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  1. added 2020-02-14
    Proving Quadratic Reciprocity: Explanation, Disagreement, Transparency and Depth.William D'Alessandro - forthcoming - Synthese.
    Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late 18th century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss (...)
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  2. added 2020-01-26
    Vài suy nghĩ về Tết và các mốc công việc nhân dịp Xuân Canh Tý 2020.Vương Q. Hoàng - 2020 - AISDL 2020 (1):1-10.
    Xuân Canh Tý, cá nhân tôi có một dự án quan trọng nhất là CSDL của VIASM, vốn dĩ đã được bàn thảo cũng lâu, và tới năm 2020 là lúc cần về đích và đóng góp vào việc tạo ra sản phẩm thông tin khoa học cho xã hội. Có lẽ không có dịp nào nhấn mạnh yêu cầu công việc dự án này hơn là thời điểm giữa dịp Tết, lúc những dòng suy nghĩ theo lệ đang dành (...)
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  3. added 2020-01-04
    Deleuze on Leibniz : Difference, Continuity, and the Calculus.Daniel W. Smith - 2005 - In Current Continental Theory and Modern Philosophy. Northwestern University Press.
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  4. added 2019-02-27
    Religion and Ideological Confrontations in Early Soviet Mathematics: The Case of P.A. Nekrasov.Dimitris Kilakos - 2018 - Almagest 9 (2):13-38.
    The influence of religious beliefs to several leading mathematicians in early Soviet years, especially among members of the Moscow Mathematical Society, had drawn the attention of militant Soviet marxists, as well as Soviet authorities. The issue has also drawn significant attention from scholars in the post-Soviet period. According to the currently prevailing interpretation, reported purges against Moscow mathematicians due to their religious inclination are the focal point of the relevant history. However, I maintain that historical data arguably offer reasons to (...)
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  5. added 2019-02-24
    Mathematics, Core of the Past and Hope of the Future.James Franklin - 2018 - In Catherine A. Runcie & David Brooks (eds.), Reclaiming Education: Renewing Schools and Universities in Contemporary Western Society. Sydney, Australia: Edwin H. Lowe Publishing. pp. 149-162.
    Mathematics has always been a core part of western education, from the medieval quadrivium to the large amount of arithmetic and algebra still compulsory in high schools. It is an essential part. Its commitment to exactitude and to rigid demonstration balances humanist subjects devoted to appreciation and rhetoric as well as giving the lie to postmodernist insinuations that all “truths” are subject to political negotiation. In recent decades, the character of mathematics has changed – or rather broadened: it has become (...)
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  6. added 2017-07-07
    Whitehead and Pythagoras.Arran Gare - 2006 - Concrescence 7:3 - 19.
    While the appeal of scientific materialism has been weakened by developments in theoretical physics, chemistry and biology, Pythagoreanism still attracts the allegiance of leading scientists and mathematicians. It is this doctrine that process philosophers must confront if they are to successfully defend their metaphysics. Peirce, Bergson and Whitehead were acutely aware of the challenge of Pythagoreanism, and attempted to circumvent it. The problem addressed by each of these thinkers was how to account for the success of mathematical physics if the (...)
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  7. added 2017-02-17
    The Interplay Between Mathematical Practices and Results.Mélissa Arneton, Amirouche Moktefi & Catherine Allamel-Raffin - 2014 - In Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science After the Practice Turn in the Philosophy, History, and Social Studies of Science. New York - London: Routledge. pp. 269-276.
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  8. added 2017-02-17
    La Logique Symbolique En Débat À Oxford À la Fin du XIXe Siècle : Les Disputes Logiques de Lewis Carroll Et John Cook Wilson.Mathieu Marion & Amirouche Moktefi - 2014 - Revue D’Histoire des Sciences 67 (2):185-205.
    The development of symbolic logic is often presented in terms of a cumulative story of consecutive innovations that led to what is known as modern logic. This narrative hides the difficulties that this new logic faced at first, which shaped its history. Indeed, negative reactions to the emergence of the new logic in the second half of the nineteenth century were numerous and we study here one case, namely logic at Oxford, where one finds Lewis Carroll, a mathematical teacher who (...)
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  9. added 2017-02-11
    Mathematics, Explanation and Reductionism: Exposing the Roots of the Egyptianism of European Civilization.Arran Gare - 2005 - Cosmos and History 1 (1):54-89.
    We have reached the peculiar situation where the advance of mainstream science has required us to dismiss as unreal our own existence as free, creative agents, the very condition of there being science at all. Efforts to free science from this dead-end and to give a place to creative becoming in the world have been hampered by unexamined assumptions about what science should be, assumptions which presuppose that if creative becoming is explained, it will be explained away as an illusion. (...)
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  10. added 2016-05-19
    Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory.Valérie Lynn Therrien - 2012 - Ithaque 10:43-65.
    In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the concept (...)
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  11. added 2016-01-02
    Corcoran Reviews Boute’s 2013 Paper “How to Calculate Proofs”.John Corcoran - 2014 - MATHEMATICAL REVIEWS 14:444-555.
    Corcoran reviews Boute’s 2013 paper “How to calculate proofs”. -/- There are tricky aspects to classifying occurrences of variables: is an occurrence of ‘x’ free as in ‘x + 1’, is it bound as in ‘{x: x = 1}’, or is it orthographic as in ‘extra’? The trickiness is compounded failure to employ conventions to separate use of expressions from their mention. The variable occurrence is free in the term ‘x + 1’ but it is orthographic in that term’s quotes (...)
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  12. added 2014-12-24
    Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
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  13. added 2014-03-07
    Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. [REVIEW]Françoise Monnoyeur-Broitman - 2010 - Journal of the History of Philosophy 48 (4):527-528.
    Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...)
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  14. added 2012-05-15
    Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution.James Franklin - 2000 - In Guy Freeland & Anthony Corones (eds.), 1543 and All That: Image and Word, Change and Continuity in the Proto-Scientific Revolution. Kluwer Academic Publishers.
    Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.
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  15. added 2012-04-20
    Jeremy Gray. Plato's Ghost: The Modernist Transformation of Mathematics. Princeton: Princeton University Press, 2008. Isbn 978-0-69113610-3. Pp. VIII + 515. [REVIEW]A. Arana - 2012 - Philosophia Mathematica 20 (2):252-255.
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