Search results for 'Music theory Mathematics' (try it on Scholar)

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  1. Edward Rothstein (1995/2006). Emblems of Mind: The Inner Life of Music and Mathematics. University of Chicago Press.score: 357.0
    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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  2. G. Mazzola (2002). The Topos of Music: Geometric Logic of Concepts, Theory, and Performance. Birkhauser Verlag.score: 345.0
    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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  3. G. Menendez Torrellas (1999). Mathematics and Harmony. A Possible Influence of Pythagorean Sources on the Music Theory of Leibniz. Studia Leibnitiana 31 (1):34-54.score: 261.0
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  4. William B. Conner (1983). Math's Metasonics: Creativity Through Calculator Harmonic Braiding. Tesla Book Co..score: 180.0
     
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  5. Suzannah Clark & Alexander Rehding (eds.) (2005). Music Theory and Natural Order From the Renaissance to the Early Twentieth Century. Cambridge University Press.score: 168.0
    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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  6. Anthony Pople (ed.) (1994/2006). Theory, Analysis and Meaning in Music. Cambridge University Press.score: 152.0
    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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  7. Henry Chadwick (1981). Boethius, the Consolations of Music, Logic, Theology, and Philosophy. Oxford University Press.score: 147.0
    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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  8. Michele Barontini & Tito M. Tonietti (2010). ʿumar Al-Khayyām's Contribution to the Arabic Mathematical Theory of Music. Arabic Sciences and Philosophy 20 (02):255-280.score: 145.0
    We here present the Arabic text, with an English translation, of certain pages dedicated by al-Khayym with other Arabic theories of Music, and with those coming from other traditions.
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  9. Tito M. Tonietti (2010). ʿumar Al-Khayyām's Contribution to the Arabic Mathematical Theory of Music. Arabic Sciences and Philosophy 20 (2):255-280.score: 145.0
    We here present the Arabic text, with an English translation, of certain pages dedicated by al-Khayym with other Arabic theories of Music, and with those coming from other traditions.
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  10. Paul Benioff (2002). Towards a Coherent Theory of Physics and Mathematics. Foundations of Physics 32 (7):989-1029.score: 144.0
    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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  11. Alison Pease, Alan Smaill, Simon Colton & John Lee (2009). Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics. Foundations of Science 14 (1-2):111-135.score: 144.0
    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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  12. Peter Verdée (2013). Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics. Foundations of Science 18 (4):655-680.score: 144.0
    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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  13. Arkady Plotnitsky (2006). A New Book of Numbers: On the Precise Definition of Quantum Variables and the Relationships Between Mathematics and Physics in Quantum Theory. [REVIEW] Foundations of Physics 36 (1):30-60.score: 144.0
    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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  14. Elizabeth Gould (2011). Feminist Imperative(s) in Music and Education: Philosophy, Theory, or What Matters Most. Educational Philosophy and Theory 43 (2):130-147.score: 132.0
    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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  15. Krzysztof Wójtowicz (2010). Theory of Quantum Computation and Philosophy of Mathematics. Part I. Logic and Logical Philosophy 18 (3-4):313-332.score: 132.0
    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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  16. Lazare Saminsky (1957). Physics and Metaphysics of Music and Essays on the Philosophy of Mathematics. The Hague, M. Nijhoff.score: 126.0
    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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  17. William Gasarch & Jeffry L. Hirst (1998). Reverse Mathematics and Recursive Graph Theory. Mathematical Logic Quarterly 44 (4):465-473.score: 122.0
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  18. Paul Benioff (2005). Towards a Coherent Theory of Physics and Mathematics: The Theory–Experiment Connection. Foundations of Physics 35 (11):1825-1856.score: 120.0
  19. O. Bradley Bassler (2005). Book Review: J. P. Mayberry. Foundations of Mathematics in the Theory of Sets. [REVIEW] Notre Dame Journal of Formal Logic 46 (1):107-125.score: 120.0
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  20. J. C. Kassler & D. R. Oldroyd (2006). Robert Hooke's Trinity College 'Musick Scripts', His Music Theory and the Role of Music in His Cosmology. Annals of Science 40 (6):559-595.score: 112.0
    (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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  21. M. J. Grant (2001). Serial Music, Serial Aesthetics: Compositional Theory in Post-War Europe. Cambridge University Press.score: 108.0
    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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  22. Samantha Matherne (2014). Kant's Expressive Theory of Music. Journal of Aesthetics and Art Criticism 72 (2):129-145.score: 108.0
    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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  23. Joanne Hardman (2007). An Activity Theory Approach to Surfacing the Pedagogical Object in a Primary School Mathematics Classroom. Outlines. Critical Practice Studies 9 (1):53-69.score: 108.0
    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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  24. Owen Wright (ed.) (2011). On Music: An Arabic Critical Edition and English Translation of Epistle 5. OUP in association with the Institute of Ismaili Studies/Institute of Ismaili Studies.score: 108.0
    The Ikhwan al-Safa' (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasa'il Ikhwan al-Safa' (Epistles of the Brethren of Purity). This compendium contains fifty-two epistles offering synoptic accounts of the classical sciences and philosophies of the age; divided into four classificatory parts, it treats themes in mathematics, (...)
     
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  25. Byron Almén (2008). A Theory of Musical Narrative. Indiana University Press.score: 104.0
    A theory of musical narrative. An introduction to narrative analysis : Chopin's prelude in G major, op. 28, no. 3 ; Perspectives and critiques ; A theory of musical narrative : conceptual considerations ; A theory of musical narrative : analytical considerations ; Narrative and topic -- Archetypal narratives and phases. Romance narratives and Micznik's degrees of narrativity ; Tragic narratives : an extended analysis of Schubert, piano sonata in B flat major, D. 960, first movement ; (...)
     
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  26. Jean-Pierre Marquis (1995). Category Theory and the Foundations of Mathematics: Philosophical Excavations. Synthese 103 (3):421 - 447.score: 96.0
    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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  27. Andrew Arana (2010). Proof Theory in Philosophy of Mathematics. Philosophy Compass 5 (4):336-347.score: 96.0
    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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  28. Steven French (2000). The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics. Synthese 125 (1-2):103 - 120.score: 96.0
    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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  29. Gerhard Preyer, Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism.score: 96.0
    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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  30. Elaine Landry (1999). Category Theory: The Language of Mathematics. Philosophy of Science 66 (3):27.score: 96.0
    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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  31. Sébastien Gandon (2009). Toward a Topic-Specific Logicism? Russell's Theory of Geometry in the Principles of Mathematics. Philosophia Mathematica 17 (1):35-72.score: 96.0
    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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  32. J. M. Dieterle (2010). Social Construction in the Philosophy of Mathematics: A Critical Evaluation of Julian Cole's Theory. Philosophia Mathematica 18 (3):311-328.score: 96.0
    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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  33. Christopher Pincock (2010). Mathematics, Science, and Confirmation Theory. Philosophy of Science 77 (5):959-970.score: 96.0
    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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  34. Frank Waaldijk (2005). On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions. Foundations of Science 10 (3):249-324.score: 96.0
    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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  35. Douglas Bridges & Steeve Reeves (1999). Constructive Mathematics in Theory and Programming Practice. Philosophia Mathematica 7 (1):65-104.score: 96.0
    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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  36. Gerhard Jäger & Thomas Strahm (2001). Upper Bounds for Metapredicative Mahlo in Explicit Mathematics and Admissible Set Theory. Journal of Symbolic Logic 66 (2):935-958.score: 96.0
    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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  37. Benjamin Wardhaugh (2007). The Logarithmic Ear: Pietro Mengoli's Mathematics of Music. Annals of Science 64 (3):327-348.score: 96.0
    Summary In 1670, the Bolognese mathematician Pietro Mengoli published his Speculationi di musica, a highly original work attempting to found the mathematical study of music on the anatomy of the ear. His anatomy was idiosyncratic and his mathematics extraordinarily complex, and he proposed a unique double mechanism of hearing. He analysed in detail the supposed behaviour of the subtle part of the air inside the ear, and the patterns of strokes made on the eardrum by simultaneous sounds. Most (...)
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  38. John Dempsher (1980). A Bio-Physical Basis of Mathematics in Synaptic Function of the Nervous System: A Theory. Acta Biotheoretica 29 (3-4).score: 96.0
    The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction (...)
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  39. Giorgio Venturi (2014). Foundation of Mathematics Between Theory and Practice. Philosophia Scientiæ 18:45-80.score: 96.0
    In this article I propose to look at set theory not only as a founda­tion of mathematics in a traditional sense, but as a foundation for mathemat­ical practice. For this purpose I distinguish between a standard, ontological, set theoretical foundation that aims to find a set theoretical surrogate to every mathematical object, and a practical one that tries to explain mathematical phenomena, giving necessary and sufficient conditions for the proof of mathematical propositions. I will present some example of (...)
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  40. Irène Deliège (ed.) (2000). Musique Contemporaine: Théories Et Philosophie: Textes d'Étude = Contemporary Music: Theories and Philosophy: Working Papers. Escom Publications.score: 96.0
     
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  41. Jirí Kulka (1995). A Semio-Psychological Theory of Communication in Music. In Eero Tarasti (ed.), Musical Signification: Essays in the Semiotic Theory and Analysis of Music. Mouton de Gruyter. 279--284.score: 96.0
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  42. Roman Murawski (2010). Philosophy of Mathematics in the Warsaw Mathematical School. Axiomathes 20 (2-3):279-293.score: 92.7
    The aim of this paper is to present and discuss the philosophical views concerning mathematics of the founders of the so called Warsaw Mathematical School, i.e., Wacław Sierpiński, Zygmunt Janiszewski and Stefan Mazurkiewicz. Their interest in the philosophy of mathematics and their philosophical papers will be considered. We shall try to answer the question whether their philosophical views influenced their proper mathematical investigations. Their views towards set theory and its rôle in mathematics will be emphasized.
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  43. Patrik N. Juslin & Daniel Västfjäll (2008). Emotional Responses to Music: The Need to Consider Underlying Mechanisms. Behavioral and Brain Sciences 31 (5):559-575.score: 90.0
    Research indicates that people value music primarily because of the emotions it evokes. Yet, the notion of musical emotions remains controversial, and researchers have so far been unable to offer a satisfactory account of such emotions. We argue that the study of musical emotions has suffered from a neglect of underlying mechanisms. Specifically, researchers have studied musical emotions without regard to how they were evoked, or have assumed that the emotions must be based on the mechanism for emotion induction, (...)
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  44. Mary Tiles (1989/2004). The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. Dover Publications.score: 90.0
    David Hilbert famously remarked, “No one will drive us from the paradise that Cantor has created.” This volume offers a guided tour of modern mathematics’ Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor’s transfinite paradise; axiomatic set theory; logical objects and logical types; independence results and the universe of sets; and the constructs and reality of mathematical structure. (...)
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  45. Jean-Pierre Marquis (2013). Mathematical Forms and Forms of Mathematics: Leaving the Shores of Extensional Mathematics. Synthese 190 (12):2141-2164.score: 90.0
    In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all (...), at least according to some speculative research programs. (shrink)
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  46. Jason L. Megill, Tim Melvin & Alex Beal (2014). On Some Properties of Humanly Known and Humanly Knowable Mathematics. Axiomathes 24 (1):81-88.score: 90.0
    We argue that the set of humanly known mathematical truths (at any given moment in human history) is finite and so recursive. But if so, then given various fundamental results in mathematical logic and the theory of computation (such as Craig’s in J Symb Log 18(1): 30–32(1953) theorem), the set of humanly known mathematical truths is axiomatizable. Furthermore, given Godel’s (Monash Math Phys 38: 173–198, 1931) First Incompleteness Theorem, then (at any given moment in human history) humanly known (...) must be either inconsistent or incomplete. Moreover, since humanly known mathematics is axiomatizable, it can be the output of a Turing machine. We then argue that any given mathematical claim that we could possibly know could be the output of a Turing machine, at least in principle. So the Lucas-Penrose (Lucas in Philosophy 36:112–127, 1961; Penrose, in The Emperor’s new mind. Oxford University Press, Oxford (1994)) argument cannot be sound. (shrink)
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  47. Stojan Obradović & Slobodan Ninković (2009). The Heuristic Function of Mathematics in Physics and Astronomy. Foundations of Science 14 (4):351-360.score: 90.0
    This paper considers the role of mathematics in the process of acquiring new knowledge in physics and astronomy. The defining of the notions of continuum and discreteness in mathematics and the natural sciences is examined. The basic forms of representing the heuristic function of mathematics at theoretical and empirical levels of knowledge are studied: deducing consequences from the axiomatic system of theory, the method of generating mathematical hypotheses, “pure” proofs for the existence of objects and processes, (...)
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  48. Juliette Kennedy & Roman Kossak (eds.) (2012). Set Theory, Arithmetic, and Foundations of Mathematics: Theorems, Philosophies. Cambridge University Press.score: 90.0
    Machine generated contents note: 1. Introduction Juliette Kennedy and Roman Kossak; 2. Historical remarks on Suslin's problem Akihiro Kanamori; 3. The continuum hypothesis, the generic-multiverse of sets, and the [OMEGA] conjecture W. Hugh Woodin; 4. [omega]-Models of finite set theory Ali Enayat, James H. Schmerl and Albert Visser; 5. Tennenbaum's theorem for models of arithmetic Richard Kaye; 6. Hierarchies of subsystems of weak arithmetic Shahram Mohsenipour; 7. Diophantine correct open induction Sidney Raffer; 8. Tennenbaum's theorem and recursive reducts James (...)
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  49. Thomas A. Regelski (2005). Music and Music Education: Theory and Praxis for 'Making a Difference'. Educational Philosophy and Theory 37 (1):7–27.score: 90.0
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  50. William M. Farmer & Joshua D. Guttman (2000). A Set Theory with Support for Partial Functions. Studia Logica 66 (1):59-78.score: 90.0
    Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for (...)
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