David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Thought: A Journal of Philosophy 1 (2):81-89 (2012)
One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on the books: a measure that assigns the same infinitesimal probability to each number between zero and one. I will show that such a measure, while mathematically interesting, is pathological for use in confirmation theory, for the same reason that a measure that assigns an infinitesimal probability to each possible outcome in a countably infinite lottery is pathological. The pathology is that one can force someone to assign a probability within an infinitesimal of one to an unlikely event
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References found in this work BETA
Leonard J. Savage (1954). The Foundations of Statistics. Wiley Publications in Statistics.
Frank Arntzenius, Adam Elga & John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251 - 283.
Timothy Williamson (2007). How Probable Is an Infinite Sequence of Heads? Analysis 67 (3):173 - 180.
Ruth Weintraub (2008). How Probable is an Infinite Sequence of Heads? A Reply to Williamson. Analysis 68 (299):247–250.
I. J. Good (1967). On the Principle of Total Evidence. British Journal for the Philosophy of Science 17 (4):319-321.
Citations of this work BETA
Jonathan Weisberg (forthcoming). You’Ve Come a Long Way, Bayesians. Journal of Philosophical Logic:1-18.
Alexander R. Pruss (2014). Infinitesimals Are Too Small for Countably Infinite Fair Lotteries. Synthese 191 (6):1051-1057.
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