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The Hardest Paradox for Closure

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  1. The Lottery Paradox, Knowledge, and Rationality.Dana K. Nelkin - 2000 - Philosophical Review 109 (3):373-409.
    Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in its chances (...)
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  • The Normative Role of Knowledge.Declan Smithies - 2012 - Noûs 46 (2):265-288.
    What is the normative role of knowledge? I argue that knowledge plays an important role as a norm of assertion and action, which is explained and unified by its more fundamental role as a norm of belief. Moreover, I propose a distinctive account of what this normative role consists in. I argue that knowledge is the aim of belief, which sets a normative standard of correctness and a corresponding normative standard of justification. According to my proposal, it is correct to (...)
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  • A Survey of Ranking Theory.Wolfgang Spohn - 2009 - In Franz Huber & Christoph Schmidt-Petri (eds.), Degrees of Belief. Springer.
    "A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...)
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  • No Justificatory Closure Without Truth.Francesco Praolini - 2019 - Australasian Journal of Philosophy 97 (4):715-726.
    It is well-known that versions of the lottery paradox and of the preface paradox show that the following three principles are jointly inconsistent: (Sufficiency) very probable propositions are justifiably believable; (Conjunction Closure) justified believability is closed under conjunction introduction; (No Contradictions) propositions known to be contradictory are not justifiably believable. This paper shows that there is a hybrid of the lottery and preface paradoxes that does not require Sufficiency to arise, but only Conjunction Closure and No Contradictions; and it argues (...)
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  • What Else Justification Could Be1.Martin Smith - 2010 - Noûs 44 (1):10-31.
    According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...)
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  • Coming to Terms with Our Human Fallibility: Christensen on the Preface.Mark Kaplan - 2013 - Philosophy and Phenomenological Research 87 (1):1-35.
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  • The Lottery Paradox and Our Epistemic Goal.Igor Douven - 2008 - Pacific Philosophical Quarterly 89 (2):204-225.
    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 (...)
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  • Counterfactuals.David Kellogg Lewis - 1973 - Cambridge, MA, USA: Blackwell.
    Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.
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  • Probability and the Logic of Rational Belief.Henry Ely Kyburg - 1961 - Middletown, CT, USA: Middletown, Conn., Wesleyan University Press.
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  • Putting Logic in its Place: Formal Constraints on Rational Belief.David Phiroze Christensen - 2004 - Oxford, England: Oxford University Press.
    What role, if any, does formal logic play in characterizing epistemically rational belief? Traditionally, belief is seen in a binary way - either one believes a proposition, or one doesn't. Given this picture, it is attractive to impose certain deductive constraints on rational belief: that one's beliefs be logically consistent, and that one believe the logical consequences of one's beliefs. A less popular picture sees belief as a graded phenomenon.
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  • Normalcy, Justification, and the Easy-Defeat Problem.Marvin Backes - 2019 - Philosophical Studies 176 (11):2877-2895.
    Recent years have seen the rise of a new family of non-probabilistic accounts of epistemic justification. According to these views—we may call them Normalcy Views—a belief in P is justified only if, given the evidence, there exists no normal world in which S falsely beliefs that P. This paper aims to raise some trouble for this new approach to justification by arguing that Normalcy Views, while initially attractive, give rise to problematic accounts of epistemic defeat. As we will see, on (...)
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  • A Bitter Pill for Closure.Marvin Backes - 2019 - Synthese 196:3773-3787.
    The primary objective of this paper is to introduce a new epistemic paradox that puts pressure on the claim that justification is closed under multi premise deduction. The first part of the paper will consider two well-known paradoxes—the lottery and the preface paradox—and outline two popular strategies for solving the paradoxes without denying closure. The second part will introduce a new, structurally related, paradox that is immune to these closure-preserving solutions. I will call this paradox, The Paradox of the Pill. (...)
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  • Believing Conjunctions.Simon J. Evnine - 1999 - Synthese 118 (2):201-227.
    I argue that it is rational for a person to believe the conjunction of her beliefs. This involves responding to the Lottery and Preface Paradoxes. In addition, I suggest that in normal circumstances, what it is to believe a conjunction just is to believe its conjuncts.
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  • The Epistemic Virtues of Consistency.Sharon Ryan - 1996 - 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 (...)
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  • Between Probability and Certainty: What Justifies Belief.Martin Smith - 2016 - Oxford University Press UK.
    This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...)
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  • The Laws of Belief: Ranking Theory and its Philosophical Applications.Wolfgang Spohn - 2012 - Oxford University Press.
    Wolfgang Spohn presents the first full account of the dynamic laws of belief, by means of ranking theory. This book is his long-awaited presentation of ranking theory and its ramifications.
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  • No Match Point for the Permissibility Account.Anna-Maria A. Eder - 2015 - Erkenntnis 80 (3):657-673.
    In the literature, one finds two accounts of the normative status of rational belief: the ought account and the permissibility account. Both accounts have their advantages and shortcomings, making it difficult to favour one over the other. Imagine that there were two principles of rational belief or rational degrees of belief commonly considered plausible, but which, however, yielded a paradox together with one account, but not with the other. One of the accounts therefore requires us to give up one of (...)
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  • The Logic of Epistemic Justification.Martin Smith - 2018 - Synthese 195 (9):3857-3875.
    Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...)
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  • This Paper Surely Contains Some Errors.Brian Kim - 2015 - Philosophical Studies 172 (4):1013-1029.
    The preface paradox can be motivated by appealing to a plausible inference from an author’s reasonable assertion that her book is bound to contain errors to the author’s rational belief that her book contains errors. By evaluating and undermining the validity of this inference, I offer a resolution of the paradox. Discussions of the preface paradox have surprisingly failed to note that expressions of fallibility made in prefaces typically employ terms such as surely, undoubtedly, and bound to be. After considering (...)
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  • The Preface Paradox.Sharon Ryan - 1991 - Philosophical Studies 64 (3):293-307.
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  • Without Justification.Jonathan Sutton - 2007 - MIT Press.
    An argument that takes issue with the contemporary epistemological consensus that justification is distinct from knowledge, proposing instead that justified belief simply is knowledge, and arguing in detail that a belief is justified when ...
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  • Justification and the Truth-Connection.Clayton Littlejohn - 2012 - Cambridge University Press.
    The internalism-externalism debate is one of the oldest debates in epistemology. Internalists assert that the justification of our beliefs can only depend on facts internal to us, while externalists insist that justification can depend on additional, for example environmental, factors. Clayton Littlejohn proposes and defends a new strategy for resolving this debate. Focussing on the connections between practical and theoretical reason, he explores the question of whether the priority of the good to the right might be used to defend an (...)
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  • Justification, knowledge, and normality.Clayton Littlejohn & Julien Dutant - 2020 - Philosophical Studies 177 (6):1593-1609.
    There is much to like about the idea that justification should be understood in terms of normality or normic support (Smith 2016, Goodman and Salow 2018). The view does a nice job explaining why we should think that lottery beliefs differ in justificatory status from mundane perceptual or testimonial beliefs. And it seems to do that in a way that is friendly to a broadly internalist approach to justification. In spite of its attractions, we think that the normic support view (...)
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  • Relevance: A Fallacy?John P. Burgess - 1981 - Notre Dame Journal of Formal Logic 22 (2):97-104.
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  • The Paradox of the Preface.David C. Makinson - 1965 - Analysis 25 (6):205.
    By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.
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  • Accuracy, Coherence and Evidence.Branden Fitelson & Kenny Easwaran - 2015 - Oxford Studies in Epistemology 5:61-96.
    Taking Joyce’s (1998; 2009) recent argument(s) for probabilism as our point of departure, we propose a new way of grounding formal, synchronic, epistemic coherence requirements for (opinionated) full belief. Our approach yields principled alternatives to deductive consistency, sheds new light on the preface and lottery paradoxes, and reveals novel conceptual connections between alethic and evidential epistemic norms.
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  • A New Solution to the Paradoxes of Rational Acceptability.Igor Douven - 2002 - British Journal for the Philosophy of Science 53 (3):391-410.
    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 (...)
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  • Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
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  • Justifications, Excuses, and Sceptical Scenarios.Timothy Williamson - forthcoming - In Fabian Dorsch & Julien Dutant (eds.), The New Evil Demon. Oxford: Oxford University Press.
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  • ``The Paradox of the Preface".D. Makinson - 1965 - Analysis 25 (6):205-207.
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  • Change in View.Gilbert Harman - 1986 - Behaviorism 16 (1):93-96.
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  • The Lottery Paradox, Epistemic Justification and Permissibility.Thomas Kroedel - 2012 - Analysis 72 (1):57-60.
    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, (...)
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  • Are There Counterexamples to the Closure Principle.Jonathan Vogel - 1990 - In Michael David Roth & Glenn Ross (eds.), Doubting: Contemporary Perspectives on Skepiticism. Dordrecht: Kluwer Academic Publishers. pp. 13-29.
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