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Are there Counterexamples to the Closure Principle

In Michael David Roth & Glenn Ross (eds.), Doubting: Contemporary Perspetcives on Scepticism. Dordrecht: Kluwer Academic Publishers. pp. 13-29 (1990)

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  1. Judgment & Agency.Ernest Sosa - 2015 - Oxford, GB: Oxford University Press UK.
    Ernest Sosa extends his distinctive approach to epistemology, intertwining issues concerning the role of the will in judgment and belief with issues of epistemic evaluation. Questions about skepticism and the nature of knowledge are at the forefront. The answers defended are new in their explicit and sustained focus on judgment and epistemic agency. While noting that human knowledge trades on distinctive psychological capacities, Sosa also emphasizes the role of the social in human knowledge. Basic animal knowledge is supplemented by a (...)
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  • The Radicalism of Truth‐insensitive Epistemology: Truth's Profound Effect on the Evaluation of Belief.John Turri - 2015 - Philosophy and Phenomenological Research 93 (2):348-367.
    Many philosophers claim that interesting forms of epistemic evaluation are insensitive to truth in a very specific way. Suppose that two possible agents believe the same proposition based on the same evidence. Either both are justified or neither is; either both have good evidence for holding the belief or neither does. This does not change if, on this particular occasion, it turns out that only one of the two agents has a true belief. Epitomizing this line of thought are thought (...)
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  • Western Skeptic vs Indian Realist. Cross-Cultural Differences in Zebra Case Intuitions.Krzysztof Sękowski, Adrian Ziółkowski & Maciej Tarnowski - 2021 - Review of Philosophy and Psychology 14 (2):711-733.
    The cross-cultural differences in epistemic intuitions reported by Weinberg, Nichols and Stich (2001; hereafter: WNS) laid the ground for the negative program of experimental philosophy. However, most of WNS’s findings were not corroborated in further studies. The exception here is the study concerning purported differences between Westerners and Indians in knowledge ascriptions concerning the Zebra Case, which was never properly replicated. Our study replicates the above-mentioned experiment on a considerably larger sample of Westerners (n = 211) and Indians (n = (...)
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  • McDowell on reasons, externalism and scepticism.Duncan Pritchard - 2003 - European Journal of Philosophy 11 (3):273-294.
    At the very least, externalists about content will accept something like the following claim.
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  • Closure, Defeasibility and Conclusive Reasons.Claudio Almeida - 2007 - Acta Analytica 22 (4):301-319.
    It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or epistemic rationality ) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.
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  • Epistemic Disjunctivism and the Evidential Problem.José Zalabardo - 2015 - Analysis 75 (4):615-627.
    I argue that Epistemic Disjunctivism doesn’t sustain a successful anti-sceptical strategy. I contend, in particular, that the treatment of scepticism that Duncan Pritchard puts forward on behalf of Epistemic Disjunctivism is unsatisfactory.
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  • Knowledge, justification, and (a sort of) safe belief.Daniel Whiting - 2020 - Synthese 197 (8):3593-3609.
    An influential proposal is that knowledge involves safe belief. A belief is safe, in the relevant sense, just in case it is true in nearby metaphysically possible worlds. In this paper, I introduce a distinct but complementary notion of safety, understood in terms of epistemically possible worlds. The main aim, in doing so, is to add to the epistemologist’s tool-kit. To demonstrate the usefulness of the tool, I use it to advance and assess substantive proposals concerning knowledge and justification.
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  • Hierarchical Propositions.Bruno Whittle - 2017 - Journal of Philosophical Logic 46 (2):215-231.
    The notion of a proposition is central to philosophy. But it is subject to paradoxes. A natural response is a hierarchical account and, ever since Russell proposed his theory of types in 1908, this has been the strategy of choice. But in this paper I raise a problem for such accounts. While this does not seem to have been recognized before, it would seem to render existing such accounts inadequate. The main purpose of the paper, however, is to provide a (...)
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  • Belief, information and reasoning.Bruno Whittle - 2012 - Philosophical Perspectives 26 (1):431-446.
    Here are two plausible ideas about belief. First: beliefs are our means of storing information. Second: if we believe something, then we are willing to use it in reasoning. But in this paper I introduce a puzzle that seems to show that these cannot both be right. The solution, I argue, is a new picture, on which there is a kind of belief for each idea. An account of these two kinds of belief is offered in terms of two components: (...)
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  • Induction, Normality and Reasoning with Arbitrary Objects.Markos Valaris - 2016 - Ratio 29 (4).
    This paper concerns the apparent fact — discussed by Sinan Dogramaci and Brian Weatherson — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis (...)
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  • Skeptical Appeal: The Source‐Content Bias.John Turri - 2014 - Cognitive Science 38 (5):307-324.
    Radical skepticism is the view that we know nothing or at least next to nothing. Nearly no one actually believes that skepticism is true. Yet it has remained a serious topic of discussion for millennia and it looms large in popular culture. What explains its persistent and widespread appeal? How does the skeptic get us to doubt what we ordinarily take ourselves to know? I present evidence from two experiments that classic skeptical arguments gain potency from an interaction between two (...)
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  • Evidence of factive norms of belief and decision.John Turri - 2015 - Synthese 192 (12):4009-4030.
    According to factive accounts of the norm of belief and decision-making, you should not believe or base decisions on a falsehood. Even when the evidence misleadingly suggests that a false proposition is true, you should not believe it or base decisions on it. Critics claim that factive accounts are counterintuitive and badly mischaracterize our ordinary practice of evaluating beliefs and decisions. This paper reports four experiments that rigorously test the critic’s accusations and the viability of factive accounts. The results undermine (...)
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  • Descartes’s Schism, Locke’s Reunion: Completing the Pragmatic Turn in Epistemology.John Turri & Wesley Buckwalter - 2017 - American Philosophical Quarterly 54 (1):25-46.
    Centuries ago, Descartes and Locke initiated a foundational debate in epistemology over the relationship between knowledge, on the one hand, and practical factors, on the other. Descartes claimed that knowledge and practice are fundamentally separate. Locke claimed that knowledge and practice are fundamentally united. After a period of dormancy, their disagreement has reignited on the contemporary scene. Latter-day Lockeans claim that knowledge itself is essentially connected to, and perhaps even constituted by, practical factors such as how much is at stake, (...)
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  • A New Paradigm for Epistemology From Reliabilism to Abilism.John Turri - 2016 - Ergo: An Open Access Journal of Philosophy 3.
    Contemporary philosophers nearly unanimously endorse knowledge reliabilism, the view that knowledge must be reliably produced. Leading reliabilists have suggested that reliabilism draws support from patterns in ordinary judgments and intuitions about knowledge, luck, reliability, and counterfactuals. That is, they have suggested a proto-reliabilist hypothesis about “commonsense” or “folk” epistemology. This paper reports nine experimental studies (N = 1262) that test the proto-reliabilist hypothesis by testing four of its principal implications. The main findings are that (a) commonsense fully embraces the possibility (...)
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  • Beliefs, buses and lotteries: Why rational belief can’t be stably high credence.Julia Staffel - 2016 - Philosophical Studies 173 (7):1721-1734.
    Until recently, it seemed like no theory about the relationship between rational credence and rational outright belief could reconcile three independently plausible assumptions: that our beliefs should be logically consistent, that our degrees of belief should be probabilistic, and that a rational agent believes something just in case she is sufficiently confident in it. Recently a new formal framework has been proposed that can accommodate these three assumptions, which is known as “the stability theory of belief” or “high probability cores.” (...)
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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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  • When Does Evidence Suffice for Conviction?Martin Smith - 2018 - Mind 127 (508):1193-1218.
    There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of statistical frequency. (...)
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  • The Hardest Paradox for Closure.Martin Smith - 2022 - Erkenntnis 87 (4):2003-2028.
    According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...)
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  • Two accounts of assertion.Martin Smith - 2022 - Synthese 200 (3):1-18.
    In this paper I will compare two competing accounts of assertion: the knowledge account and the justified belief account. When it comes to the evidence that is typically used to assess accounts of assertion – including the evidence from lottery propositions, the evidence from Moore’s paradoxical propositions and the evidence from conversational patterns – I will argue that the justified belief account has at least as much explanatory power as its rival. I will argue, finally, that a close look at (...)
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  • Knowledge, Justification and Normative Coincidence1.Martin Smith - 2014 - Philosophy and Phenomenological Research 89 (2):273-295.
    Say that two goals are normatively coincident just in case one cannot aim for one goal without automatically aiming for the other. While knowledge and justification are distinct epistemic goals, with distinct achievement conditions, this paper begins from the suggestion that they are nevertheless normatively coincident—aiming for knowledge and aiming for justification are one and the same activity. A number of surprising consequences follow from this—both specific consequences about how we can ascribe knowledge and justification in lottery cases and more (...)
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  • Knowledge and lotteries.Donald Smith - 2005 - Philosophical Books 46 (2):123-131.
    John Hawthorne’s recent monograph Knowledge and Lotteries1 is centred on the following puzzle: Suppose you claim to know that you will not be able to afford to summer in the Hamptons next year. Aware of your modest means, we believe you. But suppose you also claim to know that a ticket you recently purchased in a multi-million dollar lottery is a loser. Most of us have the intuition that you do not know that your ticket is a loser. However, your (...)
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  • Accuracy Across Doxastic Attitudes: Recent Work on the Accuracy of Belief.Robert Weston Siscoe - 2022 - American Philosophical Quarterly 59 (2):201-217.
    James Joyce's article “A Nonpragmatic Vindication of Probabilism” introduced an approach to arguing for credal norms by appealing to the epistemic value of accuracy. The central thought was that credences ought to accurately represent the world, a guiding thought that has gone on to generate an entire research paradigm on the rationality of credences. Recently, a number of epistemologists have begun to apply this same thought to full beliefs, attempting to explain and argue for norms of belief in terms of (...)
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  • Transmission Failure Failure.Nicholas Silins - 2005 - Philosophical Studies 126 (1):71-102.
    I set out the standard view about alleged examples of failure of transmission of warrant, respond to two cases for the view, and argue that the view is false. The first argument for the view neglects the distinction between believing a proposition on the basis of a justification and merely having a justification to believe a proposition. The second argument for the view neglects the position that one's justification for believing a conclusion can be one's premise for the conclusion, rather (...)
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  • Evidence and the openness of knowledge.Assaf Sharon & Levi Spectre - 2017 - Philosophical Studies 174 (4):1001-1037.
    The paper argues that knowledge is not closed under logical inference. The argument proceeds from the openness of evidential support and the dependence of empirical knowledge on evidence, to the conclusion that knowledge is open. Without attempting to provide a full-fledged theory of evidence, we show that on the modest assumption that evidence cannot support both a proposition and its negation, or, alternatively, that information that reduces the probability of a proposition cannot constitute evidence for its truth, the relation of (...)
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  • Rational Self-Doubt and the Failure of Closure.Joshua Schechter - 2013 - Philosophical Studies 163 (2):428-452.
    Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...)
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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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  • A Puzzle about Knowing Conditionals.Daniel Rothschild & Levi Spectre - 2018 - Noûs 52 (2):473-478.
    We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...)
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  • 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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  • Assertibility and Sensitivity.Geoff Pynn - 2014 - Acta Analytica 29 (1):99-117.
    Epistemologists have proposed various norms of assertion to explain when a speaker is in an epistemic position to assert a proposition. In this article I propose a distinct necessary condition on assertibility: that a speaker should assert only what she sensitively believes, where a subject's belief is sensitive just in case the subject would not hold it if it were false. I argue that the Sensitivity Rule underwrites simple explanations for three key features of assertibility that pose explanatory challenges to (...)
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  • The skeptic and the dogmatist.James Pryor - 2000 - Noûs 34 (4):517–549.
    Consider the skeptic about the external world. Let’s straightaway concede to such a skeptic that perception gives us no conclusive or certain knowledge about our surroundings. Our perceptual justification for beliefs about our surroundings is always defeasible—there are always possible improvements in our epistemic state which would no longer support those beliefs. Let’s also concede to the skeptic that it’s metaphysically possible for us to have all the experiences we’re now having while all those experiences are false. Some philosophers dispute (...)
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  • Highlights of recent epistemology.James Pryor - 2001 - British Journal for the Philosophy of Science 52 (1):95--124.
    This article surveys work in epistemology since the mid-1980s. It focuses on contextualism about knowledge attributions, modest forms of foundationalism, and the internalism/externalism debate and its connections to the ethics of belief.
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  • Have a Cake and Eat it Too: Identifying a Missing Link in the Skeptical Puzzle.Nenad Popovic - 2019 - Philosophia 47 (5):1539-1546.
    The skeptical puzzle consists of three allegedly incompatible claims: S knows that O, S doesn’t know that ~U, and the claim that knowledge is closed under the known entailment. I consider several famous instances of the puzzle and conclude that in all of those cases the presupposition that O entails ~U is false. I also consider two possible ways for trying to make it true and argue that both strategies ultimate fail. I conclude that this result at least completely discredits (...)
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  • Denying knowledge.Esben Nedenskov Petersen - 2014 - Canadian Journal of Philosophy 44 (1):36-55.
    Intuitions about contextualist cases such as Cohen’s airport case pose a problem for classical anti-skeptical versions of invariantism. Recently, Tim Black, Jessica Brown, and Patrick Rysiew have argued that the classical invariantist can respond by arguing that pragmatic aspects of epistemic discourse are responsible for the relevant problematic intuitions. This paper identifies the mechanisms of conversational implicature and impliciture as the basic sources of hope for this explanatory strategy. It then argues that neither of these sources provides the classical invariantist (...)
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  • Lay Denial of Knowledge for Justified True Beliefs.Jennifer Nagel, Valerie San Juan & Raymond A. Mar - 2013 - Cognition 129 (3):652-661.
    Intuitively, there is a difference between knowledge and mere belief. Contemporary philosophical work on the nature of this difference has focused on scenarios known as “Gettier cases.” Designed as counterexamples to the classical theory that knowledge is justified true belief, these cases feature agents who arrive at true beliefs in ways which seem reasonable or justified, while nevertheless seeming to lack knowledge. Prior empirical investigation of these cases has raised questions about whether lay people generally share philosophers’ intuitions about these (...)
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  • Lotteries, Quasi-Lotteries, and Scepticism.Eugene Mills - 2012 - Australasian Journal of Philosophy 90 (2):335-352.
    I seem to know that I won't experience spaceflight but also that if I win the lottery, then I will take a flight into space. Suppose I competently deduce from these propositions that I won't win the lottery. Competent deduction from known premises seems to yield knowledge of the deduced conclusion. So it seems that I know that I won't win the lottery; but it also seems clear that I don't know this, despite the minuscule probability of my winning (if (...)
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  • Easy Knowledge, Closure Failure, or Skepticism: A Trilemma.Guido Melchior - 2016 - Metaphilosophy 47 (2):214-232.
    This article aims to provide a structural analysis of the problems related to the easy knowledge problem. The easy knowledge problem is well known. If we accept that we can have basic knowledge via a source without having any prior knowledge about the reliability or accuracy of this source, then we can acquire knowledge about the reliability or accuracy of this source too easily via information delivered by the source. Rejecting any kind of basic knowledge, however, leads into an infinite (...)
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  • A modal theory of discrimination.Guido Melchior - 2021 - Synthese 198 (11):10661-10684.
    Discrimination is a central epistemic capacity but typically, theories of discrimination only use discrimination as a vehicle for analyzing knowledge. This paper aims at developing a self-contained theory of discrimination. Internalist theories of discrimination fail since there is no compelling correlation between discriminatory capacities and experiences. Moreover, statistical reliabilist theories are also flawed. Only a modal theory of discrimination is promising. Versions of sensitivity and adherence that take particular alternatives into account provide necessary and sufficient conditions on discrimination. Safety in (...)
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  • Getting Luck Properly Under Control.Rachel McKinnon - 2013 - Metaphilosophy 44 (4):496-511.
    This article proposes a new account of luck and how luck impacts attributions of credit for agents' actions. It proposes an analogy with the expected value of a series of wagers and argues that luck is the difference between actual outcomes and expected value. The upshot of the argument is that when considering the interplay of intention, chance, outcomes, skill, and actions, we ought to be more parsimonious in our attributions of credit when exercising a skill and obtaining successful outcomes, (...)
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  • Believing Things Unknown.Aidan McGlynn - 2011 - Noûs 47 (2):385-407.
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  • Two skeptical arguments or only one?Kevin McCain - 2013 - Philosophical Studies 164 (2):289-300.
    The first step in responding to the challenge of external world skepticism is to get clear on the structure of the skeptic’s argument. The most prominent varieties of skeptical arguments either rely on closure principles or underdetermination principles. The relationship between these two sorts of arguments is contentious. Some argue that these arguments can independently motivate skepticism. Others argue that they are really equivalent. I argue that although these two arguments are distinct, their independence is not as obvious as some (...)
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  • The Easy Argument.Steven Luper - 2007 - Acta Analytica 22 (4):321 - 331.
    Suppose Ted is in an ordinary house in good viewing conditions and believes red, his table is red, entirely because he sees his table and its color; he also believes not-white, it is false that his table is white and illuminated by a red light, because not-white is entailed by red. The following three claims about this table case clash, but each seems plausible: 1. Ted’s epistemic position is strong enough for him to know red. 2. Ted cannot know not-white (...)
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  • The Concept of Testimony.Nicola Mößner - 2007 - In Christoph Jäger & Winfried Löffler (eds.), Epistemology: Contexts, Values, Disagreement. Papers of the 34th International Ludwig Wittgenstein-Symposium in Kirchberg, 2011. The Austrian Ludwig Wittgenstein Society. pp. 207-209.
    Many contributors of the debate about knowledge by testimony concentrate on the problem of justification. In my paper I will stress a different point – the concept of testimony itself. As a starting point I will use the definitional proposal of Jennifer Lackey. She holds that the concept of testimony should be regarded as entailing two aspects – one corresponding to the speaker, the other one to the hearer. I will adopt the assumption that we need to deal with both (...)
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  • The Lottery Paradox, the No-Justification Account, and Taiwan.Kok Yong Lee - 2023 - Episteme 20 (2):459-478.
    To resolve the lottery paradox, the “no-justification account” proposes that one is not justified in believing that one's lottery ticket is a loser. The no-justification account commits to what I call “the Harman-style skepticism”. In reply, proponents of the no-justification account typically downplay the Harman-style skepticism. In this paper, I argue that the no-justification reply to the Harman-style skepticism is untenable. Moreover, I argue that the no-justification account is epistemically ad hoc. My arguments are based on a rather surprising finding (...)
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  • Replies to Leite, Turri, and Gerken.Krista Lawlor - 2015 - Philosophy and Phenomenological Research 90 (1):235-255.
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  • Single premise deduction and risk.Maria Lasonen-Aarnio - 2008 - Philosophical Studies 141 (2):157 - 173.
    It is tempting to think that multi premise closure creates a special class of paradoxes having to do with the accumulation of risks, and that these paradoxes could be escaped by rejecting the principle, while still retaining single premise closure. I argue that single premise deduction is also susceptible to risks. I show that what I take to be the strongest argument for rejecting multi premise closure is also an argument for rejecting single premise closure. Because of the symmetry between (...)
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  • Relativism, sceptical paradox, and semantic blindness.Dirk Kindermann - 2013 - Philosophical Studies 162 (3):585-603.
    Abstract Relativism about knowledge attributions is the view that a single occurrence of ‘S knows [does not know] that p’ may be true as assessed in one context and false as assessed in another context. It has been argued that relativism is equipped to accommodate all the data from speakers’ use of ‘know’ without recourse to an error theory. This is supposed to be relativism’s main advantage over contextualist and invariantist views. This paper argues that relativism does require the attribution (...)
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  • No way to WAM.Dirk Kindermann - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (7):775-788.
    ABSTRACT Many epistemologists explain the empirically attested contextual variation in knowledge ascriptions by appeal to a kind of warranted assertability maneuver that finds the locus of variability in epistemic norms of assertion. I show that this way to WAM fails. It cannot explain the variability of embedded uses of knowledge sentences in assertoric speech acts in which the knowledge sentences are not themselves asserted.
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  • Common sense as evidence: Against revisionary ontology and skepticism.Thomas Kelly - 2008 - Midwest Studies in Philosophy 32 (1):53-78.
    In this age of post-Moorean modesty, many of us are inclined to doubt that philosophy is in possession of arguments that might genuinely serve to undermine what we ordinarily believe. It may perhaps be conceded that the arguments of the skeptic appear to be utterly compelling; but the Mooreans among us will hold that the very plausibility of our ordinary beliefs is reason enough for supposing that there must be something wrong in the skeptic’s arguments, even if we are unable (...)
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  • Internalism and the Generality Problem.Masashi Kasaki - 2012 - Kagaku Tetsugaku 45 (2):83-98.
    The generality problem is usually taken to arise only for externalist theories of knowledge or justification. In this paper, first, I argue that even internalist theories run afoul of a variant of the generality problem. This is because S may have multiple pieces of evidence concerning the reliability of the token process by which S forms the belief in question, and they determine the degree of Sʼs internalist justification differently. Second, I offer a solution to the generality problem for internalist (...)
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  • Skepticism, Information, and Closure: Dretske’s Theory of Knowledge.Christoph Jäger - 2004 - Erkenntnis 61 (2-3):187 - 201.
    According to Fred Dretske's externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretske's epistemology is his denial that knowledge is closed under known entailment. I argue that, given Dretske's construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. Hence, if it is true (...)
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