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  1. Charles Alunni (2006). Continental Genealogies. Mathematical Confrontations in Albert Lautman and Gaston Bachelard. Translated by Simon B. Duffy and Stephen W. Sawyer. In Simon B. Duffy (ed.), Virtual Mathematics: the logic of difference. Clinamen.
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  2. Andrew W. Appel (ed.) (2012). Alan Turing's Systems of Logic: The Princeton Thesis. Princeton University Press.
  3. A. Arana (2012). Jeremy Gray. Plato's Ghost: The Modernist Transformation of Mathematics. Princeton: Princeton University Press, 2008. Isbn 978-0-69113610-3. Pp. VIII + 515. [REVIEW] Philosophia Mathematica 20 (2):252-255.
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  4. Alain Badiou (2006). Mathematics and Philosophy. Translated by Simon B. Duffy. In Simon B. Duffy (ed.), Virtual Mathematics: the logic of difference. Clinamen.
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  5. Piotr Błaszczyk, Mikhail G. Katz & David Sherry (2013). Ten Misconceptions From the History of Analysis and Their Debunking. Foundations of Science 18 (1):43-74.
    The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...)
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  6. Stefania Centrone (2013). The Origin of the Logic of Symbolic Mathematics. Edmund Husserl and Jacob Klein. History and Philosophy of Logic 34 (2):187-193.
  7. Mark Colyvan (2005). Myths and Mathematics in Our Vision of the World. Australian Review of Public Affairs.
    There was a time when science, myth, and religion were one. Our best theories of the world were a strange mixture of demons, gods, magic, and mathematics. The Babylonians believed in gods and a universe consisting of six disks. Early Christians believed that a single god created the universe in seven days. And Plato believed that the world we see is an imperfect shadow of the real world of forms and numbers.
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  8. Alexis de Saint-Ours (2007). Review of Simon B. Duffy (Ed.) Virtual Mathematics: The Logic of Difference (Clinamen, 2006). [REVIEW] Cahiers Critiques de Philosophie 3:224-9.
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  9. Simon B. Duffy (2013). Deleuze and the History of Mathematics: In Defense of the New. Bloomsbury.
    Gilles Deleuze’s engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems – for example, the problem of individuation – and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction of Deleuze’s philosophy, (...)
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  10. Simon B. Duffy (2012). The Question of Deleuze’s Neo-Leibnizianism. In Patricia Pisters, Rosi Braidotti & Alan D. Schrift (eds.), Down by Law: Revisiting Normativity with Deleuze. Bloomsbury.
    Much has been made of Deleuze’s Neo-Leibnizianism,3 however not very much detailed work has been done on the specific nature of Deleuze’s critique of Leibniz that positions his work within the broader framework of Deleuze’s own philo- sophical project. The present chapter undertakes to redress this oversight by providing an account of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold. Deleuze provides a systematic account of the structure of Leibniz’s metaphys- ics in terms of its mathematical underpinnings. (...)
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  11. Simon B. Duffy (2006). The Mathematics of Deleuze’s Differential Logic and Metaphysics. In , Virtual Mathematics: the logic of difference. Clinamen.
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  12. Massa Esteve & Maria Rosa (2012). The Role of Symbolic Language in the Transformation of Mathematics. Philosophica 87.
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  13. Brandon Fogel (2009). Review of Hermann Weyl, Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics. [REVIEW] Notre Dame Philosophical Reviews 2009 (11).
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  14. Jonh A. Fossa (2010). Review of I. Grattan-Guiness, The Norton History of the Mathematical Sciences: The Rainbow Of Mathematics. [REVIEW] Princípios 6 (7):133-134.
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  15. James Franklin (2000). Diagrammatic Reasoning and Modelling in the Imagination: The Secret Weapons of the Scientific Revolution. In Guy Freeland & Anthony Corones (eds.), 1543 and All That: Image and Word, Change and Continuity in the Proto-Scientific Revolution. Kluwer.
    Just before the Scientific Revolution, there was a "Mathematical Revolution", heavily based on geometrical and machine diagrams. The "faculty of imagination" (now called scientific visualization) was developed to allow 3D understanding of planetary motion, human anatomy and the workings of machines. 1543 saw the publication of the heavily geometrical work of Copernicus and Vesalius, as well as the first Italian translation of Euclid.
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  16. Donald Gillies (1978). The Development of Mathematics: Review of M. Kline, Mathematical Thought From Ancient to Modern Times. [REVIEW] British Journal for the Philosophy of Science 29 (1):68-87.
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  17. Ivor Grattan-Guinness (1997). Vida En Común, Vidas Separadas. Sobre Las Interacciones Entre Matematicas Y Lógicas Desde la Revolución Francesa Hasta la Primera Guerra Mundial [Living Together and Living Apart. On the Interactions Between Mathematics and Logics From the French Revolution to the First World War]. Theoria 12 (1):13-37.
    Este artículo presenta un alnplio panorama histórico de las conexiones existentes entre ramas de las matematícas y tipos de lógica durante el periodo 1800-1914. Se observan dos corrientes principales,bastante diferentes entre sí: la lógica algebraica, que hunde sus raíces en la logique yen las algebras de la época revolucionaria francesa y culmina, a través de Boole y De Morgan, en los sistemas de Peirce y de Schröder; y la lógica matematíca, que tiene una fuente de inspiraeión en el analisis matemático (...)
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  18. Karl Hall (2012). Review of L. R. Graham and J. Kantor, Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity. [REVIEW] Metascience 21 (2):317-320.
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  19. Albrecht Heeffer (2008). Regiomontanus and Chinese Mathematics. Philosophica 82:87-114.
    This paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem (CRT) through the Shù shū Jiǔ zhāng (SSJZ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ. CRT problems appear in earlier European arithmetic and can be solved by the method (...)
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  20. Ahmad Ighbariah (2012). Between Logic and Mathematics: Al-Kindī's Approach to the Aristotelian Categories. Arabic Sciences and Philosophy 22 (1):51-68.
    What is the function of logic in al-Kind's theory of categories as it was presented in his epistle On the Number of Aristotle's Books (F treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. He ascribes a special status to the categories Quantity (kammiyya) and Quality (kayfiyya), whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The (...)
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  21. Doug Jesseph (2008). Review of Emily R. Grosholz, Representation and Productive Ambiguity in Mathematics and the Sciences. [REVIEW] Notre Dame Philosophical Reviews 2008 (5).
  22. Mikhail G. Katz & David Sherry (2013). Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, and Their Foes From Berkeley to Russell and Beyond. [REVIEW] Erkenntnis 78 (3):571-625.
    Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, (...)
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  23. Juliette Kennedy (ed.) (forthcoming). Interpreting Gödel. Cambridge.
  24. Ansten Klev (2011). Dedekind and Hilbert on the Foundations of the Deductive Sciences. Review of Symbolic Logic 4 (4):645-681.
    We offer an interpretation of the words and works of Richard Dedekind and the David Hilbert of around 1900 on which they are held to entertain diverging views on the structure of a deductive science. Firstly, it is argued that Dedekind sees the beginnings of a science in concepts, whereas Hilbert sees such beginnings in axioms. Secondly, it is argued that for Dedekind, the primitive terms of a science are substantive terms whose sense is to be conveyed by elucidation, whereas (...)
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  25. Eberhard Knobloch (2002). The Knowledge of Arabic Mathematics by Clavius. Arabic Sciences and Philosophy 12 (2):257-284.
    The article deals with the Arabic sources of Chr. Clavius in Rome and the six different ways they were used by him in mathematics and astronomy. It inquires especially into his attitude towards al-Farghani, Thabit ibn Qurra, al-Bi[tdotu]ruji, Ibn Rushd, Mu[hdotu]ammad al-Baghdadi, Pseudo-Ibn al-Haytham, Jabir ibn Afla[hdotu], and Pseudo-al-[Tuotu]usi.
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  26. Zbigniew Król (2012). Scientific Heritage. Dialogue and Universalism 22 (4):41-65.
    This paper presents sources pertinent to the transmission of Euclid’s Elements in Western medieval civilization. Some important observations follow from the pure description of the sources concerning the development of mathematics, e.g., the text of the Elements was supplemented with new axioms, proofs and theorems as if an “a priori skeleton” lost in Dark Ages was reconstructed and rediscovered during the late Middle Ages. Such historical facts indicate the aprioricity of mathematics.
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  27. Paolo Mancosu (2010). The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900-1940. Oxford University Press.
    At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of .
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  28. Paolo Mancosu (2003). The Russellian Influence on Hilbert and His School. Synthese 137 (1-2):59 - 101.
    The aim of the paper is to discuss the influence exercised by Russell's thought inGöttingen in the period leading to the formulation of Hilbert's program in theearly twenties. I show that after a period of intense foundational work, culminatingwith the departure from Göttingen of Zermelo and Grelling in 1910 we witnessa reemergence of interest in foundations of mathematics towards the end of 1914. Itis this second period of foundational work that is my specific interest. Through theuse of unpublished archival sources (...)
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  29. Paolo Mancosu (ed.) (1998). From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press.
    From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...)
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  30. Paolo Mancosu (1996). Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century. 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. Starting with (...)
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  31. Paolo Mancosu (1991). On the Status of Proofs by Contradiction in the Seventeenth Century. Synthese 88 (1):15 - 41.
    In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations (...)
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  32. Eli Maor (1987/1991). To Infinity and Beyond: A Cultural History of the Infinite. Princeton University Press.
    Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes (...)
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  33. András Máté (2006). Árpád Szabó and Imre Lakatos, or the Relation Between History and Philosophy of Mathematics. Perspectives on Science 14 (3):282-301.
    The thirty year long friendship between Imre Lakatos and the classic scholar and historian of mathematics Árpád Szabó had a considerable influence on the ideas, scholarly career and personal life of both scholars. After recalling some relevant facts from their lives, this paper will investigate Szabó's works about the history of pre-Euclidean mathematics and its philosophy. We can find many similarities with Lakatos' philosophy of mathematics and science, both in the self-interpretation of early axiomatic Greek mathematics as Szabó reconstructs it, (...)
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  34. Edward A. Maziarz (1959). Review of J. E. Hofmann, The History of Mathematics. Translated by F. Gaynor and H. P. Midonick. [REVIEW] Philosophy of Science 26 (4):378-.
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  35. Colin McLarty (2007). Saunders Mac Lane. Saunders Mac Lane: A Mathematical Autobiography. Philosophia Mathematica 15 (3):400-404.
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  36. Colin McLarty (2005). Saunders Mac Lane (1909–2005): His Mathematical Life and Philosophical Works. Philosophia Mathematica 13 (3):237-251.
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  37. Colin Mclarty (1997). Poincaré: Mathematics & Logic & Intuition. Philosophia Mathematica 5 (2):97-115.
    often insisted existence in mathematics means logical consistency, and formal logic is the sole guarantor of rigor. The paper joins this to his view of intuition and his own mathematics. It looks at predicativity and the infinite, Poincaré's early endorsement of the axiom of choice, and Cantor's set theory versus Zermelo's axioms. Poincaré discussed constructivism sympathetically only once, a few months before his death, and conspicuously avoided committing himself. We end with Poincaré on Couturat, Russell, and Hilbert.
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  38. E. Mendelson (2005). Anita Burdman Feferman and Solomon Feferman. Alfred Tarski: Life and Logic. Cambridge: Cambridge University Press, 2004. Pp. Vi + 435. ISBN 0-521-80240-7. [REVIEW] Philosophia Mathematica 13 (2):231-232.
  39. B. Michael (2007). Review of J. Weiner, Frege Explained: From Arithmetic to Analytic Philosophy. [REVIEW] Philosophia Mathematica 15 (1):126-128.
  40. Françoise Monnoyeur-Broitman (2010). Review of U. Goldenbaum and D. Jesseph (Eds.), Infinitesimal Differences: Controversies Between Leibniz and His Contemporaries. [REVIEW] Journal of the History of Philosophy 48 (4):527-528.
    Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...)
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  41. A. W. Moore (1996). Review of N. Ya. Vilenkin, In Search of Infinity [Translated From V Poiskakh Beskonechnosti by Abe Shenitzer]. [REVIEW] Philosophia Mathematica 4 (3).
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  42. Tuyoshi Mori (1978). The Social History of Mathematics in Modern Japan. Philosophia Mathematica (1):88-105.
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  43. lan Mueller (1992). Pythagoras Revived: Mathematics and Philosophy in Late Antiquity. Ancient Philosophy 12 (2):528-531.
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  44. P. H. Nidditch (1962). The Development of Mathematical Logic. New York, Free Press of Glencoe.
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  45. Matthew W. Parker (1998). Did Poincare Really Discover Chaos? [REVIEW] Studies in the History and Philosophy of Modern Physics 29 (4):575-588.
  46. Volker Peckhaus (1997). The Way of Logic Into Mathematics. Theoria 12 (1):39-64.
    Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal (symbolic, mathematical) logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical means. As a (...)
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  47. David Rabouin (2009). Mathesis Universalis: L'Idée de Mathématique Universelle d'Aristote à Descartes. Presses Universitaires de France.
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  48. Mircea Radu (2013). Otto Hölder's 1892 “Review of Robert Graßmann's 1891 Theory of Number”. Introductory Note. Philosophia Scientiæ 17 (17-1):53-56.
    Hölder’s review of Robert Graßmann’s Theory of Number provides the first statement of Hölder’s most significant tenets concerning the distinction between the genetic and axiomatic presentation of mathematics, the mature expression of which is found in Hölder’s book The Mathematical Method of 1924. By translating Hölder’s review into English, I hope to make this unique document known to a wider public. In my introductory note I provide some context to Hölder’s paper and a few other remarks concerning the translation work.
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  49. David Reed (1995). Figures of Thought: Mathematics and Mathematical Texts. Routledge.
    Figures of Thought looks at how mathematical works can be read as texts and examines their textual strategies. David Reed offers the first sustained and critical attempt to find a consistent argument or narrative thread in mathematical texts. Reed selects mathematicians from a range of historical periods and compares their approaches to organizing and arguing texts, using an extended commentary on Euclid's Elements as a central structuring framework. He develops fascinating interpretations of mathematicians' work throughout history, from Descartes to Hilbert, (...)
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  50. John M. Reiner (1941). Review of E. T. Bell, The Development of Mathematics. [REVIEW] Philosophy of Science 8 (3):464-.
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