Results for 'Being in a position to know '

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  1. Being in a Position to Know and Closure.Jan Heylen - 2016 - Thought: A Journal of Philosophy 5 (1):63-67.
    The focus of this article is the question whether the notion of being in a position to know is closed under modus ponens. The question is answered negatively.
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  2. Being in a Position to Know is the Norm of Assertion.Christopher Willard-Kyle - 2020 - Pacific Philosophical Quarterly 101 (2):328-352.
    This paper defends a new norm of assertion: Assert that p only if you are in a position to know that p. We test the norm by judging its performance in explaining three phenomena that appear jointly inexplicable at first: Moorean paradoxes, lottery propositions, and selfless assertions. The norm succeeds by tethering unassertability to unknowability while untethering belief from assertion. The PtK‐norm foregrounds the public nature of assertion as a practice that can be other‐regarding, allowing asserters to act (...)
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  3. The Importance of Being in a Position to Know.Mark Schroeder - 2020 - Philosophy and Phenomenological Research 100 (2):457-462.
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  4. Rosenkranz’s Logic of Justification and Unprovability.Jan Heylen - 2020 - Journal of Philosophical Logic 49 (6):1243-1256.
    Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know, 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that (...)
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  5. Sensitivity has Multiple Heterogeneity Problems: a Reply to Wallbridge.Guido Melchior - 2017 - Philosophia 45 (4):1741-1747.
    In this paper, I defend the heterogeneity problem for sensitivity accounts of knowledge against an objection that has been recently proposed by Wallbridge in Philosophia. I argue in, 479–496, 2015) that sensitivity accounts of knowledge face a heterogeneity problem when it comes to higher-level knowledge about the truth of one’s own beliefs. Beliefs in weaker higher-level propositions are insensitive, but beliefs in stronger higher-level propositions are sensitive. The resulting picture that we can know the stronger propositions without being (...)
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  6. 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 (...)
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  7. It Can Be Irrational to Knowingly Choose the Best.J. Dmitri Gallow - forthcoming - Australasian Journal of Philosophy.
    Jack Spencer argues we should reject a decision rule called MaxRat because it's incompatible with this principle: If you know that you will choose an option, x, and you know that x is better than every other option available to you, then it is permissible for you to choose x. I agree with Spencer that defenders of MaxRat should reject this principle. However, I disagree insofar as he suggests that he and orthodox causalists are in a position (...)
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  8. How to Include the Severely Disabled in a Contractarian Theory of Justice.Cynthia A. Stark - 2007 - Journal of Political Philosophy 15 (2):127-145.
    This paper argues that, with modification, Rawls's social contract theory can produce principles of distributive justice applying to the severely disabled. It is a response to critics who claim that Rawls's assumption that the parties in the original position represent fully cooperating citizens excludes the disabled from the social contract. I propose that this idealizing assumption should be dropped at the constitutional stage of the contract where the parties decide on a social minimum. Knowing that they might not be (...)
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  9. Reasons Fundamentalism and Rational Uncertainty – Comments on Lord, The Importance of Being Rational.Julia Staffel - 2020 - Philosophy and Phenomenological Research 100 (2):463-468.
    In his new book "The Importance of Being Rational", Errol Lord aims to give a real definition of the property of rationality in terms of normative reasons. If he can do so, his work is an important step towards a defense of ‘reasons fundamentalism’ – the thesis that all complex normative properties can be analyzed in terms of normative reasons. I focus on his analysis of epistemic rationality, which says that your doxastic attitudes are rational just in case they (...)
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  10. Interacting mindreaders.Stephen Andrew Butterfill - 2013 - Philosophical Studies 165 (3):841-863.
    Could interacting mindreaders be in a position to know things which they would be unable to know if they were manifestly passive observers? This paper argues that they could. Mindreading is sometimes reciprocal: the mindreader’s target reciprocates by taking the mindreader as a target for mindreading. The paper explains how such reciprocity can significantly narrow the range of possible interpretations of behaviour where mindreaders are, or appear to be, in a position to interact. A consequence is (...)
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  11. If you don't know that you know, you could be surprised.Eli Pitcovski & Levi Spectre - 2021 - Noûs 55 (4):917-934.
    Before the semester begins, a teacher tells his students: “There will be exactly one exam this semester. It will not take place on a day that is an immediate-successor of a day that you are currently in a position to know is not the exam-day”. Both the students and the teacher know – it is common knowledge – that no exam can be given on the first day of the semester. Since the teacher is truthful and reliable, (...)
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  12. Kumārila Bhaṭṭa and Pārthasārathi Miśra on First- and Higher-Order Knowing.Malcolm Keating - 2022 - Philosophy East and West 72 (2):396-414.
    According to the seventh-century C.E. philosopher Kumārila Bhat.t.a, epistemic agents are warranted in taking their world-presenting experiences as veridical, if they lack defeaters. For him, these experiences are defeasibly sources of knowledge without the agent reflecting on their content or investigating their causal origins. This position is known as svatah prāmāṇya in Sanskrit (henceforth the SP principle). -/- As explicated by the eleventh-century commentator, Pārthasārathi Misŕa, this position entails that epistemic agents know things without simultaneously knowing that (...)
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  13. Surprising Suspensions: The Epistemic Value of Being Ignorant.Christopher Willard-Kyle - 2021 - Dissertation, Rutgers University - New Brunswick
    Knowledge is good, ignorance is bad. So it seems, anyway. But in this dissertation, I argue that some ignorance is epistemically valuable. Sometimes, we should suspend judgment even though by believing we would achieve knowledge. In this apology for ignorance (ignorance, that is, of a certain kind), I defend the following four theses: 1) Sometimes, we should continue inquiry in ignorance, even though we are in a position to know the answer, in order to achieve more than mere (...)
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  14. What It's Like To Have a Cognitive Home.Matt Duncan - 2018 - European Journal of Philosophy 26 (1):66-81.
    Many people believe that the mind is an epistemic refuge of sorts. The idea is that when it comes to certain core mental states, one’s being in such a state automatically puts one in a position to know that one is in that state. This idea has come under attack in recent years. One particularly influential attack comes from Timothy Williamson (2000), who argues that there is no central core of states or conditions—mental or otherwise—to which we (...)
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  15. Practical conflicts as a problem for epistemic reductionism about practical reasons.Benjamin Kiesewetter & Jan Gertken - 2021 - Philosophy and Phenomenological Research 105 (3):677-686.
    According to epistemic reductionism about practical reasons, facts about practical reasons can be reduced to facts about evidence for ought-judgements. We argue that this view misconstrues practical conflicts. At least some conflicts between practical reasons put us in a position to know that an action ϕ is optional, i.e. that we neither ought to perform nor ought to refrain from performing the action. By understanding conflicts of practical reasons as conflicts of evidence about what one ought to do, (...)
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  16. From Standpoint Epistemology to Epistemic Oppression.Briana Toole - 2019 - Hypatia 34 (4):598-618.
    Standpoint epistemology is committed to a cluster of views that pays special attention to the role of social identity in knowledge‐acquisition. Of particular interest here is the situated knowledge thesis. This thesis holds that for certain propositions p, whether an epistemic agent is in a position to know that p depends on some nonepistemic facts related to the epistemic agent's social identity. In this article, I examine two possible ways to interpret this thesis. My first goal here is (...)
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  17. Assertion and the semantics of force-markers.Manuel Garcia-Carpintero - 2004 - In Claudia Bianchi (ed.), the semantics/pragmatics distinction. CSLI. pp. 133--166.
    In recent work, Williamson has defended a suggestive account of assertion. Williamson claims that the following norm or rule (the knowledge rule) is constitutive of assertion, and individuates it: (KR) One must ((assert p) only if one knows p) Williamson is not directly concerned with the semantics of assertion-markers, although he assumes that his view has implications for such an undertaking; he says: “in natural languages, the default use of declarative sentences is to make assertions” (op. cit., 258). In this (...)
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  18. Transparent Vessels?: What Organ Donors Should Be Allowed to Know about Their Recipients.Richard H. Dees - 2013 - Journal of Law, Medicine and Ethics 41 (1):323-332.
    After a long search, Jonathan has finally found someone willing to donate a kidney to him and thereby free him from dialysis. Meredith is Jonathan's second cousin, and she considers herself a generous person, so although she barely knows Jonathan, she is willing to help. However, as Meredith learns more about the donation process, she begins to ask questions about Jonathan: “Is he HIV positive? I heard he got it using drugs. Has he been in jail? He's already had one (...)
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  19. Coherence and Knowability.Luis Rosa - 2022 - The Philosophical Quarterly 72 (4):960-978.
    Why should we avoid incoherence? An influential view tells us that incoherent combinations of attitudes are such that it is impossible for all of those attitudes to be simultaneously vindicated by the evidence. But it is not clear whether this view successfully explains what is wrong with certain akratic doxastic states. In this paper I flesh out an alternative response to that question, one according to which the problem with incoherent combinations of attitudes is that it is impossible for all (...)
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  20. Possessing reasons: why the awareness-first approach is better than the knowledge-first approach.Paul Silva - 2021 - Synthese 199 (1-2):2925-2947.
    [Significantly updated in Chapter 6 of Awareness and the Substructure of Knowledge] In order for a reason to justify an action or attitude it must be one that is possessed by an agent. Knowledge-centric views of possession ground our possession of reasons, at least partially, either in our knowledge of them or in our being in a position to know them. On virtually all accounts, knowing P is some kind of non-accidental true belief that P. This entails (...)
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  21. A Realistic Argument for Scientific Realism: How to be a Realist Without Really Knowing It.Samuel Kahn - 2020 - Philosophia 48 (5):1901-1914.
    In this paper I provide a novel argument for scientific realism. In contrast to most recent defenses of SR, my defense of SR does not rely on the no-miracles argument. Instead, I take a more unconventional approach: I focus on the different kinds of justification available to different individuals in relation to different kinds of propositions. I maintain that this alternative focus shows that most people are warranted in believing many propositions about unobservables. The paper is divided into three main (...)
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  22. Justification as ignorance and epistemic Geach principles.Julien Dutant - 2022 - Asian Journal of Philosophy 1 (1):1-7.
    Sven Rosenkranz’s Justification as Ignorance shows how a strongly internalist conception of justification can be derived from a strongly externalist conception of knowledge, given an identification of justification with second-order ignorance and a set of structural principles concerning knowing and being in a position to know. Among these principles is an epistemic analogue of the Geach modal schema which states that one is always in a position to know that one doesn’t know p or (...)
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  23. Luminous margins.Brian Weatherson - 2004 - Australasian Journal of Philosophy 82 (3):373 – 383.
    Timothy Williamson has recently argued that few mental states are luminous , meaning that to be in that state is to be in a position to know that you are in the state. His argument rests on the plausible principle that beliefs only count as knowledge if they are safely true. That is, any belief that could easily have been false is not a piece of knowledge. I argue that the form of the safety rule Williamson uses is (...)
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  24. Epistemic characterizations of validity and level-bridging principles.Joshua Schechter - 2024 - Philosophical Studies 181 (1):153-178.
    How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to (...)
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  25. A puzzle about enkratic reasoning.Jonathan Way - 2020 - Philosophical Studies 178 (10):3177-3196.
    Enkratic reasoning—reasoning from believing that you ought to do something to an intention to do that thing—seems good. But there is a puzzle about how it could be. Good reasoning preserves correctness, other things equal. But enkratic reasoning does not preserve correctness. This is because what you ought to do depends on your epistemic position, but what it is correct to intend does not. In this paper, I motivate these claims and thus show that there is a puzzle. I (...)
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  26. The Knowledge Norm of Belief.Zachary Mitchell Swindlehurst - 2020 - Thought: A Journal of Philosophy 9 (1):43-50.
    Doxastic normativism is the thesis that norms are constitutive of or essential to belief, such that no mental state not subject to those norms counts as a belief. A common normativist view is that belief is essentially governed by a norm of truth. According to Krister Bykvist and Anandi Hattiangadi, truth norms for belief cannot be formulated without unpalatable consequences: they are either false or they impose unsatisfiable requirements on believers. I propose that we construe the fundamental norm of belief (...)
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  27. An epistemic modal norm of practical reasoning.Tim Henning - 2021 - Synthese 199 (3-4):6665-6686.
    When are you in a position to rely on p in practical reasoning? Existing accounts say that you must know that p, or be in a position to know that p, or be justified in believing that p, or be in a position to justifiably believe it, and so on. This paper argues that all of these proposals face important problems, which I call the Problems of Negative Bootstrapping and of Level Confusions. I offer a (...)
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  28. Modal Epistemology.Juhani Yli-Vakkuri & John Hawthorne - manuscript
    Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.
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  29. Kumārila and Knows-Knows.Daniel Immerman - 2018 - Philosophy East and West 68 (2):408-422.
    This essay defends a principle that promises to help illuminate the nature of reflective knowledge. The principle in question belongs to a broader category called knows-knows principles, or KK principles for short. Such principles say that if you know some proposition, then you're in a position to know that you know it.KK principles were prominent among various historical philosophers and can be fruitfully integrated with many views in contemporary epistemology and beyond—and yet almost every contemporary analytic (...)
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  30. The contingent a priori and the publicity of a priori knowledge.Daniel Z. Korman - 2010 - Philosophical Studies 149 (3):387 - 393.
    Kripke maintains that one who stipulatively introduces the term ' one meter' as a rigid designator for the length of a certain stick s at time t is in a position to know a priori that if s exists at t then the length of s at t is one meter. Some (e.g., Soames 2003) have objected to this alleged instance of the contingent a priori on the grounds that the stipulator's knowledge would have to be based in (...)
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  31. (1 other version)Knowledgeably Responding to Reasons.Joseph Cunningham - 2017 - Erkenntnis 85 (3):673-692.
    Jennifer Hornsby has defended the Reasons-Knowledge Thesis : the claim that \-ing because p requires knowing that p, where the ‘because’ at issue is a rationalising ‘because’. She defends by appeal to the thought that it provides the best explanation of why the subject in a certain sort of Gettier case fails to be in a position to \ because p. Dustin Locke and, separately, Nick Hughes, present some modified barn-façade cases which seem to constitute counterexamples to and undermine (...)
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  32. Don’t Be an Ass: Rational Choice and its Limits.Marc Champagne - 2015 - Reason Papers 37 (1):137-147.
    Deliberation is often seen as the site of human freedom, but the binding power of rationality seems to imply that deliberation is, in its own way, a deterministic process. If one knows the starting preferences and circumstances of an agent, then, assuming that the agent is rational and that those preferences and circumstances don’t change, one should be in a position to predict what the agent will decide. However, given that an agent could conceivably confront equally attractive alternatives, it (...)
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  33. Demarginalizing Standpoint Epistemology.Briana Toole - 2022 - Episteme 19 (1):47-65.
    Standpoint epistemology, the view that social identity is relevant to knowledge-acquisition, has been consigned to the margins of mainstream philosophy. In part, this is because the principles of standpoint epistemology are taken to be in opposition to those which guide traditional epistemology. One goal of this paper is to tease out the characterization of traditional epistemology that is at odds with standpoint epistemology. The characterization of traditional epistemology that I put forth is one which endorses the thesis of intellectualism, the (...)
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  34. A Reason to Know.Olof Leffler - 2023 - Journal of Value Inquiry 57 (3):557-575.
    It is often thought that desire-based versions of reasons internalism, according to which our practical reasons depend on what we desire, are committed to denying that we have any categorical reasons. I shall argue, however, that such theories are committed to a universal desire which gives rise to an unexpected categorical reason – a reason to know our surroundings. I will arrive at this conclusion by using Fichte’s argument for thinking that security from unpredictable and powerful forces of nature (...)
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  35. A Guide to Constructive Disagreement.Chris Tucker - manuscript
    Philosophers use disagreement as a way to discover truth. It is constructive. It can lead one to refine one's own position and/or better understand the opposing position. When you are comfortable with the people you disagree with, it can be a fun way to learn. It can even build community. Yet students often see disagreement as divisive. There are winners and losers, and it's not much fun when you are losing. Rarely do students actively use it as a (...)
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  36. Metaethical Experientialism.Andrew Y. Lee - forthcoming - In Geoffrey Lee & Adam Pautz (eds.), The Importance of Being Conscious. Oxford University Press.
    I develop and defend "metaethical experientialism," the thesis that phenomenal facts explain certain kinds of value facts. I argue, for example, that anyone who knows what it’s like to feel extreme pain is in a position to know that that kind of experience is bad. I argue that metaethical experientialism yields genuine counterexamples to the principle that no ethical conclusion can be derived from purely descriptive premises. I also discuss the prospects for a pluralistic metaethics, whereby different metaethical (...)
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  37. The epistemic objection against perdurantism.Emanuele Tullio & Tommaso Soriani - 2024 - Synthese 204 (3):1-20.
    According to Perdurantism, persons are identical to maximal aggregates of appropriately interrelated temporal parts. Within the Perdurantist framework, an epistemic concern arises, targeting the perduring persons’ belief that they are persons, suggesting that, ultimately, they are not in a position to know that they are persons as opposed to temporal parts. Despite the consideration it has received over the years, this concern has not yet been converted into a full-fledged objection. This paper aims to address this gap by (...)
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  38. Defeaters as Indicators of Ignorance.Clayton Litlejohn & Julien Dutant - 2021 - In Jessica Brown & Mona Simion (eds.), Reasons, Justification, and Defeat. Oxford Oxford: Oxford University Press. pp. 223–246.
    In this paper, we propose a new theory of rationality defeat. We propose that defeaters are "indicators of ignorance", evidence that we’re not in a position to know some target proposition. When the evidence that we’re not in a position to know is sufficiently strong and the probability that we can know is too low, it is not rational to believe. We think that this account retains all the virtues of the more familiar approaches that (...)
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  39. Pessimism and procreation.Daniel Pallies - 2023 - Philosophy and Phenomenological Research 108 (3):751-771.
    The pessimistic hypothesis is the hypothesis that life is bad for us, in the sense that we are worse off for having come into existence. Suppose this hypothesis turns out to be correct — existence turns out to be more of a burden than a gift. A natural next thought is that we should stop having children. But I contend that this is a mistake; procreation would often be permissible even if the pessimistic hypothesis turned out to be correct. Roughly, (...)
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  40. Some Thoughts on the JK-Rule1.Martin Smith - 2012 - Noûs 46 (4):791-802.
    In ‘The normative role of knowledge’ (2012), Declan Smithies defends a ‘JK-rule’ for belief: One has justification to believe that P iff one has justification to believe that one is in a position to know that P. Similar claims have been defended by others (Huemer, 2007, Reynolds, forthcoming). In this paper, I shall argue that the JK-rule is false. The standard and familiar way of arguing against putative rules for belief or assertion is, of course, to describe putative (...)
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  41. Abortion and the veil of ignorance: a response to Minehan.Joona Räsänen - 2022 - Journal of Medical Ethics 48 (6):411-412.
    In a recent JME paper, Matthew John Minehan applies John Rawls’ veil of ignorance against Judith Thomson’s famous violinist argument for the permissibility of abortion. Minehan asks readers to ‘imagine that one morning you are back to back in bed with another person. One of you is conscious and the other unconscious. You do not know which one you are’. Since from this position of ignorance, you have an equal chance of being the unconscious violinist and the (...)
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  42. Luminosity Regained.Selim Berker - 2008 - Philosophers' Imprint 8:1-22.
    The linchpin of Williamson (2000)'s radically externalist epistemological program is an argument for the claim that no non-trivial condition is luminous—that no non-trivial condition is such that whenever it obtains, one is in a position to know that it obtains. I argue that Williamson's anti-luminosity argument succeeds only if one assumes that, even in the limit of ideal reflection, the obtaining of the condition in question and one's beliefs about that condition can be radically disjoint from one another. (...)
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  43.  85
    The Dogmatism Puzzle Undone.James Simpson - forthcoming - Analytic Philosophy.
    According to the dogmatism puzzle, for any S and any p, if S knows that p, then she’s entitled to be dogmatic about p, and so disregard any evidence against p, for she knows that (or is in a position to know that) that evidence is misleading. But this seems clearly problematically dogmatic. The standard solution to the dogmatism puzzle involves appealing to the view that acquiring new evidence (even misleading evidence) can undermine one’s knowledge that p. That’s (...)
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  44. Let ‘Let n be such an x’ Be: A Reply to Meléndez Gutiérrez.Tristan Grøtvedt Haze - 2024 - Philosophia 52 (4):1203-1208.
    I defend Haze’s argument against the Breckenridge-Magidor theory of instantial reasoning from an objection by Meléndez Gutiérrez. According to Breckenridge and Magidor, in reasoning like ‘Some x is mortal. Let n be such an x…’, the ‘n’ refers to a particular object but we cannot know which. This surprisingly defensible view poses an obvious threat to widespread notions in the philosophy of language. Haze argues that the theory leads to absurdity in cases like ‘Some x is unreferred-to by any (...)
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  45. The Hard Problem of Access for Epistemological Disjunctivism.Grad Paweł - forthcoming - Episteme:1-20.
    In this paper, I identify the hard problem of access for epistemological disjunctivism (ED): given that perceptual experience E is opaque with respect to its own epistemic properties, subject S is not in a position to know epistemic proposition (i) (that E is factive with respect to empirical proposition p) just by having E and/or reflecting on E. This is the case even if (i) is true. I first motivate the hard problem of access (Section 2) and then (...)
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  46. Does luck exclude knowledge or certainty?Asbjørn Steglich-Petersen - 2020 - Synthese 197 (6):2387-2397.
    A popular account of luck, with a firm basis in common sense, holds that a necessary condition for an event to be lucky, is that it was suitably improbable. It has recently been proposed that this improbability condition is best understood in epistemic terms. Two different versions of this proposal have been advanced. According to my own proposal :361–377, 2010), whether an event is lucky for some agent depends on whether the agent was in a position to know (...)
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  47. An instrumentalist explanation of pragmatic encroachment.Asbjørn Steglich-Petersen - 2024 - Analytic Philosophy 65 (3):374-392.
    Many have found it plausible that practical circumstances can affect whether someone is in a position to know or rationally believe a proposition. For example, whether it is rational for a person to believe that the bank will be open tomorrow can depend not only on the person's evidence but also on how practically important it is for the person not to be wrong about the bank being open tomorrow. This supposed phenomenon is known as “pragmatic encroachment” (...)
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  48. Compensation for Mere Exposure to Risk.Nicole A. Vincent - 2004 - Australian Journal of Legal Philosophy 29:89-101.
    It could be argued that tort law is failing, and arguably an example of this failure is the recent public liability and insurance (‘PL&I’) crisis. A number of solutions have been proposed, but ultimately the chosen solution should address whatever we take to be the cause of this failure. On one account, the PL&I crisis is a result of an unwarranted expansion of the scope of tort law. Proponents of this position sometimes argue that the duty of care owed (...)
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  49. The puzzle of plausible deniability.Andrew Peet - 2024 - Synthese 203 (5):1-20.
    How is it that a speaker _S_ can at once make it obvious to an audience _A_ that she intends to communicate some proposition _p_, and yet at the same time retain plausible deniability with respect to this intention? The answer is that _S_ can bring it about that _A_ has a high justified credence that ‘_S_ intended _p_’ without putting _A_ in a position to know that ‘_S_ intended _p_’. In order to achieve this _S_ has to (...)
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  50. Size and Function.Bruno Whittle - 2018 - Erkenntnis 83 (4):853-873.
    Are there different sizes of infinity? That is, are there infinite sets of different sizes? This is one of the most natural questions that one can ask about the infinite. But it is of course generally taken to be settled by mathematical results, such as Cantor’s theorem, to the effect that there are infinite sets without bijections between them. These results settle the question, given an almost universally accepted principle relating size to the existence of functions. The principle is: for (...)
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