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Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Dordrecht, Netherland: Springer (2013)

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  1. The Rationality of Science.W. Newton-Smith - 1981 - Boston: Routledge.
    First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.
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  • A Companion to Phenomenology and Existentialism.Hubert L. Dreyfus & Mark A. Wrathall (eds.) - 2006 - Oxford: Wiley-Blackwell.
    A Companion to Phenomenology and Existentialism is a complete guide to two of the dominant movements of philosophy in the twentieth century. Written by a team of leading scholars, including Dagfinn Føllesdal, J. N. Mohanty, Robert Solomon, Jean–Luc Marion Highlights the area of overlap between the two movements Features longer essays discussing each of the main schools of thought, shorter essays introducing prominent themes, and problem–oriented chapters Organised topically, around concepts such as temporality, intentionality, death and nihilism Features essays on (...)
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  • Aesthetic/Non-aesthetic and the concept of taste: a critique of Sibley's position.Ted Cohen - 1973 - Theoria 39 (1-3):113-152.
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  • Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
    Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.
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  • (1 other version)Languages of Art: An Approach to a Theory of Symbols.Nelson Goodman - 1968 - Indianapolis,: Bobbs-Merrill.
    . . . Unlike Dewey, he has provided detailed incisive argumentation, and has shown just where the dogmas and dualisms break down." -- Richard Rorty, The Yale Review.
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  • Introduction to a philosophy of music.Peter Kivy - 2002 - New York: Clarendon Press.
    Philosophy of music has flourished in the last thirty years, with great advances made in the understanding of the nature of music and its aesthetics. Peter Kivy has been at the center of this flourishing, and now offers his personal introduction to philosophy of music, a clear and lively explanation of how he sees the most important and interesting philosophical issues relating to music. Anyone interested in music will find this a stimulating introduction to some fascinating questions and ideas.
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  • The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
    This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
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  • Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
    In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument (...)
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  • The philosophy of music : Formalism and beyond.Philip Alperson - 2004 - In Peter Kivy (ed.), Blackwell Guide to Aesthetics. Malden, MA: Wiley-Blackwell. pp. 254–275.
    This chapter contains sections titled: Formalism Enhanced Formalism Beyond Formalism.
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  • Boethius.John Marenbon - 2003 - New York: Oxford University Press.
    This book offers a brief, accessible introduction to the thought of Boethius. After a survey of Boethius's life and work, Marenbon explicates his theological method, and devotes separate chapters to his arguments about good and evil, fortune, fate and free will, and the problem of divine foreknowledge. Marenbon also traces Boethius's influence on the work of such thinkers as Aquinas and Duns Scotus.
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  • Philosophies of arts: an essay in differences.Peter Kivy - 1997 - New York: Cambridge University Press.
    Since the beginning of the eighteenth century the philosophy of art has been engaged on the project of trying to find out what the fine arts have in common and, thus, how they might be defined. Peter Kivy's purpose in this accessible and lucid book is to trace the history of that enterprise and argue that the definitional project has been unsuccessful. He offers a fruitful change of strategy: instead of engaging in an obsessive quest for sameness, let us explore (...)
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  • Aesthetic value.Alan H. Goldman - 1995 - Boulder, Colo.: Westview Press.
    In this concise survey, intended for advanced undergraduate students of aesthetics, Alan Goldman focuses on the question of aesthetic value, using many practical examples from painting, music, and literature to make his case. Although he treats a wide variety of views, he argues for a nonrealist view of aesthetic value, showing that the personal element can never be factored out of evaluative aesthetic judgments and explaining why this is so.
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  • Truth and objectivity.Crispin Wright - 1992 - Cambridge: Harvard University Press.
    Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...
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  • Music alone: philosophical reflections on the purely musical experience.Peter Kivy - 1990 - Ithaca: Cornell University Press.
    In the Essai sur Vorigine des langues (), Jean-Jacques Rousseau reports on an eighteenth-century curiosity that has, from time to time, fascinated musicians ...
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  • Aesthetic judgment.Nick Zangwill - 2003 - The Stanford Encyclopedia of Philosophy.
    Beauty is an important part of our lives. Ugliness too. It is no surprise then that philosophers since antiquity have been interested in our experiences of and judgments about beauty and ugliness. They have tried to understand the nature of these experiences and judgments, and they have also wanted to know whether these experiences and judgments were legitimate. Both these projects took a sharpened form in the twentieth century, when this part of our lives came under a sustained attack in (...)
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  • The phenomenology of mathematical beauty.Gian-Carlo Rota - 1997 - Synthese 111 (2):171-182.
    It has been observed that whereas painters and musicians are likely to be embarrassed by references to the beauty in their work, mathematicians instead like to engage in discussions of the beauty of mathematics. Professional artists are more likely to stress the technical rather than the aesthetic aspects of their work. Mathematicians, instead, are fond of passing judgment on the beauty of their favored pieces of mathematics. Even a cursory observation shows that the characteristics of mathematical beauty are at variance (...)
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  • Beauty, a road to the truth.Theo A. F. Kuipers - 2002 - Synthese 131 (3):291-328.
    In this article I give a naturalistic-cum-formal analysis of therelation between beauty, empirical success, and truth. The analysis is based on the onehand on a hypothetical variant of the so-called `mere-exposure effect'' which has been more orless established in experimental psychology regarding exposure-affect relationshipsin general and aesthetic appreciation in particular (Zajonc 1968; Temme 1983; Bornstein 1989;Ye 2000). On the other hand it is based on the formal theory of truthlikeness andtruth approximation as presented in my From Instrumentalism to Constructive Realism (...)
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  • The four-color problem and its philosophical significance.Thomas Tymoczko - 1979 - Journal of Philosophy 76 (2):57-83.
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  • Aesthetic Concepts.Frank Sibley - 1959 - Philosophical Review 68 (4):421-450.
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  • (2 other versions)Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
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  • Descartes' Error: Emotion, Reason, and the Human Brain.Antonio R. Damasio - 1994 - Putnam.
    Linking the process of rational decision making to emotions, an award-winning scientist who has done extensive research with brain-damaged patients notes the dependence of thought processes on feelings and the body's survival-oriented regulators. 50,000 first printing.
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  • The Emotions.Nico Frijda - 1986 - Cambridge University Press.
    What are 'emotions'? This book offers a balanced survey of facts and theory.
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  • Truth and Objectivity.Crispin Wright - 1992 - Philosophy and Phenomenological Research 56 (4):883-890.
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  • Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Bulletin of Symbolic Logic 8 (4):516-518.
    This book does three main things. First, it defends mathematical platonism against the main objections to that view (most notably, the epistemological objection and the multiple-reductions objection). Second, it defends anti-platonism (in particular, fictionalism) against the main objections to that view (most notably, the Quine-Putnam indispensability objection and the objection from objectivity). Third, it argues that there is no fact of the matter whether abstract mathematical objects exist and, hence, no fact of the matter whether platonism or anti-platonism is true.
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  • A Mathematician's Apology.G. H. Hardy - 1941 - Philosophy 16 (63):323-326.
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  • (2 other versions)Languages of Art: An Approach to a Theory of Symbols.Nelson Goodman - 1971 - British Journal for the Philosophy of Science 22 (2):187-198.
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  • Beauty and Revolution in Science.James W. Mcallister - 1999 - Philosophical Quarterly 49 (194):125-128.
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  • (2 other versions)Languages of Art. An Approach to a Theory of Symbols.Nelson Goodman - 1970 - Critica 4 (11/12):164-171.
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  • Music and the Emotions: The Philosophical Theories.Malcolm Budd - 1985 - Boston: Routledge.
    It has often been claimed, and frequently denied, that music derives some or all of its artistic value from the relation in which it stands to the emotions. This book presents and subjects to critical examination the chief theories about the relationship between the art of music and the emotions.
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  • Subjectivity.R. C. Solomon - 1995 - In Ted Honderich (ed.), The Oxford companion to philosophy. New York: Oxford University Press. pp. 900.
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  • Francis Hutcheson: an inquiry concerning beauty, order, harmony, design.Francis Hutcheson - 1725 - The Hague,: Martinus Nijhoff. Edited by Peter Kivy & Francis Hutcheson.
    THE SENSE OF BEAUTY: A FIRST APPROXIMATION It is generally acknowledged that during the first half of the eighteenth century a profound change was wrought in the theory of art and natural beauty. To this period we owe the establishment of the modem system of the arts. 1 In England, the notion of a separate and autonomous disci pline devoted solely to art and to beauty came into being through the concept of "aesthetic disinterestedness. " 2 In addition, emphasis in (...)
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  • (1 other version)Beauty.Nick Zangwill - 2003 - In Jerrold Levinson (ed.), Oxford Companion to Aesthetics. Oxford University Press.
    I shall discuss several related issues about beauty. These are: (1) The place of beauty among other aesthetic properties. (2) The general principle of aesthetic supervenience. (3) The problem of aesthetic relevance. (4) The distinction between free and dependent beauty. (5) The primacy of our appreciation of free beauty over our appreciation of dependent beauty. (6) Personal beauty as a species of beauty. (7) The metaphysics of beauty.
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  • (4 other versions)The Logic of Scientific Discovery.K. Popper - 1959 - British Journal for the Philosophy of Science 10 (37):55-57.
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  • From Instrumentalism to Constructive Realism: On Some Relations Between Confirmation, Empirical Progress, and Truth Approximation.Theodorus Antonius Franciscus Kuipers - 2000 - Dordrecht, Netherland: Springer.
    Surprisingly, modified versions of the confirmation theory (Carnap and Hempel) and truth approximation theory (Popper) turn out to be smoothly sythesizable. The glue between the two appears to be the instrumentalist methodology, rather than that of the falsificationalist. The instrumentalist methodology, used in the separate, comparative evaluation of theories in terms of their successes and problems (hence, even if already falsified), provides in theory and practice the straight road to short-term empirical progress in science ( à la Laudan). It is (...)
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  • Aesthetic concepts: essays after Sibley.Emily Brady & Jerrold Levinson (eds.) - 2001 - New York: Oxford University Press.
    Exploring key topics in contemporary aesthetics, this work analyzes the issues that arise from the unique works of Frank Sibley (1923-1996), who developed a distinctive aesthetic theory through a number of papers published between 1955 and 1995. Here, thirteen philosophical aestheticians bring Sibley's insight into a contemporary framework, exploring the ways his ideas foster important new discussion about issues in aesthetics. This collection will interest anyone interested in philosophy, art theory, and art criticism.
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  • The fine art of repetition: essays in the philosophy of music.Peter Kivy - 1993 - New York: Cambridge University Press.
    Peter Kivy is the author of many books on the history of art and, in particular, the aesthetics of music. This collection of essays spans a period of some thirty years and focuses on a richly diverse set of issues: the biological origins of music, the role of music in the liberal education, the nature of the musical work and its performance, the aesthetics of opera, the emotions of music, and the very nature of music itself. Some of these subjects (...)
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  • The Phenomenology of Mathematical Proof.Gian-Carlo Rota - 1997 - Synthese 111 (2):183-196.
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  • Mathematical Beauty and the Evolution of the Standards of Mathematical Proof.J. W. McAllister - unknown
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  • Sound sentiment: an essay on the musical emotions, including the complete text of The Corded shell.Peter Kivy - 1989 - Philadelphia: Temple University Press. Edited by Peter Kivy.
    Incorporating the complete, corrected text of The Corded Shell, Kivy brings his earlier arguments up to date in light of recent work in the field, and discusses ...
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  • Philosophy in a New Key: A Study in the Symbolism of Reason, Rite, and Art.Susanne Katherina Knauth Langer - 1942 - Cambridge, MA, USA: Harvard University Press.
    The new key -- Symbolic transformation -- The logic of signs and symbols -- Discursive and presentational forms -- Language -- Life-symbols : the roots of sacrament -- Life-symbols : the roots of myth -- On significance in music -- The genesis of artistic import -- The fabric of meaning.
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  • (1 other version)Beauty.Nick Zangwill - 2003 - In Jerrold Levinson (ed.), The Oxford handbook of aesthetics. New York: Oxford University Press.
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  • A Short History of Greek Mathematics.James Gow - 1923 - Cambridge University Press.
    James Gow's A Short History of Greek Mathematics provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II (...)
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  • Newton's Philosophy of Nature: Selections From His Writings.Isaac Newton - 1953 - New York,: Dover Publications. Edited by H. S. Thayer.
    Aside from the Principia and occasional appearances of the Opticks , Newton' writings have remained largely inaccessible to students of philosophy, science, and literature as well as to other readers. This book provides a remedy with wide representation of the interests, problems, and diverse philosophic issues that preoccupied the greatest scientific mind of the seventeenth century. Grouped in sections corresponding to methods, principles, and theological considerations, these selections feature explanatory notes and cross-references to related essays.
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  • What makes "aesthetic" terms aesthetic?Peter Kivy - 1975 - Philosophy and Phenomenological Research 36 (2):197-211.
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  • (1 other version)Les grands courants de la pensée mathématique.F. Le Lionnais - 1965 - Revue Philosophique de la France Et de l'Etranger 155:254-256.
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  • (3 other versions)Progress and its problems: Towards a theory of scientific growth.L. Laudan - 1978 - British Journal for the Philosophy of Science 32 (1):57-71.
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  • Aesthetic terms, metaphor, and the nature of aesthetic properties.Rafael De Clercq - 2005 - Journal of Aesthetics and Art Criticism 63 (1):27–32.
    The paper argues that an important class of aesthetic terms cannot be used as metaphors because it is impossible to commit a category mistake with them. It then uses this fact to provide a general definition of 'aesthetic property'.
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  • (3 other versions)Proofs and Refutations: The Logic of Mathematical Discovery.I. Lakatos, John Worrall & Elie Zahar - 1977 - British Journal for the Philosophy of Science 28 (1):81-82.
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  • The Logic of Aesthetic Concepts.Isabel C. Hungerland - 1962 - Proceedings and Addresses of the American Philosophical Association 36:43 - 66.
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  • Is Beauty a Sign of Truth in Scientific Theories?J. W. McAllister - unknown
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