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  1. The Best Laid Schemes of Mice and Me.Randall G. McCutcheon - manuscript
    Adam Elga has argued that holders of imprecise credences fall prey to missed arbitrages, so that rational credences should be sharp. A decision rule proposed by Rohan Sud, Forward Looking, enables imprecise Bayesians to sidestep missed arbitrages and other ``bad books'' in isolated fixed-evidence binary betting sequences such as those of Elga. We show that Forward Looking imprecise Bayesians are committed to a bad book of bets when faced with a particular 3-bet variable-evidence binary betting sequence.
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  2. If We Can’T Tell What Theism Predicts, We Can’T Tell Whether God Exists: Skeptical Theism and Bayesian Arguments From Evil.Nevin Climenhaga - forthcoming - Oxford Studies in Philosophy of Religion.
    According to a simple Bayesian argument from evil, the evil we observe is less likely given theism than given atheism, and therefore lowers the probability of theism. I consider the most common skeptical theist response to this argument, according to which our cognitive limitations make the probability of evil given theism inscrutable. I argue that if skeptical theists are right about this, then the probability of theism given evil is itself largely inscrutable, and that if this is so, we ought (...)
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  3. Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - forthcoming - Mind:fzab031.
    We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural way (...)
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  4. Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - forthcoming - Mind.
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  5. Evidentialism, Inertia, and Imprecise Probability.William Peden - forthcoming - The British Journal for the Philosophy of Science:1-23.
    Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state of ambivalence towards hypotheses. Additionally, (...)
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  6. Distention for Sets of Probabilities.Rush T. Stewart & Michael Nielsen - forthcoming - Philosophy of Science:1-16.
    A prominent pillar of Bayesian philosophy is that, relative to just a few constraints, priors “wash out” in the limit. Bayesians often appeal to such asymptotic results as a defense against charges of excessive subjectivity. But, as Seidenfeld and coauthors observe, what happens in the short run is often of greater interest than what happens in the limit. They use this point as one motivation for investigating the counterintuitive short run phenomenon of dilation since, it is alleged, “dilation contrasts with (...)
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  7. Policy Evaluation Under Severe Uncertainty: A Cautious, Egalitarian Approach.Alex Voorhoeve - forthcoming - In Conrad Heilmann & Julian Reiss (eds.), Routledge Handbook of Philosophy of Economics.
    In some severely uncertain situations, exemplified by climate change and novel pandemics, policymakers lack a reasoned basis for assigning probabilities to the possible outcomes of the policies they must choose between. I outline and defend an uncertainty averse, egalitarian approach to policy evaluation in these contexts. The upshot is a theory of distributive justice which offers especially strong reasons to guard against individual and collective misfortune.
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  8. Less is More for Bayesians, Too.Gregory Wheeler - forthcoming - In Routledge Handbook on Bounded Rationality.
  9. Global Constraints on Imprecise Credences: Solving Reflection Violations, Belief Inertia, and Other Puzzles.Sarah Moss - 2022 - Wiley: Philosophy and Phenomenological Research 103 (3).
    Philosophy and Phenomenological Research, Volume 103, Issue 3, Page 620-638, November 2021.
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  10. Logics of Imprecise Comparative Probability.Yifeng Ding, Wesley H. Holliday & Thomas F. Icard - 2021 - International Journal of Approximate Reasoning 132:154-180.
    This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures.
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  11. Consequences of Comparability.Cian Dorr, Jacob M. Nebel & Jake Zuehl - 2021 - Philosophical Perspectives 35 (1):70-98.
    We defend three controversial claims about preference, credence, and choice. First, all agents (not just rational ones) have complete preferences. Second, all agents (again, not just rational ones) have real-valued credences in every proposition in which they are confident to any degree. Third, there is almost always some unique thing we ought to do, want, or believe.
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  12. Why Should We Try to Be Sustainable? Expected Consequences and the Ethics of Making an Indeterminate Difference.Howard Nye - 2021 - In Chelsea Miya, Oliver Rossier & Geoffrey Rockwell (eds.), Right Research: Modelling Sustainable Research Practices in the Anthropocene. Open Book Publishers. pp. 3-35.
    Why should we refrain from doing things that, taken collectively, are environmentally destructive, if our individual acts seem almost certain to make no difference? According to the expected consequences approach, we should refrain from doing these things because our individual acts have small risks of causing great harm, which outweigh the expected benefits of performing them. Several authors have argued convincingly that this provides a plausible account of our moral reasons to do things like vote for policies that will reduce (...)
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  13. Reliabilism and Imprecise Credences.Weng Hong Tang - 2021 - Philosophical Studies 178 (5):1463-1480.
    What is it for an imprecise credence to be justified? It might be thought that this is not a particularly urgent question for friends of imprecise credences to answer. For one might think that its answer just depends on how a well-trodden issue in epistemology plays out—namely, that of which theory of doxastic justification, be it reliabilism, evidentialism, or some other theory, is correct. I’ll argue, however, that it’s difficult for reliabilists to accommodate imprecise credences, at least if we understand (...)
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  14. Moving Beyond Sets of Probabilities.Gregory Wheeler - 2021 - Statistical Science 36 (2):201--204.
    The theory of lower previsions is designed around the principles of coherence and sure-loss avoidance, thus steers clear of all the updating anomalies highlighted in Gong and Meng's "Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox" except dilation. In fact, the traditional problem with the theory of imprecise probability is that coherent inference is too complicated rather than unsettling. Progress has been made simplifying coherent inference by demoting sets of probabilities from fundamental building blocks to secondary representations (...)
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  15. Accuracy and Credal Imprecision.Dominik Berger & Nilanjan Das - 2020 - Noûs 54 (3):666-703.
    Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove some (...)
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  16. Limitation of Analogy in the Sleeping Beauty Debate: The Case of Singer’s Argument.Namjoong Kim - 2020 - Synthese 198 (11):10513-10528.
    Ever since Elga presented his famous puzzle of Sleeping Beauty, philosophers have debated between the Thirder and the Halfer positions. In his recent article, Daniel Singer proposes a new position, according to which Beauty ought to assign [0, 1/2] to the coin’s landing heads. For this argument, he exploits the similarity between Elga’s original puzzle and Bovens’s modified one. According to Singer, Beauty ought to assign the same credence to H in both versions of Sleeping Beauty. Since Beauty ought to (...)
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  17. The Dispositional Account of Credence.Anna Mahtani - 2020 - Philosophical Studies 177 (3):727-745.
    In this paper I offer an alternative - the ‘dispositional account’ - to the standard account of imprecise probabilism. Whereas for the imprecise probabilist, an agent’s credal state is modelled by a set of credence functions, on the dispositional account an agent’s credal state is modelled by a set of sets of credence functions. On the face of it, the dispositional account looks less elegant than the standard account – so why should we be interested? I argue that the dispositional (...)
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  18. Policymaking Under Scientific Uncertainty.Joe Roussos - 2020 - Dissertation, London School of Economics
    Policymakers who seek to make scientifically informed decisions are constantly confronted by scientific uncertainty and expert disagreement. This thesis asks: how can policymakers rationally respond to expert disagreement and scientific uncertainty? This is a work of non-ideal theory, which applies formal philosophical tools developed by ideal theorists to more realistic cases of policymaking under scientific uncertainty. I start with Bayesian approaches to expert testimony and the problem of expert disagreement, arguing that two popular approaches— supra-Bayesianism and the standard model of (...)
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  19. Can Imprecise Probabilities Be Practically Motivated? A Challenge to the Desirability of Ambiguity Aversion.Miriam Schoenfield - 2020 - Philosophers Imprint 20 (30):1-21.
    The usage of imprecise probabilities has been advocated in many domains: A number of philosophers have argued that our belief states should be “imprecise” in response to certain sorts of evidence, and imprecise probabilities have been thought to play an important role in disciplines such as artificial intelligence, climate science, and engineering. In this paper I’m interested in the question of whether the usage of imprecise probabilities can be given a practical motivation (a motivation based on practical rather than epistemic, (...)
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  20. A Counterexample to Three Imprecise Decision Theories.Seamus Bradley - 2019 - Theoria 85 (1):18-30.
    There is currently much discussion about how decision making should proceed when an agent's degrees of belief are imprecise; represented by a set of probability functions. I show that decision rules recently discussed by Sarah Moss, Susanna Rinard and Rohan Sud all suffer from the same defect: they all struggle to rationalize diachronic ambiguity aversion. Since ambiguity aversion is among the motivations for imprecise credence, this suggests that the search for an adequate imprecise decision rule is not yet over.
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  21. Imprecise Probabilities.Anna Mahtani - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 107-130.
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  22. Counterexamples to Some Characterizations of Dilation.Michael Nielsen & Rush T. Stewart - 2019 - Erkenntnis 86 (5):1107-1118.
    Pedersen and Wheeler (2014) and Pedersen and Wheeler (2015) offer a wide-ranging and in-depth exploration of the phenomenon of dilation. We find that these studies raise many interesting and important points. However, purportedly general characterizations of dilation are reported in them that, unfortunately, admit counterexamples. The purpose of this note is to show in some detail that these characterization results are false.
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  23. Dilation and Asymmetric Relevance.Arthur Paul Pedersen & Gregory Wheeler - 2019 - Proceedings in Machine Learning Research, Vol. 103.
    A characterization result of dilation in terms of positive and negative association admits an extremal counterexample, which we present together with a minor repair of the result. Dilation may be asymmetric whereas covariation itself is symmetric. Dilation is still characterized in terms of positive and negative covariation, however, once the event to be dilated has been specified.
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  24. Problems of Precision in Fuzzy Theories of Vagueness and Bayesian Epistemology.Nicholas J. J. Smith - 2019 - In Richard Dietz (ed.), Vagueness and Rationality in Language Use and Cognition. Springer Verlag. pp. 31-48.
    A common objection to theories of vagueness based on fuzzy logics centres on the idea that assigning a single numerical degree of truth -- a real number between 0 and 1 -- to each vague statement is excessively precise. A common objection to Bayesian epistemology centres on the idea that assigning a single numerical degree of belief -- a real number between 0 and 1 -- to each proposition is excessively precise. In this paper I explore possible parallels between these (...)
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  25. Resolving Peer Disagreements Through Imprecise Probabilities.Lee Elkin & Gregory Wheeler - 2018 - Noûs 52 (2):260-278.
    Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...)
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  26. Another Approach to Consensus and Maximally Informed Opinions with Increasing Evidence.Rush T. Stewart & Michael Nielsen - 2018 - Philosophy of Science (2):236-254.
    Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...)
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  27. Probabilistic Opinion Pooling with Imprecise Probabilities.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Journal of Philosophical Logic 47 (1):17-45.
    The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...)
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  28. Bayesian Variations: Essays on the Structure, Object, and Dynamics of Credence.Aron Vallinder - 2018 - Dissertation, London School of Economics
    According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...)
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  29. Imprecise Bayesianism and Global Belief Inertia.Aron Vallinder - 2018 - British Journal for the Philosophy of Science 69 (4):1205-1230.
    Traditional Bayesianism requires that an agent’s degrees of belief be represented by a real-valued, probabilistic credence function. However, in many cases it seems that our evidence is not rich enough to warrant such precision. In light of this, some have proposed that we instead represent an agent’s degrees of belief as a set of credence functions. This way, we can respect the evidence by requiring that the set, often called the agent’s credal state, includes all credence functions that are in (...)
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  30. Nonclassical Probability and Convex Hulls.Seamus Bradley - 2017 - Erkenntnis 82 (1):87-101.
    It is well known that the convex hull of the classical truth value functions contains all and only the probability functions. Work by Paris and Williams has shown that this also holds for various kinds of nonclassical logics too. This note summarises the formal details of this topic and extends the results slightly.
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  31. Causation, Probability, and the Continuity Bind.Anthony F. Peressini - 2017 - British Journal for the Philosophy of Science 69 (3):881-909.
    Analyses of singular causation often make use of the idea that a cause increases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analysed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way, it becomes clearer that the ‘behaviour’ of probability functions in (...)
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  32. 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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  33. 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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  34. Direct Inference From Imprecise Frequencies.Paul D. Thorn - 2017 - In Michela Massimi, Jan-Willem Romeijn & Gerhard Schurz (eds.), EPSA15 Selected Papers: The 5th conference of the European Philosophy of Science Association in Düsseldorf. Springer. pp. 347-358.
    It is well known that there are, at least, two sorts of cases where one should not prefer a direct inference based on a narrower reference class, in particular: cases where the narrower reference class is gerrymandered, and cases where one lacks an evidential basis for forming a precise-valued frequency judgment for the narrower reference class. I here propose (1) that the preceding exceptions exhaust the circumstances where one should not prefer direct inference based on a narrower reference class, and (...)
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  35. A Note on Cancellation Axioms for Comparative Probability.Matthew Harrison-Trainor, Wesley H. Holliday & Thomas F. Icard - 2016 - Theory and Decision 80 (1):159-166.
    We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Rios Insua and Alon and Lehrer is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott, relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature.
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  36. Imprecise Probabilities and Unstable Betting Behaviour.Anna Mahtani - 2016 - Noûs 52 (1):69-87.
    Many have argued that a rational agent's attitude towards a proposition may be better represented by a probability range than by a single number. I show that in such cases an agent will have unstable betting behaviour, and so will behave in an unpredictable way. I use this point to argue against a range of responses to the ‘two bets’ argument for sharp probabilities.
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  37. Scoring Imprecise Credences: A Mildly Immodest Proposal.Conor Mayo-Wilson & Gregory Wheeler - 2016 - Philosophy and Phenomenological Research 92 (1):55-78.
    Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that (...)
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  38. Imprecise Probability and Chance.Anthony F. Peressini - 2016 - Erkenntnis 81 (3):561-586.
    Understanding probabilities as something other than point values has often been motivated by the need to find more realistic models for degree of belief, and in particular the idea that degree of belief should have an objective basis in “statistical knowledge of the world.” I offer here another motivation growing out of efforts to understand how chance evolves as a function of time. If the world is “chancy” in that there are non-trivial, objective, physical probabilities at the macro-level, then the (...)
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  39. Qualitative Probabilistic Inference Under Varied Entropy Levels.Paul D. Thorn & Gerhard Schurz - 2016 - Journal of Applied Logic 19 (2):87-101.
    In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended to yield (...)
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  40. Ambiguity Attitudes, Framing and Consistency.Alex Voorhoeve, Ken G. Binmore, Arnaldur Stefansson & Lisa Stewart - 2016 - Theory and Decision 81 (3):313-337.
    We use probability-matching variations on Ellsberg’s single-urn experiment to assess three questions: (1) How sensitive are ambiguity attitudes to changes from a gain to a loss frame? (2) How sensitive are ambiguity attitudes to making ambiguity easier to recognize? (3) What is the relation between subjects’ consistency of choice and the ambiguity attitudes their choices display? Contrary to most other studies, we find that a switch from a gain to a loss frame does not lead to a switch from ambiguity (...)
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  41. Probabilistic Reasoning in Cosmology.Yann Benétreau-Dupin - 2015 - Dissertation, The University of Western Ontario
    Cosmology raises novel philosophical questions regarding the use of probabilities in inference. This work aims at identifying and assessing lines of arguments and problematic principles in probabilistic reasoning in cosmology. -/- The first, second, and third papers deal with the intersection of two distinct problems: accounting for selection effects, and representing ignorance or indifference in probabilistic inferences. These two problems meet in the cosmology literature when anthropic considerations are used to predict cosmological parameters by conditionalizing the distribution of, e.g., the (...)
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  42. 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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  43. Blurring Out Cosmic Puzzles.Yann Benétreau-Dupin - 2015 - Philosophy of Science 82 (5):879–891.
    The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of (...)
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  44. Dilation, Disintegrations, and Delayed Decisions.Arthur Paul Pedersen & Gregory Wheeler - 2015 - In Thomas Augistin, Serena Dora, Enrique Miranda & Erik Quaeghebeur (eds.), Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015). Aracne Editrice. pp. 227–236.
    Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although (...)
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  45. A Decision Theory for Imprecise Probabilities.Susanna Rinard - 2015 - Philosophers' Imprint 15.
    Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to vagueness (...)
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  46. Evidential Incomparability and the Principle of Indifference.Martin Smith - 2015 - Erkenntnis 80 (3):605-616.
    The _Principle of Indifference_ was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called _problem of multiple of partitions_. In ‘Evidential symmetry and mushy credence’ Roger White suggests that we have been too quick to jettison this principle and argues that the problem of multiple partitions rests on a mistake. In this paper I will criticise White’s attempt to revive POI. In so doing, I will argue that what underlies (...)
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  47. Decisions Without Sharp Probabilities.Paul Weirich - 2015 - Philosophia Scientiae 19:213-225.
    Adam Elga [Elga 2010] argues that no principle of rationality leads from unsharp probabilities to decisions. He concludes that a perfectly rational agent does not have unsharp probabilities. This paper defends unsharp probabilities. It shows how unsharp probabilities may ground rational decisions.
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  48. Should Subjective Probabilities Be Sharp?Seamus Bradley & Katie Siobhan Steele - 2014 - Episteme 11 (3):277-289.
    There has been much recent interest in imprecise probabilities, models of belief that allow unsharp or fuzzy credence. There have also been some influential criticisms of this position. Here we argue, chiefly against Elga, that subjective probabilities need not be sharp. The key question is whether the imprecise probabilist can make reasonable sequences of decisions. We argue that she can. We outline Elga's argument and clarify the assumptions he makes and the principles of rationality he is implicitly committed to. We (...)
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  49. Subjective Probabilities Need Not Be Sharp.Jake Chandler - 2014 - Erkenntnis 79 (6):1273-1286.
    It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be borne out (...)
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  50. Demystifying Dilation.Arthur Paul Pedersen & Gregory Wheeler - 2014 - Erkenntnis 79 (6):1305-1342.
    Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...)
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