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  1. D. J. Allan (1955). Aristotle's Philosophy of Mathematics. By H. G. Apostle (Cambridge University Press, for the University of Chicago Press. 1953. 45s.). [REVIEW] Philosophy 30 (114):270-.
  2. Alessandro Andretta, Keith Kearnes & Domenico Zambella (eds.) (2008). Logic Colloquium 2004: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Torino, Italy, July 25-31, 2004. [REVIEW] Cambridge University Press.
    Highlights of this volume from the 2004 Annual European Meeting of the Association for Symbolic Logic (ASL) include a tutorial survey of the recent highpoints of universal algebra, written by a leading expert; explorations of foundational questions; a quartet of model theory papers giving an excellent reflection of current work in model theory, from the most abstract aspect "abstract elementary classes" to issues around p-adic integration.
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  3. Andrew Arana (2008). Review of Ferreiros and Gray's The Architecture of Modern Mathematics. [REVIEW] Mathematical Intelligencer 30 (4).
    This collection of essays explores what makes modern mathematics ‘modern’, where ‘modern mathematics’ is understood as the mathematics done in the West from roughly 1800 to 1970. This is not the trivial matter of exploring what makes recent mathematics recent. The term ‘modern’ (or ‘modernism’) is used widely in the humanities to describe the era since about 1900, exemplified by Picasso or Kandinsky in the visual arts, Rilke or Pound in poetry, or Le Corbusier or Loos in architecture (a building (...)
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  4. Andrew Arana (2007). Review of D. Corfield's Toward A Philosophy Of Real Mathematics. [REVIEW] Mathematical Intelligencer 29 (2).
    When mathematicians think of the philosophy of mathematics, they probably think of endless debates about what numbers are and whether they exist. Since plenty of mathematical progress continues to be made without taking a stance on either of these questions, mathematicians feel confident they can work without much regard for philosophical reflections. In his sharp–toned, sprawling book, David Corfield acknowledges the irrelevance of much contemporary philosophy of mathematics to current mathematical practice, and proposes reforming the subject accordingly.
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  5. John L. Bell (2006). Paul Rusnock. Bolzano's Philosophy and the Emergence of Modern Mathematics. Studien Zur Österreichischen Philosophie [Studies in Austrian Philosophy], Vol. 30. Amsterdam & Atlanta: Editions Rodopi, 2000. Isbn 90-420-1501-2. Pp. 218. [REVIEW] Philosophia Mathematica 14 (3):362-364.
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  6. J. L. Berggren (1996). WS Anglin. Mathematics: A Concise History and Philosophy. Philosophia Mathematica 4 (2):196-197.
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  7. Francesco Berto (2009). There's Something About Gödel: The Complete Guide to the Incompleteness Theorem. Wiley-Blackwell.
    The Gödelian symphony -- Foundations and paradoxes -- This sentence is false -- The liar and Gödel -- Language and metalanguage -- The axiomatic method or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers (...)
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  8. Evert Willem Beth (1965). Mathematical Thought. Dordrecht, Holland, D. Reidel Pub. Co..
    Another striking deviation with regard to philosophical tradition consists in the fact that contemporary schools in the philosophy of mathematics, with the exception again of Brouwer's intuitionism, hardly ever refer to mathematical thought.
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  9. Evert Willem Beth (1959). The Foundations of Mathematics. Amsterdam, North-Holland Pub. Co..
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  10. Max Black (1959). The Nature of Mathematics. Paterson, N.J.Littlefield, Adams.
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  11. George Boolos, John Burgess, Richard P. & C. Jeffrey (2007). Computability and Logic. Cambridge University Press.
    Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel’s incompleteness theorems, but also a large number of optional topics, from Turing’s theory of computability to Ramsey’s theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a (...)
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  12. Emile Borel (1952). L'imaginaire Et Le Réel En Mathématiques Et En Physique. Paris, A. Michel.
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  13. David Bostock (1997). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. International Philosophical Quarterly 37 (3):353-354.
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  14. Andrew Boucher, Dedekind's Proof by V2.0 Last Updated: 10 Dec 2001 Created: 1 Sept 2000 Please Send Your Comments to Abo.
    In "The Nature and Meaning of Numbers," Dedekind produces an original, quite remarkable proof for the holy grail in the foundations of elementary arithmetic, that there are an infinite number of things. It goes like this. [p, 64 in the Dover edition.] Consider the set S of things which can be objects of my thought. Define the function phi(s), which maps an element s of S to the thought that s can be an object of my thought. Then phi is (...)
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  15. James Robert Brown (2010). D Avid B Ostock . Philosophy of Mathematics: An Introduction. Philosophia Mathematica 18 (1):127-129.
    (No abstract is available for this citation).
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  16. James Robert Brown (2004). Review of M. Giaquinto, The Search for Certainty: A Philosophical Account of Foundations of Mathematics. [REVIEW] Mind 113 (449):177-179.
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  17. James Robert Brown (2003). Kitcher's Mathematical Naturalism. Croatian Journal of Philosophy 3 (1):1-20.
    Recent years have seen a number of naturalist accounts of mathematics. Philip Kitcher’s version is one of the most important and influential. This paper includes a critical exposition of Kitcher’s views and a discussion of several issues including: mathematical epistemology, practice, history, the nature of applied mathematics. It argues that naturalism is an inadequate account and compares it with mathematical Platonism, to the advantage of the latter.
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  18. James Robert Brown (2002). Review of A. George and D. J. Velleman, Philosophies of Mathematics. [REVIEW] Mind 111 (444):860-862.
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  19. Otavio Bueno & Jour AZZOUNI, Critical Studies/Book Reviews 319.
    Ask a philosopher what a proof is, and you’re likely to get an answer hii empaszng one or another regimentationl of that notion in terms of a finite sequence of formalized statements, each of which is either an axiom or is derived from an axiom by certain inference rules. (Wecan call this the formal conception of proof) Ask a mathematician what a proof is, and you will rbbl poay get a different-looking answer. Instead of stressing a partic- l uar regimented (...)
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  20. Paul J. Campbell & Louise S. Grinstein (1976). Women in Mathematics: A Preliminary Selected Bibliography. Philosophia Mathematica (1):171-172.
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  21. Carlo Cellucci (2003). Review of M. Giaquinto, The Search for Certainty. [REVIEW] European Journal of Philosophy 11:420-423.
    Giaquinto’s book is a philosophical examination of how the search for certainty was carried out within the philosophy of mathematics from the late nineteenth to roughly the mid-twentieth century. It is also a good introduction to the philosophy of mathematics and the views expressed in the body of the book, in addition to being thorough and stimulating, seem generally undisputable. Some doubts, however, could be raised about the concluding remarks concerning the present situation in the philosophy of mathematics, specifically Zermelo's (...)
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  22. Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
    This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.
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  23. P. A. Ebert (2011). Guillermo E. Rosado Haddock. A Critical Introduction to the Philosophy of Gottlob Frege. Aldershot, Hampshire, and Burlington, Vermont: Ashgate Publishing, 2006. Isbn 978-0-7546-5471-1. Pp. X+157. [REVIEW] Philosophia Mathematica 19 (3):363-367.
  24. William Bragg Ewald (ed.) (1996). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford University Press.
    This massive two-volume reference presents a comprehensive selection of the most important works on the foundations of mathematics. While the volumes include important forerunners like Berkeley, MacLaurin, and D'Alembert, as well as such followers as Hilbert and Bourbaki, their emphasis is on the mathematical and philosophical developments of the nineteenth century. Besides reproducing reliable English translations of classics works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare, William Ewald also includes selections from Gauss, Cantor, Kronecker, and Zermelo, all translated here for (...)
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  25. George R. Exner (1997). An Accompaniment to Higher Mathematics. Springer.
    This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, (...)
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  26. J. Fang (1987). The “Needham Question”: Toward a “Sociology of Mathematics”. Philosophia Mathematica (2):180-210.
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  27. J. Fang (1980). A “Mathematical Talent” in the Age of Androgyny. Philosophia Mathematica (1):50-96.
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  28. J. Fang (1978). Mathematics and “Das Philosophieren”. Philosophia Mathematica (1):23-55.
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  29. J. Fang (1978). The Politics of the Infinite. Philosophia Mathematica (1):127-165.
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  30. J. Fang (1976). Mathematicians, Man or Woman: Exercises in a “Verstehen-Approach”. Philosophia Mathematica (1):15-72.
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  31. J. Fang (1976). Woman and Mathematics, Past and Present. Philosophia Mathematica (1):5-14.
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  32. J. Fang (1976). Women and the so-Called “Mathematical Talent”: A Prelude to Sociopsychology. Philosophia Mathematica (1):130-170.
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  33. J. Fang (1975). Per Analogiam Vs Per Definitionem Relative to the Patterns of Discovery. Philosophia Mathematica (1):5-22.
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  34. J. Fang (1975). “J'accuse …”: A Politics of Mathematics. Philosophia Mathematica (2):124-148.
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  35. J. Fang (1972). Towards a Certain “Contextualism” II. (Foresight Vs. Hindsight) Vs. Insight. Philosophia Mathematica 2:158-167.
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  36. J. Fang (1972). Towards a Certain “Contextualism”. Philosophia Mathematica (1):53-92.
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  37. J. Fang (1971). A Selective Bibliography : 1940–1970. Philosophia Mathematica (1-2):1-48.
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  38. J. Fang (1969). Hilbert's Problems. Philosophia Mathematica (1-2):38-53.
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  39. J. Fang (1967). What is, and Ought to Be, Philosophy of Mathematics? Philosophia Mathematica (1-2):71-75.
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  40. J. Fang (1966). What is, and Ought to Be, History of Mathematics? Philosophia Mathematica (1-2):39-44.
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  41. J. Fang (1965). Aftermath of New Math: A Philosophical Rejoinder. Philosophia Mathematica (2):88-92.
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  42. J. Fang (1965). Kant and Modern Mathematics. Philosophia Mathematica (2):57-68.
  43. J. Fang (1964). Certain “Nonbooks” on Mathematics. Philosophia Mathematica (2):113-117.
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  44. Joong Fang (1970). Towards a Philosophy of Modern Mathematics. [Hauppauge, N.Y.]Paideia.
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  45. Solomon Feferman, Deciding the Undecidable: Wrestling with Hilbert's Problems.
    In the year 1900, the German mathematician David Hilbert gave a dramatic address in Paris, at the meeting of the 2nd International Congress of Mathematicians—an address which was to have lasting fame and importance. Hilbert was at that point a rapidly rising star, if not superstar, in mathematics, and before long he was to be ranked with Henri Poincar´.
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  46. Solomon Feferman, For Philosophy of Mathematics: 5 Questions.
    When I was a teenager growing up in Los Angeles in the early 1940s, my dream was to become a mathematical physicist: I was fascinated by the ideas of relativity theory and quantum mechanics, and I read popular expositions which, in those days, besides Einstein’s The Meaning of Relativity, was limited to books by the likes of Arthur S. Eddington and James Jeans. I breezed through the high-school mathematics courses (calculus was not then on offer, and my teachers barely understood (...)
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  47. Solomon Feferman, The Development of Programs for the Foundations of Mathematics in the First Third of the 20th Century.
    The most prominent “schools” or programs for the foundations of mathematics that took shape in the first third of the 20th century emerged directly from, or in response to, developments in mathematics and logic in the latter part of the 19th century. The first of these programs, so-called logicism, had as its aim the reduction of mathematics to purely logical principles. In order to understand properly its achievements and resulting problems, it is necessary to review the background from that previous (...)
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  48. Jens Erik Fenstad (ed.) (1971). Proceedings of the Second Scandinavian Logic Symposium. Amsterdam,North-Holland Pub. Co..
    Provability, Computability and Reflection.
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  49. J. Folina (2000). Ontology, Logic, and Mathematics: Review of M. Schirn (Ed.), The Philosophy of Mathematics Today. [REVIEW] British Journal for the Philosophy of Science 51 (2):319-332.
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  50. Alexander George (ed.) (1994). Mathematics and Mind. Oxford University Press.
    Those inquiring into the nature of mind have long been interested in the foundations of mathematics, and conversely this branch of knowledge is distinctive in that our access to it is purely through thought. A better understanding of mathematical thought should clarify the conceptual foundations of mathematics, and a deeper grasp of the latter should in turn illuminate the powers of mind through which mathematics is made available to us. The link between conceptions of mind and of mathematics has been (...)
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