Results for 'A. Hütterman'

960 found
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  1. Deference Done Better.Kevin Dorst, Benjamin A. Levinstein, Bernhard Salow, Brooke E. Husic & Branden Fitelson - 2021 - Philosophical Perspectives 35 (1):99-150.
    There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...)
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  2. To see or not to see: The need for attention to perceive changes in scenes.Ronald A. Rensink, J. Kevin O'Regan & James J. Clark - 1997 - Psychological Science 8:368-373.
    When looking at a scene, observers feel that they see its entire structure in great detail and can immediately notice any changes in it. However, when brief blank fields are placed between alternating displays of an original and a modified scene, a striking failure of perception is induced: identification of changes becomes extremely difficult, even when changes are large and made repeatedly. Identification is much faster when a verbal cue is provided, showing that poor visibility is not the cause of (...)
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  3. Aristotle and Alexander on Perceptual Error.Mark A. Johnstone - 2015 - Phronesis 60 (3):310-338.
    Aristotle sometimes claims that the perception of special perceptibles by their proper sense is unerring. This claim is striking, since it might seem that we quite often misperceive things like colours, sounds and smells. Aristotle also claims that the perception of common perceptibles is more prone to error than the perception of special perceptibles. This is puzzling in its own right, and also places constraints on the interpretation of. I argue that reading Alexander of Aphrodisias on perceptual error can help (...)
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  4. Responsibility.Neal A. Tognazzini - 2013 - In Hugh LaFollette (ed.), The International Encyclopedia of Ethics. Hoboken, NJ: Blackwell. pp. 4592-4602.
    In this encyclopedia entry I sketch the way contemporary theorists understand moral responsibility -- its varieties, its requirements, and its puzzles.
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  5. Subjective Facts about Consciousness.Martin A. Lipman - 2023 - Ergo: An Open Access Journal of Philosophy 10:530-553.
    The starting point of this paper is the thought that the phenomenal appearances that accompany mental states are somehow only there, or only real, from the standpoint of the subject of those mental states. The world differs across subjects in terms of which appearances obtain. Not only are subjects standpoints across which the world varies, subjects are standpoints that we can ‘adopt’ in our own theorizing about the world (or stand back from). The picture that is suggested by these claims (...)
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  6. Diagnosis of Pneumonia Using Deep Learning.Alaa M. A. Barhoom & Samy S. Abu-Naser - 2022 - International Journal of Academic Engineering Research (IJAER) 6 (2):48-68.
    Artificial intelligence (AI) is an area of computer science that emphasizes the creation of intelligent machines or software that work and react like humans. Some of the activities computers with artificial intelligence are designed for include, Speech, recognition, Learning, Planning and Problem solving. Deep learning is a collection of algorithms used in machine learning, It is part of a broad family of methods used for machine learning that are based on learning representations of data. Deep learning is a technique used (...)
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  7. Seeing, sensing, and scrutinizing.Ronald A. Rensink - 2000 - Vision Research 40:1469-1487.
    Large changes in a scene often become difficult to notice if made during an eye movement, image flicker, movie cut, or other such disturbance. It is argued here that this _change blindness_ can serve as a useful tool to explore various aspects of vision. This argument centers around the proposal that focused attention is needed for the explicit perception of change. Given this, the study of change perception can provide a useful way to determine the nature of visual attention, and (...)
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  8. Which Attitudes for the Fitting Attitude Analysis of Value?Julien A. Deonna & Fabrice Teroni - 2021 - Theoria 87 (5):1099-1122.
    According to the fitting attitude (FA) analysis of value concepts, to conceive of an object as having a given value is to conceive of it as being such that a certain evaluative attitude taken towards it would be fitting. Among the challenges that this analysis has to face, two are especially pressing. The first is a psychological challenge: the FA analysis must call upon attitudes that shed light on our value concepts while not presupposing the mastery of these concepts. The (...)
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  9. The Auditory Field: The Spatial Character of Auditory Experience.Keith A. Wilson - 2023 - Ergo: An Open Access Journal of Philosophy 9 (40):1080-1106.
    It is widely accepted that there is a visual field, but the analogous notion of an auditory field is rejected by many philosophers on the grounds that the metaphysics or phenomenology of audition lack the necessary spatial or phenomenological structure. In this paper, I argue that many of the common objections to the existence of an auditory field are misguided and that, contrary to a tradition of philosophical scepticism about the spatiality of auditory experience, it is as richly spatial as (...)
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  10. Subversive Humor as Art and the Art of Subversive Humor.Chris A. Kramer - 2020 - The Philosophy of Humor Yearbook 1 (1):153–179.
    This article investigates the relationships between forms of humor that conjure up possible worlds and real-world social critiques. The first part of the article will argue that subversive humor, which is from or on behalf of historically and continually marginalized communities, constitutes a kind of aesthetic experience that can elicit enjoyment even in adversarial audiences. The second part will be a connecting piece, arguing that subversive humor can be constructed as brief narrative thought experiments that employ the use of fictionalized (...)
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  11. Altering the Narrative of Champions: Recognition, Excellence, Fairness, and Inclusion.Leslie A. Howe - 2020 - Sport, Ethics and Philosophy 14 (4):496-510.
    This paper is an examination of the concept of recognition and its connection with identity and respect. This is related to the question of how women are or are not adequately recognised or respected for their achievements in sport and whether eliminating sex segregation in sport is a solution. This will require an analysis of the concept of excellence in sport, as well as the relationship between fairness and inclusion in an activity that is fundamentally about bodily movement. I argue (...)
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  12. Knowledge is the Norm of Assertion.Matthew A. Benton - 2024 - In Blake Roeber, Ernest Sosa, Matthias Steup & John Turri (eds.), Contemporary Debates in Epistemology, 3rd edition. Wiley-Blackwell. pp. 329-339.
    Assertion is governed by an epistemic norm requiring knowledge. This idea has been hotly debated in recent years, garnering attention in epistemology, philosophy of language, and linguistics. This chapter presents and extends the main arguments in favor of the knowledge norm, from faulty conjunctions, several conversational patterns, judgments of permission, excuse, and blame, and from showing how. (Paired with a chapter by Peter J. Graham and Nikolaj J. L. L. Pedersen, "Knowledge is Not Our Norm of Assertion.").
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  13. The strong emergence of molecular structure.Vanessa A. Seifert - 2020 - European Journal for Philosophy of Science 10 (3):1-25.
    One of the most plausible and widely discussed examples of strong emergence is molecular structure. The only detailed account of it, which has been very influential, is due to Robin Hendry and is formulated in terms of downward causation. This paper explains Hendry’s account of the strong emergence of molecular structure and argues that it is coherent only if one assumes a diachronic reflexive notion of downward causation. However, in the context of this notion of downward causation, the strong emergence (...)
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  14. Gauge Invariance for Classical Massless Particles with Spin.Jacob A. Barandes - 2021 - Foundations of Physics 51 (1):1-14.
    Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle (...)
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  15. Why kinship is progeneratively constrained: Extending anthropology.Robert A. Wilson - 2022 - Synthese 200 (2):1-20.
    The conceptualisation of kinship and its study remain contested within anthropology. This paper draws on recent cognitive science, developmental cognitive psychology, and the philosophy of science to offer a novel argument for a view of kinship as progeneratively or reproductively constrained. I shall argue that kinship involves a form of extended cognition that incorporates progenerative facts, going on to show how the resulting articulation of kinship’s progenerative nature can be readily expressed by an influential conception of kinds, the homeostatic property (...)
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  16. Disagreement and Religion.Matthew A. Benton - 2021 - In Matthew A. Benton & Jonathan L. Kvanvig (eds.), Religious Disagreement and Pluralism. Oxford: Oxford University Press. pp. 1-40.
    This chapter covers contemporary work on disagreement, detailing both the conceptual and normative issues in play in the debates in mainstream analytic epistemology, and how these relate to religious diversity and disagreement. §1 examines several sorts of disagreement, and considers several epistemological issues: in particular, what range of attitudes a body of evidence can support, how to understand higher-order evidence, and who counts as an epistemic “peer”. §2 considers how these questions surface when considering disagreements over religion, including debates over (...)
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  17. Kinmaking, Progeneration, and Ethnography.Robert A. Wilson - 2022 - Studies in History and Philosophy of Science 91 (C):77-85.
    Philosophers of biology and biologists themselves for the most part assume that the concept of kin is progenerative: what makes two individuals kin is a direct or indirect function of reproduction. Derivatively, kinship might likewise be presumed to be progenerative in nature. Yet a prominent view of kinship in contemporary cultural anthropology is a kind of constructivism or performativism that rejects such progenerativist views. This paper critically examines an influential line of thinking used to critique progenerativism and support performativism that (...)
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  18. Newton on active and passive quantities of matter.Adwait A. Parker - 2020 - Studies in History and Philosophy of Science Part A 84:1-11.
    Newton published his deduction of universal gravity in Principia (first ed., 1687). To establish the universality (the particle-to-particle nature) of gravity, Newton must establish the additivity of mass. I call ‘additivity’ the property a body's quantity of matter has just in case, if gravitational force is proportional to that quantity, the force can be taken to be the sum of forces proportional to each particle's quantity of matter. Newton's argument for additivity is obscure. I analyze and assess manuscript versions of (...)
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  19. Dilemma for appeals to the moral significance of birth.Christopher A. Bobier & Adam Omelianchuk - 2020 - Journal of Medical Ethics (12).
    Giubilini and Minerva argue that the permissibility of abortion entails the permissibility of infanticide. Proponents of what we refer to as the Birth Strategy claim that there is a morally significant difference brought about at birth that accounts for our strong intuition that killing newborns is morally impermissible. We argue that strategy does not account for the moral intuition that late-term, non-therapeutic abortions are morally impermissible. Advocates of the Birth Strategy must either judge non-therapeutic abortions as impermissible in the later (...)
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  20. Why does God exist?C. A. Mcintosh - 2022 - Religious Studies 58 (1):236-257.
    Many philosophers have appealed to the PSR in arguments for a being that exists a se, a being whose explanation is in itself. But what does it mean, exactly, for something to have its explanation ‘in itself’? Contemporary philosophers have said next to nothing about this, relying instead on phrases plucked from the accounts of various historical figures. In this article, I analyse five such accounts – those of Anselm, Aquinas, Descartes, Spinoza, and Leibniz – and argue that none are (...)
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  21. This Body of Art: The Singular Plural of the Feminine.Helen A. Fielding - 2005 - Journal of the British Society for Phenomenology 36 (3):277-292.
    I explore the possibility that the feminine, like art, can be thought in terms of Jean-Luc Nancy’s concept of the singular plural. In Les Muses, Nancy claims that art provides for the rethinking of a technë not ruled by instrumentality. Specifically, in rethinking aesthetics in terms of the debates laid out by Kant, Hegel and Heidegger, he resituates the ontological in terms of the specificity of the techniques of each particular artwork; each artwork establishes relations particular to its world or (...)
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  22. Students’ Evaluation of Faculty-Prepared Instructional Modules: Inferences for Instructional Materials Review and Revision.Lovina A. Hamora, Merline B. Rabaya, Jupeth Pentang, Aylene D. Pizaña & Mary Jane D. Gamozo - 2022 - Journal of Education, Management and Development Studies 2 (2):20-29.
    Academic institutions migrated to modular teaching-learning amid the COVID-19 pandemic. To ensure the quality of the pedagogical innovations employed, the study determined the students’ evaluation of the faculty prepared instructional modules for the courses they enrolled in during the first and second semesters of Academic Year 2020-2021. Employing a descriptive-correlational research design, the study was participated by 644 students from three colleges who were then available during the data gathering. Data gathered through online surveys were then analyzed using descriptive statistics (...)
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  23. Legitimate, but unjust; just, but illegitimate.Silje A. Langvatn - 2016 - Philosophy and Social Criticism 42 (2):132-153.
    The article offers a reconstruction of John Rawls views on political legitimacy, from A Theory of Justice to his late writings on political liberalism. It argues that Rawls had three conceptions of legitimacy, not two as one might expect based on the distinction between his two major works. Its argument is that the most radical change in Rawls’ thinking about legitimacy occurs in ‘Introduction to the Paperback Edition’ and ‘The Idea of Public Reason Revisited’. Here Rawls assumes that there can (...)
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  24. Blaming for Unreasonableness: Accountability without Ill Will.Alisabeth A. Ayars - 2021 - Journal of Ethics and Social Philosophy 19 (1).
    Quality of will accounts of moral responsibility hold that ill will is necessary for blameworthiness. But all such accounts are false to ordinary moral practice, which licenses blame for agents who act wrongly from epistemically unreasonable ignorance even if the act is not ill willed. This should be especially concerning to Strawsonians about moral responsibility, who think the genuine conditions of blameworthiness are derived from the standards internal to our practice. In response, I provide a theory of moral blameworthiness on (...)
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  25. Aesthetics is the grammar of desire.Jennifer A. McMahon - 2015 - Aesthetic Investigations 1 (1):156-164.
    This essay presents the nature of aesthetic judgment, the significance of aesthetic judgment and finally, the relevance of art to understanding aesthetic judgment.
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  26. XV.—The Ontological Argument for the Existence of God.Albert A. Cock - 1918 - Proceedings of the Aristotelian Society 18 (1):363-384.
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  27. The Moral Self and Moral Duties.Jim A. C. Everett, Joshua August Skorburg & Julian Savulescu - 2020 - Philosophical Psychology (7):1-22.
    Recent research has begun treating the perennial philosophical question, “what makes a person the same over time?” as an empirical question. A long tradition in philosophy holds that psychological continuity and connectedness of memories are at the heart of personal identity. More recent experimental work, following Strohminger & Nichols (2014), has suggested that persistence of moral character, more than memories, is perceived as essential for personal identity. While there is a growing body of evidence supporting these findings, a critique by (...)
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  28. Intentionality and phenomenology.Robert A. Wilson - 2003 - Pacific Philosophical Quarterly 84 (4):413-431.
    This paper is a critique of some ideas about narrow content owing to Horgan and Tienson and Brian Loar.
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  29. Eugenics, Disability, and Bioethics.Robert A. Wilson - 2022 - In Joel Michael Reynolds & Christine Wieseler (eds.), The Disability Bioethics Reader. Oxford; New York: Routledge. pp. 21-29.
    This paper begins by saying enough about eugenics to explain why disability is central to eugenics (section 2), then elaborates on why cognitive disability has played and continues to play a special role in eugenics and in thinking about moral status (section 3) before identifying three reasons why eugenics remains a live issue in contemporary bioethics (section 4). After a reminder of the connections between Nazi eugenics, medicine, and bioethics (section 5), it returns to take up two more specific clusters (...)
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  30. Discretion.H. L. A. Hart - 2013 - Harvard Law Review 127 (2):652-665.
    In this field questions arise which are certainly difficult; but as I listened last time to members of the group, I felt that the main difficulty perhaps lay in determining precisely what questions we are trying to answer. I have the conviction that if we could only say clearly what the questions are, the answers to them might not appear so elusive. So I have begun with a simple list of questions about discretion which in one form or another were, (...)
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  31. Early completion of occluded objects.Ronald A. Rensink & James T. Enns - 1998 - Vision Research 38:2489-2505.
    We show that early vision can use monocular cues to rapidly complete partially-occluded objects. Visual search for easily detected fragments becomes difficult when the completed shape is similar to others in the display; conversely, search for fragments that are difficult to detect becomes easy when the completed shape is distinctive. Results indicate that completion occurs via the occlusion-triggered removal of occlusion edges and linking of associated regions. We fail to find evidence for a visible filling-in of contours or surfaces, but (...)
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  32. Aristotle on the Unity of Touch.Mark A. Johnstone - 2021 - Journal of the History of Philosophy 59 (1):23-43.
    Aristotle is history’s most famous and influential proponent of the view that there are exactly five senses. But was he entitled to hold this view, given his other commitments? In particular, was he entitled to treat touch as a single sense, given the diversity of its correlated objects? In this paper I argue that Aristotle wished to individuate touch on the basis of its correlated objects, just as he had the other four senses. I also argue, contrary to what is (...)
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  33. Perception and Attention.Ronald A. Rensink - 2013 - In Daniel Reisberg (ed.), The Oxford Handbook of Cognitive Psychology. Oup Usa. pp. 97-116.
    Our visual experience of the world is one of diverse objects and events, each with particular colors, shapes, and motions. This experience is so coherent, so immediate, and so effortless that it seems to result from a single system that lets us experience everything in our field of view. But however appealing, this belief is mistaken: there are severe limits on what can be visually experienced. -/- For example, in a display for air-traffic control it is important to track all (...)
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  34. Locke and Burnet.S. A. Grave - 1981
    Amongst the anonymous critics of Locke's "Essay concerning Human Understanding" was a writer of very considerable contemporary eminence, Thomas Burnet. Burnet's criticism is contained in "Remarks upon an Essay Concerning Humane Understanding" and in two subsequent sets of Remarks. This monograph surveys the clash between Locke and Burnet on morality, certainty in revealed religion, and the immortality of the soul.
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  35. (1 other version)‘An Uncanny Re-Awakening’: Nietzsche’s Renascence of the Renaissance out of the Spirit of Jacob Burckhardt.Martin A. Ruehl - 2008 - In Manuel Dries (ed.), Nietzsche on Time and History. Walter de Gruyter. pp. 231--72.
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  36. Is Laughing at Morally Oppressive Jokes Like Being Disgusted by Phony Dog Feces? An Analysis of Belief and Alief in the Context of Questionable Humor.Chris A. Kramer - 2022 - The Philosophy of Humor Yearbook 3 (1):179-207.
    In two very influential papers from 2008, Tamar Gendler introduced the concept of “alief” to describe the mental state one is in when acting in ways contrary to their consciously professed beliefs. For example, if asked to eat what they know is fudge, but shaped into the form of dog feces, they will hesitate, and behave in a manner that would be consistent with the belief that the fudge is really poop. They alieve that it is disgusting, while they believe (...)
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  37. COVID-19 Vaccine Refusal and Fair Allocation of Scarce Medical Resources.Govind Persad & Emily A. Largent - 2022 - JAMA Health Forum 3 (4):e220356.
    When hospitals face surges of patients with COVID-19, fair allocation of scarce medical resources remains a challenge. Scarcity has at times encompassed not only hospital and intensive care unit beds—often reflecting staffing shortages—but also therapies and intensive treatments. Safe, highly effective COVID-19 vaccines have been free and widely available since mid-2021, yet many Americans remain unvaccinated by choice. Should their decision to forgo vaccination be considered when allocating scarce resources? Some have suggested it should, while others disagree. We offer a (...)
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  38. Plato on the Enslavement of Reason.Mark A. Johnstone - 2020 - Canadian Journal of Philosophy 50 (3):382-394.
    In Republic 8–9, Socrates describes four main kinds of vicious people, all of whose souls are “ruled” by an element other than reason, and in some of whom reason is said to be “enslaved.” What role does reason play in such souls? In this paper, I argue, based on Republic 8–9 and related passages, and in contrast to some common alternative views, that for Plato the “enslavement” of reason consists in this: instead of determining for itself what is good, reason (...)
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  39. The Meta-Dynamic Nature of Consciousness.John A. Barnden - 2020 - Entropy 22.
    How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects of the theory. Because the philosophical side has radical elements, so does the physical-theory side. The philosophical side is radical, first, in proposing that the productivity or dynamism in the universe that many believe to be responsible for (...)
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  40. Early Thinking about Likings and Dislikings.Thomas A. Blackson - 2022 - Ancient Philosophy Today 4 (2):176-195.
    In Plato’s Protagoras, Socrates argues that ‘the many’ are confused about the experience they describe as ‘being overcome by pleasure’. They think the cause is ‘something other than ignorance’. He argues it follows from what they believe that the cause is ‘ignorance’ and ‘false belief’. I show that his argument depends on a premise he does not introduce but they should deny: that when someone is overcome by pleasure, the desire stems from a belief. To explain why Plato does not (...)
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  41. Verbal reports on the contents of consciousness: Reconsidering introspectionist methodology.Eddy A. Nahmias - 2002 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 8.
    Doctors must now take a fifth vital sign from their patients: pain reports. I use this as a case study to discuss how different schools of psychology (introspectionism, behaviorism, cognitive psychology) have treated verbal reports about the contents of consciousness. After examining these differences, I suggest that, with new methods of mapping data about neurobiological states with behavioral data and with verbal reports about conscious experience, we should reconsider some of the introspectionists' goals and methods. I discuss examples from cognitive (...)
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  42. Epicureanism.Thomas A. Blackson - 2016 - In Tom Angier, Chad Meister & Charles Taliaferro (eds.), The History of Evil in Antiquity: 2000 Bce to 450 Ce. Routledge.
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  43. Plato (ca. 427 - ca. 347 BC E ): Apology of Socrates.Thomas A. Blackson - forthcoming - In AUTOBIOGRAPHY/AUTOFICTION. An International and Interdisciplinary Handbook. Volume III: Exemplary autobiographical/autofictional texts. Edited by Martina Wagner-Egelhaaf. De Gruyter, Berlin.
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  44. Individuating the Senses of ‘Smell’: Orthonasal versus Retronasal Olfaction.Keith A. Wilson - 2021 - Synthese 199:4217-4242.
    The dual role of olfaction in both smelling and tasting, i.e. flavour perception, makes it an important test case for philosophical theories of sensory individuation. Indeed, the psychologist Paul Rozin claimed that olfaction is a “dual sense”, leading some scientists and philosophers to propose that we have not one, but two senses of smell: orthonasal and retronasal olfaction. In this paper I consider how best to understand Rozin’s claim, and upon what grounds one might judge there to be one or (...)
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  45. Rousseau's Debate with Machiavelli in the "Social Contract".Lionel A. McKenzie - 1982 - Journal of the History of Ideas 43 (2):209.
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  46. Meaning vs. Power: Are Thick Description and Power Analysis intrinsically at odds? Response to Interpretation, Explanation, and Clifford Geertz.Jason A. Springs - 2012 - Religion Compass 6 (12):534-542.
    This essay clarifies and defends the methodological multidimensionality and improvisational character of Clifford Geertz’s account of interpretation and explanation. In contrast to accounts of power analysis offered by Michel Foucault and Talal Asad, I argue that Geertz’s work can simultaneously attend to meaning, power, identity, and experience in understanding and assessing religious practices and cultural formations.
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  47. Innate Mathematical Characteristics and Number Sense Competencies of Junior High School Students.Raymundo A. Santos, Leila M. Collantes, Edwin D. Ibañez, Florante P. Ibarra & Jupeth Pentang - 2022 - International Journal of Learning, Teaching and Educational Research 21 (10):325-340.
    The study determined the influence of innate mathematical characteristics on the number sense competencies of junior high school students in a Philippine public school. The descriptive-correlational research design was used to accomplish the study involving a nonrandom sample of sixty 7th-grade students attending synchronous math sessions. Data obtained from the math-specific Learning Style and Self-Efficacy questionnaires and the modified Number Sense Test (NST) were analyzed and interpreted using descriptive statistics, Pearson’s Chi-Square, and Simple Linear Regression analysis. The research instruments and (...)
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  48. How Museums Make Us Feel: Affective Niche Construction and the Museum of Non-Objective Painting.Jussi A. Saarinen - 2021 - British Journal of Aesthetics 61 (4):543-558.
    Art museums are built to elicit a wide variety of feelings, emotions, and moods from their visitors. While these effects are primarily achieved through the artworks on display, museums commonly deploy numerous other affect-inducing resources as well, including architectural solutions, audio guides, lighting fixtures, and informational texts. Art museums can thus be regarded as spaces that are designed to influence affective experiencing through multiple structures and mechanisms. At face value, this may seem like a somewhat self-evident and trivial statement to (...)
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  49. Finger-counting and numerical structure.Karenleigh A. Overmann - 2021 - Frontiers in Psychology 2021 (12):723492.
    Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of (...)
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  50. Arithmetical algorithms for elementary patterns.Samuel A. Alexander - 2015 - Archive for Mathematical Logic 54 (1-2):113-132.
    Elementary patterns of resemblance notate ordinals up to the ordinal of Pi^1_1-CA_0. We provide ordinal multiplication and exponentiation algorithms using these notations.
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