Results for 'Music theory Mathematics'

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  1. Mathematics and Harmony. A Possible Influence of Pythagorean Sources on the Music Theory of Leibniz.G. Menendez Torrellas - 1999 - Studia Leibnitiana 31 (1):34-54.
     
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  2. Emblems of Mind: The Inner Life of Music and Mathematics.Edward Rothstein - 1995 - University of Chicago Press.
    One is a science, the other an art; one useful, the other seemingly decorative, but mathematics and music share common origins in cult and mystery and have been linked throughout history. Emblems of Mind is Edward Rothstein’s classic exploration of their profound similarities, a journey into their “inner life.” Along the way, Rothstein explains how mathematics makes sense of space, how music tells a story, how theories are constructed, how melody is shaped. He invokes the poetry (...)
     
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  3. The Topos of Music: Geometric Logic of Concepts, Theory, and Performance.G. Mazzola - 2002 - Birkhauser Verlag.
    The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification (...)
     
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  4. Music Theory and Natural Order From the Renaissance to the Early Twentieth Century.Suzannah Clark & Alexander Rehding (eds.) - 2005 - Cambridge University Press.
    Music theorists of almost all ages employ a concept of "Nature" to justify observations or statements about music. The understanding of what "Nature" is, however, is subject to cultural and historical differences. In tracing these explanatory strategies and their changes in music theories between c. 1600 and 1900, these essays explore (for the first time in a book-length study) how the multifarious conceptions of nature, located variously between scientific reason and divine power, are brought to bear on (...)
     
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  5.  31
    Theory, Analysis and Meaning in Music.Anthony Pople (ed.) - 1994 - Cambridge University Press.
    Recent encounters with structuralist and poststructuralist critical theory, linguistics, and cognitive sciences have brought the theory and analysis of music into the orbit of important developments in present-day intellectual history. Without seeking to impose an explicit redefinition of either theory or analysis, this book explores the limits of both. Essays on decidability, ambiguity, metaphor, music as text, and music analysis as cognitive theory are complemented by studies of works by Debussy, Schoenberg, Birtwistle and (...)
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  6. Music in the Mirror Reflections on the History of Music Theory and Literature for the 21st Century.Andreas Giger & Thomas J. Mathiesen - 2002
     
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  7.  26
    Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics.Peter Verdée - 2013 - Foundations of Science 18 (4):655-680.
    In this paper I propose a new approach to the foundation of mathematics: non-monotonic set theory. I present two completely different methods to develop set theories based on adaptive logics. For both theories there is a finitistic non-triviality proof and both theories contain (a subtle version of) the comprehension axiom schema. The first theory contains only a maximal selection of instances of the comprehension schema that do not lead to inconsistencies. The second allows for all the instances, (...)
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  8.  63
    Towards a Coherent Theory of Physics and Mathematics.Paul Benioff - 2002 - Foundations of Physics 32 (7):989-1029.
    As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description (...)
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  9.  40
    Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics.Alison Pease, Alan Smaill, Simon Colton & John Lee - 2009 - Foundations of Science 14 (1-2):111-135.
    We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in (...)
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  10.  13
    A New Book of Numbers: On the Precise Definition of Quantum Variables and the Relationships Between Mathematics and Physics in Quantum Theory[REVIEW]Arkady Plotnitsky - 2006 - Foundations of Physics 36 (1):30-60.
    Following Asher Peres’s observation that, as in classical physics, in quantum theory, too, a given physical object considered “has a precise position and a precise momentum,” this article examines the question of the definition of quantum variables, and then the new type (as against classical physics) of relationships between mathematics and physics in quantum theory. The article argues that the possibility of the precise definition and determination of quantum variables depends on the particular nature of these relationships.
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  11.  56
    Feminist Imperative(s) in Music and Education: Philosophy, Theory, or What Matters Most.Elizabeth Gould - 2011 - Educational Philosophy and Theory 43 (2):130-147.
    A historically feminized profession, education in North America remains remarkably unaffected by feminism, with the notable exception of pedagogy and its impact on curriculum. The purpose of this paper is to describe characteristics of feminism that render it particularly useful and appropriate for developing potentialities in education and music education. As a set of flexible methodological tools informed by Gilles Deleuze's notions of philosophy and art, I argue feminism may contribute to education's becoming more efficacious, reflexive, and reflective of (...)
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  12. Math's Metasonics: Creativity Through Calculator Harmonic Braiding.William B. Conner - 1983 - Tesla Book Co..
     
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  13.  10
    Reverse Mathematics and Recursive Graph Theory.William Gasarch & Jeffry L. Hirst - 1998 - Mathematical Logic Quarterly 44 (4):465-473.
    We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs, Euler paths, and Hamilton paths.
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  14.  9
    Theory of Quantum Computation and Philosophy of Mathematics. Part I.Krzysztof Wójtowicz - 2009 - Logic and Logical Philosophy 18 (3-4):313-332.
    The aim of this paper is to present some basic notions of the theory of quantum computing and to compare them with the basic notions of the classical theory of computation. I am convinced, that the results of quantum computation theory (QCT) are not only interesting in themselves, but also should be taken into account in discussions concerning the nature of mathematical knowledge. The philosophical discussion will however be postponed to another paper. QCT seems not to be (...)
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  15.  2
    Physics and Metaphysics of Music and Essays on the Philosophy of Mathematics.Lazare Saminsky - 1957 - The Hague: M. Nijhoff.
    A green philosopher's peripeteia.--Physics and metaphysics of music.--The roots of arithmetic.--Critique of new geometrical abstractions.--The philosophical value of science.
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  16.  80
    Towards a Coherent Theory of Physics and Mathematics: The Theory–Experiment Connection.Paul Benioff - 2005 - Foundations of Physics 35 (11):1825-1856.
  17.  4
    The Role of Acoustics and Music Theory in the Scientific Work of Robert Hooke.Penelope Gouk - 1980 - Annals of Science 37 (5):573-605.
    The work of Robert Hooke on acoustics and music theory is a larger subject than might seem the case from studies of his career so far available. First, there are his experiments for the Royal Society which can be defined as purely acoustical, which anticipate later experiments performed by men such as J. Sauveur and E. Chladni. Second, there are passages in many of his writings which by extensive use of musical analogy attempt to account for all physical (...)
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  18.  6
    Robert Hooke's Trinity College 'Musick Scripts', His Music Theory and the Role of Music in His Cosmology.J. C. Kassler & D. R. Oldroyd - 1983 - Annals of Science 40 (6):559-595.
    (1983). Robert Hooke's Trinity College ‘Musick Scripts’, his music theory and the role of music in his cosmology. Annals of Science: Vol. 40, No. 6, pp. 559-595.
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  19.  14
    Book Review: J. P. Mayberry. Foundations of Mathematics in the Theory of Sets. [REVIEW]O. Bradley Bassler - 2005 - Notre Dame Journal of Formal Logic 46 (1):107-125.
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  20.  10
    Aristides Quintilianus and Constructions in Early Music Theory.Andrew Barker - 1982 - Classical Quarterly 32 (01):184-.
    Aristides Quintilianus' dates are not known, but he can hardly be earlier than the first century A.D. or later than the third. Several passages in the early pages of his de Musica1 purport to record facts about the practice of much older theorists, in contexts which make it clear that his references are to the period before Aristoxenus. Since our knowledge of music theory in that period is extremely sketchy, it is obviously worth trying to assess the reliability (...)
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  21. Aristides Quintilianus and Constructions in Early Music Theory.Andrew Barker - 1982 - Classical Quarterly 32 (1):184-197.
    Aristides Quintilianus' dates are not known, but he can hardly be earlier than the first century A.D. or later than the third. Several passages in the early pages of his de Musica1 purport to record facts about the practice of much older theorists, in contexts which make it clear that his references are to the period before Aristoxenus. Since our knowledge of music theory in that period is extremely sketchy, it is obviously worth trying to assess the reliability (...)
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  22. Boethius, the Consolations of Music, Logic, Theology, and Philosophy.Henry Chadwick - 1981 - Oxford University Press.
    The Consolations of Philosophy by Boethius, whose English translators include King Alfred, Geoffrey Chaucer, and Queen Elizabeth I, ranks among the most remarkable books to be written by a prisoner awaiting the execution of a tyrannical death sentence. Its interpretation is bound up with his other writings on mathematics and music, on Aristotelian and propositional logic, and on central themes of Christian dogma. -/- Chadwick begins by tracing the career of Boethius, a Roman rising to high office under (...)
     
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  23. Music and Mathematics: From Pythagoras to Fractals.John Fauvel, Raymond Flood & Robin Wilson - 2006 - Oxford University Press UK.
    From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authored by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional, and analytical relationships between mathematics and (...)
     
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  24. Becoming Heinrich Schenker: Music Theory and Ideology.Robert P. Morgan - 2014 - Cambridge University Press.
    Much controversy surrounds Schenker's mature theory and its attempt to explain musical pitch motion. Becoming Heinrich Schenker brings a new perspective to Schenker's theoretical work, showing that ideas characteristic of his mature theory, although in many respects fundamentally different, developed logically out of his earlier ideas. Robert P. Morgan provides an introduction to Schenker's mature theory and traces its development through all of his major publications, considering each in detail and with numerous music examples. Morgan also (...)
     
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  25.  34
    Non-Bifurcatory Diairesis and Greek Music Theory: A Resource for Plato in the Statesman?Mitchell Miller - 2013 - In Ales Havlicek, Jakub Jirsa & Karel Thein (eds.), Plato's Statesman: Proceedings of the Eighth Symposium Platonicum Pragense. OIKOUMENH. pp. 178-200.
    At 287c of the Statesman the Eleatic Visitor — or, more deeply, Plato — faces a daunting task. Because statesmanship has been shown to collaborate with “countless” other arts that share with it the work of “caring” for the city, to understand statesmanship requires distinguishing these arts into an intelligible set of kinds and recognizing how these might go together. Accordingly, the Visitor abandons the mode of division he has practiced without exception up until this moment, bifurcation or “halving,” and (...)
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  26.  16
    Kant's Expressive Theory of Music.Samantha Matherne - 2014 - Journal of Aesthetics and Art Criticism 72 (2):129-145.
    Several prominent philosophers of art have worried about whether Kant has a coherent theory of music on account of two perceived tensions in his view. First, there appears to be a conflict between his formalist and expressive commitments. Second (and even worse), Kant defends seemingly contradictory claims about music being beautiful and merely agreeable, that is, not beautiful. Against these critics, I show that Kant has a consistent view of music that reconciles these tensions. I argue (...)
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  27.  2
    An Activity Theory Approach to Surfacing the Pedagogical Object in a Primary School Mathematics Classroom.Joanne Hardman - 2007 - Outlines. Critical Practice Studies 9 (1):53-69.
    This paper develops a methodology for using Activity Theory (AT) to investigate pedagogical practices in primary school mathematics classrooms by selecting object-oriented pedagogical activity as the unit of analysis. While an understanding of object-oriented activity is central to Activity Theory (AT), the notion of object is a frequently debated and often misunderstood one. The conceptual confusion surrounding the object arises both from difficulties related to translating the original Russian conceptualisation of object-oriented activity into English as well as (...)
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  28.  18
    Serial Music, Serial Aesthetics: Compositional Theory in Post-War Europe.M. J. Grant - 2001 - Cambridge University Press.
    Serial music was one of the most important aesthetic movements to emerge in post-war Europe, but its uncompromising music and modernist aesthetic has often been misunderstood. This book focuses on the controversial journal die Reihe, whose major contributors included Stockhausen, Eimert, Pousseur, Dieter Schnebel and G. M. Koenig, and discusses it in connection with many lesser-known sources in German musicology. It traces serialism's debt to the theories of Klee and Mondrian, and its relationship to developments in concrete art, (...)
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  29. Music and Mathematics: Modest Support for the Oft-Claimed Relationship.Kathryn Vaughn - forthcoming - Journal of Aesthetic Education.
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  30.  58
    Does Homotopy Type Theory Provide a Foundation for Mathematics?James Ladyman & Stuart Presnell - forthcoming - British Journal for the Philosophy of Science:axw006.
    Homotopy Type Theory is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the foundations provided by ZFC set theory and category theory. This article explains and motivates an account of how to define, justify, and think about HoTT in a way that is self-contained, and argues that, so construed, it is a candidate for being an autonomous foundation for mathematics. We first consider various questions that (...)
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  31. The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics.Steven French - 2000 - Synthese 125 (1-2):103 - 120.
    Wigner famously referred to the `unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics, I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.
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  32.  10
    Upper Bounds for Metapredicative Mahlo in Explicit Mathematics and Admissible Set Theory.Gerhard Jäger & Thomas Strahm - 2001 - Journal of Symbolic Logic 66 (2):935-958.
    In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established.
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  33.  4
    Explicit mathematics and operational set theory: Some ontological comparisons.Gerhard Jäger & Rico Zumbrunnen - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.
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  34.  5
    How Did Zhong Ziqi Understand Bo Ya’s Heart-Mind?: Hetero-Referential Aspects of Early Chinese Music Theory.Ken Berthel - 2016 - Philosophy East and West 66 (1):259-270.
    Words are signs that refer to particular things. … The meaning of a tone, however, lies not in what it points to but in the pointing itself; more precisely, in the different way, in the individual gesture, with which each tone points toward the same place.The five tones deafen our ears.In comparing the semiotics of language and music, Western music theorist Victor Zuckerkandl identified what he saw as a fundamental difference: words had the hetero-referential capability of pointing beyond (...)
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  35.  42
    Social Construction in the Philosophy of Mathematics: A Critical Evaluation of Julian Cole's Theory.J. M. Dieterle - 2010 - Philosophia Mathematica 18 (3):311-328.
    Julian Cole argues that mathematical domains are the products of social construction. This view has an initial appeal in that it seems to salvage much that is good about traditional platonistic realism without taking on the ontological baggage. However, it also has problems. After a brief sketch of social constructivist theories and Cole’s philosophy of mathematics, I evaluate the arguments in favor of social constructivism. I also discuss two substantial problems with the theory. I argue that unless and (...)
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  36. Category Theory and the Foundations of Mathematics: Philosophical Excavations.Jean-Pierre Marquis - 1995 - Synthese 103 (3):421 - 447.
    The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It is (...)
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  37. Realization of Constructive Set Theory Into Explicit Mathematics: A Lower Bound for Impredicative Mahlo Universe.Sergei Tupailo - 2003 - Annals of Pure and Applied Logic 120 (1-3):165-196.
    We define a realizability interpretation of Aczel's Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T 0 , thus providing relative lower bounds for the proof-theoretic strength of the latter.
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  38.  6
    The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics.Steven French - 2000 - Synthese 125 (1):103-120.
    Wigner famously referred to the 'unreasonable effectiveness' of mathematics in its application to science. Using Wigner's own application of group theory to nuclear physics. I hope to indicate that this effectiveness can be seen to be not so unreasonable if attention is paid to the various idealising moves undertaken. The overall framework for analysing this relationship between mathematics and physics is that of da Costa's partial structures programme.
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  39.  93
    Category Theory: The Language of Mathematics.Elaine Landry - 1999 - Philosophy of Science 66 (3):27.
    In this paper I argue that category theory ought to be seen as providing the language for mathematical discourse. Against foundational approaches, I argue that there is no need to reduce either the content or structure of mathematical concepts and theories to the constituents of either the universe of sets or the category of categories. I assign category theory the role of organizing what we say about the content and structure of both mathematical concepts and theories. Insofar, then, (...)
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  40.  79
    Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics.Sébastien Gandon - 2008 - Philosophia Mathematica 17 (1):35-72.
    Russell's philosophy is rightly described as a programme of reduction of mathematics to logic. Now the theory of geometry developed in 1903 does not fit this picture well, since it is deeply rooted in the purely synthetic projective approach, which conflicts with all the endeavours to reduce geometry to analytical geometry. The first goal of this paper is to present an overview of this conception. The second aim is more far-reaching. The fact that such a theory of (...)
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  41.  29
    Constructive Mathematics in Theory and Programming Practice.Douglas Bridges & Steeve Reeves - 1999 - Philosophia Mathematica 7 (1):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
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  42. Proof Theory in Philosophy of Mathematics.Andrew Arana - 2010 - Philosophy Compass 5 (4):336-347.
    A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Gödel's incompleteness theorems, conservation results, independence results, ordinal analysis, predicativity, reverse mathematics, speed-up results, and provability logics.
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  43.  33
    Mathematics, Science, and Confirmation Theory.Christopher Pincock - 2010 - Philosophy of Science 77 (5):959-970.
    This paper begins by distinguishing intrinsic and extrinsic contributions of mathematics to scientific representation. This leads to two investigations into how these different sorts of contributions relate to confirmation. I present a way of accommodating both contributions that complicates the traditional assumptions of confirmation theory. In particular, I argue that subjective Bayesianism does best accounting for extrinsic contributions, while objective Bayesianism is more promising for intrinsic contributions.
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  44. Social Construction in the Philosophy of Mathematics: A Critical Evaluation of Julian Cole’s Theory†: Articles.J. M. Dieterle - 2010 - Philosophia Mathematica 18 (3):311-328.
    Julian Cole argues that mathematical domains are the products of social construction. This view has an initial appeal in that it seems to salvage much that is good about traditional platonistic realism without taking on the ontological baggage. However, it also has problems. After a brief sketch of social constructivist theories and Cole’s philosophy of mathematics, I evaluate the arguments in favor of social constructivism. I also discuss two substantial problems with the theory. I argue that unless and (...)
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  45.  1
    The Recognition of Emotions in Music and Landscapes: Extending Contour Theory.Marta Benenti & Cristina Meini - forthcoming - Philosophia:1-18.
    While inanimate objects can neither experience nor express emotions, in principle they can be expressive of emotions. In particular, music is a paradigmatic example of something expressive of emotions that surely cannot feel anything at all. The Contour theory accounts for music expressiveness in terms of those resemblances that hold between its external and perceivable properties and the typical contour of human emotional behavior. Provided that some critical aspects are emended – notably, the stress on the perception (...)
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  46.  35
    On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions.Frank Waaldijk - 2004 - Foundations of Science 10 (3):249-324.
    We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to (...)
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  47.  23
    Troubles with Indispensability: Applying Pure Mathematics in Physical Theory.Anthony Peressini - 1997 - Philosophia Mathematica 5 (3):210-227.
    Much of the current thought concerning mathematical ontology in volves in some way the Quine/Putnam indispensability argument. The indispensability approach needs to be more thoroughly specified, however, before substantive progress can be made in assessing it. To this end I examine in some detail the ways in which pure mathematics is applied to physical theory; such considerations give rise to three specific issues with which the indispensability approach must come to grips.
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  48.  52
    Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism.Gerhard Preyer - unknown
    The ten contributions in this volume range widely over topics in the philosophy of mathematics. The four papers in Part I (entitled "Set Theory, Inconsistency, and Measuring Theories") take up topics ranging from proposed resolutions to the paradoxes of naïve set theory, paraconsistent logics as applied to the early infinitesimal calculus, the notion of "purity of method" in the proof of mathematical results, and a reconstruction of Peano's axiom that no two distinct numbers have the same successor. (...)
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  49.  51
    Music and Music Education: Theory and Praxis for 'Making a Difference'.Thomas A. Regelski - 2005 - Educational Philosophy and Theory 37 (1):7–27.
    The ‘music appreciation as contemplation’ paradigm of traditional aesthetics and music education assumes that music exists to be contemplated for itself. The resulting distantiation of music and music education from life creates a legitimation crisis for music education. Failing to make a noteworthy musical difference for society, a politics of advocacy attempts to justify music education. Praxial theories of music, instead, see music as pragmatically social in origin, meaning, and value. A (...)
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  50. Constructive Mathematics in Theory and Programming Practice.Douglas Bridges & Steeve Reeves - 1998 - Philosophia Mathematica 6 (3):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics. it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
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