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  1. Bayesians Commit the Gambler's Fallacy.Kevin Dorst - manuscript
    The gambler’s fallacy is the tendency to expect random processes to switch more often than they actually do—for example, to think that after a string of tails, a heads is more likely. It’s often taken to be evidence for irrationality. It isn’t. Rather, it’s to be expected from a group of Bayesians who begin with causal uncertainty, and then observe unbiased data from an (in fact) statistically independent process. Although they converge toward the truth, they do so in an asymmetric (...)
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  2. The Psychology of The Two Envelope Problem.J. S. Markovitch - manuscript
    This article concerns the psychology of the paradoxical Two Envelope Problem. The goal is to find instructive variants of the envelope switching problem that are capable of clear-cut resolution, while still retaining paradoxical features. By relocating the original problem into different contexts involving commutes and playing cards the reader is presented with a succession of resolved paradoxes that reduce the confusion arising from the parent paradox. The goal is to reduce confusion by understanding how we sometimes misread mathematical statements; or, (...)
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  3. Unbounded Expectations and the Shooting Room.Randall McCutcheon - manuscript
    Several treatments of the Shooting Room Paradox have failed to recognize the crucial role played by its involving a number of players unbounded in expectation. We indicate Reflection violations and/or Dutch Book vulnerabilities in extant ``solutions''and show that the paradox does not arise when the expected number of participants is finite; the Shooting Room thus takes its place in the growing list of puzzles that have been shown to require infinite expectation. Recognizing this fact, we conclude that prospects for a (...)
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  4. Indifference, Sample Space, and the Wine/Water Paradox.Marc Burock - unknown - PhilSci Archive.
  5. Just Probabilities.Chad Lee-Stronach - forthcoming - Noûs.
    I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof can be (...)
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  6. Does Non-Measurability Favour Imprecision?Cian Dorr - 2024 - Mind 133 (530):472-503.
    In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, whether a (...)
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  7. The Paradox Paradox Non-Paradox and Conjunction Fallacy Non-Fallacy.Noah Greenstein - 2023 - Australasian Journal of Logic 20 (3):478-489.
    Brock and Glasgow recently introduced a new definition of paradox and argue that this conception of paradox itself leads to paradox, the so-called Paradox Paradox. I show that they beg the questions during the course of their argument, but, more importantly, do so in a philosophically interesting way: it reveals a counterexample to the equivalence between being a logical truth and having a probability of one. This has consequences regarding norms of rationality, undermining the grounds for the Conjunction Fallacy.
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  8. From Art to Information System.Miro Brada - 2021 - AGI Laboratory.
    This insight to art came from chess composition concentrating art in a very dense form. To identify and mathematically assess the uniqueness is the key applicable to other areas eg. computer programming. Maximization of uniqueness is minimization of entropy that coincides as well as goes beyond Information Theory (Shannon, 1948). The reusage of logic as a universal principle to minimize entropy, requires simplified architecture and abstraction. Any structures (e.g. plugins) duplicating or dividing functionality increase entropy and so unreliability (eg. British (...)
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  9. Solving a Paradox of Evidential Equivalence.Cian Dorr, John Hawthorne & Yoaav Isaacs - 2021 - Mind 130 (520):1159–82.
    David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2.
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  10. A puzzle about experts, evidential screening-off and conditionalization.Ittay Nissan-Rozen - 2020 - Episteme 17 (1):64-72.
    I present a puzzle about the epistemic role beliefs about experts' beliefs play in a rational agent's system of beliefs. It is shown that accepting the claim that an expert's degree of belief in a proposition, A, screens off the evidential support another proposition, B, gives to A in case the expert knows and is certain about whether B is true, leads in some cases to highly unintuitive conclusions. I suggest a solution to the puzzle according to which evidential screening (...)
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  11. Uma resposta ao problema do brinco das princesas.Renato Rocha - 2020 - Fundamento: Revista de Pesquisa Em Filosofia 2018 (16):1-6.
    I present in this note an alternative answer to the princesses' earring problem, found in the first chapter of Cezar Augusto Mortari's book "Introdução à Lógica”.
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  12. Rational understanding: toward a probabilistic epistemology of acceptability.Finnur Dellsén - 2019 - Synthese 198 (3):2475-2494.
    To understand something involves some sort of commitment to a set of propositions comprising an account of the understood phenomenon. Some take this commitment to be a species of belief; others, such as Elgin and I, take it to be a kind of cognitive policy. This paper takes a step back from debates about the nature of understanding and asks when this commitment involved in understanding is epistemically appropriate, or ‘acceptable’ in Elgin’s terminology. In particular, appealing to lessons from the (...)
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  13. How to Avoid Maximizing Expected Utility.Bradley Monton - 2019 - Philosophers' Imprint 19.
    The lesson to be learned from the paradoxical St. Petersburg game and Pascal’s Mugging is that there are situations where expected utility maximizers will needlessly end up poor and on death’s door, and hence we should not be expected utility maximizers. Instead, when it comes to decision-making, for possibilities that have very small probabilities of occurring, we should discount those probabilities down to zero, regardless of the utilities associated with those possibilities.
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  14. Influence of Conditionals on Belief Updating.Borut Trpin - 2018 - Dissertation, University of Ljubljana
    This doctoral dissertation investigates what influence indicative conditionals have on belief updating and how learning from conditionals may be modelled in a probabilistic framework. Because the problem is related to the interpretation of conditionals, we first assess different semantics of indicative conditionals. We propose that conditionals should be taken as primary concepts. This allows us to defend a claim that learning a conditional is equivalent to learning that the relevant conditional probability is 1. This implies that learning a conditional can (...)
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  15. Frá skoðunum til trúnaðar og aftur til baka: Yfirlit um bayesíska þekkingarfræði [English title: "From Belief to Credence and Back Again: An Overview of Bayesian Epistemology"].Finnur Dellsén - 2017 - Hugur 28:146-162.
    English abstract: This paper discusses the delicate relationship between traditional epistemology and the increasingly influential probabilistic (or ‘Bayesian’) approach to epistemology. The paper introduces some of the key ideas of probabilistic epistemology, including credences or degrees of belief, Bayes’ theorem, conditionalization, and the Dutch Book argument. The tension between traditional and probabilistic epistemology is brought out by considering the lottery and preface paradoxes as they relate to rational (binary) belief and credence respectively. It is then argued that this tension can (...)
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  16. Explanation, confirmation, and Hempel's paradox.William Roche - 2017 - In Kevin McCain & Ted Poston (eds.), Best Explanations: New Essays on Inference to the Best Explanation. New York, NY: Oxford University Press. pp. 219-241.
    Hempel’s Converse Consequence Condition (CCC), Entailment Condition (EC), and Special Consequence Condition (SCC) have some prima facie plausibility when taken individually. Hempel, though, shows that they have no plausibility when taken together, for together they entail that E confirms H for any propositions E and H. This is “Hempel’s paradox”. It turns out that Hempel’s argument would fail if one or more of CCC, EC, and SCC were modified in terms of explanation. This opens up the possibility that Hempel’s paradox (...)
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  17. Against Deductive Closure.Paul D. Thorn - 2017 - Theoria 83 (2):103-119.
    The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.
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  18. Belief, Credence, and the Preface Paradox.Alex Worsnip - 2016 - Australasian Journal of Philosophy 94 (3):549-562.
    ABSTRACTMany discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is in fact itself a reductive (...)
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  19. Simpson's Paradox and Causality.Prasanta S. Bandyopadhyay, Mark Greenwood, Don Dcruz & Venkata Raghavan - 2015 - American Philosophical Quarterly 52 (1):13-25.
    There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and logic-based (...)
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  20. For Bayesians, Rational Modesty Requires Imprecision.Brian Weatherson - 2015 - Ergo: An Open Access Journal of Philosophy 2.
    Gordon Belot has recently developed a novel argument against Bayesianism. He shows that there is an interesting class of problems that, intuitively, no rational belief forming method is likely to get right. But a Bayesian agent’s credence, before the problem starts, that she will get the problem right has to be 1. This is an implausible kind of immodesty on the part of Bayesians. My aim is to show that while this is a good argument against traditional, precise Bayesians, the (...)
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  21. Giving your knowledge half a chance.Andrew Bacon - 2014 - Philosophical Studies (2):1-25.
    One thousand fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncomfortable for those, like Timothy Williamson, who take these probabilities to play a (...)
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  22. What is the Permissibility Solution a Solution of? -- A Question for Kroedel.Franz Huber - 2014 - Logos and Episteme 5 (3):333-342.
    Kroedel has proposed a new solution, the permissibility solution, to the lottery paradox. The lottery paradox results from the Lockean thesis according to which one ought to believe a proposition just in case one’s degree of belief in it is sufficiently high. The permissibility solution replaces the Lockean thesis by the permissibility thesis according to which one is permitted to believe a proposition if one’s degree of belief in it is sufficiently high. This note shows that the epistemology of belief (...)
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  23. Scepticism, defeasible evidence and entitlement.Daniele Sgaravatti - 2014 - Philosophical Studies 168 (2):439-455.
    The paper starts by describing and clarifying what Williamson calls the consequence fallacy. I show two ways in which one might commit the fallacy. The first, which is rather trivial, involves overlooking background information; the second way, which is the more philosophically interesting, involves overlooking prior probabilities. In the following section, I describe a powerful form of sceptical argument, which is the main topic of the paper, elaborating on previous work by Huemer. The argument attempts to show the impossibility of (...)
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  24. Akaike’s Theorem and weak predictivism in science.Wang-Yen Lee - 2013 - Studies in History and Philosophy of Science Part A 44 (4):594-599.
  25. The Review Paradox: On The Diachronic Costs of Not Closing Rational Belief Under Conjunction.Hannes Leitgeb - 2013 - Noûs 48 (4):781-793.
    We argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions.
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  26. The Doomsday Argument and the Simulation Argument.Peter J. Lewis - 2013 - Synthese 190 (18):4009-4022.
    The Doomsday Argument and the Simulation Argument share certain structural features, and hence are often discussed together. Both are cases where reflecting on one’s location among a set of possibilities yields a counter-intuitive conclusion—in the first case that the end of humankind is closer than you initially thought, and in the second case that it is more likely than you initially thought that you are living in a computer simulation. Indeed, the two arguments do have some structural similarities. But there (...)
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  27. Ultralarge lotteries: Analyzing the Lottery Paradox using non-standard analysis.Sylvia Wenmackers - 2013 - Journal of Applied Logic 11 (4):452-467.
    A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that is intrinsically (...)
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  28. Fair infinite lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
    This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.
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  29. The Sequential Lottery Paradox.I. Douven - 2012 - Analysis 72 (1):55-57.
    The Lottery Paradox is generally thought to point at a conflict between two intuitive principles, to wit, that high probability is sufficient for rational acceptability, and that rational acceptability is closed under logical derivability. Gilbert Harman has offered a solution to the Lottery Paradox that allows one to stick to both of these principles. The solution requires the principle that acceptance licenses conditionalization. The present study shows that adopting this principle alongside the principle that high probability is sufficient for rational (...)
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  30. The Lottery Paradox and the Pragmatics of Belief.Igor Douven - 2012 - Dialectica 66 (3):351-373.
    The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.
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  31. How Serious Is the Paradox of Serious Possibility?Simone Duca & Hannes Leitgeb - 2012 - Mind 121 (481):1-36.
    The so-called Paradox of Serious Possibility is usually regarded as showing that the standard axioms of belief revision do not apply to belief sets that are introspectively closed. In this article we argue to the contrary: we suggest a way of dissolving the Paradox of Serious Possibility so that introspective statements are taken to express propositions in the standard sense, which may thus be proper members of belief sets, and accordingly the normal axioms of belief revision apply to them. Instead (...)
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  32. Rationality and indeterminate probabilities.Alan Hájek & Michael Smithson - 2012 - Synthese 187 (1):33-48.
    We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with our (...)
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  33. Propositional Reasoning that Tracks Probabilistic Reasoning.Hanti Lin & Kevin Kelly - 2012 - Journal of Philosophical Logic 41 (6):957-981.
    This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (T) that is revised to the new propositional belief state B(E) upon receipt of information E. An acceptance rule tracks Bayesian conditioning when B p (E) = B p|E (T), for (...)
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  34. A geo-logical solution to the lottery paradox, with applications to conditional logic.Hanti Lin & Kevin Kelly - 2012 - Synthese 186 (2):531-575.
    We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we (...)
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  35. Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference.David Makinson - 2012 - Synthese 186 (2):511-529.
    We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the (...)
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  36. Infinite Lotteries, Perfectly Thin Darts and Infinitesimals.Alexander R. Pruss - 2012 - Thought: A Journal of Philosophy 1 (2):81-89.
    One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...)
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  37. Rational Feedback.Grant Reaber - 2012 - Philosophical Quarterly 62 (249):797-819.
    Suppose you think that whether you believe some proposition A at some future time t might have a causal influence on whether A is true. For instance, maybe you think a woman can read your mind, and either (1) you think she will snap her fingers shortly after t if and only if you believe at t that she will, or (2) you think she will snap her fingers shortly after t if and only if you don't believe at t (...)
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  38. Fine-tuning and the infrared bull’s-eye.John T. Roberts - 2012 - Philosophical Studies 160 (2):287-303.
    I argue that the standard way of formalizing the fine-tuning argument for design is flawed, and I present an alternative formalization. On the alternative formalization, the existence of life is not treated as the evidence that confirms design; instead it is treated as part of the background knowledge, while the fact that fine tuning is required for life serves as the evidence. I argue that the alternative better captures the informal line of thought that gives the fine-tuning argument its intuitive (...)
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  39. Reconsidering the lessons of the lottery for knowledge and belief.Glenn Ross - 2012 - Philosophical Studies 161 (1):37-46.
    In this paper, I propose that one can have reason to choose a few tickets in a very large lottery and arbitrarily believe of them that they will lose. Such a view fits nicely within portions of Lehrer's theory of rational acceptance. Nonetheless, the reasonability of believing a lottery ticket will lose should not be taken to constitute the kind of justification required in an analysis of knowledge. Moreover, one should not accept what one takes to have a low chance (...)
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  40. Two Problems of Direct Inference.Paul D. Thorn - 2012 - Erkenntnis 76 (3):299-318.
    The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...)
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  41. Explanation through representation, and its limits.Bas Van Fraassen - 2012 - Epistemologia 1:30-46.
    Why-questions and how-possibly-questions are two common forms of explanation request. Answers to the former ones require factual assertions, but the latter ones can be answered by displaying a representation of the targeted phenomenon. However, in an extreme case, a representation could come accompanied by the assertion that it displays the only possible way a phenomenon could develop. Using several historical controversies concerning statistical modeling, it is argued that such cases must inevitably involve tacit or explicit empirical assumptions.
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  42. The argument from divine indifference.Jonathan Weisberg - 2012 - Analysis 72 (4):707-714.
    I argue that the rationale behind the fine-tuning argument for design is self-undermining, refuting the argument’s own premise that fine-tuning is to be expected given design. In (Weisberg 2010) I argued on informal grounds that this premise is unsupported. White (2011) countered that it can be derived from three plausible assumptions. But White’s third assumption is based on a fallacious rationale, and is even objectionable by the design theorist’s own lights. The argument that shows this, the argument from divine indifference, (...)
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  43. Ultralarge and infinite lotteries.Sylvia Wenmackers - 2012 - In B. Van Kerkhove, T. Libert, G. Vanpaemel & P. Marage (eds.), Logic, Philosophy and History of Science in Belgium II (Proceedings of the Young Researchers Days 2010). Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten.
    By exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. We solve the 'adding problems' that occur in these two contexts using a similar strategy, based on non-standard analysis.
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  44. Probability in the Many-Worlds Interpretation of Quantum Mechanics.Lev Vaidman - 2011 - In Yemima Ben-Menahem & Meir Hemmo (eds.), Probability in Physics. Springer. pp. 299--311.
    It is argued that, although in the Many-Worlds Interpretation of quantum mechanics there is no ``probability'' for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: a). A ``sleeping pill'' gedanken experiment which makes correspondence between an illegitimate question: ``What is the probability of an outcome of a quantum measurement?'' with a legitimate question: ``What is the probability that ``I'' am in the world corresponding to that (...)
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  45. The eternal Coin: A puzzle about self-locating conditional credence.Cian Dorr - 2010 - Philosophical Perspectives 24 (1):189-205.
    The Eternal Coin is a fair coin has existed forever, and will exist forever, in a region causally isolated from you. It is tossed every day. How confident should you be that the Coin lands heads today, conditional on (i) the hypothesis that it has landed Heads on every past day, or (ii) the hypothesis that it will land Heads on every future day? I argue for the extremely counterintuitive claim that the correct answer to both questions is 1.
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  46. Probability and Danger.Timothy Williamson - 2009 - Amherst Lecture in Philosophy.
    What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. (...)
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  47. Fallibilism and the Lottery paradox.Baron Reed - 2008 - Proceedings of the Xxii World Congress of Philosophy 53:217-225.
    Any theory of knowledge that is fallibilist—i.e., that allows for one to have knowledge that could have been false or accidentally true—faces the lottery paradox. The paradox arises from the combination of two plausible claims: first, no one can know that one’s lottery ticket will lose prior to learning that it in fact has lost, and, second, the justification one has for the belief that one’s ticket will lose is just as good as the justification one has for paradigmatic instances (...)
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  48. Handbook of Probability Theory with Applications.Tamas Rudas (ed.) - 2008
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  49. Paradoxes of Probability.Nicholas Shackel - 2008 - In Tamas Rudas (ed.), Handbook of Probability Theory with Applications. Thousand Oaks: Sage. pp. 49-66.
    We call something a paradox if it strikes us as peculiar in a certain way, if it strikes us as something that is not simply nonsense, and yet it poses some difficulty in seeing how it could make sense. When we examine paradoxes more closely, we find that for some the peculiarity is relieved and for others it intensifies. Some are peculiar because they jar with how we expect things to go, but the jarring is to do with imprecision and (...)
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  50. Solving the Tacking Problem with Contrast Classes.Jake Chandler - 2007 - British Journal for the Philosophy of Science 58 (3):489-502.
    The traditional Bayesian qualitative account of evidential support (TB) takes assertions of the form 'E evidentially supports H' to affirm the existence of a two-place relation of evidential support between E and H. The analysans given for this relation is $C(H,E) =_{def} Pr(H\arrowvertE) \models Pr(H)$ . Now it is well known that when a hypothesis H entails evidence E, not only is it the case that C(H,E), but it is also the case that C(H&X,E) for any arbitrary X. There is (...)
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