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- Sharon Ryan (1996). The Epistemic Virtues of Consistency. Synthese 109 (2):121-141.The lottery paradox has been discussed widely. The standard solution to the lottery paradox is that a ticket holder is justified in believing each ticket will lose but the ticket holder is also justified in believing not all of the tickets will lose. If the standard solution is true, then we get the paradoxical result that it is possible for a person to have a justified set of beliefs that she knows is inconsistent. In this paper, I argue that the best solution to the paradox is that a ticket holder is not justified in believing any of the tickets are losers. My solution avoids the paradoxical result of the standard solution. The solution I defend has been hastily rejected by other philosophers because it appears to lead to skepticism. I defend my solution from the threat of skepticism and give two arguments in favor of my conclusion that the ticket holder in the original lottery case is not justified in believing that his ticket will lose.Reading list | Discuss | Edit | Categorize |My bibliography
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We commonly speak of people as being ‘‘justified’’ or ‘‘unjustified’’ in believing as they do. These terms describe a person’s epistemic condition. To be justified in believing as one does is to have a positive epistemic status in virtue of holding one’s belief in a way which fully satisfies the relevant epistemic requirements or norms. This requires something more (or other) than simply believing a proposition whose truth is well-supported by evidence, even by evidence which one possesses oneself, since one could entirely miss the relevance of this evidence and hold the belief as a result of wishful thinking or for some other bad reason. My topic in this paper is the notion of being justified which precludes beliefs flawed in this way. I will take the notion of something’s telling in favor of the truth of a proposition—that is, the notion of evidential support—for granted.
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| | Other links: blackwell-synergy.com indiana.edu dx.doi.org | Scholar | At my library | More options ... I argue that the standard Bayesian solution to the ravens paradox— generally accepted as the most successful solution to the paradox—is insufficiently general. I give an instance of the paradox which is not solved by the standard Bayesian solution. I defend a new, more general solution, which is compatible with the Bayesian account of confirmation. As a solution to the paradox, I argue that the ravens hypothesis ought not to be held equivalent to its contrapositive; more interestingly, I argue that how we formally represent hypotheses ought to vary with the context of inquiry. This explains why the paradox is compelling, while dealing with standard objections to holding hypotheses inequivalent to their contrapositives.
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| | Scholar | At my library | More options ... The Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will be defended against a seemingly obvious objection. 1 The paradoxes of rational acceptability 2 The standard solution 3 A new solution to the paradoxes 4 Basic assumptions 5 The new solution defended 6 Conclusion 7 Appendix.
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| | Other links: bjps.oupjournals.org jstor.org dx.doi.org | Scholar | At my library | More options ... The following principles may plausibly be included in a wide range of theories of epistemic justification: (1) There are circumstances in which an agent is justified in believing a falsehood, (2) There are circumstances in which an agent is justified in believing a principle of epistemic justification, (3) Beliefs acquired in compliance with a justifiably-believed epistemic principle are justified. I argue that it follows from these three individually plausible claims that an agent's belief may be both justified and unjustified. I consider how theories may avoid this paradox, and conclude that deontological theories of epistemic justification face considerable, perhaps insurmountable, difficulties.
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| | Other links: blackwell-synergy.com dx.doi.org | Scholar | At my library | More options ... There is widespread agreement that we cannot know of a lottery ticket we own that it is a loser prior to the drawing of the lottery. At the same time we appear to have knowledge of events that will occur only if our ticket is a loser. Supposing any plausible closure principle for knowledge, the foregoing seems to yield a paradox. Appealing to some broadly Gricean insights, the present paper argues that this paradox is apparent only.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no valid reason not to give preference to the derived accounts over the accounts from which they come.
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| | Other links: interscience.wiley.com dx.doi.org | Scholar | At my library | More options ... The lottery paradox can be solved if epistemic justification is assumed to be a species of permissibility. Given this assumption, the starting point of the paradox can be formulated as the claim that, for each lottery ticket, I am permitted to believe that it will lose. This claim is ambiguous between two readings, depending on the scope of ‘permitted’. On one reading, the claim is false; on another, it is true, but, owing to the general failure of permissibility to agglomerate, does not generate the paradox. The solution generalizes to formulations of the paradox in terms of rational acceptability and doxastic rationality.
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| | Other links: analysis.oxfordjournals.org dx.doi.org | Scholar | At my library | More options ... Henry Kyburg’s lottery paradox (1961, p. 197) arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that one ticket will win. Suppose that an event is very likely if the probability of its occurring is greater than 0.99. On these grounds it is presumed rational to accept the proposition that ticket 1 of the lottery will not win. Since the lottery is fair, it is rational to accept that ticket 2 won’t win either—indeed, it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 won’t win, accepting that ticket 2 won’t win, . . . , and accepting that ticket 1000 won’t win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins.
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| | Scholar | At my library | More options ... The four primary epistemic paradoxes are the lottery, preface, knowability, and surprise examination paradoxes. The lottery paradox begins by imagining a fair lottery with a thousand tickets in it. Each ticket is so unlikely to win that we are justified in believing that it will lose.
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| | Scholar | More options ... I am justified in believing that my lottery ticket—call it t1—will not win, on statistical grounds. Those grounds apply equally to any other ticket, so I am justified in believing of any other ticket ti (let i take values from 2 to 1000000) that it will not win. I am not, however, justified in believing the giant conjunctive proposition that t1 will not win & t2 will not win & . . . & t1,000,000 will not win. On the contrary, I am justified in believing that some ticket will win, hence that one of those conjuncts is false. Suggested solution: justified belief is not closed under conjunction. It does not follow from the fact that I am justified in believing p and justified in believing q that I am justified in believing p & q.
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| | Scholar | More options ... Discussion of Sharon Ryan, The epistemic virtues of consistency
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