Search results for 'Mathematics Philosophy' (try it on Scholar)

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  1. Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.score: 210.0
    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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  2. Charles Parsons (1983). Mathematics in Philosophy: Selected Essays. Cornell University Press.score: 210.0
    This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics.
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  3. Paul Benacerraf & Hilary Putnam (eds.) (1983). Philosophy of Mathematics: Selected Readings. Cambridge University Press.score: 206.0
    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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  4. Richard L. Tieszen (2005). Phenomenology, Logic, and the Philosophy of Mathematics. Cambridge University Press.score: 204.0
    Offering a collection of fifteen essays that deal with issues at the intersection of phenomenology, logic, and the philosophy of mathematics, this book is divided into three parts. Part I, Reason, Science, and Mathematics 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 (...)
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  5. James Robert Brown (1999). Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures. Routledge.score: 204.0
    Philosophy of Mathematics is clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.
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  6. Stewart Shapiro (2000). Thinking About Mathematics: The Philosophy of Mathematics. Oxford University Press.score: 204.0
    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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  7. Stewart Shapiro (ed.) (2005). The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press.score: 204.0
    Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance (...)
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  8. David Corfield (2003). Towards a Philosophy of Real Mathematics. Cambridge University Press.score: 204.0
    In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically, and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or (...)
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  9. W. S. Anglin (1996). Mathematics, a Concise History and Philosophy. Springer.score: 204.0
    This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed (...)
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  10. Dale Jacquette (ed.) (2002). Philosophy of Mathematics: An Anthology. Blackwell Publishers.score: 204.0
    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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  11. José Ferreirós Domínguez & Jeremy Gray (eds.) (2006). The Architecture of Modern Mathematics: Essays in History and Philosophy. Oxford University Press.score: 204.0
    This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.
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  12. Paul Benacerraf (1964). Philosophy of Mathematics. Englewood Cliffs, N.J.,Prentice-Hall.score: 204.0
    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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  13. Stefania Centrone (2010). Logic and Philosophy of Mathematics in the Early Husserl. Springer.score: 204.0
    This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...
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  14. J. R. Lucas (2000). The Conceptual Roots of Mathematics: An Essay on the Philosophy of Mathematics. Routledge.score: 204.0
    The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
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  15. Mark Colyvan (2012). An Introduction to the Philosophy of Mathematics. Cambridge University Press.score: 204.0
    Machine generated contents note: 1. Mathematics and its philosophy; 2. The limits of mathematics; 3. Plato's heaven; 4. Fiction, metaphor, and partial truths; 5. Mathematical explanation; 6. The applicability of mathematics; 7. Who's afraid of inconsistent mathematics?; 8. A rose by any other name; 9. Epilogue: desert island theorems.
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  16. Otávio Bueno & Øystein Linnebo (eds.) (2009). New Waves in Philosophy of Mathematics. Palgrave Macmillan.score: 204.0
    Thirteen up-and-coming researchers in the philosophy of mathematics have been invited to write on what they take to be the right philosophical account of mathematics, examining along the way where they think the philosophy of mathematics is and ought to be going. A rich and diverse picture emerges. Some broader tendencies can nevertheless be detected: there is increasing attention to the practice, language and psychology of mathematics, a move to reassess the orthodoxy, as well (...)
     
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  17. W. D. Hart (ed.) (1996). The Philosophy of Mathematics. Oxford University Press.score: 204.0
    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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  18. Edmund Husserl (1994). Early Writings in the Philosophy of Logic and Mathematics. Kluwer Academic Publishers.score: 204.0
    This book makes available to the English reader nearly all of the shorter philosophical works, published or unpublished, that Husserl produced on the way to the phenomenological breakthrough recorded in his Logical Investigations of 1900-1901. Here one sees Husserl's method emerging step by step, and such crucial substantive conclusions as that concerning the nature of Ideal entities and the status the intentional `relation' and its `objects'. Husserl's literary encounters with many of the leading thinkers of his day illuminates both the (...)
     
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  19. T. Koetsier (1991). Lakatos' Philosophy of Mathematics: A Historical Approach. Distributors for the U.S. And Canada, Elsevier Science Pub. Co..score: 204.0
    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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  20. Lisa Shabel (2003). Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice. Routledge.score: 204.0
    Mathematics in Kant's Critical Philosophy provides a much needed reading (and re-reading) of Kant's theory of the construction of mathematical concepts through a fully contextualized analysis. In this work Lisa Shabel convincingly argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, can the material and context necessary for a successful interpretation of Kant's philosophy be provided. This is borne out through sustained readings of Euclid and (...)
     
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  21. Ian Hacking (2011). Why is There Philosophy of Mathematics AT ALL? South African Journal of Philosophy 30 (1):1-15.score: 198.0
    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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  22. Feng Ye (2007). Indispensability Argument and Anti-Realism in Philosophy of Mathematics. Frontiers of Philosophy in China 2 (4):614-628.score: 198.0
    The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create (...)
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  23. Charalampos Toumasis (1997). The NCTM Standards and the Philosophy of Mathematics. Studies in Philosophy and Education 16 (3):317-330.score: 198.0
    It is argued that the philosophical and epistemological beliefs about the nature of mathematics have a significant influence on the way mathematics is taught at school. In this paper, the philosophy of mathematics of the NCTM's Standards is investigated by examining is explicit assumptions regarding the teaching and learning of school mathematics. The main conceptual tool used for this purpose is the model of two dichotomous philosophies of mathematics-absolutist versus- fallibilist and their relation to (...)
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  24. Mikhail G. Katz & Thomas Mormann, Infinitesimals and Other Idealizing Completions in Neo-Kantian Philosophy of Mathematics.score: 192.0
    We seek to elucidate the philosophical context in which the so-called revolution of rigor in inifinitesimal calculus and mathematical analysis took place. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at that time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our main thesis is that Marburg Neo-Kantian philosophy formulated (...)
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  25. Carlo Cellucci (1996). Mathematical Logic: What has It Done for the Philosophy of Mathematics? In Piergiorgio Odifreddi (ed.), Kreiseliana. About and Around Georg Kreisel, pp. 365-388. A K Peters.score: 192.0
    onl y to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community and so seem worth discussing anyhow. Such claims will be used as reference to make some remarks about the present state of relations between mathematical logic and the philosophy of (...). (shrink)
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  26. Feng Ye (2010). What Anti-Realism in Philosophy of Mathematics Must Offer. Synthese 175 (1):13 - 31.score: 192.0
    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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  27. Stewart Shapiro (1997). Philosophy of Mathematics: Structure and Ontology. Oxford University Press.score: 192.0
    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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  28. James Franklin (2014). Aristotelian Realist Philosophy of Mathematics. Palgrave MacMillan.score: 192.0
    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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  29. Michael Gabbay (2010). A Formalist Philosophy of Mathematics Part I: Arithmetic. Studia Logica 96 (2):219-238.score: 192.0
    In this paper I present a formalist philosophy mathematics and apply it directly to Arithmetic. I propose that formalists concentrate on presenting compositional truth theories for mathematical languages that ultimately depend on formal methods. I argue that this proposal occupies a lush middle ground between traditional formalism, fictionalism, logicism and realism.
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  30. James Franklin (2011). Aristotelianism in the Philosophy of Mathematics. Studia Neoaristotelica 8 (1):3-15.score: 192.0
    Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio (...)
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  31. Roman Murawski (2010). Philosophy of Mathematics in the Warsaw Mathematical School. Axiomathes 20 (2-3):279-293.score: 192.0
    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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  32. Stuart Shanker (ed.) (1996). Philosophy of Science, Logic, and Mathematics in the Twentieth Century. Routledge.score: 192.0
    Volume 9 of the Routledge History of Philosophy surveys ten key topics in the Philosophy of Science, Logic and Mathematics in the Twentieth Century. Each article is written by one of the world's leading experts in that field. The papers provide a comprehensive introduction to the subject in question, and are written in a way that is accessible to philosophy undergraduates and to those outside of philosophy who are interested in these subjects. Each chapter contains (...)
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  33. Alison Pease, Alan Smaill, Simon Colton & John Lee (2009). Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics. Foundations of Science 14 (1-2):111-135.score: 192.0
    We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which (...)
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  34. Roman Murawski (2014). Benedykt Bornstein's Philosophy of Logic and Mathematics. Axiomathes 24 (4):549-558.score: 192.0
    The aim of this paper is to present and discuss main philosophical ideas concerning logic and mathematics of a significant but forgotten Polish philosopher Benedykt Bornstein. He received his doctoral degree with Kazimierz Twardowski but is not included into the Lvov–Warsaw School of Philosophy founded by the latter. His philosophical views were unique and quite different from the views of main representatives of Lvov–Warsaw School. We shall discuss Bornstein’s considerations on the philosophy of geometry, on the infinity, (...)
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  35. John Bigelow (1988). The Reality of Numbers: A Physicalist's Philosophy of Mathematics. Oxford University Press.score: 186.0
    Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.
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  36. Pasquale Frascolla (1994). Wittgenstein's Philosophy of Mathematics. Routledge.score: 186.0
    Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.
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  37. James Robert Brown (2008). Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures. Routledge.score: 186.0
    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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  38. Stephan Körner (1968/1986). The Philosophy of Mathematics: An Introductory Essay. Dover Publications.score: 186.0
    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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  39. J. Philip Miller (1982). Numbers in Presence and Absence: A Study of Husserl's Philosophy of Mathematics. Distributors for the U.S. And Canada, Kluwer Boston, Inc..score: 186.0
    CHAPTER I THE EMERGENCE AND DEVELOPMENT OF HUSSERL'S 'PHILOSOPHY OF ARITHMETIC'. HISTORICAL BACKGROUND: WEIERSTRASS AND THE ARITHMETIZATION OF ANALYSIS In ...
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  40. Bart Van Kerkhove (ed.) (2009). New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics. [REVIEW] World Scientific.score: 186.0
    This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics.
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  41. S. Korner (1960/2009). The Philosophy of Mathematics. Hutchinson.score: 186.0
    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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  42. Stephan Körner (1960/2009). The Philosophy of Mathematics: An Introductory Essay. Dover Publications.score: 186.0
    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. Ian Mueller (1981/2006). Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Dover Publications.score: 186.0
    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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  44. William Demopoulos (ed.) (1995). Frege's Philosophy of Mathematics. Harvard University Press.score: 180.0
  45. Michael A. E. Dummett (1991). Frege: Philosophy of Mathematics. Harvard University Press.score: 180.0
    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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  46. Michael D. Resnik (1980). Frege and the Philosophy of Mathematics. Cornell University Press.score: 180.0
  47. Hermann Weyl (1949). Philosophy of Mathematics and Natural Science. Princeton University Press.score: 180.0
    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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  48. David Bostock (2009). Philosophy of Mathematics: An Introduction. Wiley-Blackwell.score: 180.0
    Finally the book concludes with a discussion of the most recent debates between realists and nominalists.
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  49. Paul Pritchard (1995). Plato's Philosophy of Mathematics. Academia Verlag.score: 180.0
  50. Janet Folina (1992). Poincaré and the Philosophy of Mathematics. St. Martin's Press.score: 180.0
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