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Mathematical Discourse vs. Mathematical Intuition

In Carlo Cellucci & Donald Gillies (eds.), Mathematical Reasoning and Heuristics. College Publications. pp. 137-165. (2005)

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  1. Helmholtz’s Vortex Motion: An Embodied View of Mathematics in the Heuristics of Fluid Mechanics.Alain Ulazia & Enetz Ezenarro - 2020 - Topoi 39 (4):949-961.
    Some viewpoints on the foundations of mathematics and its philosophy are more connected to scientific practice and its heuristics, mainly with the construction of physical theories and the search for the best explanations of physical phenomena by means of abduction or the solution of problems by the analytical method. Some researchers have introduced the importance of human cultural activities into the cognitive aspects of the mental processes of scientists, proposing an embodied approach in the bridge between mathematics and reality. Fluid (...)
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  • Theological Underpinnings of the Modern Philosophy of Mathematics.Vladislav Shaposhnikov - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):147-168.
    The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.
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  • How to think about informal proofs.Brendan Larvor - 2012 - Synthese 187 (2):715-730.
    It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it (...)
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  • The nature of mathematical explanation.Carlo Cellucci - 2008 - Studies in History and Philosophy of Science Part A 39 (2):202-210.
    Although in the past three decades interest in mathematical explanation revived, recent literature on the subject seems to neglect the strict connection between explanation and discovery. In this paper I sketch an alternative approach that takes such connection into account. My approach is a revised version of one originally considered by Descartes. The main difference is that my approach is in terms of the analytic method, which is a method of discovery prior to axiomatized mathematics, whereas Descartes’s approach is in (...)
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  • Philosophy of mathematics: Making a fresh start.Carlo Cellucci - 2013 - Studies in History and Philosophy of Science Part A 44 (1):32-42.
    The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...)
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