Results for 'Bryan Cheng'

304 found
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  1. Susan Stebbing's Intellectualism.Bryan Pickel - 2022 - Journal for the History of Analytical Philosophy 10 (4).
    This paper reconstructs Susan Stebbing’s account of intelligent dealing with a problem and defends this account against charges that it relies on a “censurable kind” of intellectualism. This charge was made in Stebbing’s own time by Laird and Wittgenstein. Michael Kremer has recently made the case that Stebbing is also a proximate target of Gilbert Ryle’s attack on intellectualism. This paper argues that Stebbing should indeed be counted as an intellectualist since she holds that intelligent dealing with a problem requires (...)
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  2. Reversing the arrow of time.Bryan W. Roberts - 2022 - Cambridge: Cambridge University Press.
    'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...)
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  3. Against Second-Order Primitivism.Bryan Pickel - 2024 - In Peter Fritz & Nicholas K. Jones, Higher-Order Metaphysics. Oxford University Press.
    In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to which (...)
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  4. Building Community Capacity with Philosophy: Toolbox Dialogue and Climate Resilience.Bryan Cwik, Chad Gonnerman, Michael O'Rourke, Brian Robinson & Daniel Schoonmaker - 2022 - Ecology and Society 27 (2).
    In this article, we describe a project in which philosophy, in combination with methods drawn from mental modeling, was used to structure dialogue among stakeholders in a region-scale climate adaptation process. The case study we discuss synthesizes the Toolbox dialogue method, a philosophically grounded approach to enhancing communication and collaboration in complex research and practice, with a mental modeling approach rooted in risk analysis, assessment, and communication to structure conversations among non-academic stakeholders who have a common interest in planning for (...)
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  5. Practical Wisdom, Well‐Being, and Success.Cheng-Hung Tsai - 2022 - Wiley: Philosophy and Phenomenological Research 104 (3):606-622.
    Philosophy and Phenomenological Research, Volume 104, Issue 3, Page 606-622, May 2022.
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  6. Colloquium 1: Theophrastus on Intellect in Aristotle’s De Anima.Bryan C. Reece - 2024 - Proceedings of the Boston Area Colloquium of Ancient Philosophy 38 (1):1-27.
    Aristotle’s cryptic De Anima III 5 has precipitated an enormous volume of commentary, especially about the identity of what has come to be known as active intellect and how it relates to potential intellect. Some take active intellect to be the prime mover of Metaphysics Λ, others a hypostatic or cosmic principle (for example, an ideal Intellect, intellect associated with the tenth celestial sphere, etc.), and others a faculty, potentiality, or power of the human soul that is distinct in function, (...)
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  7. Aristotle on Divine and Human Contemplation.Bryan C. Reece - 2020 - Ergo: An Open Access Journal of Philosophy 7:131–160.
    Aristotle’s theory of human happiness in the Nicomachean Ethics explicitly depends on the claim that contemplation (theôria) is peculiar to human beings, whether it is our function or only part of it. But there is a notorious problem: Aristotle says that divine beings also contemplate. Various solutions have been proposed, but each has difficulties. Drawing on an analysis of what divine contemplation involves according to Aristotle, I identify an assumption common to all of these proposals and argue for rejecting it. (...)
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  8. The Reflective Epistemic Renegade.Bryan Frances - 2010 - Philosophy and Phenomenological Research 81 (2):419 - 463.
    Philosophers often find themselves in disagreement with contemporary philosophers they know full well to be their epistemic superiors on the topics relevant to the disagreement. This looks epistemically irresponsible. I offer a detailed investigation of this problem of the reflective epistemic renegade. I argue that although in some cases the renegade is not epistemically blameworthy, and the renegade situation is significantly less common than most would think, in a troublesome number of cases in which the situation arises the renegade is (...)
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  9. The myth of occurrence-based semantics.Bryan Pickel & Brian Rabern - 2021 - Linguistics and Philosophy 44:813-837.
    The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims (...)
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  10. Against Fregean Quantification.Bryan Pickel & Brian Rabern - 2023 - Ergo: An Open Access Journal of Philosophy 9 (37):971-1007.
    There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...)
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  11. The dominating effects of economic crises.Alexander Bryan - 2021 - Critical Review of International Social and Political Philosophy 24 (6):884-908.
    This article argues that economic crises are incompatible with the realisation of non-domination in capitalist societies. The ineradicable risk that an economic crisis will occur undermines the robust security of the conditions of non-domination for all citizens, not only those who are harmed by a crisis. I begin by demonstrating that the unemployment caused by economic crises violates the egalitarian dimensions of freedom as non-domination. The lack of employment constitutes an exclusion from the social bases of self-respect, and from a (...)
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  12. On the Explanatory Deficiencies of Linguistic Content.Bryan Frances - 1999 - Philosophical Studies 93 (1):45-75.
    The Burge-Putnam thought experiments have generated the thesis that beliefs are not fixed by the constitution of the body. However, many philosophers have thought that if this is true then there must be another content-like property. Even if the contents of our attitudes such as the one in ‘believes that aluminum is a light metal’, do not supervene on our physical makeups, nevertheless people who are physical duplicates must be the same when it comes to evaluating their rationality and explaining (...)
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  13. The material conditions of non-domination: Property, independence, and the means of production.Alexander Bryan - 2023 - European Journal of Political Theory 22 (3):425-444.
    While it is a point of agreement in contemporary republican political theory that property ownership is closely connected to freedom as non-domination, surprisingly little work has been done to elucidate the nature of this connection or the constraints on property regimes that might be required as a result. In this paper, I provide a systematic model of the boundaries within which republican property systems must sit and explore some of the wider implications that thinking of property in these terms may (...)
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  14. The Epistemic Dimensions of Civil Disobedience.Alexander Bryan - forthcoming - Journal of Political Philosophy.
    Journal of Political Philosophy, EarlyView.
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  15. Aristotle's Four Causes of Action.Bryan C. Reece - 2018 - Australasian Journal of Philosophy 97 (2):213-227.
    Aristotle’s typical procedure is to identify something's four causes. Intentional action has typically been treated as an exception: most think that Aristotle has the standard causalist account, according to which an intentional action is a bodily movement efficiently caused by an attitude of the appropriate sort. I show that action is not an exception to Aristotle’s typical procedure: he has the resources to specify four causes of action, and thus to articulate a powerful theory of action unlike any other on (...)
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  16. Habit: A Rylean Conception.Cheng-Hung Tsai - 2022 - Philosophies 7 (2):45.
    Tennis champion Maria Sharapova has a habit of grunting when she plays on the court. Assume that she also has a habit of hitting the ball in a certain way in a certain situation. The habit of on-court grunting might be bad, but can the habit of hitting the ball in a certain way in a certain situation be classified as intelligent? The fundamental questions here are as follows: What is habit? What is the relation between habit and skill? Is (...)
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  17. Philosophical proofs against common sense.Bryan Frances - 2021 - Analysis 81 (1):18-26.
    Many philosophers are sceptical about the power of philosophy to refute commonsensical claims. They look at the famous attempts and judge them inconclusive. I prove that, even if those famous attempts are failures, there are alternative successful philosophical proofs against commonsensical claims. After presenting the proofs I briefly comment on their significance.
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  18. Beyond Intuitive Know-How.Cheng-Hung Tsai - 2022 - Phenomenology and the Cognitive Sciences:1-14.
    According to Dreyfusian anti-intellectualism, know-how or expertise cannot be explained in terms of know-that and its cognates but only in terms of intuition. Hubert Dreyfus and Stuart Dreyfus do not exclude know-that and its cognates in explaining skilled action. However, they think that know-that and its cognates (such as calculative deliberation and perspectival deliberation) only operate either below or above the level of expertise. In agreement with some critics of Dreyfus and Dreyfus, in this paper, I argue that know-that and (...)
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  19. Why AI May Undermine Phronesis and What to Do about It.Cheng-Hung Tsai & Hsiu-lin Ku - forthcoming - AI and Ethics.
    Phronesis, or practical wisdom, is a capacity the possession of which enables one to make good practical judgments and thus fulfill the distinctive function of human beings. Nir Eisikovits and Dan Feldman convincingly argue that this capacity may be undermined by statistical machine-learning-based AI. The critic questions: why should we worry that AI undermines phronesis? Why can’t we epistemically defer to AI, especially when it is superintelligent? Eisikovits and Feldman acknowledge such objection but do not consider it seriously. In this (...)
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  20. Spirituality, Expertise, and Philosophers.Bryan Frances - 2013 - In L. Kvanvig Jonathan, Oxford Studies in Philosophy of Religion. Oxford University Press. pp. 44-81.
    We all can identify many contemporary philosophy professors we know to be theists of some type or other. We also know that often enough their nontheistic beliefs are as epistemically upstanding as the non-theistic beliefs of philosophy professors who aren’t theists. In fact, the epistemic-andnon-theistic lives of philosophers who are theists are just as epistemically upstanding as the epistemic-and-non-theistic lives of philosophers who aren’t theists. Given these and other, similar, facts, there is good reason to think that the pro-theistic beliefs (...)
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  21. The Recurrent Model of Bodily Spatial Phenomenology.Tony Cheng & Patrick Haggard - 2018 - Journal of Consciousness Studies 25 (3-4):55-70.
    In this paper, we introduce and defend the recurrent model for understanding bodily spatial phenomenology. While Longo, Azañón and Haggard (2010) propose a bottom-up model, Bermúdez (2017) emphasizes the top-down aspect of the information processing loop. We argue that both are only half of the story. Section 1 intro- duces what the issues are. Section 2 starts by explaining why the top- down, descending direction is necessary with the illustration from the ‘body-based tactile rescaling’ paradigm (de Vignemont, Ehrsson and Haggard, (...)
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  22. Mirror, Mirror, Who Is the Wisest Person in the World? (in Chinese).Cheng-Hung Tsai - 2022 - In Hsiu-lin Ku, Doing Philosophy. Taipei: Sanmin Book. pp. 139-160.
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    Is Knowing-How a Species of Knowing-That? (in Chinese).Cheng-Hung Tsai - 2009 - In R. Chen, The Art of Analysis. Taipei: Pro-Ed. pp. 63-88..
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  24. The Antinomy of the Variable: A Tarskian Resolution.Bryan Pickel & Brian Rabern - 2016 - Journal of Philosophy 113 (3):137-170.
    Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...)
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  25. Externalism, Physicalism, Statues, and Hunks.Bryan Frances - 2007 - Philosophical Studies 133 (2):199-232.
    Content externalism is the dominant view in the philosophy of mind. Content essentialism, the thesis that thought tokens have their contents essentially, is also popular. And many externalists are supporters of such essentialism. However, endorsing the conjunction of those views either (i) commits one to a counterintuitive view of the underlying physical nature of thought tokens or (ii) commits one to a slightly different but still counterintuitive view of the relation of thought tokens to physical tokens as well as a (...)
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  26. Ontology.Bryan Lueck - 2015 - In Marie-Eve Morin & Peter Gratton, The Nancy Dictionary. Edinburgh: Edinburgh University Press. pp. 169-171.
    A brief description of ontology and of its relation to the work of Jean-Luc Nancy.
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  27. The Unfortunate Consequences of Progress in Philosophy.Bryan Frances - 2024 - In Maria Baghramian, J. Adam Carter & Rach Cosker-Rowland, Routledge Handbook of Philosophy of Disagreement. New York, NY: Routledge.
    We tend to think that philosophical progress, to the extent that it exists, is a good thing. I agree. Even so, it has some surprising unfortunate consequences for the rationality of philosophical belief.
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  28. Iconic Memory and Attention in the Overflow Debate.Tony Cheng - 2017 - Cogent Psychology 4 (1):01-11.
    The overflow debate concerns this following question: does conscious iconic memory have a higher capacity than attention does? In recent years, Ned Block has been invoking empirical works to support the positive answer to this question. The view is called the “rich view” or the “Overflow view”. One central thread of this discussion concerns the nature of iconic memory: for example how rich they are and whether they are conscious. The first section discusses a potential misunderstanding of “visible persistence” in (...)
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  29. (1 other version)Disagreement.Bryan Frances - 2010 - In Sven Bernecker & Duncan Pritchard, The Routledge Companion to Epistemology. New York: Routledge.
    This is a short essay that presents what I take to be the main questions regarding the epistemology of disagreement.
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  30. Frege and saving substitution.Bryan Pickel & Brian Rabern - 2021 - Philosophical Studies 178 (8):2687-2697.
    Goodman and Lederman (2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires.
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  31. Philosophical Renegades.Bryan Frances - 2013 - In David Christensen & Jennifer Lackey, The Epistemology of Disagreement: New Essays. Oxford: Oxford University Press. pp. 121-166.
    If you retain your belief upon learning that a large number and percentage of your recognized epistemic superiors disagree with you, then what happens to the epistemic status of your belief? I investigate that theoretical question as well has the applied case of philosophical disagreement—especially disagreement regarding purely philosophical error theories, theories that do not have much empirical support and that reject large swaths of our most commonsensical beliefs. I argue that even if all those error theories are false, either (...)
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  32. (1 other version)Religious Disagreement.Bryan Frances - 2014 - In Graham Robert Oppy, Routledge Handbook of Contemporary Philosophy of Religion. London: Routledge.
    In this essay I try to motivate and formulate the main epistemological questions to ask about the phenomenon of religious disagreement. I will not spend much time going over proposed answers to those questions. I address the relevance of the recent literature on the epistemology of disagreement. I start with some fiction and then, hopefully, proceed with something that has at least a passing acquaintance with truth.
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  33. The Functional Composition of Sense.Bryan Pickel - 2021 - Synthese 199 (3-4):6917-6942.
    A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional (...)
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  34. Aristotle and Eudoxus on the Argument from Contraries.Wei Cheng - 2020 - Archiv für Geschichte der Philosophie 102 (4):588-618.
    The debate over the value of pleasure among Eudoxus, Speusippus, and Aristotle is dramatically documented by the Nicomachean Ethics, particularly in the dialectical pros-and-cons concerning the so-called argument from contraries. Two similar versions of this argument are preserved at EN VII. 13, 1153b1–4, and X. 2, 1172b18–20. Many scholars believe that the argument at EN VII is either a report or an appropriation of the Eudoxean argument in EN X. This essay aims to revise this received view. It will explain (...)
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  35. Speusippus, teleology and the metaphysics of value: Theophrastus’ Metaphysics 11a18–26.Wei Cheng - 2020 - Journal of Hellenic Studies 140:143-175.
    This paper reexamines Theophrastus’ Metaphysics 11a18–26, an obscure testimony about Speusippus, the second head of the Platonic Academy. As opposed to the traditional interpretation, which takes this passage as Theophrastus’ polemic against Speusippus’ doctrine of value, I argue that he here dialectically takes advantage of, rather than launches an attack on, the Platonist. Based on this new reading, I further propose a revision and a reassessment of the ‘gloomy metaphysics’ of Speusippus which will shed new light on his ethics.
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  36. The only thing I want is for people to stop seeing me naked: Consent, contracts, and sexual media.Joan O'Bryan - 2024 - Hypatia 38.
    In pornography, standard modelling contracts often require a performer to surrender rights over their public image and sexual media in perpetuity and across mediums. Under these contracts, performers are unable to determine who accesses, for what duration, and under what conditions, their sexual media. As a result, pornography has been described by some performers as a “life sentence” - a phrase which, if true, violates some strong intuitions we share about the importance of autonomy in sexual activity. Using the framework (...)
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  37. Does Semantic Relationism Solve Frege's Puzzle?Bryan Pickel & Brian Rabern - 2017 - Journal of Philosophical Logic 46 (1):97-118.
    In a series of recent works, Kit Fine, 605–631, 2003, 2007) has sketched a novel solution to Frege’s puzzle. Radically departing from previous solutions, Fine argues that Frege’s puzzle forces us to reject compositionality. In this paper we first provide an explicit formalization of the relational semantics for first-order logic suggested, but only briefly sketched, by Fine. We then show why the relational semantics alone is technically inadequate, forcing Fine to enrich the syntax with a coordination schema. Given this enrichment, (...)
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  38. Extensive Philosophical Agreement and Progress.Bryan Frances - 2017 - Metaphilosophy 48 (1-2):47-57.
    This article argues, first, that there is plenty of agreement among philosophers on philosophically substantive claims, which fall into three categories: reasons for or against certain views, elementary truths regarding fundamental notions, and highly conditionalized claims. This agreement suggests that there is important philosophical progress. It then argues that although it's easy to list several potential kinds of philosophical progress, it is much harder to determine whether the potential is actual. Then the article attempts to articulate the truth that the (...)
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  39. How Much Suffering Is Enough?Bryan Frances - forthcoming - Religious Studies.
    Isn’t there something like an amount and density of horrific suffering whose discovery would make it irrational to think God exists? Use your imagination to think of worlds that are much, much, much worse than you think Earth is when it comes to horrific suffering. Isn’t there some conceivable scenario which, if you were in it, would make you say “Ok, ok. God doesn’t exist, at least in the way we thought God was. We were wrong about that”? Pursuing this (...)
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  40. Frege on the Tolerability of Sense Variation: A Reply to Michaelson and Textor.Bryan Pickel & J. Adam Carter - 2024 - Australasian Journal of Philosophy.
    In several passages, Frege suggests that successful communication requires that speaker and audience understand the uttered words and sentences to have the same sense. On the other hand, Frege concedes that, in many ordinary cases, variation in sense is tolerable. In a recent article in this journal, Michaelson and Textor (2023) offer a new interpretation of Frege on the tolerability of sense variation according to which variation in sense is tolerable when the conversation aims at joint action, but not when (...)
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  41. The New Leibniz's Law Arguments for Pluralism.Bryan Frances - 2006 - Mind 115 (460):1007-1022.
    For years philosophers argued for the existence of distinct yet materially coincident things by appealing to modal and temporal properties. For instance, the statue was made on Monday and could not survive being flattened; the lump of clay was made months before and can survive flattening. Such arguments have been thoroughly examined. Kit Fine has proposed a new set of arguments using the same template. I offer a critical evaluation of what I take to be his central lines of reasoning.
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  42. Time-energy uncertainty does not create particles.Bryan W. Roberts & Jeremy Butterfield - 2020 - Journal of Physics 1638:012005.
    In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.
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  43. Contradictory Belief and Epistemic Closure Principles.Bryan Frances - 1999 - Mind and Language 14 (2):203–226.
    Kripke’s puzzle has puts pressure on the intuitive idea that one can believe that Superman can fly without believing that Clark Kent can fly. If this idea is wrong then many theories of belief and belief ascription are built from faulty data. I argue that part of the proper analysis of Kripke’s puzzle refutes the closure principles that show up in many important arguments in epistemology, e.g., if S is rational and knows that P and that P entails Q, then (...)
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  44. 意识的起源、本质和属性.Cheng Gong - manuscript
    关于人类意识起源和本质问题的探讨由来已久,各领域如哲学、社会学、生物学和心理学等都有不同定义和解释,但是至今为止都没有得到广泛的认同,主要原因是由意识的复杂性导致了各领域都不能全面、合理和充分地认识其 起源和本质,成为千古奇案,所以有必要对其进行深入探讨。 本文根据各学科的知识分析、汇总和归纳,得出如下结论:意识的起源来自自然物质;意识的本质为物质信息;意识的能力是物质信息的复杂度和有序度的利用程度;意识具有先天性、物质性、系统性、复杂性、动态性、差异性 和自我性属性 .
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  45. Aristotle’s Vocabulary of Pain.Wei Cheng - 2019 - Philologus: Zeitschrift für Antike Literatur Und Ihre Rezeption 163 (1):47-71.
    This paper examines Aristotle’s vocabulary of pain, that is the differences and relations of the concepts of pain expressed by synonyms in the same semantic field. It investigates what is particularly Aristotelian in the selection of the pain-words in comparison with earlier authors and specifies the special semantic scope of each word-cluster. The result not only aims to pin down the exact way these terms converge with and diverge from each other, but also serves as a basis for further understanding (...)
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  46. Obstacles to Testing Molyneux's Question Empirically.Tony Cheng - 2015 - I-Perception 6 (4).
    There have recently been various empirical attempts to answer Molyneux’s question, for example, the experiments undertaken by the Held group. These studies, though intricate, have encountered some objections, for instance, from Schwenkler, who proposes two ways of improving the experiments. One is “to re-run [the] experiment with the stimulus objects made to move, and/or the subjects moved or permitted to move with respect to them” (p. 94), which would promote three dimensional or otherwise viewpoint-invariant representations. The other is “to use (...)
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  47. When a Skeptical Hypothesis Is Live.Bryan Frances - 2005 - Noûs 39 (4):559–595.
    I’m going to argue for a set of restricted skeptical results: roughly put, we don’t know that fire engines are red, we don’t know that we sometimes have pains in our lower backs, we don’t know that John Rawls was kind, and we don’t even know that we believe any of those truths. However, people unfamiliar with philosophy and cognitive science do know all those things. The skeptical argument is traditional in form: here’s a skeptical hypothesis; you can’t epistemically neutralize (...)
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  48. Worrisome Skepticism About Philosophy.Bryan Frances - 2016 - Episteme 13 (3):289-303.
    A new kind of skepticism about philosophy is articulated and argued for. The key premise is the claim that many of us are well aware that in the past we failed to have good responses to substantive objections to our philosophical beliefs. The conclusion is disjunctive: either we are irrational in sticking with our philosophical beliefs, or we commit some other epistemic sin in having those beliefs.
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  49. Defending Millian Theories.Bryan Frances - 1998 - Mind 107 (428):703-728.
    In this article I offer a three-pronged defense of Millian theories, all of which share the rough idea that all there is to a proper name is its referent, so it has no additional sense. I first give what I believe to be the first correct analysis of Kripke’s puzzle and its anti-Fregean lessons. The main lesson is that the Fregean’s arguments against Millianism and for the existence of semantically relevant senses (that is, individuative elements of propositions or belief contents (...)
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  50. Big-Oh Notations, Elections, and Hyperreal Numbers: A Socratic Dialogue.Samuel Alexander & Bryan Dawson - 2023 - Proceedings of the ACMS 23.
    We provide an intuitive motivation for the hyperreal numbers via electoral axioms. We do so in the form of a Socratic dialogue, in which Protagoras suggests replacing big-oh complexity classes by real numbers, and Socrates asks some troubling questions about what would happen if one tried to do that. The dialogue is followed by an appendix containing additional commentary and a more formal proof.
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