Results for 'second-order belief'

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  1.  84
    Shoemaker on second-order belief.Anthony Brueckner - 1998 - Philosophy and Phenomenological Research 58 (2):361-64.
    In a number of papers, Sydney Shoemaker has argued that first-order belief plus rationality implies second-order belief. This paper is a critical discussion of Shoemaker's argument.
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  2.  13
    Shoemaker on Second-Order Belief.Anthony Brueckner - 1998 - Philosophy and Phenomenological Research 58 (2):361-364.
    In a number of papers, Sydney Shoemaker has argued that first-order belief plus rationality implies second-order belief. This paper is a critical discussion of Shoemaker’s argument.
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  3. Self-Intimation and Second Order Belief.Sydney Shoemaker - 2009 - Erkenntnis 71 (1):35-51.
    The paper defends the view that there is a constitutive relation between believing something and believing that one believes it. This view is supported by the incoherence of affirming something while denying that one believes it, and by the role awareness of the contents one’s belief system plays in the rational regulation of that system. Not all standing beliefs are accompanied by higher-order beliefs that self-ascribe them; those that are so accompanied are ones that are “available” in the (...)
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  4.  69
    Shoemaker on second-order belief and self-deception.Byeong D. Lee - 2002 - Dialogue 41 (2):279-289.
    In a number of papers, Sydney Shoemaker has argued that first-order belief plus rationality implies second-order belief. This paper is a critical discussion of Shoemaker's argument.
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  5.  37
    Second-order probabilities and belief functions.Jonathan Baron - 1987 - Theory and Decision 23 (1):25-36.
  6. Animal Minds: The Possibility of Second-Order Beliefs in Non-Linguistic Animals.Robert W. Lurz - 1998 - Dissertation, Temple University
    I defend the thesis that it is conceptually possible for non-linguistic creatures to possess second-order beliefs--that is, beliefs about their own beliefs and those of others. I defend this thesis against Donald Davidson and Jonathan Bennett who argue that the thesis is false on the grounds that non-linguistic creatures cannot manifest second-order beliefs. In reply, I present a case that I argue shows a non-linguistic creature manifesting second-order beliefs. Also, I examine and criticize two (...)
     
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  7.  85
    Children’s first and second-order false-belief reasoning in a verbal and a low-verbal task.Bart Hollebrandse, Angeliek van Hout & Petra Hendriks - 2014 - Synthese 191 (3).
    We can understand and act upon the beliefs of other people, even when these conflict with our own beliefs. Children’s development of this ability, known as Theory of Mind, typically happens around age 4. Research using a looking-time paradigm, however, established that toddlers at the age of 15 months old pass a non-verbal false-belief task (Onishi and Baillargeon in Science 308:255–258, 2005). This is well before the age at which children pass any of the verbal false-belief tasks. In (...)
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  8. Children's first and second-order false-belief reasoning in a verbal and a low-verbal task.Bart Hollebrandse, Angeliek Hout & Petra Hendriks - 2014 - Synthese 191 (3).
    We can understand and act upon the beliefs of other people, even when these conflict with our own beliefs. Children’s development of this ability, known as Theory of Mind, typically happens around age 4. Research using a looking-time paradigm, however, established that toddlers at the age of 15 months old pass a non-verbal false-belief task (Onishi and Baillargeon in Science 308:255–258, 2005). This is well before the age at which children pass any of the verbal false-belief tasks. In (...)
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  9.  9
    Language and second order thinking (the analysis of false belief task)(jezyk a myslenie drugiego rzedu (analiza testów falszywego przekonania)).Gut Arkadiusz - 2009 - Filozofia Nauki 17 (3 (67)).
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  10.  23
    Being Deceived: Information Asymmetry in SecondOrder False Belief Tasks.Torben Braüner, Patrick Blackburn & Irina Polyanskaya - 2020 - Topics in Cognitive Science 12 (2):504-534.
    Braüner, Blackburn and Polyanskaya relate children’s being deceived to their theory of mind skills. Secondorder false‐belief tasks are often used to test children’s secondorder theory of mind development. The article gives a logical analysis of the reasoning needed to solve four types of secondorder false belief tasks, distinguished on whether a story character is deceived, and on whether the story hinges on facts in the world changing. The principle of inertia plays an (...)
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  11. Five-Year-Olds’ Systematic Errors in Second-Order False Belief Tasks Are Due to First-Order Theory of Mind Strategy Selection: A Computational Modeling Study.Burcu Arslan, Niels A. Taatgen & Rineke Verbrugge - 2017 - Frontiers in Psychology 8.
  12. Language and second order thinking (the analysis of false belief task).Arkadiusz Gut - 2009 - Filozofia Nauki 17 (3):99.
  13.  37
    Second-Order Assessment of Scientific Expert Claims and Sharing Epistemic Burdens in Science Communication.George Kwasi Barimah - forthcoming - Episteme:1-17.
    When laypersons are presented with scientific information which seeks to modify their way of life, they are expected to believe, suspend belief, or reject it. Second-order assessment of scientific experts helps laypersons to make an informed decision in such situations. This is an assessment of the trustworthiness of the person making the scientific claim. In this paper I challenge the optimistic view of Anderson, regarding the ease with which laypersons can perform second-order assessment of experts, (...)
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  14.  25
    A Defense of First and Second-Order Theism: The Limits of Empirical Inquiry and the Rationality of Religious Belief.Charles Taliaferro & Christophe Porot - 2016 - European Journal for Philosophy of Religion 8 (3):213-235.
    We argue that the use of the term “supernatural” is problematic in philosophy of religion in general, and in the contribution by Thornhill-Miller and Millican in particular. We address the disturbing parallel between Hume’s case against the rationality of belief in miracles and his dismissal of reports of racial equality. We do not argue that because Hume was a racist therefore his view against miracles is faulty, but we draw attention to how Hume sets up a framework that, for (...)
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  15.  14
    Second-Order Confidence in Supervaluationism.Jonas Karge - 2023 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 55 (1):43-58.
    Recently, Wilcox (JGPS 51: 65–87, 2020) argued against the so-called wide interval view and in favor of the principle of indifference as the correct response to unspecific evidence. Embedded in a formal model of the beliefs of an agent, the former presupposes imprecise probabilities and the latter numerically precise degrees of belief. His argument is illustrated by a thought experiment that comes with a fundamental intuition. According to Wilcox, the wide interval view is incompatible with this intuition and, thus, (...)
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  16. Second-Order Predication and the Metaphysics of Properties.Andy Egan - 2004 - Australasian Journal of Philosophy 82 (1):48-66.
    Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, (...)
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  17.  16
    Second-Order Predication and the Metaphysics of Properties.F. Jackson & G. Priest - 2004 - Australasian Journal of Philosophy 82 (1):48-66.
    Problems about the accidental properties of properties motivate us--force us, I think--not to identify properties with the sets of their instances. If we identify them instead with functions from worlds to extensions, we get a theory of properties that is neutral with respect to disputes over counterpart theory, and we avoid a problem for Lewis's theory of events. Similar problems about the temporary properties of properties motivate us--though this time they probably don't force us--to give up this theory as well, (...)
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  18. Akrasia, self-control, and second-order desires.Alfred R. Mele - 1992 - Noûs 26 (3):281-302.
    Pristine belief/desire psychology has its limitations. Recognizing this, some have attempted to fill various gaps by adding more of the same, but at higher levels. Thus, for example, second-order desires have been imported into a more stream- lined view to explicate such important notions as freedom of the will, personhood, and valuing. I believe that we need to branch out as well as up, augmenting a familiar 'philosophical psychology' with psychological items that are irreducible to beliefs and (...)
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  19. Fallibilism, Contextualism and SecondOrder Skepticism.Alexander S. Harper - 2010 - Philosophical Investigations 33 (4):339-359.
    Fallibilism is ubiquitous in contemporary epistemology. I argue that a paradox about knowledge, generated by considerations of truth, shows that fallibilism can only deliver knowledge in lucky circumstances. Specifically, since it is possible that we are brains‐in‐vats (BIVs), it is possible that all our beliefs are wrong. Thus, the fallibilist can know neither whether or not we have much knowledge about the world nor whether or not we know any specific proposition, and so the warrant of our knowledge‐claims is much (...)
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  20.  63
    Uncertainty, credal sets and second order probability.Jonas Clausen Mork - 2013 - Synthese 190 (3):353-378.
    The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function (...)
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  21. On the coherence of higher-order beliefs.Stefan Schubert & Erik J. Olsson - 2012 - Southern Journal of Philosophy 50 (1):112-135.
    Let us by ‘first-order beliefs’ mean beliefs about the world, such as the belief that it will rain tomorrow, and by ‘second-order beliefs’ let us mean beliefs about the reliability of first-order, belief-forming processes. In formal epistemology, coherence has been studied, with much ingenuity and precision, for sets of first-order beliefs. However, to the best of our knowledge, sets including second-order beliefs have not yet received serious attention in that literature. In (...)
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  22.  40
    Querying linguistic treebanks with monadic second-order logic in linear time.Stephan Kepser - 2004 - Journal of Logic, Language and Information 13 (4):457-470.
    In recent years large amounts of electronic texts have become available. While the first of these corpora had only a low level of annotation, the more recent ones are annotated with refined syntactic information. To make these rich annotations accessible for linguists, the development of query systems has become an important goal. One of the main difficulties in this task consists in the choice of the right query language, a language which at the same time should be powerful enough to (...)
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  23.  17
    The Epistemic Puzzle of Perception. Conscious Experience, Higher-Order Beliefs, and Reliable Processes.Harmen Ghijsen - 2014 - Dissertation, Ku Leuven
    This thesis mounts an attack against accounts of perceptual justification that attempt to analyze it in terms of evidential justifiers, and has defended the view that perceptual justification should rather be analyzed in terms of non-evidential justification. What matters most to perceptual justification is not a specific sort of evidence, be it experiential evidence or factive evidence, what matters is that the perceptual process from sensory input to belief output is reliable. I argue for this conclusion in the following (...)
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  24.  32
    First-Order Theistic Religion: Intentional Power Beyond Belief.Paul K. Moser - 2017 - European Journal for Philosophy of Religion 9 (3):31-48.
    Diversity and disagreement in the religious beliefs among many religious people seem here to stay, however much they bother some inquirers. Even so, the latter inquirers appear not to be similarly bothered by diversity and disagreement in the scientific beliefs among many scientists. They sometimes propose that we should take religious beliefs to be noncognitive and perhaps even nonontological and noncausal regarding their apparent referents, but they do not propose the same for scientific beliefs. Perhaps they would account for this (...)
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  25. A solution for Russellians to a puzzle about belief.Sean Crawford - 2004 - Analysis 64 (3):223-29.
    According to Russellianism (or Millianism), the two sentences ‘Ralph believes George Eliot is a novelist’ and ‘Ralph believes Mary Ann Evans is a novelist’ cannot diverge in truth-value, since they express the same proposition. The problem for the Russellian (or Millian) is that a puzzle of Kaplan’s seems to show that they can diverge in truth-value and that therefore, since the Russellian holds that they express the same proposition, the Russellian view is contradictory. I argue that the standard Russellian appeal (...)
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  26. Knowledge of Our Own Beliefs.Sherrilyn Roush - 2016 - Philosophy and Phenomenological Research 93 (3):45-69.
    There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and (...)
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  27.  18
    Beliefs’ self-knowledge: an objection to the method of transparency.Javier Vidal - 2019 - Humanities Journal of Valparaiso 14:429-448.
    According to the method of transparency, genuine self-knowledge is the outcome of an inference from world to mind. A. Byrne has developed a theory in which the method of transparency consists in following an epistemic rule in order to form self-verifying second-order beliefs. In this paper, I argue that Byrne’s theory does not establish sufficient conditions for having self-knowledge of first-order beliefs. Examining a case of self-deception, I strive to show that following such a rule might (...)
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  28.  10
    Beliefs’ self-knowledge: an objection to the method of transparency.Javier Vidal - 2019 - Revista de Humanidades de Valparaíso 14:429-448.
    According to the method of transparency, genuine self-knowledge is the outcome of an inference from world to mind. A. Byrne has developed a theory in which the method of transparency consists in following an epistemic rule in order to form self-verifying second-order beliefs. In this paper, I argue that Byrne’s theory does not establish sufficient conditions for having self-knowledge of first-order beliefs. Examining a case of self-deception, I strive to show that following such a rule might (...)
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  29. Second Guessing: A Self-Help Manual.Sherrilyn Roush - 2009 - Episteme 6 (3):251-268.
    I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled (...)
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  30. Naughty beliefs.Andrew Huddleston - 2012 - Philosophical Studies 160 (2):209-222.
    Can a person ever occurrently believe p and yet have the simultaneous, occurrent belief q that this very belief that p is false? Surely not, most would say: that description of a person’s epistemic economy seems to misunderstand the very concept of belief. In this paper I question this orthodox assumption. There are, I suggest, cases where we have a first-order mental state m that involves taking the world to be a certain way, yet although we (...)
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  31. Higher-Order Evidence and the Normativity of Logic.Mattias Skipper - forthcoming - In Scott Stapleford, Kevin McCain & Matthias Steup (eds.), Epistemic Duties: New Arguments, New Angles. Routledge.
    Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential (...)
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  32.  86
    The Order of Public Reason: A Theory of Freedom and Morality in a Diverse and Bounded World.Gerald Gaus - 2010 - New York: Cambridge University Press.
    In this innovative and important work, Gerald Gaus advances a revised and more realistic account of public reason liberalism, showing how, in the midst of fundamental disagreement about values and moral beliefs, we can achieve a moral and political order that treats all as free and equal moral persons. The first part of this work analyzes social morality as a system of authoritative moral rules. Drawing on an earlier generation of moral philosophers such as Kurt Baier and Peter Strawson (...)
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  33. Mental files and belief: A cognitive theory of how children represent belief and its intensionality.Josef Perner, Michael Huemer & Brian Leahy - 2015 - Cognition 145 (C):77-88.
    We provide a cognitive analysis of how children represent belief using mental files. We explain why children who pass the false belief test are not aware of the intensionality of belief. Fifty-one 3½- to 7-year old children were familiarized with a dual object, e.g., a ball that rattles and is described as a rattle. They observed how a puppet agent witnessed the ball being put into box 1. In the agent’s absence the ball was taken from box (...)
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  34.  1
    Rational Belief and Dialetheism.Paolo Bonardi - 2021 - Intercultural Pragmatics 18 (Pragmatics and Philosophy):309-335.
    It is usually maintained that a subject with manifestly contradictory beliefs is irrational. How can we account, then, for the intuitive rationality of dialetheists, who believe that some manifest contradictions are true? My paper aims to answer this question. Its ultimate goal is to determine a characterization of (or rather a constraint for) rational belief approvable by both the theorists of Dialetheism and its opponents. In order to achieve this goal, a two-step strategy will be adopted. First, a (...)
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  35. Pragmatic Interests and Imprecise Belief.Brad Armendt - 2013 - Philosophy of Science 80 (5):758-768.
    Does the strength of a particular belief depend upon the significance we attach to it? Do we move from one context to another, remaining in the same doxastic state concerning p yet holding a stronger belief that p in one context than in the other? For that to be so, a doxastic state must have a certain sort of context-sensitive complexity. So the question is about the nature of belief states, as we understand them, or as we (...)
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  36.  62
    Justified and Justifiable Beliefs: The Case of Question-Begging.Juho Ritola - 2006 - Philosophical Studies 128 (3):565-583.
    This paper discusses Lippert-Rasmussen’s [Philosophical Studies 104, (2001) 123–141] claim that there are reasonable question-begging arguments. It is first argued that his arguments devalue the distinction between justifiable and justified beliefs, a distinction that is important for the fallacy theory. Second, it is argued that the role of the argument in the discussed cases can be questioned. In addition, the role of second order beliefs is discussed.
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  37.  21
    Religious Belief and Self‐Deception.Adèle Mercier - 2009-09-10 - In Russell Blackford & Udo Schüklenk (eds.), 50 Voices of Disbelief. Wiley‐Blackwell. pp. 41–47.
  38. Moore's paradox and the structure of conscious belief.Uriah Kriegel - 2004 - Erkenntnis 61 (1):99-121.
    Propositions such as are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore’s paradox. Sydney Shoemaker has recently ar- gued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker’s own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account is the (...)
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  39.  21
    Beliefs, make-beliefs, and making believe that beliefs are not make-beliefs.Alberto Voltolini - 2021 - Synthese 199 (1-2):5061-5078.
    In this paper I want to hold, first, that one may suitably reconstruct the relevant kind of mental representational states that fiction typically involves, make-beliefs, as contextually unreal beliefs that, outside fiction, are either matched or non-matched by contextually real beliefs. Yet moreover, I want to claim that the kind of make-believe that may yield the mark of fictionality is not Kendall Walton’s invitation or prescription to imagine. Indeed, in order to appeal in terms of make-believe to a specific (...)
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  40. Is higher-order evidence evidence?Eyal Tal - 2020 - Philosophical Studies 178 (10):3157-3175.
    Suppose we learn that we have a poor track record in forming beliefs rationally, or that a brilliant colleague thinks that we believe P irrationally. Does such input require us to revise those beliefs whose rationality is in question? When we gain information suggesting that our beliefs are irrational, we are in one of two general cases. In the first case we made no error, and our beliefs are rational. In that case the input to the contrary is misleading. In (...)
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  41. Computationally Constrained Beliefs.Drew Mcdermott - 2013 - Journal of Consciousness Studies 20 (5-6):124-150.
    People and intelligent computers, if there ever are any, will both have to believe certain things in order to be intelligent agents at all, or to be a particular sort of intelligent agent. I distinguish implicit beliefs that are inherent in the architecture of a natural or artificial agent, in the way it is 'wired', from explicit beliefs that are encoded in a way that makes them easier to learn and to erase if proven mistaken. I introduce the term (...)
     
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  42. Whither Higher-Order Evidence?Daniel Whiting - 2019 - In Mattias Skipper & Asbjørn Steglich-Petersen (eds.), Higher-Order Evidence: New Essays. Oxford, United Kingdom: Oxford University Press.
    First-order evidence is evidence which bears on whether a proposition is true. Higher-order evidence is evidence which bears on whether a person is able to assess her evidence for or against a proposition. A widespread view is that higher-order evidence makes a difference to whether it is rational for a person to believe a proposition. In this paper, I consider in what way higher-order evidence might do this. More specifically, I consider whether and how higher-order (...)
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  43. Mindful belief: Accountability, expertise, and cognitive kinds.Josefa Toribio - 2002 - Theoria 68 (3):224-49.
    It is sometimes said that humans are unlike other animals in at least one crucial respect. We do not simply form beliefs, desires and other mental states, but are capable of caring about our mental states in a distinctive way. We can care about the justification of our beliefs, and about the desirability of our desires. This kind of observation is usually made in discussions of free will and moral responsibility. But it has profound consequences, or so I shall argue, (...)
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  44.  87
    Second best epistemology: fallibility and normativity.Joshua DiPaolo - 2019 - Philosophical Studies 176 (8):2043-2066.
    The Fallibility Norm—the claim that we ought to take our fallibility into account when managing our beliefs—appears to conflict with several other compelling epistemic norms. To shed light on these apparent conflicts, I distinguish two kinds of norms: norms of perfection and norms of compensation. Roughly, norms of perfection tell us how agents ought to behave if they’re to be perfect; norms of compensation tell us how imperfect agents ought to behave in order to compensate for their imperfections. I (...)
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  45. If You Believe You Believe, You Believe. A Constitutive Account of Knowledge of One’s Own Beliefs.Peter Baumann - 2017 - Logos and Episteme:389-416.
    Can I be wrong about my own beliefs? More precisely: Can I falsely believe that I believe that p? I argue that the answer is negative. This runs against what many philosophers and psychologists have traditionally thought and still think. I use a rather new kind of argument, – one that is based on considerations about Moore's paradox. It shows that if one believes that one believes that p then one believes that p – even though one can believe that (...)
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  46.  41
    Bayesian Belief Revision Based on Agent’s Criteria.Yongfeng Yuan - 2021 - Studia Logica 109 (6):1311-1346.
    In the literature of belief revision, it is widely accepted that: there is only one revision phase in belief revision which is well characterized by the Bayes’ Rule, Jeffrey’s Rule, etc.. However, as I argue in this article, there are at least four successive phases in belief revision, namely first/second order evaluation and first/second order revision. To characterize these phases, I propose mainly four rules of belief revision based on agent’s criteria, and (...)
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  47. The Fixation of Belief.C. S. Peirce - 1877 - Popular Science Monthly 12 (1):1-15.
    “Probably Peirce’s best-known works are the first two articles in a series of six that originally were collectively entitled Illustrations of the Logic of Science and published in Popular Science Monthly from November 1877 through August 1878. The first is entitled ‘The Fixation of Belief’ and the second is entitled ‘How to Make Our Ideas Clear.’ In the first of these papers Peirce defended, in a manner consistent with not accepting naive realism, the superiority of the scientific method (...)
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  48. Delusional Beliefs, Two-Factor Theories, and Bizarreness.Chenwei Nie - 2016 - Frontiers of Philosophy in China 11 (2):263-278.
    In order to explain delusional beliefs, one must first consider what factors should be included in a theory of delusion. Unlike a one-factor theory, a two-factor theory of delusion argues that not only anomalous experience (the first factor) but also an impairment of the belief-evaluation system (the second factor) is required. Recently, two-factor theorists have adopted various Bayesian approaches in order to give a more accurate description of delusion formation. By reviewing the progression from a one-factor (...)
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  49. Moore’s Paradox, Defective Interpretation, Justified Belief and Conscious Belief.John N. Williams - 2010 - Theoria 76 (3):221-248.
    In this journal, Hamid Vahid argues against three families of explanation of Moore-paradoxicality. The first is the Wittgensteinian approach; I assert that p just in case I assert that I believe that p. So making a Moore-paradoxical assertion involves contradictory assertions. The second is the epistemic approach, one committed to: if I am justified in believing that p then I am justified in believing that I believe that p. So it is impossible to have a justified omissive Moore-paradoxical (...). The third is the conscious belief approach, being committed to: if I consciously believe that p then I believe that I believe that p. So if I have a conscious omissive Moore-paradoxical belief, then I have contradictory second-order beliefs. In their place, Vahid argues for the defective-interpretation approach, broadly that charity requires us to discount the utterer of a Moore-paradoxical sentence as a speaker. I agree that the Wittgensteinian approach is unsatisfactory. But so is the defective-interpretation approach. However, there is a satisfactory version of each of the epistemic and conscious-belief approaches. (shrink)
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  50. Belief Revision in Dynamic Epistemic Logic and Ranking Theory.Peter Fritz - manuscript
    I want to look at recent developments of representing AGM-style belief revision in dynamic epistemic logics and the options for doing something similar for ranking theory. Formally, my aim will be modest: I will define a version of basic dynamic doxastic logic using ranking functions as the semantics. I will show why formalizing ranking theory this way is useful for the ranking theorist first by showing how it enables one to compare ranking theory more easily with other approaches to (...)
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