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  1. Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy.José Antonio Pérez-Escobar & Deniz Sarikaya - 2021 - European Journal for Philosophy of Science 12 (1):1-22.
    In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...)
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  • Mathematizing as a virtuous practice: different narratives and their consequences for mathematics education and society.Deborah Kant & Deniz Sarikaya - 2020 - Synthese 199 (1-2):3405-3429.
    There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...)
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  • 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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  • Philosophy of Mathematical Practice — Motivations, Themes and Prospects†.Jessica Carter - 2019 - Philosophia Mathematica 27 (1):1-32.
    A number of examples of studies from the field ‘The Philosophy of Mathematical Practice’ (PMP) are given. To characterise this new field, three different strands are identified: an agent-based, a historical, and an epistemological PMP. These differ in how they understand ‘practice’ and which assumptions lie at the core of their investigations. In the last part a general framework, capturing some overall structure of the field, is proposed.
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  • Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Studia Logica 81 (2):285-289.
    In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically, and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of new ways to think philosophically about mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, (...)
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  • Wittgenstein and Mannheim on the sociology of mathematics.David Bloor - 1973 - Studies in History and Philosophy of Science Part A 4 (2):173.
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  • Indispensability and Practice.Penelope Maddy - 1992 - Journal of Philosophy 89 (6):275.
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  • Wittgenstein on Mathematical Meaningfulness, Decidability, and Application.Victor Rodych - 1997 - Notre Dame Journal of Formal Logic 38 (2):195-224.
    From 1929 through 1944, Wittgenstein endeavors to clarify mathematical meaningfulness by showing how (algorithmically decidable) mathematical propositions, which lack contingent "sense," have mathematical sense in contrast to all infinitistic "mathematical" expressions. In the middle period (1929-34), Wittgenstein adopts strong formalism and argues that mathematical calculi are formal inventions in which meaningfulness and "truth" are entirely intrasystemic and epistemological affairs. In his later period (1937-44), Wittgenstein resolves the conflict between his intermediate strong formalism and his criticism of set theory by requiring (...)
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  • The unreasonable effectiveness of mathematics in the natural sciences.Eugene Wigner - 1960 - Communications in Pure and Applied Mathematics 13:1-14.
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  • Wittgenstein's philosophy of mathematics.Michael Wrigley - 1977 - Philosophical Quarterly 27 (106):50-59.
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  • Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free.Deniz Sarikaya, José Antonio Pérez-Escobar & Deborah Kant - 2021 - Kriterion – Journal of Philosophy 35 (3):247-278.
    This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...)
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  • On Wittgenstein's Philosophy of Mathematics.Hilary Putnam & James Conant - 1996 - Aristotelian Society Supplementary Volume 70 (1):243-266.
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  • (2 other versions)Wittgenstein's philosophy of mathematics.Michael Dummett - 1959 - Philosophical Review 68 (3):324-348.
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  • Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs.Stanisław Krajewski - 2020 - Studia Humana 9 (3-4):154-164.
    The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the (...)
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  • (1 other version)Wittgenstein on Philosophy of Logic and Mathematics.Juliet Floyd - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press.
    This article is a survey of Wittgenstein’s writings on logic and mathematics; an analytical bibliography of contemporary articles on rule-following, social constructivism, Wittgenstein, Gödel, and constructivism is appended. Various historical accounts of the nature of mathematical knowledge have glossed over the effects of linguistic expression on our understanding of its status and content. Initially Wittgenstein rejected Frege’s and Russell’s logicism, aiming to operationalize the notions of logical consequence, necessity, and sense. Vienna positivists took this to place analysis of meaning at (...)
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  • The availability of Wittgenstein's later philosophy.Stanley Cavell - 1962 - Philosophical Review 71 (1):67-93.
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  • David Hilbert and the axiomatization of physics (1894–1905).Leo Corry - 1997 - Archive for History of Exact Sciences 51 (2):83-198.
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  • (1 other version)Wittgenstein: A Social Theory of Knowledge.David Bloor - 1984 - Human Studies 7 (3):375-386.
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  • Arithmetic and Reality: A Development of Popper's Ideas.Frank Gregory - 2011 - Philosophy of Mathematics Education Journal 26.
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  • Wittgenstein on pure and applied mathematics.Ryan Dawson - 2014 - Synthese 191 (17):4131-4148.
    Some interpreters have ascribed to Wittgenstein the view that mathematical statements must have an application to extra-mathematical reality in order to have use and so any statements lacking extra-mathematical applicability are not meaningful (and hence not bona fide mathematical statements). Pure mathematics is then a mere signgame of questionable objectivity, undeserving of the name mathematics. These readings bring to light that, on Wittgenstein’s offered picture of mathematical statements as rules of description, it can be difficult to see the role of (...)
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  • Wittgenstein's Later Logic.B. H. Slater - 1979 - Philosophy 54 (208):199 - 209.
    Wittgenstein's Remarks on the Foundations of Mathematics was poorly received by the critics when it was first published, and only a few sympathetic commentators have made much of it since then. The book has not had a great success, because the majority of people interested in the philosophy of mathematics these days have a quite different approach to the subject from Wittgenstein. But not only that, they have a quite different logic from Wittgenstein. I believe one of the main sources (...)
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  • How to Frame Understanding in Mathematics: A Case Study Using Extremal Proofs.Merlin Carl, Marcos Cramer, Bernhard Fisseni, Deniz Sarikaya & Bernhard Schröder - 2021 - Axiomathes 31 (5):649-676.
    The frame concept from linguistics, cognitive science and artificial intelligence is a theoretical tool to model how explicitly given information is combined with expectations deriving from background knowledge. In this paper, we show how the frame concept can be fruitfully applied to analyze the notion of mathematical understanding. Our analysis additionally integrates insights from the hermeneutic tradition of philosophy as well as Schmid’s ideal genetic model of narrative constitution. We illustrate the practical applicability of our theoretical analysis through a case (...)
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  • (3 other versions)Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos, John Worrall & Elie Zahar - 1977 - Philosophy 52 (201):365-366.
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  • Some Proposals for Reviving the Philosophy of Mathematics.Reuben Hersh - 1983 - Journal of Symbolic Logic 48 (3):871-872.
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  • Wittgenstein on irrationals and algorithmic decidability.Victor Rodych - 1999 - Synthese 118 (2):279-304.
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  • (1 other version)The Rise of Twentieth Century Analytic Philosophy.Peter Michael Stephan Hacker - 1996 - Ratio 9 (3):243-268.
    The classificatory concept of analytic philosophy cannot fruitfully be given an analytic definition, nor is it a family-resemblance concept. Dummett's contention that it is 'the philosophy of thought' whose main tenet is that an account of thought is to be attained through an account of language is rejected for historical and analytic reasons. Analytic philosophy is most helpfully understood as a historical category earmarking a leading trend in twentieth-century philosophy originating in Cambridge. Its first three phases, viz. Cambridge Platonist pluralism, (...)
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  • The Weak Objectivity of Mathematics and Its Reasonable Effectiveness in Science.Daniele Molinini - 2020 - Axiomathes 30 (2):149-163.
    Philosophical analysis of mathematical knowledge are commonly conducted within the realist/antirealist dichotomy. Nevertheless, philosophers working within this dichotomy pay little attention to the way in which mathematics evolves and structures itself. Focusing on mathematical practice, I propose a weak notion of objectivity of mathematical knowledge that preserves the intersubjective character of mathematical knowledge but does not bear on a view of mathematics as a body of mind-independent necessary truths. Furthermore, I show how that the successful application of mathematics in science (...)
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  • Wittgenstein, Rules and Institutions.David Bloor - 1997 - Tijdschrift Voor Filosofie 62 (2):400-401.
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  • (2 other versions)Wittgenstein's Philosophy of Mathematics.Michael Dummett - 1997 - Journal of Philosophy 94 (7):166--85.
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  • Empirical regularities in Wittgenstein's philosophy of mathematics.Mark Steiner - 2009 - Philosophia Mathematica 17 (1):1-34.
    During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e. , that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assigns to empirical regularities had profound implications for all (...)
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  • Conatus mathematico-philosophicus.Roy Wagner - 2020 - Allgemeine Zeitschrift für Philosophie 45 (1).
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  • Introduction: Interpolations—essays in honor of William Craig.Paolo Mancosu - 2008 - Synthese 164 (3):313-319.
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  • (2 other versions)Wittgenstein's Philosophy of Mathematics.Pasquale Frascolla - 1994 - Philosophical Quarterly 47 (189):552-555.
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  • (1 other version)Introduction.María de Paz & José Ferreirós - 2020 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 51 (1):89-92.
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