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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. Ambrose Ambrose (1957). ITTGENSTEIN'S Remarks on the Foundations of Mathematics. [REVIEW] Philosophy and Phenomenological Research 18:262.
  3. 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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  4. 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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  5. 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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  6. R. J. B. (1964). Review of P. Benacerraf and H. Putnam (Eds.), Philosophy of Mathematics: Selected Readings. [REVIEW] Review of Metaphysics 18 (2):390-390.
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  7. Arnold Beckmann, Costas Dimitracopoulos & Benedikt Löwe (2010). Computability in Europe 2008. Archive for Mathematical Logic 49 (2):119-121.
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  8. 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.
    Bernard Bolzano , one of the leading figures of the Bohemian Enlightenment, made important contributions both to mathematics and philosophy which were virtually unknown in his lifetime and are still largely unacknowledged today. As a mathematician, he was a pioneer in the clarification and rigorization of mathematical analysis; as a philosopher, he may be considered a forerunner of the analytic movement later to emerge with Frege and Russell.Rusnock's account of Bolzano's work is laid out in five chapters and two appendices. (...)
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  9. Paul Benacerraf & Hilary Putnam (1983). Philosophy of Mathematics Selected Readings /Edited by Paul Benacerraf, Hilary Putnam. --. --. Cambridge University Press,1983.
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  10. Paul Benacerraf & Hilary Putnam (1964). Philosophy of Mathematics Selected Readings. Edited and with an Introd. By Paul Benacerraf and Hilary Putnam. Prentice-Hall.
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  11. Jan Berg (1994). The Ontological Foundations of Bolzano's Philosophy of Mathematics. In Dag Prawitz & Dag Westerståhl (eds.), Logic and Philosophy of Science in Uppsala. Kluwer. 265--271.
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  12. J. L. Berggren (1996). WS Anglin. Mathematics: A Concise History and Philosophy. Philosophia Mathematica 4 (2):196-197.
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  13. 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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  14. 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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  15. Evert Willem Beth (1959). The Foundations of Mathematics. Amsterdam, North-Holland Pub. Co..
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  16. Max Black (1959). The Nature of Mathematics. Paterson, N.J.Littlefield, Adams.
  17. 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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  18. Emile Borel (1952). L'imaginaire Et Le Réel En Mathématiques Et En Physique. Paris, A. Michel.
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  19. D. Bostock (2000). SCHIRN, M.(Ed.)-The Philosophy of Mathematics Today. Philosophical Books 41 (2):97-103.
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  20. David Bostock (1997). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. International Philosophical Quarterly 37 (3):353-354.
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  21. 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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  22. 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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  23. 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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  24. 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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  25. 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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  26. 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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  27. J. R. Cameron (1968). Review: Logic and Philosophy of Mathematics. [REVIEW] Philosophical Quarterly 18 (70):73 - 75.
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  28. Paul J. Campbell & Louise S. Grinstein (1976). Women in Mathematics: A Preliminary Selected Bibliography. Philosophia Mathematica (1):171-172.
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  29. Rudolf Carnap (1939). Foundations of Logic and Mathematics. Journal of Philosophy 36 (23):636-637.
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  30. Rudolf Carnap, Arend Heyting & Johann von Neumann (1964). Symposium on the Foundations of Mathematics. In P. Benacerraf H. Putnam (ed.), Philosophy of Mathematics. Prentice-Hall.
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  31. 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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  32. Douglas Cenzer, Barbara F. Csima & Bakhadyr Khoussainov (2009). Linear Orders with Distinguished Function Symbol. Archive for Mathematical Logic 48 (1):63-76.
    We consider certain linear orders with a function on them, and discuss for which types of functions the resulting structure is or is not computably categorical. Particularly, we consider computable copies of the rationals with a fixed-point free automorphism, and also ω with a non-decreasing function.
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  33. Douglas Cenzer, Valentina Harizanov, David Marker & Carol Wood (2009). Preface. Archive for Mathematical Logic 48 (1):1-6.
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  34. Douglas Cenzer & Rebecca Weber (2008). Preface. Archive for Mathematical Logic 46 (7-8):529-531.
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  35. Gregory J. Chaitin (2000). A Century of Controversy Over the Foundations of Mathematics. Complexity 5 (5):12-21.
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  36. Eugenio Chinchilla (2005). Models of Replacement Schemes. Archive for Mathematical Logic 44 (7):851-867.
    In the context of bounded arithmetic we consider some general replacement schemes and construct models for them. A new proof of a conservation result between and is derived.
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  37. Peter Cholak, Richard A. Shore & Reed Solomon (2006). A Computably Stable Structure with No Scott Family of Finitary Formulas. Archive for Mathematical Logic 45 (5):519-538.
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  38. 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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  39. Brian Coffey (1948). KATTSOFF, LOUIS O. "A Philosophy of Mathematics". [REVIEW] Modern Schoolman 26:190.
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  40. Mark Colyvan (2004). The Search for Certainty: A Philosophical Account of Foundations of Mathematics. Bulletin of Symbolic Logic 10 (2):214-216.
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  41. Colleen E. Crangle, Adolfo García de la Sienra & Helen E. Longino (eds.) (forthcoming). Foundations and Methods From Mathematics to Neuroscience. CSLI Publications.
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  42. J. C. Dumoncel (2003). M. Giaquinto The Search for Certainty. A Philosophical Account of Foundations of Mathematics. History and Philosophy of Logic 24 (3):244-247.
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  43. 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.
    Guillermo E. Rosado Haddock's critical introduction to the philosophy of Gottlob Frege is based on twenty-five years of teaching Frege's philosophy at the University of Puerto Rico. It developed from an earlier publication by Rosado Haddock on Frege's philosophy which was, however, available only in Spanish. This introduction to Frege is meant to steer a path between the two main approaches to Frege studies: on the one hand, we have interpretations of Frege which portray him as a neo-Kantian and thus (...)
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  44. Eva-Maria Engelen, Kurt Gödels mathematische Anschauung und John P. Burgess’ mathematische Intuition. XXIII Deutscher Kongress für Philosophie Münster 2014, Konferenzveröffentlichung.
  45. 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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  46. 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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  47. J. Fang (1987). The “Needham Question”: Toward a “Sociology of Mathematics”. Philosophia Mathematica (2):180-210.
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  48. J. Fang (1980). A “Mathematical Talent” in the Age of Androgyny. Philosophia Mathematica (1):50-96.
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  49. J. Fang (1978). Mathematics and “Das Philosophieren”. Philosophia Mathematica (1):23-55.
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  50. J. Fang (1978). The Politics of the Infinite. Philosophia Mathematica (1):127-165.
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