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  1. Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
    On knowledge and practices: a manifesto -- The web of practices -- Agents and frameworks -- Complementarity in mathematics -- Ancient Greek mathematics: a role for diagrams -- Advanced math: the hypothetical conception -- Arithmetic certainty -- Mathematics developed: the case of the reals -- Objectivity in mathematical knowledge -- The problem of conceptual understanding.
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  • An Inquiry into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2014 - In Giorgio Venturi, Marco Panza & Gabriele Lolli (eds.), From Logic to Practice: Italian Studies in the Philosophy of Mathematics. Cham: Springer International Publishing. pp. 315-336.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...)
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  • Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012-2014. Springer International Publishing. pp. 25-50.
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...)
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  • The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford, England: Oxford University Press. pp. 80--133.
    This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...)
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  • Proof in C17 Algebra.Brendan Larvor - 2005 - Philosophia Scientiae:43-59.
    By the middle of the seventeenth century we that find that algebra is able to offer proofs in its own right. That is, by that time algebraic argument had achieved the status of proof. How did this transformation come about?
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  • (1 other version)Mathematics and Plausible Reasoning: Induction and analogy in mathematics.George Pólya - 1954 - Princeton, NJ, USA: Princeton University Press.
    Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.
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  • A Stroll Through The Worlds Of Animats And Humans: Review of Being There: Putting Brain, Body and World Together Again by Andy Clark. [REVIEW]Anthony Chemero - 1998 - PSYCHE: An Interdisciplinary Journal of Research On Consciousness 4.
    Every few years Andy Clark writes a book designed to help philosophers of mind get up to speed with the most recent developments in cognitive science. In his first two such books, Microcognition (1989) and Associative Engines (1993), Clark introduced the then-cutting-edge field of connectionist networks. In his newest one, Being There: Putting Brain, Body and World Together Again (1997), he once again provides a concise, readable introduction to the state of the art. This time, though, Clark has moved beyond (...)
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  • Magic words: How language augments human computation.Andy Clark - 1998 - In Peter Carruthers & Jill Boucher (eds.), Language and Thought: Interdisciplinary Themes. New York: Cambridge University Press. pp. 162-183.
    Of course, words aren’t magic. Neither are sextants, compasses, maps, slide rules and all the other paraphenelia which have accreted around the basic biological brains of homo sapiens. In the case of these other tools and props, however, it is transparently clear that they function so as to either carry out or to facilitate computational operations important to various human projects. The slide rule transforms complex mathematical problems (ones that would baffle or tax the unaided subject) into simple tasks of (...)
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  • On distinguishing epistemic from pragmatic action.David Kirsh & Paul Maglio - 1994 - Cognitive Science 18 (4):513-49.
    We present data and argument to show that in Tetris - a real-time interactive video game - certain cognitive and perceptual problems are more quickly, easily, and reliably solved by performing actions in the world rather than by performing computational actions in the head alone. We have found that some translations and rotations are best understood as using the world to improve cognition. These actions are not used to implement a plan, or to implement a reaction; they are used to (...)
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  • Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice.Roi Wagner - 2017 - Princeton, USA: Princeton University Press.
    In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes (...)
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  • Mathematical Cognition: A Case of Enculturation.Richard Menary - 2015 - Open Mind.
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  • (1 other version)Mathematics and plausible reasoning.George Pólya - 1968 - Princeton, N.J.,: Princeton University Press.
    2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive (...)
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  • Why do mathematicians need different ways of presenting mathematical objects? The case of cayley graphs.Irina Starikova - 2010 - Topoi 29 (1):41-51.
    This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed as exact mathematical (...)
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