Switch to: Citations

Add references

You must login to add references.
  1. A Definable Nonstandard Enlargement.Frederik Herzberg - 2008 - Mathematical Logic Quarterly 54 (2):167-175.
    This article establishes the existence of a definable , countably saturated nonstandard enlargement of the superstructure over the reals. This nonstandard universe is obtained as the union of an inductive chain of bounded ultrapowers . The underlying ultrafilter is the one constructed by Kanovei and Shelah [10].
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?Nicolas Gisin - 2019 - Erkenntnis:1-13.
    It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
    Download  
     
    Export citation  
     
    Bookmark   36 citations  
  • Calcul des Probabilités.Joseph Louis François Bertrand - 1888 - Gauthier-Villars Et Fils.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   57 citations  
  • Philosophical Papers.David K. Lewis - 1983 - Oxford University Press.
    This is the second volume of philosophical essays by one of the most innovative and influential philosophers now writing in English. Containing thirteen papers in all, the book includes both new essays and previously published papers, some of them with extensive new postscripts reflecting Lewis's current thinking. The papers in Volume II focus on causation and several other closely related topics, including counterfactual and indicative conditionals, the direction of time, subjective and objective probability, causation, explanation, perception, free will, and rational (...)
    Download  
     
    Export citation  
     
    Bookmark   568 citations  
  • Philosophical Papers.Graeme Forbes & David Lewis - 1985 - Philosophical Review 94 (1):108.
    Download  
     
    Export citation  
     
    Bookmark   97 citations  
  • Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
    Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP (...)
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • Internal Laws of Probability, Generalized Likelihoods and Lewis' Infinitesimal Chances–a Response to Adam Elga.Frederik Herzberg - 2007 - British Journal for the Philosophy of Science 58 (1):25-43.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • How Probable is an Infinite Sequence of Heads?Timothy Williamson - 2007 - Analysis 67 (3):173-180.
    Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...)
    Download  
     
    Export citation  
     
    Bookmark   68 citations  
  • A Definable Nonstandard Model of the Reals.Vladimir Kanovei & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (1):159-164.
    We prove, in ZFC,the existence of a definable, countably saturated elementary extension of the reals.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • Internal Set Theory: A New Approach to Nonstandard Analysis.Edward Nelson - 1977 - Journal of Symbolic Logic 48 (4):1203-1204.
    Download  
     
    Export citation  
     
    Bookmark   52 citations  
  • Conversion From Nonstandard to Standard Measure Spaces and Applications in Probability Theory.Peter A. Loeb & Robert M. Anderson - 1975 - Journal of Symbolic Logic 50 (1):243-243.
    Download  
     
    Export citation  
     
    Bookmark   17 citations  
  • Nonstandard Methods in Stochastic Analysis and Mathemetical Physics.Sergio Albeverio & Jens Erik Fenstad - 1986 - Journal of Symbolic Logic 55 (1):362-363.
    Download  
     
    Export citation  
     
    Bookmark   28 citations  
  • The Possibility of Infinitesimal Chances.Martin Barrett - 2010 - In Ellery Eells & James H. Fetzer (eds.), The Place of Probability in Science. Springer. pp. 65--79.
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • Minimal Axiomatic Frameworks for Definable Hyperreals with Transfer.Frederik S. Herzberg, Vladimir Kanovei, Mikhail Katz & Vassily Lyubetsky - 2018 - Journal of Symbolic Logic 83 (1):385-391.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Regularity and Infinitely Tossed Coins.Colin Howson - 2017 - European Journal for Philosophy of Science 7 (1):97-102.
    Timothy Williamson has claimed to prove that regularity must fail even in a nonstandard setting, with a counterexample based on tossing a fair coin infinitely many times. I argue that Williamson’s argument is mistaken, and that a corrected version shows that it is not regularity which fails in the non-standard setting but a fundamental property of shifts in Bernoulli processes.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • A Definable Nonstandard Model Of The Reals.Vladimir Kanovei & Saharon Shelah - 2004 - Journal of Symbolic Logic 69 (1):159-164.
    We prove, in ZFC, the existence of a definable, countably saturated elementary extension of the reals.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Assigning Probabilities to Logical Formulas.Dana Scott & Peter Krauss - 1966 - In Jaakko Hintikka & Patrick Suppes (eds.), Aspects of Inductive Logic. Elsevier: Amsterdam. pp. 219 -- 264.
    Download  
     
    Export citation  
     
    Bookmark   32 citations