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On Indeterminate Probabilities

Journal of Philosophy 71 (13):233--261 (1978)

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  1. Perspectival Plurality, Relativism, and Multiple Indexing.Dan Zeman - 2018 - In Rob Truswell, Chris Cummins, Caroline Heycock, Brian Rabern & Hannah Rohde (eds.), Proceedings of Sinn und Bedeutung 21. Semantics Archives. pp. 1353-1370.
    In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...)
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  • Impossible worlds and partial belief.Edward Elliott - 2019 - Synthese 196 (8):3433-3458.
    One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most of the propositions (...)
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  • The Accuracy and Rationality of Imprecise Credences.Miriam Schoenfield - 2017 - Noûs 51 (4):667-685.
    It has been claimed that, in response to certain kinds of evidence, agents ought to adopt imprecise credences: doxastic states that are represented by sets of credence functions rather than single ones. In this paper I argue that, given some plausible constraints on accuracy measures, accuracy-centered epistemologists must reject the requirement to adopt imprecise credences. I then show that even the claim that imprecise credences are permitted is problematic for accuracy-centered epistemology. It follows that if imprecise credal states are permitted (...)
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  • On the Rationality of Decisions with Unreliable Probabilities.Birman Fernando - 2009 - Disputatio 3 (26):97-116.
    The standard Bayesian recipe for selecting the rational choice is presented. A familiar example in which the recipe fails to produce any definite result is introduced. It is argued that a generalization of Gärdenfors’ and Sahlin’s theory of unreliable probabilities — which itself does not guarantee a solution to the problem — offers the best available approach. But a number of challenges to this approach are also presented and discussed.
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  • 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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  • Conditional choice with a vacuous second tier.Rush T. Stewart - 2016 - Synthese 193 (1):219-243.
    This paper studies a generalization of rational choice theory. I briefly review the motivations that Helzner gives for his conditional choice construction . Then, I focus on the important class of conditional choice functions with vacuous second tiers. This class is interesting for both formal and philosophical reasons. I argue that this class makes explicit one of conditional choice’s normative motivations in terms of an account of neutrality advocated within a certain tradition in decision theory. The observations recorded—several of which (...)
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  • Uncertainty, Learning, and the “Problem” of Dilation.Seamus Bradley & Katie Siobhan Steele - 2014 - Erkenntnis 79 (6):1287-1303.
    Imprecise probabilism—which holds that rational belief/credence is permissibly represented by a set of probability functions—apparently suffers from a problem known as dilation. We explore whether this problem can be avoided or mitigated by one of the following strategies: (a) modifying the rule by which the credal state is updated, (b) restricting the domain of reasonable credal states to those that preclude dilation.
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  • Epistemic utility arguments for Probabilism.Richard Pettigrew - 2011 - Stanford Encyclopedia.
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  • A Challenge to the Compound Lottery Axiom: A Two-Stage Normative Structure and Comparison to Other Theories.Donald B. Davis - 1994 - Theory and Decision 37 (3):267.
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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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  • The psychology and rationality of decisions from experience.Ralph Hertwig - 2012 - Synthese 187 (1):269-292.
    Most investigations into how people make risky choices have employed a simple drosophila: monetary gambles involving stated outcomes and probabilities. People are asked to make decisions from description . When people decide whether to back up their computer hard drive, cross a busy street, or go out on a date, however, they do not enjoy the convenience of stated outcomes and probabilities. People make such decisions either in the void of ignorance or in the twilight of their own often limited (...)
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  • De Finetti on the Insurance of Risks and Uncertainties.Alberto Feduzi, Jochen Runde & Carlo Zappia - 2012 - British Journal for the Philosophy of Science 63 (2):329-356.
    In the insurance literature, it is often argued that private markets can provide insurance against ‘risks’ but not against ‘uncertainties’ in the sense of Knight ([1921]) or Keynes ([1921]). This claim is at odds with the standard economic model of risk exchange which, in assuming that decision-makers are always guided by point-valued subjective probabilities, predicts that all uncertainties can, in theory, be insured. Supporters of the standard model argue that the insuring of highly idiosyncratic risks by Lloyd's of London proves (...)
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  • Rational Belief and Probability Kinematics.Bas C. Van Fraassen - 1980 - Philosophy of Science 47 (2):165-187.
    A general form is proposed for epistemological theories, the relevant factors being: the family of epistemic judgments, the epistemic state, the epistemic commitment, and the family of possible epistemic inputs. First a simple theory is examined in which the states are probability functions, and the subject of probability kinematics introduced by Richard Jeffrey is explored. Then a second theory is examined in which the state has as constituents a body of information and a recipe that determines the accepted epistemic judgments (...)
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  • Decision theory and cognitive choice.John R. Welch - 2011 - European Journal for Philosophy of Science 1 (2):147-172.
    The focus of this study is cognitive choice: the selection of one cognitive option (a hypothesis, a theory, or an axiom, for instance) rather than another. The study proposes that cognitive choice should be based on the plausibilities of states posited by rival cognitive options and the utilities of these options' information outcomes. The proposal introduces a form of decision theory that is novel because comparative; it permits many choices among cognitive options to be based on merely comparative plausibilities and (...)
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  • Introduction.Horacio Arló-Costa & Jeffrey Helzner - 2010 - Synthese 172 (1):1-6.
    Daniel Ellsberg presented in Ellsberg various examples questioning the thesis that decision making under uncertainty can be reduced to decision making under risk. These examples constitute one of the main challenges to the received view on the foundations of decision theory offered by Leonard Savage in Savage. Craig Fox and Amos Tversky have, nevertheless, offered an indirect defense of Savage. They provided in Fox and Tversky an explanation of Ellsberg’s two-color problem in terms of a psychological effect: ambiguity aversion. The (...)
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  • Acting on belief functions.Nicholas J. J. Smith - 2023 - Theory and Decision 95 (4):575-621.
    The degrees of belief of rational agents should be guided by the evidence available to them. This paper takes as a starting point the view—argued elsewhere—that the formal model best able to capture this idea is one that represents degrees of belief using Dempster–Shafer belief functions. However degrees of belief should not only respect evidence: they also guide decision and action. Whatever formal model of degrees of belief we adopt, we need a decision theory that works with it: that takes (...)
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  • Philosophical foundations for worst-case arguments.Lara Buchak - 2023 - Politics, Philosophy and Economics 22 (3):215-242.
    Certain ethical views hold that we should pay more attention, even exclusive attention, to the worst-case scenario. Prominent examples include Rawls's Difference Principle and the Precautionary Principle. These views can be anchored in formal principles of decision theory, in two different ways. On the one hand, they can rely on ambiguity-aversion: the idea that we cannot assign sharp probabilities to various scenarios, and that if we cannot assign sharp probabilities, we should decide pessimistically, as if the probabilities are unfavorable. On (...)
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  • Suspending belief in credal accounts.Andrew del Rio - 2024 - Noûs 58 (1):3-25.
    Traditionally epistemologists have taken doxastic states to come in three varieties—belief, disbelief, and suspension. Recently many epistemologists have taken our doxastic condition to be usefully represented by credences—quantified degrees of belief. Moreover, some have thought that this new credal picture is sufficient to account for everything we want to explain with the old traditional picture. Therefore, belief, disbelief, and suspension must map onto the new picture somehow. In this paper I challenge that possibility. Approaching the question from the angle of (...)
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  • Learning by Ignoring the Most Wrong.Seamus Bradley - 2022 - Kriterion – Journal of Philosophy 36 (1):9-31.
    Imprecise probabilities are an increasingly popular way of reasoning about rational credence. However they are subject to an apparent failure to display convincing inductive learning. This paper demonstrates that a small modification to the update rule for IP allows us to overcome this problem, albeit at the cost of satisfying only a weaker concept of coherence.
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  • Global Constraints on Imprecise Credences: Solving Reflection Violations, Belief Inertia, and Other Puzzles.Sarah Moss - 2020 - Philosophy and Phenomenological Research 103 (3):620-638.
    Philosophy and Phenomenological Research, Volume 103, Issue 3, Page 620-638, November 2021.
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  • Imprecise probability in epistemology.Elkin Lee - 2017 - Dissertation, Ludwig–Maximilians–Universitat
    There is a growing interest in the foundations as well as the application of imprecise probability in contemporary epistemology. This dissertation is concerned with the application. In particular, the research presented concerns ways in which imprecise probability, i.e. sets of probability measures, may helpfully address certain philosophical problems pertaining to rational belief. The issues I consider are disagreement among epistemic peers, complete ignorance, and inductive reasoning with imprecise priors. For each of these topics, it is assumed that belief can be (...)
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  • Can free evidence be bad? Value of informationfor the imprecise probabilist.Seamus Bradley & Katie Steele - 2016 - Philosophy of Science 83 (1):1-28.
    This paper considers a puzzling conflict between two positions that are each compelling: it is irrational for an agent to pay to avoid `free' evidence before making a decision, and rational agents may have imprecise beliefs and/or desires. Indeed, we show that Good's theorem concerning the invariable choice-worthiness of free evidence does not generalise to the imprecise realm, given the plausible existing decision theories for handling imprecision. A key ingredient in the analysis, and a potential source of controversy, is the (...)
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  • Laplace's demon and the adventures of his apprentices.Roman Frigg, Seamus Bradley, Hailiang Du & Leonard A. Smith - 2014 - Philosophy of Science 81 (1):31-59.
    The sensitive dependence on initial conditions (SDIC) associated with nonlinear models imposes limitations on the models’ predictive power. We draw attention to an additional limitation than has been underappreciated, namely, structural model error (SME). A model has SME if the model dynamics differ from the dynamics in the target system. If a nonlinear model has only the slightest SME, then its ability to generate decision-relevant predictions is compromised. Given a perfect model, we can take the effects of SDIC into account (...)
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  • Probabilistic Belief Contraction.Raghav Ramachandran, Arthur Ramer & Abhaya C. Nayak - 2012 - Minds and Machines 22 (4):325-351.
    Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure (...)
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  • Chance without Credence.John T. Roberts - 2013 - British Journal for the Philosophy of Science 64 (1):33-59.
    It is a standard view that the concept of chance is inextricably related to the technical concept of credence . One influential version of this view is that the chance role is specified by (something in the neighborhood of) David Lewis's Principal Principle, which asserts a certain definite relation between chance and credence. If this view is right, then one cannot coherently affirm that there are chance processes in the physical world while rejecting the theoretical framework in which credence is (...)
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  • A defense of imprecise credences in inference and decision making1.James M. Joyce - 2010 - Philosophical Perspectives 24 (1):281-323.
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  • Scotching Dutch Books?Alan Hájek - 2005 - Philosophical Perspectives 19 (1):139-151.
    The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...)
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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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  • Bayesian and Non-Bayesian Evidential Updating.Henry E. Kyburg - 1987 - Artificial Intelligence 31 (3):271--294.
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  • Decision making with imprecise probabilities.Brian Weatherson - 1998
    Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a gamble will be imprecise. This paper looks at the attempts to extend Bayesian decision theory to deal with such cases, and concludes (...)
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  • Unreliable probabilities, risk taking, and decision making.Peter Gärdenfors & Nils-Eric Sahlin - 1982 - Synthese 53 (3):361-386.
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  • Imprecise Credences and Acceptance.Benjamin Lennertz - 2022 - Ergo: An Open Access Journal of Philosophy 9.
    Elga (2010) argues that no plausible decision rule governs action with imprecise credences. I follow Moss (2015a) in claiming that the solution to Elga’s challenge is found in the philosophy of mind, not in devising a special new decision rule. Moss suggests that in decision situations that involve imprecise credences, we must identify with a precise credence, but she says little about identification. By reflecting on the common conception of identification and on what is necessary for Moss’s solution to succeed, (...)
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  • Respecting Evidence: Belief Functions not Imprecise Probabilities.Nicholas J. J. Smith - 2022 - Synthese 200 (475):1-30.
    The received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot make room for the idea that an agent’s degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster–Shafer belief functions and then presents (...)
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  • The Precautionary Principle and Expert Disagreement.Lee Elkin - 2023 - Erkenntnis 88 (6):2717-2726.
    The Precautionary Principle is typically construed as a conservative decision rule aimed at preventing harm. But Martin Peterson (JME 33: 5–10, 2007; The ethics of technology: A geometric analysis of five moral principles, Oxford University Press, Oxford, 2017) has argued that the principle is better understood as an epistemic rule, guiding decision-makers in forming beliefs rather than choosing among possible acts. On the epistemic view, he claims there is a principle concerning expert disagreement underlying precautionary-based reasoning called the ecumenical principle: (...)
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  • How to be imprecise and yet immune to sure loss.Katie Steele - 2020 - Synthese 199 (1-2):427-444.
    Towards the end of Decision Theory with a Human Face, Richard Bradley discusses various ways a rational yet human agent, who, due to lack of evidence, is unable to make some fine-grained credibility judgments, may nonetheless make systematic decisions. One proposal is that such an agent can simply “reach judgments” on the fly, as needed for decision making. In effect, she can adopt a precise probability function to serve as proxy for her imprecise credences at the point of decision, and (...)
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  • Subjective causal networks and indeterminate suppositional credences.Jiji Zhang, Teddy Seidenfeld & Hailin Liu - 2019 - Synthese 198 (Suppl 27):6571-6597.
    This paper has two main parts. In the first part, we motivate a kind of indeterminate, suppositional credences by discussing the prospect for a subjective interpretation of a causal Bayesian network, an important tool for causal reasoning in artificial intelligence. A CBN consists of a causal graph and a collection of interventional probabilities. The subjective interpretation in question would take the causal graph in a CBN to represent the causal structure that is believed by an agent, and interventional probabilities in (...)
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  • Bayesian Cognitive Science, Monopoly, and Neglected Frameworks.Matteo Colombo & Stephan Hartmann - 2015 - British Journal for the Philosophy of Science 68 (2):451–484.
    A widely shared view in the cognitive sciences is that discovering and assessing explanations of cognitive phenomena whose production involves uncertainty should be done in a Bayesian framework. One assumption supporting this modelling choice is that Bayes provides the best approach for representing uncertainty. However, it is unclear that Bayes possesses special epistemic virtues over alternative modelling frameworks, since a systematic comparison has yet to be attempted. Currently, it is then premature to assert that cognitive phenomena involving uncertainty are best (...)
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  • Smart Representations: Rationality and Evolution in a Richer Environment.Paolo Galeazzi & Michael Franke - 2017 - Philosophy of Science 84 (3):544-573.
    Standard applications of evolutionary game theory look at a single game and focus on the evolution of behavior for that game alone. Instead, this article uses tools from evolutionary game theory to study the competition between choice mechanisms in a rich and variable multigame environment. A choice mechanism is a way of subjectively representing a decision situation, paired with a method for choosing an act based on this subjective representation. We demonstrate the usefulness of this approach by a case study (...)
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  • Nonprobabilistic chance?Seamus Bradley - unknown
    "Chance" crops up all over philosophy, and in many other areas. It is often assumed -- without argument -- that chances are probabilities. I explore the extent to which this assumption is really sanctioned by what we understand by the concept of chance.
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  • Making climate decisions.Richard Bradley & Katie Steele - 2015 - Philosophy Compass 10 (11):799-810.
    Many fine-grained decisions concerning climate change involve significant, even severe, uncertainty. Here, we focus on modelling the decisions of single agents, whether individual persons or groups perceived as corporate entities. We offer a taxonomy of the sources and kinds of uncertainty that arise in framing these decision problems, as well as strategies for making a choice in spite of uncertainty. The aim is to facilitate a more transparent and structured treatment of uncertainty in climate decision making.
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  • The Bayesian Who Knew Too Much.Yann Benétreau-Dupin - 2015 - Synthese 192 (5):1527-1542.
    In several papers, John Norton has argued that Bayesianism cannot handle ignorance adequately due to its inability to distinguish between neutral and disconfirming evidence. He argued that this inability sows confusion in, e.g., anthropic reasoning in cosmology or the Doomsday argument, by allowing one to draw unwarranted conclusions from a lack of knowledge. Norton has suggested criteria for a candidate for representation of neutral support. Imprecise credences (families of credal probability functions) constitute a Bayesian-friendly framework that allows us to avoid (...)
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  • 'Along an imperfectly-lighted path': practical rationality and normative uncertainty.Andrew Sepielli - unknown
    Nobody's going to object to the advice "Do the right thing", but that doesn't mean everyone's always going to follow it. Sometimes this is because of our volitional limitations; we cannot always bring ourselves to make the sacrifices that right action requires. But sometimes this is because of our cognitive limitations; we cannot always be sure of what is right. Sometimes we can't be sure of what's right because we don't know the non-normative facts. But sometimes, even if we were (...)
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  • Sobre la justificación de las proposiciones ante los desafíos escépticos.Federico Matías Pailós - 2014 - Logos. Anales Del Seminario de Metafísica [Universidad Complutense de Madrid, España] 47:249-258.
    Los desafíos escépticos cuestionan la justificación de las proposiciones que aceptamos. Pero es posible justificar en términos probabilísticos cada una de las proposiciones empíricas aceptadas. Para eso, su probabilidad condicional al resto de las proposiciones aceptadas, deberá ser mayor que su probabilidad absoluta. Esta justificación es circular, pero virtuosa. Sin embargo, carece de eficacia dialéctica frente al escéptico.
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  • Obligation and permission when there is a second best and when there is a second worst.Isaac Levi - 2006 - Análisis Filosófico 26 (2):356-372.
    A comparison is made between the criterion of choice of E-admissibility I proposed in Levi, 1974 and elaborated in Levi, 1980 and 1986, and the ideas about norms elaborated by Alchourrón and Bulygin with an emphasis on the fact that choice cannot always be evaluated in terms of binary comparisons as the distinction between second worst and not second worst illustrates. Se establece una comparación entre el criterio de E-admisibilidad propuesto en Levi,1974 y elaborado en Levi,1980 y 1986 y las (...)
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  • Logic of Change, Change of Logic.Hans van Ditmarsch, Brian Hill & Ondrej Majer - 2009 - Synthese 171 (2):227 - 234.
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  • Rationality and uncertainty.Amartya Sen - 1985 - Theory and Decision 18 (2):109-127.
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  • Newcomb’s Many Problems.Isaac Levi - 1975 - Theory and Decision 6 (2):161-175.
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  • Why Rational Agents Should Not Be Liberal Maximizers.Isaac Levi - 2008 - Canadian Journal of Philosophy 38 (S1):1-17.
    Hans Herzberger's 1973 essay 'Ordinal Preference and Rational Choice' is a classic milestone in the erosion of the idea that rational agents are maximizers of utility. By the time Herzberger wrote, many authors had replaced this claim with the thesis that rational agents are maximizers of preference. That is to say, it was assumed that at the moment of choice a rational agent has a weak ordering representing his or her preferences among the options available to the agent for choice (...)
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  • Axiomatic justifications of the utility principle: A formal investigation.Per-Erik Malmnäs - 1994 - Synthese 99 (2):233 - 249.
    It is argued that existing axiomatic theories of utility do not provide the utility principle or the principle of maximising expected utility with a formal justification. It is also argued that these theories only put mild constraints on a decision-maker in a decision-context. Finally, it is argued that the prospects are not particularly bright for finding formal non-circular arguments for the utility principle that do not rely on the law of large numbers.
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  • Subjunctives, dispositions and chances.Isaac Levi - 1977 - Synthese 34 (4):423 - 455.
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