Results for 'philosophy of mathematics'

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  1. Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - 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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  2.  65
    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.
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  3.  28
    Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of Science Today. Clarendon Press.
    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.  18
    Frege: Philosophy of Mathematics[REVIEW]Charles Parsons - 1996 - Philosophical Review 105 (4):540.
    This work is the long awaited sequel to the author’s classic Frege: Philosophy of Language. But it is not exactly what the author originally planned. He tells us that when he resumed work on the book in the summer of 1989, after a long interruption, he decided to start afresh. The resulting work followed a different plan from the original drafts. The reader does not know what was lost by their abandonment, but clearly much was gained: The present work (...)
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  5. Thinking About Mathematics: The Philosophy of Mathematics.Stewart Shapiro - 2000 - Oxford University Press.
    This unique book by Stewart Shapiro looks at a range of philosophical issues and positions concerning mathematics in four comprehensive sections. Part I describes questions and issues about mathematics that have motivated philosophers since the beginning of intellectual history. Part II is an historical survey, discussing the role of mathematics in the thought of such philosophers as Plato, Aristotle, Kant, and Mill. Part III covers the three major positions held throughout the twentieth century: the idea that (...) is logic (logicism), the view that the essence of mathematics is the rule-governed manipulation of characters (formalism), and a revisionist philosophy that focuses on the mental activity of mathematics (intuitionism). Finally, Part IV brings the reader up-to-date with a look at contemporary developments within the discipline. This sweeping introductory guide to the philosophy of mathematics makes these fascinating concepts accessible to those with little background in either mathematics or philosophy. (shrink)
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  6. 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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  7.  19
    Philosophy of Mathematics and Natural Science.Stephen Toulmin - 1950 - Philosophical Review 59 (3):385.
  8.  31
    Philosophy of Mathematics.Paul Benacerraf - 1964 - 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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  9. Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century.Paolo Mancosu - 1996 - 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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  10. Philosophy of Mathematics: Selected Readings.Paul Benacerraf & Hilary Putnam (eds.) - 1964 - 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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  11. 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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  12. 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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  13. The Philosophy of Mathematics Today.Matthias Schirn (ed.) - 1998 - Clarendon Press.
    This comprehensive volume gives a panorama of the best current work in this lively field, through twenty specially written essays by the leading figures in the field. All essays deal with foundational issues, from the nature of mathematical knowledge and mathematical existence to logical consequence, abstraction, and the notions of set and natural number. The contributors also represent and criticize a variety of prominent approaches to the philosophy of mathematics, including platonism, realism, nomalism, constructivism, and formalism.
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  14. 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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  15.  12
    Philosophy of Mathematics and Natural Science.Heinrich Scholz - 1950 - Journal of Symbolic Logic 15 (3):206-208.
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  16.  93
    Pasch’s Philosophy of Mathematics.Dirk Schlimm - 2010 - Review of Symbolic Logic 3 (1):93-118.
    Moritz Pasch (1843ber neuere Geometrie (1882), in which he also clearly formulated the view that deductions must be independent from the meanings of the nonlogical terms involved. Pasch also presented in these lectures the main tenets of his philosophy of mathematics, which he continued to elaborate on throughout the rest of his life. This philosophy is quite unique in combining a deductivist methodology with a radically empiricist epistemology for mathematics. By taking into consideration publications from the (...)
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  17.  10
    Philosophy of Mathematics and Natural Science.Harry M. Gehman - 1951 - Philosophy and Phenomenological Research 11 (3):433-435.
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  18.  76
    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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  19. Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1981 - Dover Publications.
    A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions — rather than strictly historical and mathematical issues — and features several helpful appendixes.
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  20. An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Stucture.James Franklin - 2014 - 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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  21.  90
    The Philosophy of Mathematics Today.Fraser MacBride - 2003 - Mind 112 (448):792-799.
  22. The Philosophy of Mathematics.W. D. Hart (ed.) - 1996 - 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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  23. Oxford Handbook of Philosophy of Mathematics and Logic.Stewart Shapiro (ed.) - 2005 - Oxford University Press.
    This Oxford Handbook covers the current state of the art in the philosophy of maths and logic in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 newly-commissioned chapters are by established experts in the field and contain both exposition and criticism as well as substantial development of their own positions. Select major positions are represented by two chapters - one supportive and one critical. The book includes a (...)
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  24.  4
    The Philosophy of Mathematics.Atwell R. Turquette & Stephan Korner - 1962 - Philosophical Review 71 (2):248.
  25.  71
    Frege's Philosophy of Mathematics.William Demopoulos (ed.) - 1995 - Harvard University Press.
  26.  97
    Frege and the Philosophy of Mathematics.Michael D. Resnik - 1980 - Cornell University Press.
  27. Philosophy of Mathematics: Selected Readings.Paul Benacerraf & Hilary Putnam (eds.) - 1984 - Cambridge University Press.
    The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox, a challenge to 'classical' mathematics from a world-famous mathematician, a new foundational school, 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 with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon (...)
     
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  28.  74
    Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures.James Robert Brown - 2008 - Routledge.
    1. Introduction : the mathematical image -- 2. Platonism -- 3. Picture-proofs and Platonism -- 4. What is applied mathematics? -- 5. Hilbert and Gödel -- 6. Knots and notation -- 7. What is a definition? -- 8. Constructive approaches -- 9. Proofs, pictures and procedures in Wittgenstein -- 10. Computation, proof and conjecture -- 11. How to refute the continuum hypothesis -- 12. Calling the bluff.
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  29. What Anti-Realism in Philosophy of Mathematics Must Offer.Feng Ye - 2010 - Synthese 175 (1):13 - 31.
    This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of (...)
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  30.  75
    Plato's Philosophy of Mathematics.Paul Pritchard - 1995 - Academia Verlag.
    Available from UMI in association with The British Library. ;Plato's philosophy of mathematics must be a philosophy of 4th century B.C. Greek mathematics, and cannot be understood if one is not aware that the notions involved in this mathematics differ radically from our own notions; particularly, the notion of arithmos is quite different from our notion of number. The development of the post-Renaissance notion of number brought with it a different conception of what mathematics (...)
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  31. 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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  32.  48
    The Philosophy of Mathematics of Imre Lakatos.Mark Steiner - 1983 - Journal of Philosophy 80 (9):502-521.
  33.  30
    Frege’s Philosophy of Mathematics[REVIEW]Sanford Shieh - 1997 - Philosophical Review 106 (2):275.
    The days when Frege was more footnoted than read are now long gone; still, until very recently he has been read rather selectively. No doubt many had an inkling that there’s more to Frege than the sense/reference distinction; but few, one suspects, thought that his philosophy of mathematics was as fertile and intriguing as the present collection demonstrates. Perhaps, as Paul Benacerraf’s essay in this collection suggests, logical positivism should be held partly responsible for the neglect of this (...)
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  34.  39
    The Philosophy of Mathematics: An Introductory Essay.S. KÖRNER - 1960 - Hutchinson.
    This lucid and comprehensive essay by a distinguished philosopher surveys the views of Plato, Aristotle, Leibniz, and Kant on the nature of mathematics. It examines the propositions and theories of the schools these philosophers inspired, and it concludes by discussing the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
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  35.  77
    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 (...)
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  36.  16
    New Directions in the Philosophy of Mathematics: An Anthology.Thomas Tymoczko (ed.) - 1998 - Princeton University Press.
    This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
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  37.  67
    Book Review: Stewart Shapiro. Philosophy of Mathematics: Structure and Ontology. [REVIEW]John P. Burgess - 1999 - Notre Dame Journal of Formal Logic 40 (2):283-291.
  38.  23
    The Philosophy of Mathematics Education.Paul Ernest - 1991 - Falmer Press.
  39.  80
    Formalism in the Philosophy of Mathematics.Alan Weir - unknown
    The guiding idea behind formalism is that mathematics is not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than ludo or chess. This idea has some intuitive plausibility: consider the tyro toiling at multiplication tables or the student using a standard algorithm for differentiating or integrating a function. It also corresponds to some aspects of the practice (...)
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  40.  41
    Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Michael Boylan - 1983 - Philosophy of Science 50 (4):665-668.
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  41. Why is There Philosophy of Mathematics AT ALL?Ian Hacking - 2011 - South African Journal of Philosophy 30 (1):1-15.
    Mathematics plays an inordinate role in the work of many of famous Western philosophers, from the time of Plato, through Husserl and Wittgenstein, and even to the present. Why? This paper points to the experience of learning or making mathematics, with an emphasis on proof. It distinguishes two sources of the perennial impact of mathematics on philosophy. They are classified as Ancient and Enlightenment. Plato is emblematic of the former, and Kant of the latter. The Ancient (...)
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  42.  45
    The Philosophy of Mathematics: An Introductory Essay.Stephan Körner - 1960 - Dover Publications.
    This lucid and comprehensive essay by a distinguished philosopher surveys the views of Plato, Aristotle, Leibniz, and Kant on the nature of mathematics. It examines the propositions and theories of the schools these philosophers inspired, and it concludes by discussing the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
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  43. Strict Constructivism and the Philosophy of Mathematics.Feng Ye - 2000 - Dissertation, Princeton University
    The dissertation studies the mathematical strength of strict constructivism, a finitistic fragment of Bishop's constructivism, and explores its implications in the philosophy of mathematics. ;It consists of two chapters and four appendixes. Chapter 1 presents strict constructivism, shows that it is within the spirit of finitism, and explains how to represent sets, functions and elementary calculus in strict constructivism. Appendix A proves that the essentials of Bishop and Bridges' book Constructive Analysis can be developed within strict constructivism. Appendix (...)
     
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  44.  27
    Philosophy of Mathematics: An Introduction.David Bostock - 2009 - Wiley-Blackwell.
    Finally the book concludes with a discussion of the most recent debates between realists and nominalists.
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  45.  33
    Plato's Philosophy of Mathematics.ANDERS WEDBERG - 1955 - Greenwood Press.
  46. Phimsamp: Philosophy of Mathematics: Sociological Aspsects and Mathematical Practice.Benedikt Löwe & Thomas Müller (eds.) - 2010 - College Publications.
  47.  83
    Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.Roy T. Cook - 2004 - Mind 113 (449):154-157.
  48.  15
    Philosophy of Mathematics : Bolzano's Responses to Kant and Lagrange / La Philosophie des Mathématiques : Les Réponses de Bolzano À Kant Et Lagrange.Paul Rusnock - 1999 - Revue d'Histoire des Sciences 52 (3):399-428.
  49.  5
    Philosophy of Mathematics and Natural Science.E. N. - 1951 - Journal of Philosophy 48 (2):48.
  50. Philosophy of Mathematics Selected Readings /Edited by Paul Benacerraf, Hilary Putnam. --. --.Paul Benacerraf & Hilary Putnam - 1983 - Cambridge University Press, 1983.
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