The Inference Fallacy From Bernoulli to Kolmogorov

Xavier De Scheemaekere () and Ariane Szafarz

No 11-006, Working Papers CEB from ULB -- Universite Libre de Bruxelles

Abstract: Bernoulli’s (1713) well-known Law of Large Numbers (LLN) establishes a legitimate one-way transition from mathematical probability to observed frequency. However, Bernoulli went one step further and abusively introduced the inverse proposition. Based on a careful analysis of Bernoulli’s original proof, this paper identifies this appealing, but illegitimate, inversion of LLN as a strong driver of confusion among probabilists. Indeed, during more than two centuries this “inference fallacy” hampered the emergence of rigorous mathematical foundations for the theory of probability. In particular, the confusion pertaining to the status of statistical inference was detrimental to both Laplace’s approach based on “equipossibility” and Mises’ approach based on “collectives”. Only Kolmogorov’s (1933) axiomatization made it possible to adequately frame statistical inference within probability theory. This paper argues that a key factor in Kolmogorov’s success has been his ability to overcome the inference fallacy.

Keywords: Probability; Bernoulli; Kolmogorov; Statistics; Law of Large Numbers (search for similar items in EconPapers)
JEL-codes: N01 B31 C65 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-hpe
Date: 2011-02
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