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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.

Suggested Citation

  • Xavier De Scheemaekere & Ariane Szafarz, 2008. "The special status of mathematical probability: a historical sketch," Working Papers CEB 08-017.RS, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:sol:wpaper:08-017
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    References listed on IDEAS

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    1. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    2. 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 & Kim Oosterlinck & Ariane Szafarz, 2012. "Addressing Economic Crises: The Reference-Class Problem," Working Papers CEB 12-024, ULB -- Universite Libre de Bruxelles.
    2. Xavier De Scheemaekere & Kim Oosterlinck & Ariane Szafarz, 2014. "Issues in Identifying Economic Crises: Insights from History," Working Papers CEB 14-014, ULB -- Universite Libre de Bruxelles.
    3. Xavier De Scheemaekere & Ariane Szafarz, 2011. "The Inference Fallacy From Bernoulli to Kolmogorov," Working Papers CEB 11-006, ULB -- Universite Libre de Bruxelles.
    4. 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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    More about this item

    Keywords

    probability; Kolmogorov; von Mises; axioms; epistemology;
    All these keywords.

    JEL classification:

    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C00 - Mathematical and Quantitative Methods - - General - - - General

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