Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances–a response to Adam Elga
Graduate studies at Western
British Journal for the Philosophy of Science 58 (1):25-43 (2007)
|Abstract||The rejection of an infinitesimal solution to the zero-fit problem by A. Elga () does not seem to appreciate the opportunities provided by the use of internal finitely-additive probability measures. Indeed, internal laws of probability can be used to find a satisfactory infinitesimal answer to many zero-fit problems, not only to the one suggested by Elga, but also to the Markov chain (that is, discrete and memory-less) models of reality. Moreover, the generalization of likelihoods that Elga has in mind is not as hopeless as it appears to be in his article. In fact, for many practically important examples, through the use of likelihoods one can succeed in circumventing the zero-fit problem. 1 The Zero-fit Problem on Infinite State Spaces 2 Elga's Critique of the Infinitesimal Approach to the Zero-fit Problem 3 Two Examples for Infinitesimal Solutions to the Zero-fit Problem 4 Mathematical Modelling in Nonstandard Universes? 5 Are Nonstandard Models Unnatural? 6 Likelihoods and Densities A Internal Probability Measures and the Loeb Measure Construction B The (Countable) Coin Tossing Sequence Revisited C Solution to the Zero-fit Problem for a Finite-state Model without Memory D An Additional Note on ‘Integrating over Densities’ E Well-defined Continuous Versions of Density Functions.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Yaroslav Sergeyev (2007). Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers. Chaos, Solitons and Fractals 33 (1):50-75.
Prasanta S. Bandyopadhayay, Robert J. Boik & Prasun Basu (1996). The Curve Fitting Problem: A Bayesian Approach. Philosophy of Science 63 (3):272.
Yaroslav D. Sergeyev (2008). A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities. Informatica 19 (4):567-596.
Yaroslav Sergeyev (2009). Numerical Point of View on Calculus for Functions Assuming Finite, Infinite, and Infinitesimal Values Over Finite, Infinite, and Infinitesimal Domains. Nonlinear Analysis Series A 71 (12):e1688-e1707.
Christopher J. G. Meacham (2008). Sleeping Beauty and the Dynamics of de Se Beliefs. Philosophical Studies 138 (2):245-269.
Bradley Monton (2002). Sleeping Beauty and the Forgetful Bayesian. Analysis 62 (1):47–53.
Yaroslav Sergeyev (2009). Numerical Computations and Mathematical Modelling with Infinite and Infinitesimal Numbers. Journal of Applied Mathematics and Computing 29:177-195.
J. Dunn (2011). Fried Eggs, Thermodynamics, and the Special Sciences. British Journal for the Philosophy of Science 62 (1):71-98.
Frank Jackson, Graham Priest & Adam Elga (2004). Infinitesimal Chances and the Laws of Nature. Australasian Journal of Philosophy 82 (1):67 – 76.
Adam Elga (2004). Infinitesimal Chances and the Laws of Nature. Australasian Journal of Philosophy 82 (1):67 – 76.
Added to index2009-01-28
Total downloads4 ( #189,291 of 739,396 )
Recent downloads (6 months)0
How can I increase my downloads?