Results for 'George Cantor'

946 found
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  1.  22
    The Companionship of Books: Essays in Honor of Laurence Berns.John E. Alvis, George Anastaplo, Paul A. Cantor, Jerrold R. Caplan, Michael Davis, Robert Goldberg, Kenneth Hart Green, Harry V. Jaffa, Antonio Marino-López, Joshua Parens, Sharon Portnoff, Robert D. Sacks, Owen J. Sadlier & Martin D. Yaffe (eds.) - 2011 - Lexington Books.
    This volume is a collection of essays by various contributors in honor of the late Laurence Berns, Richard Hammond Elliot Tutor Emeritus at St. John's College, Annapolis. The essays address the literary, political, theological, and philosophical themes of his life's work as a scholar, teacher, and constant companion of the "great books.".
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  2. (1 other version)Georg Cantor: His Mathematics and Philosophy of the Infinite.Joseph Warren Dauben - 1979 - Hup.
    One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets.
  3.  55
    Letters: Criminal Law, Pain Relief, and Physician Aid in Dying.Faye Girsh, Norman L. Cantor & George Conner Thomas - 1997 - Kennedy Institute of Ethics Journal 7 (1):103-104.
    In lieu of an abstract, here is a brief excerpt of the content:Criminal Law, Pain Relief, and Physician Aid in DyingFaye Girsh, Ed.D., Executive DirectorMadam:The article by Cantor and Thomas on “Pain Relief, Acceleration of Death, and Criminal Law” (KIEJ, June 1996) was a tortured attempt to develop criteria for the humane and compassionate physician who tries to serve the needs of a patient in unremitting pain. There are three areas that merit comment.The authors dealt with pain medications that (...)
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  4. 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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  5. Did Georg Cantor influence Edmund Husserl?Claire Ortiz Hill - 1997 - Synthese 113 (1):145-170.
    Few have entertained the idea that Georg Cantor, the creator of set theory, might have influenced Edmund Husserl, the founder of the phenomenological movement. Yet an exchange of ideas took place between them when Cantor was at the height of his creative powers and Husserl in the throes of an intellectual struggle during which his ideas were particularly malleable and changed considerably and definitively. Here their writings are examined to show how Husserl's and Cantor's ideas overlapped and (...)
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  6.  69
    Georg cantor's influence on bertrand russell.I. Grattan-Guinness - 1980 - History and Philosophy of Logic 1 (1-2):61-93.
    This paper is concerned with the influence that the set theory of Georg Cantor bore upon the mathematical logic of Bertrand Russell. In some respects the influence is positive, and stems directly from Cantor's writings or through intermediary figures such as Peano; but in various ways negative influence is evident, for Russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, six sections compare and contrast their views on matters of common (...)
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  7. Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite.Joseph W. Dauben - 1977 - Journal of the History of Ideas 38 (1):85-108.
  8. Towards a biography of Georg Cantor.I. Grattan-Guinness - 1971 - Annals of Science 27 (4):345-391.
    The great influence of Georg Cantor's theory of sets and transfinite arithmetic has led to a considerable interest in his life. It is well known that he had a remarkable and unusual personality, and that he suffered from attacks of mental illness; but the ‘popular’ account of his life is richer in falsehood and distortion than in factual content. This paper attempts to correct these misrepresentations by drawing on a wide variety of manuscript sources concerning Cantor's life and (...)
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  9.  66
    Georg Cantor, His Mathematics and Philosophy of the Infinite.Colin C. Graham - 1980 - Philosophy of Science 47 (1):159-160.
  10.  21
    Georg Cantor: His Mathematics and Philosophy of the Infinite.Mary Tiles - 1982 - Philosophical Books 23 (1):21-23.
  11.  16
    Georg Cantor's paradise, metaphysics, and Husserlian logic.Claire Ortiz Hill - 2012 - In Leila Haaparanta & Heikki J. Koskinen, Categories of Being: Essays on Metaphysics and Logic. Oxford, England: OUP USA.
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  12. 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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  13.  48
    Georg Cantor, 1845-1918Walter Purkert Hans Joachim Ilgauds.Joseph Dauben - 1988 - Isis 79 (4):700-702.
  14. Georg Cantor i idea jedności nauki.Jerzy Dadaczyński - 2009 - Zagadnienia Filozoficzne W Nauce 44.
     
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  15.  62
    Georg Cantor: The Personal Matrix of His Mathematics.Joseph Dauben - 1978 - Isis 69 (4):534-550.
  16.  83
    Constructing Cantorian counterexamples.George Boolos - 1997 - Journal of Philosophical Logic 26 (3):237-239.
    Cantor's diagonal argument provides an indirect proof that there is no one-one function from the power set of a set A into A. This paper provides a somewhat more constructive proof of Cantor's theorem, showing how, given a function f from the power set of A into A, one can explicitly define a counterexample to the thesis that f is one-one.
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  17.  48
    Georg Cantor: His Mathematics and Philosophy of the InfiniteJoseph Warren Dauben.Albert Lewis - 1980 - Isis 71 (3):493-494.
  18.  19
    Omniscience.George I. Mavrodes - 1997 - In Charles Taliaferro & Philip L. Quinn, A Companion to Philosophy of Religion. Cambridge, Mass.: Wiley-Blackwell. pp. 251–257.
    This chapter contains sections titled: Works cited.
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  19. Frege's theorem and the peano postulates.George Boolos - 1995 - Bulletin of Symbolic Logic 1 (3):317-326.
    Two thoughts about the concept of number are incompatible: that any zero or more things have a number, and that any zero or more things have a number only if they are the members of some one set. It is Russell's paradox that shows the thoughts incompatible: the sets that are not members of themselves cannot be the members of any one set. The thought that any things have a number is Frege's; the thought that things have a number only (...)
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  20. Georg Cantor.Alexander Koyré - 1922 - Jahrbuch für Philosophie Und Phänomenologische Forschung 5:620.
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  21.  17
    Mathematik und Realität bei Georg Cantor.Herbert Meschkowski - 1975 - Dialectica 29 (1):55-70.
    RésuméCantor tenait pour impossible de fonder une science exacte « sans un brin de meta‐physique ». Il fonda sa théorie à l'aide de la doctrine platonicienne classique des Idées. Poussée par les antinomies, la mathématique moderne a formalisé la théorie cantorienne des ensembles et en a fait le fondement de l'interprétation structurelle de toute la mathématique. A la suite de certains physiciens, on propose aujourd'hui de revenir à un platonisme modifié . En allant dans le měme sens que Cantor, (...)
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  22.  53
    On Some Philosophical Aspects of the Background to Georg Cantor’s theory of sets.Christian Tapp - 2005 - Philosophia Scientiae:157-173.
    Georg Cantor a cherché à assurer les fondements de sa théorie des ensembles. Cet article présente les differentiations cantoriennes concernant la notion d’infinité et une perspective historique de l’émergence de sa notion d’ensemble.
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  23.  12
    DAUBEN, JOSEPH WARREN, Georg Cantor. His Mathematics ans Philosophy of the Infinite, Princeton University Press, Princeton, 1990.Carlos Ortiz de Landázuri - 1996 - Anuario Filosófico:1454-1455.
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  24.  18
    Nikolai Gogol and Georg Cantor: Paired Vistas of Ulimate Reality and Immortality.Alexander A. Berezin - 2021 - Ultimate Reality and Meaning 38 (1-2):37-49.
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  25. Louis Couturat et Georg Cantor.Pierre Dugac - 1983 - In Louis Couturat, L'oeuvre de Louis Couturat (1868-1914): de Leibniz à Russell. Paris: Rue d'Ulm.
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  26.  87
    Natural Numbers and Infinitesimals: A Discussion between Benno Kerry and Georg Cantor.Carlo Proietti - 2008 - History and Philosophy of Logic 29 (4):343-359.
    During the first months of 1887, while completing the drafts of his Mitteilungen zur Lehre vom Transfiniten, Georg Cantor maintained a continuous correspondence with Benno Kerry. Their exchange essentially concerned two main topics in the philosophy of mathematics, namely, (a) the concept of natural number and (b) the infinitesimals. Cantor's and Kerry's positions turned out to be irreconcilable, mostly because of Kerry's irremediably psychologistic outlook, according to Cantor at least. In this study, I will examine and reconstruct (...)
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  27.  34
    George J. Agich, Ph. D., is the FJ O'Neil Chair in the Department of Bioethics, The Cleveland Clinic Foundation, Cleveland, Ohio. Bette Anton, MLS, is the Head Librarian of the Optometry Library/Health Sciences Information Service. This library serves the University of California at Berkeley–University of California at San Francisco Joint Medical Program and. [REVIEW]Norman L. Cantor, Ann Freeman Cook, Linda L. Emanuel, Colin Gavaghan, Katarina Guttmannova, Carlton Hegwood Jr & Helena Hoas - 2000 - Cambridge Quarterly of Healthcare Ethics 9:147-149.
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  28. Abstraction and idealization in Edmund Husserl and Georg Cantor prior to 1895.Claire Ortiz Hill - 2004 - Poznan Studies in the Philosophy of the Sciences and the Humanities 82 (1):217-244.
    Little is known of Edmund Husserl's direct encounter with Georg Cantor's ideas on Platonic idealism and the abstraction of number concepts during the late 19th century, when Husserl's philosophical orientation changed considerably and definitely. Closely analyzing and comparing the two men's writings during that important time in their intellectual careers, I describe the crucial shift in Husserl's views on psychologism and metaphysical idealism as it relates to Cantor's philosophy of arithmetic. I thus establish connections between their ideas which (...)
     
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  29.  60
    Some Choice: Law, Medicine, and the Market (1998) by George J. Annas. New York, N.Y.: Oxford University Press, 1998. 320 pp. $29.95. [REVIEW]Norman L. Cantor - 2000 - Cambridge Quarterly of Healthcare Ethics 9 (2):288-291.
    George Annas serves a critical function as an incisive commentator on the interactions between law and medicine and law and public health. Along with Alex Capron, Dena Davis, Rebecca Dresser, and Larry GostinProfessor Annas analyses legal aspects of a spectrum of medicolegal issues both in a forum and in a manner that makes them accessible and understandable to a broad community of healthcare providers. His latest book, SomeChoice, continues that valuable tradition. The bulk of the volume (17 out of (...)
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  30. J. W. DAUBEN "Georg Cantor: his mathematics and philosophy of the infinite". [REVIEW]G. H. Moore - 1980 - History and Philosophy of Logic 1:238.
     
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  31.  81
    Joseph Warren Dauben. Georg Cantor, his mathematics and philosophy of the infinite. Harvard University Press, Cambridge, Mass. and London, 1979, ix + 404 pp. [REVIEW]Arnold Oberschelp - 1982 - Journal of Symbolic Logic 47 (2):456-457.
  32.  58
    Le concept scientifique du continu zénon d'élée et Georg Cantor.Paul Tannery - 1885 - Revue Philosophique de la France Et de l'Etranger 20:385 - 410.
  33.  45
    Twentieth Century Georg Cantor: His Mathematics and Philosophy of the Infinite. By Joseph Warren Dauben. Cambridge, Mass. & London: Harvard University Press, 1979. Pp. ix + 404. $27.50/£19.00. [REVIEW]Dale M. Johnson - 1981 - British Journal for the History of Science 14 (1):101-103.
  34.  11
    Pensare l'infinito: filosofia e matematica dell'infinito in Bernard Bolzano e Georg Cantor.Filippo Costantini - 2016 - Milano: Mimesis.
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  35.  63
    Surprises in the History of Infinity from Anaximander to George Cantor.Leo Sweeney - 1981 - Proceedings of the American Catholic Philosophical Association 55:3-23.
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  36. Intertwining metaphysics and mathematics: The development of Georg Cantor's set theory 1871-1887.Anne Newstead - 2008 - Review of Contemporary Philosophy 7:35-55.
  37.  27
    Missing Materials concerning the Life and Work of Georg Cantor.I. Grattan-Guinness - 1971 - Isis 62 (4):516-517.
  38. Book Review. [REVIEW]Norman Cantor - 2000 - Cambridge Quarterly of Healthcare Ethics 9 (2):288-291.
    George Annas serves a critical function as an incisive commentator on the interactions between law and medicine and law and public health. Along with Alex Capron, Dena Davis, Rebecca Dresser, and Larry Gostin—to pinpoint a few—Professor Annas analyses legal aspects of a spectrum of medicolegal issues both in a forum and in a manner that makes them accessible and understandable to a broad community of healthcare providers. His latest book, Some Choice, continues that valuable tradition. The bulk of the (...)
     
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  39. W. PURKERT and H. J. ILGAUDS "Georg Cantor". [REVIEW]A. C. Lewis - 1988 - History and Philosophy of Logic 9 (1):118.
     
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  40.  66
    Cantor, God, and Inconsistent Multiplicities.Aaron R. Thomas-Bolduc - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):133-146.
    The importance of Georg Cantor’s religious convictions is often neglected in discussions of his mathematics and metaphysics. Herein I argue, pace Jan ́e (1995), that due to the importance of Christianity to Cantor, he would have never thought of absolutely infinite collections/inconsistent multiplicities,as being merely potential, or as being purely mathematical entities. I begin by considering and rejecting two arguments due to Ignacio Jan ́e based on letters to Hilbert and the generating principles for ordinals, respectively, showing that (...)
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  41. Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik.Marcus Rossberg & Philip A. Ebert - 2009 - History and Philosophy of Logic 30 (4):341-348.
    In 1885, Georg Cantor published his review of Gottlob Frege's Grundlagen der Arithmetik . In this essay, we provide its first English translation together with an introductory note. We also provide a translation of a note by Ernst Zermelo on Cantor's review, and a new translation of Frege's brief response to Cantor. In recent years, it has become philosophical folklore that Cantor's 1885 review of Frege's Grundlagen already contained a warning to Frege. This warning is said (...)
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  42. Cantor and the Burali-Forti Paradox.Christopher Menzel - 1984 - The Monist 67 (1):92-107.
    In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and (...)
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  43. 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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  44.  47
    (1 other version)La notion husserlienne de multiplicité : au-delà de Cantor et Riemann.Carlo Ierna - 2012 - Methodos. Savoirs Et Textes 12 (12).
    The concept of a Mannigfaltigkeit in Husserl has been given various interpretations, due to its shifting role in his works. Many authors have been misled by this term, placing it in the context of Husserl’s early period in Halle, while writing the Philosophy of Arithmetic, as a friend and colleague of Georg Cantor.Yet at the time, Husserl distanced himself explicitly from Cantor’s definition and rather took Bernhard Riemann as example, having studied and lectured extensively on Riemann’s theories of (...)
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  45.  22
    Kundakunda, Cantor, and the 'Inaccessibility' of the Absolute: A Set-Theoretical Approach to Sarvajñatā.Jesse Berger - 2022 - Philosophy East and West 72 (3):626-647.
    Abstract:In this article, Kundakunda's theory of omniscience is defended using formal principles derived from set theory. More precisely, analogous features in the work of Jain mystic Kundakunda and the German mathematician Georg Cantor are described, demonstrating that both thinkers demanded an independently existent, transcendental Absolute to render consistent their own systems of thought. Both of their projects entailed resolving the formal quandary of inaccessibility, or the inability for any sequential, determinate objectifications to ever mereologically sum up to a genuine (...)
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  46. The influence of Spinoza’s concept of infinity on Cantor’s set theory.Paolo Bussotti & Christian Tapp - 2009 - Studies in History and Philosophy of Science Part A 40 (1):25-35.
    Georg Cantor, the founder of set theory, cared much about a philosophical foundation for his theory of infinite numbers. To that end, he studied intensively the works of Baruch de Spinoza. In the paper, we survey the influence of Spinozean thoughts onto Cantor’s; we discuss Spinoza’s philosophy of infinity, as it is contained in his Ethics; and we attempt to draw a parallel between Spinoza’s and Cantor’s ontologies. Our conclusion is that the study of Spinoza provides deepening (...)
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  47. The negative theology of absolute infinity: Cantor, mathematics, and humility.Rico Gutschmidt & Merlin Carl - 2024 - International Journal for Philosophy of Religion 95 (3):233-256.
    Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to (...)
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  48. Absolute Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor (ABSTRACT ONLY).Anne Newstead - 2024 - In Mirosław Szatkowski, Ontology of Divinity. Boston: 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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  49. The Motives Behind Cantor’s Set Theory: Physical, biological and philosophical questions.José Ferreirós - 2004 - Science in Context 17 (1/2):1–35.
    The celebrated “creation” of transfinite set theory by Georg Cantor has been studied in detail by historians of mathematics. However, it has generally been overlooked that his research program cannot be adequately explained as an outgrowth of the mainstream mathematics of his day. We review the main extra-mathematical motivations behind Cantor's very novel research, giving particular attention to a key contribution, the Grundlagen (Foundations of a general theory of sets) of 1883, where those motives are articulated in some (...)
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  50.  20
    The Immanence of Truths and the Absolutely Infinite in Spinoza, Cantor, and Badiou.Jana Ndiaye Berankova - 2021 - Filozofski Vestnik 41 (2).
    The following article compares the notion of the absolute in the work of Georg Cantor and in Alain Badiou’s third volume of Being and Event: The Immanence of Truths and proposes an interpretation of mathematical concepts used in the book. By describing the absolute as a universe or a place in line with the mathematical theory of large cardinals, Badiou avoided some of the paradoxes related to Cantor’s notion of the “absolutely infinite” or the set of all that (...)
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