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Higher order degrees of belief

In David Hugh Mellor (ed.), Prospects for Pragmatism: Essays in Memory of F P Ramsey. New York: Cambridge University Press. pp. 109--137 (1980)

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  1. Probabilities for new theories.Patrick Maher - 1995 - Philosophical Studies 77 (1):103 - 115.
    Contrary to what has been widely supposed, Bayesian theory deals successfully with the introduction of new theories that have never previously been entertained. The theory enables us to say what sorts of method should be used to assign probabilities to these new theories, and it allows that the probabilities of existing theories may be modified as a result.
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  • A two-level system of knowledge representation based on evidential probability.Henry E. Kyburg - 1991 - Philosophical Studies 64 (1):105 - 114.
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  • Probabilism and induction.Richard Jeffrey - 1986 - Topoi 5 (1):51-58.
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  • De finetti's probabilism.Richard Jeffrey - 1984 - Synthese 60 (1):73 - 90.
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  • A probabilistic theory of second order causation.Christopher Hitchcock - 1996 - Erkenntnis 44 (3):369 - 377.
    Larry Wright and others have advanced causal accounts of functional explanation, designed to alleviate fears about the legitimacy of such explanations. These analyses take functional explanations to describe second order causal relations. These second order relations are conceptually puzzling. I present an account of second order causation from within the framework of Eells' probabilistic theory of causation; the account makes use of the population-relativity of causation that is built into this theory.
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  • An economic model of scientific activity and truth acquisition.Alvin I. Goldman & Moshe Shaked - 1991 - Philosophical Studies 63 (1):31-55.
    Economic forms of analysis have penetrated to many disciplines in the last 30 years: political science, sociology, law, social and political philosophy, and so forth. We wish to extend the economic paradigm to certain problems in epistemology and the philosophy of science. Scientific agents, and scholarly inquirers generally, act in some ways like vendors, trying to "sell" their findings, theories, analyses, or arguments to an audience of prospective "buyers". The analogy with the marketplace is imperfect. The ideas or discoveries that (...)
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  • Second Guessing: A Self-Help Manual.Sherrilyn Roush - 2009 - Episteme 6 (3):251-268.
    I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled way of (...)
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  • Stakes and beliefs.Brad Armendt - 2010 - Philosophical Studies 147 (1):71 - 87.
    The idea that beliefs may be stake-sensitive is explored. This is the idea that the strength with which a single, persistent belief is held may vary and depend upon what the believer takes to be at stake. The stakes in question are tied to the truth of the belief—not, as in Pascal’s wager and other cases, to the belief’s presence. Categorical beliefs and degrees of belief are considered; both kinds of account typically exclude the idea and treat belief as stake-invariant (...)
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  • Higher order probabilities.Zoltan Domotor - 1981 - Philosophical Studies 40 (1):31 - 46.
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  • Ideal evidence, relevance and second-order probabilities.Maya Bar-Hillel - 1982 - Erkenntnis 17 (3):273 - 290.
    The concepts of supportive evidence and of relevant evidence seem very closely related to each other. Supportive evidence is clearly always relevant as well. But must relevant evidence be defined as evidence which is either supportive or weakeking? In an explicit or implicit manner, this is indeed the position of many philosophers. The paradox of ideal evidence, however, shows us that this is to restrictive. Besides increasing or decreasing the probability attached to some hypothesis, evidence can alter or interact with (...)
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  • Stake-invariant belief.Brad Armendt - 2008 - Acta Analytica 23 (1):29-43.
    What can rational deliberation indicate about belief? Belief clearly influences deliberation. The principle that rational belief is stake-invariant rules out at least one way that deliberation might influence belief. The principle is widely, if implicitly, held in work on the epistemology of categorical belief, and it is built into the model of choice-guiding degrees of belief that comes to us from Ramsey and de Finetti. Criticisms of subjective probabilism include challenges to the assumption of additive values (the package principle) employed (...)
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  • Who's afraid of undermining?Peter B. M. Vranas - 2002 - Erkenntnis 57 (2):151-174.
    The Principal Principle (PP) says that, for any proposition A, given any admissible evidence and the proposition that the chance of A is x%, one's conditional credence in A should be x%. Humean Supervenience (HS) claims that, among possible worlds like ours, no two differ without differing in the spacetime-point-by-spacetime-point arrangement of local properties. David Lewis (1986b, 1994a) has argued that PP contradicts HS, and the validity of his argument has been endorsed by Bigelow et al. (1993), Thau (1994), Hall (...)
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  • Belief and the problem of Ulysses and the sirens.Bas C. van Fraassen - 1995 - Philosophical Studies 77 (1):7-37.
    This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...)
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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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  • Doxastic paradoxes without self-reference.Robert C. Koons - 1990 - Australasian Journal of Philosophy 68 (2):168 – 177.
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  • Conditional probabilities and probabilities given knowledge of a condition.Paul Weirich - 1983 - Philosophy of Science 50 (1):82-95.
    The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate.
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  • 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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  • Probabilistic foundations for operator logic.B. H. Slater - 1993 - British Journal for the Philosophy of Science 44 (3):517-530.
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  • Dynamic coherence and probability kinematics.Brian Skyrms - 1987 - Philosophy of Science 54 (1):1-20.
    The question of coherence of rules for changing degrees of belief in the light of new evidence is studied, with special attention being given to cases in which evidence is uncertain. Belief change by the rule of conditionalization on an appropriate proposition and belief change by "probability kinematics" on an appropriate partition are shown to have like status.
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  • Why scientists gather evidence.Patrick Maher - 1990 - British Journal for the Philosophy of Science 41 (1):103-119.
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  • Tough enough? Robust satisficing as a decision norm for long-term policy analysis.Andreas Mogensen & David Thorstad - manuscript
    This paper aims to open a dialogue between philosophers working in decision theory and operations researchers and engineers whose research addresses the topic of decision making under deep uncertainty. Specifically, we assess the recommendation to follow a norm of robust satisficing when making decisions under deep uncertainty in the context of decision analyses that rely on the tools of Robust Decision Making developed by Robert Lempert and colleagues at RAND. We discuss decision-theoretic and voting-theoretic motivations for robust satisficing, then use (...)
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  • Deference Done Better.Kevin Dorst, Benjamin A. Levinstein, Bernhard Salow, Brooke E. Husic & Branden Fitelson - 2021 - Philosophical Perspectives 35 (1):99-150.
    There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...)
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  • XIII—Dutch Book and Accuracy Theorems.Anna Mahtani - 2021 - Proceedings of the Aristotelian Society 120 (3):309-327.
    Dutch book and accuracy arguments are used to justify certain rationality constraints on credence functions. Underlying these Dutch book and accuracy arguments are associated theorems, and I show that the interpretation of these theorems can vary along a range of dimensions. Given that the theorems can be interpreted in a variety of different ways, what is the status of the associated arguments? I consider three possibilities: we could aggregate the results of the differently interpreted theorems in some way, and motivate (...)
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  • Epistemic Self-Doubt.Sherrilyn Roush - 2017 - Stanford Encyclopedia of Philosophy.
    When we get evidence that tells us our belief-forming mechanisms may not be reliable this presents a thorny set of questions about whether and how to revise our original belief. This article analyzes aspects of the problem and a variety of approaches to its solution.
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  • Revising Probabilities and Full Beliefs.Sven Ove Hansson - 2020 - Journal of Philosophical Logic 49 (5):1005-1039.
    A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information (...)
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  • Imaginary Foundations.Wolfgang Schwarz - 2018 - Ergo: An Open Access Journal of Philosophy 5.
    Our senses provide us with information about the world, but what exactly do they tell us? I argue that in order to optimally respond to sensory stimulations, an agent’s doxastic space may have an extra, “imaginary” dimension of possibility; perceptual experiences confer certainty on propositions in this dimension. To some extent, the resulting picture vindicates the old-fashioned empiricist idea that all empirical knowledge is based on a solid foundation of sense-datum propositions, but it avoids most of the problems traditionally associated (...)
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  • Evidence: A Guide for the Uncertain.Kevin Dorst - 2019 - Philosophy and Phenomenological Research 100 (3):586-632.
    Assume that it is your evidence that determines what opinions you should have. I argue that since you should take peer disagreement seriously, evidence must have two features. (1) It must sometimes warrant being modest: uncertain what your evidence warrants, and (thus) uncertain whether you’re rational. (2) But it must always warrant being guided: disposed to treat your evidence as a guide. Surprisingly, it is very difficult to vindicate both (1) and (2). But diagnosing why this is so leads to (...)
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  • Fading Foundations: Probability and the Regress Problem.Jeanne Peijnenburg - 2017 - Cham, Switzerland: Springer. Edited by Jeanne Peijnenburg.
    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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  • Rational Relations Between Perception and Belief: The Case of Color.Peter Brössel - 2017 - Review of Philosophy and Psychology 8 (4):721-741.
    The present paper investigates the first step of rational belief acquisition. It, thus, focuses on justificatory relations between perceptual experiences and perceptual beliefs, and between their contents, respectively. In particular, the paper aims at outlining how it is possible to reason from the content of perceptual experiences to the content of perceptual beliefs. The paper thereby approaches this aim by combining a formal epistemology perspective with an eye towards recent advances in philosophy of cognition. Furthermore the paper restricts its focus, (...)
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  • Knowledge of Our Own Beliefs.Sherrilyn Roush - 2016 - Philosophy and Phenomenological Research 93 (3):45-69.
    There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and second-order beliefs. (...)
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  • Safeguards of a Disunified Mind.Wlodek Rabinowicz - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (3):356-383.
    The papers focuses on pragmatic arguments for various rationality constraints on a decision maker’s state of mind: on her beliefs or preferences. An argument of this kind typically targets constraint violations. It purports to show that a violator of a given constraint can be confronted with a decision problem in which she will act to her guaranteed disadvantage. Dramatically put, she can be exploited by a clever bookie who doesn’t know more than the agent herself. Examples of pragmatic arguments of (...)
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  • A Defense of Temperate Epistemic Transparency.Eleonora Cresto - 2012 - Journal of Philosophical Logic 41 (6):923-955.
    Epistemic transparency tells us that, if an agent S knows a given proposition p , then S knows that she knows that p . This idea is usually encoded in the so-called KK principle of epistemic logic. The paper develops an argument in favor of a moderate version of KK , which I dub quasi-transparency , as a normative rather than a descriptive principle. In the second Section I put forward the suggestion that epistemic transparency is not a demand of (...)
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  • The notion of consistency for partial belief.Susan Vineberg - 2001 - Philosophical Studies 102 (3):281 - 296.
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  • Expert Deference De Se.J. Dmitri Gallow - manuscript
    Principles of expert deference say that you should align your credences with those of an expert. This expert could be your doctor, the objective chances, or your future self, after you've learnt something new. These kinds of principles face difficulties in cases in which you are uncertain of the truth-conditions of the thoughts in which you invest credence, as well as cases in which the thoughts have different truth-conditions for you and the expert. For instance, you shouldn't defer to your (...)
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  • Do We Need Second‐Order Probabilities?Sven Ove Hansson - 2008 - Dialectica 62 (4):525-533.
    Although it has often been claimed that all the information contained in second‐order probabilities can be contained in first‐order probabilities, no practical recipe for the elimination of second‐order probabilities without loss of information seems to have been presented. Here, such an elimination method is introduced for repeatable events. However, its application comes at the price of losses in cognitive realism. In spite of their technical eliminability, second‐order probabilities are useful because they can provide models of important features of the world (...)
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  • Fitch’s Paradox and Probabilistic Antirealism.Igor Douven - 2007 - Studia Logica 86 (2):149-182.
    Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.
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  • Belief without credence.J. Adam Carter, Benjamin W. Jarvis & Katherine Rubin - 2016 - Synthese 193 (8):2323-2351.
    One of the deepest ideological divides in contemporary epistemology concerns the relative importance of belief versus credence. A prominent consideration in favor of credence-based epistemology is the ease with which it appears to account for rational action. In contrast, cases with risky payoff structures threaten to break the link between rational belief and rational action. This threat poses a challenge to traditional epistemology, which maintains the theoretical prominence of belief. The core problem, we suggest, is that belief may not be (...)
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  • Conditionalization and not Knowing that One Knows.Aaron Bronfman - 2014 - Erkenntnis 79 (4):871-892.
    Bayesian Conditionalization is a widely used proposal for how to update one’s beliefs upon the receipt of new evidence. This is in part because of its attention to the totality of one’s evidence, which often includes facts about what one’s new evidence is and how one has come to have it. However, an increasingly popular position in epistemology holds that one may gain new evidence, construed as knowledge, without being in a position to know that one has gained this evidence. (...)
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  • Measuring Uncertainty.Sven Ove Hansson - 2009 - Studia Logica 93 (1):21-40.
    Two types of measures of probabilistic uncertainty are introduced and investigated. Dispersion measures report how diffused the agent’s second-order probability distribution is over the range of first-order probabilities. Robustness measures reflect the extent to which the agent’s assessment of the prior (objective) probability of an event is perturbed by information about whether or not the event actually took place. The properties of both types of measures are investigated. The most obvious type of robustness measure is shown to coincide with one (...)
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  • Diachronic Coherence and Radical Probabilism.Brian Skyrms - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer. pp. 253--261.
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  • Reconsidering authority.Michael Strevens - 2007 - In Tamar Szabó Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology: Volume 3. Oxford University Press UK. pp. 294-330.
    How to regard the weight we give to a proposition on the grounds of its being endorsed by an authority? I examine this question as it is raised within the epistemology of science, and I argue that “authority-based weight” should receive special handling, for the following reason. Our assessments of other scientists’ competence or authority are nearly always provisional, in the sense that to save time and money, they are not made nearly as carefully as they could be---indeed, they are (...)
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  • Diachronic Coherence and Radical Probabilism.Brian Skyrms - 2006 - Philosophy of Science 73 (5):959-968.
    The question of diachronic coherence, coherence of degrees of belief across time, is investigated within the context of Richard Jeffrey’s radical probabilism. Diachronic coherence is taken as fundamental, and coherence results for degrees of belief at a single time, such as additivity, are recovered only with additional assumptions. Additivity of probabilities of probabilities is seen to be less problematic than additivity of first-order probabilities. Without any assumed model of belief change, diachronic coherence applied to higher-order degrees of belief yields the (...)
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  • A paradox of confirmation.Ruth Weintraub - 1988 - Erkenntnis 29 (2):169 - 180.
    I present a puzzle which seems simple, but is found to have interesting implications for confirmation. Its dissolution also helps us to throw light on the relationship between first- and second-order probabilities construed as rational degrees of belief.
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  • Updating Probability: Tracking Statistics as Criterion.Bas C. van Fraassen & Joseph Y. Halpern - 2016 - British Journal for the Philosophy of Science:axv027.
    ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. (...)
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  • A non-probabilist principle of higher-order reasoning.William J. Talbott - 2016 - Synthese 193 (10).
    The author uses a series of examples to illustrate two versions of a new, nonprobabilist principle of epistemic rationality, the special and general versions of the metacognitive, expected relative frequency principle. These are used to explain the rationality of revisions to an agent’s degrees of confidence in propositions based on evidence of the reliability or unreliability of the cognitive processes responsible for them—especially reductions in confidence assignments to propositions antecedently regarded as certain—including certainty-reductions to instances of the law of excluded (...)
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  • Updating, supposing, and maxent.Brian Skyrms - 1987 - Theory and Decision 22 (3):225-246.
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  • Maximum entropy inference as a special case of conditionalization.Brian Skyrms - 1985 - Synthese 63 (1):55 - 74.
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  • Objects of Choice.Wolfgang Schwarz - 2021 - Mind 111.
    Rational agents are supposed to maximize expected utility. But what are the options from which they choose? I outline some constraints on an adequate representation of an agent’s options. The options should, for example, contain no information of which the agent is unsure. But they should be sufficiently rich to distinguish all available acts from one another. These demands often come into conflict, so that there seems to be no adequate representation of the options at all. After reviewing existing proposals (...)
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  • Biased Coins: A model for higher-order probabilities.Jeanne Peijnenburg & David Atkinson - 2014 - In Maria Carla Galavotti, Elisabeth Nemeth & Friedrich Stadler (eds.), European Philosophy of Science: Philosophy of Science in Europe and the Vienna Heritage. Cham: Springer. pp. 241-248.
    Is it coherent to speak of the probability of a probability, and the probability of a probability of a probability, and so on? We show that it is, in the sense that a regress of higher-order probabilities can lead to convergent sequences that determine all these probabilities. By constructing an implementable model which is based on coin-making machines, we demonstrate the consistency of our regress.
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  • An Endless Hierarchy of Probabilities.Jeanne Peijnenburg & David Atkinson - 2012 - American Philosophical Quarterly 49 (3):267-276.
    Suppose q is some proposition, and let P(q) = v0 (1) be the proposition that the probability of q is v0.1 How can one know that (1) is true? One cannot know it for sure, for all that may be asserted is a further probabilistic statement like P(P(q) = v0) = v1, (2) which states that the probability that (1) is true is v1. But the claim (2) is also subject to some further statement of an even higher probability: P(P(P(q) (...)
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