Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances–a response to Adam Elga


Abstract
The rejection of an infinitesimal solution to the zero-fit problem by A. Elga ([2004]) 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.
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DOI 10.1093/bjps/axl028
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References found in this work BETA

Humean Supervenience Debugged.David K. Lewis - 1994 - Mind 103 (412):473--490.
Infinitesimal Chances and the Laws of Nature.Adam Elga - 2004 - Australasian Journal of Philosophy 82 (1):67 – 76.
A Definable Nonstandard Model of the Reals.Vladimir Kanovei & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (1):159-164.

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Comparative Expectations.Arthur Paul Pedersen - 2014 - Studia Logica 102 (4):811-848.
A New Argument for Mind-Brain Identity.István Aranyosi - 2011 - British Journal for the Philosophy of Science 62 (3):489-517.

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