David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
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
Saul A. Kripke (1982). Wittgenstein on Rules and Private Language. Harvard University Press.
David K. Lewis (1973). Counterfactuals. Blackwell Publishers.
David K. Lewis (1983). Philosophical Papers. Oxford University Press.
Rudolf Carnap (1962). Logical Foundations of Probability. Chicago]University of Chicago Press.
Citations of this work BETA
Alexander Reutlinger (2014). Do Statistical Laws Solve the 'Problem of Provisos'? Erkenntnis 79 (10):1759-1773.
Marshall Abrams (2012). Mechanistic Probability. Synthese 187 (2):343-375.
Marshall Abrams (2015). Probability and Manipulation: Evolution and Simulation in Applied Population Genetics. Erkenntnis 80 (S3):519-549.
Jacob Rosenthal (2012). Probabilities as Ratios of Ranges in Initial-State Spaces. Journal of Logic, Language and Information 21 (2):217-236.
Thomas Bartelborth (2011). Propensities and Transcendental Assumptions. Erkenntnis 74 (3):363-381.
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