Archive for History of Exact Sciences

, Volume 48, Issue 3–4, pp 201–342 | Cite as

Peano's axioms in their historical context

  • Michael Segre
Article

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Historical Context 
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Selected Bibliography

  1. Abrusci, V. Michele. “Peano e Hilbert: G. Peano nelle prime fasi delle ricerche fondazionali di D. Hilbert.” In Peano e i fondamenti della matematica, 185–195.Google Scholar
  2. Agassi, Joseph. Towards an Historiography of Science. The Hague: Mouton, 1963; Middletown, Conn.: Wesleyan Univ. Press, 1967.Google Scholar
  3. Agassi, Joseph. “Logic and Logic of,” Poznań Studies 4 (1978): 1–11.Google Scholar
  4. Agassi, Joseph. “Presuppositions for Logic.” The Monist 65 (1982): 465–480.Google Scholar
  5. Aimonetto, Italo. “Il concetto di numero naturale in Frege, Dedekind e Peano.” Filosofia (1969) 20: 579–606.Google Scholar
  6. Archimedes. The Method of Archimedes, Recently Discovered by Heiberg: A Supplement to The Works of Archimedes 1897. Thomas L. Heath, ed. Cambridge: At the University Press, 1912.Google Scholar
  7. Ashurst, Gareth F. Founders of Modern Mathematics. London: Frederick Muller, 1982.Google Scholar
  8. Aspray, William, & Kitcher, Philip, eds. History and Philosophy of Modern Mathematics. Minneapolis: University of Minnesota Press, 1988.Google Scholar
  9. Baker, G. P., & Hacker, P. M. S. Frege: Logical Excavations. New York; Oxford: Oxford Univ. Press; Basil Blackwell, 1984.Google Scholar
  10. Becker, Oskar. Grundlagen der Mathematik: in geschichtlicher Entwicklung. 4th ed. Frankfurt a. M.: Suhrkamp, 1990.Google Scholar
  11. Beth Evert W. The Foundations of Mathematics. Amsterdam: North-Holland, 1959.Google Scholar
  12. Berkeley, George. Works. 9 vols. A. A. Luce & T. E. Jessop, eds. London: Nelson, 1948–1957.Google Scholar
  13. Black, Max. The Nature of Mathematics: A Critical Survey. London: Kegan Paul, Trench, Trubner & Co., 1933.Google Scholar
  14. Bolzano, Bernard. Schriften. Vol 1: Functionenlehre, Karel Rychlík, ed. Prague: Königliche Böhmische Gesellschaft der Wissenschaften, 1930.Google Scholar
  15. Bolzano, Bernard. Rein analytischer Beweis des Lehrsatzes..., Prague, 1814–17. Ostwald's Klassiker no. 153. Leipzig: Engelmann, 1905.Google Scholar
  16. Bolzano, Bernard. Paradoxien des Unendlichen. F. Přihonsky, ed. Berlin, 1889.Google Scholar
  17. Boole, George. The Mathematical Analysis of Logic. Cambridge, 1847. Reprint. Oxford: Blackwell, 1965.Google Scholar
  18. Boole, George. An Investigation of the Laws of Thought. Reprint. New York: Dover, 1958.Google Scholar
  19. Borga, Marco. “La logica, il metodo assiomatico e la problematica metateorica”, in Borga, Freguglia & Palladino, I contributi fondazionali della scuola di Peano, pp. 11–75, 1985.Google Scholar
  20. Borga, M., Freguglia, P., & Palladino, D. I contributi fondazionali della scuola di Peano. Milan: Franco Angeli, 1985.Google Scholar
  21. Bottazzini, Umberto. Il calcolo sublime: storia dell'analisi matematica da Euler a Weierstrass. Turin: Boringhieri, 1981.Google Scholar
  22. Bottazzini, Umberto. The Higher Calculus: A History of Real and Complex Analysis from Euler to Weierstrass. Warren Van Egmond, trans. New York: Springer, 1986.Google Scholar
  23. Bottazzini, Umberto. “Peano e la logica dei controesempi.” In Peano e i fondamenti della matematica, 237–253.Google Scholar
  24. Boyer, Carl B. The History of the Calculus and its Conceptual Development (The Concepts of the Calculus). New York: Dover, 1959.Google Scholar
  25. Breidert, Wolfgang. George Berkeley. Basel: Birkhäuser, 1989.Google Scholar
  26. Brouwer, Luitzen Egbertus Jan. “Intuitionism and Formalism”. Bulletin of the American Mathematical Society 20 (October 1913–July 1914): 81–96.Google Scholar
  27. Brouwer, Luitzen Egbertus Jan. Collected Works. 2 vols. Vol 1: A. Heyting, ed. Vol. 2: Hans Freudenthal, ed. Amsterdam: North-Holland, 1975, 1976.Google Scholar
  28. Cajori, Florian. A History of the Conceptions of Limits and Fluxions in Great Britain. Chicago: The Open Court, 1919.Google Scholar
  29. Cajori, Florian. A History of Mathematical Notations. 2 vols. Chicago: The Open Court, 1928–1929.Google Scholar
  30. Cassina, Ugo. “L'Opera scientifica di Giuseppe Peano.” Rendiconti del Seminario Matematico e Fisico di Milano 7 (1933): 323–389.Google Scholar
  31. Cassina, Ugo. “L'Oeuvre philosophique de G. Peano.” Revue de Métaphysique et de Morale 40 (1933): 481–491.Google Scholar
  32. Cassina, Ugo. “Storia ed analisi del ‘Formulario completo’ di Peano.” Bollettino della Unione Matematica Italiana 10 (1955): 244–265, 544–574.Google Scholar
  33. Cassina, Ugo. “Sul ‘Formulario Matematico’ di Peano,” in Terracini (ed.), In memoria di Giuseppe Peano, pp. 71–102, 1955.Google Scholar
  34. Cauchy, Augustin. Oeuvres complètes d'Augustin Cauchy. Series 1, 12 vols., series 2, 15 vols. Paris: Gauthier-Villars, 1882-.Google Scholar
  35. Celebrazioni in memoria di Giuseppe Peano nel cinquantenario della morte. Atti del Convegno organizzato dal Dipartimento di Matematica dell'Università di Torino, 27–28 ottobre 1982. Turin, 1982.Google Scholar
  36. Cellucci, Carlo, “Gli scopi della logica matematica.” in Peano e i Fondamenti della Matematica: 73–138.Google Scholar
  37. Cohen, I. Bernard. Introduction to Newton's ‘Principia’. Cambridge (Mass.): Harvard University Press, 1971.Google Scholar
  38. Couturat, Louis. “La logique mathématique de M. Peano.” Revue de Métaphysique et de Morale 7 (1899): 616–646.Google Scholar
  39. Couturat, Louis. La logique de Leibniz. Paris, 1901. Reprint. Hildesheim: Olms, 1969.Google Scholar
  40. Crowe, Michael J. A History of Vector Analysis. Notre Dame: University of Notre Dame Press, 1967.Google Scholar
  41. Davis, Philip, J., & Hersh, Reuben. The Mathematical Experience. Penguin Books 1990.Google Scholar
  42. Dedekind, Richard. Gesammelte mathematische Werke. 3 vols. Robert Fricke, Emmy Noether & Öystein Ore, eds. Braunschweig: Friedr. Vieweg & Sohn, 1930–1932.Google Scholar
  43. Dedekind, Richard. Essays on the Theory of Numbers. Wooster Woodruff Beman, trans. New York: Dover Publications, 1963.Google Scholar
  44. Dictionary of Scientific Biography. Charles Coulston Gillispie, ed. 18 vols. New York: Charles Scribner's Sons, 1970–1990.Google Scholar
  45. Dieudonné, Jean A. “The Work of Nicholas Bourbaki.” The American Mathematical Monthly 77 (1970): 134–145.Google Scholar
  46. Dugac, Pierre, “Eléments d'analyse de Karl Weierstrass.” Archive for History of Exact Sciences 10 (1973): 41–176.Google Scholar
  47. Dummett, Michael. The Interpretation of Frege's Philosophy. Cambridge, Mass.: Harvard Univ. Press, 1981.Google Scholar
  48. Edwards, Charles Henry. The Historical Development of the Calculus. New York: Springer, 1979.Google Scholar
  49. Euler, Leonhard. Opera omnia, 3 series. Leipzig, Berlin, Zurich, etc.: Teubner, 1911.Google Scholar
  50. Fauvel, John, & Gray, Jeremy, eds. The History of Mathematics: A Reader. London: MacMillan, Milton Keynes: The Open University 1987.Google Scholar
  51. Fourier, Joseph. Oeuvres de Fourier. 2 vols. Gaston Darboux, ed. Paris, 1888–1890.Google Scholar
  52. Fourier, Joseph. The Analytical Theory of Heat. Alexandre Freeman, trans. New York: Dover, 1955.Google Scholar
  53. Fraenkel, Abraham A., Bar-Hillel, Yehoshua, & Levy, Azriel. Foundations of Set Theory. 2nd ed. Amsterdam: North-Holland, 1984.Google Scholar
  54. Frege, Gottlob. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle, 1879. Reprint. Hildesheim: Olms, 1964.Google Scholar
  55. Frege, Gottlob. Grundgesetze der Arithmetik. Jena, 1893. Reprint. Hildesheim: Olms, 1962.Google Scholar
  56. Frege, Gottlob. Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl. Breslau, 1884.Google Scholar
  57. Frege, Gottlob. The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number. J. L. Austin, trans. Oxford: Blackwell, 1950.Google Scholar
  58. Freguglia, Paolo, “La logica matematica di Peano: un'analisi,” Physis, 23 (1981): 325–336.Google Scholar
  59. Freudenthal, Hans. “Die Grundlagen der Geometrie um die Wende des 19. Jahrhunderts.” Mathematisch-Physikalische Semester berichte 7 (1960): 2–25.Google Scholar
  60. Freudenthal, Hans. “The Main Trends in the Foundations of Geometry in the 19th Century.” In Logic, Methodology and Philosophy of Science, edited by E. Nagel, P. Suppes & A. Tarski, 613–621. Stanford: Stanford Univ. Press, 1962.Google Scholar
  61. Galuzzi, Massimo. “Geometria algebrica e logica tra Otto e Novecento.” In Gianni Micheli (ed.) Storia d'Italia. Annali 3. Storia e tecnica nella cultura e nella società dal Rinascimento a oggi. Turin: Einaudi, 1980, pp. 1004–1105.Google Scholar
  62. Gericke, Helmuth. Geschichte des Zahlbegriffs. Mannheim: Bibliographisches Institut, 1970.Google Scholar
  63. Gillies, Donald A. Frege, Dedekind, and Peano on the Foundations of Arithmetic. Assen: Van Gorcum, 1982.Google Scholar
  64. Gillies, Donald A, ed. Revolutions in Mathematics. Oxford: Clarendon Press, 1992.Google Scholar
  65. Giusti, Enrico. “Gli “errori” di Cauchy e i fondamenti dell'analisi.” Bollettino di Storia delle Scienze Matematiche 4, fasc. 2 (1984): 24–54.Google Scholar
  66. Grabiner, Judith V. “Is Mathematical Truth Time-Dependent?” The American Mathematical Monthly 81 (1974): 354–365.Google Scholar
  67. Grabiner, Judith V. The Origins of Cauchy's Rigorous Calculus. Cambridge, Mass: MIT Press, 1981.Google Scholar
  68. Grabiner, Judith V. “Changing Attitudes toward Mathematical Rigor: Lagrange and Analysis in the Eighteenth and Nineteenth Centuries.” In H. N. Jahnke & M. Otte, eds. Epistemological and Social Problems of the Sciences in the Early Nineteenth Century (Dordrecht: Reidel, 1981), pp. 311–330.Google Scholar
  69. Grassmann, Hermann. Gesammelte mathematische und physikalische Werke. 3 vols. S. Study, G. Scheffers & F. Engel, eds. Leipzig: Teubner, 1894–1911. Reprint. New York: Johnson Reprint, 1972.Google Scholar
  70. Grassmann, Robert. Die Formenlehre oder Mathematik. Stettin, 1872. Reprint. Hildesheim: Olms, 1966.Google Scholar
  71. Grattan-Guinness, Ivor. The Development of the Foundations of Mathematical Analysis from Euler to Riemann. Cambridge, Mass: MIT Press, 1970.Google Scholar
  72. Grattan-Guinness, Ivor. “From Weierstrass to Russell: A Peano Medley.” Rivista di storia della scienza, 2 (1) (1985): 1–16.Google Scholar
  73. Grattan-Guinness, Ivor. “Living Together and Living Apart. On the Interactions between Mathematics and Logics from the French Revolution to the First World War.” S. Afr. J. Philos. 7 (2), (1988): 73–82.Google Scholar
  74. Grattan-Guinness, Ivor. “Bertrand Russell (1872–1970) After Twenty Years.” Notes Rec. R. Soc. Lond. (1990) 44: 280–306.Google Scholar
  75. Grattan-Guinness, Ivor. ed. Joseph Fourier: 1768–1830. Cambridge, Mass.: MIT Press, 1972.Google Scholar
  76. Grattan-Guinness, Ivor. ed. From the Calculus to Set Theory: 1630–1919. London: Duckworth, 1980.Google Scholar
  77. Guicciardini, Niccolò. The Development of Newtonian Calculus in Britain, 1700–1800. Cambridge: Cambridge Univ. Press, 1987.Google Scholar
  78. Heijenoort, Jean Van, ed. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Cambridge, Mass: Harvard University Press, 1971.Google Scholar
  79. Hilbert, David. Grundlagen der Geometrie. Leipzig, 1899.Google Scholar
  80. Hilbert, David. The Foundations of Geometry. E. J. Townsend, trans. La Salle: The Open Court, 1947.Google Scholar
  81. Hilbert, David. Gesammelte Abhandlungen. 3 vols. Berlin, 1932–1935. Reprint. New York: Chelsea, 1965.Google Scholar
  82. Hilbert, David. “Über den Zahlbegriff.” Jahresbericht der Deutschen Mathematiker-Vereinigung (1900) 8: 180–184.Google Scholar
  83. Hilbert, David. “Mathematical Problems”. Bulletin of the American Mathematical Society 8 (October 1901–July 1902): 437–479.Google Scholar
  84. Hilbert, David. “Probleme der Grundlegung der Mathematik”. Atti del Congresso Internazionale dei Matematici, Bologna 3–10 Settembre 1928, Vol. 1. Bologna: Zanichelli, 1929. Pp. 135–141.Google Scholar
  85. Hilbert, David. Ricerche sui fondamenti della matematica. V. Michele Abrusci, ed. Naples: Bibliopolis, 1978.Google Scholar
  86. Israel, Giorgio. “‘Rigore’ ed ‘assiomatica’ nella matematica moderna.” Scienza e storia: analisi critica e problemi attuali. Rome: Editori Riuniti, 1980. Pp. 427–450.Google Scholar
  87. Israel, Giorgio. “‘Rigor’ and ‘Axiomatica’ in Modern Mathematics.” Fundamenta Scientiae 2 (1981): 205–219.Google Scholar
  88. Jevons, Stanley W. The Principles of Science: a Treatise on Logic and Scientific Method. London, 1874, 1877, 1879. Reprint. New York: Dover, 1958.Google Scholar
  89. Jevons, Stanley W. Pure Logic and Other Minor Works. London, 1980. Robert Adamson, ed. New York: Franklin, 1971.Google Scholar
  90. Jourdain, Philip E. B. “The Development of the Theories of Mathematical Logic and the Principles of Mathematics.” The Quarterly Journal of Pure and Applied Mathematics 41 (1910): 324–352; 43 (1912): 219–314; 44 (1913): 113–128.Google Scholar
  91. Kennedy, Hubert C. “The Mathematical Philosophy of Giuseppe Peano.” Philosophy of Science 30 (1963): 262–266.Google Scholar
  92. Kennedy, Hubert C. “Giuseppe Peano at the University of Turin.” The Mathematics Teacher 61 (November 1968): 703–706.Google Scholar
  93. Kennedy, Hubert C. “The Origins of Modern Axiomatics: Pasch to Peano.” The American Mathematical Monthly 79 (1972): 133–136.Google Scholar
  94. Kennedy, Hubert C. “Peano's Concept of Number.” Historia Mathematica 1 (1974): 387–408.Google Scholar
  95. Kennedy, Hubert C. “Nine Letters from Giuseppe Peano to Bertrand Russell.” Journal of the History of Philosophy 13 (1975): 205–220, p. 207.Google Scholar
  96. Kennedy, Hubert C. Peano: Life and Works of Giuseppe Peano. Dordrecht: Reidel, 1980.Google Scholar
  97. Kennedy, Hubert C. Peano: Storia di un matematico. Paolo Pagli, trans. Turin: Boringhieri, 1983.Google Scholar
  98. Kitcher, Philip. “Mathematical Rigor — Who Needs It?” Noûs 15 (March 1981): 469–493.Google Scholar
  99. Kitcher, Philip. “The Foundations of Mathematics.” In Companion to the History of Modern Science, edited by R. C. Olby, G. N. Cantor, J. R. R. Christie & M. J. S. Hodge, 677–689. London: Routledge, 1990.Google Scholar
  100. Kleene, Stephen Cole. Introduction to Metamathematics. New York / Amsterdam / Groningen: Van Nostrand / North-Holland / P. Noordhoff, 1952.Google Scholar
  101. Kline, Morris. Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press, 1972.Google Scholar
  102. Kline, Morris. Mathematics: The Loss of Certainty. Oxford: Oxford University Press, 1982.Google Scholar
  103. Knobloch, Eberhard. “Einfluß der Symbolik und des Formalismus auf die Entwicklung des mathematischen Denkens.” Berichte zur Wissenschaftsgeschichte 3 (1980): 77–94.Google Scholar
  104. Kronecker, Leopold. Werke. 5 vols. Kurt Hensel, ed. Reprint. New York: Chelsea, 1968.Google Scholar
  105. Lagrange, Joseph Louis. Oeuvres. 14 vols. J.-A. Serret & G. Darboux, eds. Paris: Gauthier-Villars, 1867–1892.Google Scholar
  106. Lakatos, Imre. Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press, 1976.Google Scholar
  107. Lakatos, Imre. “Cauchy and the Continuum: the Significance of Non-Standard Analysis for the History and Philosophy of Mathematics”. in John Worrall & Gregory Currie, eds., Mathematics, Science and Epistemology, Vol. 2. Cambridge: Cambridge University Press, 1978. Pp. 43–60.Google Scholar
  108. Leibniz, Gottfried Wilhelm. Mathematische Schriften. 7 vols. C. I. Gerhardt, ed. Berlin 1849–1864. Reprint. Hildesheim: Olms, 1961–1962.Google Scholar
  109. Leibniz, Gottfried Wilhelm. Opuscules et fragments inédits. Louis Couturat, ed. Paris, 1903. Reprint. Hildesheim: Olms, 1961.Google Scholar
  110. Levi, Beppo. “L'opera matematica di Giuseppe Peano.” Bollettino della Unione Matematica Italiana, 11 (1932): 253–262.Google Scholar
  111. Levi, Beppo. “Intorno alle vedute di G. Peano circa la logica matematica.” Bollettino della Unione Matematica Italiana 12 (1933): 65–68.Google Scholar
  112. Maclaurin, Colin. A Treatise of Fluxions. Edinburgh, 1742.Google Scholar
  113. Mehrtens, Herbert. “Anschauungswelt versus Papierwelt — Zur historischen Interpretation der Grundlagenkrise der Mathematik.” In H. Poser & H.-W. Schütt (eds.) Ontologie und Wissenschaft. Berlin: TU-Berlin, 1984, pp. 231–276.Google Scholar
  114. Mehrtens, Herbert. Moderne Sprache Mathematik. Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme. Frankfurt: Suhrkamp, 1990.Google Scholar
  115. Mehrtens, H., Bos, H., & Schneider, I. Social History of Nineteenth Century Mathematics. Boston: Birkhäuser, 1981.Google Scholar
  116. Nagel, Ernst, & Newman, James R. Gödel's Proof. New York: University Press, 1958.Google Scholar
  117. Newton, Isaac. Philosophiae naturalis principia mathematica. London, 1687.Google Scholar
  118. Newton, Isaac. Mathematical Principles. 2 vols. Motte's translation revised by Florian Cajori. Berkeley: University of California Press, 1962.Google Scholar
  119. Padoa, Alessandro. “Il contributo di G. Peano all'ideografia logica.” Periodico di Matematiche 13 (January 1933): 15–22.Google Scholar
  120. Padoa, Alessandro. “Ce que la logique doit à Peano.” Actualités scientifiques et industrielles (1936): 31–37.Google Scholar
  121. Palladino, Franco. “Le lettere di Giuseppe Peano nella corrispondenza di Ernesto Cesàro.” Nuncius, Anno 8 (1993), fasc. 1, pp. 249–273.Google Scholar
  122. Peano e i Fondamenti della Matematica. Modena: Mucchi, 1992.Google Scholar
  123. Peano, Giuseppe. Opere scelte. 3 vols. Rome: Cremonese, 1957–1959.Google Scholar
  124. Peano, Giuseppe. Selected Works. Hubert C. Kennedy, trans. and ed. Toronto: University of Toronto Press, 1973.Google Scholar
  125. Peano, Giuseppe. Arbeiten zur Analysis und zur mathematischen Logik. Edited by G. Asser. Leipzig: Teubner, 1990.Google Scholar
  126. Peckhaus, Volker. Hilbertprogramm und Kritische Philosophie. Göttingen: Vandenhoek & Ruprecht, 1990.Google Scholar
  127. Peirce, Charles S. Collected Papers. Charles Hartshorne & Paul Weiss, eds. Cambridge, Mass.: Harvard University Press, 1931–1938.Google Scholar
  128. Pincherle, Salvatore. “Saggio di una introduzione alla teoria delle funzioni analitiche secondo i principii del prof. C. Weierstrass.” Giornale di Matematiche 18 (1880): 178–254, 317–357.Google Scholar
  129. Poincaré, Henri. “L'Oeuvre mathématique de Weierstrass.” Acta Mathematica 22 (1899): 1–18.Google Scholar
  130. Poincaré, Henri. “Du role de l'intuition et de la logique en mathématiques”. Compte rendu du Deuxième Congrès International des Mathématiciens, edited by E. Duporcq, 115–130. Paris: Gauthier-Villars, 1902. Reprint. Nendeln/Liechtenstein: Kraus, 1967.Google Scholar
  131. Poincaré, Henri. Oeuvres. 11 vols. Paris: Gauthier-Villars, 1950–1956.Google Scholar
  132. Pringsheim, Alfred. “Grundlagen der Allgemeinen Funktionenlehre”. Enzyklopädie der mathematischen Wissenschaften, Vol. 2, Part 1, First half: Analysis (Leipzig: Teubner, 1899–1916): 1–53.Google Scholar
  133. Quine, Willard van Orman. “Peano as a Logician.” History and Philosophy of Logic 8 (1987): 15–24.Google Scholar
  134. Reid, Constance. Hilbert. Berlin: Springer, 1970.Google Scholar
  135. Robinson, Abraham. Non-Standard Analysis. Revised edition. Amsterdam: North-Holland; New York: American Elsevier, 1974.Google Scholar
  136. Rodríguez-Consuegra, Francisco. “Elementos logicistas en la obra de Peano y su escuela.” Mathesis 4 (1988): 221–299.Google Scholar
  137. Rodríguez-Consuegra, Francisco. The Mathematical Philosophy of Bertrand Russell: Origins and Development. Basel: Birkhäuser, 1991.Google Scholar
  138. Romano, Lalla. “Lo spirito creativo è leggero.” Spirali, Anno. 3 (June 1980), n. 6, pp. 5–6.Google Scholar
  139. Russell, Bertrand. “Sur la logique des relations, avec des applications à la théorie de séries.” Revue de Mathématiques (Rivista di Matematica) 7 (1900–1901): 115–148.Google Scholar
  140. Russell, Bertrand. The Principles of Mathematics. Cambridge: At the University Press, 1903. 2nd ed. London: Allen & Unwin, 1937.Google Scholar
  141. Russell, Bertrand. Introduction to Mathematical Philosophy London: George Allen & Unwin, New York: Macmillan, 1919.Google Scholar
  142. Russell, Bertrand. The Autobiography of Bertrand Russell. 2 vols. London: George Allen and Unwin, 1967–1968.Google Scholar
  143. Russell, Bertrand, & Whitehead, Alfred N. Principia Mathematica. 3 vols. Cambridge: At the University Press, 1910–1913.Google Scholar
  144. Sageng, Erik L. Colin MacLaurin and the Foundations of the Method of Fluxions. Ph.D. dissertation. Princeton University, 1989.Google Scholar
  145. Schneider, Ivo. Archimedes: Ingenieur, Naturwissenschaftler und Mathematiker. Darmstadt: Wissenschaftliche Buchgesellschaft, 1979.Google Scholar
  146. Schneider, Ivo. Isaac Newton. Munich: Beck, 1988.Google Scholar
  147. Segre, Michael. In the Wake of Galileo. New Brunswick: Rutgers University Press, 1991.Google Scholar
  148. Segre, Michael. “Peano, Logicism and Formalism.” In I. C. Jarvie & N. Laor, (eds.) The Enterprise of Critical Rationalism. Festschrift Agassi. Vol. I: Critical Rationalism, Metaphysics and Science. Dordrecht: Kluwer, forthcoming.Google Scholar
  149. Spalt, Detlef D. Vom Mythos der Mathematischen Vernunft. Darmstadt: Wissenschaftliche Buchgesellschaft, 1987.Google Scholar
  150. Stigt, Walter P. van. Brouwer's Intuitionism. Amsterdam: North-Holland, 1990.Google Scholar
  151. Struik, Dirk J. A Concise History of Mathematics. 2 vols. New York: Dover, 1948, 1967.Google Scholar
  152. Styazhkin, N. I. History of Mathematical Logic from Leibniz to Peano. Cambridge; Mass: MIT Press, 1969.Google Scholar
  153. Terracini, Alessandro, ed. In memoria di Giuseppe Peano. Cuneo: Liceo Scientifico Statale, 1955.Google Scholar
  154. Toepell, Michael-Markus. Über die Entstehung von David Hilberts “Grundlagen der Geometrie”. Göttingen: Vandenhoeck & Ruprecht, 1986.Google Scholar
  155. Toepell, Michael-Markus. “On the Origins of Hilbert's ‘Grundlagen der Geometrie’.” Archive for History of Exact Sciences, 35 (1986): 329–344.Google Scholar
  156. Torretti, Robert. Philosophy of Geometry from Riemann to Poincaré. Dordrecht: Reidel, 1978.Google Scholar
  157. Tropfke, Johannes. Geschichte der Elementarmathematik. 4th edition, Vol. 1: Arithmetik und Algebra. Revised by Kurt Vogel, Karin Reich, & Helmuth Gericke. Berlin: Walter de Gruyter, 1980.Google Scholar
  158. Vailati, Giovanni, “La logique mathématique et sa nouvelle phase de développement dans les écrits de M. J. Peano.” Revue de Métaphysique et de Morale 7 (1899): 86–102.Google Scholar
  159. Volkert, Klaus T. Die Krise der Anschauung. Göttingen: Vandenhoeck & Ruprecht, 1986.Google Scholar
  160. Wang, Hao. “The Axiomatization of Arithmetic”. The Journal of Symbolic Logic, 22 (June 1957): 145–158.Google Scholar
  161. Weierstrass, Karl. Mathematische Werke. 7 vols. Reprint. Hildesheim: Olms, New York: Johnson, 1967.Google Scholar
  162. Weyl, Hermann. Gesammelte Abhandlungen. 4 vols. Berlin: Springer, 1968.Google Scholar
  163. Wisdom, J. O. “The Analyst Controversy: Berkeley's Influence on the Development of Mathematics.” Hermathena, 54 (1939): 3–29.Google Scholar
  164. Wisdom, J. O. “The Analyst Controversy: Berkeley as a Mathematician.” Hermathena, 59 (1942): 111–128.Google Scholar
  165. Wisdom, J. O. “Berkeley's Criticism of the Infinitesimal.” The British Journal for the Philosophy of Science, 4 (May 1953–February 1954): 22–25.Google Scholar
  166. Youschkevitch, A. P. “Lazare Carnot and the Competition of the Berlin Academy in 1786 on the Mathematical Theory of the Infinite.” In C. C. Gillispie, Lazare Carnot Savant, 147–168. Princeton: Princeton University Press, 1971.Google Scholar

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© Springer-Verlag 1994

Authors and Affiliations

  • Michael Segre
    • 1
  1. 1.Institut für Geschichte der Naturwissenschaften der Universität MünchenMünchen

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