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Erkenntnis

, Volume 70, Issue 2, pp 211–235 | Cite as

Fifteen Arguments Against Hypothetical Frequentism

  • Alan Hájek
Original article

Abstract

This is the sequel to my “Fifteen Arguments Against Finite Frequentism” (Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts:

The probability of an attribute A in a reference class B is p

iff

the limit of the relative frequency of A’s among the B’s would be p if there were an infinite sequence of B’s.

I offer fifteen arguments against this analysis. I consider various frequentist responses, which I argue ultimately fail. I end with a positive proposal of my own, ‘hyper-hypothetical frequentism’, which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim.

Keywords

Relative Frequency Infinite Sequence Objective Probability Reference Class Fair Coin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Philosophy Program, Research School of Social SciencesAustralian National UniversityCanberraAustralia

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