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  1. added 2020-05-22
    The Principal Principle Does Not Imply the Principle of Indifference.Richard Pettigrew - 2017 - British Journal for the Philosophy of Science:axx060.
    In a recent paper in this journal, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson argue that the principal principle entails the principle of indifference. In this paper, I argue that it does not. Lewis’s version of the principal principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW base their argument on certain intuitions concerning when one proposition is admissible for another: Conditions 1 and 2. There are two ways of reading their (...)
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  2. added 2020-05-05
    Improving Bayesian Statistics Understanding in the Age of Big Data with the Bayesvl R Package.Quan-Hoang Vuong, Viet-Phuong La, Minh-Hoang Nguyen, Manh-Toan Ho, Manh-Tung Ho & Peter Mantello - 2020 - Software Impacts 4 (1):100016.
    The exponential growth of social data both in volume and complexity has increasingly exposed many of the shortcomings of the conventional frequentist approach to statistics. The scientific community has called for careful usage of the approach and its inference. Meanwhile, the alternative method, Bayesian statistics, still faces considerable barriers toward a more widespread application. The bayesvl R package is an open program, designed for implementing Bayesian modeling and analysis using the Stan language’s no-U-turn (NUTS) sampler. The package combines the ability (...)
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  3. added 2019-09-14
    Non-Deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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  4. added 2019-09-14
    The Objective Bayesian Conceptualisation of Proof and Reference Class Problems.James Franklin - 2011 - Sydney Law Review 33 (3):545-561.
    The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...)
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  5. added 2019-09-14
    The Science of Conjecture: Evidence and Probability Before Pascal.James Franklin - 2001 - Baltimore, USA: Johns Hopkins University Press.
    How were reliable predictions made before Pascal and Fermat's discovery of the mathematics of probability in 1654? What methods in law, science, commerce, philosophy, and logic helped us to get at the truth in cases where certainty was not attainable? The book examines how judges, witch inquisitors, and juries evaluated evidence; how scientists weighed reasons for and against scientific theories; and how merchants counted shipwrecks to determine insurance rates. Also included are the problem of induction before Hume, design arguments for (...)
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  6. added 2019-09-13
    No Interpretation of Probability.Wolfgang Schwarz - 2018 - Erkenntnis 83 (6):1195-1212.
    I argue that none of the usual interpretations of probability provide an adequate interpretation of probabilistic theories in science. Assuming that the aim of such theories is to capture noisy relationships in the world, I suggest that we do not have to give them classical truth-conditional content at all: their probabilities can remain uninterpreted. Indirectly, this account turns out to explain what is right about the frequency interpretation, the best-systems interpretation, and the epistemic interpretation.
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  7. added 2019-09-13
    The Only Probability Is Verbal Probability.George Masterton - 2014 - Metaphysica 15 (1).
    In 1977 van Fraassen showed convincingly, and in detail, how one can give a dissentive answer to the question `[a]re there necessities in nature?'. In this paper I follow his lead and show in a similar fashion and detail, how it is possible to give a dissentive answer to: Are there probabilities in nature? This is achieved by giving a partial analysis—with the aid of Kaplanian pragmatics—of objective chance in terms of that credence that is reasonable where prevailing laws and (...)
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  8. added 2019-06-06
    Combining Analogical Support in Pure Inductive Logic.J. B. Paris & A. Vencovská - 2016 - Erkenntnis (2):01-19.
    We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...)
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  9. added 2019-01-06
    A Comprehensive Theory of Induction and Abstraction, Part II.Cael Hasse - manuscript
    This is part II in a series of papers outlining Abstraction Theory, a theory that I propose provides a solution to the characterisation or epistemological problem of induction. Logic is built from first principles severed from language such that there is one universal logic independent of specific logical languages. A theory of (non-linguistic) meaning is developed which provides the basis for the dissolution of the `grue' problem and problems of the non-uniqueness of probabilities in inductive logics. The problem of counterfactual (...)
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  10. added 2019-01-05
    Imprecise Probability and the Measurement of Keynes's "Weight of Arguments".William Peden - 2018 - IfCoLog Journal of Logics and Their Applications 5 (4):677-708.
    Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the usefulness (...)
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  11. added 2018-08-13
    Probability: A Philosophical Introduction.D. H. Mellor - 2004 - Routledge.
    _Probability: A Philosophical Introduction_ introduces and explains the principal concepts and applications of probability. It is intended for philosophers and others who want to understand probability as we all apply it in our working and everyday lives. The book is not a course in mathematical probability, of which it uses only the simplest results, and avoids all needless technicality. The role of probability in modern theories of knowledge, inference, induction, causation, laws of nature, action and decision-making makes an understanding of (...)
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  12. added 2018-02-17
    Probability Logic, Logical Probability, and Inductive Support.Isaac Levi - 2010 - Synthese 172 (1):97-118.
    This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...)
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  13. added 2018-02-17
    An Empirical Approach to Symmetry and Probability.Jill North - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):27-40.
    We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...)
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  14. added 2018-02-16
    On the Proximity of the Logical and ‘Objective Bayesian’ Interpretations of Probability.Darrell Patrick Rowbottom - 2008 - Erkenntnis 69 (3):335-349.
    In his Bayesian Nets and Causality, Jon Williamson presents an ‘Objective Bayesian’ interpretation of probability, which he endeavours to distance from the logical interpretation yet associate with the subjective interpretation. In doing so, he suggests that the logical interpretation suffers from severe epistemological problems that do not affect his alternative. In this paper, I present a challenge to his analysis. First, I closely examine the relationship between the logical and ‘Objective Bayesian’ views, and show how, and why, they are highly (...)
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  15. added 2017-12-28
    Случайности. Историческа типология.Vassil Vidinsky - 2017 - Sofia: Sofia University Press.
    В настоящата книга се изследва идеята за случайността през нейното историческо и концептуално развитие и са отделени пет основни и типични понятия. Анализът тръгва от класическите примери – Платон, Аристотел, Кант и Хегел – и стига до съвременния контекст на случайността, който е представен през теорията на вероятностите и теорията на сложността. Някои от изведените понятия са формализирани и имат по-логически, математически или пък информационен характер, а други са по-скоро физически или субектни, но всички те са представени в една обща (...)
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  16. added 2017-02-24
    Carnap's Inductive Probabilities as a Contribution to Decision Theory.Joachim Hornung - 1980 - Theoretical Medicine and Bioethics 1 (3):325-367.
    Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...)
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  17. added 2017-02-13
    Ancient Indian Logic and Analogy.J. B. Paris & A. Vencovska - 2017 - In S. Ghosh & S. Prasad (eds.), Logic and its Applications, Lecture Notes in Computer Science 10119. Springer. pp. 198-210.
    B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.
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  18. added 2017-02-13
    The Theory of Spectrum Exchangeability.E. Howarth & J. B. Paris - 2015 - Review of Symbolic Logic 8 (1):108-130.
  19. added 2017-02-13
    The Twin Continua of Inductive Methods.Alena Vencovská & Jeff B. Paris - 2015 - In Andrés Villaveces, Roman Kossak, Juha Kontinen & Åsa Hirvonen (eds.), Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics. De Gruyter. pp. 355-366.
  20. added 2017-02-13
    Second Order Inductive Logic and Wilmers' Principle.M. S. Kliess & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
    We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.
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  21. added 2017-02-13
    Predicate Exchangeability and Language Invariance in Pure Inductive Logic.M. S. Kliess & J. B. Paris - 2014 - Logique Et Analyse 57 (228):513-540.
    In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.
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  22. added 2017-02-13
    Principles of Remembering and Forgetting.E. Howarth & J. B. Paris - 2014 - Logique Et Analyse 57 (228):489-511.
    We propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A partial classification is given of the probability functions which satisfy these principles.
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  23. added 2017-02-13
    Second Order Inductive Logic and Wilmers' Principle.M. S. Kließ & J. B. Paris - 2014 - Journal of Applied Logic 12 (4):462-476.
  24. added 2017-02-13
    An Analogy Principle in Inductive Logic.A. Hill & J. B. Paris - 2013 - Annals of Pure and Applied Logic 164 (12):1293-1321.
    We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrmsʼ ‘Wheel of Fortune’.
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  25. added 2017-02-13
    An Observation on Carnapʼs Continuum and Stochastic Independencies.J. B. Paris - 2013 - Journal of Applied Logic 11 (4):421-429.
    We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.
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  26. added 2017-02-13
    Symmetry in Polyadic Inductive Logic.J. B. Paris & A. Vencovská - 2012 - Journal of Logic, Language and Information 21 (2):189-216.
    A family of symmetries of polyadic inductive logic are described which in turn give rise to the purportedly rational Permutation Invariance Principle stating that a rational assignment of probabilities should respect these symmetries. An equivalent, and more practical, version of this principle is then derived.
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  27. added 2017-02-13
    A Note on Irrelevance in Inductive Logic.Jeff B. Paris & Alena Vencovská - 2011 - Journal of Philosophical Logic 40 (3):357 - 370.
    We consider two formalizations of the notion of irrelevance as a rationality principle within the framework of (Carnapian) Inductive Logic: Johnson's Sufficientness Principle, JSP, which is classically important because it leads to Carnap's influential Continuum of Inductive Methods and the recently proposed Weak Irrelevance Principle, WIP. We give a complete characterization of the language invariant probability functions satisfying WIP which generalizes the Nix-Paris Continuum. We argue that the derivation of two very disparate families of inductive methods from alternative perceptions of (...)
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  28. added 2017-02-13
    Pure Inductive Logic.J. B. Paris & A. Vencovska - 2011 - Cambridge, UK: Cambridge University Press.
    Pure Inductive Logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years, plus the main contributions of the authors and their collaborators over the last decade, to present a comprehensive account of the discipline within a single unified context.
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  29. added 2017-02-13
    Reasoning by Analogy in Inductive Logic.Alexandra Hill & J. B. Paris - 2011 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications. pp. 63--76.
  30. added 2017-02-13
    A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic.J. Landes, J. B. Paris & A. Vencovská - 2011 - Synthese 181 (S1):19 - 47.
    We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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  31. added 2017-02-11
    On the Logical Form of Probability-Statements.C. G. Hempel - 1937 - Erkenntnis 7 (1):154-160.
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  32. added 2017-02-05
    An Examination of the SEP Candidate Analogical Inference Rule Within Pure Inductive Logic.E. Howarth, J. B. Paris & A. Vencovská - 2016 - Journal of Applied Logic 14:22-45.
  33. added 2017-01-29
    The Logical Structure of Probability.Stephen Martin Spielman - 1967 - Dissertation, University of Pennsylvania
  34. added 2017-01-26
    The Development of Logical Probability.Colin Howson - 1976 - In R. S. Cohen, P. K. Feyerabend & M. Wartofsky (eds.), Essays in Memory of Imre Lakatos. Reidel. pp. 277--298.
  35. added 2016-12-18
    Remarks on Probability.Rudolf Carnap - 1963 - Philosophical Studies 14 (5):65 - 75.
  36. added 2016-12-18
    The Two Concepts of Probability: The Problem of Probability.Rudolf Carnap - 1945 - Philosophy and Phenomenological Research 5 (4):513-532.
  37. added 2016-12-18
    The Two Concepts of Probability.Rudolph Carnap - 1944 - Philosophy and Phenomenological Research 5:513.
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  38. added 2016-12-08
    Inductive Inference Based on Probability and Similarity.Matthew Weber & Daniel Osherson - unknown
    We advance a theory of inductive inference designed to predict the conditional probability that certain natural categories satisfy a given predicate given that others do (or do not). A key component of the theory is the similarity of the categories to one another. We measure such similarities in terms of the overlap of metabolic activity in voxels of various posterior regions of the brain in response to viewing instances of the category. The theory and similarity measure are tested against averaged (...)
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  39. added 2016-09-28
    A Comprehensive Theory of Induction and Abstraction, Part I.Cael L. Hasse - manuscript
    I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...)
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  40. added 2015-06-09
    The Rationality of Induction.D. C. Stove - 1986 - Oxford, UK: Oxford University Press.
    Writing on the justification of certain inductive inferences, the author proposes that sometimes induction is justified and that arguments to prove otherwise are not cogent. In the first part he defends the argument of D.C. Williams' The Ground of Induction that induction is justified as a matter of logic by the proportional syllogism: "The vast majority of large samples match the population, therefore (probably) this sample matches the population"). In the second part he deals with such topics as deductive logic (...)
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  41. added 2015-06-09
    Probability and Hume's Inductive Scepticism.D. C. Stove - 1973 - Oxford, UK: Oxford, Clarendon Press.
    This book aims to discuss probability and David Hume's inductive scepticism. For the sceptical view which he took of inductive inference, Hume only ever gave one argument. That argument is the sole subject-matter of this book. The book is divided into three parts. Part one presents some remarks on probability. Part two identifies Hume's argument for inductive scepticism. Finally, the third part evaluates Hume's argument for inductive scepticism. Hume's argument that induction must be either deductively valid or circular because based (...)
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  42. added 2015-06-09
    Deductivism.D. Stove - 1970 - Australasian Journal of Philosophy 48 (1):76 – 98.
    "Deductivism" is the thesis that all logic is deductive. Stove lays out the arguments for the existence of non-deductive logic.
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  43. added 2015-04-05
    Methodological Problems of Logical Probability.Michael Harry Kelley - 1969 - Dissertation, The University of Wisconsin - Madison
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  44. added 2015-02-16
    Remarks on the Idealist and Empiricist Interpretation of Frequentism: Robert Leslie Ellis Versus John Venn.Lukas M. Verburgt - 2014 - BSHM Bulletin: Journal of the British Society for the History of Mathematics 29 (3):184-195.
    The goal of this paper is to correct a widespread misconception about the work of Robert Leslie Ellis and John Venn, namely that it can be considered as the ‘British empiricist’ reaction against the traditional theory of probability. It is argued, instead, that there was no unified ‘British school’ of frequentism during the nineteenth century. Where Ellis arrived at frequentism from a metaphysical idealist transformation of probability theory’s mathematical calculations, Venn did so on the basis of an empiricist critique of (...)
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  45. added 2015-01-17
    Wittgenstein on Prior Probabilities.Michael E. Cuffaro - 2010 - Proceedings of the Canadian Society for History and Philosophy of Mathematics 23:85-98.
    Wittgenstein did not write very much on the topic of probability. The little we have comes from a few short pages of the Tractatus, some 'remarks' from the 1930s, and the informal conversations which went on during that decade with the Vienna Circle. Nevertheless, Wittgenstein's views were highly influential in the later development of the logical theory of probability. This paper will attempt to clarify and defend Wittgenstein's conception of probability against some oft-cited criticisms that stem from a misunderstanding of (...)
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  46. added 2014-05-15
    Philosophies of Probability: Objective Bayesianism and its Challenges.Jon Williamson - manuscript
    This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general.
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  47. added 2014-05-15
    The Principle of Maximum Entropy and a Problem in Probability Kinematics.Stefan Lukits - 2014 - Synthese 191 (7):1-23.
    Sometimes we receive evidence in a form that standard conditioning (or Jeffrey conditioning) cannot accommodate. The principle of maximum entropy (MAXENT) provides a unique solution for the posterior probability distribution based on the intuition that the information gain consistent with assumptions and evidence should be minimal. Opponents of objective methods to determine these probabilities prominently cite van Fraassen’s Judy Benjamin case to undermine the generality of maxent. This article shows that an intuitive approach to Judy Benjamin’s case supports maxent. This (...)
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  48. added 2014-05-15
    Evidential Probability and Objective Bayesian Epistemology.Gregory Wheeler & Jon Williamson - 2011 - In Prasanta S. Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier.
    In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.
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  49. added 2014-05-15
    Indifference : The Symmetries of Probability.Bas C. van Fraassen - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge.
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  50. added 2014-05-15
    John Maynard Keynes and Ludwig von Mises on Probability.Ludwig van den Hauwe - 2010 - Journal of Libertarian Studies 22 (1):471-507.
    The economic paradigms of Ludwig von Mises on the one hand and of John Maynard Keynes on the other have been correctly recognized as antithetical at the theoretical level, and as antagonistic with respect to their practical and public policy implications. Characteristically they have also been vindicated by opposing sides of the political spectrum. Nevertheless the respective views of these authors with respect to the meaning and interpretation of probability exhibit a closer conceptual affinity than has been acknowledged in the (...)
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