David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Frank Arntzenius, Adam Elga & and John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251-283.
Frank Arntzenius, Adam Elga & John Hawthorne (2004). Bayesianism, Infinite Decisions, and Binding. Mind 113 (450):251 - 283.
I. J. Good (1967). On the Principle of Total Evidence. British Journal for the Philosophy of Science 17 (4):319-321.
Leonard J. Savage (1954). The Foundations of Statistics. Wiley Publications in Statistics.
Ruth Weintraub (2008). How Probable is an Infinite Sequence of Heads? A Reply to Williamson. Analysis 68 (299):247–250.
Citations of this work BETA
No citations found.
Similar books and articles
Sylvia Wenmackers (2011). Philosophy of Probability: Foundations, Epistemology, and Computation. Dissertation, University of Groningen
Vieri Benci, Leon Horsten & Sylvia Wenmackers (2013). Non-Archimedean Probability. Milan Journal of Mathematics 81 (1):121-151.
Sylvia Wenmackers & Leon Horsten (2013). Fair Infinite Lotteries. Synthese 190 (1):37-61.
Yaroslav Sergeyev (2010). Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals. Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
Yaroslav D. Sergeyev (2008). A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities. Informatica 19 (4):567-596.
G. Schurz & H. Leitgeb (2008). Finitistic and Frequentistic Approximation of Probability Measures with or Without Σ -Additivity. Studia Logica 89 (2):257 - 283.
Frederik Herzberg (2007). Internal Laws of Probability, Generalized Likelihoods and Lewis' Infinitesimal Chances–a Response to Adam Elga. British Journal for the Philosophy of Science 58 (1):25-43.
Yaroslav Sergeyev (2009). Numerical Computations and Mathematical Modelling with Infinite and Infinitesimal Numbers. Journal of Applied Mathematics and Computing 29:177-195.
Paul Bartha & Christopher Hitchcock (1999). The Shooting-Room Paradox and Conditionalizing on Measurably Challenged Sets. Synthese 118 (3):403-437.
Jeremy Gwiazda (2013). Throwing Darts, Time, and the Infinite. Erkenntnis 78 (5):971-975.
John C. Bigelow (1979). Quantum Probability in Logical Space. Philosophy of Science 46 (2):223-243.
J. Ellenberg & E. Sober (2011). Objective Probabilities in Number Theory. Philosophia Mathematica 19 (3):308-322.
Balazs Gyenis & Miklos Redei (2004). When Can Statistical Theories Be Causally Closed? Foundations of Physics 34 (9):1285-1303.
Piers Rawling (1997). Perspectives on a Pair of Envelopes. Theory and Decision 43 (3):253-277.
Added to index2012-07-10
Total downloads24 ( #112,516 of 1,700,306 )
Recent downloads (6 months)5 ( #128,702 of 1,700,306 )
How can I increase my downloads?