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  1. Deleuze and the Conceptualizable Character of Mathematical Theories.Simon B. Duffy - 2017 - In Nathalie Sinclair & Alf Coles Elizabeth de Freitas (ed.), What is a Mathematical Concept? Cambridge University Press.
    To make sense of what Gilles Deleuze understands by a mathematical concept requires unpacking what he considers to be the conceptualizable character of a mathematical theory. For Deleuze, the mathematical problems to which theories are solutions retain their relevance to the theories not only as the conditions that govern their development, but also insofar as they can contribute to determining the conceptualizable character of those theories. Deleuze presents two examples of mathematical problems that operate in this way, which he considers (...)
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  2. The Mathematical Intelligencer Flunks the Olympics.Alexander E. Gutman, Mikhail G. Katz, Taras S. Kudryk & Semen S. Kutateladze - 2017 - Foundations of Science 22 (3):539-555.
    The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and (...)
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  3. Counting on Strong Composition as Identity to Settle the Special Composition Question.Joshua Spencer - 2017 - Erkenntnis 82 (4):857-872.
    Strong Composition as Identity is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what’s true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence is mistaken. (...)
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  4. Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  5. Is Mathematics a Domain for Philosophers of Explanation?Erik Weber & Joachim Frans - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (1):125-142.
    In this paper we discuss three interrelated questions. First: is explanation in mathematics a topic that philosophers of mathematics can legitimately investigate? Second: are the specific aims that philosophers of mathematical explanation set themselves legitimate? Finally: are the models of explanation developed by philosophers of science useful tools for philosophers of mathematical explanation? We argue that the answer to all these questions is positive. Our views are completely opposite to the views that Mark Zelcer has put forward recently. Throughout this (...)
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  6. The Idea of Infinity in its Physical and Spiritual Meanings.Graham Nicholson - manuscript
    Abstract -/- The concept of infinity is of ancient origins and has puzzled deep thinkers ever since up to the present day. Infinity remains somewhat of a mystery in a physical world in which our comprehension is largely framed around the concept of boundaries. This is partly because we live in a physical world that is governed by certain dimensions or limits – width, breadth, depth, mass, space, age and time. To our ordinary understanding, it is a seemingly finite world (...)
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  7. The Physicalization of Mathematics.Peter Milne - 1994 - British Journal for the Philosophy of Science 45 (1):305-340.
  8. Review Article. Ontology, Logic, and Mathematics.J. Folina - 2000 - British Journal for the Philosophy of Science 51 (2):319-332.
  9. Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures James Robert Brown.T. Hofweber - 2001 - British Journal for the Philosophy of Science 52 (2):413-416.
  10. Visualization, Explanation and Reasoning Styles in Mathematics.Paolo Mancosu (ed.) - 2005 - Springer.
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  11. Genealogical Mathematics: Observations on a Conference and Prospects for the Future.P. A. Ballonoff - 1974 - Social Science Information 13 (4-5):45-57.
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  12. Between Reality and Mentality -Fifteenth Century Mathematics and Natural Philosophy Reconsidered-.İhsan Fazlıoğlu - 2014 - Nazariyat, Journal for the History of Islamic Philosophy and Sciences 1 (1):1-39.
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  13. Loss of Vision: How Mathematics Turned Blind While It Learned to See More Clearly.Bernd Buldt & Dirk Schlimm - unknown
    To discuss the developments of mathematics that have to do with the introduction of new objects, we distinguish between ‘Aristotelian’ and ‘non-Aristotelian’ accounts of abstraction and mathematical ‘top-down’ and ‘bottom-up’ approaches. The development of mathematics from the 19th to the 20th century is then characterized as a move from a ‘bottom-up’ to a ‘top-down’ approach. Since the latter also leads to more abstract objects for which the Aristotelian account of abstraction is not well-suited, this development has also lead to a (...)
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  14. Review of "Frank Quinn: A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today". [REVIEW]Bernd Buldt - unknown
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  15. On Questions Relating to Philosophy of Mathematics.Chung-Ying Cheng - 1972 - NTU Philosophical Review 2:113-120.
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  16. The Impact of the Interaction Between Verbal and Mathematical Languages in Education.Atieno Kili K’Odhiambo & Samson O. Gunga - 2010 - Thought and Practice: A Journal of the Philosophical Association of Kenya 2 (2):79-99.
    Since the methods employed during teacher-learner interchange are constrained by the internal structure of a discipline, a study of the interaction amongst verbal language, technical language and structure of disciplines is at the heart of the classic problem of transfer in teaching-learning situations. This paper utilizes the analytic method of philosophy to explore aspects of the role of language in mathematics education, and attempts to harmonize mathematical meanings exposed by verbal language and the precise meanings expressed by the mathematics register (...)
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  17. Two Principles of Leibniz’s Philosophy in Relation to the History of Mathematics.Michael Otte - 1993 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 8 (1):113-125.
  18. Symbolism in Mathematics and Logic.J. J. Callahan - 1953 - Proceedings of the XIth International Congress of Philosophy 5:166-171.
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  19. The World of Mathematics.James Newman - 1956
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  20. Mathematics in the Classroom: Conceptual Cartography of Differential Calculus.de Lourdes Rodr - 2015 - Revista Romaneasca pentru Educatie Multidimensionala 7 (2):47-54.
    This paper presents the results of a documentary investigation with the intention of substantiate how and why, and the level and depth of the topics used by the teacher in the classroom for the development of the mathematical knowledge on the part of higher level engineering students. The analysis of the mathematical object was made through the construction of conceptual cartography, being the core of the derivative concept. To construct the axes, the socio-formative theory of Sergio Tob.
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  21. What is a Mathematical Concept?Elizabeth de Freitas, Nathalie Sinclair & Alf Coles (eds.) - 2017 - Cambridge University Press.
    Responding to widespread interest within cultural studies and social inquiry, this book addresses the question 'what is a mathematical concept?' using a variety of vanguard theories in the humanities and posthumanities. Tapping historical, philosophical, sociological and psychological perspectives, each chapter explores the question of how mathematics comes to matter. Of interest to scholars across the usual disciplinary divides, this book tracks mathematics as a cultural activity, drawing connections with empirical practice. Unlike other books in this area, it is highly interdisciplinary, (...)
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  22. Mathematical Intuition and Wittgenstein.David Henley - 1992 - In Christopher Ormell (ed.), New Thinking About the Nature of Mathematics. pp. 39-43.
    This paper covers some large subjects: as well as intuition and Wittgenstein, it also discusses modern computing. However it only traces one thread through these topics. Basically it proposes that a computational analysis of Wittgenstein's Tractatus can shed light upon processes of discovery in mathematics.
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  23. On the New Foundational Crisis of Mathematics.Hermann Weyl - 1998 - In ¸ Itemancosu1998. Oxford University Press.
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  24. Mathematicians as Philosophers of Mathematics: Part 2.Jeremy Gray - 1999 - For the Learning of Mathematics 19:28-91.
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  25. Mathematicians as Philosophers of Mathematics: Part 1.Jeremy Gray - 1998 - For the Learning of Mathematics 18:20-24.
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  26. Type-Theoretical Checking and the Philosophy of Mathematics.Nicolaas Govert de Bruijn - 1998 - In ¸ Itesambin1998. Clarendon Press, Oxford.
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  27. Consciousness, Philosophy and Mathematics.L. E. J. Brouwer - 1949 - In E. W. Beth, H. J. Pos & H. J. A. Hollak (eds.), Library of the Tenth International Congress in Philosophy, August 1948. North-Holland. pp. 1235--1249.
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  28. What Are the Limits of Mathematical Explanation? Interview with Charles McCarty by Piotr Urbańczyk.David Charles McCarty & Piotr Urbańczyk - 2016 - Zagadnienia Filozoficzne W Nauce 60:119-137.
    An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.
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  29. Introduction to the Philosophy of Mathematics.Timothy McCarthy & Hugh Lehman - 1981 - Philosophical Review 90 (3):461.
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  30. The Philosophy of Mathematics.Atwell R. Turquette & Stephan Korner - 1962 - Philosophical Review 71 (2):248.
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  31. Plato's Philosophy of Mathematics.B. F. McGuinness & Anders Wedberg - 1959 - Philosophical Review 68 (3):389.
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  32. The Philosophy of Mathematics.Atwell R. Turquette & Edward A. Maziarz - 1951 - Philosophical Review 60 (4):597.
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  33. Philosophy of Mathematics and Natural Science.Stephen Toulmin & Hermann Weyl - 1950 - Philosophical Review 59 (3):385.
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  34. A Philosophy of Mathematics.S. C. Kleene & Louis O. Kattsoff - 1949 - Philosophical Review 58 (2):187.
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  35. Ian Hacking Why is There Philosophy of Mathematics at All? [REVIEW]Christopher Pincock - 2016 - British Journal for the Philosophy of Science 67 (3):907-912.
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  36. Emergent Mathematics in a Grade-Two Classroom: A Search for Complex Relationships.Noel Geoghegan - unknown
    In light of the organically interconnected relationships of learning mathematics, a theoretical heuristic was developed to exemplify the implications of the findings of the study. Called SEARCH, the heuristic highlighted learning mathematics as a synergistic relationship constituted by an interconnectedness among social, emotional, physical, and cognitive development, each of which requires a balanced consideration in order to pursue the epistemological, ontological, and methodological paradigmatic frameworks embedded in current mathematics reform agendas. SEARCH is an acronym that stands for Social Emancipation, Active (...)
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  37. The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations.Reviel Netz - 2011 - Cambridge University Press.
    The transformation of mathematics from ancient Greece to the medieval Arab-speaking world is here approached by focusing on a single problem proposed by Archimedes and the many solutions offered. In this trajectory Reviel Netz follows the change in the task from solving a geometrical problem to its expression as an equation, still formulated geometrically, and then on to an algebraic problem, now handled by procedures that are more like rules of manipulation. From a practice of mathematics based on the localized (...)
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  38. What Has Mathematics Got to Do with Values?Stephen Lerman - unknown
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  39. Mathematics and Philosophy.D. Bushaw - unknown
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  40. A Short History of Greek Mathematics.James Gow - 2010 - 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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  41. Why is There Philosophy of Mathematics at All?Ian Hacking - 2014 - Cambridge University Press.
    This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that (...)
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  42. Pappus of Alexandria and the Mathematics of Late Antiquity.Serafina Cuomo - 2000 - Cambridge University Press.
    This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. An important first chapter looks at the mathematicians of the period and how mathematics was perceived by people at large. The central chapters of the book analyse sections of the Collection, identifying features typical of Pappus's mathematical practice. The final chapter draws (...)
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  43. On Philosophy of Mathematics.Charles Parsons - 2010 - The Harvard Review of Philosophy 17 (1):137-150.
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  44. What is Mathematics?S. M. Antakov - 2015 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 4 (5):358.
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  45. Philosophy and Mathematics in the Teaching of Plato: The Development of Idea and Modernity.N. V. Mikhailova - 2014 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 3 (6):468.
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  46. Whether Philosophers Need Contemporary Mathematics?V. A. Erovenko - 2013 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 2 (6):523.
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  47. The Concept of Formality in Mathematics.Hiroshi Nagai - 1960 - Annals of the Japan Association for Philosophy of Science 1 (5):289-312.
  48. Essay Review: Islamic Mathematics: The Muslim Contribution to Mathematics.David A. King - 1979 - History of Science 17 (4):295-296.
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  49. Domain Extension and the Philosophy of Mathematics.Kenneth Manders - 1989 - Journal of Philosophy 86 (10):553-562.
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  50. Philosophy of Mathematics and Natural Science.E. N., Hermann Weyl & Olaf Helmer - 1951 - Journal of Philosophy 48 (2):48.
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