## Results for 'Probabilistic opinion pooling'

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1. Probabilistic Opinion Pooling.Franz Dietrich & Christian List - 2016 - In Alan Hajek & Christopher Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford: Oxford University Press.
Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of (...)

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2. Probabilistic Opinion Pooling Generalized. Part One: General Agendas.Franz Dietrich & Christian List - 2017 - Social Choice and Welfare 48 (4):747–786.
How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability (...)

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3. Probabilistic Opinion Pooling Generalised. Part Two: The Premise-Based Approach.Franz Dietrich & Christian List - 2017 - Social Choice and Welfare 48 (4):787–814.
How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...)

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4. There are many reasons we might want to take the opinions of various individuals and aggregate them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of aggregation functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, (...)

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5. 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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6. The Aggregation of Propositional Attitudes: Towards a General Theory.Franz Dietrich & Christian List - 2010 - Oxford Studies in Epistemology 3.
How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...)

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7. A Theory of Bayesian Groups.Franz Dietrich - 2019 - Noûs 53 (3):708-736.
A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all (...)

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8. Aggregating Causal Judgments.Richard Bradley, Franz Dietrich & Christian List - 2014 - Philosophy of Science 81 (4):491-515.
Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of (...)

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9. Introduction to the Special Issue “Beliefs in Groups” of Theory and Decision.Franz Dietrich & Wlodek Rabinowicz - 2018 - Theory and Decision 85 (1):1-4.
This symposium in the overlap of philosophy and decision theory is described well by its title “Beliefs in Groups”. Each word in the title matters, with one intended ambiguity. The symposium is about beliefs rather than other attitudes such as preferences; these beliefs take the form of probabilities in the first three contributions, binary yes/no beliefs (‘judgments’) in the fourth contribution, and qualitative probabilities (‘probability grades’) in the fifth contribution. The beliefs occur in groups, which is ambiguous between beliefs of (...)

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10. Support for Geometric Pooling.Jean Baccelli & Rush T. Stewart - forthcoming - Review of Symbolic Logic:1-40.
Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be non-trivially Bayes-compatible. We show by contrast that geometric pooling can be non-trivially Bayes-compatible. Indeed, we show that, (...)

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11. Independent Opinions? On the Causal Foundations of Belief Formation and Jury Theorems.Franz Dietrich & Kai Spiekermann - 2013 - Mind 122 (487):655-685.
Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally (...)

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12. Regret Averse Opinion Aggregation.Lee Elkin - forthcoming - Ergo: An Open Access Journal of Philosophy.
It is often suggested that when opinions differ among individuals in a group, the opinions should be aggregated to form a compromise. This paper compares two approaches to aggregating opinions, linear pooling and what I call opinion agglomeration. In evaluating both strategies, I propose a pragmatic criterion, No Regrets, entailing that an aggregation strategy should prevent groups from buying and selling bets on events at prices regretted by their members. I show that only opinion agglomeration is able (...)

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13. Arguments From Expert Opinion – An Epistemological Approach.Christoph Lumer - 2020 - In Catarina Dutilh Novaes, Henrike Jansen, Jan Albert Van Laar & Bart Verheij (eds.), Reason to Dissent. Proceedings of the 3rd European Conference on Argumentation. College Publications. pp. 403-422.
In times of populist mistrust towards experts, it is important and the aim of the paper to ascertain the rationality of arguments from expert opinion and to reconstruct their rational foundations as well as to determine their limits. The foundational approach chosen is probabilistic. However, there are at least three correct probabilistic reconstructions of such argumentations: statistical inferences, Bayesian updating, and interpretive arguments. To solve this competition problem, the paper proposes a recourse to the arguments' justification strengths (...)

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14. On Accuracy and Coherence with Infinite Opinion Sets.Mikayla Kelley - forthcoming - Philosophy of Science.
There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, I establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, I establish the necessary results to extend the classic accuracy (...)

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15. Abstract: Four main forms of Doomsday Argument (DA) exist—Gott’s DA, Carter’s DA, Grace’s DA and Universal DA. All four forms use different probabilistic logic to predict that the end of the human civilization will happen unexpectedly soon based on our early location in human history. There are hundreds of publications about the validity of the Doomsday argument. Most of the attempts to disprove the Doomsday Argument have some weak points. As a result, we are uncertain about the validity of (...)

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16. On the Accuracy of Group Credences.Richard Pettigrew - 2020 - Oxford Studies in Epistemology 6.
to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6 We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? (...)

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17. Aggregation for Potentially Infinite Populations Without Continuity or Completeness.David McCarthy, Kalle M. Mikkola & J. Teruji Thomas - 2019 - arXiv:1911.00872 [Econ.TH].
We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to (...)

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18. Bayesian Group Belief.Franz Dietrich - 2010 - Social Choice and Welfare 35 (4):595-626.
If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with different priors and different information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all information spread over the individuals without (...)

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19. Fully Bayesian Aggregation.Franz Dietrich - forthcoming - Journal of Economic Theory.
Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static (...)

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20. Vorwort und Einführung.Sara Di Giulio & Alberto Frigo - 2020 - In Sara Di Giulio & Alberto Frigo (eds.), Kasuistik und Theorie des Gewissens. Von Pascal bis Kant. Berlino, Germania: pp. vii–viii; 1–15.
Kant scholars have rarely addressed the centuries-old tradition of casuistry and the concept of conscience in Kant’s writings. This book offers a detailed exploration of the period from Pascal’s Provincial Letters to Kant’s critique of probabilism and discusses his proposal of a (new) casuistry as part of an moral education. *** -/- Die Debatte um Kasuistik und Probabilismus zählt zu den wichtigsten Themen der Moraltheologie und Moralphilosophie der frühen Neuzeit. In der enormen Verbreitung der Literatur über die Gewissensfälle (casus conscientiae) (...)
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21. God, Fine-Tuning, and the Problem of Old Evidence.Bradley Monton - 2006 - British Journal for the Philosophy of Science 57 (2):405-424.
The fundamental constants that are involved in the laws of physics which describe our universe are finely-tuned for life, in the sense that if some of the constants had slightly different values life could not exist. Some people hold that this provides evidence for the existence of God. I will present a probabilistic version of this fine-tuning argument which is stronger than all other versions in the literature. Nevertheless, I will show that one can have reasonable opinions such that (...)

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22. Higher-Order Uncertainty.Kevin Dorst - forthcoming - In Mattias Skipper & Asbjørn Steglich Petersen (eds.), Higher-Order Evidence: New Essays.
You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of disagreement. Third, the answer is (...)

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23. Four Approaches to Supposition.Benjamin Eva, Ted Shear & Branden Fitelson - forthcoming - Ergo: An Open Access Journal of Philosophy.
Suppositions can be introduced in either the indicative or subjunctive mood. The introduction of either type of supposition initiates judgments that may be either qualitative, binary judgments about whether a given proposition is acceptable or quantitative, numerical ones about how acceptable it is. As such, accounts of qualitative/quantitative judgment under indicative/subjunctive supposition have been developed in the literature. We explore these four different types of theories by systematically explicating the relationships canonical representatives of each. Our representative qualitative accounts of indicative (...)

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24. A wide variety of ontologies relevant to the biological and medical domains are available through the OBO Foundry portal, and their number is growing rapidly. Integration of these ontologies, while requiring considerable effort, is extremely desirable. However, heterogeneities in format and style pose serious obstacles to such integration. In particular, inconsistencies in naming conventions can impair the readability and navigability of ontology class hierarchies, and hinder their alignment and integration. While other sources of diversity are tremendously complex and challenging, agreeing (...)

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25. Be Modest: You're Living on the Edge.Kevin Dorst - forthcoming - Analysis.
Many have claimed that whenever an investigation might provide evidence for a claim, it might also provide evidence against it. Similarly, many have claimed that your credence should never be on the edge of the range of credences that you think might be rational. Surprisingly, both of these principles imply that you cannot rationally be modest: you cannot be uncertain what the rational opinions are.

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26. The policy makers or lawyers may face the need of legal research for reasons. The congressmen may plan to make new laws to address the challenges of their constituent or to the interest of nation. The lawyers may need to serve their clients who like to know the legal issues involved, the strategies to deal with their loss and recovery, and prospect for winning the case if the dispute has gotten worse. The lawyers may practice in a solo business or (...)

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27. Логические Посылки Научного Метода Галена.Andrey Shcheglov - 2018 - Schole 12 (1):147-166.
The article is devoted to the analysis of the evident scientific method of Galen, which establishes the necessity of correct diagnosis of diseases, determination of true symptoms and causes of diseases, which results in the choice of the exact method of treatment. The article focuses on how Galen seeks to achieve reliable knowledge based on an undeniable logical necessity. Logical reliability is contrasted with “dialectical”, that is, probabilistic judgments, often leading to the opposite of what was originally asserted in (...)

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28. Are Probabilism and Special Relativity Incompatible?Nicholas Maxwell - 1985 - Philosophy of Science 52 (1):23-43.
In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

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29. Probabilistic Semantics for Epistemic Modals: Normality Assumptions, Conditional Epistemic Spaces, and the Strength of `Must' and `Might'.Guillermo Del Pinal - forthcoming - Linguistics and Philosophy:1-42.
The epistemic modal auxiliaries 'must' and 'might' are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, 'must' is a maximally strong epistemic operator and 'might' is a bare possibility one. A competing account---popular amongst proponents of a probabilisitic turn---says that, given a body of evidence, 'must p' entails that Pr(p) (...)

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30. Context Probabilism.Seth Yalcin - 2012 - In M. Aloni, Maria Aloni, Vadim Kimmelmann, Floris Roelofson, Galit W. Sassoon, Katrin Schulz & Matthijs Westera (eds.), Logic, Language, and Meaning: 18th Amsterdam Colloquium, Amsterdam, The Netherlands, December 19-21, 2011, Revised Selected Papers. Berlin: Springer. pp. 12-21.
We investigate a basic probabilistic dynamic semantics for a fragment containing conditionals, probability operators, modals, and attitude verbs, with the aim of shedding light on the prospects for adding probabilistic structure to models of the conversational common ground.
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31. Probabilistic Arguments in the Epistemological Approach to Argumentation.Christoph Lumer - 2011 - In Frans H. Van Eemeren, Bart Garssen, David Godden & Gordon Mitchell (eds.), Proceedings of the 7th Conference of the International Society for the Study of Argumentation. Amsterdam, Netherlands: Rozenberg; Sic Sat. pp. 1141-1154.
The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With (...)

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32. Are Probabilism and Special Relativity Compatible?Nicholas Maxwell - 1988 - Philosophy of Science 55 (4):640-645.
Are special relativity and probabilism compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal "now" (and is thus incompatible with special relativity), or amounts to a many world universe (which I have discussed, and rejected as too ad hoc to be taken seriously), or fails to have any one definite overall Minkowskian-type space-time structure (and thus differs drastically from special relativity as ordinarily understood). Probabilism and (...)

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33. Probabilistic Causation and the Explanatory Role of Natural Selection.Pablo Razeto-Barry & Ramiro Frick - 2011 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 42 (3):344-355.
The explanatory role of natural selection is one of the long-term debates in evolutionary biology. Nevertheless, the consensus has been slippery because conceptual confusions and the absence of a unified, formal causal model that integrates different explanatory scopes of natural selection. In this study we attempt to examine two questions: (i) What can the theory of natural selection explain? and (ii) Is there a causal or explanatory model that integrates all natural selection explananda? For the first question, we argue that (...)

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34. Pooled Beneficence.Garrett Cullity - 2000 - In Michael Almeida (ed.), Imperceptible Harms and Benefits. Dordrecht: Kluwer. pp. 9-42.
There can be situations in which, if I contribute to a pool of resources for helping a large number of people, the difference that my contribution makes to any of the people helped from the pool will be imperceptible at best, and maybe even non-existent. And this can be the case where it is also true that giving the same amount directly to one of the intended beneficiaries of the pool would have made a very large difference to her. Can (...)

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35. A Probabilistic Analysis of Argument Cogency.David Godden & Frank Zenker - 2018 - Synthese 195 (4):1715-1740.
This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, (...)

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36. Probabilistic Causation and Causal Processes: A Critique of Lewis.Peter Menzies - 1989 - Philosophy of Science 56 (4):642-663.
This paper examines a promising probabilistic theory of singular causation developed by David Lewis. I argue that Lewis' theory must be made more sophisticated to deal with certain counterexamples involving pre-emption. These counterexamples appear to show that in the usual case singular causation requires an unbroken causal process to link cause with effect. I propose a new probabilistic account of singular causation, within the framework developed by Lewis, which captures this intuition.

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37. Probabilistic Representations in Perception: Are There Any, and What Would They Be?Steven Gross - 2020 - Mind and Language 35 (3):377-389.
Nick Shea’s Representation in Cognitive Science commits him to representations in perceptual processing that are about probabilities. This commentary concerns how to adjudicate between this view and an alternative that locates the probabilities rather in the representational states’ associated “attitudes”. As background and motivation, evidence for probabilistic representations in perceptual processing is adduced, and it is shown how, on either conception, one can address a specific challenge Ned Block has raised to this evidence.

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38. Is Probabilistic Evidence a Source of Knowledge?Ori Friedman & John Turri - 2015 - Cognitive Science 39 (5):1062-1080.
We report a series of experiments examining whether people ascribe knowledge for true beliefs based on probabilistic evidence. Participants were less likely to ascribe knowledge for beliefs based on probabilistic evidence than for beliefs based on perceptual evidence or testimony providing causal information. Denial of knowledge for beliefs based on probabilistic evidence did not arise because participants viewed such beliefs as unjustified, nor because such beliefs leave open the possibility of error. These findings rule out traditional philosophical (...)

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39. Probabilistic Knowledge in Action.Carlotta Pavese - 2020 - Analysis 80 (2):342-356.
According to a standard assumption in epistemology, if one only partially believes that p , then one cannot thereby have knowledge that p. For example, if one only partially believes that that it is raining outside, one cannot know that it is raining outside; and if one only partially believes that it is likely that it will rain outside, one cannot know that it is likely that it will rain outside. Many epistemologists will agree that epistemic agents are capable of (...)

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40. A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic (...)

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41. Probabilistic Promotion and Ability.Luke Elson - 2019 - Ergo: An Open Access Journal of Philosophy 6.
We often have some reason to do actions insofar as they promote outcomes or states of affairs, such as the satisfaction of a desire. But what is it to promote an outcome? I defend a new version of 'probabilism about promotion'. According to Minimal Probabilistic Promotion, we promote some outcome when we make that outcome more likely than it would have been if we had done something else. This makes promotion easy and reasons cheap.

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42. A Probabilistic Analysis of Causation.Luke Glynn - 2011 - British Journal for the Philosophy of Science 62 (2):343-392.
The starting point in the development of probabilistic analyses of token causation has usually been the naïve intuition that, in some relevant sense, a cause raises the probability of its effect. But there are well-known examples both of non-probability-raising causation and of probability-raising non-causation. Sophisticated extant probabilistic analyses treat many such cases correctly, but only at the cost of excluding the possibilities of direct non-probability-raising causation, failures of causal transitivity, action-at-a-distance, prevention, and causation by absence and omission. I (...)

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43. A Probabilistic Framework for Analysing the Compositionality of Conceptual Combinations.Peter Bruza, Kirsty Kitto, Brentyn Ramm & Laurianne Sitbon - 2015 - Journal of Mathematical Psychology 67:26-38.
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and (...)
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44. 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 (...)

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45. Probabilistic Measures of Coherence and the Problem of Belief Individuation.Luca Moretti & Ken Akiba - 2007 - Synthese 154 (1):73 - 95.
Coherentism in epistemology has long suffered from lack of formal and quantitative explication of the notion of coherence. One might hope that probabilistic accounts of coherence such as those proposed by Lewis, Shogenji, Olsson, Fitelson, and Bovens and Hartmann will finally help solve this problem. This paper shows, however, that those accounts have a serious common problem: the problem of belief individuation. The coherence degree that each of the accounts assigns to an information set (or the verdict it gives (...)

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46. Accuracy, Probabilism, and the Insufficiency of the Alethic.Corey Dethier - forthcoming - Philosophical Studies:1-17.
The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent's degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant (...)

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47. Probabilistic Proofs, Lottery Propositions, and Mathematical Knowledge.Yacin Hamami - 2021 - Philosophical Quarterly 72 (1):77-89.
In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know (...)

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48. Purely Probabilistic Measures of Explanatory Power – A Critique.William Roche & Elliott Sober - forthcoming - Philosophy of Science.
All extant purely probabilistic measures of explanatory power satisfy the following technical condition: if Pr(E | H1) > Pr(E | H2) and Pr(E | ~H1) < Pr(E | ~H2), then H1’s explanatory power with respect to E is greater than H2’s explanatory power with respect to E. We argue that any measure satisfying this condition faces three serious problems – the Problem of Temporal Shallowness, the Problem of Negative Causal Interactions, and the Problem of Non-Explanations. We further argue that (...)

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49. Generalized Probabilism: Dutch Books and Accuracy Domi- Nation.J. Robert G. Williams - 2012 - Journal of Philosophical Logic 41 (5):811-840.
Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination deﬁnes a (...)