Results for 'George Cantor'

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  1. Georg Cantor’s Ordinals, Absolute Infinity & Transparent Proof of the Well-Ordering Theorem.Hermann G. W. Burchard - 2019 - Philosophy Study 9 (8).
    Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add (...)
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  2. Ortega y Gasset on Georg Cantor’s Theory of Transfinite Numbers.Lior Rabi - 2016 - Kairos (15):46-70.
    Ortega y Gasset is known for his philosophy of life and his effort to propose an alternative to both realism and idealism. The goal of this article is to focus on an unfamiliar aspect of his thought. The focus will be given to Ortega’s interpretation of the advancements in modern mathematics in general and Cantor’s theory of transfinite numbers in particular. The main argument is that Ortega acknowledged the historical importance of the Cantor’s Set Theory, analyzed it and (...)
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  3. Halfway Up To the Mathematical Infinity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transfinite Design.Edward G. Belaga - manuscript
    Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of (...)
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  4. Cantor on Infinity in Nature, Number, and the Divine Mind.Anne Newstead - 2009 - American Catholic Philosophical Quarterly 83 (4):533-553.
    The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in (...)’s thought with reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885). (shrink)
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  5. Absolute Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor (ABSTRACT ONLY).Anne Newstead - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. De Gruyter. pp. 561-580.
    Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...)
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  6. Retrieving the Mathematical Mission of the Continuum Concept from the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract.Edward G. Belaga - forthcoming - International Journal of Pure and Applied Mathematics.
    What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock of (...)
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  7. "Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor" (Manuscript draft of first page of forthcoming book chapter ).Anne Newstead (ed.) - forthcoming - Berlin: De Gruyter.
    Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...)
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  8. From Traditional Set Theory – that of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension.Edward G. Belaga - manuscript
    The original purpose of the present study, 2011, started with a preprint «On the Probable Failure of the Uncountable Power Set Axiom», 1988, is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum — this genuine, even if mostly forgotten today raison d’être of all traditional set-theoretical enterprises to Infinity and beyond, from Georg Cantor to David Hilbert to Kurt Gödel to W. Hugh Woodin to Buzz Lightyear.
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  9. Aristotle and modern mathematical theories of the continuum.Anne Newstead - 2001 - In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
    This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed (...)
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  10. Review of The Art of the Infinite by R. Kaplan, E. Kaplan 324p(2003).Michael Starks - 2016 - In Suicidal Utopian Delusions in the 21st Century: Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2017 2nd Edition Feb 2018. Las Vegas, USA: Reality Press. pp. 619.
    This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don´t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don´t know any and don´t (...)
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  11. Identification of antinomies by complementary analysis.Andrzej Burkiet - manuscript
    It has been noticed that self-referential, ambiguous definitional formulas are accompanied by complementary self-referential antinomy formulas, which gives rise to contradictions. This made it possible to re-examine ancient antinomies and Cantor’s Diagonal Argument (CDA), as well as the method of nested intervals, which is the basis for evaluating the existence of uncountable sets. Using Georg Cantor’s remark that every real number can be represented as an infinite digital expansion (usually decimal or binary), a simplified system for verifying the (...)
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  12. Spojrzenia w kierunku matematyki [recenzja]. [REVIEW]Paweł Polak - 2004 - Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce) 34:140--144.
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  13. Laozi Through the Lens of the White Rose: Resonance or Dissonance?Lea Cantor - 2023 - Oxford German Studies 52 (1):62-79.
    A surprising feature of the White Rose anti-Nazi resistance pamphlets is their appeal to a foundational classical Chinese text, the Laozi (otherwise known as the Daodejing), to buttress their critique of fascism and authoritarianism. I argue that from the perspective of a 1942 educated readership, the act of quoting the Laozi functioned as a subtle and pointed nod to anti-fascist intellectuals in pre-war Germany, many of whom had interpreted the Laozi as an anti-authoritarian and pacifist text. To a sympathetic reader, (...)
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  14. Quality and concept.George Bealer - 1982 - New York: Oxford University Press.
    This study provides a unified theory of properties, relations, and propositions (PRPs). Two conceptions of PRPs have emerged in the history of philosophy. The author explores both of these traditional conceptions and shows how they can be captured by a single theory.
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  15. Modelling Deep Indeterminacy.George Darby & Martin Pickup - 2021 - Synthese 198:1685–1710.
    This paper constructs a model of metaphysical indeterminacy that can accommodate a kind of ‘deep’ worldly indeterminacy that arguably arises in quantum mechanics via the Kochen-Specker theorem, and that is incompatible with prominent theories of metaphysical indeterminacy such as that in Barnes and Williams (2011). We construct a variant of Barnes and Williams's theory that avoids this problem. Our version builds on situation semantics and uses incomplete, local situations rather than possible worlds to build a model. We evaluate the resulting (...)
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  16. Beliefs About the True Self Explain Asymmetries Based on Moral Judgment.George E. Newman, Julian De Freitas & Joshua Knobe - 2015 - Cognitive Science 39 (1):96-125.
    Past research has identified a number of asymmetries based on moral judgments. Beliefs about what a person values, whether a person is happy, whether a person has shown weakness of will, and whether a person deserves praise or blame seem to depend critically on whether participants themselves find the agent's behavior to be morally good or bad. To date, however, the origins of these asymmetries remain unknown. The present studies examine whether beliefs about an agent's “true self” explain these observed (...)
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  17. Modal Epistemology and the Rationalist Renaissance.George Bealer - 2002 - In Tamar Gendler & John Hawthorne (eds.), Conceivability and Possibility. New York: Oxford University Press. pp. 71-125.
    The paper begins with a clarification of the notions of intuition (and, in particular, modal intuition), modal error, conceivability, metaphysical possibility, and epistemic possibility. It is argued that two-dimensionalism is the wrong framework for modal epistemology and that a certain nonreductionist approach to the theory of concepts and propositions is required instead. Finally, there is an examination of moderate rationalism’s impact on modal arguments in the philosophy of mind -- for example, Yablo’s disembodiment argument and Chalmers’s zombie argument. A less (...)
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  18. (1 other version)A Theory of the a Priori.George Bealer - 1999 - Philosophical Perspectives 13:29-55.
    The topic of a priori knowledge is approached through the theory of evidence. A shortcoming in traditional formulations of moderate rationalism and moderate empiricism is that they fail to explain why rational intuition and phenomenal experience count as basic sources of evidence. This explanatory gap is filled by modal reliabilism -- the theory that there is a qualified modal tie between basic sources of evidence and the truth. This tie to the truth is then explained by the theory of concept (...)
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  19. Paternalism and intimate relationships.George Tsai - 2018 - In Kalle Grill & Jason Hanna (eds.), The Routledge Handbook of the Philosophy of Paternalism. New York: Routledge.
    This paper argues that participation in an intimate relationship can generate additional or stronger reasons for one to act paternalistically toward the intimate. Moreover, participation in such a relationship can also weaken or cancel some of the presumptive reasons of respect one would otherwise have not to interfere. The paper also reflects, more generally, on the nature of intimate relationships, the normative significance of paternalism, and the normative differences between paternalism in larger-scale institutional contexts and paternalism in closer, interpersonal ones. (...)
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  20. A priori knowledge and the scope of philosophy.George Bealer - 1996 - Philosophical Studies 81 (2-3):121-142.
    This paper provides a defense of two traditional theses: the Autonomy of Philosophy and the Authority of Philosophy. The first step is a defense of the evidential status of intuitions (intellectual seemings). Rival views (such as radical empiricism), which reject the evidential status of intuitions, are shown to be epistemically self-defeating. It is then argued that the only way to explain the evidential status of intuitions is to invoke modal reliabilism. This theory requires that intuitions have a certain qualified modal (...)
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  21. Reason and Experience.George P. Adams - 1924 - University of California Publications in Philosophy 5:143-69.
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  22. The incoherence of empiricism.George Bealer - 1992 - Aristotelian Society Supplementary Volume 66 (1):99-138.
    Radical empiricism is the view that a person's experiences (sensory and introspective), or a person's observations, constitute the person's evidence. This view leads to epistemic self-defeat. There are three arguments, concerning respectively: (1) epistemic starting points; (2) epistemic norms; (3) terms of epistemic appraisal. The source of self-defeat is traced to the fact that empiricism does not count a priori intuition as evidence (where a priori intuition is not a form of belief but rather a form of seeming, specifically intellectual (...)
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  23. Temporal Form and Existence.George P. Adams - 1935 - University of California Publications in Philosophy 18:203-225.
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  24. Truths of Existence and of Meaning.George P. Adams - 1929 - University of California Publications in Philosophy 11:35-61.
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  25. Truth, Discourse, and Reality.George P. Adams - 1928 - University of California Publications in Philosophy 10:177-205.
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  26. Remarks on classical analysis.George Bealer - 1983 - Journal of Philosophy 80 (11):711-712.
    Abstract of a paper to be presented in an APA symposium on Classical Analysis, December 30, 1983, commenting on a paper by Ernest Sosa.
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  27. Making Artists of Us All: The Evolution of an Educational Aesthetic.George E. Abaunza - 2005 - Dissertation, Florida State University
    The history of philosophy is replete with attempts at invoking rationality as a means of directing and even subduing human desire and emotion. Understood as that which moves human beings to action, desire and emotion come to be associated with human freedom and rationality as a means of curbing that freedom. Plato, for instance, takes for granted a separation between thought and action that drives a wedge between our rational ability to exercise self-discipline and the free expression of desire and (...)
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  28. What Makes Possibility Possible?George P. Adams - 1934 - University of California Publications in Philosophy 17:3-24.
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  29. The Nature and Validity of the Causal Principle.George P. Adams - 1932 - University of California Publications in Philosophy 15:207-31.
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  30. The Nature and Habitat of Mind.George P. Adams - 1923 - University of California Publications in Philosophy 4:47-73.
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  31. Norms and Reason.George P. Adams - 1925 - University of California Publications in Philosophy 7:3-30.
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  32. The philosophical limits of scientific essentialism.George Bealer - 1987 - Philosophical Perspectives 1:289-365.
    Scientific essentialism is the view that some necessities can be known only with the aid of empirical science. The thesis of the paper is that scientific essentialism does not extend to the central questions of philosophy and that these questions can be answered a priori. The argument is that the evidence required for the defense of scientific essentialism is reliable only if the intuitions required by philosophy to answer its central questions is also reliable. Included is an outline of a (...)
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  33. The Epsilon Calculus and Herbrand Complexity.Georg Moser & Richard Zach - 2006 - Studia Logica 82 (1):133-155.
    Hilbert's ε-calculus is based on an extension of the language of predicate logic by a term-forming operator εx. Two fundamental results about the ε-calculus, the first and second epsilon theorem, play a rôle similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential (...)
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  34. Anomalous Mind-Matter Interaction, Free Will, and the Nature of Causality.George Williams - 2023 - Journal of Anomalous Experience and Cognition 3 (1):140-173.
    In this paper, I propose a framework that supports both free will and anomalous mind-matter interaction (psychokinesis). I begin by considering the argument by the physicist Sean Carroll that the laws of physics as we understand them rule out psychokinesis (and other modes of psi). I find Carroll’s claims problematic, in part due to what I believe are misunderstandings of arguments borrowed from David Hume. I proceed to consider a more dispositional notion of causality (in contrast to one characterized by (...)
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  35. An inconsistency in direct reference theory.George Bealer - 2004 - Journal of Philosophy 101 (11):574 - 593.
    Direct reference theory faces serious prima facie counterexamples which must be explained away (e.g., that it is possible to know a priori that Hesperus = Phosphorus). This is done by means of various forms of pragmatic explanation. But when those explanations that provisionally succeed are generalized to deal with analogous prima facie counterexamples concerning the identity of propositions, a fatal dilemma results. Either identity must be treated as a four-place relation (contradicting what just about everyone, including direct reference theorists, takes (...)
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  36. Propositions.George Bealer - 1998 - Mind 107 (425):1-32.
    Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...)
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  37. On the possibility of philosophical knowledge.George Bealer - 1996 - Philosophical Perspectives 10:1-34.
    The paper elaborates upon various points and arguments in the author’s “A Priori Knowledge and the Scope of Philosophy” (Philosophical Studies, 1993), in which the author defends the autonomy of philosophy from the empirical sciences. It provides, for example, an extended defense of the modal reliabilist theory of basic evidence, including a new argument against evolutionary explanations of the reliability of intuitions. It also contains a fuller discussion of how to neutralize the threat of scientific essentialism to the autonomy of (...)
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  38. Double or nothing: Deconstructing cultural heritage.George Rossolatos - 2015 - Chinese Semiotic Studies 11 (3):297-315.
    This paper draws on the deconstruction(ist) toolbox and specifically on the textual unweaving tactics of supplementarity, exemplarity, and parergonality, with a view to critically assessing institutional (UNESCO’s) and ordinary tourists’ claims to authenticity as regards artifacts and sites of ‘cultural heritage’. Through the ‘destru[k]tion’ of claims to ‘originality’ and ‘myths of origin’, that function as preservatives for canning such artifacts and sites, the cultural arche-writing that forces signifiers to piously bow before a limited string of ‘transcendental signifieds’ is brought to (...)
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  39. Möglichkeiten und Grenzen von Ethikberatung im Rahmen der COVID-19-Pandemie.Georg Marckmann, Gerald Neitzke, Annette Riedel, Silke Schicktanz, Jan Schildmann, Alfred Simon, Ralf Stoecker, Jochen Vollmann, Eva Winkler & Christin Zang - 2020 - Ethik in der Medizin 32 (2):195-199.
    Das deutsche Gesundheitswesen steht durch die schnell steigende Anzahl an CO- VID-19-Erkrankten vor erheblichen Herausforderungen. In dieser Krisensituation sind alle Beteiligten mit ethischen Fragen konfrontiert, beispielsweise nach gerech- ten Verteilungskriterien bei begrenzten Ressourcen und dem gesundheitlichen Schutz des Personals angesichts einer bisher nicht therapierbaren Erkrankung. Daher werden schon jetzt klinische und ambulante Ethikberatungsangebote verstärkt mit Anfragen nach Unterstützung konfrontiert. Wie können Ethikberater*innen Entscheidungen in der Krankenversorgung im Rahmen der COVID-19-Pandemie unterstützen? Welche Grenzen von Ethikberatung sind zu beachten? Bislang liegen hierzu (...)
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  40. The Virtue of Being Supportive.George Tsai - 2016 - Pacific Philosophical Quarterly 99 (2):317-342.
    I develop an account of the nature and value of being supportive in interpersonal relationships. In particular, I argue that the virtue of being supportive, construed as a modally demanding value, facilitates the autonomy of one's intimate and promotes a sense of unity in one's relationship. Moreover, the practice of being supportive plays an important role with regard to the familiar need to reconcile the normative demands of one's own projects with one's responsibilities to intimates.
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  41. Mental properties.George Bealer - 1994 - Journal of Philosophy 91 (4):185-208.
    It is argued that, because of scientific essentialism, two currently popular arguments against the mind-body identity thesis -- the multiple-realizability argument and the Nagel-Jackson knowledge argument -- are unsatisfactory as they stand and that their problems are incurable. It is then argued that a refutation of the identity thesis in its full generality can be achieved by weaving together two traditional Cartesian arguments -- the modal argument and the certainty argument. This argument establishes, not just the falsity of the identity (...)
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  42. Universals.George Bealer - 1993 - Journal of Philosophy 90 (1):5-32.
    Presented here is an argument for the existence of universals. Like Church's translation- test argument, the argument turns on considerations from intensional logic. But whereas Church's argument turns on the fine-grained informational content of intensional sentences, this argument turns on the distinctive logical features of 'that'-clauses embedded within modal contexts. And unlike Church's argument, this argument applies against truth-conditions nominalism and also against conceptualism and in re realism. So if the argument is successful, it serves as a defense of full (...)
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  43. Mind and anti-mind: Why thinking has no functional definition.George Bealer - 1984 - Midwest Studies in Philosophy 9 (1):283-328.
    Functionalism would be mistaken if there existed a system of deviant relations (an “anti-mind”) that had the same functional roles as the standard mental relations. In this paper such a system is constructed, using “Quinean transformations” of the sort associated with Quine’s thesis of the indeterminacy of translation. For example, a mapping m from particularistic propositions (e.g., that there exists a rabbit) to universalistic propositions (that rabbithood is manifested). Using m, a deviant relation thinking* is defined: x thinks* p iff (...)
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  44. Quantum Mechanics, Metaphysics, and Bohm's Implicate Order.George Williams - 2019 - Mind and Matter 2 (17):155-186.
    The persistent interpretation problem for quantum mechanics may indicate an unwillingness to consider unpalatable assumptions that could open the way toward progress. With this in mind, I focus on the work of David Bohm, whose earlier work has been more influential than that of his later. As I’ll discuss, I believe two assumptions play a strong role in explaining the disparity: 1) that theories in physics must be grounded in mathematical structure and 2) that consciousness must supervene on material processes. (...)
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  45. A solution to Frege's puzzle.George Bealer - 1993 - Philosophical Perspectives 7:17-60.
    This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege's puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is also (...)
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  46. Psi and the Problem of Consciousness.George Williams - 2013 - Journal of Mind and Behavior 34:259-284.
    In this paper, I consider what the growing evidence in parapsychology can tell us about the nature of consciousness. Parapsychology remains controversial because it implies deviations from the understanding that many scientists and philosophers hold about the nature of reality. However, given the difficulties in explaining consciousness, a growing number of philosophers have called for new, possibly radical explanations, which include versions of dualism or panpsychism. In this spirit, I briefly review the evidence on psi to see what explanation of (...)
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  47. Thematic Analysis and its Interdisciplinary Interest.Georges Alahou - 2023 - Conatus 8 (1):29-53.
    The term “thematic analysis” abounds in research articles and appears in the titles of books, without the authors of these writings being primarily concerned with defining what thematic analysis is. Thematic analysis is present in the current vocabulary of several disciplines and is presented as a working method of choice in psychology, sociology, or linguistics, to name but a few. This article seeks to situate thematic analysis in the thinking of Holton Gerald, who introduced it into the philosophy of science (...)
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  48. The Morality of State Symbolic Power.George Tsai - 2016 - Social Theory and Practice 42 (2):318-342.
    Philosophical interest in state power has tended to focus on the state’s coercive powers rather than its expressive powers. I consider an underexplored aspect of the state’s expressive capacity: its capacity to use symbols (such as monuments, memorials, and street names) to promote political ends. In particular, I argue that the liberal state’s deployment of symbols to promote its members’ commitment to liberal ideals is in need of special justification. This is because the state’s exercise of its capacity to use (...)
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  49. Intensional Entities.George Bealer - 1996 - In Edward Craig (ed.), Routledge Encyclopedia of Philosophy: Genealogy to Iqbal. New York: Routledge. pp. 803-7.
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  50. ’Do Not Do Unto Others…’: Cultural Misrecognition and the Harms of Appropriation in an Open Source World.George P. Nicholas & Alison Wylie - 2013 - In Geoffrey Scarre & Robin Coningham (eds.), Appropriating the past: philosophical perspectives on the practice of archaeology. Cambridge: Cambridge University Press. pp. 195-221.
    In this chapter we explore two important questions that we believe should be central to any discussion of the ethics and politics of cultural heritage: What are the harms associated with appropriation and commodification, specifically where the heritage of Indigenous peoples is concerned? And how can these harms best be avoided? Archaeological concerns animate this discussion; we are ultimately concerned with fostering postcolonial archaeological practices. But we situate these questions in a broader context, addressing them as they arise in connection (...)
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