Results for 'A. Michalopoulos'

966 found
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  1. a.A. A. (ed.) - 2015 - Universidad Técnica Particular de Loja.
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  2.  85
    Modeling and Using Context, volume 2116 of.Varol Akman, Paolo Bouquet, Richmond Thomason & Roger A. Young - 2001 - In P. Bouquet (ed.), Lecture Notes in Artificial Intelligence. Kluwer Academic Publishers. pp. 465.
    Context has emerged as a central concept in a variety of contemporary approaches to reasoning. The conference at which the papers in this volume were presented, CONTEXT 2001, was the third international, interdisciplinary conference on the topic of context, and was held in Dundee, Scotland on July 27-30, 2001.
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  3. Hedged Assertion.Matthew A. Benton & Peter Van Elswyk - 2018 - In Sanford C. Goldberg (ed.), The Oxford Handbook of Assertion. Oxford University Press. pp. 245-263.
    Surprisingly little has been written about hedged assertion. Linguists often focus on semantic or syntactic theorizing about, for example, grammatical evidentials or epistemic modals, but pay far less attention to what hedging does at the level of action. By contrast, philosophers have focused extensively on normative issues regarding what epistemic position is required for proper assertion, yet they have almost exclusively considered unqualified declaratives. This essay considers the linguistic and normative issues side-by-side. We aim to bring some order and clarity (...)
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  4. Epistemology Personalized.Matthew A. Benton - 2017 - Philosophical Quarterly 67 (269):813-834.
    Recent epistemology has focused almost exclusively on propositional knowledge. This paper considers an underexplored area of epistemology, namely knowledge of persons: if propositional knowledge is a state of mind, consisting in a subject's attitude to a (true) proposition, the account developed here thinks of interpersonal knowledge as a state of minds, involving a subject's attitude to another (existing) subject. This kind of knowledge is distinct from propositional knowledge, but it exhibits a gradability characteristic of context-sensitivity, and admits of shifty thresholds. (...)
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  5. Gricean Quality.Matthew A. Benton - 2016 - Noûs 50 (4):689-703.
    Some philosophers oppose recent arguments for the Knowledge Norm of Assertion by claiming that assertion, being an act much like any other, will be subject to norms governing acts generally, such as those articulated by Grice for the purpose of successful, cooperative endeavours. But in fact, Grice is a traitor to their cause; or rather, they are his dissenters, not his disciples. Drawing on Grice's unpublished papers, I show that he thought of asserting as a special linguistic act in need (...)
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  6. Knowledge, Attitude, and Infringement of Tort Law Among Public Secondary School Heads on Students in Osun State, Nigeria.Olugbenga Timothy Ajadi & Musibau A. Lateef - 2023 - Universal Journal of Educational Research 2 (3):204-216.
    One of the challenges in secondary schools today is infringements on students’ rights, in a tortious way that may also constitute breach of the Child’s Right Act of 2003 in Nigeria. These breach on rights usually come through the administration of corporal punishments on students, and mainly because the school heads see themselves as loco parentis of the students who can, therefore, enforce any form of punishment on them in the school. This study investigated knowledge, attitude, and infringement of tort (...)
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  7. Evil and Evidence.Matthew A. Benton, John Hawthorne & Yoaav Isaacs - 2016 - Oxford Studies in Philosophy of Religion 7:1-31.
    The problem of evil is the most prominent argument against the existence of God. Skeptical theists contend that it is not a good argument. Their reasons for this contention vary widely, involving such notions as CORNEA, epistemic appearances, 'gratuitous' evils, 'levering' evidence, and the representativeness of goods. We aim to dispel some confusions about these notions, in particular by clarifying their roles within a probabilistic epistemology. In addition, we develop new responses to the problem of evil from both the phenomenal (...)
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  8. Lying, accuracy and credence.Matthew A. Benton - 2018 - Analysis 78 (2):195-198.
    Traditional definitions of lying require that a speaker believe that what she asserts is false. Sam Fox Krauss seeks to jettison the traditional belief requirement in favour of a necessary condition given in a credence-accuracy framework, on which the liar expects to impose the risk of increased inaccuracy on the hearer. He argues that this necessary condition importantly captures nearby cases as lies which the traditional view neglects. I argue, however, that Krauss's own account suffers from an identical drawback of (...)
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  9.  94
    Thou Art In Paradise Today: A Nietzschean Treatise On the Life-Affirming Properties of Post-Modern Christianity.A. Zachman - manuscript
    On what conditions, if it all possible, can Christianity be life-affirming in line with the general schema outlined throughout Nietzsche's wide-ranging corpus? Through a post-modern interpretation of Christ as OverMan of course. Pack your crosses and your pentagrams and buckle up for this visual transmission of my most recent brainchild.
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  10. Pragmatic Encroachment and Theistic Knowledge.Matthew A. Benton - 2018 - In Matthew A. Benton, John Hawthorne & Dani Rabinowitz (eds.), Knowledge, Belief, and God: New Insights in Religious Epistemology. Oxford: Oxford University Press. pp. 267-287.
    If knowledge is sensitive to practical stakes, then whether one knows depends in part on the practical costs of being wrong. When considering religious belief, the practical costs of being wrong about theism may differ dramatically between the theist (if there is no God) and the atheist (if there is a God). This paper explores the prospects, on pragmatic encroachment, for knowledge of theism (even if true) and of atheism (even if true), given two types of practical costs: namely, by (...)
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  11. Being-in-the-flow: expert coping as beyond both thought and automaticity.Joshua A. Bergamin - 2017 - Phenomenology and the Cognitive Sciences 16 (3):403-424.
    Hubert Dreyfus argues that explicit thought disrupts smooth coping at both the level of everyday tasks and of highly-refined skills. However, Barbara Montero criticises Dreyfus for extending what she calls the ‘principle of automaticity’ from our everyday actions to those of trained experts. In this paper, I defend Dreyfus’ account while refining his phenomenology. I examine the phenomenology of what I call ‘esoteric’ expertise to argue that the explicit thought Montero invokes belongs rather to ‘gaps’ between or above moments of (...)
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  12. Knowledge and Evidence You Should Have Had.Matthew A. Benton - 2016 - Episteme 13 (4):471-479.
    Epistemologists focus primarily on cases of knowledge, belief, or credence where the evidence which one possesses, or on which one is relying, plays a fundamental role in the epistemic or normative status of one's doxastic state. Recent work in epistemology goes beyond the evidence one possesses to consider the relevance for such statuses of evidence which one does not possess, particularly when there is a sense in which one should have had some evidence. I focus here on Sanford Goldberg's approach (...)
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  13. Artificially Geistige: A Hegelian Perspective on the Developing History of AI.A. Zachman - manuscript
    Modern philosophy can often appear to be mere cryptomnesia, redressed and resuited to fit the particular mouth from which it is espoused. This notion is but a sorrowful chimera binding the 21st-century mind to the confines of an eternal shadow, an eternal prison of doubt in the face of limitless potential. As a species, we are rapidly approaching the precipice of Yahweh's original position as instantiators of consciousness, as the I AM in relation to our artificial progeny. Could one fabricate (...)
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  14. Expert Opinion and Second‐Hand Knowledge.Matthew A. Benton - 2016 - Philosophy and Phenomenological Research 92 (2):492-508.
    Expert testimony figures in recent debates over how best to understand the norm of assertion and the domain-specific epistemic expectations placed on testifiers. Cases of experts asserting with only isolated second-hand knowledge (Lackey 2011, 2013) have been used to shed light on whether knowledge is sufficient for epistemically permissible assertion. I argue that relying on such cases of expert testimony introduces several problems concerning how we understand expert knowledge, and the sharing of such knowledge through testimony. Refinements are needed to (...)
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  15. Collective Intentionality in Non-Human Animals.Robert A. Wilson - 2017 - In Marija Jankovic and Kirk Ludwig (ed.), Routledge Handbook on Collective Intentionality. pp. 420-432.
    I think there is something to be said in a positive and constructive vein about collective intentionality in non-human animals. Doing so involves probing at the concept of collective intentionality fairly directly (Section 2), considering the various forms that collective intentionality might take (Section 3), showing some sensitivity to the history of appeals to that concept and its close relatives (Section 4), and raising some broader questions about the relationships between sociality, cognition, and institutions by discussing two different possible cases (...)
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  16. Philosophical Silences: Race, Gender, Disability, and Philosophical Practice.Robert A. Wilson - 2023 - Journal of Philosophy of Education 57 (4):1004-1024.
    Who is recognised as a philosopher and what counts as philosophy influence both the content of a philosophical education and academic philosophy’s continuing demographic skew. The “philosophical who” and the “philosophical what” themselves are a partial function of matters that have been passed over in collective silence, even if that now feels to some like a silence belonging to the distant past. This paper discusses some philosophical silences regarding race, gender, and disability in the context of reflection on philosophical education (...)
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  17. Adaptive Intelligent Tutoring System for learning Computer Theory.Mohammed A. Al-Nakhal & Samy S. Abu Naser - 2017 - European Academic Research 4 (10).
    In this paper, we present an intelligent tutoring system developed to help students in learning Computer Theory. The Intelligent tutoring system was built using ITSB authoring tool. The system helps students to learn finite automata, pushdown automata, Turing machines and examines the relationship between these automata and formal languages, deterministic and nondeterministic machines, regular expressions, context free grammars, undecidability, and complexity. During the process the intelligent tutoring system gives assistance and feedback of many types in an intelligent manner according to (...)
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  18. Job Motivation and Its Impact on Job Satisfaction Among Accountants.Arianna Dacanay, Giannah D. V. Gonzales, Carl Xaviery A. Baldonado, Nicolai Renz S. P. Guballa, Hanz S. Marquez, Hazel Anne M. Domingo, Kyle Gian S. Diaz, Denise Iresh S. Catolico, Edward Gabriel Gotis & Jhoselle tus - 2023 - Psychology and Education: A Multidisciplinary Journal 9 (1):412-418.
    Job motivation remains an area of concern among researchers due to the rising issues of poor or lack of motivation among workers. This refers to one’s personal will or drives to perform a task at work. Meanwhile, job satisfaction refers to an employee’s sense of fulfillment with his or her work experience. Therefore, the current study utilized the descriptive- correlational research design to investigate the impact of job motivation on the job satisfaction of accountants. To gather essential data and achieve (...)
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  19. 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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  20.  49
    Metaphysical Debates about Words: What Does It Mean to Be a Realist about Words?A. Nekhaev - 2023 - Tomsk State University Journal of Philosophy, Sociology, and Political Science 17 (75):64–75.
    In current discussions on the problem of the metaphysical nature of the word, four factions – eliminativism, nominalism, originalism, and the type-token theory – take an active part. For eliminativism, words as separate entities do not exist; they are only a useful cognitive illusion. In the process of communication, competent speakers make sounds and inscriptions through which they are able to infer certain intentional contents of each other’s cognitive states. However, these sounds and inscriptions cannot be regarded as instances of (...)
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  21. Religious Diversity and Disagreement.Matthew A. Benton - 2019 - In Miranda Fricker, Peter Graham, David Henderson & Nikolaj Jang Pedersen (eds.), The Routledge Handbook of Social Epistemology. New York, USA: Routledge. pp. 185-195.
    Epistemologists have shown increased interest in the epistemic significance of disagreement, and in particular, in whether there is a rational requirement concerning belief revision in the face of peer disagreement. This article examines some of the general issues discussed by epistemologists, and then considers how they may or may not apply to the case of religious disagreement, both within religious traditions and between religious (and non-religious) views.
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  22. On 'Logos' in Heraclitus.Mark A. Johnstone - 2014 - Oxford Studies in Ancient Philosophy 47:1-29.
    In this paper, I offer a new solution to the old problem of how best to understand the meaning of the word ‘logos’ in the extant writings of Heraclitus, especially in fragments DK B1, B2 and B50. On the view I defend, Heraclitus was neither using the word in a perfectly ordinary way in these fragments, as some have maintained, nor denoting by it some kind of general principle or law governing change in the cosmos, as many have claimed. Rather, (...)
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  23. The Autonomy of Social Epistemology.Michael A. Bishop - 2005 - Episteme 2 (1):65-78.
    Social epistemology is autonomous: When applied to the same evidential situations, the principles of social rationality and the principles of individual rationality sometimes recommend inconsistent beliefs. If we stipulate that reasoning rationally from justified beliefs to a true belief is normally sufficient for knowledge, the autonomy thesis implies that some knowledge is essentially social. When the principles of social and individual rationality are applied to justified evidence and recommend inconsistent beliefs and the belief endorsed by social rationality is true, then (...)
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  24.  83
    The inverse conjunction fallacy.Martin Jönsson & James A. Hampton - 2006 - Journal of Memory and Language 55:317-334.
    If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the (...)
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  25. Contemporary Forms of Eugenics.Robert A. Wilson - 2017 - eLS Wiley Online.
    Eugenics is commonly thought of as having endured as science and social movement only until 1945. With the advance of both reproductive and enhancement technologies, however, concern has arisen that eugenics has resurfaced in new forms. In particular, the eugenic potential of the Human Genome Project led to talk of the rise of ‘newgenics’ and of a backdoor to eugenics. This article focuses on such concerns deriving from the practice of prenatal screening and technologies that increase our ability to generate (...)
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  26. The Theory Theory Thrice Over: The Child as Scientist, Superscientist or Social Institution?Michael A. Bishop & Stephen M. Downes - 2002 - Studies in History and Philosophy of Science Part A 33 (1):117-132.
    Alison Gopnik and Andrew Meltzoff have argued for a view they call the ‘theory theory’: theory change in science and children are similar. While their version of the theory theory has been criticized for depending on a number of disputed claims, we argue that there is a fundamental problem which is much more basic: the theory theory is multiply ambiguous. We show that it might be claiming that a similarity holds between theory change in children and (i) individual scientists, (ii) (...)
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  27. Tyrannized Souls: Plato's Depiction of the ‘Tyrannical Man’.Mark A. Johnstone - 2015 - British Journal for the History of Philosophy 23 (3):423-437.
    In book 9 of Plato's Republic, Socrates describes the nature and origins of the ‘tyrannical man’, whose soul is said to be ‘like’ a tyrannical city. In this paper, I examine the nature of the ‘government’ that exists within the tyrannical man's soul. I begin by demonstrating the inadequacy of three potentially attractive views sometimes found in the literature on Plato: the view that the tyrannical man's soul is ruled by his ‘lawless’ unnecessary appetites, the view that it is ruled (...)
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  28. Influencing choice without awareness.Jay A. Olson, Alym A. Amlani, Amir Raz & Ronald A. Rensink - 2015 - Consciousness and Cognition 37 (C):225-236.
    Forcing occurs when a magician influences the audience's decisions without their awareness. To investigate the mechanisms behind this effect, we examined several stimulus and personality predictors. In Study 1, a magician flipped through a deck of playing cards while participants were asked to choose one. Although the magician could influence the choice almost every time (98%), relatively few (9%) noticed this influence. In Study 2, participants observed rapid series of cards on a computer, with one target card shown longer than (...)
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  29. 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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  30. Expanding the vector model for dispositionalist approaches to causation.Joseph A. Baltimore - 2019 - Synthese 196 (12):5083-5098.
    Neuron diagrams are heavily employed in academic discussions of causation. Stephen Mumford and Rani Lill Anjum, however, offer an alternative approach employing vector diagrams, which this paper attempts to develop further. I identify three ways in which dispositionalists have taken the activities of powers to be related: stimulation, mutual manifestation, and contribution combination. While Mumford and Anjum do provide resources for representing contribution combination, which might be sufficient for their particular brand of dispositionalism, I argue that those resources are not (...)
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  31. Believing on Authority.Matthew A. Benton - 2014 - European Journal for Philosophy of Religion 6 (4):133-144.
    Linda Zagzebski's "Epistemic Authority" (Oxford University Press, 2012) brings together issues in social epistemology with topics in moral and political philosophy as well as philosophy of religion. In this paper I criticize her discussion of self-trust and rationality, which sets up the main argument of the book; I consider how her view of authority relates to some issues of epistemic authority in testimony; and I raise some concerns about her treatment of religious epistemology and religious authority in particular.
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  32. Lotteries and Prefaces.Matthew A. Benton - 2017 - In Jonathan Jenkins Ichikawa (ed.), The Routledge Handbook of Epistemic Contextualism. New York: Routledge. pp. 168-176.
    The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties encountered by those (...)
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  33. Heil’s Two-Category Ontology and Causation.Joseph A. Baltimore - 2015 - Erkenntnis 80 (5):1091-1099.
    In his recent book, The Universe As We Find It, John Heil offers an updated account of his two-category ontology. One of his major goals is to avoid including relations in his basic ontology. While there can still be true claims positing relations, such as those of the form “x is taller than y” and “x causes y,” they will be true in virtue of substances and their monadic, non-relational properties. That is, Heil’s two-category ontology is deployed to provide non-relational (...)
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  34. Interference in short-term retention of discrete movements.A. S. Faust-Adams - 1972 - Journal of Experimental Psychology 96 (2):400.
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  35.  19
    Editorial: Towards 2030: Sustainable Development Goal 8: Decent Work and Economic Growth. A Sociological Perspective.Andrzej Klimczuk, Delali A. Dovie, Minela Kerla, Magdalena Klimczuk-Kochańska & Piotr Toczyski - 2024 - Frontiers in Sociology 9:1487233.
    This Research Topic explores Sustainable Development Goal (SDG) eight, which is to “promote sustained, inclusive, and sustainable economic growth, full and productive employment, and decent work for all.” It highlights the COVID-19 pandemic’s severe impact and triggered global economic recession, worsened gender pay gaps, increased undeclared employment, and significantly raised unemployment (United Nations, 2024). From a sociology-specific perspective, this Research Topic examines the global and local implementation of SDG8, its adaptation to different geographical contexts, stakeholder involvement, and issues related to (...)
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  36.  49
    Attention and Representational Precision.A. Lopez - 2024 - In Robert French & Berit Brogaard (eds.), The Roles of Representations in Visual Perception. Springer.
    Visual experiences often feel crisper, sharper or more vivid when one pays attention to the seen object. According to some representationalist theories of perception, these felt effects occur because attentive experiences represent more determinate or precise properties than their inattentive counterparts: a color experience represents vermillion rather than red if the color is perceived with attention rather than without it. Recently, this idea has been expressed in terms of ranges of feature values represented, so that attentive experiences shall represent narrower (...)
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  37.  29
    Assessment of current community pharmacist labeling practice: A simulated client approaches.Nesren A. Jaaida - 2024 - Mediterranean Journal of Pharmacy and Pharmaceutical Sciences 4 (3):1-6.
    The labeling of medications includes the provision of information and instructions as well as a unique identity for the medical product. It is one of the most important sources of information for patients. Good labeling practice is critical to ensuring patients' safe and effective use of products. Misreading the label, insufficient data on the label, inappropriate labeling font, writing style, and placement on the dosage form can all have disastrous consequences. The objective of this study was to assess medication labeling (...)
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  38. La filosofía en forma: el fondo metafórico.José A. Marín-Casanova - 2001 - Logos. Anales Del Seminario de Metafísica [Universidad Complutense de Madrid, España] 34:267-281.
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  39. Conjunctions of social categories considered from different points of view.James A. Hampton, Margaret Dillane, Laura Oren & Louise Worgan - 2011 - Anthropology and Philosophy 10:31-57.
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  40. Isaiah in Luke.James A. Sanders - 1982 - Interpretation 36 (2):144-155.
    Luke, steeped in the Old Testament, makes clear that to understand what God was doing in Christ, one has to know Scripture; and especially the Book of Isaiah.
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  41. Continuity and Discontinuity in Visual Experience.Michael A. R. Biggs - 1992 - Critica 24 (70):3-15.
    This paper investigates the role of visual experience in Wittgenstein's work. The specific thesis is that visual experience provides not only diverse illustrative examples of what could be an explanation of meaning, but that it also provides a recurrent metaphor for the whole process of meaning and understanding. Wittgenstein uses a great number of visual examples in his texts. Their diversity may be accounted for by the great diversity of ways in which he attempts to describe the relationship between a (...)
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  42. A. ROUGES: Las jerarquías del ser y la eternidad.A. Caturelli - 1963 - Sapientia 18 (69/70):293.
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  43. The Liar Syndrome.Albert A. Johnstone - 2002 - SATS 3 (1):37-55.
    This article examines the various Liar paradoxes and their near kin, Grelling’s paradox and Gödel’s Incompleteness Theorem with its self-referential Gödel sentence. It finds the family of paradoxes to be generated by circular definition–whether of statements, predicates, or sentences–a manoeuvre that generates pseudo-statements afflicted with the Liar syndrome: semantic vacuity, semantic incoherence, and predicative catalepsy. Such statements, e.g., the self-referential Liar statement, are meaningless, and hence fail to say anything, a point that invalidates the reasoning on which the various paradoxes (...)
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  44.  32
    A Theory of Knowledge.Thomas A. Roll - 2024 - Dissertation, No Affiliation
    A brief dissertation on what knowledge is.
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  45.  33
    A Theory of Knowledge.Thomas A. Roll - 2024 - Dissertation, University of Cincinnati
    A short dissertation on a definition for knowledge. Although similar to binary opposition, this treatise follows the logic to conclude that knowledge is finite.
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  46. G.W. Leibniz: Sign and the Problem of Expression.Dimitri A. Bayuk & Olga B. Fedorova - 2020 - Epistemology and Philosophy of Science 57 (1):146-165.
    The disciplinary differentiation of sciences attracted Leibniz’s attention for a long period of time. From nowadays prospects it looks very well grounded as soon as in Leibniz’s manuscripts a modern scholar finds clue ideas of any research field which would tempt him to consider Leibniz as one of the founders of this particular discipline. We argue that this is possible only in retrospection and would significantly distort the essence of Leibniz’s epistemology. Our approach implies, in contrary, the investigation of the (...)
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  47. Varieties and Directions of Interdomain Influence in Metaphor.John A. Barnden, Sheila R. Glasbey, Mark G. Lee & Alan M. Wallington - 2004 - Metaphor and Symbol 19 (1):1-30.
    We consider the varieties and directions of influence that the source and target domains involved in a conceptual metaphor can have on each other during the course of understanding metaphorical utterances based on the metaphor. Previous studies have been restricted both as to direction of influence and as to type of influence. They have been largely confined to the “forward” (source to target) direction of influence, and they have concentrated on the transfer of features or propositions and (to some extent) (...)
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  48. Macbeth's Last Words.José A. Benardete - 1970 - Interpretation 1 (1):63-75.
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  49. Generalized Trust in Taiwan and (as Evidence for) Hirschman’s doux commerce Thesis.Marc A. Cohen - 2020 - Social Theory and Practice 46 (1):1-25.
    Data from the World Values Survey shows that generalized trust in Mainland China—trust in out-group members—is very low, but generalized trust in Taiwan is much higher. The present article argues that positive interactions with out-group members in the context of Taiwan’s export-oriented economy fostered generalized trust—and so explains this difference. This line of argument provides evidence for Albert O. Hirschman’s doux commerce thesis, that market interaction can improve persons and even stabilize the social order. The present article defends this point (...)
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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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