David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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.
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References found in this work BETA
Paul Bartha & Christopher Hitchcock (1999). The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets. Synthese 118 (3):403-437.
Rudolf Carnap (1962). Logical Foundations of Probability. Chicago]University of Chicago Press.
Adam Elga (2004). Infinitesimal Chances and the Laws of Nature. Australasian Journal of Philosophy 82 (1):67 – 76.
Alan Hájek (2003). What Conditional Probability Could Not Be. Synthese 137 (3):273--323.
Citations of this work BETA
Thomas Bartelborth (2011). Propensities and Transcendental Assumptions. Erkenntnis 74 (3):363-381.
Carl Hoefer (2012). Calibration: Being in Tune with Frequencies. Dialectica 66 (3):435-452.
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Peter M. Williams (1992). Review Essay: A Theory of Logical Frequentism. [REVIEW] Synthese 91 (3):337 - 346.
Alan Hájek (2009). Fifteen Arguments Against Hypothetical Frequentism. Erkenntnis 70 (2):211 - 235.
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