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  1. Understanding Conditionalization.Christopher J. G. Meacham - 2015 - Canadian Journal of Philosophy 45 (5):767-797.
    At the heart of the Bayesianism is a rule, Conditionalization, which tells us how to update our beliefs. Typical formulations of this rule are underspecified. This paper considers how, exactly, this rule should be formulated. It focuses on three issues: when a subject’s evidence is received, whether the rule prescribes sequential or interval updates, and whether the rule is narrow or wide scope. After examining these issues, it argues that there are two distinct and equally viable versions of Conditionalization to (...)
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  • Testimony as Evidence: More Problems for Linear Pooling. [REVIEW]Katie Steele - 2012 - Journal of Philosophical Logic 41 (6):983-999.
    This paper considers a special case of belief updating—when an agent learns testimonial data, or in other words, the beliefs of others on some issue. The interest in this case is twofold: (1) the linear averaging method for updating on testimony is somewhat popular in epistemology circles, and it is important to assess its normative acceptability, and (2) this facilitates a more general investigation of what it means/requires for an updating method to have a suitable Bayesian representation (taken here as (...)
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  • Maximum Entropy Inference as a Special Case of Conditionalization.Brian Skyrms - 1985 - Synthese 63 (1):55 - 74.
  • Comment on Jeffrey ('Smith & Jones').Julian Nida-Rümelin - 1987 - Erkenntnis 26 (3):401 - 405.
  • Alias Smith and Jones: The Testimony of the Senses. [REVIEW]Richard Jeffrey - 1987 - Erkenntnis 26 (3):391 - 399.
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  • The Consistency Argument for Ranking Functions.Franz Huber - 2007 - Studia Logica 86 (2):299-329.
    The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules.
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  • Evidential Externalism.Jeffrey Dunn - 2012 - Philosophical Studies 158 (3):435-455.
    Consider the Evidence Question: When and under what conditions is proposition P evidence for some agent S? Silins (Philos Perspect 19:375–404, 2005) has recently offered a partial answer to the Evidence Question. In particular, Silins argues for Evidential Internalism (EI), which holds that necessarily, if A and B are internal twins, then A and B have the same evidence. In this paper I consider Silins’s argument, and offer two response on behalf of Evidential Externalism (EE), which is the denial of (...)
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  • Measuring Truthlikeness.R. D. Rosenkrantz - 1980 - Synthese 45 (3):463 - 487.
  • Simultaneous Belief Updates Via Successive Jeffrey Conditionalization.Ilho Park - 2013 - Synthese 190 (16):3511-3533.
    This paper discusses simultaneous belief updates. I argue here that modeling such belief updates using the Principle of Minimum Information can be regarded as applying Jeffrey conditionalization successively, and so that, contrary to what many probabilists have thought, the simultaneous belief updates can be successfully modeled by means of Jeffrey conditionalization.
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  • Three Models of Sequential Belief Updating on Uncertain Evidence.James Hawthorne - 2004 - Journal of Philosophical Logic 33 (1):89-123.
    Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating that maintain order-independence. I will (...)
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  • Probability Kinematics.Zoltan Domotor, Mario Zanotti & Henson Graves - 1980 - Synthese 44 (3):421 - 442.
    Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.
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  • Probability Kinematics, Conditionals, and Entropy Principles.Zoltan Domotor - 1985 - Synthese 63 (1):75 - 114.
  • Commutativity, Normativity, and Holism: Lange Revisited.Lisa Cassell - forthcoming - Canadian Journal of Philosophy:1-15.
    Lange famously argues that although Jeffrey Conditionalization is non-commutative over evidence, it’s not defective in virtue of this feature. Since reversing the order of the evidence in a sequence of updates that don’t commute does not reverse the order of the experiences that underwrite these revisions, the conditions required to generate commutativity failure at the level of experience will fail to hold in cases where we get commutativity failure at the level of evidence. If our interest in commutativity is, fundamentally, (...)
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  • Radical Probabilism and Bayesian Conditioning.Richard Bradley - 2005 - Philosophy of Science 72 (2):342-364.
    Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves one’s (...)
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  • Evidential Support and Instrumental Rationality.Peter Broessel, Anna-Maria A. Eder & Franz Huber - 2013 - Philosophy and Phenomenological Research 87 (2):279-300.
  • The Commutativity of Evidence: A Problem for Conciliatory Views of Peer Disagreement.Georgi Gardiner - 2014 - Episteme 11 (1):83-95.
    Conciliatory views of peer disagreement hold that when an agent encounters peer disagreement she should conciliate by adjusting her doxastic attitude towards that of her peer. In this paper I distinguish different ways conciliation can be understood and argue that the way conciliationism is typically understood violates the principle of commutativity of evidence. Commutativity of evidence holds that the order in which evidence is acquired should not influence what it is reasonable to believe based on that evidence. I argue that (...)
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  • How to Learn Concepts, Consequences, and Conditionals.Franz Huber - 2015 - Analytica: an electronic, open-access journal for philosophy of science 1 (1):20-36.
    In this brief note I show how to model conceptual change, logical learning, and revision of one's beliefs in response to conditional information such as indicative conditionals that do not express propositions.
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  • Ranking Theory.Franz Huber - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 397-436.
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  • Why Follow the Royal Rule?Franz Huber - 2017 - Synthese 194 (5).
    This note is a sequel to Huber. It is shown that obeying a normative principle relating counterfactual conditionals and conditional beliefs, viz. the royal rule, is a necessary and sufficient means to attaining a cognitive end that relates true beliefs in purely factual, non-modal propositions and true beliefs in purely modal propositions. Along the way I will sketch my idealism about alethic or metaphysical modality.
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  • Updating for Externalists.J. Dmitri Gallow - forthcoming - Noûs.
    The externalist says that your evidence could fail to tell you what evidence you do or not do have. In that case, it could be rational for you to be uncertain about what your evidence is. This is a kind of uncertainty which orthodox Bayesian epistemology has difficulty modeling. For, if externalism is correct, then the orthodox Bayesian learning norms of conditionalization and reflection are inconsistent with each other. I recommend that an externalist Bayesian reject conditionalization. In its stead, I (...)
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  • Bayesian Confirmation: A Means with No End.Peter Brössel & Franz Huber - 2015 - British Journal for the Philosophy of Science 66 (4):737-749.
    Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry? In this article, we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be making a claim about how worthy of belief various hypotheses are. Then we consider a different use to which Bayesian confirmation might be put, namely, determining the epistemic value of experimental outcomes, and thus to decide (...)
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  • An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy.Hannes Leitgeb & Richard Pettigrew - 2010 - Philosophy of Science 77 (2):236-272.
    One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...)
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  • General Dynamic Triviality Theorems.Jeffrey Sanford Russell & John Hawthorne - 2016 - Philosophical Review 125 (3):307-339.
    Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. A (...)
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  • Groupthink.Jeffrey Sanford Russell, John Hawthorne & Lara Buchak - 2015 - Philosophical Studies 172 (5):1287-1309.
    How should a group with different opinions (but the same values) make decisions? In a Bayesian setting, the natural question is how to aggregate credences: how to use a single credence function to naturally represent a collection of different credence functions. An extension of the standard Dutch-book arguments that apply to individual decision-makers recommends that group credences should be updated by conditionalization. This imposes a constraint on what aggregation rules can be like. Taking conditionalization as a basic constraint, we gather (...)
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  • Holistic Conditionalization and Underminable Perceptual Learning.Brian T. Miller - forthcoming - Philosophy and Phenomenological Research.
    Seeing a red hat can (i) increase my credence in the hat is red, and (ii) introduce a negative dependence between that proposition and po- tential undermining defeaters such as the light is red. The rigidity of Jeffrey Conditionalization makes this awkward, as rigidity preserves inde- pendence. The picture is less awkward given ‘Holistic Conditionalization’, or so it is claimed. I defend Jeffrey Conditionalization’s consistency with underminable perceptual learning and its superiority to Holistic Conditionalization, arguing that the latter is merely (...)
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  • Reasoning with Comparative Moral Judgements: An Argument for Moral Bayesianism.Ittay Nissan-Rozen - 2017 - In Rafal Urbaniak & Gillman Payette (eds.), Applications of Formal Philosophy. The Road Less Travelled. Cham: Springer. pp. 113-136.
    The paper discusses the notion of reasoning with comparative moral judgements (i.e judgements of the form “act a is morally superior to act b”) from the point of view of several meta-ethical positions. Using a simple formal result, it is argued that only a version of moral cognitivism that is committed to the claim that moral beliefs come in degrees can give a normatively plausible account of such reasoning. Some implications of accepting such a version of moral cognitivism are discussed.
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  • Probability Kinematics and Commutativity.Carl G. Wagner - 2002 - Philosophy of Science 69 (2):266-278.
    The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.
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  • Synthetic Versus Analytic Approaches to Protein and DNA Structure Determination.Agnes Bolinska - 2018 - Biology and Philosophy 33 (3-4):26.
    The structures of protein and DNA were discovered primarily by means of synthesizing component-level information about bond types, lengths, and angles, rather than analyzing X-ray diffraction photographs of these molecules. In this paper, I consider the synthetic and analytic approaches to exemplify alternative heuristics for approaching mid-twentieth-century macromolecular structure determination. I argue that the former was, all else being equal, likeliest to generate the correct structure in the shortest period of time. I begin by characterizing problem solving in these cases (...)
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  • Commutativity or Holism? A Dilemma for Conditionalizers.Jonathan Weisberg - 2009 - British Journal for the Philosophy of Science 60 (4):793-812.
    Conditionalization and Jeffrey Conditionalization cannot simultaneously satisfy two widely held desiderata on rules for empirical learning. The first desideratum is confirmational holism, which says that the evidential import of an experience is always sensitive to our background assumptions. The second desideratum is commutativity, which says that the order in which one acquires evidence shouldn't affect what conclusions one draws, provided the same total evidence is gathered in the end. (Jeffrey) Conditionalization cannot satisfy either of these desiderata without violating the other. (...)
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  • Conditionalizing on Knowledge.Timothy Williamson - 1998 - British Journal for the Philosophy of Science 49 (1):89-121.
    A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is (...)
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  • Learning and Pooling, Pooling and Learning.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Erkenntnis 83 (3):1-21.
    We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.
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  • Structural Equations and Beyond.Franz Huber - 2013 - Review of Symbolic Logic 6 (4):709-732.
    Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...)
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  • Varieties of Bayesianism.Jonathan Weisberg - manuscript
    Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming.
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  • Formal Representations of Belief.Franz Huber - 2008 - Stanford Encyclopedia of Philosophy.
    Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...)
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  • Belief Revision II: Ranking Theory.Franz Huber - 2013 - Philosophy Compass 8 (7):613-621.
    Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research.
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  • Bayesianism I: Introduction and Arguments in Favor.Kenny Easwaran - 2011 - Philosophy Compass 6 (5):312-320.
    Bayesianism is a collection of positions in several related fields, centered on the interpretation of probability as something like degree of belief, as contrasted with relative frequency, or objective chance. However, Bayesianism is far from a unified movement. Bayesians are divided about the nature of the probability functions they discuss; about the normative force of this probability function for ordinary and scientific reasoning and decision making; and about what relation (if any) holds between Bayesian and non-Bayesian concepts.
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  • Updating, Undermining, and Independence.Jonathan Weisberg - 2015 - British Journal for the Philosophy of Science 66 (1):121-159.
    Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a more difficult (...)
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  • New Foundations for Counterfactuals.Franz Huber - 2014 - Synthese 191 (10):2167-2193.
    Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the (...)
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  • Popper's Severity of Test as an Intuitive Probabilistic Model of Hypothesis Testing.Fenna H. Poletiek - 2009 - Behavioral and Brain Sciences 32 (1):99-100.
    Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.
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  • The Uncertain Reasoner: Bayes, Logic, and Rationality.Mike Oaksford & Nick Chater - 2009 - Behavioral and Brain Sciences 32 (1):105-120.
    Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...)
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  • Deterministic Convergence and Strong Regularity.Michael Nielsen - forthcoming - British Journal for the Philosophy of Science.
    Bayesians since Savage (1972) have appealed to asymptotic results to counter charges of excessive subjectivity. Their claim is that objectionable differences in prior probability judgments will vanish as agents learn from evidence, and individual agents will converge to the truth. Glymour (1980), Earman (1992) and others have voiced the complaint that the theorems used to support these claims tell us, not how probabilities updated on evidence will actually}behave in the limit, but merely how Bayesian agents believe they will behave, suggesting (...)
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  • Notes on Bayesian Confirmation Theory.Michael Strevens - manuscript
    Bayesian confirmation theory—abbreviated to in these notes—is the predominant approach to confirmation in late twentieth century philosophy of science. It has many critics, but no rival theory can claim anything like the same following. The popularity of the Bayesian approach is due to its flexibility, its apparently effortless handling of various technical problems, the existence of various a priori arguments for its validity, and its injection of subjective and contextual elements into the process of confirmation in just the places where (...)
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  • Higher-Order Beliefs and the Undermining Problem for Bayesianism.Lisa Cassell - 2019 - Acta Analytica 34 (2):197-213.
    Jonathan Weisberg has argued that Bayesianism’s rigid updating rules make Bayesian updating incompatible with undermining defeat. In this paper, I argue that when we attend to the higher-order beliefs we must ascribe to agents in the kinds of cases Weisberg considers, the problem he raises disappears. Once we acknowledge the importance of higher-order beliefs to the undermining story, we are led to a different understanding of how these cases arise. And on this different understanding of things, the rigid nature of (...)
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  • Sleeping Beauty and De Nunc Updating.Namjoong Kim - 2010 - Dissertation, University of Massachusetts
    About a decade ago, Adam Elga introduced philosophers to an intriguing puzzle. In it, Sleeping Beauty, a perfectly rational agent, undergoes an experiment in which she becomes ignorant of what time it is. This situation is puzzling for two reasons: First, because there are two equally plausible views about how she will change her degree of belief given her situation and, second, because the traditional rules for updating degrees of belief don't seem to apply to this case. In this dissertation, (...)
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  • Belief and Degrees of Belief.Franz Huber - 2009 - In F. Huber & C. Schmidt-Petri (eds.), Degrees of Belief. Springer.
    Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...)
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  • Merging of Opinions and Probability Kinematics.Simon M. Huttegger - 2015 - Review of Symbolic Logic 8 (4):611-648.
  • Confirmation and Induction.Franz Huber - 2007 - Internet Encyclopedia of Philosophy.
  • General Properties of General Bayesian Learning.Miklós Rédei & Zalán Gyenis - unknown
    We investigate the general properties of general Bayesian learning, where ``general Bayesian learning'' means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability measure. If (...)
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  • Jeffrey Conditioning and External Bayesianity.Carl Wagner - 2010 - Logic Journal of the IGPL 18 (2):336-345.
    Suppose that several individuals who have separately assessed prior probability distributions over a set of possible states of the world wish to pool their individual distributions into a single group distribution, while taking into account jointly perceived new evidence. They have the option of first updating their individual priors and then pooling the resulting posteriors or first pooling their priors and then updating the resulting group prior. If the pooling method that they employ is such that they arrive at the (...)
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  • Confirmation Measures and Collaborative Belief Updating.Ilho Park - 2014 - Synthese 191 (16):3955-3975.
    There are some candidates that have been thought to measure the degree to which evidence incrementally confirms a hypothesis. This paper provides an argument for one candidate—the log-likelihood ratio measure. For this purpose, I will suggest a plausible requirement that I call the Requirement of Collaboration. And then, it will be shown that, of various candidates, only the log-likelihood ratio measure \(l\) satisfies this requirement. Using this result, Jeffrey conditionalization will be reformulated so as to disclose explicitly what determines new (...)
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