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A History of Mathematics: From Mesopotamia to Modernity

Oxford University Press UK (2005)

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  1. Incomplete understanding of complex numbers Girolamo Cardano: a case study in the acquisition of mathematical concepts.Denis Buehler - 2014 - Synthese 191 (17):4231-4252.
    In this paper, I present the case of the discovery of complex numbers by Girolamo Cardano. Cardano acquires the concepts of (specific) complex numbers, complex addition, and complex multiplication. His understanding of these concepts is incomplete. I show that his acquisition of these concepts cannot be explained on the basis of Christopher Peacocke’s Conceptual Role Theory of concept possession. I argue that Strong Conceptual Role Theories that are committed to specifying a set of transitions that is both necessary and sufficient (...)
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  • Islam in Gramsci’s Journalism and Prison Notebooks: The Shifting Patterns of Hegemony.Derek Boothman - 2012 - Historical Materialism 20 (4):115-140.
    Gramsci recognised the inestimable historical contribution of Muslim and Arab civilisations, writing on these in his newspaper articles, his pre-prison letters and the Prison Notebooks. The Islamic world contemporary with him was largely rural, with the masses heavily influenced by religion, analogous in some ways to Italy whose economy was still largely oriented towards a peasantry among whom the Vatican played a leading role. In addition to factors such as the politics-religion nexus, what Gramsci was also analysing, without saying as (...)
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  • (2 other versions)From Alexandria to Islam: the algebraic translation of Euclides and the convergence of mathematical knowledge in the House of Wisdom.Carlos Gamas - 2015 - Archai: Revista de Estudos Sobre as Origens Do Pensamento Ocidental 15:33-36.
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  • Replies to Rosen, Leiter, and Dutilh Novaes.Justin Clarke-Doane - 2023 - Philosophy and Phenomenological Research 107 (3):817-837.
    Gideon Rosen, Brian Leiter, and Catarina Dutilh Novaes raise deep questions about the arguments in Morality and Mathematics (M&M). Their objections bear on practical deliberation, the formulation of mathematical pluralism, the problem of universals, the argument from moral disagreement, moral ‘perception’, the contingency of our mathematical practices, and the purpose of proof. In this response, I address their objections, and the broader issues that they raise.
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  • The ‘Miracle’ of Applicability? The Curious Case of the Simple Harmonic Oscillator.Sorin Bangu & Robert H. C. Moir - 2018 - Foundations of Physics 48 (5):507-525.
    The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner’s famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of (...)
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  • Reviewing the Concept of Technological Singularities: How Can It Explain Human Evolution?De Leon Petta Gomes da Costa - 2019 - NanoEthics 13 (2):119-130.
    The concept of “technological singularity”, while controversial, is typically applied to predict the next explosion of intelligence related to advances in computers and artificial intelligence. A potential “rise of machines” has been explored at length by Ray Kurzweil, Vernor Vinge, and many other scholars and futuristic enthusiasts. This study focuses on the fundamentals of the concept of technological singularity to understand the technological evolution of humankind based on the four main characteristics that constitute this concept. When this method is applied (...)
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  • Reflective judgment vs. investigation of things – a comparative study of Kant and Zhu Xi.Yangxiao Ou - unknown
    This thesis is devoted to studying two historical philosophical events that happened in the West and the East. A metaphysical crisis stimulated Kant’s writings during his late critical period towards the notion of the supersensible. It further motivated a methodological shift and his coining of reflective judgment, which eventually brought about a systemic unfolding of his critical philosophy via Kantian moral teleology. Zhu Xi and his Neo-Confucian contemporaries confronted a transformed intellectual landscape resulting from the Neo-Daoist and Buddhist discourses of (...)
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