The significance of Jacob Bernoulli's \textit{Ars Conjectandi} for the philosophy of probability today
This is a non-comprehensive discussion of the ``Ars Conjectandi'' and even its date of publication is stated wrongly. The connection between Jakob's deliberations and the theory of probabilism (allowing a person to follow any probable opinion of any Father of the Catholic Church, and leading to non-additive probabilities recently introduced into mathematics) is not mentioned. His law of large numbers is downgraded as being obsolete with respect to Niklaus Bernoulli's finding of 1713, and Jakob's insistence that, for the ``Bernoulli trials'', induction was not inferior to deduction (``woran vielleicht niemand bisher auch nur gedacht hat'') is passed over. The ``De Moivre--Laplace'' limit theorem (1733 rather than 1738) is not seen as a development of Jakob's result. That Niklaus had plagiarized Jakob and became acquainted with his law before 1713 is apparent now since Jakob's ``Werke'', Bd. 3, are published (1975). The author did not refer to the Russian source, ``O zakone bolshikh chisel'' (On the law of large numbers), Yu. V. Prokhorov (ed.), Moskva: Nauka (1986; Zbl 0646.01008) containing Prokhorov's, A. P. Yushkevich's and the reviewer's comments; or to \textit{A. P. Yushkevich}'s paper, N. Bernoulli and the publication of J. Bernoulli's Ars Conjectandi, Theory Probab. Appl. 31, 286--303 (1987); translation from Teor. Veroyatn. Primen. 31, No. 2, 333--352 (1986; Zbl 0616.01008); or to the reviewer's description of Niklaus' finding [Studies in the history of statistics and probability, E. S. Pearson and M. G. Kendall (ed.) (London, 1970), p. 232]. The author approvingly mentions T. Porter, for whom everything goes, see the reviewer's pertinent review in Centaurus 31, 171--172 (1988).
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