Results for 'philosophy of mathematics'

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  1. Debunking, supervenience, and Hume’s Principle.in Particular Science & in Metaethics Realism/Anti-Realism Debates She is Currently Working on Analogies Between Debates Over Realism/Anti-Realism in the Philosophy of Mathematics - 2019 - Canadian Journal of Philosophy 49 (8):1083-1103.
    Debunking arguments against both moral and mathematical realism have been pressed, based on the claim that our moral and mathematical beliefs are insensitive to the moral/mathematical facts. In the mathematical case, I argue that the role of Hume’s Principle as a conceptual truth speaks against the debunkers’ claim that it is intelligible to imagine the facts about numbers being otherwise while our evolved responses remain the same. Analogously, I argue, the conceptual supervenience of the moral on the natural speaks presents (...)
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  2.  37
    PhiMSAMP: philosophy of mathematics: sociological aspsects and mathematical practice.Benedikt Löwe & Thomas Müller (eds.) - 2010 - London: 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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  3. 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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  4. 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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  5.  37
    Philosophy of mathematics: an anthology.Dale Jacquette (ed.) - 2001 - 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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  6.  90
    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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  7.  20
    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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  8. 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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  9. The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - New York: Cambridge University Press.
    This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the (...)
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  10.  83
    Philosophy of Mathematics in the Warsaw Mathematical School.Roman Murawski - 2010 - Axiomathes 20 (2-3):279-293.
    The aim of this paper is to present and discuss the philosophical views concerning mathematics of the founders of the so called Warsaw Mathematical School, i.e., Wacław Sierpiński, Zygmunt Janiszewski and Stefan Mazurkiewicz. Their interest in the philosophy of mathematics and their philosophical papers will be considered. We shall try to answer the question whether their philosophical views influenced their proper mathematical investigations. Their views towards set theory and its rôle in mathematics will be emphasized.
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  11.  82
    The philosophy of mathematics.Wilbur Dyre Hart (ed.) - 1996 - New York: 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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  12. The Philosophy of Mathematical Practice.Paolo Mancosu - 2009 - Studia Logica 92 (1):137-141.
     
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  13.  14
    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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  14. 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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  15. 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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  16.  19
    The Philosophy of Mathematics Education Today.Paul Ernest (ed.) - 2018 - Springer Verlag.
    This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in (...)
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  17. Philosophy of Mathematics.Paul Benacerraf & Hilary Putnam - 1985 - Philosophy of Science 52 (3):488-489.
     
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  18. (1 other version)Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
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  19. 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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  20.  14
    Philosophy of Mathematics.Otávio Bueno - 2010 - In Fritz Allhoff, Philosophies of the Sciences. Malden, MA: Wiley‐Blackwell. pp. 68–91.
    This chapter contains sections titled: Introduction Platonism in Mathematics Nominalism in Mathematics Conclusion References.
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  21. (1 other version)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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  22.  97
    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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  23. Plato's philosophy of mathematics.Paul Pritchard - 1995 - Sankt Augustin: 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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  24.  24
    Philosophy of mathematics.Stephen Francis Barker - 1964 - Englewood Cliffs, N.J.,: Prentice-Hall.
  25.  33
    Philosophy of Mathematics and Natural Science.Stephen Toulmin - 1950 - Philosophical Review 59 (3):385.
  26. Philosophy of mathematics in early Ernst Cassirer.Robert Maco - 2010 - Filozofia 65 (1):27-39.
    The paper deals with some major themes in early Cassirer’s philosophy of mathema- tics. It appears, that the basis of his thinking about mathematical objects and mathematical concept formation is his Neo-Kantian idealistic theory of concepts which he developed in opposition to what is called the „traditional theory of concepts“ going back to Aristotle. Cassirer often seeks to confirm his philo- sophical insights concerning mathematics by the interpretations the works of significant mathematicians. Therefore, the second part of the (...)
     
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  27. 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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  28.  24
    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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  29.  18
    A Philosophy of Mathematics?John Lake - 1974 - Dialectica 28 (3‐4):263-270.
    SummaryThis note attempts to give a description of mathematics in terms of a process applied to certain ideas. The process is split into a number of distinct stages, each of which is considered seperately. Also, some philosophical problems are briefly discussed in the light of this view of mathematics.
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  30. (1 other version)Frege: Philosophy of Mathematics.Michael DUMMETT - 1991 - Philosophy 68 (265):405-411.
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  31.  13
    Philosophy of Mathematics and Its Logic.Stewart Shapiro - 2005 - In Oxford Handbook of Philosophy of Mathematics and Logic. Oxford and New York: Oxford University Press.
    This chapter provides a broad overview of the philosophy of mathematics and the philosophy of logic. It gives brief coverage to the various issues and positions, such as platonism or realism, varieties of nominalism, or anti-realism, logicism, intuitionism, empiricism, and structuralism.
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  32.  79
    Philosophy of Mathematics: Set Theory, Measuring Theories, and Nominalism.Gerhard Preyer (ed.) - 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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  33.  92
    (2 other versions)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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  34. 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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  35.  41
    "Abraham, Planter of Mathematics"': Histories of Mathematics and Astrology in Early Modern Europe.Nicholas Popper - 2006 - Journal of the History of Ideas 67 (1):87-106.
    In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be (...)
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  36.  48
    Is the uncertainty of mathematics the real source of its intellectual charm?Christopher Ormell - 1993 - Journal of Philosophy of Education 27 (1):125–133.
    Christopher Ormell; Is the Uncertainty of Mathematics the Real Source of Its Intellectual Charm?, Journal of Philosophy of Education, Volume 27, Issue 1, 30 May.
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  37.  39
    Aristotle’s Philosophy of Mathematics and Mathematical Abstraction.Murat Keli̇kli̇ - 2017 - Beytulhikme An International Journal of Philosophy 7 (2):33-49.
    Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this reason, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come (...)
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  38. Philosophies of Mathematics.Alexander George & Daniel J. Velleman - 2004 - Philosophical Quarterly 54 (214):194-196.
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  39. 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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  40. Philosophy of mathematics: Prospects for the 1990s.Penelope Maddy - 1991 - Synthese 88 (2):155 - 164.
    For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers (...)
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  41.  7
    The Philosophy of Mathematics: An Introduction.Stephan Körner - 1962 - Harper & Row.
  42.  80
    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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  43.  11
    In praise of mathematics.Alain Badiou - 2016 - Malden, MA: Polity Press. Edited by Gilles Haéri & Susan Spitzer.
    Why bother to praise mathematics when you claim, as Alain Badiou does, that philosophy is first and foremost a metaphysics of happiness, or else it’s not worth an hour of trouble? What possible relationship can there be between mathematics and happiness? That is precisely the issue at stake in this dialogue, which serves as a very accessible introduction to what mathematics is and an exploration of the crucial influence it has always exerted on the greatest philosophers. (...)
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  44. 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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  45.  10
    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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  46. (1 other version)A philosophy of mathematics.Louis Osgood Kattsoff - 1948 - Ames,: Iowa State College Press.
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  47.  23
    Reductions of Mathematics: Foundation or Horizon?Felix Mühlhölzer - 2018 - In Gabriele Mras, Paul Weingartner & Bernhard Ritter, Philosophy of Logic and Mathematics: Proceedings of the 41st International Ludwig Wittgenstein Symposium. Berlin, Boston: De Gruyter. pp. 327-342.
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  48. Mathematical logic and the foundations of mathematics: an introductory survey.G. T. Kneebone - 1963 - Mineola, N.Y.: Dover Publications.
    Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert’s metamathematics. Part III focuses on the philosophy of mathematics. Each chapter has extensive supplementary notes; a detailed appendix charts modern developments.
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  49.  31
    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.
  50. Phenomenology, Logic, and the Philosophy of Mathematics.Richard L. 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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