The significance of Jacob Bernoulli's \textit{Ars Conjectandi} for the philosophy of probability today
type: Item
instance of: scholarly article
title: The significance of Jacob Bernoulli's \textit{Ars Conjectandi} for the philosophy of probability today
zbMATH Open document ID: 0858.01014
DOI: 10.1016/0304-4076(95)01766-6
published in: Journal of Econometrics
publication date: 1997-03-25T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 01A50
Mathematics Subject Classification ID: 60-03
zbMATH DE Number: 955382
zbMATH Keywords: Niklaus Bernoulli
zbMATH Keywords: limit theorem
Wikidata QID: Q55953742
author: Glenn Shafer
reviewed by: O. B. Sheĭnin
MaRDI profile type: Publication
full work available at URL: 0304-4076(95)01766-6
OpenAlex ID: W2033664129
cites work: Q4357638
cites work: Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach
cites work: Q3781705
cites work: Q4068666
cites work: Q3996908
cites work: Non-additive probabilities in the work of Bernoulli and Lambert
cites work: Perspectives on the theory and practice of belief functions
cites work: Q4888750
cites work: Q3803965
cites work: Q4272802
cites work: The probabilistic analysis of testimony
Recommended article: BERNOULLI'S LAW OF LARGE NUMBERS
Recommended article: The difficult birth of stochastics: Jacob Bernoulli's \textit{Ars conjectandi} (1713)
Recommended article: Q4266137
Recommended article: Q3789507
Recommended article: Q6058219
Recommended article: Nicholas Bernoulli's Theorem
Recommended article: Q3099423
Recommended article: Q5431151
Recommended article: Tercentenary of Ars Conjectandi (1713): Jacob Bernoulli and the Founding of Mathematical Probability
Recommended article: Tercentennial anniversary of Bernoulli's law of large numbers
description: scientific article; zbMATH DE number 955382