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The special status of mathematical probability: a historical sketch

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  • Xavier De Scheemaekere
  • Ariane Szafarz

Abstract

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines.

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Bibliographic Info

Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers CEB with number 08-017.RS.

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Length: 15 p.
Date of creation: May 2008
Date of revision:
Publication status: Published by: Université Libre de Bruxelles, Solvay Business School, Centre Emile Bernheim (CEB)
Handle: RePEc:sol:wpaper:08-017

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Keywords: probability; Kolmogorov; von Mises; axioms; epistemology;

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  1. Shafer, Glenn, 1996. "The significance of Jacob Bernoulli's Ars Conjectandi for the philosophy of probability today," Journal of Econometrics, Elsevier, vol. 75(1), pages 15-32, November.
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Cited by:
  1. Xavier De Scheemaekere & Ariane Szafarz, 2011. "The Inference Fallacy From Bernoulli to Kolmogorov," Working Papers CEB 11-006, ULB -- Universite Libre de Bruxelles.
  2. Xavier De Scheemaekere & Ariane Szafarz, 2008. "Inverting Bernoulli's theorem: the original sin," Working Papers CEB 08-029.RS, ULB -- Universite Libre de Bruxelles.

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