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A Mathematical Theory of Evidence

Princeton University Press (1976)

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  1. 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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  • A Gentle Approach to Imprecise Probabilities.Gregory Wheeler - 2022 - In 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.
    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 difficult to (...)
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  • Introduction: Severe Uncertainty in Science, Medicine, and Technology.Mattia Andreoletti, Daniele Chiffi & Behnam Taebi - 2022 - Perspectives on Science 30 (2):201-209.
    This Special Issue titled "Severe Uncertainty in Science, Medicine and Technology" aims to shed new light on the understanding of severe uncertainty and its multifaceted implications. The main idea of the papers of this collection is that, despite possible sophisticated statistical judgments towards future risks in science, medicine, and technology, severe forms of uncertainty still exist.While ignorance is usually assumed to be a total absence of knowledge, uncertainty often refers to the incompleteness of knowledge or information. In its extreme form, (...)
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  • Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - 2021 - Mind 131 (523):892-916.
    – 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 (...)
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  • Non-Classical Probabilities for Decision Making in Situations of Uncertainty.Dominik Klein, Ondrej Majer & Soroush Rafiee Rad - 2020 - Roczniki Filozoficzne 68 (4):315-343.
    Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, we also compare various dynamical rules of the two frameworks, all seen as (...)
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  • Regret Averse Opinion Aggregation.Lee Elkin - 2021 - Ergo: An Open Access Journal of Philosophy 8 (16):473-495.
    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 to satisfy the (...)
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  • Sketch of a Proof-Theoretic Semantics for Necessity.Nils Kürbis - 2020 - In Nicola Olivetti, Rineke Verbrugge & Sara Negri (eds.), Advances in Modal Logic 13. Booklet of Short Papers. Helsinki: pp. 37-43.
    This paper considers proof-theoretic semantics for necessity within Dummett's and Prawitz's framework. Inspired by a system of Pfenning's and Davies's, the language of intuitionist logic is extended by a higher order operator which captures a notion of validity. A notion of relative necessary is defined in terms of it, which expresses a necessary connection between the assumptions and the conclusion of a deduction.
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  • Ranking Theory.Gabriele Kern-Isberner, Niels Skovgaard-Olsen & Wolfgang Spohn - 2021 - In Markus Knauff & Wolfgang Spohn (eds.), The Handbook of Rationality. London: MIT Press. pp. 337-345.
    Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...)
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  • Full & Partial Belief.Konstantin Genin - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 437-498.
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  • Precise Credences.Michael Titelbaum - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 1-55.
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  • Probability and nonclassical logic.Robert Williams - 2016 - In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press.
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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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  • Intelligent Diagnosis Systems.K. Balakrishnan & V. Honavar - 1998 - Journal of Intelligent Systems 8 (3-4):239-290.
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  • Borderlines and probabilities of borderlines: On the interconnection between vagueness and uncertainty.Jonathan Lawry - 2016 - Journal of Applied Logic 14:113-138.
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  • 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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  • Deductively Definable Logics of Induction.John D. Norton - 2010 - Journal of Philosophical Logic 39 (6):617-654.
    A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This no-go (...)
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  • For True Conditionalizers Weisberg’s Paradox is a False Alarm.Franz Huber - 2014 - Symposion: Theoretical and Applied Inquiries in Philosophy and Social Sciences 1 (1):111-119.
    Weisberg introduces a phenomenon he terms perceptual undermining. He argues that it poses a problem for Jeffrey conditionalization, and Bayesian epistemology in general. This is Weisberg’s paradox. Weisberg argues that perceptual undermining also poses a problem for ranking theory and for Dempster-Shafer theory. In this note I argue that perceptual undermining does not pose a problem for any of these theories: for true conditionalizers Weisberg’s paradox is a false alarm.
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  • Logic and the epistemic foundations of game theory: special issue.Michael O. L. Bacharach & Philippe Mongin - 1994 - Theory and Decision 37 (1):1-6.
    An introduction to the special issue on epistemic logic and the foundations of game theory edited by Michael Bacharach and Philippe Mongin. Contributors are Michael Bacharach, Robert Stalnaker, Salvatore Modica and Aldo Rustichini, Luc Lismont and Philippe Mongin, and Hyun-Song Shin and Timothy Williamson.
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  • Rational animal?Simon Blackburn - 1981 - Behavioral and Brain Sciences 4 (3):331-332.
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  • Philosophical arguments, psychological experiments, and the problem of consistency.D. Kahneman - 1983 - Behavioral and Brain Sciences 6 (2):253-254.
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  • A theory of probability should tutor our intuitions.Glenn Shafer - 1983 - Behavioral and Brain Sciences 6 (3):508.
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  • The plasticity of human rationality.Norman Daniels & George E. Smith - 1983 - Behavioral and Brain Sciences 6 (3):490.
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  • Expert intuitions and the interpretation of social psychological experiments.André Gallois & Michael Siegal - 1983 - Behavioral and Brain Sciences 6 (3):492.
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  • Another vote for rationality.Mary Henle - 1981 - Behavioral and Brain Sciences 4 (3):339-339.
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  • Who shall be the arbiter of our intuitions?Daniel Kahneman - 1981 - Behavioral and Brain Sciences 4 (3):339-340.
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  • Unphilosophical probability.Sandy L. Zabell - 1981 - Behavioral and Brain Sciences 4 (3):358-359.
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  • Luminosity and vagueness.Elia Zardini - 2012 - Dialectica 66 (3):375-410.
    The paper discusses some ways in which vagueness and its phenomena may be thought to impose certain limits on our knowledge and, more specifically, may be thought to bear on the traditional philosophical idea that certain domains of facts are luminous, i.e., roughly, fully open to our view. The discussion focuses on a very influential argument to the effect that almost no such interesting domains exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts (...)
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  • Dynamic Update with Probabilities.Johan van Benthem, Jelle Gerbrandy & Barteld Kooi - 2009 - Studia Logica 93 (1):67 - 96.
    Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...)
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  • Recovery Recovered.Stephen Murray Glaister - 2000 - Journal of Philosophical Logic 29 (2):171 - 206.
    The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more closely to the (...)
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  • Consensus for belief functions and related uncertainty measures.Carl G. Wagner - 1989 - Theory and Decision 26 (3):295-304.
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  • Decisions with indeterminate probabilities.Ronald P. Loui - 1986 - Theory and Decision 21 (3):283-309.
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  • Idealisations in normative models.Mark Colyvan - 2013 - Synthese 190 (8):1337-1350.
    In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (in (...)
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  • Bayesianism II: Applications and Criticisms.Kenny Easwaran - 2011 - Philosophy Compass 6 (5):321-332.
    In the first paper, I discussed the basic claims of Bayesianism (that degrees of belief are important, that they obey the axioms of probability theory, and that they are rationally updated by either standard or Jeffrey conditionalization) and the arguments that are often used to support them. In this paper, I will discuss some applications these ideas have had in confirmation theory, epistemol- ogy, and statistics, and criticisms of these applications.
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  • A unifying framework of probabilistic reasoning: Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler and Jon Williamson: Probabilistic logic and probabilistic networks. Dordrecht: Springer, 2011, xiii+155pp, €59.95 HB. [REVIEW]Jan Sprenger - 2011 - Metascience 21 (2):459-462.
    A unifying framework of probabilistic reasoning Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9573-x Authors Jan Sprenger, Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  • 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 (...)
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  • Probability Operators.Seth Yalcin - 2010 - Philosophy Compass 5 (11):916-37.
    This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.
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  • From Classical to Intuitionistic Probability.Brian Weatherson - 2003 - Notre Dame Journal of Formal Logic 44 (2):111-123.
    We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable (...)
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  • Representation theorems and the foundations of decision theory.Christopher Meacham & Jonathan Weisberg - 2011 - Australasian Journal of Philosophy 89 (4):641 - 663.
    Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...)
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  • Degrees of belief.Franz Huber & Christoph Schmidt-Petri (eds.) - 2009 - London: Springer.
    Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...
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  • Ranking Functions, AGM Style.Wolfgang Spohn - 1999 - Internet Festschrift for Peter Gärdenfors.
    First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious.
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  • A Survey of Ranking Theory.Wolfgang Spohn - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer.
    "A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...)
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  • What is the Normative Role of Logic?Hartry Field - 2009 - Aristotelian Society Supplementary Volume 83 (1):251-268.
    The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...)
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  • Popper's severity of test as an intuitive probabilistic model of hypothesis testing.Fenna H. Poletiek - 2009 - Behavioral and Brain Sciences 32 (1):99-100.
    Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.
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  • 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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  • On the nature of the conjunction fallacy.Rodrigo Moro - 2009 - Synthese 171 (1):1 - 24.
    In a seminal work, Tversky and Kahneman showed that in some contexts people tend to believe that a conjunction of events (e.g., Linda is a bank teller and is active in the feminist movement) is more likely to occur than one of the conjuncts (e.g., Linda is a bank teller). This belief violates the conjunction rule in probability theory. Tversky and Kahneman called this phenomenon the “conjunction fallacy”. Since the discovery of the phenomenon in 1983, researchers in psychology and philosophy (...)
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  • Ranking Functions.Franz Huber - 2009 - In A. Pazos Sierra, J. R. Rabunal Dopico & J. Dorado de la Calle (eds.), Encyclopedia of Artificial Intelligence. Hershey.
    Ranking functions have been introduced under the name of ordinal conditional functions in Spohn (1988; 1990). They are representations of epistemic states and their dynamics. The most comprehensive and up to date presentation is Spohn (manuscript).
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  • Begging the Question and Bayesians.Brian Weatherson - 1999 - Studies in History and Philosophy of Science Part A 30:687-697.
    The arguments for Bayesianism in the literature fall into three broad categories. There are Dutch Book arguments, both of the traditional pragmatic variety and the modern ‘depragmatised’ form. And there are arguments from the so-called ‘representation theorems’. The arguments have many similarities, for example they have a common conclusion, and they all derive epistemic constraints from considerations about coherent preferences, but they have enough differences to produce hostilities between their proponents. In a recent paper, Maher (1997) has argued that the (...)
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  • Keynes, Uncertainty and Interest Rates.Brian Weatherson - 2002 - Cambridge Journal of Economics 26 (1):47-62.
    Uncertainty plays an important role in The General Theory, particularly in the theory of interest rates. Keynes did not provide a theory of uncertainty, but he did make some enlightening remarks about the direction he thought such a theory should take. I argue that some modern innovations in the theory of probability allow us to build a theory which captures these Keynesian insights. If this is the right theory, however, uncertainty cannot carry its weight in Keynes’s arguments. This does not (...)
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  • Belief and Degrees of Belief.Franz Huber - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of belief. London: Springer.
    Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...)
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  • Should we respond to evil with indifference?Brian Weatherson - 2005 - Philosophy and Phenomenological Research 70 (3):613–635.
    In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...)
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