Philosophy of Probability

Edited by Darrell P. Rowbottom (Lingnan University)
Assistant editor: Joshua Luczak (University of Western Ontario)
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  1. Scientific Metaphysics and Information.Bruce Long - forthcoming - Springer.
    This book investigates the interplay between two new and influential subdisciplines in the philosophy of science and philosophy: contemporary scientific metaphysics and the philosophy of information. Scientific metaphysics embodies various scientific realisms and has a partial intellectual heritage in some forms of neo-positivism, but is far more attuned than the latter to statistical science, theory defeasibility, scale variability, and pluralist ontological and explanatory commitments, and is averse to a-priori conceptual analysis. The philosophy of information is the combination of what has (...)
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  2. Countable Additivity, Idealization, and Conceptual Realism.Yang Liu - forthcoming - Economics and Philosophy.
    This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of (...)
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    Chance and Objective Probability
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     Chance and Objective Probability, Misc
     Frequentism
     Logical Probability
     Probabilistic Laws
     Propensities
     Chance-Credence Principles
     Humeanism and Nonhumeanism about Chance
    Subjective Probability
     Betting Interpretations and Dutch Books
     Conditional Probability
     Degrees of Belief
     Imprecise Credences
     Subjective Probability, Misc
    Probabilistic Reasoning
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     Probabilistic Principles
     Probabilistic Frameworks
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    Phil of Statistics
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     Probability in the Philosophy of Religion
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  3. Sarah Moss, Probabilistic Knowledge.Tim Smartt - 2018 - Ethics 129 (2):430-438.
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     Humeanism and Nonhumeanism about Chance
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  4. A Study of Mathematical Determination Through Bertrand’s Paradox.Davide Rizza - 2018 - Philosophia Mathematica 26 (3):375-395.
    Certain mathematical problems prove very hard to solve because some of their intuitive features have not been assimilated or cannot be assimilated by the available mathematical resources. This state of affairs triggers an interesting dynamic whereby the introduction of novel conceptual resources converts the intuitive features into further mathematical determinations in light of which a solution to the original problem is made accessible. I illustrate this phenomenon through a study of Bertrand’s paradox.
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     Probabilistic Laws
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     Humeanism and Nonhumeanism about Chance
    Subjective Probability
     Betting Interpretations and Dutch Books
     Conditional Probability
     Degrees of Belief
     Imprecise Credences
     Subjective Probability, Misc
    Probabilistic Reasoning
     Bayesian Reasoning
     Probabilistic Principles
     Probabilistic Frameworks
     Probabilistic Puzzles
    Mathematics of Probability
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     Infinitesimals and Probability
     Mathematics of Probability, Misc
    Phil of Statistics
    Applications of Probability
     Probability in the Philosophy of Religion
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     Decision Theory
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     Decision-Theoretic Frameworks
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     Topics in Decision Theory
    Phil of Probability, Misc
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  5. Ramsey and Joyce on Deliberation and Prediction.Yang Liu & Huw Price - forthcoming - Synthese:1-22.
    Can an agent deliberating about an action A hold a meaningful credence that she will do A? 'No', say some authors, for 'Deliberation Crowds Out Prediction' (DCOP). Others disagree, but we argue here that such disagreements are often terminological. We explain why DCOP holds in a Ramseyian operationalist model of credence, but show that it is trivial to extend this model so that DCOP fails. We then discuss a model due to Joyce, and show that Joyce's rejection of DCOP rests (...)
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     Chance and Objective Probability, Misc
     Frequentism
     Logical Probability
     Probabilistic Laws
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     Humeanism and Nonhumeanism about Chance
    Subjective Probability
     Betting Interpretations and Dutch Books
     Conditional Probability
     Degrees of Belief
     Imprecise Credences
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    Phil of Statistics
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     Probability in the Philosophy of Religion
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     Decision Theory
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     Decision-Theoretic Frameworks
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     Game Theory
     Topics in Decision Theory
    Phil of Probability, Misc
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  6. Petroleum & Public Safety: Risk Management in the Gulf South 1901-2015 (LSU 2018).James B. Mcswain - 2018 - Baton Rouge, LA, USA: Louisiana State University Press.
    Throughout the twentieth century, cities such as Houston, Galveston, New Orleans, and Mobile grappled with the safety hazards created by oil and gas industries as well as the role municipal governments should play in protecting the public from these threats. James B. McSwain’s Petroleum and Public Safety reveals how officials in these cities created standards based on technical, scientific, and engineering knowledge to devise politically workable ordinances related to the storage and handling of fuel. -/- Each of the cities studied (...)
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    Chance and Objective Probability
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     Chance and Objective Probability, Misc
     Frequentism
     Logical Probability
     Probabilistic Laws
     Propensities
     Chance-Credence Principles
     Humeanism and Nonhumeanism about Chance
    Subjective Probability
     Betting Interpretations and Dutch Books
     Conditional Probability
     Degrees of Belief
     Imprecise Credences
     Subjective Probability, Misc
    Probabilistic Reasoning
     Bayesian Reasoning
     Probabilistic Principles
     Probabilistic Frameworks
     Probabilistic Puzzles
    Mathematics of Probability
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     Infinitesimals and Probability
     Mathematics of Probability, Misc
    Phil of Statistics
    Applications of Probability
     Probability in the Philosophy of Religion
     Probability in the Physical Sciences
     Applications of Probability, Misc
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    Phil of Probability, Misc
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  7. Logic of Probability and Conjecture.Harry Crane - unknown
    I introduce a formalization of probability which takes the concept of 'evidence' as primitive. In parallel to the intuitionistic conception of truth, in which 'proof' is primitive and an assertion A is judged to be true just in case there is a proof witnessing it, here 'evidence' is primitive and A is judged to be probable just in case there is evidence supporting it. I formalize this outlook by representing propositions as types in Martin-Lof type theory (MLTT) and defining a (...)
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    Chance and Objective Probability
     Chance and Determinism
     Chance and Objective Probability, Misc
     Frequentism
     Logical Probability
     Probabilistic Laws
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     Humeanism and Nonhumeanism about Chance
    Subjective Probability
     Betting Interpretations and Dutch Books
     Conditional Probability
     Degrees of Belief
     Imprecise Credences
     Subjective Probability, Misc
    Probabilistic Reasoning
     Bayesian Reasoning
     Probabilistic Principles
     Probabilistic Frameworks
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    Mathematics of Probability
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     Infinitesimals and Probability
     Mathematics of Probability, Misc
    Phil of Statistics
    Applications of Probability
     Probability in the Philosophy of Religion
     Probability in the Physical Sciences
     Applications of Probability, Misc
     Decision Theory
     Probabilistic Reasoning
    Decision Theory
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     Game Theory
     Topics in Decision Theory
    Phil of Probability, Misc
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  8. The Design Inference: Eliminating Chance Through Small Probabilities. [REVIEW]Jordan Howard Sobel - 2003 - Mind 112 (447):521-525.
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     Chance and Objective Probability, Misc
     Frequentism
     Logical Probability
     Probabilistic Laws
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     Humeanism and Nonhumeanism about Chance
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     Betting Interpretations and Dutch Books
     Conditional Probability
     Degrees of Belief
     Imprecise Credences
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    Probabilistic Reasoning
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     Probabilistic Principles
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    Phil of Statistics
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  9. Of Miracles and Evidential Probability: Hume’s “Abject Failure” Vindicated.William L. Vanderburgh - 2005 - Hume Studies 31 (1):37-61.
    This paper defends David Hume's "Of Miracles" from John Earman's (2000) Bayesian attack by showing that Earman misrepresents Hume's argument against believing in miracles and misunderstands Hume's epistemology of probable belief. It argues, moreover, that Hume's account of evidence is fundamentally non-mathematical and thus cannot be properly represented in a Bayesian framework. Hume's account of probability is show to be consistent with a long and laudable tradition of evidential reasoning going back to ancient Roman law.
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  10. Probability Theory and Probability Semantics.Peter Roeper & Hugues Leblanc (eds.) - 1999 - University of Toronto Press.
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  11. Causes as Probability Raisers of Processes.Jonathan Schaffe - 2001 - Journal of Philosophy 98 (2):75.
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  12. From Values to Probabilities.Wlodek Rabinowicz - unknown
    According to the fitting-attitude analysis of value, to be valuable is to be a fitting object of a pro-attitude. In earlier publications, setting off from this format of analysis, I proposed a modelling of value relations which makes room for incommensurability in value. In this paper, I first recapitulate the value modelling and then move on to suggest adopting a structurally similar analysis of probability. Indeed, many probability theorists from Poisson onwards did adopt an analysis of this kind. This move (...)
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     Degrees of Belief
     Imprecise Credences
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  13. Hegel's Philosophical Psychology.Luca Corti - 2016
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  14. Relacja między nauką o logicznych możliwościach a zasadą zachowania energii. Rola badań Huygensa i Leibniza dla nowożytnej refleksji nad wolnością woli.Anna Szyrwińska - 2015 - IDEA – Studia Nad Strukturą I Rozwojem Pojęć Filozoficznych:191-202.
    The article investigates the relationship between Leibniz’s and Huygens’ theory of possibility and the principle of conservation of energy. It assumes that their criticisms of Cartesian views concerning those questions as well as their own achievements contributed to the formation of a new metaphysical basis for modern discussions on the freedom of the will. There are especially two problems whose role is crucial in this context, namely the question of God’s knowledge of future conditionals (contingentia futura) and the mind-body distinction.
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     Logical Probability
     Probabilistic Laws
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     Conditional Probability
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    Phil of Statistics
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  15. Johannes von Kries's Conception of Probability, its Roots, Impact, and Modern Developments: Introduction.Jacob Rosenthal & Carsten Seck - 2016 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 47 (1):105-107.
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  16. On Quantum Conditional Probability.Isabel Guerra Bobo - 2013 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 28 (1):115-137.
    We argue that quantum theory does not allow for a generalization of the notion of classical conditional probability by showing that the probability defined by the Lüders rule, standardly interpreted in the literature as the quantum-mechanical conditionalization rule, cannot be interpreted as such.Argumentamos que la teoría cuántica no admite una generalización de la noción clásica de probabilidad condicionada. Mostramos que la probabilidad definida por la regla de Lüders, interpretada generalmente como la regla de condicionalización mecánico-cuántica, no puede ser interpretada como (...)
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  17. A Study in Probability.D. Taylor - 1935 - Australasian Journal of Psychology and Philosophy 13 (4):290-298.
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  18. Probability Dynamics.Amos Nathan - 2006 - Synthese 148 (1):229-256.
    ‘Probability dynamics’ (PD) is a second-order probabilistic theory in which probability distribution d X = (P(X 1), . . . , P(X m )) on partition U m X of sample space Ω is weighted by ‘credence’ (c) ranging from −∞ to +∞. c is the relative degree of certainty of d X in ‘α-evidence’ α X =[c; d X ] on U m X . It is shown that higher-order probabilities cannot provide a theory of PD. PD applies to (...)
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  19. Indifference, Neutrality and Informativeness: Generalizing the Three Prisoners Paradox.Sergio Wechsler, L. G. Esteves, A. Simonis & C. Peixoto - 2005 - Synthese 143 (3):255-272.
    . The uniform prior distribution is often seen as a mathematical description of noninformativeness. This paper uses the well-known Three Prisoners Paradox to examine the impossibility of maintaining noninformativeness throughout hierarchization. The Paradox has been solved by Bayesian conditioning over the choice made by the Warder when asked to name a prisoner who will be shot. We generalize the paradox to situations of N prisoners, k executions and m announcements made by the Warder. We then extend the consequences of hierarchically (...)
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  20. The No Probabilities For Acts-Principle.Marion Ledwig - 2005 - Synthese 144 (2):171-180.
    One can interpret the No Probabilities for Acts-Principle, namely that any adequate quantitative decision model must in no way contain subjective probabilities for actions in two ways: it can either refer to actions that are performable now and extend into the future or it can refer to actions that are not performable now, but will be in the future. In this paper, I will show that the former is the better interpretation of the principle.
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  21. Against Probabilistic Measures of Coherence.Mark Siebel - 2005 - Erkenntnis 63 (3):335-360.
    It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if P(B)=P(C). But (...)
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  22. The Place of Probability in Hilbert’s Axiomatization of Physics, Ca. 1900–1928.Lukas M. Verburgt - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:28-44.
    Although it has become a common place to refer to the ׳sixth problem׳ of Hilbert׳s (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert׳s project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory (...)
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  23. Foundations of Probability with Applications: Selected Papers 1974–1995.Patrick Suppes & Mario Zanotti - 1996 - Cambridge University Press.
    This is an important collection of essays dealing with the foundations of probability that will be of value to philosophers of science, mathematicians, statisticians, psychologists and educationalists. The collection falls into three parts. Part I comprises five essays on the axiomatic foundations of probability. Part II contains seven articles on probabilistic causality and quantum mechanics, with an emphasis on the existence of hidden variables. The third part consists of a single extended essay applying probabilistic theories of learning to practical questions (...)
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  24. A New Way to Block a Dutch Book Argument, or The Stubborn Non-Probabilist.Leszek Wronski - manuscript
    We point out a yet unnoticed flaw in Dutch Book arguments that relates to a link between degrees of belief and betting quotients. We offer a set of precise conditions governing when a nonprobabilist is immune to the classical Dutch Book argument. We suggest that diachronic Dutch Book arguments are also affected.
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  25. A History of the Mathematical Theory of Probability: From the Time of Pascal to That of Laplace.Isaac Todhunter - 1865 - Macmillan and Company: London.
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  26. Mellor. 2005 Probability: A Philosophical Introduction.Mauricio Suárez - 2011 - Theoria : An International Journal for Theory, History and Fundations of Science 26 (1):99-103.
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  27. Unificatory Power in the Old Quantum Theory: Informational Relevance of the Quantum Hypothesis.Molly Kao - forthcoming - Philosophy of Science.
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  28. WEATHERFORD, R.: "Philosophical Foundations of Probability Theory". [REVIEW]Peter Milne - 1984 - British Journal for the Philosophy of Science 35:95.
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  29. À propos du terme "probabilité".H. Breny - 1983 - Logique Et Analyse 26 (2):129.
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  30. The Notion of Probability in the Theistic Argument of F. R. Tennant.John Thomas Stahl - 1967 - Dissertation, Boston University Graduate School
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  31. HACKING, I. "The Emergence of Probability". [REVIEW]J. R. Lucas - 1977 - Mind 86:466.
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  32. REICHENBACH, H. -The Theory of Probability. [REVIEW]J. O. Urmson - 1951 - Mind 60:290.
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  33. Classical Fundamentals and a Modern Foundation of Probability Calculus.M. Malatesta - 1989 - Metalogicon 2:94-132.
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  34. The Pragmatic Justification of Induction: A Critical Examination.Lewis Graham Creary - 1969 - Dissertation, Princeton University
    The dissertation is a detailed critique of the main elements of Hans Reichenbach's pragmatic treatment of the problem of induction. In the introductory Chapter I we give a broad overview of Reichenbach's theory of probability and induction, indicating that he approaches the problem of justifying inductive inference in general by attempting first to reduce all kinds of non-deductive reasoning to combinations of inferences in accordance with the rules of deductive logic together with RRI -- the "rule of induction." Having thus (...)
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  35. The Theory of Probability. An Inquiry Into the Logical and Mathematical Foundations of the Calculus of Probability.Ernest Nagel - 1950 - Journal of Philosophy 47 (19):551-555.
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  36. Poincaré’s Probabilities, Kantified, Post-Modernized.Clark Glymour - 2014 - Biological Theory 9 (1):113-114.
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  37. How to Solve Probability Teasers-Discussion.M. Barhillel - 1989 - Philosophy of Science 56 (2):348-358.
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  38. Probability and Choice in the Selection Task.David W. Green, David E. Over & Robin A. Pyne - 1997 - Thinking and Reasoning 3 (3):209-235.
    Two experiments using a realistic version of the selection task examined the relationship between participants' probability estimates of finding a counter example and their selections. Experiment 1 used everyday categories in the context of a scenario to determine whether or not the number of instances in a category affected the estimated probability of a counter-example. Experiment 2 modified the scenario in order to alter participants' estimates of finding a specific counter-example. Unlike Kirby 1994a, but consistent with his proposals, both studies (...)
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  39. Empiricism, Probability, and Knowledge of Arithmetic.Sean Walsh - 2014 - Journal of Applied Logic 12 (3):319–348.
    The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy (...)
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  40. When Speaking of Probability in Behavior Analysis.Lisa M. Johnson & Edward K. Morris - 1987 - Behaviorism 15 (2):107-129.
    Probability is not an unambiguous concept within the sciences or in vernacular language, yet it is fundamental to much of behavior analysis. The present paper examines some problems this ambiguity creates in general,as well as within the experimental analysis of behavior, in particular. As background material, we first introduce the three most common theories of probability in mathematics and science, discussing their advantages and disadvantages, and their relevance to behavior analysis. Next, we discuss the concept of probability as encountered in (...)
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  41. Husserlian Foundations of Sartre's Treatment of Time Consciousness.V. C. Thomas - 1992 - In D. P. Chattopadhyaya, Lester E. Embree & Jitendranath Mohanty (eds.), Phenomenology and Indian Philosophy. Indian Council of Philosophical Research in Association with Motilal Banarsidass Publishers. pp. 126-132.
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  42. A Commentary on Mel Rutherford’s ‘On the Use and Misuse of the “Two Children” Brainteaser’.Maya Bar-Hillel - 2010 - Pragmatics and Cognition 18 (1):175-179.
    Rutherford criticizes the way some people have analyzed the 2-children problem, claiming that slight nuances in the problem’s formulation can change the correct answer. However, his own data demonstrate that even when there is a unique correct answer, participants give intuitive answers that differ from it systematically — replicating the data reported by those he criticizes. Thus, his critique reduces to an admonition to use care in formulating and analyzing this brainteaser — which is always a good idea — but (...)
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  43. Bruno de Finetti. Philosophical Lectures on Probability. Collected, Edited, and Annotated by Alberto Mura. Translated by Hykel Hosni. Synthese Library; 340. [REVIEW]Jon Williamson - 2010 - Philosophia Mathematica 18 (1):130-135.
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  44. Might God Toss Coins?Philip Pearle - 1982 - Foundations of Physics 12 (3):249-263.
    In the problem of the gambler's ruin, a classic problem in probability theory, a number of gamblers play against each other until all but one of them is “wiped out.” It is shown that this problem is identical to a previously presented formulation of the reduction of the state vector, so that the state vectors in a linear superposition may be regarded as “playing” against each other until all but one of them is “wiped out.” This is a useful part (...)
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  45. Ensemble Steering, Weak Self-Duality, and the Structure of Probabilistic Theories.Howard Barnum, Carl Philipp Gaebler & Alexander Wilce - 2013 - Foundations of Physics 43 (12):1411-1427.
    In any probabilistic theory, we say that a bipartite state ω on a composite system AB steers its marginal state ω B if, for any decomposition of ω B as a mixture ω B =∑ i p i β i of states β i on B, there exists an observable {a i } on A such that the conditional states $\omega_{B|a_{i}}$ are exactly the states β i . This is always so for pure bipartite states in quantum mechanics, a fact (...)
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  46. The Special Status of Mathematical Probability: A Historical Sketch.Xavier De Scheemaekere & Ariane Szafarz - 2008 - Epistemologia 32 (1):91.
    The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike (...)
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  47. A Toy Model for Quantum Mechanics.S. J. van Enk - 2007 - Foundations of Physics 37 (10):1447-1460.
    The toy model used by Spekkens (Phys. Rev. A 75, 032110, 2007) to argue in favor of an epistemic view of quantum mechanics is extended by generalizing his definition of pure states (i.e. states of maximal knowledge) and by associating measurements with all pure states. The new toy model does not allow signaling but, in contrast to the Spekkens model, does violate Bell-CHSH inequalities. Negative probabilities are found to arise naturally within the model, and can be used to explain the (...)
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  48. Book Review: Probability Theory: The Logic of Science. By Edwin T. Jaynes, Edited by G. Larry Bretthorst. Cambridge University Press, Cambridge, United Kingdom, 2003, Xxix + 727 Pp., S60.00 (Hardcover). ISBN 0-521-59271-2. [REVIEW]W. T. Grandy Jr - 2004 - Foundations of Physics 34 (3):533-536.
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  49. What Is Fuzzy Probability Theory?S. Gudder - 2000 - Foundations of Physics 30 (10):1663-1678.
    The article begins with a discussion of sets and fuzzy sets. It is observed that identifying a set with its indicator function makes it clear that a fuzzy set is a direct and natural generalization of a set. Making this identification also provides simplified proofs of various relationships between sets. Connectives for fuzzy sets that generalize those for sets are defined. The fundamentals of ordinary probability theory are reviewed and these ideas are used to motivate fuzzy probability theory. Observables (fuzzy (...)
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  50. Observables and Statistical Maps.Stan Gudder - 1999 - Foundations of Physics 29 (6):877-897.
    This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the σ-effect algebra of effects (fuzzy events) $\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ and the set of probability measures $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ on a measurable space $\left( {\Omega ,\mathcal{A}} \right)$ . An observable $X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ is defined, where $\begin{gathered} X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right) \\ \left( {\Lambda ,{\text{ }}\mathcal{B}} \right) (...)
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