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Probabilistic forecasting: why model imperfection is a poison pillIn Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science, Springer Verlag. pp. 479-492. 2013.This volume is a serious attempt to open up the subject of European philosophy of science to real thought, and provide the structural basis for the interdisciplinary development of its specialist fields, but also to provoke reflection on the idea of ‘European philosophy of science’. This efforts should foster a contemporaneous reflection on what might be meant by philosophy of science in Europe and European philosophy of science, and how in fact awareness of it could assist philosophers interpre…Read more
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41Possible semantics for a common framework of probabilistic logicsIn V. N. Huynh (ed.), International Workshop on Interval Probabilistic Uncertainty and Non-Classical Logics, Springer. 2008.In V. N. Huynh (ed.): Interval / Probabilistic Uncertainty and Non-Classical Logics, Advances in Soft Computing Series, Springer 2008, pp. 268-279. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it…Read more
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98“Visualizing High-Dimensional Loss Landscapes with Hessian Directions”Journal of Statistical Mechanics: Theory and Experiment. forthcoming.Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the …Read more
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189On the imprecision of full conditional probabilitiesSynthese 199 (1-2): 3761-3782. 2021.The purpose of this paper is to show that if one adopts conditional probabilities as the primitive concept of probability, one must deal with the fact that even in very ordinary circumstances at least some probability values may be imprecise, and that some probability questions may fail to have numerically precise answers.
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Formal epistemologyIn Andrew Cullison (ed.), The Continuum Companion to Epistemology, Continuum. 2012.
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11Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld (edited book)Springer. 2022.This festschrift for Teddy Seidenfeld is a collection of newly commissioned essays on imprecise probability by leading experts in the field. Each contribution touches on Teddy’s seminal contributions to the field of imprecise probability, and gives an up-to-date state of the field that cannot be found elsewhere. The title, “a reflection on the foundations of probability and statistics”, calls back to Teddy’s seminal book, “Rethinking the Foundations of Probability and Statistics”, bookends to a …Read more
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152A Gentle Approach to Imprecise ProbabilitiesIn Thomas Augustin, Fabio Gagliardi Cozman & Gregory Wheeler (eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld, Springer. pp. 37-67. 2022.The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can be diffic…Read more
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248Discounting Desirable GamblesProceedings of Machine Learning Research 147 331-341. 2021.The desirable gambles framework offers the most comprehensive foundations for the theory of lower pre- visions, which in turn affords the most general ac- count of imprecise probabilities. Nevertheless, for all its generality, the theory of lower previsions rests on the notion of linear utility. This commitment to linearity is clearest in the coherence axioms for sets of desirable gambles. This paper considers two routes to relaxing this commitment. The first preserves the additive structure of …Read more
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479Why formal objections to the error theory are soundAnalysis 82 (4): 608-616. 2022.Recent debate about the error theory has taken a ‘formal turn’. On the one hand, there are those who argue that the error theory should be rejected because of its difficulties in providing a convincing formal account of the logic and semantics of moral claims. On the other hand, there are those who claim that such formal objections fail, maintaining that arguments against the error theory must be of a substantive rather than a formal kind. In this paper, we argue that formal objections to the er…Read more
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502Changing use of formal methods in philosophy: late 2000s vs. late 2010sSynthese 199 (5-6): 14555-14576. 2021.Traditionally, logic has been the dominant formal method within philosophy. Are logical methods still dominant today, or have the types of formal methods used in philosophy changed in recent times? To address this question, we coded a sample of philosophy papers from the late 2000s and from the late 2010s for the formal methods they used. The results indicate that the proportion of papers using logical methods remained more or less constant over that time period but the proportion of papers usin…Read more
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253Moving Beyond Sets of ProbabilitiesStatistical Science 36 (2): 201--204. 2021.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 demotin…Read more
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42Conditionals and TestimonyCognitive Psychology 122. 2020.Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much—perhaps most—of what we believe through the testimony of others, the simple matter of acquiring conditionals via others’ assertion of a conditional seems integral to any full under…Read more
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334A sound and complete axiomatization of two tabloid blogs is presented, Leiter Logic (KB) and Deontic Leiter Logic (KDB), the latter of which can be extended to Shame Game Logic for multiple agents. The (B) schema describes the mechanism behind this class of tabloids, and illustrates the perils of interpreting a provability operator as an epistemic modal. To mark this difference, and to avoid sullying Brouwer's good name, the (B) schema for epistemic modals should be called the Blog Schema.
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196Error, Consistency and TrivialityNoûs 56 (3): 602-618. 2022.In this paper, we present a new semantic challenge to the moral error theory. Its first component calls upon moral error theorists to deliver a deontic semantics that is consistent with the error-theoretic denial of moral truths by returning the truth-value false to all moral deontic sentences. We call this the ‘consistency challenge’ to the moral error theory. Its second component demands that error theorists explain in which way moral deontic assertions can be seen to differ in meaning despite…Read more
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340Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.
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29Logical relations in a statistical problemIn Benedikt Löwe, Eric Pacuit & Jan-Willem Romeijn (eds.), Foundations of the Formal Sciences Vi: Probabilistic Reasoning and Reasoning With Probabilities. Studies in Logic, College Publication. 2008.This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The f…Read more
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199Evidential Probability and Objective Bayesian EpistemologyIn Prasanta S. Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics, Elsevier B.v.. 2011.In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other
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66Possible Semantics for a Common Framework of Probabilistic LogicsIn V. N. Huynh (ed.), International Workshop on Interval Probabilistic Uncertainty and Non-Classical Logics, Springer. 2008.Summary. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
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803Coherence and Confirmation through CausationMind 122 (485): 135-170. 2013.Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be …Read more
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120Error statistics and Duhem's problemPhilosophy of Science 67 (3): 410-420. 2000.No one has a well developed solution to Duhem's problem, the problem of how experimental evidence warrants revision of our theories. Deborah Mayo proposes a solution to Duhem's problem in route to her more ambitious program of providing a philosophical account of inductive inference and experimental knowledge. This paper is a response to Mayo's Error Statistics (ES) program, paying particular attention to her response to Duhem's problem. It turns out that Mayo's purported solution to Duhem's pro…Read more
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414Less is More for Bayesians, Too.In Riccardo Viale (ed.), Routledge Handbook on Bounded Rationality, . pp. 471-483. 2020.
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249Dilation and Asymmetric RelevanceProceedings of Machine Learning Research 103 324-26. 2019.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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19A sound and complete axiomatization of two philosophy tabloids is given, Leiter Logic (KB) and Deontic Leiter Logic (KDB), in single agent format, the latter of which can be extended to Shame Game Logic for multiple players. The (B) schema captures the mechanism of tabloid inference, illustrating the perils of interpreting a provability operator as an epistemic modal. To mark this hazard, and to preserve Brouwer's good name, the (B) schema interpreted to govern epistemic modals should be called …Read more
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10Vincent F. Hendricks and John Symons , Formal Philosophy: Aim, Scope, Direction. Copenhagen: Automatic Press , 264 pp., $40.00 (review)Philosophy of Science 76 (1): 112-115. 2009.
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20Hans Rott, Change, Choice and Inference: A Study of Belief and Revision and Nonmonotonic Reasoning. New York: Oxford University Press , 400 pp., $156.00 (review)Philosophy of Science 72 (3): 498-503. 2005.
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65An implementation of statistical default logicIn Jose Alferes & Joao Leite (eds.), Logics in Artificial Intelligence (JELIA 2004), Springer. 2004.Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniqu…Read more
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27Book review: Change, Choice and Inference: A Study of Belief and Revision and Nonmonotonic Reasoning (review)Philosophy of Science 72 (3): 498-503. 2005.
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120Formal EpistemologyIn Andrew Cullison (ed.), A Companion to Epistemology, Continuum Press. 2010.Yet, in broader terms, formal epistemology is not merely a methodological tool for epistemologists, but a discipline in its own right. On this programmatic view, formal epistemology is an interdisciplinary research program that covers work by philosophers, mathematicians, computer scientists, statisticians, psychologists, operations researchers, and economists who aim to give mathematical and sometimes computational representations of, along with sound strategies for reasoning about, knowledge, …Read more
Gregory Wheeler
Frankfurt School Of Finance And Management
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Frankfurt School Of Finance And ManagementProfessor
Areas of Specialization
Probabilistic Frameworks |
Machine Learning |
Formal Epistemology |