** probabilism as 1611 or (p. 74)even as 1577. Similar pronouncements on probabilities **of** opinion go backto John **of** Salisbury (the 12 th century) and even to Cicero (Garber & Zabell1979, p. 46).Bernoulli (1713/1999, p. 233) wrote ars conjectandi sive stochastice, andBortkiewicz (1917, p. x) put that Greek word into circulation. Prevost &Lhuillier (1799, p. 3) anticipated him, but apparently their attempt wasforgotten. The Oxford English Dictionary included it with a reference to asource published in 1662.28