Results for 'Philosophy of mathematics'

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  1. Aristotelianism in the Philosophy of Mathematics.James Franklin - 2011 - Studia Neoaristotelica 8 (1):3-15.
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio (...)
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  2. Nietzsche’s Philosophy of Mathematics.Eric Steinhart - 1999 - International Studies in Philosophy 31 (3):19-27.
    Nietzsche has a surprisingly significant and strikingly positive assessment of mathematics. I discuss Nietzsche's theory of the origin of mathematical practice in the division of the continuum of force, his theory of numbers, his conception of the finite and the infinite, and the relations between Nietzschean mathematics and formalism and intuitionism. I talk about the relations between math, illusion, life, and the will to truth. I distinguish life and world affirming mathematical practice from its ascetic perversion. For Nietzsche, (...)
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  3.  48
    Redrawing Kant's Philosophy of Mathematics.Joshua M. Hall - 2013 - South African Journal of Philosophy 32 (3):235-247.
    This essay offers a strategic reinterpretation of Kant’s philosophy of mathematics in Critique of Pure Reason via a broad, empirically based reconception of Kant’s conception of drawing. It begins with a general overview of Kant’s philosophy of mathematics, observing how he differentiates mathematics in the Critique from both the dynamical and the philosophical. Second, it examines how a recent wave of critical analyses of Kant’s constructivism takes up these issues, largely inspired by Hintikka’s unorthodox conception (...)
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  4.  7
    Practising Philosophy of Mathematics with Children.Elisa Bezencon - 2020 - Philosophy of Mathematics Education Journal 36.
    This article examines the possibility of philosophizing about mathematics with children. It aims at outlining the nature of the practice of philosophy of mathematics with children in a mainly theoretical and exploratory way. First, an attempt at a definition is proposed. Second, I suggest some reasons that might motivate such a practice. My thesis is that one can identify an intrinsic as well as two extrinsic goals of philosophizing about mathematics with children. The intrinsic goal is (...)
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  5. Ian Hacking, Why Is There Philosophy of Mathematics at All? [REVIEW]Max Harris Siegel - forthcoming - Mind 124.
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  6. The Philosophy of Mathematics and the Independent 'Other'.Penelope Rush - unknown
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  7.  83
    Dummett and Wittgenstein's Philosophy of Mathematics.Carlo Penco - 1994 - In Brian McGuiness & Gianluigi Oliveri (eds.), The Philosophy of Michael Dummett. Kluwer Academic Publishers. pp. 113--136.
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  8.  58
    Reconstruction in Philosophy of Mathematics.Davide Rizza - 2018 - Dewey Studies 2 (2):31-53.
    Throughout his work, John Dewey seeks to emancipate philosophical reflection from the influence of the classical tradition he traces back to Plato and Aristotle. For Dewey, this tradition rests upon a conception of knowledge based on the separation between theory and practice, which is incompatible with the structure of scientific inquiry. Philosophical work can make progress only if it is freed from its traditional heritage, i.e. only if it undergoes reconstruction. In this study I show that implicit appeals to the (...)
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  9. Spinoza and the Philosophy of Science: Mathematics, Motion, and Being.Eric Schliesser - 2012
    This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in (...)
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  10. Assessing the “Empirical Philosophy of Mathematics”.Markus Pantsar - 2015 - Discipline Filosofiche:111-130.
    Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of (...)
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  11.  95
    Some Remarks on Wittgenstein’s Philosophy of Mathematics.Richard Startup - 2020 - Open Journal of Philosophy 10 (1):45-65.
    Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation (...)
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  12. Walter Dubislav’s Philosophy of Science and Mathematics.Nikolay Milkov - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):96-116.
    Walter Dubislav (1895–1937) was a leading member of the Berlin Group for scientific philosophy. This “sister group” of the more famous Vienna Circle emerged around Hans Reichenbach’s seminars at the University of Berlin in 1927 and 1928. Dubislav was to collaborate with Reichenbach, an association that eventuated in their conjointly conducting university colloquia. Dubislav produced original work in philosophy of mathematics, logic, and science, consequently following David Hilbert’s axiomatic method. This brought him to defend formalism in these (...)
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  13. Mario Bunge’s Philosophy of Mathematics: An Appraisal.Jean-Pierre Marquis - 2012 - Science & Education 21 (10):1567-1594.
    In this paper, I present and discuss critically the main elements of Mario Bunge’s philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge’s systemic emergent materialism.To Mario, with gratitude.
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  14. Lakatos’ Quasi-Empiricism in the Philosophy of Mathematics.Michael J. Shaffer - 2015 - Polish Journal of Philosophy 9 (2):71-80.
    Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and (...)
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  15.  70
    Review of O. Linnebo Philosophy of Mathematics[REVIEW]Fraser MacBride - 2018 - Notre Dame Philosophical Reviews.
    In this review, as well as discussing the pedagogical of this text book, I also discuss Linnebo's approach to the Caesar problem and the use of metaphysical notions to explicate mathematics.
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  16.  76
    An Aristotelian Realist Philosophy of Mathematics by James Franklin. [REVIEW]Alex Koo - 2016 - Mathematical Intelligencer 38:81-84.
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  17. Categorical Foundations of Mathematics or How to Provide Foundations for Abstract Mathematics.Jean-Pierre Marquis - 2013 - Review of Symbolic Logic 6 (1):51-75.
    Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.
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  18. On Jain Anekantavada and Pluralism in Philosophy of Mathematics.Landon D. C. Elkind - 2019 - International School for Jain Studies-Transactions 2 (3):13-20.
    I claim that a relatively new position in philosophy of mathematics, pluralism, overlaps in striking ways with the much older Jain doctrine of anekantavada and the associated doctrines of nyayavada and syadvada. I first outline the pluralist position, following this with a sketch of the Jain doctrine of anekantavada. I then note the srrong points of overlaps and the morals of this comparison of pluralism and anekantavada.
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  19. 'Explanatory Indispensability Arguments in Metaethics and Philosophy of Mathematics'.Debbie Roberts - 2016 - In Uri D. Leibowitz & Neil Sinclair (eds.), Explanation in Ethics and Mathematics: Debunking and Dispensability. Oxford University Press.
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  20. Tales of Wonder: Ian Hacking: Why is There Philosophy of Mathematics at All? Cambridge University Press, 2014, 304pp, $80 HB.Brendan Larvor - 2015 - Metascience 24 (3):471-478.
    Why is there Philosophy of Mathematics at all? Ian Hacking. in Metascience (2015).
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  21.  82
    Math by Pure Thinking: R First and the Divergence of Measures in Hegel's Philosophy of Mathematics.Ralph M. Kaufmann & Christopher Yeomans - 2017 - European Journal of Philosophy 25 (4):985-1020.
    We attribute three major insights to Hegel: first, an understanding of the real numbers as the paradigmatic kind of number ; second, a recognition that a quantitative relation has three elements, which is embedded in his conception of measure; and third, a recognition of the phenomenon of divergence of measures such as in second-order or continuous phase transitions in which correlation length diverges. For ease of exposition, we will refer to these three insights as the R First Theory, Tripartite Relations, (...)
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  22. Justification and Explanation in Mathematics and Morality.Justin Clarke-Doane - 2015 - Oxford Studies in Metaethics 10.
    In his influential book, The Nature of Morality, Gilbert Harman writes: “In explaining the observations that support a physical theory, scientists typically appeal to mathematical principles. On the other hand, one never seems to need to appeal in this way to moral principles.” What is the epistemological relevance of this contrast, if genuine? This chapter argues that ethicists and philosophers of mathematics have misunderstood it. They have confused what the chapter calls the justificatory challenge for realism about an area, (...)
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  23. From Mathematics to Quantum Mechanics - On the Conceptual Unity of Cassirer’s Philosophy of Science.Thomas Mormann - 2015 - In Sebastian Luft & J. Tyler Friedman (eds.), The Philosophy of Ernst Cassirer: A Novel Assessment. De Gruyter. pp. 31-64.
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  24. Aristotle’s Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities.Paola Cantù - 2010 - Synthese 174 (2):225-235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...)
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  25.  36
    The Fundamental Cognitive Approaches of Mathematics.Salvador Daniel Escobedo Casillas - manuscript
    We propose a way to explain the diversification of branches of mathematics, distinguishing the different approaches by which mathematical objects can be studied. In our philosophy of mathematics, there is a base object, which is the abstract multiplicity that comes from our empirical experience. However, due to our human condition, the analysis of such multiplicity is covered by other empirical cognitive attitudes (approaches), diversifying the ways in which it can be conceived, and consequently giving rise to different (...)
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  26.  65
    Mark Steiner: The Applicability of Mathematics as a Philosophical Problem. [REVIEW]Rinat Nugayev - 2003 - Philosophy of Science 70 (3):628-631.
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  27. Fourteen Arguments in Favour of a Formalist Philosophy of Real Mathematics.Karlis Podnieks - 2015 - Baltic Journal of Modern Computing 3 (1):1-15.
    The formalist philosophy of mathematics (in its purest, most extreme version) is widely regarded as a “discredited position”. This pure and extreme version of formalism is called by some authors “game formalism”, because it is alleged to represent mathematics as a meaningless game with strings of symbols. Nevertheless, I would like to draw attention to some arguments in favour of game formalism as an appropriate philosophy of real mathematics. For the most part, these arguments have (...)
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  28. Review of Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics[REVIEW]Chris Smeenk - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):194-199.
    Book Review for Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, La Salle, IL: Open Court, 2002. Edited by David Malament. This volume includes thirteen original essays by Howard Stein, spanning a range of topics that Stein has written about with characteristic passion and insight. This review focuses on the essays devoted to history and philosophy of physics.
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  29. Mathematics and Conceptual Analysis.Antony Eagle - 2008 - Synthese 161 (1):67–88.
    Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number (...)
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  30. Tools for Thought: The Case of Mathematics.Valeria Giardino - 2018 - Endeavour 2 (42):172-179.
    The objective of this article is to take into account the functioning of representational cognitive tools, and in particular of notations and visualizations in mathematics. In order to explain their functioning, formulas in algebra and logic and diagrams in topology will be presented as case studies and the notion of manipulative imagination as proposed in previous work will be discussed. To better characterize the analysis, the notions of material anchor and representational affordance will be introduced.
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  31. Mathematics as Make-Believe: A Constructive Empiricist Account.Sarah Elizabeth Hoffman - 1999 - Dissertation, University of Alberta (Canada)
    Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics (...)
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  32. Avoiding Reification: Heuristic Effectiveness of Mathematics and the Prediction of the Omega Minus Particle.Michele Ginammi - 2016 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 53:20-27.
    According to Steiner (1998), in contemporary physics new important discoveries are often obtained by means of strategies which rely on purely formal mathematical considerations. In such discoveries, mathematics seems to have a peculiar and controversial role, which apparently cannot be accounted for by means of standard methodological criteria. M. Gell-Mann and Y. Ne׳eman׳s prediction of the Ω− particle is usually considered a typical example of application of this kind of strategy. According to Bangu (2008), this prediction is apparently based (...)
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  33. Models, Mathematics and Deleuze's Philosophy: Some Remarks on Simon Duffy's Deleuze and the History of Mathematics: In Defence of the New.James Williams - 2017 - Deleuze and Guatarri Studies 11 (3):475-481.
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  34. Mathematics and the Theory of Multiplicities: Badiou and Deleuze Revisited.Daniel W. Smith - 2003 - Southern Journal of Philosophy 41 (3):411-449.
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  35. Critical Review of Mathematics and Scientific Representation. [REVIEW]Sean Walsh, Eleanor Knox & Adam Caulton - 2014 - Philosophy of Science 81 (3):460-469.
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  36. Wisdom Mathematics.Nicholas Maxwell - 2010 - Friends of Wisdom Newsletter (6):1-6.
    For over thirty years I have argued that all branches of science and scholarship would have both their intellectual and humanitarian value enhanced if pursued in accordance with the edicts of wisdom-inquiry rather than knowledge-inquiry. I argue that this is true of mathematics. Viewed from the perspective of knowledge-inquiry, mathematics confronts us with two fundamental problems. (1) How can mathematics be held to be a branch of knowledge, in view of the difficulties that view engenders? What could (...)
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  37. The Role of Mathematics in Deleuze’s Critical Engagement with Hegel.Simon Duffy - 2009 - International Journal of Philosophical Studies 17 (4):563 – 582.
    The role of mathematics in the development of Gilles Deleuze's (1925-95) philosophy of difference as an alternative to the dialectical philosophy determined by the Hegelian dialectic logic is demonstrated in this paper by differentiating Deleuze's interpretation of the problem of the infinitesimal in Difference and Repetition from that which G. W. F Hegel (1770-1831) presents in the Science of Logic . Each deploys the operation of integration as conceived at different stages in the development of the infinitesimal (...)
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  38. Can Mathematics Explain the Evolution of Human Language?Guenther Witzany - 2011 - Communicative and Integrative Biology 4 (5):516-520.
    Investigation into the sequence structure of the genetic code by means of an informatic approach is a real success story. The features of human language are also the object of investigation within the realm of formal language theories. They focus on the common rules of a universal grammar that lies behind all languages and determine generation of syntactic structures. This universal grammar is a depiction of material reality, i.e., the hidden logical order of things and its relations determined by natural (...)
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  39. Imagination in Mathematics.Andrew Arana - 2016 - In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477.
    This article will consider imagination in mathematics from a historical point of view, noting the key moments in its conception during the ancient, modern and contemporary eras.
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  40.  98
    Review of D. Corfield's Toward A Philosophy Of Real Mathematics[REVIEW]Andrew Arana - 2007 - Mathematical Intelligencer 29 (2).
    When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject (...)
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  41. Mathematics and Argumentation.Andrew Aberdein - 2009 - Foundations of Science 14 (1-2):1-8.
    Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory, but also psychology, education, and computer science. This introduction provides some background to their work.
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  42. Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.
    I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the (...)
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  43.  11
    What is Mathematics: School Guide to Conceptual Understanding of Mathematics.Catalin Barboianu - 2021 - Targu Jiu: PhilScience Press.
    This is not a mathematics book, but a book about mathematics, which addresses both student and teacher, with a goal as practical as possible, namely to initiate and smooth the way toward the student’s full understanding of the mathematics taught in school. The customary procedural-formal approach to teaching mathematics has resulted in students’ distorted vision of mathematics as a merely formal, instrumental, and computational discipline. Without the conceptual base of mathematics, students develop over time (...)
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  44.  60
    The "Unreasonable" Effectiveness of Mathematics: The Foundational Approach of the Theoretic Alternatives.Catalin Barboianu - 2015 - Revista de Filosofie 62 (1):58-71.
    The attempts of theoretically solving the famous puzzle-dictum of physicist Eugene Wigner regarding the “unreasonable” effectiveness of mathematics as a problem of analytical philosophy, started at the end of the 19th century, are yet far from coming out with an acceptable theoretical solution. The theories developed for explaining the empirical “miracle” of applied mathematics vary in nature, foundation and solution, from denying the existence of a genuine problem to structural theories with an advanced level of mathematical formalism. (...)
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  45. Leibniz on Mathematics, Methodology, and the Good: A Reconsideration of the Place of Mathematics in Leibniz's Philosophy.Christia Mercer - 2006 - Early Science and Medicine 11 (4):424-454.
    Scholars have long been interested in the relation between Leibniz, the metaphysician-theologian, and Leibniz, the logician-mathematician. In this collection, we consider the important roles that rhetoric and the "art of thinking" have played in the development of mathematical ideas. By placing Leibniz in this rhetorical tradition, the present essay shows the extent to which he was a rhetorical thinker, and thereby answers the question about the relation between his work as a logician-mathematician and his other work. It becomes clear that (...)
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  46. Explanation in Mathematics: Proofs and Practice.William D'Alessandro - 2019 - Philosophy Compass 14 (11).
    Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do (...)
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  47. Discrete and Continuous: A Fundamental Dichotomy in Mathematics.James Franklin - 2017 - Journal of Humanistic Mathematics 7 (2):355-378.
    The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last (...)
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  48. Computability. Computable Functions, Logic, and the Foundations of Mathematics[REVIEW]R. Zach - 2002 - History and Philosophy of Logic 23 (1):67-69.
    Epstein and Carnielli's fine textbook on logic and computability is now in its second edition. The readers of this journal might be particularly interested in the timeline `Computability and Undecidability' added in this edition, and the included wall-poster of the same title. The text itself, however, has some aspects which are worth commenting on.
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  49.  69
    Historicity, Value and Mathematics.Barry Smith - 1975 - In A. T. Tymieniecka (ed.), Analecta Husserliana, vol. 4. Dordrecht: Reidel. pp. 219-239.
    At the beginning of the present century, a series of paradoxes were discovered within mathematics which suggested a fundamental unclarity in traditional mathemati­cal methods. These methods rested on the assumption of a realm of mathematical idealities existing independently of our thinking activity, and in order to arrive at a firmly grounded mathematics different attempts were made to formulate a conception of mathematical objects as purely human constructions. It was, however, realised that such formulations necessarily result in a (...) which lacks the richness and power of the old ‘platonistic’ methods, and the latter are still defended, in various modified forms, as embodying truths about self-existent mathematical entities. Thus there is an idealism-realism dispute in the philosophy of mathematics in some respects parallel to the controversy over the existence of the experiential world to the settle­ment of which lngarden devoted his life. The present paper is an attempt to apply Ingarden’s methods to the sphere of mathematical existence. This exercise will reveal new modes of being applicable to non-real objects, and we shall put forward arguments to suggest that these modes of being have an importance outside mathematics, especially in the areas of value theory and the ontology of art. (shrink)
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  50. Editorial. Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.Plamen L. Simeonov, Arran Gare, Seven M. Rosen & Denis Noble - 2015 - Progress in Biophysics and Molecular Biology 119 (3):208-218.
    The is the Editorial of the 2015 JPBMB Special Issue on Integral Biomathics: Life Sciences, Mathematics and Phenomenological Philosophy.
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