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Probabilistic Reasoning

Assistant editor: Joshua Luczak (University of Western Ontario)
About this topic
Summary What principles govern uncertain reasoning?  And how do they apply to other philosophical problems; like whether a decision is rational, or whether one thing is a cause of another? Most philosophers think uncertain reasoning should at least obey the axioms of the mathematical theory of probability; though some prefer other axioms, like those of Dempster-Shafer theory or ranking theory.  Many also endorse principles governing beliefs about physical probabilities (chance-credence principles), and principles for responding to new evidence (updating principles).  Some also endorse principles for reasoning in the absence of relevant information (indifference principles).  A perennial question is how many principles we should accept: how "objective" is probabilistic reasoning? Probabilistic principles have traditionally been applied to the study of scientific reasoning (confirmation theory) and practical rationality (decision theory).  But they also apply to more traditional epistemological issues, like foundationalism vs. coherentism, and to metaphysical questions, e.g. about the nature of causality and our access to it.
Key works Key works defending the probability axioms as normative principles are Ramsey 1926, De 1989, Savage 1954, and Joyce 1998.  Locus classici for additional probabilistic principles are Lewis 1980 (chance-credence), van Fraassen 1984 (reflection), Carnap 1950, Jaynes 1973 (indifference), and Lewis 1999 (updating). Alternative axiomatic frameworks originate with Shafer 1976 (Dempster-Shafer theory) and Spohn 1988 (ranking theory). Some classic applications of probabilistic principles to epistemological and other problems are Good 1960 (the raven paradox), Pearl 2000 (causal inference), and Elga 2000 (sleeping beauty and self-location). 
Introductions Skyrms 1966 is an excellent and gentle introduction for non-initiates.  A next step up is Jeffrey 1965.  More advanced introductions are Urbach & Howson 1993 and Earman 1992.  More recently, Halpern 2003 provides an excellent overview of the mathematical options.  A recent overview of the more philosophical issues can be found in Weisberg 2011.
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  1. Look at the Time!David Builes - 2022 - Analysis 82 (1):15-23.
    I argue that we can get evidence for the temporal ontology of the universe simply by looking at the time. The argument is an extension of the ‘epistemic objection’ towards Growing Block theories.
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  2. Speed-Optimal Induction and Dynamic Coherence.Michael Nielsen & Eric Wofsey - 2022 - British Journal for the Philosophy of Science 73 (2):439-455.
    A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.
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  3. Knowledge from multiple experiences.Simon Goldstein & John Hawthorne - 2021 - Philosophical Studies 179 (4):1341-1372.
    This paper models knowledge in cases where an agent has multiple experiences over time. Using this model, we introduce a series of observations that undermine the pretheoretic idea that the evidential significance of experience depends on the extent to which that experience matches the world. On the basis of these observations, we model knowledge in terms of what is likely given the agent’s experience. An agent knows p when p is implied by her epistemic possibilities. A world is epistemically possible (...)
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  4. Reconsidering the Rule of Consideration: Probabilistic Knowledge and Legal Proof.Tim Smartt - 2022 - Episteme 19 (2):303-318.
    In this paper, I provide an argument for rejecting Sarah Moss's recent account of legal proof. Moss's account is attractive in a number of ways. It provides a new version of a knowledge-based theory of legal proof that elegantly resolves a number of puzzles about mere statistical evidence in the law. Moreover, the account promises to have attractive implications for social and moral philosophy, in particular about the impermissibility of racial profiling and other harmful kinds of statistical generalisation. In this (...)
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  5. Statistik und Einheit der Wissenschaften von Quetelets Physique Sociale zu Neuraths Soziologie im Physikalismus.Donata Romizi - 2016 - In C. Bonnet & E. Nemeth (eds.), .): Wissenschaft und Praxis. Zur Wissenschaftsphilosophie in Österreich und Frankreich in der ersten Hälfte des 20. Jahrhunderts. Wien; New York:
    The present paper focuses on the work of Adolphe Quetelet (1796-1874), the Belgian author of the Social Physics who worked in the tradition of the French mathématique sociale, and of Otto Neurath (1882-1945), the Vienna Circle’s member who supported a “sociology within physicalism”. They shared some important philosophical and methodological positions: an empiricist approach to the social sciences, a unitary conception of the natural and the social sciences, and the appreciation of statistics as a tool for investigating and also reforming (...)
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  6. Erratum To: Is Global Consequentialism More Expressive Than Act Consequentialism?Elliott Thornley - forthcoming - Analysis.
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  7. Three Forms of Actualist Direct Consequentialism.Shyam Nair - forthcoming - Utilitas.
    One family of maximizing act consequentialist theories actualist direct theories. Indeed, historically there are at least three different forms of actualist direct consequentialism (due to Bentham, Moore, and contemporary consequentialists). This paper is about the logical differences between these three actualist direct theories and the differences between actualist direct theories and their competitors. Three main points emerge. First, the sharpest separation between actualist direct theories and their competitors concerns the so-called inheritance principle. Second, there are a myriad of other logical (...)
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  8. New Wave Consequentialism: An Introduction.Christian Seidel - 2019 - In Consequentialism: New Directions, New Problems. Oxford, New York 13830, USA: pp. 1-28.
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  9. The Ineffability of Induction.David Builes - 2022 - Philosophy and Phenomenological Research 104 (1):129-149.
    My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such a metaphysics (...)
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  10. Paraconsistent Logics for Knowledge Representation and Reasoning: Advances and Perspectives.Walter A. Carnielli & Rafael Testa - 2020 - 18th International Workshop on Nonmonotonic Reasoning.
    This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the importance of (...)
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  11. A Probabilistic Analysis of Cross-Examination Using Bayesian Networks.Marcello Di Bello - 2021 - Philosophical Issues 31 (1):41-65.
    The legal scholar Henry Wigmore asserted that cross-examination is ‘the greatest legal engine ever invented for the discovery of truth.’ Was Wigmore right? Instead of addressing this question upfront, this paper offers a conceptual ground clearing. It is difficult to say whether Wigmore was right or wrong without becoming clear about what we mean by cross-examination; how it operates at trial; what it is intended to accomplish. Despite the growing importance of legal epistemology, there is virtually no philosophical work that (...)
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  12. Dynamic Formal Epistemology.Patrick Girard, Olivier Roy & Mathieu Marion (eds.) - 2010 - Berlin, Germany: Springer.
    This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and (...)
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  13. Naturalized Formal Epistemology of Uncertain Reasoning.Niki Pfeifer - 2012 - Dissertation, The Tilburg Center for Logic and Philosophy of Science, Tilburg University
    This thesis consists of a collection of five papers on naturalized formal epistemology of uncertain reasoning. In all papers I apply coherence based probability logic to make fundamental epistemological questions precise and propose new solutions to old problems. I investigate the rational evaluation of uncertain arguments, develop a new measure of argument strength, and explore the semantics of uncertain indicative conditionals. Specifically, I study formally and empirically the semantics of negated apparently selfcontradictory conditionals (Aristotle’s theses), resolve a number of paradoxes (...)
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  14. On Argument Strength.Niki Pfeifer - 2013 - In Frank Zenker (ed.), Bayesian argumentation. The practical side of probability. Dordrecht, Netherlands: pp. 185-193.
    Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...)
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  15. Square of Opposition Under Coherence.Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, Alessandro Giordani, B. Vantaggi, M. Gagolewski, M. Á Gil, P. Grzegorzewski & O. Hryniewicz (eds.), Soft Methods for Data Science. Cham, Switzerland: pp. 407-414.
    Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...)
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  16. Centering and Compound Conditionals Under Coherence.A. Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, Gilgameshgodman Gilgameshgodman, P. Grzegorzewski & O. Hryniewicz (eds.), Soft Methods for Data Science. Cham, Switzerland: pp. 253-260.
    There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti’s conditional event, B | A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, (...)
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  17. Generalized Probabilistic Modus Ponens.Giuseppe Sanfilippo, Niki Pfeifer & Angelo Gilio - 2017 - In A. Antonucci, L. Cholvy & O. Papini (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (Lecture Notes in Artificial Intelligence, vol. 10369). Cham, Switzerland: pp. 480-490.
    Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the (...)
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  18. Probabilistic Semantics for Categorical Syllogisms of Figure II.Niki Pfeifer & Giuseppe Sanfilippo - 2018 - In D. Ciucci, G. Pasi & B. Vantaggi (eds.), Scalable Uncertainty Management. Cham, Switzerland: pp. 196-211.
    A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, ~????|????} is not informative, (...)
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  19. Probabilistic Interpretations of Argumentative Attacks: Logical and Experimental Foundations.Niki Pfeifer & C. G. Fermüller - 2018 - In V. Kratochvíl & J. Vejnarová (eds.), 11th Workshop on Uncertainty Processing (WUPES'18). Prague, Czechia: pp. 141-152.
    We present an interdisciplinary approach to study systematic relations between logical form and attacks between claims in an argumentative framework. We propose to generalize qualitative attack principles by quantitative ones. Specifically, we use coherent conditional probabilities to evaluate the rationality of principles which govern the strength of argumentative attacks. Finally, we present an experiment which explores the psychological plausibility of selected attack principles.
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  20. What Society Can and Cannot Learn From Coherence: Theoretical and Practical Considerations.Niki Pfeifer & Andrea Capotorti - 2020 - In H. Yama & V. Salvano-Pardieu (eds.), Adapting Human Thinking and Moral Reasoning in Contemporary Society. Hershey, PA, USA: pp. 176-198.
    Society is facing uncertainty on a multitude of domains and levels: usually, reasoning and decisions about political, economic, or health issues must be made under uncertainty. Among various approaches to probability, this chapter presents the coherence approach to probability as a method for uncertainty management. The authors explain the role of uncertainty in the context of important societal issues like legal reasoning and vaccination hesitancy. Finally, the chapter presents selected psychological factors which impact probabilistic representation and reasoning and discusses what (...)
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  21. Probabilistic Entailment and Iterated Conditionals.A. Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2020 - In S. Elqayam, Igor Douven, J. St B. T. Evans & N. Cruz (eds.), Logic and uncertainty in the human mind: a tribute to David E. Over. London, UK: pp. 71-101.
    In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval [0,1]. We examine the iterated conditional (B|K)|(A|H), by showing that A|H p-entails B|K if and only if (B|K)|(A|H) = 1. Then, we show that a p-consistent family F={E1|H1, E2|H2} p-entails a conditional event E3|H3 if and only if E3|H3= 1, or (E3|H3)|QC(S) = 1 for some nonempty subset S (...)
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  22. Probabilistic Squares and Hexagons of Opposition Under Coherence.Niki Pfeifer & Giuseppe Sanfilippo - 2017 - International Journal of Approximate Reasoning 88:282-294.
    Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the (...)
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  23. Probabilistic Inferences From Conjoined to Iterated Conditionals.Giuseppe Sanfilippo, Niki Pfeifer, D. E. Over & A. Gilio - 2018 - International Journal of Approximate Reasoning 93:103-118.
    There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate (...)
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  24. A Multinational Data Set of Game Players' Behaviors in a Virtual World and Environmental Perceptions.Vuong Quan-Hoang, Manh-Toan Ho, Viet-Phuong La, Tam-Tri Le, Thanh Huyen T. Nguyen & Minh-Hoang Nguyen - 2021 - Data Intelligence 3 (4):606-630.
    Video gaming has been rising rapidly to become one of the primary entertainment media, especially during the COVID-19 pandemic. Playing video games has been reported to associate with many psychological and behavioral traits. However, little is known about the connections between game players' behaviors in the virtual environment and environmental perceptions. Thus, the current data set offers valuable resources regarding environmental worldviews and behaviors in the virtual world of 640 Animal Crossing: New Horizons (ACNH) game players from 29 countries around (...)
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  25. Independent Natural Extension for Choice Functions.Jason Konek, Arthur Van Camp & Kevin Blackwell - 2021 - PMLR 147:320-330.
    We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware (...)
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  26. Wishing, Decision Theory, and Two-Dimensional Content.Kyle H. Blumberg - forthcoming - Journal of Philosophy.
    This paper is about two requirements on wish reports whose interaction motivates a novel semantics for these ascriptions. The first requirement concerns the ambiguities that arise when determiner phrases, e.g. definite descriptions, interact with `wish'. More specifically, several theorists have recently argued that attitude ascriptions featuring counterfactual attitude verbs license interpretations on which the determiner phrase is interpreted relative to the subject's beliefs. The second requirement involves the fact that desire reports in general require decision-theoretic notions for their analysis. The (...)
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  27. 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) is (...)
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  28. Legal Probabilism.Rafal Urbaniak & Marcello Di Bello - 2021 - Stanford Encyclopedia of Philosophy.
  29. Un alegato a favor del enfoque lógico en la teoría de la argumentación.Marc Jiménez-Rolland - 2020 - Quadripartita Ratio 10:21-35.
    El estudio actual de la argumentación se encuentra distanciado de la lógica. En este artículo sostengo que restaurar el vínculo del estudio de la argumentación con esta disciplina podría resultar benéfico para la metas descriptivas y normativas de este campo de investigación. Tras destacar algunos aspectos del surgimiento la teoría de la argumentación contemporánea, enfatizando la idea de "perspectivas", explico cómo el reconocimiento de sus objetivos y tareas volvió problemática la coexistencia de varios enfoques o aproximaciones para el estudio de (...)
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  30. Local Explanations Via Necessity and Sufficiency: Unifying Theory and Practice.David Watson, Limor Gultchin, Taly Ankur & Luciano Floridi - 2022 - Minds and Machines 32:185-218.
    Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing explanatory factors (...)
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  31. Algebraic Aspects and Coherence Conditions for Conjoined and Disjoined Conditionals.Angelo Gilio & Giuseppe Sanfilippo - 2020 - International Journal of Approximate Reasoning 126:98-123.
    We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and (...)
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  32. Reflective Intuition and the Copi Card Problem.Terence Horgan - 2021 - Philosophical Psychology 34 (3):327-344.
    In the 1970’s, a controversy arose about a probability problem posed by Irving Copi. One side argued that a common spontaneous intuition about the problem is correct; the other side argued that this intuition is mistaken. Here, I argue (1) that the naïve intuition yields the correct answer, but accidentally and for a wrong reason; (2) that a more reflective intuition yields a wrong answer, and hence, is also mistaken; and (3) that an even more reflective intuition yields the correct (...)
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  33. Reasoning Without the Conjunction Closure.Alicja Kowalewska - forthcoming - Episteme:1-14.
    Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is (...)
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  34. Decision-Theoretic and Risk-Based Approaches to Naked Statistical Evidence: Some Consequences and Challenges.Rafal Urbaniak, Alicja Kowalewska, Pavel Janda & Patryk Dziurosz-Serafinowicz - 2020 - Law, Probability and Risk 19 (1):67-83.
    In the debate about the legal value of naked statistical evidence, Di Bello argues that (1) the likelihood ratio of such evidence is unknown, (2) the decision-theoretic considerations indicate that a conviction based on such evidence is unacceptable when expected utility maximization is combined with fairness constraints, and (3) the risk of mistaken conviction based on such evidence cannot be evaluated and is potentially too high. We argue that Di Bello’s argument for (1) works in a rather narrow context, and (...)
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  35. Permissivism and the Truth Connection.Michele Palmira - forthcoming - Erkenntnis:1-16.
    Permissivism is the view that, sometimes, there is more than one doxastic attitude that is perfectly rationalised by the evidence. Impermissivism is the denial of Permissivism. Several philosophers, with the aim to defend either Impermissivism or Permissivism, have recently discussed the value of (im)permissive rationality. This paper focuses on one kind of value-conferring considerations, stemming from the so-called “truth-connection” enjoyed by rational doxastic attitudes. The paper vindicates the truth-connected value of permissive rationality by pursuing a novel strategy which rests on (...)
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  36. How to (Blind)Spot the Truth: An Investigation on Actual Epistemic Value.Danilo Fraga Dantas - 2021 - Erkenntnis:1572-8420.
    This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...)
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  37. Knowledge Closure and Knowledge Openness: A Study of Epistemic Closure Principles.Levi Spectre - 2009 - Stockholm: Stockholm University.
    The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...)
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  38. Knowledge Closure and Knowledge Openness: A Study of Epistemic Closure Principles.Levi Spectre - 2009 - Stockholm: Stockholm University.
    The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...)
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  39. A Causal Safety Criterion for Knowledge.Jonathan Vandenburgh - manuscript
    Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, numerous examples suggest that safety fails as a condition on knowledge: a belief can be safe even when one's evidence is clearly insufficient for knowledge and knowledge is compatible with the nearby possibility of error, a situation ruled out by the safety condition. In this paper, I argue for a new modal condition designed to capture (...)
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  40. Triviality Results, Conditional Probability, and Restrictor Conditionals.Jonathan Vandenburgh - manuscript
    Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the rival restrictor (...)
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  41. The Logic of Conditional Belief.Benjamin Eva - 2020 - Philosophical Quarterly 70 (281):759-779.
    The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic of the (...)
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  42. 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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  43. Sensitivity and Closure.Sherrilyn Roush - 2012 - In Kelly Becker & Tim Black (eds.), The Sensitivity Principle in Epistemology. Cambridge, UK: pp. 242-268.
    This paper argues that if knowledge is defined in terms of probabilistic tracking then the benefits of epistemic closure follow without the addition of a closure clause. (This updates my definition of knowledge in Tracking Truth 2005.) An important condition on this result is found in "Closure Failure and Scientific Inquiry" (2017).
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  44. What Was Fair in Actuarial Fairness?Antonio J. Heras, Pierre-Charles Pradier & David Teira - 2020 - History of the Human Sciences 33 (2):91-114.
    In actuarial parlance, the price of an insurance policy is considered fair if customers bearing the same risk are charged the same price. The estimate of this fair amount hinges on the expected value obtained by weighting the different claims by their probability. We argue that, historically, this concept of actuarial fairness originates in an Aristotelian principle of justice in exchange. We will examine how this principle was formalized in the 16th century and shaped in life insurance during the following (...)
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  45. Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy.Thomas Icard - 2020 - Journal of Mathematical Psychology 95.
    A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools (...)
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  46. Being Rational and Being Wrong.Kevin Dorst - manuscript
    Do people tend to be overconfident in their opinions? Many think so. They’ve run studies to test whether people are calibrated: whether their confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically “over-calibrated”—for example, of the opinions they’re 80% confident in, only 60% are true. From this observed over-calibration, it’s inferred that people are irrationally overconfident. My question: When—and why—is this inference warranted? Answering this question requires articulating a general connection (...)
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  47. Evidential Probabilities and Credences.Anna-Maria Eder - 2019 - British Journal for the Philosophy of Science:1-21.
    Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual credences of human (...)
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  48. 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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  49. 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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  50. Mathematical Models of Games of Chance: Epistemological Taxonomy and Potential in Problem-Gambling Research.Catalin Barboianu - 2015 - UNLV Gaming Research and Review Journal 19 (1):17-30.
    Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...)
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