Fifteen arguments against hypothetical frequentism

Erkenntnis 70 (2):211 - 235 (2009)
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 Philosophy   Philosophy   Epistemology   Ontology   Ethics   Logic
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Jacob Rosenthal (2012). Probabilities as Ratios of Ranges in Initial-State Spaces. Journal of Logic, Language and Information 21 (2):217-236.

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