Results for 'Probability'

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  1. Probability for Epistemic Modalities.Simon Goldstein & Paolo Santorio - forthcoming - Philosophers' Imprint.
    This paper develops an information sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking probability and modality, including the principle that the probability of a conditional 'If A, then C' equals the probability of C, updated with A. The theory avoids so-called triviality results, which are standardly taken to show that principles of this sort cannot be validated. To achieve this, we deny that (...)
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  2. Between Probability and Certainty: What Justifies Belief.Martin Smith - 2016 - Oxford University Press UK.
    This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...)
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  3. Probability and Scepticism.Brian Weatherson - 2014 - In Dylan Dodd Elia Zardini (ed.), Scepticism and Perceptual Justification. Oxford University Press. pp. 71-86.
    If we add as an extra premise that the agent does know H, then it is possible for her to know E — H, we get the conclusion that the agent does not really know H. But even without that closure premise, or something like it, the conclusion seems quite dramatic. One possible response to the argument, floated by both Descartes and Hume, is to accept the conclusion and embrace scepticism. We cannot know anything that goes beyond our evidence, so (...)
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  4. Probability and Nonclassical Logic.Robert Williams - 2016 - In Alan Hajek & Christopher Hitchcock (eds.), The oxford handbook of probability and philosophy. Oxford university press.
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  5. Subjective Probability as Sampling Propensity.Thomas Icard - 2016 - Review of Philosophy and Psychology 7 (4):863-903.
    Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work (...)
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  6. Imprecise Probability and Higher Order Vagueness.Susanna Rinard - 2017 - Res Philosophica 94 (2):257-273.
    There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...)
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  7. Philosophy of Probability: Foundations, Epistemology, and Computation.Sylvia Wenmackers - 2011 - Dissertation, University of Groningen
    This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the (...)
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  8. Probability and Randomness.Antony Eagle - 2016 - In Alan Hájek & Christopher Hitchcock (eds.), Oxford Handbook of Probability and Philosophy. Oxford, U.K.: Oxford University Press. pp. 440-459.
    Early work on the frequency theory of probability made extensive use of the notion of randomness, conceived of as a property possessed by disorderly collections of outcomes. Growing out of this work, a rich mathematical literature on algorithmic randomness and Kolmogorov complexity developed through the twentieth century, but largely lost contact with the philosophical literature on physical probability. The present chapter begins with a clarification of the notions of randomness and probability, conceiving of the former as a (...)
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  9. Probability in Ethics.David McCarthy - 2016 - In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Philosophy and Probability. Oxford University Press. pp. 705–737.
    The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation theorem; (...)
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  10. Justification, Normalcy and Evidential Probability.Martin Smith - manuscript
    NOTE: This paper is a reworking of some aspects of an earlier paper – ‘What else justification could be’ and also an early draft of chapter 2 of Between Probability and Certainty. I'm leaving it online as it has a couple of citations and there is some material here which didn't make it into the book (and which I may yet try to develop elsewhere). My concern in this paper is with a certain, pervasive picture of epistemic justification. On (...)
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  11. Deontic Modals and Probability: One Theory to Rule Them All?Fabrizio Cariani - forthcoming - In Nate Charlow & Matthew Chrisman (eds.), Deontic Modality. Oxford University Press.
    This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that (...)
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  12. Coherence, Probability and Explanation.William Roche & Michael Schippers - 2014 - Erkenntnis 79 (4):821-828.
    Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability distribution (...)
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  13. Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew Parker - 2018 - European Journal for Philosophy of Science 9 (1):8.
    A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson (...)
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  14. Inter-World Probability and the Problem of Induction.Chase B. Wrenn - 2006 - Pacific Philosophical Quarterly 87 (3):387–402.
    Laurence BonJour has recently proposed a novel and interesting approach to the problem of induction. He grants that it is contingent, and so not a priori, that our patterns of inductive inference are reliable. Nevertheless, he claims, it is necessary and a priori that those patterns are highly likely to be reliable, and that is enough to ground an a priori justification induction. This paper examines an important defect in BonJour's proposal. Once we make sense of the claim that inductive (...)
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  15. Coherence and Probability: A Probabilistic Account of Coherence.Roche William - 2013 - In M. Araszkiewicz & J. Savelka (eds.), Coherence: Insights from philosophy, jurisprudence and artificial intelligence. Dordrecht: Springer. pp. 59-91.
    I develop a probabilistic account of coherence, and argue that at least in certain respects it is preferable to (at least some of) the main extant probabilistic accounts of coherence: (i) Igor Douven and Wouter Meijs’s account, (ii) Branden Fitelson’s account, (iii) Erik Olsson’s account, and (iv) Tomoji Shogenji’s account. Further, I relate the account to an important, but little discussed, problem for standard varieties of coherentism, viz., the “Problem of Justified Inconsistent Beliefs.”.
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  16. From Classical to Intuitionistic Probability.Brian Weatherson - 2003 - Notre Dame Journal of Formal Logic 44 (2):111-123.
    We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of (...)
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  17. Dogmatism, Probability, and Logical Uncertainty.David Jehle & Brian Weatherson - 2012 - In Greg Restall & Gillian Kay Russell (eds.), New Waves in Philosophical Logic. Palgrave-Macmillan. pp. 95--111.
    Many epistemologists hold that an agent can come to justifiably believe that p is true by seeing that it appears that p is true, without having any antecedent reason to believe that visual impressions are generally reliable. Certain reliabilists think this, at least if the agent’s vision is generally reliable. And it is a central tenet of dogmatism (as described by Pryor (2000) and Pryor (2004)) that this is possible. Against these positions it has been argued (e.g. by Cohen (2005) (...)
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  18. A New Defence of Probability Discounting.Kian Mintz-Woo - 2017 - In Adrian Walsh, Säde Hormio & Duncan Purves (eds.), The Ethical Underpinnings of Climate Economics. Oxford: Routledge. pp. 87-102.
    When probability discounting (or probability weighting), one multiplies the value of an outcome by one's subjective probability that the outcome will obtain in decision-making. The broader import of defending probability discounting is to help justify cost-benefit analyses in contexts such as climate change. This chapter defends probability discounting under risk both negatively, from arguments by Simon Caney (2008, 2009), and with a new positive argument. First, in responding to Caney, I argue that small costs and (...)
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  19. Response to Wunder: Objective Probability, Non-Contingent Theism, and the EAAN.Perry Hendricks - 2018 - Religious Studies:1-5.
    This paper is a response to Tyler Wunder’s ‘The modality of theism and probabilistic natural theology: a tension in Alvin Plantinga's philosophy’ (this journal). In his article, Wunder argues that if the proponent of the Evolutionary Argument Against Naturalism (EAAN) holds theism to be non-contingent and frames the argument in terms of objective probability, that the EAAN is either unsound or theism is necessarily false. I argue that a modest revision of the EAAN renders Wunder’s objection irrelevant, and that (...)
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  20. Vagueness, Conditionals and Probability.Robert Williams - 2009 - Erkenntnis 70 (2):151 - 171.
    This paper explores the interaction of well-motivated (if controversial) principles governing the probability conditionals, with accounts of what it is for a sentence to be indefinite. The conclusion can be played in a variety of ways. It could be regarded as a new reason to be suspicious of the intuitive data about the probability of conditionals; or, holding fixed the data, it could be used to give traction on the philosophical analysis of a contentious notion—indefiniteness. The paper outlines (...)
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  21.  65
    Confirmation, Increase in Probability, and Partial Discrimination: A Reply to Zalabardo.William Roche - 2016 - European Journal for Philosophy of Science 6 (1):1-7.
    There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and (...)
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  22. A Generalised Lottery Paradox for Infinite Probability Spaces.Martin Smith - 2010 - British Journal for the Philosophy of Science 61 (4):821-831.
    Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite (...)
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  23.  35
    Symmetry Arguments Against Regular Probability: A Reply to Recent Objections.Matthew Parker - 2019 - European Journal for Philosophy of Science 9 (1):1-21.
    A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson (...)
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  24.  96
    Probability as a Guide to Life.Helen Beebee & David Papineau - 2003 - In David Papineau (ed.), The Roots of Reason. Oxford: Oxford University Press. pp. 217-243.
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  25.  96
    Probability-Lowering Causes and the Connotations of Causation.Andrés Páez - 2013 - Ideas Y Valores 62 (151):43-55.
    A common objection to probabilistic theories of causation is that there are prima facie causes that lower the probability of their effects. Among the many replies to this objection, little attention has been given to Mellor's (1995) indirect strategy to deny that probability-lowering factors are bona fide causes. According to Mellor, such factors do not satisfy the evidential, explanatory, and instrumental connotations of causation. The paper argues that the evidential connotation only entails an epistemically relativized form of causal (...)
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  26.  72
    Is an Increase in Probability Always an Increase in Evidential Support?Artūrs Logins - forthcoming - Erkenntnis:1-25.
    Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be (...)
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  27.  30
    Fading Foundations. Probability and the Regress Problem.Jeanne Peijnenburg - 2017 - Cham, Switzerland: Springer.
    This Open Access book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary way. Taking seriously the idea that good reasons are (...)
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  28. Probability and Skepticism About Reason in Hume's Treatise.Antonia Lolordo - 2000 - British Journal for the History of Philosophy 8 (3):419 – 446.
    This paper attempts to reconstruct Hume's argument in Treatise 1.4.1, 'Of Scepticism with Regard to Reason'.
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  29. Interpretations of Probability in Evolutionary Theory.Roberta L. Millstein - 2003 - Philosophy of Science 70 (5):1317-1328.
    Evolutionary theory (ET) is teeming with probabilities. Probabilities exist at all levels: the level of mutation, the level of microevolution, and the level of macroevolution. This uncontroversial claim raises a number of contentious issues. For example, is the evolutionary process (as opposed to the theory) indeterministic, or is it deterministic? Philosophers of biology have taken different sides on this issue. Millstein (1997) has argued that we are not currently able answer this question, and that even scientific realists ought to remain (...)
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  30. Self-Referential Probability.Catrin Campbell-Moore - 2016 - Dissertation, Ludwig-Maximilians-Universität München
    This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect (...)
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  31. Relevance Differently Affects the Truth, Acceptability, and Probability Evaluations of “and”, “but”, “Therefore”, and “If–Then”.Niels Skovgaard-Olsen, David Kellen, Hannes Krahl & Karl Christoph Klauer - 2017 - Thinking and Reasoning 23 (4):449-482.
    In this study we investigate the influence of reason-relation readings of indicative conditionals and ‘and’/‘but’/‘therefore’ sentences on various cognitive assessments. According to the Frege-Grice tradition, a dissociation is expected. Specifically, differences in the reason-relation reading of these sentences should affect participants’ evaluations of their acceptability but not of their truth value. In two experiments we tested this assumption by introducing a relevance manipulation into the truth-table task as well as in other tasks assessing the participants’ acceptability and probability evaluations. (...)
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  32. Intuitionistc Probability and the Bayesian Objection to Dogmatism.Martin Smith - 2017 - Synthese 194 (10):3997-4009.
    Given a few assumptions, the probability of a conjunction is raised, and the probability of its negation is lowered, by conditionalising upon one of the conjuncts. This simple result appears to bring Bayesian confirmation theory into tension with the prominent dogmatist view of perceptual justification – a tension often portrayed as a kind of ‘Bayesian objection’ to dogmatism. In a recent paper, David Jehle and Brian Weatherson observe that, while this crucial result holds within classical probability theory, (...)
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  33.  58
    Probability of Immortality and God’s Existence. A Mathematical Perspective.Jesús Sánchez - manuscript
    What are the probabilities that this universe is repeated exactly the same with you in it again? Is God invented by human imagination or is the result of human intuition? The intuition that the same laws/mechanisms (evolution, stability winning probability) that have created something like the human being capable of self-awareness and controlling its surroundings, could create a being capable of controlling all what it exists? Will be the characteristics of the next universes random or tend to something? All (...)
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  34. Is There a Dutch Book Argument for Probability Kinematics?Brad Armendt - 1980 - Philosophy of Science 47 (4):583-588.
    Dutch Book arguments have been presented for static belief systems and for belief change by conditionalization. An argument is given here that a rule for belief change which under certain conditions violates probability kinematics will leave the agent open to a Dutch Book.
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  35. Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics.Charles T. Sebens & Sean M. Carroll - 2016 - British Journal for the Philosophy of Science (1):axw004.
    A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers are in a position of self-locating uncertainty during the period between the branches of the wave function splitting via decoherence and the observer registering the outcome of the measurement. In this period it is tempting to regard each branch as equiprobable, but (...)
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  36. Climate Change Assessments: Confidence, Probability and Decision.Richard Bradley, Casey Helgeson & Brian Hill - 2017 - Philosophy of Science 84 (3):500–522.
    The Intergovernmental Panel on Climate Change has developed a novel framework for assessing and communicating uncertainty in the findings published in their periodic assessment reports. But how should these uncertainty assessments inform decisions? We take a formal decision-making perspective to investigate how scientific input formulated in the IPCC’s novel framework might inform decisions in a principled way through a normative decision model.
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  37. Conditional Probability and Defeat.Trenton Merricks - 2002 - In James Beilby (ed.), Naturalism Defeated? Essays on Plantinga's Evolutionary Argument Against Naturalism. Cornell University Press. pp. 165-175.
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  38. The Whole Truth About Linda: Probability, Verisimilitude and a Paradox of Conjunction.Gustavo Cevolani, Vincenzo Crupi & Roberto Festa - 2010 - In Marcello D'Agostino, Federico Laudisa, Giulio Giorello, Telmo Pievani & Corrado Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. College Publications. pp. 603--615.
    We provide a 'verisimilitudinarian' analysis of the well-known Linda paradox or conjunction fallacy, i.e., the fact that most people judge the probability of the conjunctive statement "Linda is a bank teller and is active in the feminist movement" (B & F) as more probable than the isolated statement "Linda is a bank teller" (B), contrary to an uncontroversial principle of probability theory. The basic idea is that experimental participants may judge B & F a better hypothesis about Linda (...)
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  39. 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 (...)
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  40. Triviality Results, Conditional Probability, and Restrictor Conditionals.Jonathan Vandenburgh - manuscript
    Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory (...)
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  41. Natural-Born Determinists: A New Defense of Causation as Probability-Raising.Robert Northcott - 2010 - Philosophical Studies 150 (1):1-20.
    A definition of causation as probability-raising is threatened by two kinds of counterexample: first, when a cause lowers the probability of its effect; and second, when the probability of an effect is raised by a non-cause. In this paper, I present an account that deals successfully with problem cases of both these kinds. In doing so, I also explore some novel implications of incorporating into the metaphysical investigation considerations of causal psychology.
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  42. The Perspectival Nature of Probability and Inference.Arnold Zuboff - 2000 - Inquiry: An Interdisciplinary Journal of Philosophy 43 (3):353 – 358.
    It is argued that two observers with the same information may rightly disagree about the probability of an event that they are both observing. This is a correct way of describing the view of a lottery outcome from the perspective of a winner and from the perspective of an observer not connected with the winner - the outcome is improbable for the winner and not improbable for the unconnected observer. This claim is both argued for and extended by developing (...)
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  43. Religious Experience and the Probability of Theism: Comments on Swinburne.Christoph Jäger - 2017 - Religious Studies 53 (3):353-370.
    I discuss Richard Swinburne’s account of religious experience in his probabilistic case for theism. I argue, pace Swinburne, that even if cosmological considerations render theism not too improbable, religious experience does not render it more probable than not.
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  44. Twenty-One Arguments Against Propensity Analyses of Probability.Antony Eagle - 2004 - Erkenntnis 60 (3):371–416.
    I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.
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  45.  40
    Probability and Certainty.Jonny Blamey - 2008 - Praxis 1 (1).
    Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both beliefs (...)
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  46. 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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  47. The Concept of Probability in Physics: An Analytic Version of von Mises’ Interpretation.Louis Vervoort - manuscript
    In the following we will investigate whether von Mises’ frequency interpretation of probability can be modified to make it philosophically acceptable. We will reject certain elements of von Mises’ theory, but retain others. In the interpretation we propose we do not use von Mises’ often criticized ‘infinite collectives’ but we retain two essential claims of his interpretation, stating that probability can only be defined for events that can be repeated in similar conditions, and that exhibit frequency stabilization. The (...)
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  48.  55
    Association, Madness, and the Measures of Probability in Locke and Hume.John Wright - 1987 - In Christopher Fox (ed.), Psychology and Literature in the Eighteenth Century. New York: AMS Press. pp. 103-28.
    This paper argues for the importance of Chapter 33 of Book 2 of Locke's _Essay Concerning Human Understanding_ ("Of the Association of Ideas) both for Locke's own philosophy and for its subsequent reception by Hume. It is argued that in the 4th edition of the Essay of 1700, in which the chapter was added, Locke acknowledged that many beliefs, particularly in religion, are not voluntary and cannot be eradicated through reason and evidence. The author discusses the origins of the chapter (...)
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  49.  79
    Probability Theory with Superposition Events.David Ellerman - manuscript
    In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density matrices. Then probabilities for experiments or `measurements' of all these events can be determined in a manner exactly like in quantum mechanics (QM) using density matrices. Moreover the transformation of the (...)
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  50. Confirmation, Increase in Probability, and the Likelihood Ratio Measure: A Reply to Glass and McCartney.William Roche - 2017 - Acta Analytica 32 (4):491-513.
    Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any of (...)
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