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Briggs, Rachael, , . Distorted Reflection
2009, Philosophical Review 118(1): 59-85.
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Added by: Berta Grimau, Contributed by: Antony Eagle

Abstract: Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen’s Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new ‘Qualified Reflection’ principle, which states that an agent should obey Reflection only if he or she is certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a ‘Distorted Reflection’ principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence – some dramatize a less blameworthy sort of epistemic frailty that the essay calls ‘self-doubt’. The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt.

Comment: Appropriate for a graduate level philosophy of probability or formal philosophy seminar. It’s a useful adjunct to other readings on the reflection principle which has been recently much discussed.

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Briggs, Ray, , . The Metaphysics of Chance
2010, Philosophy Compass 5(11): 938-952.
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Added by: Emily Paul, Contributed by:

Abstract: This article surveys several interrelated issues in the metaphysics of chance. First, what is the relationship between the probabilities associated with types of trials (for instance, the chance that a twenty?eight?year old develops diabetes before age thirty) and the probabilities associated with individual token trials (for instance, the chance that I develop diabetes before age thirty)? Second, which features of the the world fix the chances: are there objective chances at all, and if so, are there non?chancy facts on which they supervene? Third, can chance be reconciled with determinism, and if so, how?

Comment: A nice introduction to the Metaphysics of Chance, suitable for an intermediate metaphysics course. Could also be a good bridge into a determinism or decision theory course element. Requires prior knowledge of some concepts e.g. token/type distinction and supervenience – but could also be a good way to learn what these are. Alternatively, a particular section of the article could be set (e.g. the final section on whether chance can be reconciled with determinism).

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Buchak, Lara, , . Can it be Rational to Have Faith?
2012, in Jake Chandler & Victoria Harrison (eds.) Probability in the Philosophy of Religion. Oxford University Press: 225-247.
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Added by: Emily Paul, Contributed by:

Abstract: This paper provides an account of what it is to have faith in a proposition p, in both religious and mundane contexts. It is argued that faith in p doesn’t require adopting a degree of belief that isn’t supported by one’s evidence but rather it requires terminating one’s search for further evidence and acting on the supposition that p. It is then shown, by responding to a formal result due to I.J. Good, that doing so can be rational in a number of circumstances. If expected utility theory is the correct account of practical rationality, then having faith can be both epistemically and practically rational if the costs associated with gathering further evidence or postponing the decision are high. If a more permissive framework is adopted, then having faith can be rational even when there are no costs associated with gathering further evidence

Comment: A great paper for an intermediate philosophy of religion course, especially because many arguments from students are to the contrary: it’s irrational to believe in God when we don’t have satisfactory evidence. It could be nice to set up a debate centering around this paper. It could work particularly well towards the end of the course.

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Buchak, Lara, , . Rational Faith and Justified Belief
2014, in Laura Frances Callahan & Timothy O’Connor (eds.) Reigious Faith and Intellectual Virtue. Oxford University Press: 49-73.
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Added by: Emily Paul, Contributed by:

Abstract: In ‘Can it be rational to have faith?’, it was argued that to have faith in some proposition consists, roughly speaking, in stopping one’s search for evidence and committing to act on that proposition without further evidence. That paper also outlined when and why stopping the search for evidence and acting is rationally required. Because the framework of that paper was that of formal decision theory, it primarily considered the relationship between faith and degrees of belief, rather than between faith and belief full stop. This paper explores the relationship between rational faith and justified belief, by considering four prominent proposals about the relationship between belief and degrees of belief, and by examining what follows about faith and belief according to each of these proposals. It is argued that we cannot reach consensus concerning the relationship between faith and belief at present because of the more general epistemological lack of consensus over how belief relates to rationality: in particular, over how belief relates to the degrees of belief it is rational to have given one’s evidence.

Comment: This could be a great paper to set for further reading, with Buchak’s ‘Can it be Rational to Have Faith?’ as a primary reading. If being discussed as a primary reading, it would be good to get very clear on Buchak’s four candidates for the relationship between belief and degrees of belief: perhaps by splitting the room into four groups, and getting each group to discuss one proposal – as well as what follows about the relationship between faith and belief according to that proposal.

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Dizadji-Bahmani, Foad, Frigg, Roman, Hartmann, Stephan. Confirmation and reduction: A bayesian account
2011, Synthese,79(2): 321-338.
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Added by: Laura Jimenez, Contributed by:

Abstract: Various scientific theories stand in a reductive relation to each other. In a recent article, the authors argue that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, they present a Bayesian analysis of how GNS impacts on confirmation. They formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. They ask when a purported reduction should be accepted on epistemic grounds. To do so, they compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence

Comment: This article is an interesting reading for advanced courses in philosophy of science or logic. It could serve as further reading for modules focused on Bayesian networks, reduction or confirmation. Previous knowledge of bayesianism is required for understanding the article. No previous knowledge of thermodynamics is needed.

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Emery, Nina, , . Chance, Possibility and explanation
2015, The British Journal for the Philosophy of Science 0(2015): 1–64.
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Added by: Laura Jimenez, Contributed by:

Summary: In this paper the author argues against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, she claims, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting a much stronger, and far less attractive, position. Emery suggests an alternative account, according to which chances are probabilities that play a certain explanatory role: they are probabilities that explain associated frequencies.

Comment: This could serve as a secondary reading for those studying metaphysic theories of chance. Previous background in metaphysics is needed. The paper is recommended for postgraduate students.

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Emery, Nina, , . The Metaphysical Consequences of Counterfactual Skepticism
2015, Philosophy and Phenomenological Research 92 (3).
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Added by: Laura Jimenez, Contributed by:

Abstract: A series of recent arguments purport to show that most counterfactuals of the form if A had happened then C would have happened are not true. These arguments pose a challenge to those of us who think that counterfactual discourse is a useful part of ordinary conversation, of philosophical reasoning, and of scientific inquiry. Either we find a way to revise the semantics for counterfactuals in order to avoid these arguments, or we find a way to ensure that the relevant counterfactuals, while not true, are still assertible. In this paper, the author argues that regardless of which of these two strategies we choose, the natural ways of implementing these strategies all share a surprising consequence: they commit us to a particular metaphysical view about chance.

Comment: Really detailed article about counterfactual skepticism and chance pluralism. Could be useful in metaphysics classes, although the paper has consequences for many other fields (eg. philosophy of science). In principle it is recomendable for postgraduate students or senior undergraduate students who are confident enough with the topic

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Eriksson, Lina, , Alan Hájek. What are Degrees of Belief?
2007, Studia Logica 86(2): 185-215.
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Added by: Berta Grimau, Contributed by: Antony Eagle

Probabilism is committed to two theses:
1) Opinion comes in degrees – call them degrees of belief, or credences.
2) The degrees of belief of a rational agent obey the probability calculus.

Correspondingly, a natural way to argue for probabilism is:
i) to give an account of what degrees of belief are, and then
ii) to show that those things should be probabilities, on pain of irrationality.

Most of the action in the literature concerns stage ii). Assuming that stage i) has been adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not.

In this paper, the authors scrutinize the state of play regarding stage i). We critically examine several of the leading accounts of degrees of belief: reducing them to corresponding betting behavior (de Finetti); measuring them by that behavior (Jeffrey); and analyzing them in terms of preferences and their role in decision-making more generally (Ramsey, Lewis, Maher). We argue that the accounts fail, and so they are unfit to subserve arguments for probabilism. We conclude more positively: “degree of belief” should be taken as a primitive concept that forms the basis of our best theory of rational belief and decision: probabilism.

Comment: This paper is accessible to an advanced undergraduate audience in a formal philosophy course, since it provides an overview of the different accounts of the notion of degrees of belief. However, it’s most adequate for graduate level, where it could be used in a formal epistemology course or in a course on the philosophy of probability.

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Galavotti, Maria Carla, , . A Philosophical Introduction to Probability
2005, CSLI Publications
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Added by: Sara Peppe, Contributed by:

Publisher’s Note: Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. ‘A Philosophical Introduction to Probability’ showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace’s ‘classical’ interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability

Comment: Very good article for philosophy of science and philosophy of probability courses. It works perfectly to build basic knowledge on the theme of probability.

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Galavotti, Maria Carla, , . The notion of subjective probability in the works of Ramsey and de Finetti
1991, Theoria 57 (3): 239-259.
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Added by: Sara Peppe, Contributed by:

Introduction: The decade from the mid-twenties to the mid-thirties was undoubtedly the most crucial for the twentieth Century notion of subjective probability. It was in 1926 that Frank Ramsey wrote his essay ‘Truth and probability’, presented at the Moral Science Club in Cambridge and published posthumously in 1931. There he put forward for the first time a definition of probability as degree of belief, that had been anticipated only by E. Borel in 1924, in a review of J. M. Keynes’ Treatise on Ten years after Ramsey’s paper, namely in 1935, Bruno de Finetti gave a series of lectures at the Institut Poincare in Paris, published in 1937 under the title ‘La prévision: ses lois logiques, ses sources subjectives’. In this paper subjective probability, defined in a way analogous to that adopted by Ramsey, was implemented with the notion of exchangeability, that de Finetti had already worked out in 1928- 1930. Exchangeability confers applicability to the notion of subjective probability, and fills the gap between frequency and probability as degree of belief. It was only when these two were tied together that subjectivism could become a full-fledged interpretation of probability and gain credibility among probabilists and statisticians. One can then say that with the publication of ‘La prévision’ the formation process of a subjective notion of probability was completed.

Comment: This article is focused on subjective probability in the works of Ramsey and de Finetti even if the main part of the work is devoted to Ramsey. This text is crucial in order to understand the subjectivist line of thinking.

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Hesse, Mary, , . The Hunt for Scientific Reason
1980, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980: 3-22.
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Added by: Laura Jimenez, Contributed by:

Abstract: The thesis of underdetermination of theory by evidence has led to an opposition between realism and relationism in philosophy of science. Various forms of the thesis are examined, and it is concluded that it is true in at least a weak form that brings realism into doubt. Realists therefore need, among other things, a theory of degrees of confirmation to support rational theory choice. Recent such theories due to Glymour and Friedman are examined, and it is argued that their criterion of “unification” for good theories is better formulated in Bayesian terms. Bayesian confirmation does, however, have consequences that tell against realism. It is concluded that the prospects are dim for scientific realism as usually understood.

Comment: Good article to study in depth the concepts of realism, underdetermination, confirmation and Bayesian theory. It will be most useful for postgraduate students in philosophy of science.

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Ismael, Jenann, , . Raid! Dissolving the Big, Bad Bug
2008, Nous 42 (2): 292–307
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Added by: Simon Fokt, Contributed by: Antony Eagle

Abstract: There’s a long history of discussion of probability in philosophy, but objective chance separated itself off and came into its own as a topic with the advent of a physical theory—quantum mechanics—in which chances play a central, and apparently ineliminable, role. In 1980 David Lewis wrote a paper pointing out that a very broad class of accounts of the nature of chance apparently lead to a contradiction when combined with a principle that expresses the role of chance in guiding belief. There is still no settled agreement on the proper response to the Lewis problem. At the time he wrote the article, Lewis despaired of a solution, but, although he never achieved one that satisfied him completely, by 1994, due to work primarily by Thau and Hall, he had come to think the problem could be disarmed if we fudged a little on the meaning of ‘chance’. I’ll say more about this below. What I’m going to suggest, however, is that the qualification is unnecessary. The problem depends on an assumption that should be rejected, viz., that using information about chance to guide credence requires one to conditionalize on the theory of chance that one is using. I’m going to propose a general recipe for using information about chance to guide belief that does not require conditionalization on a theory of chance at any stage. Lewis’ problem doesn’t arise in this setting.

Comment: A useful summary and positive contribution to the large debate over Lewis’ Principal Principle connecting chance and credence. Useful for a graduate seminar in philosophy of probability or specialised topics in metaphysics and philosophy of physics.

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Millstein, Roberta L., , . Probability in Biology: The Case of Fitness
2016,
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Added by: Barbara Cohn, Contributed by: Anya Plutynski

Abstract: I argue that the propensity interpretation of fitness, properly understood, not only solves the explanatory circularity problem and the mismatch problem, but can also withstand the Pandora’s box full of problems that have been thrown at it. Fitness is the propensity (i.e., probabilistic ability, based on heritable physical traits) for organisms or types of organisms to survive and reproduce in particular environments and in particular populations for a specified number of generations; if greater than one generation, ‘reproduction’ includes descendants of descendants. Fitness values can be described in terms of distributions of propensities to produce varying number of offspring and can be modeled for any number of generations using computer simulations, thus providing both predictive power and a means for comparing the fitness of different phenotypes. Fitness is a causal concept, most notably at the population level, where fitness differences are causally responsible for differences in reproductive success. Relative fitness is ultimately what matters for natural selection.

Comment: I use this in discussions of natural selection and probability in evolution.
[This is a stub entry. Please add your comments to help us expand it]

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Nelkin, Dana, , . The lottery paradox, knowledge and rationality
2000, Philosophical Review: 109 (3): 373-409.
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Added by: Jie Gao, Contributed by:

Summary: The knowledge version of the paradox arises because it appears that we know our lottery ticket (which is not relevantly different from any other) will lose, but we know that one of the tickets sold will win. The rationality version of the paradox arises because it appears that it is rational to believe of each single ticket in, say, a million-ticket lottery that it will not win, and that it is simultaneously rational to believe that one such ticket will win. It seems, then, that we are committed to attributing two rational beliefs to a single agent at a single time, beliefs that, together with a few background assumptions, are inconsistent and can be seen by the agent to be so. This has seemed to many to be a paradoxical result: an agent in possession of two rational beliefs that she sees to be inconsistent. In my paper, I offer a novel solution to the paradox in both its rationality and knowledge versions that emphasizes a special feature of the lottery case, namely, the statistical nature of the evidence available to the agent. On my view, it is neither true that one knows nor that it is rational to believe that a particular ticket will lose. While this might seem surprising at first, it has a natural explanation and lacks the serious disadvantages of competing solutions.

Comment: The lottery paradox is one of the most central paradox in epistemology and philosophy of probability. Nelkin’s paper is a milestone in the literature on this topic after which discussions on the lottery paradox flourish. It is thus a must-have introductory paper on the lottery paradox for teachings on paradoxes of belief, justification theory, rationality, etc.

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Shogenji, Tomoji, , . The Degree of Epistemic Justification and the Conjunction Fallacy
2012, Synthese 184 (1): 29-48.
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Added by: Jie Gao, Contributed by:

Abstract: This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy.

Comment: This interesting paper on epistemic justification requires prerequisite knowledge on formal epistemology. It is hence suitable for an advanced undergraduate course or graduate course on epistemology or formal epistemology.

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