Results for 'philosophy of mathematics'

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  1. Problems in the Philosophy of Mathematics Proceedings of the International Colloquium in the Philosophy of Science, London, 1965, Volume 1.Imre Lakatos, Bedford College & British Society for the Philosophy of Science - 1967 - North-Holland Pub. Co.
  2.  14
    Philosophy of Mathematics.Øystein Linnebo - 2017 - Princeton, NJ: Princeton University Press.
    Mathematics is one of the most successful human endeavors—a paradigm of precision and objectivity. It is also one of our most puzzling endeavors, as it seems to deliver non-experiential knowledge of a non-physical reality consisting of numbers, sets, and functions. How can the success and objectivity of mathematics be reconciled with its puzzling features, which seem to set it apart from all the usual empirical sciences? This book offers a short but systematic introduction to the philosophy of (...)
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    Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
    Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.
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  4. An Aristotelian Realist Philosophy of Mathematics: Mathematics as the science of quantity and structure.James Franklin - 2014 - London and New York: Palgrave MacMillan.
    An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, (...)
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  5.  55
    Philosophy of mathematical practice: A primer for mathematics educators.Yacin Hamami & Rebecca Morris - 2020 - ZDM Mathematics Education 52:1113–1126.
    In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice (...)
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  6. The Philosophy of Mathematical Practice.Paolo Mancosu (ed.) - 2008 - Oxford, England: Oxford University Press.
    There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.
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  7. Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press.
    Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable (...)
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  8.  3
    Philosophy of Mathematics.Roman Murawski & Thomas Bedürftig (eds.) - 2018 - De Gruyter.
    The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of (...)
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  9.  1
    Logic, Philosophy of Mathematics, and Their History: Essays in Honor of W. W. Tait.Erich H. Reck (ed.) - 2018 - College Publications.
    In a career that spans 60 years so far, W.W. Tait has made many highly influential contributions to logic, the philosophy of mathematics, and their history. The present collection of new essays - contributed by former students, colleagues, and friends - is a Festschrift, i.e., a celebration of his life and work. The essays address a variety of themes prominent in his work or related to it. The collection starts with an introduction in which Tait's contributions are sketched (...)
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  10. The Philosophy of Mathematics and Logic in the 1920s and 1930s in Poland.Roman Murawski - 2014 - Basel: Imprint: Birkhäuser.
    The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those (...)
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  11.  9
    Phimsamp: Philosophy of Mathematics: Sociological Aspsects and Mathematical Practice.Benedikt Löwe & Thomas Müller (eds.) - 2010 - College Publications.
    Philosophy of mathematics is moving in a new direction: away from a foundationalism in terms of formal logic and traditional ontology, and towards a broader range of approaches that are united by a focus on mathematical practice. The scientific research network PhiMSAMP (Philosophy of Mathematics: Sociological Aspects and Mathematical Practice) consisted of researchers from a variety of backgrounds and fields, brought together by their common interest in the shift of philosophy of mathematics towards mathematical (...)
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  12. Frege: Philosophy of Mathematics.Michael Dummett - 1991 - Harvard University Press.
    In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...
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  13.  17
    Lakatos' Philosophy of Mathematics: A Historical Approach.T. Koetsier - 1991 - Distributors for the U.S. And Canada, Elsevier Science Pub. Co..
    In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The (...)
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  14.  41
    The Philosophy of Mathematics.Wilbur Dyre Hart (ed.) - 1996 - Oxford, England: Oxford University Press.
    This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, (...)
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  15. Philosophy of mathematics.Leon Horsten - 2008 - Stanford Encyclopedia of Philosophy.
    If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not (...)
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  16.  4
    Lectures on the philosophy of mathematics.Joel David Hamkins - 2020 - Cambridge, Massachusetts: The MIT Press.
    An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical (...)
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  17. Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
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  18. Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.
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  19.  12
    The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993.Matthias Schirn (ed.) - 1998 - Oxford, England: Clarendon Press.
    The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, (...)
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  20. Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
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  21. The Philosophy of Mathematical Practice.Paolo Mancosu - 2009 - Studia Logica 92 (1):137-141.
     
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  22.  28
    Philosophy of Mathematics: An Anthology.Dale Jacquette (ed.) - 2001 - Blackwell.
    This volume explores the central problems and exposes intriguing new directions in the philosophy of mathematics, making it an essential teaching resource, ...
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  23. Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1983 - British Journal for the Philosophy of Science 34 (1):57-70.
     
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  24. Philosophy of Mathematics.Christopher Pincock - 2011 - In J. Saatsi & S. French (eds.), Companion to the Philosophy of Science. Continuum. pp. 314-333.
    For many philosophers of science, mathematics lies closer to logic than it does to the ordinary sciences like physics, biology and economics. While this view may account for the relative neglect of the philosophy of mathematics by philosophers of science, it ignores at least two pressing questions about mathematics that philosophers of science need to be able to answer. First, do the similarities between mathematics and science support the view that mathematics is, after all, (...)
     
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  25.  11
    Wittgenstein's Philosophy of Mathematics.Juliet Floyd - 2021 - Cambridge University Press.
    For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics grew from his Early and Middle philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.
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  26. Philosophy of Mathematics and Natural Science.Hermann Weyl & Olaf Helmer - 1951 - British Journal for the Philosophy of Science 2 (7):257-260.
     
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  27.  1
    Introducing Philosophy of Mathematics.Michèle Friend - 2007 - Routledge.
    What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics (...)
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  28.  19
    Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta.Maria Zack & Dirk Schlimm (eds.) - 2017 - New York: Birkhäuser.
    Proceedings of the Canadian Society for History and Philosophy of Mathematics.
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  29. The Philosophy of Mathematics Today.M. Schirn - 2000 - Studia Logica 64 (1):146-146.
     
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  30.  6
    Why is There Philosophy of Mathematics at All?Ian Hacking - 2014 - New York: Cambridge University Press.
    This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary (...)
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  31.  78
    What can the Philosophy of Mathematics Learn from the History of Mathematics?Brendan Larvor - 2008 - Erkenntnis 68 (3):393-407.
    This article canvasses five senses in which one might introduce an historical element into the philosophy of mathematics: 1. The temporal dimension of logic; 2. Explanatory Appeal to Context rather than to General Principles; 3. Heraclitean Flux; 4. All history is the History of Thought; and 5. History is Non-Judgmental. It concludes by adapting Bernard Williams’ distinction between ‘history of philosophy’ and ‘history of ideas’ to argue that the philosophy of mathematics is unavoidably historical, but (...)
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  32.  10
    Philosophy of Mathematics: Selected Writings.Matthew E. Moore (ed.) - 2010 - Indiana University Press.
    The philosophy of mathematics plays a vital role in the mature philosophy of Charles S. Peirce. Peirce received rigorous mathematical training from his father and his philosophy carries on in decidedly mathematical and symbolic veins. For Peirce, math was a philosophical tool and many of his most productive ideas rest firmly on the foundation of mathematical principles. This volume collects Peirce’s most important writings on the subject, many appearing in print for the first time. Peirce’s determination (...)
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  33. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu (ed.) - 1996 - Oxford, England: Oxford University Press.
    The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. (...)
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  34. The Philosophy of Mathematics Today.Matthias Schirn - 2000 - Tijdschrift Voor Filosofie 62 (1):180-181.
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  35.  3
    Philosophy of Mathematics.Alexander Paseau (ed.) - 2016 - New York: Routledge.
    Mathematics is everywhere and yet its objects are nowhere. There may be five apples on the table but the number five itself is not to be found in, on, beside or anywhere near the apples. So if not in space and time, where are numbers and other mathematical objects such as perfect circles and functions? And how do we humans discover facts about them, be it Pythagoras’ Theorem or Fermat’s Last Theorem? The metaphysical question of what numbers are and (...)
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  36.  10
    The Philosophy of Mathematics.Jaakko Hintikka (ed.) - 1969 - London: Oxford University Press.
  37.  84
    Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton University Press.
    This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.
  38.  36
    Philosophy of Mathematics: Selected Readings.Paul Benacerraf (ed.) - 1964 - Englewood Cliffs, NJ, USA: Englewood Cliffs, N.J., Prentice-Hall.
    The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers.
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  39. Philosophy of Mathematics: Selected Readings.Paul Benacerraf & Hilary Putnam (eds.) - 1964 - Englewood Cliffs, NJ, USA: Cambridge University Press.
    The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. (...)
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  40.  84
    Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures.James Robert Brown - 1999 - Routledge.
    _Philosophy of Mathematics_ is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.
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  41. Phenomenology, Logic, and the Philosophy of Mathematics.Richard Tieszen - 2005 - Cambridge University Press.
    Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this 2005 book is divided into three parts. Part I contains a general essay on Husserl's conception of science and logic, an essay of mathematics and transcendental phenomenology, and an essay on phenomenology and modern pure geometry. Part II is focused on Kurt Godel's interest in phenomenology. It explores Godel's ideas and also some work of Quine, (...)
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  42. Philosophies of Mathematics.Alexander George & Daniel J. Velleman - 2004 - Philosophical Quarterly 54 (214):194-196.
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  43.  6
    Kant's Philosophy of Mathematics: Volume 1: The Critical Philosophy and its Roots.Carl Posy & Ofra Rechter (eds.) - 2019 - New York, NY: Cambridge University Press.
    The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context (...)
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  44. The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics.Crispin Wright & Bob Hale - 2001 - Oxford: Clarendon Press.
    Here, Bob Hale and Crispin Wright assemble the key writings that lead to their distinctive neo-Fregean approach to the philosophy of mathematics. In addition to fourteen previously published papers, the volume features a new paper on the Julius Caesar problem; a substantial new introduction mapping out the program and the contributions made to it by the various papers; a section explaining which issues most require further attention; and bibliographies of references and further useful sources. It will be recognized (...)
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  45. 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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  46.  16
    Philosophy Of Mathematics In China.Yuxin Zheng - 1991 - Philosophia Mathematica (1):174-199.
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  47.  3
    Philosophy of Mathematics: Selected Writings.Charles Sanders Peirce - 2010 - Indiana University Press.
    Peirce's determination to understand matter, the cosmos, and "the grand design" of the universe remain relevant for contemporary students of science, technology, and symbolic logic.
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  48.  60
    Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism.Gerhard Preyer - 2008 - Frankfort, Germany: Ontos.
    The ten contributions in this volume range widely over topics in the philosophy of mathematics. The four papers in Part I (entitled "Set Theory, Inconsistency, and Measuring Theories") take up topics ranging from proposed resolutions to the paradoxes of naïve set theory, paraconsistent logics as applied to the early infinitesimal calculus, the notion of "purity of method" in the proof of mathematical results, and a reconstruction of Peano's axiom that no two distinct numbers have the same successor. Papers (...)
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  49. Philosophy of mathematics in the 20th century: Main trends and doctrines.Roman Murawski - 2006 - Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):331-347.
    The aim of the paper is to present the main trends and tendencies in the philosophy of mathematics in the 20th century. To make the analysis more clear we distinguish three periods in the development of the philosophy of mathematics in this century: (1) the first thirty years when three classical doctrines: logicism, intuitionism and formalism were formulated, (2) the period from 1931 till the end of the fifties - period of stagnation, and (3) from the (...)
     
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  50.  13
    Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements". [REVIEW]Stanley Rosen - 1982 - Review of Metaphysics 36 (2):465-468.
    This very interesting and extremely useful study raises the question, by virtue of its title and what it does not do, of what is, or ought to be, meant by the philosophy of mathematics. The author begins his study of Euclid with a brief discussion of Hilbert's axiomatization of geometry. The two main points in this discussion are: "Hilbertian geometry and many other parts of modern mathematics are the study of structure", i.e., of the interpretations of axiom-systems; (...)
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