Results for 'Philosophy of Mathematics'

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  1. Philosophy of mathematics: selected readings.Paul Benacerraf & Hilary Putnam (eds.) - 1983 - New York: 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. (...)
  2.  46
    Philosophy of mathematics.Paul Benacerraf (ed.) - 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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  3.  35
    Philosophy of Mathematics.Stewart Shapiro - 2003 - In Peter Clark & Katherine Hawley (eds.), Philosophy of science today. Oxford University Press UK.
    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.  58
    Philosophies of mathematics.Alexander L. George & Daniel Velleman - 2002 - Malden, Mass.: Blackwell. Edited by Daniel J. Velleman.
    This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.
  5.  9
    Philosophy of mathematics and natural science.Hermann Weyl - 2009 - Princeton, N.J.: Princeton University Press.
  6. Philosophy of mathematics and mathematical practice in the seventeenth century.Paolo Mancosu (ed.) - 1996 - New York: 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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  7.  31
    Philosophy of mathematics: an introduction.David Bostock - 2009 - Malden, MA: Wiley-Blackwell.
    Finally the book concludes with a discussion of the most recent debates between realists and nominalists.
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  8.  63
    The philosophy of mathematics: an introductory essay.Stephan Körner - 1960 - Mineola, N.Y.: 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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  9.  33
    Philosophy of mathematics: an anthology.Dale Jacquette (ed.) - 2002 - Malden, Mass.: 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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  10.  29
    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, 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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  11.  94
    Philosophy of Mathematics: An Introduction to a World of Proofs and Pictures.James Robert Brown - 1999 - New York: 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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  12. Philosophy of mathematics: a contemporary introduction to the world of proofs and pictures.James Robert Brown - 2008 - New York: Routledge.
    In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?" "This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as (...)
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  13. The philosophy of mathematics: an introductory essay.Stephan Körner - 1968 - New York: Dover Publications.
    Lucid and comprehensive essay surveys the views of Plato, Aristotle, Leibniz and Kant on the nature of mathematics; examines the propositions and theories of the schools these philosophers inspired; and concludes with a discussion on the relation between mathematical theories, empirical data and philosophical presuppositions.
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  14. Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures.James R. Brown - 2001 - Erkenntnis 54 (3):404-407.
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  15. The Philosophy of mathematics today.Matthias Schirn (ed.) - 1998 - New York: 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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  16. Philosophy of mathematics, selected readings.Paul Benacerraf & Hilary Putnam - 1966 - Revue Philosophique de la France Et de l'Etranger 156:501-502.
     
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  17.  48
    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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  18. Phenomenology, Logic, and the Philosophy of Mathematics.Richard Tieszen - 2005 - New York: 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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  19. Philosophy of Mathematics.Paul Benacerraf & Hilary Putnam - 1985 - Philosophy of Science 52 (3):488-489.
     
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  20. The Philosophy of Mathematics (Handbook of the Philosophy of Science series).A. Irvine (ed.) - 2009 - North-Holland Elsevier.
  21. Philosophy of mathematics.Pasquale Frascolla - 2001 - In Hans-Johann Glock (ed.), Wittgenstein: a critical reader. Malden, MA: Blackwell.
  22.  93
    Frege's philosophy of mathematics.William Demopoulos (ed.) - 1995 - Cambridge: Harvard University Press.
    Widespread interest in Frege's general philosophical writings is, relatively speaking, a fairly recent phenomenon. But it is only very recently that his philosophy of mathematics has begun to attract the attention it now enjoys. This interest has been elicited by the discovery of the remarkable mathematical properties of Frege's contextual definition of number and of the unique character of his proposals for a theory of the real numbers. This collection of essays addresses three main developments in recent work (...)
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  23. Philosophy of Mathematics Today.[author unknown] - 2000 - Studia Logica 65 (2):275-278.
  24. The philosophy of mathematics and the independent 'other'.Penelope Rush - unknown
  25. 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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  26.  53
    The philosophy of mathematical practice.James Robert Brown - 2010 - International Journal of Philosophical Studies 18 (1):111 – 115.
  27. 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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  28.  28
    The Brentanist Philosophy of Mathematics in Edmund Husserl’s Early Works.Carlo Ierna - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Dordrecht, Netherland: Springer Verlag. pp. 147-168.
    A common analysis of Edmund Husserl’s early works on the philosophy of logic and mathematics presents these writings as the result of a combination of two distinct strands of influence: on the one hand a mathematical influence due to his teachers is Berlin, such as Karl Weierstrass, and on the other hand a philosophical influence due to his later studies in Vienna with Franz Brentano. However, the formative influences on Husserl’s early philosophy cannot be so cleanly separated (...)
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  29. Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: 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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  30.  18
    Philosophy of mathematics.Stephen Francis Barker - 1964 - Englewood Cliffs, N.J.,: Prentice-Hall.
  31. 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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  32. Philosophy of mathematics.Jeremy Avigad - manuscript
    The philosophy of mathematics plays an important role in analytic philosophy, both as a subject of inquiry in its own right, and as an important landmark in the broader philosophical landscape. Mathematical knowledge has long been regarded as a paradigm of human knowledge with truths that are both necessary and certain, so giving an account of mathematical knowledge is an important part of epistemology. Mathematical objects like numbers and sets are archetypical examples of abstracta, since we treat (...)
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  33. The reason's proper study: essays towards a neo-Fregean philosophy of mathematics.Crispin Wright & Bob Hale - 2001 - Oxford: Clarendon Press. Edited by Crispin Wright.
    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 (...)
  34. Philosophy of Mathematics for the Masses : Extending the scope of the philosophy of mathematics.Stefan Buijsman - 2016 - Dissertation, Stockholm University
    One of the important discussions in the philosophy of mathematics, is that centered on Benacerraf’s Dilemma. Benacerraf’s dilemma challenges theorists to provide an epistemology and semantics for mathematics, based on their favourite ontology. This challenge is the point on which all philosophies of mathematics are judged, and clarifying how we might acquire mathematical knowledge is one of the main occupations of philosophers of mathematics. In this thesis I argue that this discussion has overlooked an important (...)
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  35.  73
    An introduction to the philosophy of mathematics.Mark Colyvan - 2012 - Cambridge: Cambridge University Press.
    This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further (...)
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  36. 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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  37.  47
    Berkeley's philosophy of mathematics.Douglas M. Jesseph - 2005 - In Kenneth P. Winkler (ed.), The Cambridge Companion to Berkeley. New York: Cambridge University Press. pp. 126-128.
    The dissertation is a detailed analysis of Berkeley's writings on mathematics, concentrating on the link between his attack on the theory of abstract ideas and his philosophy of mathematics. Although the focus is on Berkeley's works, I also trace the important connections between Berkeley's views and those of Isaac Barrow, John Wallis, John Keill, and Isaac Newton . The basic thesis I defend is that Berkeley's philosophy of mathematics is a natural extension of his views (...)
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  38. 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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  39.  73
    Social Constructivism as a Philosophy of Mathematics.Paul Ernest - 1997 - Albany, NY, USA: State University of New York Press.
    Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.
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  40. Philosophy of Mathematics, an Introduction to the World of Proofs and Pictures.James Robert Brown - 2003 - Bulletin of Symbolic Logic 9 (4):504-506.
     
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  41.  7
    The Philosophy of Mathematics: The Invisible Art.W. S. Anglin - 1997
    This text is organized around the distinction between finite and infinite. It includes a brief overview of what different philosophers have said about infinity, and looks at some of the arguments to the effect that one should adopt a pro-infinity attitude. Other chapters contain an exposition of the ontological schools; interactions among these schools and various theories of truth; the relationship between mathematics and values; a history of mathematics; an analysis of mathematical knowledge; the role of mathematics (...)
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  42.  93
    Philosophy of Mathematics and Natural Science.Hermann Weyl - 1949 - Princeton, N.J.: Princeton University Press. Edited by Olaf Helmer-Hirschberg & Frank Wilczek.
    This is a book that no one but Weyl could have written--and, indeed, no one has written anything quite like it since.
  43.  17
    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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  44.  5
    Philosophy of Mathematics.Otávio Bueno - 2010-01-04 - In Fritz Allhoff (ed.), Philosophies of the Sciences. Wiley‐Blackwell. pp. 68–91.
    This chapter contains sections titled: Introduction Platonism in Mathematics Nominalism in Mathematics Conclusion References.
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  45.  9
    Philosophy of Mathematics Today.Evandro Agazzi & György Darvas (eds.) - 1997 - Kluwer Academic Publishers.
    Without attempting to cover all the philosophical questions posed by modern mathematics, provides a glimpse of a broad vision of the subject. Covering general philosophical perspectives, foundational approaches, the applicability of mathematics, and history, treats selected topics from a variety of perspectives to demonstrate the range of practices in the discipline. Among them are moderate mathematical fictionism, categorical foundations of the protean character of mathematics, the mathematical overdetermination of physics, and Hungarian traditions and the philosophy of (...)
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  46. Philosophy of mathematics and deductive structure in Euclid's Elements.Ian Mueller - 1981 - Mineola, N.Y.: 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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  47.  18
    Model Theory and the Philosophy of Mathematical Practice: Formalization Without Foundationalism.John T. Baldwin - 2018 - Cambridge University Press.
    Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact (...)
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  48. Fictionalism in the philosophy of mathematics.Mark Colyvan - 1998 - In Edward Craig (ed.), Routledge Encyclopedia of Philosophy: Genealogy to Iqbal. Routledge.
    Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘π is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or anti-realist) account of mathematics in that it denies the existence of a (...)
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  49.  36
    The Philosophy of Mathematics Education.Paul Ernest - 1991 - Falmer Press.
    Although many agree that all teaching rests on a theory of knowledge, this is an in-depth exploration of the philosophy of mathematics for education, building on the work of Lakatos and Wittgenstein.
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  50. The philosophy of mathematics.John Bell - manuscript
    THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest problems. We shall discuss some of the attempts made by philosophers and mathematicians to explain the nature of mathematics. We begin with a brief presentation of the views of (...)
     
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