Results for 'Harold F. Moore'

965 found
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  1. Cut-conditions on sets of multiple-alternative inferences.Harold T. Hodes - 2022 - Mathematical Logic Quarterly 68 (1):95 - 106.
    I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...)
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  2. One World.A. W. Moore - 2016 - European Journal of Philosophy 24 (4):934-945.
    This essay appeared as a contribution to a special issue of European Journal of Philosophy to mark the fiftieth anniversary of the publication of P. F. Strawson’s The Bounds of Sense. In that book Strawson asks whether we should agree with Kant's claim, in his Critique of Pure Reason, that there can be only one world. What Kant means by this claim is that the four-dimensional realm that we inhabit must constitute the whole of empirical reality. Strawson gives reasons for (...)
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  3. Richard Moore, Nuclear Illusion, Nuclear Reality: Britain, the United States and Nuclear Weapons, 1958-64. [REVIEW]Sean F. Johnston - 2016 - Technology and Culture 53:28-30.
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  4. Mystical Theology and Platonism in the Time of Cusanus.Jason Aleksander, Michael E. Moore, Sean Hannan & Joshua Hollmann (eds.) - 2023 - Leiden: Brill.
    Mystical Theology and Platonism in the Time of Cusanus engages with the history of mystical theology and Neoplatonic philosophy through the lens of the 15th century philosopher and theologian, Nicholas of Cusa. The volume comprises nineteen essays that break down the barriers between medieval and Renaissance studies, reinterpreting Cusanus’ place in the history of thought by exploring the archive that informed his thinking, while also interrogating his works by exploring them from the standpoint of their later reception by modern philosophers (...)
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  5. Rules of Language and First Person Authority.Martin F. Fricke - 2012 - Polish Journal of Philosophy 6 (2):15-32.
    This paper examines theories of first person authority proposed by Dorit Bar-On (2004), Crispin Wright (1989a) and Sydney Shoemaker (1988). What all three accounts have in common is that they attempt to explain first person authority by reference to the way our language works. Bar-On claims that in our language self-ascriptions of mental states are regarded as expressive of those states; Wright says that in our language such self-ascriptions are treated as true by default; and Shoemaker suggests that they might (...)
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  6.  73
    (4 other versions)Racionalidad y autoconocimiento en Shoemaker.Martin F. Fricke - 2012 - In Pedro Stepanenko (ed.), La primera persona y sus percepciones. Universidad Nacional Autónoma de México. pp. 53-73.
    En su artículo “On Knowing One’s Own Mind” (1988), Shoemaker argumenta en favor de tres afirmaciones: (1) se requiere un autoconocimiento directo (self-acquaintance) para la cooperación racional con otras personas (porque ésta depende de que podamos decirles qué es lo que creemos e intentamos hacer); (2) el autoconocimiento directo es necesario para la deliberación sobre qué creer y qué hacer (porque no podemos ajustar racionalmente creencias y deseos sin saber qué creencias y deseos tenemos); y (3) el autoconocimiento directo es (...)
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  7. On the origins of the contemporary notion of propositional content: anti-psychologism in nineteenth-century psychology and G.E. Moore’s early theory of judgment.Consuelo Preti - 2008 - Studies in History and Philosophy of Science Part A 39 (2):176-185.
    I argue that the familiar picture of the rise of analytic philosophy through the early work of G. E. Moore and Bertrand Russell is incomplete and to some degree erroneous. Archival evidence suggests that a considerable influence on Moore, especially evident in his 1899 paper ‘The nature of judgment,’ comes from the literature in nineteenth-century empirical psychology rather than nineteenth-century neo-Hegelianism, as is widely believed. I argue that the conceptual influences of Moore’s paper are more likely to (...)
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  8. MInd and Machine: at the core of any Black Box there are two (or more) White Boxes required to stay in.Lance Nizami - 2020 - Cybernetics and Human Knowing 27 (3):9-32.
    This paper concerns the Black Box. It is not the engineer’s black box that can be opened to reveal its mechanism, but rather one whose operations are inferred through input from (and output to) a companion observer. We are observers ourselves, and we attempt to understand minds through interactions with their host organisms. To this end, Ranulph Glanville followed W. Ross Ashby in elaborating the Black Box. The Black Box and its observer together form a system having different properties than (...)
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  9. The history or Russell's concepts 'sense-data' and 'knowledge by acquaintance'.Nikolay Milkov - 2001 - Archiv Fuer Begriffsgeschichte 43:221-231.
    Two concepts of utmost importance for the analytic philosophy of the twentieth century, “sense-data” and “knowledge by acquaintance”, were introduced by Bertrand Russell under the influence of two idealist philosophers: F. H. Bradley and Alexius Meinong. This paper traces the exact history of their introduction. We shall see that between 1896 and 1898, Russell had a fully-elaborated theory of “sense-data”, which he abandoned after his analytic turn of the summer of 1898. Furthermore, following a subsequent turn of August 1900—-after he (...)
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  10. Kant’s derivation of the moral ‘ought’ from a metaphysical ‘is’.Colin Marshall - 2022 - In Schafer Karl & Stang Nicholas (eds.), The Sensible and Intelligible Worlds: New Essays on Kant's Metaphysics and Epistemology. Oxforrd University Press. pp. 382-404.
    In this chapter, I argue that Kant can be read as holding that "ought" judgments follow from certain "is" judgments by mere analysis. More specifically, I defend an interpretation according to which (1) Kant holds that “S ought to F” is analytically equivalent to “If, as it can and would were there no other influences on the will, S’s faculty of reason determined S’s willing, S would F” and (2) Kant’s notions of reason, the will, and freedom are all fundamentally (...)
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  11. A Brief Introduction to Analytic Philosophy.Oleksandr Kulyk - 2019 - Dnipro: LIRA.
    This brief introduction is for people who want to know the leading approaches to philosophy in the twentieth century in English-speaking countries but do not have much time to study them. The book contains texts of lectures and quizzes with explained answers. By the end of this book, you will understand what analysis is and how to practice it in a philosophical way. Moreover, you will be able to talk confidently about some of the great ideas of such philosophers as (...)
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  12. Russell and Bradley: Rehabilitating the Creation Narrative of Analytic Philosophy.Samuel Lebens - 2017 - Journal for the History of Analytical Philosophy 5 (7).
    According to Stewart Candlish, Russell and Moore had misunderstood F. H. Bradley’s monism. According to Jonathan Schaffer, they had misunderstood monism more generally. A key thread of the creation narrative of analytic philosophy, according to which Russell and Moore successfully undermined monism to give rise to a new movement is, therefore, in doubt. In this paper, I defend the standard narrative against those who seek to revise it.
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  13. Strawson's Metacritique.Anil Gomes - 2023 - In Sybren Heyndels, Audun Bengtson & Benjamin De Mesel (eds.), P.F. Strawson and his Philosophical Legacy. Oxford, GB: Oxford University Press.
    What is the status of the claims which make up Kant’s arguments in the Critique of Pure Reason? This question seemed to Kant’s contemporaries to require a metacritique. Strawson’s criticisms of Kant should be understood in this context: as raising a metacritical challenge about Kant’s grounds for the claims which make up his arguments. What about the claims which make up Strawson’s own arguments in The Bounds of Sense? I argue in this chapter, against what I take to be the (...)
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  14. La presenza di Descartes in Mind dal 1900 al 1947.Brunello Lotti - 2023 - Noctua 10 (2–3):196-250.
    This paper examines how Descartes’ philosophy was presented and discussed in articles and reviews published in Mind from 1900 to 1947, a period in which this most prestigious British philosophical journal was edited by George F. Stout (until 1920) and then by George E. Moore (from 1921 to 1947). The survey deals with various aspects of the reception of Cartesian philosophy in the journal: articles devoted to several topics of Cartesian thought, critical notices and reviews of the secondary literature, (...)
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  15. The analytical Thomism of the Cracow circle.Miroslav Vacura - 2011 - Filosoficky Casopis 59 (5):689-705.
    The traditional picture of the development of analytical philosophy, represented especially by such thinkers as G. Frege, G. E. Moore, B. Russell or R. Carnap, whose attitude was generally anti-metaphysical, can, on closer study, be shown to be incomplete. This article treats of the Cracow circle – a group of Polish philosophers among whom are, above all, to be counted J. Salamucha, J. M. Bocheński, J. F. Drewnowski, and B. Sobociński, who were, at the beginning of the twentieth century, (...)
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  16. Ludwig Wittgenstein’s Cambridge Period.Natalia Tomashpolskaia - 2023 - Prolegomena: Journal of Philosophy 22 (2):257-294.
    This article analyses in detail Wittgenstein’s ‘Cambridge period’ from his return to Cambridge in 1929 until his decease in 1951. Within the ‘Cambridge period’, scholars usually distinguish the ‘middle’ (1929–1936) and the ‘late’ (1936–1951) periods. The trigger point of Wittgenstein’s return to Cambridge and philosophy was his visit to Brouwer’s lecture on ‘Mathematics, Science, and Language’ in Vienna in March 1928. Dutch mathematician Brouwer influenced not only Wittgenstein’s ability to do philosophy again but also the development of some of his (...)
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  17. Leer hoy «Reason in Common Sense» de Santayana.Jaime Nubiola - 2017 - Limbo 37:11-34.
    In this article I pay attention to some of the reviews that Reason in Common Sense of George Santayana received from some of the most outstanding philosophers of his time: E. Albee, J. Dewey, A.W. Moore, G. E. Moore, C. S. Peirce and F. C S. Schiller. My paper is arranged in six sections: 1) Biographical circumstances of Reason in Common Sense; 2) Peirce’s reading of Santayana; 3) The reviews of John Dewey; 4) Other readers of Reason in (...)
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  18. Comments on Mark Kalderon's “The Open Question Argument, Frege's Puzzle, and Leibniz's Law”.Peter Alward - unknown
    A standard strategy for defending a claim of non-identity is one which invokes Leibniz’s Law. (1) Fa (2) ~Fb (3) (∀x)(∀y)(x=y ⊃ (∀P)(Px ⊃ Py)) (4) a=b ⊃ (Fa ⊃ Fb) (5) a≠b In Kalderon’s view, this basic strategy underlies both Moore’s Open Question Argument (OQA) as well as (a variant formulation of) Frege’s puzzle (FP). In the former case, the argument runs from the fact that some natural property—call it “F-ness”—has, but goodness lacks, the (2nd order) property of (...)
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  19. Bene.Sergio Volodia Marcello Cremaschi - 1996 - In Virgilio Melchiorre, Guido Boffi, Eugenio Garin, Adriano Bausola, Enrico Berti, Francesca Castellani, Sergio Cremaschi, Carla Danani, Roberto Diodato, Sergio Galvan, Alessandro Ghisalberti, Giuseppe Grampa, Michele Lenoci, Roberto Maiocchi, Michele Marsonet, Emanuela Mora, Carlo Penco, Roberto Radice, Giovanni Reale, Andrea Salanti, Piero Stefani, Valerio Verra & Paolo Volonté (eds.), Enciclopedia della Filosofia e delle Scienze Umane. Virgilio Melchiorre (ed.). Novara: De Agostini. pp. 96-98.
    The genealogical deconstruction of the notion of "good" by F.Nietzsche in Genealogy of Morals highlights the arbitrariness of the Platonic unification of various kinds of good, a unification that is still shared by both objectivists and subjectivists. For the same reasons, the attempt of G.E. Moore and other neo-intuitionists to define a single property that is common to all uses of the term "good" and the specular denial of the existence of this property by the emotionalism of A.J. Ayer (...)
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  20. Contemporary legal philosophising: Schmitt, Kelsen, Lukács, Hart, & law and literature, with Marxism's dark legacy in Central Europe (on teaching legal philosophy in appendix).Csaba Varga - 2013 - Budapest: Szent István Társulat.
    Reedition of papers in English spanning from 1986 to 2009 /// Historical background -- An imposed legacy -- Twentieth century contemporaneity -- Appendix: The philosophy of teaching legal philosophy in Hungary /// HISTORICAL BACKGROUND -- PHILOSOPHY OF LAW IN CENTRAL & EASTERN EUROPE: A SKETCH OF HISTORY [1999] 11–21 // PHILOSOPHISING ON LAW IN THE TURMOIL OF COMMUNIST TAKEOVER IN HUNGARY (TWO PORTRAITS, INTERWAR AND POSTWAR: JULIUS MOÓR & ISTVÁN LOSONCZY) [2001–2002] 23–39: Julius Moór 23 / István Losonczy 29 // (...)
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  21. On Resisting Art.James Harold - 2023 - Journal of Aesthetics and Art Criticism 81 (1):35-45.
    What responsibilities do audiences have in engaging with artworks? Certain audience responses seem quite clear: for example, audiences should not vandalize or destroy artworks; they should not disrupt performances. This paper examines other kinds of resisting responses that audiences sometimes engage in, including petitioning the artist to change their works, altering copies of artworks, and creating new artworks in another artist’s fictional world. I argue for five claims: (1) while these actions can sometimes infringe on the rights of artists, the (...)
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  22. Some theorems on the expressive limitations of modal languages.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):13 - 26.
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  23. Axioms for actuality.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (1):27 - 34.
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  24. On Saying and Showing: A. W. Moore.A. W. Moore - 1987 - Philosophy 62 (242):473 - 497.
    This essay constitutes an attempt to probe the very idea of a saying/showing distinction of the kind that Wittgenstein advances in the Tractatus—to say what such a distinction consists in, to say what philosophical work it has to do, and to say how we might be justified in drawing such a distinction. Towards the end of the essay the discussion is related to Wittgenstein’s later work. It is argued that we can profitably see this work in such a way that (...)
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  25. Defending Aesthetic Internalism: Liking, Loving, and Wholeheartedness.James Harold - forthcoming - Philosophical Quarterly.
    Aesthetic internalism claims a link between judgement and motivation: aesthetic judgements bring with them motivations to act in characteristic ways. Critics object that there is a difference between merely liking something and judging it to be aesthetically good, and that it is our likings, not our aesthetic judgements, that motivate us. This paper develops a version of aesthetic internalism that can respond to this criticism. Wholehearted aesthetic judgements are characterized by stability, attention, and motivation. Making such judgements is an important (...)
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  26. Audiences’ Role in Generating Moral Understanding: Screen Stories as Sites for Interpretative Communities.James Harold - 2023 - In Carl Plantinga (ed.), Screen Stories and Moral Understanding: Interdisciplinary Perspectives. New York, New York: Oxford University Press. pp. 197-211.
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  27. Why Ramify?Harold T. Hodes - 2015 - Notre Dame Journal of Formal Logic 56 (2):379-415.
    This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...)
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  28. Lemos on the Physical Indeterminism Luck Objection.Dwayne Moore - 2023 - Philosophia 51 (3):1459-1477.
    I recently argued that reductive physicalist versions of libertarian free will face a physical indeterminism luck objection. John Lemos claims that one potential advocate of reductive physicalist libertarianism, Robert Kane, avoids this physical indeterminism luck objection. I here show how the problem remains.
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  29. Uniform Upper Bounds on Ideals of Turing Degrees.Harold T. Hodes - 1978 - Journal of Symbolic Logic 43 (3):601-612.
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  30. Hermias: On Plato's Phaedrus.Harold A. S. Tarrant & Dirk Baltzly - 2017 - In Harold Tarrant, Danielle A. Layne, Dirk Baltzly & François Renaud (eds.), Brill’s Companion to the Reception of Plato in Antiquity. Leiden: Brill.
    This article tackles the sole surviving ancient commentary on what was perhaps the second most important Platonic work, with special interest for the manner in which the ancients tackled the setting of Plato's dialogues, Socratic ignorance, Socratic eros, the central myth-like Palinode, and the question of oral as against written teaching.
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  31. One-step Modal Logics, Intuitionistic and Classical, Part 1.Harold T. Hodes - 2021 - Journal of Philosophical Logic 50 (5):837-872.
    This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...)
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  32. Classifying Psychopathology: Mental Kinds and Natural Kinds.Harold Kincaid & Jacqueline Anne Sullivan - 2014 - In Harold Kincaid & Jacqueline Anne Sullivan (eds.), Classifying Psychopathology: Mental Kinds and Natural Kinds. MIT Press. pp. 1-10.
    In this volume, leading philosophers of psychiatry examine psychiatric classification systems, including the Diagnostic and Statistical Manual of Mental Disorders, asking whether current systems are sufficient for effective diagnosis, treatment, and research. Doing so, they take up the question of whether mental disorders are natural kinds, grounded in something in the outside world. Psychiatric categories based on natural kinds should group phenomena in such a way that they are subject to the same type of causal explanations and respond similarly to (...)
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  33. Logicism and the ontological commitments of arithmetic.Harold T. Hodes - 1984 - Journal of Philosophy 81 (3):123-149.
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  34. Flexing the imagination.James Harold - 2003 - Journal of Aesthetics and Art Criticism 61 (3):247–258.
    I explore the claim that “fictive imagining” – imagining what it is like to be a character – can be morally dangerous. In particular, I consider the controversy over William Styron’s imagining the revolutionary protagonist in his Confessions of Nat Turner. I employ Ted Cohen’s model of fictive imagining to argue, following a generally Kantian line of thought, that fictive imagining can be dangerous if one has the wrong motives. After considering several possible motives, I argue that only internally directed (...)
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  35. (1 other version)A Landscape Study of Public Universities with Undergraduate-Focused Ethics Education.Sally Moore - 2023 - Teaching Ethics 23 (1):79-89.
    Little is known about the aims and impact of university-based ethics centers. Less is known about how centers leverage their unique campus positions to engage undergraduates in transformative ethics education. This article provides a foundation for future research on university-based ethics centers. First, this article addresses the history of ethics education in higher education, the rise of university ethics centers, and the factors necessary for successful ethics programs. Next, this piece shows the geographic distribution of ethics centers and which centers (...)
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  36. Individual-actualism and three-valued modal logics, part 2: Natural-deduction formalizations.Harold T. Hodes - 1987 - Journal of Philosophical Logic 16 (1):17 - 63.
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  37. The composition of Fregean thoughts.Harold T. Hodes - 1982 - Philosophical Studies 41 (2):161 - 178.
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  38. Can Expressivists Tell the Difference Between Beauty and Moral Goodness?James Harold - 2008 - American Philosophical Quarterly 45 (3):289-300.
    One important but infrequently discussed difficulty with expressivism is the attitude type individuation problem.1 Expressivist theories purport to provide a unified account of normative states. Judgments of moral goodness, beauty, humor, prudence, and the like, are all explicated in the same way: as expressions of attitudes, what Allan Gibbard calls “states of norm-acceptance”. However, expressivism also needs to explain the difference between these different sorts of attitude. It is possible to judge that a thing is both aesthetically good and morally (...)
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  39. Finite level borel games and a problem concerning the jump hierarchy.Harold T. Hodes - 1984 - Journal of Symbolic Logic 49 (4):1301-1318.
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  40. On The Sense and Reference of A Logical Constant.Harold Hodes - 2004 - Philosophical Quarterly 54 (214):134-165.
    Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...)
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  41. Gricean Communication and Cognitive Development.Richard Moore - 2017 - Philosophical Quarterly 67 (267):pqw049.
    On standard readings of Grice, Gricean communication requires (a) possession of a concept of belief, (b) the ability to make complex inferences about others’ goal-directed behaviour, and (c) the ability to entertain fourth order meta-representations. To the extent that these abilities are pre-requisites of Gricean communication they are inconsistent with the view that Gricean communication could play a role in their development. In this paper, I argue that a class of ‘minimally Gricean acts’ satisfy the intentional structure described by Grice, (...)
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  42. How to Defend the Law of Non-Contradiction without Incurring the Dialetheist’s Charge of (Viciously) Begging the Question.Marco Simionato - 2024 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 31 (2):141-182.
    According to some critics, Aristotle’s elenctic defence (elenchos, elenchus) of the Law of Non-Contradiction (Metaphysics IV) would be ineffective because it viciously begs the question. After briefly recalling the elenctic refutation of the denier of the Law of Non-Contradiction, I will first focus on Filippo Costantini’s objection to the elenchus, which, in turn, is based on the dialetheic account of negation developed by Graham Priest. Then, I will argue that there is at least one reading of the elenchus that might (...)
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  43. Compatibilism, Manipulation, and the Hard-Line Reply.Dwayne Moore - forthcoming - Erkenntnis.
    Compatibilism is the view that determinism is true, but agents nevertheless possess free will as long as they act from a compatibilist friendly agential structure (i.e., agents want to perform their actions, agents identify with the actions they perform, agents would be responsive to reasons against performing those actions, etc.). The most powerful contemporary objection to compatibilism is the manipulation argument, according to which agents determined to act as they do by the prodding of manipulative neuroscientists are not considered free, (...)
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  44. Putting philosophy of political science on the map.Harold Kincaid & Jeroen Van Bouwel - 2022 - In Harold Kincaid & Jeroen van Bouwel (eds.), The Oxford Handbook of Philosophy of Political Science. New York: Oxford University Press. pp. 1-14.
    Contrary to economics or history, for example, there does not exist an organized field dedicated to the philosophy of political science. Given that the philosophical issues raised by political science research are just as pressing and vibrant as those raised in these more organized fields, fostering a field that labels itself Philosophy of Political Science (PoPS) is important. PoPS is advanced here as a fruitful meeting place where both philosophers and practicing political scientists contribute and discuss—with philosophical discussions that are (...)
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  45. Immoralism and the Valence Constraint.James Harold - 2008 - British Journal of Aesthetics 48 (1):45-64.
    Immoralists hold that in at least some cases, moral fl aws in artworks can increase their aesthetic value. They deny what I call the valence constraint: the view that any effect that an artwork’s moral value has on its aesthetic merit must have the same valence. The immoralist offers three arguments against the valence constraint. In this paper I argue that these arguments fail, and that this failure reveals something deep and interesting about the relationship between cognitive and moral value. (...)
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  46. Modal realism, still at your convenience.Harold Noonan & Mark Jago - 2017 - Analysis 77 (2):299-303.
    Divers presents a set of de re modal truths which, he claims, are inconvenient for Lewisean modal realism. We argue that there is no inconvenience for Lewis.
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  47. On modal logics which enrich first-order S5.Harold T. Hodes - 1984 - Journal of Philosophical Logic 13 (4):423 - 454.
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  48. The Value of Fidelity in Adaptation.James Harold - 2018 - British Journal of Aesthetics 58 (1):89-100.
    © British Society of Aesthetics 2018. Published by Oxford University Press on behalf of the British Society of Aesthetics. All rights reserved. For Permissions, please email: [email protected] adaptation of literary works into films has been almost completely neglected as a philosophical topic. I discuss two questions about this phenomenon:What do we mean when we say that a film is faithful to its source?Is being faithful to its source a merit in a film adaptation?In response to, I set out two distinct (...)
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  49. Autonomism Reconsidered.James Harold - 2011 - British Journal of Aesthetics 51 (2):137-147.
    This paper has three aims: to define autonomism clearly and charitably, to offer a positive argument in its favour, and to defend a larger view about what is at stake in the debate between autonomism and its critics. Autonomism is here understood as the claim that a valuer does not make an error in failing to bring her moral and aesthetic judgements together, unless she herself values doing so. The paper goes on to argue that reason does not require the (...)
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  50. Upper bounds on locally countable admissible initial segments of a Turing degree hierarchy.Harold T. Hodes - 1981 - Journal of Symbolic Logic 46 (4):753-760.
    Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on (...)
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