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  1. Commentary On: Begoña Carrascal's "The Practice of Arguing and the Arguments: Examples From Mathematics".Andrew Aberdein - 2013 - In Dima Mohammed & Marcin Lewinski (eds.), Virtues of argumentation: Proceedings of the 10th International Conference of the Ontario Society for the Study of Argumentation (OSSA), May 22–25, 2013. OSSA.
  2. Homeomeric Lines in Greek Mathematics.Fabio Acerbi - 2010 - Science in Context 23 (1):1.
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  3. Hobbes on Natural Philosophy as "True Physics" and Mixed Mathematics.Marcus P. Adams - 2016 - Studies in History and Philosophy of Science Part A 56:43-51.
    I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows (...)
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  4. A Note on the Theory of Positive Induction, {{Rm ID}^*_1}.Bahareh Afshari & Michael Rathjen - 2010 - Archive for Mathematical Logic 49 (2):275-281.
    The article shows a simple way of calibrating the strength of the theory of positive induction, ${{\rm ID}^{*}_{1}}$ . Crucially the proof exploits the equivalence of ${\Sigma^{1}_{1}}$ dependent choice and ω-model reflection for ${\Pi^{1}_{2}}$ formulae over ACA 0. Unbeknown to the authors, D. Probst had already determined the proof-theoretic strength of ${{\rm ID}^{*}_{1}}$ in Probst, J Symb Log, 71, 721–746, 2006.
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  5. Reinhard Siegmund-Schultze, Rockefeller and the Internationalization of Mathematics Between the Two World Wars: Documents and Studies for the Social History of Mathematics in the 20th Century. Science Networks – Historical Studies, 25. Basel, Boston and Berlin: Birkhäuser Verlag, 2001. Pp. XIII+341. Isbn 3-7643-6468-8. $94.95. [REVIEW]Jon Agar - 2003 - British Journal for the History of Science 36 (1):87-127.
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  6. The Place of Mathematics in the System of the Sciences.I. A. Akchurin - 1967 - Russian Studies in Philosophy 6 (3):3-13.
    The deep and many-sided penetration of mathematical methods into virtually all branches of scientific knowledge is a characteristic feature of the present period of development of human culture. Even fields so remote from mathematics as the theory of versification, jurisprudence, archeology, and medical diagnostics have now proved to be associated with the accelerating process of application of disciplines such as probability theory, information theory, algorithm theory, etc. Mathematical methods are rapidly penetrating the sphere of the social sciences. One can no (...)
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  7. When Mathematics Mattered.Amir Alexander - 2013 - Metascience 22 (2):451-453.
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  8. Mathematics and the "Language Game".Alan Ross Anderson - 1957 - Review of Metaphysics 11 (3):446 - 458.
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  9. Mathematics in Cognitive Science.Daniel Andler - unknown
    What role does mathematics play in cognitive science today, what role should mathematics play in cognitive science tomorrow? The cautious short answers are: to the factual question, a rather modest role, except in peripheral areas; to the normative question, a far greater role, as the periphery’s place is reevaluated and as both cognitive science and mathematics grow. This paper aims at providing more detailed, perhaps more contentious answers.
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  10. What is Mathematics?S. M. Antakov - 2015 - Liberal Arts in Russiaроссийский Гуманитарный Журналrossijskij Gumanitarnyj Žurnalrossijskij Gumanitaryj Zhurnalrossiiskii Gumanitarnyi Zhurnal 4 (5):358.
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  11. Sense and Representation in Elementary Mathematics.Peter Appelbaum - 2010 - Philosophy of Mathematics Education Journal 25.
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  12. On the Consistency Proofs.Toshiyasu Arai - 2007 - Journal of the Japan Association for Philosophy of Science 34 (2):91-99.
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  13. The Mathematical Basis of the Arts. Joseph Schillinger.R. C. Archibald - 1949 - Isis 40 (3):293-295.
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  14. Babylonian Mathematics.Raymond Clare Archibald - 1936 - Isis 26 (1):63-81.
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  15. The Ethics of the Infinite.Leslie Armour & Suzie Johnston - 1999 - Maritain Studies/Etudes Maritainiennes 15.
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  16. The Relation of Logic to Mathematics.Richard A. Arms - 1919 - The Monist 29 (1):146-152.
  17. Mathematics for the Million. Lancelot Hogben.M. F. Ashley-Montagu & H. T. Davis - 1938 - Isis 28 (1):138-140.
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  18. The Mathematicians and the Mysterious Universe.John Ashton - 1931 - Thought: Fordham University Quarterly 6 (2):258-274.
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  19. [Inverted Triangle]-Structures.K. Ashton - 1972 - Auckland, N.Z., University of Auckland, Dept. Of Mathematics.
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  20. Zen and the Art of Formalization.Andrea Asperti & Jeremy Avigad - unknown
    N. G. de Bruijn, now professor emeritus of the Eindhoven University of Technology, was a pioneer in the field of interactive theorem proving. From 1967 to the end of the 1970’s, his work on the Automath system introduced the architecture that is common to most of today’s proof assistants, and much of the basic technology. But de Bruijn was a mathematician first and foremost, as evidenced by the many mathematical notions and results that bear his name, among them de Bruijn (...)
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  21. Critical Studies/Book Reviews. [REVIEW]Mark Atten - 2003 - Philosophia Mathematica 11 (2):241-244.
  22. Karen Hunger Parshall;, Adrian C. Rice . Mathematics Unbound: The Evolution of an International Mathematical Research Community, 1800–1945. Xxii + 406 Pp., Illus., Figs., Tables, Index. Providence, R.I.: American Mathematical Society; London: London Mathematical Society, 2002. $85. [REVIEW]Eisso J. Atzema - 2005 - Isis 96 (3):451-452.
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  23. The Role of Mathematics in the Exploration of Reality.Karl Egil Aubert - 1982 - Inquiry: An Interdisciplinary Journal of Philosophy 25 (3):353 – 359.
    In his well?known paper from 1954, Herbert A. Simon sets out to demonstrate that it is possible, in principle, to make public predictions within the social sciences that will be confirmed by the events. However, Simon's proof by means of the Brouwer fixed?point theorem not only rests on an illegitimate use of continuous variables, it is also founded on the questionable assumption that facts ? even on the level of possibilities ? can be established by purely mathematical means. The ?proof? (...)
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  24. Relativité restreinte et cosmologie relativiste chez K. Gödel.Eric Audureau - 2005 - Kairos 26:133-162.
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  25. The History of Mathematics in Spain.Elena Ausejo & Mariano Hormigón - 1999 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 7 (1):13-20.
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  26. By Dennis E. Hesseling.Jeremy Avigad - unknown
    The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri Poincar´e, ´.
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  27. Mathematics and Language.Jeremy Avigad - unknown
    This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping (...)
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  28. Philosophical Relevance of Computers in Mathematics.Jeremy Avigad - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press.
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  29. Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  30. Genealogical Mathematics: Observations on a Conference and Prospects for the Future.P. A. Ballonoff - 1974 - Social Science Information 13 (4-5):45-57.
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  31. Does Mathematics Form a Scientific Continent?Aristides Baltas - 2015 - Philosophical Inquiry 39 (1):49-58.
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  32. Philosophy of Mathematics as a Theoretical and Applied Discipline.A. G. Barabashev - 1989 - Philosophia Mathematica (2):121-128.
  33. The Usefulness of Mathematical Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Publick Schools at the University of Cambridge.Isaac Barrow - 1734 - London: Cass.
    (I) MATHEMATICAL LECTURES. LECTURE I. Of the Name and general Division of the Mathematical Sciences. BEING about to treat upon the Mathematical Sciences, ...
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  34. Two General Methods of Extending Mathematical Theory Creative Process in Mathematics.Marvin Barsky - 1969 - Philosophia Mathematica (1-2):22-27.
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  35. Critical Studies / Book Reviews.Jon Barwise - 1999 - Philosophia Mathematica 7 (2):238-240.
  36. Handbook of Mathematical Logic.Jon Barwise (ed.) - 1977 - North-Holland.
  37. The Principles of Mathematics Revisited. [REVIEW]O. Bradley Bassler - 1997 - Review of Metaphysics 51 (2):424-425.
  38. Informality in Teaching, and Richmond Work‐Study, Language and Mathematics Scores.Cris Baxter & William Anthony - 1987 - Educational Studies 13 (2):179-185.
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  39. Hegel’s Misunderstood Treatment of Gauss in the Science of Logic.Edward Beach - 2006 - Idealistic Studies 36 (3):191-218.
    This essay explores Hegel’s treatment of Carl Friedrich Gauss’s mathematical discoveries as examples of “Analytic Cognition.” Unfortunately, Hegel’s main point has been virtually lost due to an editorial blunder tracing back almost a century, an error that has been perpetuated in many subsequent editions and translations.The paper accordingly has three sections. In the first, I expose the mistake and trace its pervasive influence in multiple languages and editions of the Wissenschaftder Logik. In the second section, I undertake to explain the (...)
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  40. Review of Stewart Shapiro (Ed.), The Oxford Handbook of Philosophy of Mathematics and Logic[REVIEW]JC Beall - 2005 - Notre Dame Philosophical Reviews 2005 (9).
  41. Review of Paradox and Paraconsistency. [REVIEW]JC Beall & David Ripley - 2003 - Notre Dame Philosophical Reviews.
    When physicists disagree as to whose theory is right, they can (if we radically idealize) form an experiment whose results will settle the difference. When logicians disagree, there seems to be no possibility of resolution in this manner. In Paradox and Paraconsistency John Woods presents a picture of disagreement among logicians, mathematicians, and other “abstract scientists” and points to some methods for resolving such disagreement. Our review begins with (very) short sketches of the chapters. Following the sketches, we respond to (...)
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  42. Czech Project in History of Mathematics.Martina Bečvářová - 2004 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 12 (1):40-48.
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  43. Steve Russ. The Mathematical Works of Bernard Bolzano. Oxford: Oxford University Press, 2004. Pp. XXX + 698. Isbn 0-19-853930-. [REVIEW]Ali Behboud - 2006 - Philosophia Mathematica 14 (3):352-362.
    In his book on The Mathematics of Great Amateurs Coolidge starts the chapter on Bolzano saying that he included Bolzano because it seemed interesting to him ‘that a man who was a remarkable pulpit orator, only removed from his chair for his political opinions, should have thought so far into the deepest problems of a science which he never taught in a professional capacity’ [Coolidge, 1990, p. 195]. In fact, considering Bolzano's poor health and his enormous productivity in his ‘professional (...)
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  44. Filosofskie I Metodologicheskie Problemy Matematiki.E. A. Beliaev & Vasilii Iakovlevich Perminov - 1981 - Izd-Vo Moskovskogo Universiteta.
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  45. The Search for Truth.Eric Temple Bell - 1934 - Baltimore: the Williams & Wilkins Company.
  46. A Characterization Of Mathematics.Gary D. Bell - unknown
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  47. Hermann Weyl: Mathematician-Philosopher.John Bell - manuscript
    MATHEMATICS AND PHILOSOPHY ARE CLOSELY LINKED, and several great mathematicians who were at the same time great philosophers come to mind— Pythagoras, Descartes and Leibniz, for instance. One great mathematician of the modern era in whose thinking philosophy played a major role was Hermann Weyl (1885–1955), whose work encompassed analysis, number theory, topology, differential geometry, relativity theory, quantum mechanics, and mathematical logic. His many writings are informed by a vast erudition, an acute philosophical awareness, and even, on occasion, a certain (...)
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  48. Lectures on the Foundations of Mathematics.John Bell - manuscript
    THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world— explicating such facts presents philosophy with some of its subtlest problems. Let me begin by reminding you of some celebrated past attempts made by philosophers and mathematicians to explicate the nature of mathematics.
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  49. Oppositions and Paradoxes in Mathematics and Philosophy John L. Bell Abstract.John Bell - manuscript
    In this paper a number of oppositions which have haunted mathematics and philosophy are described and analyzed. These include the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable.
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  50. The Philosophy of Mathematics.John Bell - manuscript
    THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest problems. We shall discuss some of the attempts made by philosophers and mathematicians to explain the nature of mathematics. We begin with a brief presentation of the views of four major classical philosophers: (...)
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