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Volumn 17, Issue 1, 2012, Pages 51-89

A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography

Author keywords

Abraham Robinson; Adequality; Archimedean continuum; Bernoullian continuum; Burgess; Cantor; Cauchy; Completeness; Constructivism; Continuity; Dedekind; Du Bois Reymond; Epsilontics; Errett Bishop; Felix Klein; Fermat Robinson standard part; Infinitesimal; Law of excluded middle; Leibniz o transfer principle; Nominalism; Nominalistic reconstruction; Non Archimedean; Rigor; Simon Stevin; Weierstrass

Indexed keywords


EID: 84857142210     PISSN: 12331821     EISSN: 15728471     Source Type: Journal    
DOI: 10.1007/s10699-011-9223-1     Document Type: Article
Times cited : (26)

References (150)
  • 1
    • 33751414155 scopus 로고    scopus 로고
    • Exploration mathematics: the rhetoric of discovery and the rise of infinitesimal methods
    • Alexander A. (2001) Exploration mathematics: the rhetoric of discovery and the rise of infinitesimal methods. Configurations 9(1): 1-36.
    • (2001) Configurations , vol.9 , Issue.1 , pp. 1-36
    • Alexander, A.1
  • 2
    • 0019717771 scopus 로고
    • Intermolecular forces of infinite range and the Boltzmann equation
    • Arkeryd L. (1981) Intermolecular forces of infinite range and the Boltzmann equation. Archievs of Rational Mechanical Analysis 77(1): 11-21.
    • (1981) Archievs of Rational Mechanical Analysis , vol.77 , Issue.1 , pp. 11-21
    • Arkeryd, L.1
  • 3
    • 30344478815 scopus 로고    scopus 로고
    • Nonstandard analysis
    • Arkeryd L. (2005) Nonstandard analysis. American Mathematics Monthly 112(10): 926-928.
    • (2005) American Mathematics Monthly , vol.112 , Issue.10 , pp. 926-928
    • Arkeryd, L.1
  • 4
    • 84857139004 scopus 로고    scopus 로고
    • Response to questionnaire
    • F. Hendricks Vincent and H. Leitgeb (Eds.), New York: Automatic/VIP Press
    • Avigad J. (2007) Response to questionnaire. In: Hendricks Vincent F., Leitgeb H. (eds) Philosophy of mathematics: 5 Questions. Automatic/VIP Press, New York.
    • (2007) Philosophy of Mathematics: 5 Questions
    • Avigad, J.1
  • 5
    • 84876681357 scopus 로고    scopus 로고
    • Fermats "adaequare"-und kein Ende?
    • Barner, K. Fermats "adaequare"-und kein Ende? Mathematische Semesterberichte. http://www. springerlink. com/content/5r32u25207611m37/.
    • Mathematische Semesterberichte
    • Barner, K.1
  • 6
    • 80052701368 scopus 로고
    • Cambridge: Cambridge University Press
    • Barrow I. (1860) The mathematical works, vol. 2. Cambridge University Press, Cambridge.
    • (1860) The Mathematical Works , vol.2
    • Barrow, I.1
  • 9
    • 84857139002 scopus 로고    scopus 로고
    • Stanford Encyclopedia of philosophy. Revised 20 july '09
    • Bell, J. (2009). Continuity and infinitesimals. Stanford Encyclopedia of philosophy. Revised 20 july '09.
    • (2009) Continuity and infinitesimals
    • Bell, J.1
  • 11
    • 0040516463 scopus 로고    scopus 로고
    • Applied constructive mathematics: On G. Hellman's "Mathematical constructivism in spacetime
    • Billinge H. (2000) Applied constructive mathematics: On G. Hellman's "Mathematical constructivism in spacetime. British Journal of Philosophical Science 51(2): 299-318.
    • (2000) British Journal of Philosophical Science , vol.51 , Issue.2 , pp. 299-318
    • Billinge, H.1
  • 12
    • 27444442091 scopus 로고    scopus 로고
    • Did Bishop have a philosophy of mathematics?
    • Billinge H. (2003) Did Bishop have a philosophy of mathematics?. Philosophy in Mathematics (3) 11(2): 176-194.
    • (2003) Philosophy in Mathematics (3) , vol.11 , Issue.2 , pp. 176-194
    • Billinge, H.1
  • 16
    • 0002312248 scopus 로고
    • The crisis in contemporary mathematics
    • Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics (Boston, Mass., 1974)no. 4
    • Bishop, E. (1974). The crisis in contemporary mathematics. Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics (Boston, Mass., 1974). Historia Mathematics 2 ('75), no. 4, 507-517.
    • (1974) Historia Mathematics , vol.2 , Issue.75 , pp. 507-517
    • Bishop, E.1
  • 17
    • 0002818662 scopus 로고
    • Schizophrenia in contemporary mathematics [published posthumously; originally distributed in 1973]
    • In Errett Bishop: Reflections on him and his research (San Diego, Calif., 1983), Am. Math. Soc., Providence, RI
    • Bishop, E. (1985). Schizophrenia in contemporary mathematics [published posthumously; originally distributed in 1973]. In Errett Bishop: Reflections on him and his research (San Diego, Calif., 1983), pp. 1-32, Contemporary Mathematics 39, Am. Math. Soc., Providence, RI.
    • (1985) Contemporary Mathematics 39 , pp. 1-32
    • Bishop, E.1
  • 19
    • 3142677658 scopus 로고    scopus 로고
    • "Sur le concept de nombre en mathématique": Cours inédit de Leopold Kronecker à Berlin
    • (1891)
    • Boniface, J., & Schappacher, N. (2001). "Sur le concept de nombre en mathématique": Cours inédit de Leopold Kronecker à Berlin (1891). ["On the concept of number in mathematics": Leopold Kronecker's 1891 Berlin lectures] Review in Histoire Mathematics 7(2), 206-275.
    • (2001) Review in Histoire Mathematics , vol.7 , Issue.2 , pp. 206-275
    • Boniface, J.1    Schappacher, N.2
  • 21
    • 34547824184 scopus 로고    scopus 로고
    • A new look at E. G. Björling and the Cauchy sum theorem
    • Bråting K. (2007) A new look at E. G. Björling and the Cauchy sum theorem. Archive for History of Exact Sciences 61(5): 519-535.
    • (2007) Archive for History of Exact Sciences , vol.61 , Issue.5 , pp. 519-535
    • Bråting, K.1
  • 22
    • 34249771157 scopus 로고
    • The mysteries of adaequare: A vindication of Fermat
    • Breger H. (1994) The mysteries of adaequare: A vindication of Fermat. Archive for History of Exact Sciences 46(3): 193-219.
    • (1994) Archive for History of Exact Sciences , vol.46 , Issue.3 , pp. 193-219
    • Breger, H.1
  • 23
    • 0002607732 scopus 로고
    • In Real numbers, generalizations of the reals, and theories of continua, see item [45]
    • Bridges, D. (1994). A constructive look at the real number line. In Real numbers, generalizations of the reals, and theories of continua, pp. 29-92, see item [45].
    • (1994) A constructive look at the real number line , pp. 29-92
    • Bridges, D.1
  • 24
    • 0002105043 scopus 로고    scopus 로고
    • Can constructive mathematics be applied in physics?
    • Bridges D. (1999) Can constructive mathematics be applied in physics?. Journal of Philosophical Logic 28(5): 439-453.
    • (1999) Journal of Philosophical Logic , vol.28 , Issue.5 , pp. 439-453
    • Bridges, D.1
  • 26
  • 29
    • 34548780511 scopus 로고
    • Résumé des Leçons données à l'Ecole Royale Polytechnique sur le Calcul Infinitésimal (Paris: Imprimérie Royale, 1823)
    • Paris: Gauthier-Villars
    • Cauchy, A. L. (1823). Résumé des Leçons données à l'Ecole Royale Polytechnique sur le Calcul Infinitésimal (Paris: Imprimérie Royale, 1823). In Oeuvres complètes, Ser. 2, vol. 4, pp. 9-261. Paris: Gauthier-Villars.
    • (1823) Oeuvres complètes, Ser. 2 , vol.4 , pp. 9-261
    • Cauchy, A.L.1
  • 30
    • 84857138442 scopus 로고
    • Leçons sur le calcul différentiel
    • Paris: Gauthier-Villars, 1899
    • Cauchy, A. L. (1829). Leçons sur le calcul différentiel. In Oeuvres complètes, Ser. 2, vol. 4, pp. 263-609. Paris: Gauthier-Villars, 1899.
    • (1829) Oeuvres complètes, Ser. 2 , vol.4 , pp. 263-609
    • Cauchy, A.L.1
  • 31
    • 34547809097 scopus 로고
    • Note sur les séries convergentes dont les divers termes sont des fonctions continues d'une variable réelle ou imaginaire, entre des limites données
    • Paris: Gauthier-Villars, 1900
    • Cauchy, A. L. (1853). Note sur les séries convergentes dont les divers termes sont des fonctions continues d'une variable réelle ou imaginaire, entre des limites données. In Oeuvres complètes, Ser. 1, vol. 12, pp. 30-36. Paris: Gauthier-Villars, 1900.
    • (1853) Oeuvres complètes, Ser. 1 , vol.12 , pp. 30-36
    • Cauchy, A.L.1
  • 32
    • 79961090774 scopus 로고    scopus 로고
    • Axiomatics, empiricism, and Anschauung in Hilbert's conception of geometry: Between arithmetic and general relativity
    • Oxford: Oxford University Press
    • Corry, L. (2006). Axiomatics, empiricism, and Anschauung in Hilbert's conception of geometry: Between arithmetic and general relativity. The architecture of modern mathematics, pp. 133-156. Oxford: Oxford University Press.
    • (2006) The architecture of modern mathematics , pp. 133-156
    • Corry, L.1
  • 36
    • 79956384252 scopus 로고
    • Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge (1984)
    • Oxford Science Publishers. New York: Oxford University Press
    • Dauben, J. (1992). Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge (1984). In Revolutions in mathematics, pp. 49-71, Oxford Science Publishers. New York: Oxford University Press.
    • (1992) Revolutions in mathematics , pp. 49-71
    • Dauben, J.1
  • 38
    • 77953702759 scopus 로고    scopus 로고
    • Arguments, logic and proof: mathematics, logic and the infinite. History of mathematics and education: Ideas and experiences
    • (Essen, 1992), Vandenhoeck & Ruprecht, Göttingen
    • Dauben, J. (1996). Arguments, logic and proof: mathematics, logic and the infinite. History of mathematics and education: Ideas and experiences (Essen, 1992), pp. 113-148, Stud. Wiss. Soz. Bildungsgesch. Math., 11, Vandenhoeck & Ruprecht, Göttingen.
    • (1996) Stud. Wiss. Soz. Bildungsgesch. Math , vol.11 , pp. 113-148
    • Dauben, J.1
  • 39
    • 31444439644 scopus 로고    scopus 로고
    • A defence of mathematical pluralism
    • Davies E. B. (2005) A defence of mathematical pluralism. Philosophy in Mathematics (3) 13(3): 252-276.
    • (2005) Philosophy in Mathematics (3) , vol.13 , Issue.3 , pp. 252-276
    • Davies, E.B.1
  • 40
    • 0004260720 scopus 로고
    • Applied nonstandard analysis
    • New York: Wiley-Interscience. Reprinted: Dover, NY, 2005, see
    • Davis, M. (1977). Applied nonstandard analysis. Pure and Applied Mathematics. New York: Wiley-Interscience. Reprinted: Dover, NY, 2005, see http://store. doverpublications. com/0486442292. html.
    • (1977) Pure and Applied Mathematics
    • Davis, M.1
  • 43
    • 34347369994 scopus 로고    scopus 로고
    • Mathematics through diagrams: Microscopes in non-standard and smooth analysis
    • Dossena R., Magnani L. (2007) Mathematics through diagrams: Microscopes in non-standard and smooth analysis. Studies in Computational Intelligence (SCI) 64: 193-213.
    • (2007) Studies in Computational Intelligence (SCI) , vol.64 , pp. 193-213
    • Dossena, R.1    Magnani, L.2
  • 45
    • 0004282449 scopus 로고    scopus 로고
    • 2nd Edn. Oxford Logic Guides, 39 New York: The Clarendon Press/Oxford University Press
    • Dummett M. (2000) Elements of intuitionism, 2nd edn. Oxford Logic Guides, 39. The Clarendon Press/Oxford University Press, New York.
    • (2000) Elements of Intuitionism
    • Dummett, M.1
  • 46
    • 28244452257 scopus 로고
    • Real numbers, generalizations of the reals, and theories of continua
    • In P. Ehrlich & P. Ehrlich (Eds.), 242 Dordrecht: Kluwer
    • Ehrlich, P. (1994). Real numbers, generalizations of the reals, and theories of continua. In P. Ehrlich & P. Ehrlich (Eds.), Synthese Library, 242 Dordrecht: Kluwer.
    • (1994) Synthese Library
    • Ehrlich, P.1
  • 47
    • 28244451575 scopus 로고    scopus 로고
    • The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes
    • Ehrlich P. (2006) The rise of non-Archimedean mathematics and the roots of a misconception. I. The emergence of non-Archimedean systems of magnitudes. Archive for History of Exact Sciences 60(1): 1-121.
    • (2006) Archive for History of Exact Sciences , vol.60 , Issue.1 , pp. 1-121
    • Ehrlich, P.1
  • 48
    • 77950283093 scopus 로고    scopus 로고
    • Nonstandard student conceptions about infinitesimals
    • Ely R. (2010) Nonstandard student conceptions about infinitesimals. Journal for Research in Mathematics Education 41(2): 117-146.
    • (2010) Journal for Research in Mathematics Education , vol.41 , Issue.2 , pp. 117-146
    • Ely, R.1
  • 50
    • 0002398488 scopus 로고
    • Hermann Grassmann and the creation of linear algebra
    • Fearnley-Sander D. (1979) Hermann Grassmann and the creation of linear algebra. American Mathematics Monthly 86(10): 809-817.
    • (1979) American Mathematics Monthly , vol.86 , Issue.10 , pp. 809-817
    • Fearnley-Sander, D.1
  • 52
    • 84857141521 scopus 로고    scopus 로고
    • Le continu mathématique. Nouvelles conceptions, nouveaux enjeux
    • See also
    • Feferman, S. (2009). Conceptions of the continuum [Le continu mathématique. Nouvelles conceptions, nouveaux enjeux]. Intellectica, 51, 169-189. See also http://math. stanford. edu/~feferman/papers/ConceptContin. pdf.
    • (2009) Intellectica , vol.51 , pp. 169-189
    • Feferman, S.1
  • 53
    • 33748815794 scopus 로고
    • (German) Zweite Auflage. Mit E. Husserls und H. Scholz' Anmerkungen herausgegeben von Ignacio Angelelli Georg Olms Verlagsbuchhandlung, Hildesheim
    • Frege, G. (1964). Begriffsschrift und andere Aufsätze. (German) Zweite Auflage. Mit E. Husserls und H. Scholz' Anmerkungen herausgegeben von Ignacio Angelelli Georg Olms Verlagsbuchhandlung, Hildesheim.
    • (1964) Begriffsschrift und andere Aufsätze
    • Frege, G.1
  • 54
    • 84857141703 scopus 로고
    • Cauchy, Augustin-Louis
    • C. C. Gillispie (Ed.), New York: Charles Scribner's sons
    • Freudenthal H. (1971) Cauchy, Augustin-Louis. In: Gillispie C. C. (Ed.) Dictionary of scientific biography, vol. 3. Charles Scribner's sons, New York, pp 131-148.
    • (1971) Dictionary of Scientific Biography , vol.3 , pp. 131-148
    • Freudenthal, H.1
  • 56
    • 26044473270 scopus 로고
    • Dedekind's theorem:√×√
    • Fowler D. H. (1992) Dedekind's theorem:√×√. American Mathematics Monthly 99(8): 725-733.
    • (1992) AmericanMathematics Monthly , vol.99 , Issue.8 , pp. 725-733
    • Fowler, D.H.1
  • 57
    • 63149180737 scopus 로고
    • The invention of the decimal fractions and the application of the exponential calculus by Immanuel Bonfils of Tarascon (c. 1350)
    • Gandz S. (1936) The invention of the decimal fractions and the application of the exponential calculus by Immanuel Bonfils of Tarascon (c. 1350). Isis 25: 16-45.
    • (1936) Isis , vol.25 , pp. 16-45
    • Gandz, S.1
  • 58
    • 0010913896 scopus 로고
    • The Fregean revolution in logic
    • New York: Oxford Science Publ./Oxford University Press
    • Gillies, D. (1992). The Fregean revolution in logic. In: Revolutions in Mathematics (pp. 265-305). New York: Oxford Science Publ./Oxford University Press.
    • (1992) Revolutions in Mathematics , pp. 265-305
    • Gillies, D.1
  • 60
    • 79959235708 scopus 로고    scopus 로고
    • Les méthodes des maxima et minima de Fermat
    • (2009), Fascicule Special
    • Giusti, E. (2009). Les méthodes des maxima et minima de Fermat. Annals of Faculty in Science and Toulouse Mathematics (6), 18 (2009), Fascicule Special, 59-85.
    • (2009) Annals of Faculty in Science and Toulouse Mathematics , vol.18 , Issue.6 , pp. 59-85
    • Giusti, E.1
  • 63
    • 0002186150 scopus 로고
    • Who gave you the epsilon? Cauchy and the origins of rigorous calculus
    • Grabiner J. (1983) Who gave you the epsilon? Cauchy and the origins of rigorous calculus. American Mathematics Monthly 90(3): 185-194.
    • (1983) American Mathematics Monthly , vol.90 , Issue.3 , pp. 185-194
    • Grabiner, J.1
  • 64
    • 2442703106 scopus 로고    scopus 로고
    • The mathematics of the past: Distinguishing its history from our heritage
    • Grattan-Guinness, I. (2004) The mathematics of the past: Distinguishing its history from our heritage. Historia Mathematica, 163-185.
    • (2004) Historia Mathematica , pp. 163-185
    • Grattan-Guinness, I.1
  • 65
    • 0003766834 scopus 로고    scopus 로고
    • 6th edn. Revised by D. R. Heath-Brown and J. H. Silverman. Oxford University Press, Oxford
    • Hardy, G. H., & Wright, E. M. (2008). An introduction to the theory of numbers, 6th edn. Revised by D. R. Heath-Brown and J. H. Silverman. Oxford University Press, Oxford.
    • (2008) An introduction to the theory of numbers
    • Hardy, G.H.1    Wright, E.M.2
  • 66
    • 0003422445 scopus 로고
    • (J. Macquarrie and E. Robinson, trans.) New York: Harper & Row
    • Heidegger, M. (1962). Being and time. (J. Macquarrie and E. Robinson, trans.) New York: Harper & Row.
    • (1962) Being and time
    • Heidegger, M.1
  • 67
    • 77953701677 scopus 로고
    • Address to Professor A. Robinson. At the occasion of the Brouwer memorial lecture given by Prof. A. Robinson on the 26th April 1973
    • Heijting, A. (1973). Address to Professor A. Robinson. At the occasion of the Brouwer memorial lecture given by Prof. A. Robinson on the 26th April 1973. Nieuw Archievs of Wiskers (3) 21, 134-137.
    • (1973) Nieuw Archievs of Wiskers , vol.21 , Issue.3 , pp. 134-137
    • Heijting, A.1
  • 68
    • 0011636197 scopus 로고
    • Constructive mathematics and quantum mechanics: Unbounded operators and the spectral theorem
    • Hellman G. (1993) Constructive mathematics and quantum mechanics: Unbounded operators and the spectral theorem. Journal of Philosophical Logic 12: 221-248.
    • (1993) Journal of Philosophical Logic , vol.12 , pp. 221-248
    • Hellman, G.1
  • 73
    • 84857138693 scopus 로고
    • On the infinite and the infinitesimal in mathematical analysis
    • (1902), no. 1, (reprinted in Real numbers, generalizations of the reals, and theories of continua, 3-26, Synthese Lib., 242. Dordrecht: Kluwer
    • Hobson, E. W. (1994). On the infinite and the infinitesimal in mathematical analysis. Proceedings London Mathematical Society, vol. s1-35 (1902), no. 1, pp. 117-139 (reprinted in Real numbers, generalizations of the reals, and theories of continua, 3-26, Synthese Lib., 242. Dordrecht: Kluwer.
    • (1994) Proceedings London Mathematical Society , vol.35 s1 , pp. 117-139
    • Hobson, E.W.1
  • 74
    • 84989999651 scopus 로고
    • Pierre Fermat's method of determining tangents of curves and its application to the conchoid and the quadratrix
    • Jensen C. (1969) Pierre Fermat's method of determining tangents of curves and its application to the conchoid and the quadratrix. Centaurus 14: 72-85.
    • (1969) Centaurus , vol.14 , pp. 72-85
    • Jensen, C.1
  • 75
    • 84857139543 scopus 로고
    • The origins of Cauchy's conceptions of a definite integral and of the continuity of a function
    • Jourdain P. E. B. (1913) The origins of Cauchy's conceptions of a definite integral and of the continuity of a function. Isis I: 661-703.
    • (1913) Isis , vol.I , pp. 661-703
    • Jourdain, P.E.B.1
  • 77
    • 77953696483 scopus 로고    scopus 로고
    • Zooming in on infinitesimal 1-.9 in a post-triumvirate era
    • See arXiv: 1003. 1501
    • Katz, K., & Katz, M. (2010). Zooming in on infinitesimal 1-.9.in a post-triumvirate era. Educational Studies in Mathematics, 74(3), 259-273 See arXiv: 1003. 1501.
    • (2010) Educational Studies in Mathematics , vol.74 , Issue.3 , pp. 259-273
    • Katz, K.1    Katz, M.2
  • 80
    • 0004037519 scopus 로고
    • 2nd edn. Prindle, Weber & Schimidt, Boston, '86. Available online at
    • Keisler, H. J. (1986). Elementary calculus: An infinitesimal approach, 2nd edn. Prindle, Weber & Schimidt, Boston, '86. Available online at http://www. math. wisc. edu/~keisler/calc. html.
    • (1986) Elementary calculus: An infinitesimal approach
    • Keisler, H.J.1
  • 82
    • 0003752940 scopus 로고    scopus 로고
    • Elementary mathematics from an advanced standpoint
    • Translation by E. R. Hedrick and C. A. Noble [Macmillan, New York, 1932] from the third German edition [Springer, Berlin, 1924] Originally published as Elementarmathematik vom höheren Standpunkte aus (Leipzig, 1908)
    • Klein, F. Elementary mathematics from an advanced standpoint. vol. I. Arithmetic, Algebra, Analysis. Translation by E. R. Hedrick and C. A. Noble [Macmillan, New York, 1932] from the third German edition [Springer, Berlin, 1924] Originally published as Elementarmathematik vom höheren Standpunkte aus (Leipzig, 1908).
    • Arithmetic, Algebra, Analysis , vol.I
    • Klein, F.1
  • 83
    • 84857140394 scopus 로고
    • Lakatos' philosophy of mathematics. A historical approach
    • 3. Amsterdam: North-Holland
    • Koetsier, T. (1991). Lakatos' philosophy of mathematics. A historical approach. Studies in the History and Philosophy of Mathematics, 3. Amsterdam: North-Holland.
    • (1991) Studies in the History and Philosophy of Mathematics
    • Koetsier, T.1
  • 84
    • 49549137337 scopus 로고
    • Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics (Boston, Mass., 1974)
    • Commentary on E. Bishop's talk (Historia Math. 2 (1975), 507-517)
    • Kopell, N., & Stolzenberg, G. (1975) Commentary on E. Bishop's talk (Historia Math. 2 (1975), 507-517). Proceedings of the American Academy Workshop on the Evolution of Modern Mathematics (Boston, Mass., 1974). Historia Mathematics, 2(4), 519-521.
    • (1975) Historia Mathematics , vol.2 , Issue.4 , pp. 519-521
    • Kopell, N.1    Stolzenberg, G.2
  • 85
    • 0009941139 scopus 로고
    • Review: Wittgenstein's remarks on the foundations of mathematics
    • Kreisel G. (1958) Review: Wittgenstein's remarks on the foundations of mathematics. The British Journal for the Philosophy of Science 9(34): 135-158.
    • (1958) The British Journal for the Philosophy of Science , vol.9 , Issue.34 , pp. 135-158
    • Kreisel, G.1
  • 86
    • 0004005581 scopus 로고
    • Courcier. reissued by Cambridge University Press, 2009
    • Lagrange, J.-L. (1811) Mécanique Analytique. Courcier. reissued by Cambridge University Press, 2009.
    • (1811) Mécanique Analytique
    • Lagrange, J.-L.1
  • 87
    • 52549116101 scopus 로고
    • Cauchy and the continuum: The significance of nonstandard analysis for the history and philosophy of mathematics
    • (originally published in 1966) 1966
    • Lakatos, I. (1966). Cauchy and the continuum: The significance of nonstandard analysis for the history and philosophy of mathematics. Mathematics Intelligencer 1 (1978), no. 3, 151-161 (originally published in 1966).
    • (1978) Mathematics Intelligencer 1 , Issue.3 , pp. 151-161
    • Lakatos, I.1
  • 89
    • 1342321541 scopus 로고
    • Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820
    • Laugwitz D. (1989) Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820. Archive for History of Exact Sciences 39(3): 195-245.
    • (1989) Archive for History of Exact Sciences , vol.39 , Issue.3 , pp. 195-245
    • Laugwitz, D.1
  • 90
    • 84857139779 scopus 로고
    • Early delta functions and the use of infinitesimals in research
    • Laugwitz D. (1992) Early delta functions and the use of infinitesimals in research. Revue d'histoire des Sciences 45(1): 115-128.
    • (1992) Revue D'histoire Des Sciences , vol.45 , Issue.1 , pp. 115-128
    • Laugwitz, D.1
  • 91
    • 22844454016 scopus 로고    scopus 로고
    • Comments on the paper
    • Two letters by N. N. Luzin to M. Ya. Vygodskiǐ
    • Laugwitz D. (2000) Comments on the paper: "Two letters by N. N. Luzin to M. Ya. Vygodskiǐ". American Mathematics Monthly 107(3): 267-276.
    • (2000) American Mathematics Monthly , vol.107 , Issue.3 , pp. 267-276
    • Laugwitz, D.1
  • 93
    • 77956974127 scopus 로고
    • Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres
    • Amsterdam: North-Holland
    • Łoś, J. (1955). Quelques remarques, théorèmes et problèmes sur les classes définissables d'algèbres. In Mathematical interpretation of formal systems, pp. 98-113. Amsterdam: North-Holland.
    • (1955) Mathematical interpretation of formal systems , pp. 98-113
    • Łoś, J.1
  • 94
    • 84883961088 scopus 로고
    • Two letters by N. N. Luzin to M. Ya. Vygodskii. With an introduction by S. S. Demidov. Translated from the 1997 Russian original by A. Shenitzer
    • Luzin, N. N. (1931). Two letters by N. N. Luzin to M. Ya. Vygodskii. With an introduction by S. S. Demidov. Translated from the 1997 Russian original by A. Shenitzer. American Mathematics Monthly 107(1), 64-82 (2000).
    • (1931) American Mathematics Monthly , vol.107 , Issue.1 , pp. 64-82
    • Luzin, N.N.1
  • 95
    • 29544443724 scopus 로고    scopus 로고
    • Perceiving the infinite and the infinitesimal world: Unveiling and optical diagrams in mathematics
    • Magnani L., Dossena R. (2005) Perceiving the infinite and the infinitesimal world: Unveiling and optical diagrams in mathematics. Foundations in Science 10(1): 7-23.
    • (2005) Foundations in Science , vol.10 , Issue.1 , pp. 7-23
    • Magnani, L.1    Dossena, R.2
  • 97
    • 0041007250 scopus 로고
    • 2nd edn. Princeton Paperbacks. Princeton, NJ: Princeton University Press
    • Mahoney, M. (1994). The mathematical career of Pierre de Fermat, 1601-1665, 2nd edn. Princeton Paperbacks. Princeton, NJ: Princeton University Press.
    • (1994) The mathematical career of Pierre de Fermat , pp. 1601-1665
    • Mahoney, M.1
  • 98
    • 0004248158 scopus 로고
    • A course in mathematical logic
    • Translated from the Russian by Neal Koblitz, New York: Springer
    • Manin, Y. (1977). A course in mathematical logic. Translated from the Russian by Neal Koblitz. Graduate Texts in Mathematics, 53. New York: Springer.
    • (1977) Graduate Texts in Mathematics , vol.53
    • Manin, Y.1
  • 100
    • 70749087801 scopus 로고    scopus 로고
    • Archimedean intuitions
    • Moore M. (2002) Archimedean intuitions. Theoria (Stockholm) 68(3): 185-204.
    • (2002) Theoria (Stockholm) , vol.68 , Issue.3 , pp. 185-204
    • Moore, M.1
  • 102
    • 51049095323 scopus 로고    scopus 로고
    • Representational innovation and mathematical ontology. Logic and mathematical reasoning (Mexico City, 1997)
    • Muntersbjorn M. (2003) Representational innovation and mathematical ontology. Logic and mathematical reasoning (Mexico City, 1997). Synthese 134(1-2): 159-180.
    • (2003) Synthese , vol.134 , Issue.1-2 , pp. 159-180
    • Muntersbjorn, M.1
  • 103
    • 84956085576 scopus 로고
    • Internal set theory: A new approach to nonstandard analysis
    • Nelson E. (1977) Internal set theory: A new approach to nonstandard analysis. Bulletin on American Mathematical Society 83(6): 1165-1198.
    • (1977) Bulletin on American Mathematical Society , vol.83 , Issue.6 , pp. 1165-1198
    • Nelson, E.1
  • 109
    • 22844454307 scopus 로고    scopus 로고
    • The education of a pure mathematician
    • Pourciau Bruce (1999) The education of a pure mathematician. American Mathematics Monthly 106(8): 720-732.
    • (1999) American Mathematics Monthly , vol.106 , Issue.8 , pp. 720-732
    • Pourciau, B.1
  • 110
    • 0034195954 scopus 로고    scopus 로고
    • Intuitionism as a (failed) Kuhnian revolution in mathematics
    • Pourciau Bruce (2000) Intuitionism as a (failed) Kuhnian revolution in mathematics. Studies in History and Philosophy and Science 31A(2): 297-329.
    • (2000) Studies in History and Philosophy and Science , vol.31 A , Issue.2 , pp. 297-329
    • Pourciau, B.1
  • 112
    • 33744909051 scopus 로고
    • S. Kovalevsky: A mathematical lesson
    • Rappaport K. (1981) S. Kovalevsky: A mathematical lesson. American Mathematics Monthly 88(8): 564-574.
    • (1981) American Mathematics Monthly , vol.88 , Issue.8 , pp. 564-574
    • Rappaport, K.1
  • 113
    • 3042799706 scopus 로고    scopus 로고
    • The Rhetoric in Mathematics: Newton, Leibniz, the Calculus, and the Rhetorical Force of the Infinitesimal
    • Reyes G. M. (2004) The Rhetoric in Mathematics: Newton, Leibniz, the Calculus, and the Rhetorical Force of the Infinitesimal. Quarterly Journal of Speech 90(2): 159-184.
    • (2004) Quarterly Journal of Speech , vol.90 , Issue.2 , pp. 159-184
    • Reyes, G.M.1
  • 115
    • 0001703834 scopus 로고    scopus 로고
    • Interview with a constructive mathematician
    • Richman F. (1996) Interview with a constructive mathematician. Modern Logic 6(3): 247-271.
    • (1996) Modern Logic , vol.6 , Issue.3 , pp. 247-271
    • Richman, F.1
  • 117
    • 77956972417 scopus 로고
    • The metaphysics of the calculus
    • Amsterdam: North-Holland
    • Robinson, A. (1967). The metaphysics of the calculus. In Problems in the philosophy of mathematics, (pp. 28-46). Amsterdam: North-Holland.
    • (1967) Problems in the philosophy of mathematics , pp. 28-46
    • Robinson, A.1
  • 118
    • 53349141048 scopus 로고
    • Nonstandard analysis and philosophy. Edited and with introductions by W. A. J. Luxemburg and S. Körner. Yale University Press, New Haven, Conn
    • Robinson, A. (1979). Selected papers of Abraham Robinson, vol. II. Nonstandard analysis and philosophy. Edited and with introductions by W. A. J. Luxemburg and S. Körner. Yale University Press, New Haven, Conn.
    • (1979) Selected papers of Abraham Robinson , vol.II
    • Robinson, A.1
  • 119
    • 77958111188 scopus 로고    scopus 로고
    • Numbers and models, standard and nonstandard
    • Roquette P. (2010) Numbers and models, standard and nonstandard. Math Semesterber 57: 185-199.
    • (2010) Math Semesterber , vol.57 , pp. 185-199
    • Roquette, P.1
  • 122
    • 2442579780 scopus 로고
    • D. D., F. R. S. New York, NY: Chelsea Publishing Co
    • Scott, J. (1981). The Mathematical Work of John Wallis, D. D., F. R. S. (1616-1703). New York, NY: Chelsea Publishing Co.
    • (1981) The Mathematical Work of John Wallis, , pp. 1616-1703
    • Scott, J.1
  • 123
    • 14144251334 scopus 로고    scopus 로고
    • Nominalism and constructivism in seventeenth-century mathematical philosophy
    • Sepkoski D. (2005) Nominalism and constructivism in seventeenth-century mathematical philosophy. Historia Mathematica 32(1): 33-59.
    • (2005) Historia Mathematica , vol.32 , Issue.1 , pp. 33-59
    • Sepkoski, D.1
  • 124
    • 0002728845 scopus 로고
    • Reification as the birth of metaphor
    • Sfard A. (1994) Reification as the birth of metaphor. For the Learning of Mathematics 14(1): 44-55.
    • (1994) For the Learning of Mathematics , vol.14 , Issue.1 , pp. 44-55
    • Sfard, A.1
  • 126
    • 34047174312 scopus 로고    scopus 로고
    • Why anti-realists and classical mathematicians cannot get along
    • Shapiro S. (2001) Why anti-realists and classical mathematicians cannot get along. Topoi 20(1): 53-63.
    • (2001) Topoi , vol.20 , Issue.1 , pp. 53-63
    • Shapiro, S.1
  • 127
    • 0010840735 scopus 로고
    • The wake of Berkeley's Analyst: Rigor mathematicae?
    • Sherry D. (1987) The wake of Berkeley's Analyst: Rigor mathematicae?. Studies in Historical Philosophy and Science 18(4): 455-480.
    • (1987) Studies in Historical Philosophy and Science , vol.18 , Issue.4 , pp. 455-480
    • Sherry, D.1
  • 128
    • 60449114152 scopus 로고    scopus 로고
    • The role of diagrams in mathematical arguments
    • Sherry D. (2009) The role of diagrams in mathematical arguments. Foundations of science 14: 59-74.
    • (2009) Foundations of Science , vol.14 , pp. 59-74
    • Sherry, D.1
  • 130
    • 34250127402 scopus 로고
    • Cauchy's conception of rigour in analysis
    • Smithies F. (1986) Cauchy's conception of rigour in analysis. Archieves in Historical Exact Science 36(1): 41-61.
    • (1986) Archieves in Historical Exact Science , vol.36 , Issue.1 , pp. 41-61
    • Smithies, F.1
  • 131
    • 33751413972 scopus 로고
    • In: D. J. Struik, C. V. Swets & Zeitlinger (Eds.), Amsterdam 1958. Vol. IIA: v+pp. 1-455 (1 plate). Vol. IIB: 1958 iv+pp
    • Stevin, S. (1958). The principal works of Simon Stevin. Vols. IIA, IIB: Mathematics. In: D. J. Struik, C. V. Swets & Zeitlinger (Eds.), Amsterdam 1958. Vol. IIA: v+pp. 1-455 (1 plate). Vol. IIB: 1958 iv+pp, pp. 459-976.
    • (1958) The principal works of Simon Stevin. Vols. IIA, IIB: Mathematics , pp. 459-976
    • Stevin, S.1
  • 133
    • 79959239883 scopus 로고
    • Uniform continuity and rates of growth of meromorphic functions. Contributions to non-standard analysis (Sympos., Oberwolfach, 1970)
    • Amsterdam: North-Holland
    • Stroyan, K. (1972). Uniform continuity and rates of growth of meromorphic functions. Contributions to non-standard analysis (Sympos., Oberwolfach, 1970). Studies in Logic and Foundations of Math., 69, 47-64. Amsterdam: North-Holland.
    • (1972) Studies in Logic and Foundations of Math , vol.69 , pp. 47-64
    • Stroyan, K.1
  • 134
    • 0003466283 scopus 로고
    • D. Struik (Ed.), Cambridge, Mass: Harvard University Press
    • Struik, D. (Ed.) (1969) A source book in mathematics, 1200-1800. Harvard University Press, Cambridge, Mass.
    • (1969) A Source Book in Mathematics, 1200-1800
  • 135
    • 33847360474 scopus 로고
    • The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach
    • Sullivan, K. (1976). The Teaching of Elementary Calculus Using the Nonstandard Analysis Approach, American Mathematics Monthly, 83, 370-375. http://www. jstor. org/stable/2318657.
    • (1976) American Mathematics Monthly , vol.83 , pp. 370-375
    • Sullivan, K.1
  • 136
    • 24144432372 scopus 로고
    • Against intuitionism: Constructive mathematics is part of classical mathematics
    • Tait W. (1983) Against intuitionism: Constructive mathematics is part of classical mathematics. Journal of Philosophical Logic 12(2): 173-195.
    • (1983) Journal of Philosophical Logic , vol.12 , Issue.2 , pp. 173-195
    • Tait, W.1
  • 137
    • 60950441010 scopus 로고    scopus 로고
    • Beyond the axioms: The question of objectivity in mathematics. The George Boolos Memorial Symposium, II (Notre Dame, IN, 1998)
    • Tait, W. (2001). Beyond the axioms: The question of objectivity in mathematics. The George Boolos Memorial Symposium, II (Notre Dame, IN, 1998). Philosopical Mathematics (3) 9(1), 21-36.
    • (2001) Philosopical Mathematics (3) , vol.9 , Issue.1 , pp. 21-36
    • Tait, W.1
  • 138
    • 42349105928 scopus 로고
    • Looking at graphs through infinitesimal microscopes, windows and telescopes
    • Tall D. (1980) Looking at graphs through infinitesimal microscopes, windows and telescopes. Mathematics Gazette 64: 22-49.
    • (1980) Mathematics Gazette , vol.64 , pp. 22-49
    • Tall, D.1
  • 139
    • 3543001950 scopus 로고
    • The psychology of advanced mathematical thinking
    • D. O. Tall (Ed.), Dordrecht: Kluwer
    • Tall D. (1991) The psychology of advanced mathematical thinking. In: Tall D. O. (Ed.) Advanced mathematical thinking, Mathematics Education Library, 11. Kluwer, Dordrecht.
    • (1991) Advanced Mathematical Thinking, Mathematics Education Library , vol.11
    • Tall, D.1
  • 141
    • 84857141078 scopus 로고    scopus 로고
    • Review of Real numbers, generalizations of the reals, and theories of continua
    • In P. Ehrlich (Ed.), [see item [45] above]
    • Taylor, R. G. (2000). Review of Real numbers, generalizations of the reals, and theories of continua. In P. Ehrlich (Ed.), [see item [45] above]. Modern Logic, 8(1/2), 195-212.
    • (2000) Modern Logic , vol.8 , Issue.1-2 , pp. 195-212
    • Taylor, R.G.1
  • 144
    • 0042004504 scopus 로고
    • Fondamenti di geometria a più dimensioni e a più specie di unità rettilinee esposti in forma elementare, Lezioni per la Scuola di magistero in Matematica
    • Veronese, G. (1891). Fondamenti di geometria a più dimensioni e a più specie di unità rettilinee esposti in forma elementare, Lezioni per la Scuola di magistero in Matematica. Padova, Tipografia del Seminario.
    • (1891) Padova, Tipografia del Seminario
    • Veronese, G.1
  • 145
    • 0344550491 scopus 로고    scopus 로고
    • Boundaries, contingencies and rigor: Thoughts on mathematics prompted by a case study in transonic aerodynamics
    • Vincenti W., Bloor D. (2003) Boundaries, contingencies and rigor: Thoughts on mathematics prompted by a case study in transonic aerodynamics. Social studies of science 33: 469-507.
    • (2003) Social Studies of Science , vol.33 , pp. 469-507
    • Vincenti, W.1    Bloor, D.2
  • 146
    • 33646272489 scopus 로고    scopus 로고
    • The arithmetic of infinitesimals. Translated from the Latin and with an introduction by Jaequeline A. Stedall
    • New York: Springer
    • Wallis, J. (2004). The arithmetic of infinitesimals. Translated from the Latin and with an introduction by Jaequeline A. Stedall. Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer.
    • (2004) Sources and Studies in the History of Mathematics and Physical Sciences
    • Wallis, J.1
  • 147
    • 79959277676 scopus 로고
    • Book Review: The mathematical career of Pierre de Fermat
    • (review of item [94] above)
    • Weil, A. (1973). Book Review: The mathematical career of Pierre de Fermat. Bulletin in American Mathematical Society, 79(6), 1138-1149 (review of item [94] above).
    • (1973) Bulletin in American Mathematical Society , vol.79 , Issue.6 , pp. 1138-1149
    • Weil, A.1
  • 149
    • 33747654875 scopus 로고
    • Frege: The royal road from geometry
    • [reprinted in Frege's philosophy of mathematics, 108-149, Harvard University Press, Cambridge, MA, 1995]
    • Wilson, M. L. (1992). Frege: The royal road from geometry. Noûs, 26(2), 149-180 [reprinted in Frege's philosophy of mathematics, 108-149, Harvard University Press, Cambridge, MA, 1995].
    • (1992) Noûs , vol.26 , Issue.2 , pp. 149-180
    • Wilson, M.L.1
  • 150
    • 38749113628 scopus 로고    scopus 로고
    • The myth of the seven
    • M. E. Kalderon (Ed.), Oxford: Oxford University Press
    • Yablo S. (2005) The myth of the seven. In: Kalderon M. E. (Ed.) Fictionalism in metaphysics. Oxford University Press, Oxford.
    • (2005) Fictionalism in Metaphysics
    • Yablo, S.1


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