The Inference Fallacy From Bernoulli to Kolmogorov
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.
|Date of creation:||Feb 2011|
|Date of revision:|
|Publication status:||Published by:|
|Contact details of provider:|| Postal: CP114/03, 42 avenue F.D. Roosevelt, 1050 Bruxelles|
Phone: +32 (0)2 650.48.64
Fax: +32 (0)2 650.41.88
Web page: http://difusion.ulb.ac.be
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Xavier De Scheemaekere & Ariane Szafarz, 2009.
"The Special Status of Mathematical Probability: A Historical Sketch,"
ULB Institutional Repository
2013/95543, ULB -- Universite Libre de Bruxelles.
- 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.
When requesting a correction, please mention this item's handle: RePEc:sol:wpaper:2013/77259. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Benoit Pauwels)
If references are entirely missing, you can add them using this form.