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Hilbert and Logic

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Québec Studies in the Philosophy of Science

Part of the book series: Boston Studies in the Philosophy of Science ((BSPS,volume 177))

Abstract

The logical systems presented in the books by Hilbert and Ackermann (1928, 1938) and in Hilbert and Bernays (1934/39) are not too far removed from modern, axiomatic systems, those, for instance, to be found in Kleene 1952, Church 1956, or Mendelson 1964. What Hilbert et al. give is, at root, a system of (many-sorted) first-order logic, suited for the deductive purposes of all mathematical theories, and therefore (of necessity) adding no genuine content to any theory. What we have, in fact, is systems which are minimal when compared to those of Whitehead and Russell or Frege, a logica uteris as opposed to a logica magna, to echo van Heijenoort’s distinction.1 Moreover, Hilbert and Ackermann (and then Hilbert and Bernays) state clearly what are now regarded as basic questions concerning consistency, completeness and decidability. Thus, in short, whatever the similarities with systems earlier than those of Hilbert, what we see in many respects is the first modern presentation of logic.

An early version of this paper was read at a session of the Boston Colloquium for the Philosophy of Science in November 1993. I wish to thank the organisers of the Colloquium, particularly Jaakko Hintikka and Fred Tauber, for their invitation. I also wish to thank George Boolos, Emily Carson, William Demopoulos, William Ewald, Richard Heck, Moshé Machover, Mihaly Makkai, Ulrich Majer, John Mayberry, Stephen Menn and Wilfried Sieg for useful discussions on this and related work, and Mathieu Marion and Robert Cohen for their patience. The Niedersächsische Staats- und Universitätsbibliothek and the Mathematisches Institut of the Georg-August Universität, Gōttingen kindly granted permission to quote from various unpublished lecture notes and manuscripts of Hilbert. The support of the Alexander von Humboldt Stiftung, the Deutsche Forschungsgemeinschaft, the Social Sciences and Humanities Research Canada of Canada and the FCAR of Québec is gratefully acknowledged.

Unless otherwise stated, the translations below are my own, although I have tried to give additional references to published translations wherever possible.

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References

  • Benacerraf, Paul and Putnam, Hilary (eds.) 1964: Philosophy of mathematics: selected readings. First edition. Oxford: Basil Blackwell.

    Google Scholar 

  • Benacerraf, Paul and Putnam, Hilary (eds.) 1983: Philosophy of mathematics: selected readings. Second edition. Cambridge: Cambridge University Press.

    Google Scholar 

  • Bernays, Paul 1922a: ‘Über Hilberts Gedanken zur Grundlegung der Arithmetik’, Jahresbericht der deutschen Mathematiker-Vereinigung, 31, 10–19.

    Google Scholar 

  • Bernays, Paul 1922b: ‘Die Bedeutung Hilberts für die Philosophie der Mathematik’, Die Naturwissenschaften, 10, 93–9.

    Google Scholar 

  • Bernays, Paul 1935: ‘Sur le platonisme dans les mathématiques’, L’enseignement mathématique, 34, 52–69. English translation by Charles Parsons in Benacerraf and Putnam (eds.) 1964, 274–86, and 1983, 258–71. German translation by Peter Bernath in Bernays 1976, 62–78.

    Google Scholar 

  • Bernays, Paul 1950: ‘Mathematische Existenz und Widerspruchsfreiheit’ in Études de Philosophie des Sciences, Neuchâtel: Éditions de Griffon, 1950, 11–25. Republished in Bernays 1976, 92–106.

    Google Scholar 

  • Bernays, Paul *1956: ‘Are pure mathematics between logic and geometry?’, lecture delivered at Columbia on May 10th, 1956, unpublished, Bernays Nachlass (Hs 973: 18), Wissenschaftshistorische Sammlung, ETH-Bibliothek, Zürich.

    Google Scholar 

  • Bernays, Paul 1976: Abhandlungen zur Philosophie der Mathematik. Darmstadt: Wissenschaftliche Buchgesellschaft.

    Google Scholar 

  • Blumenthal, Otto 1935: ‘Leidensgeschichte’, in Hilbert 1935, 388–429.

    Google Scholar 

  • Browder, Felix (ed.) 1976: Mathematical developments arising from Hilbert problems. Proceedings of symposia in pure mathematics, volume 28, parts 1 and 2. Providence, Rhode Island: American Mathematical Society.

    Google Scholar 

  • Cantor, Georg 1872: ‘Über die Ausdehnung eines Satzes aus der Theorie der trigonometrischen Reihen’, Mathematische Annalen, 5, 123–32. Reprinted in Cantor 1932, 92–102.

    Google Scholar 

  • Cantor, Georg 1883: ‘Über unendliche lineare Punctmannigfaltigkeiten, 5’, Mathematische Annalen, 21, 545–91. Reprinted in Cantor 1932, 165–209; English translation in Ewald (ed.) 1996.

    Google Scholar 

  • Cantor, Georg 1895: ‘Beiträge zur Begründung der transfiniten Mengenlehre, I’, Mathematische Annalen, 46, 481–512. Reprinted in Cantor 1932, 282–311. English translation in Georg Cantor: Contributions to the founding of the theory of transflnite numbers, with an historical introduction and notes by P. E. B. Jourdain, La Salle, Illinois: Open Court Publishing Company, 1915, republished by Dover Publications, New York, 1955.

    Google Scholar 

  • Cantor, Georg 1897: ‘Beiträge zur Begründung der transfiniten Mengenlehre, II’, Mathematische Annalen, 49, 207–246. Reprinted in Cantor 1932, 312–56. English translation in Georg Cantor: Contributions to the founding of the theory of transflnite numbers, with an historical introduction and notes by P. E. B. Jourdain, La Salle, Illinois: Open Court Publishing Company, 1915, republished by Dover Publications, New York, 1955.

    Google Scholar 

  • Cantor, Georg 1932: Gesammelte Abhandlungen mathematischen und philosophischen Inhalts. Edited by Ernst Zermelo. Berlin: Julius Springer Verlag.

    Google Scholar 

  • Church, Alonzo 1956: Introduction to mathematical logic. Volume 1. Princeton: Princeton University Press.

    Google Scholar 

  • Cohen, Robert and Elkana, Yehuda (eds.) 1977: Hermann von Helmholtz: Epistemological Writings. Dordrecht, Holland: D. Reidel Publishing Co. [Boston Studies in the Philosophy of Science, vol. 37] Translation of Helmholtz 1921.

    Google Scholar 

  • Dedekind, Richard 1854: ‘Ūber die Einführung neuer Funktionen in der Mathematik: Habilitationsvortrag, gehalten im Hause des Prof. Hoeck, in Gegenwart von Hoeck, Gauss, Weber, Waitz, 30 Juni 1854’ in Dedekind 1932, item LX, 428–38. English translation in Ewald (ed.) 1996.

    Google Scholar 

  • Dedekind, Richard 1872: Stetigkeit und irrationale Zahlen. Braunschweig: Vieweg und Sohn. Latest reprint, 1965. Also reprinted in Dedekind 1932, 315–332. English translation in Dedekind 1901, with a revision of this translation in Ewald (ed.) 1996.

    Google Scholar 

  • Dedekind, Richard 1888: Was sind und was sollen die Zahlen? Braunschweig: Vieweg und Sohn. Latest reprint, 1969. Also reprinted in Dedekind 1932, 335–91. English translation in Dedekind 1901, with a revision of this translation in Ewald (ed.) 1996.

    Google Scholar 

  • Dedekind, Richard 1890: ‘Brief an Keferstein, vom 27ten Februar, 1890’, in Sinaceur 1974 (together with a French translation), 271–8. English translation by Hao Wang and Stefan Bauer-Mengelberg in van Heijenoort (ed.) 1967, 98–103. The original is in the Niedersächsische Staats- und Universitätsbibliothek, Göttingen (Cod. Ms. Dedekind, 13).

    Google Scholar 

  • Dedekind, Richard 1901: Essays on the theory of numbers. English translations by W. W. Beman of Dedekind 1872 and 1888. LaSalle, Illinois: Open Court Publishing Co. Reprinted by Dover Publications, New York, 1963.

    Google Scholar 

  • Dedekind, Richard 1932: Gesammelte mathematische Werke, Band 3. Herausgegeben von Robert Fricke, Emmy Noether and Öystein Ore. Braunschweig: Friedrich Vieweg und Sohn. Reprinted by Chelsea Publishing Co., New York, 1969, as three volumes in two, with some omissions from the third volume.

    Google Scholar 

  • Dummett, Michael 1991: Frege: philosophy of mathematics. London: George Duckworth or Cambridge, Ma.: Harvard University Press.

    Google Scholar 

  • Ewald, William (ed.) 1996: Readings in the philosophy of mathematics. Oxford: Clarendon Press.

    Google Scholar 

  • Frege, Gottlob 1879: Begriffsschrift; eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle an die Saale: Verlag von Louis Nebert. Reprinted in Frege 1964; English translation in van Heijenoort (ed.) 1967, 1–82.

    Google Scholar 

  • Frege, Gottlob 1880–81: ‘Booles rechnende Logik und die Begriffsschrift’ in Frege 1964, 9–52.

    Google Scholar 

  • Frege, Gottlob 1882: ‘Über die wissenschaftliche Berechtigung einer Begriffsschrift’, Zeitschrift für Philosophie und philosophische Kritik, 81, 48–56. Reprinted in Frege 1969 and in Patzig (ed.) 1986, 91–7.

    Google Scholar 

  • Frege, Gottlob 1884: Die Grundlagen der Arithmetik. Breslau: Wilhelm Koebner. Reprinted by Felix Meiner Verlag, 1986, 1988. English translation by J. L. Austin as The foundations of arithmetic, Oxford: Basil Blackwell, second edition, 1953. The Austin edition is a bilingual one, and the page numbers are the same for both the German and English texts.

    Google Scholar 

  • Frege, Gottlob 1903: Grundgesetze der Arithmetik, Band 2. Jena: Hermann Pohle. Reprinted in Frege 1966.

    Google Scholar 

  • Frege, Gottlob 1906: ‘Über die Grundlagen der Geometrie’, Jahresbericht der deutschen Mathematiker-Vereinigung, 15, 293–309

    Google Scholar 

  • Frege, Gottlob 1906: ‘Über die Grundlagen der Geometrie’, Jahresbericht der deutschen Mathematiker-Vereinigung, 15, 377–403

    Google Scholar 

  • Frege, Gottlob 1906: ‘Über die Grundlagen der Geometrie’, Jahresbericht der deutschen Mathematiker-Vereinigung, 15, 423–30. English translation in Kluge, E-H. W. (ed.) 1971, 49–112, reprinted in Frege 1984, 293–340. Both the translation in the former and its reprinting in the latter give the page numbers of the original.

    Google Scholar 

  • Frege, Gottlob 1964: Begriffsschrift und andere Aufsätze. Zweite Auflage. Mit E. Husserls und H. Scholz’ Anmerkungen herausgegeben von Ignacio Angelelli. Darmstadt: Wissenschaftliche Buchgesellschaft.

    Google Scholar 

  • Frege, Gottlob 1969: Nachgelassene Schriften und Wissenschaftlicher Briefwechsel: Erster Band, Nachgelassene Schriften, edited by H. Hermes, F. Kambartel and F. Kaulbach. Hamburg: Felix Meiner.

    Google Scholar 

  • Frege, Gottlob 1976: Nachgelassene Schriften und Wissenschaftlicher Briefwechsel: Zweiter Band, Wissenschaftlicher Briefwechsel, edited by G. Gabriel, H. Hermes, F. Kambartel, F. Kaulbach, C. Thiel and A. Veraart. Hamburg: Felix Meiner.

    Google Scholar 

  • Frege, Gottlob 1980: Philosophical and mathematical correspondence. Oxford: Basil Blackwell. Partial English translation by Hans Kaal of Frege 1976.

    Google Scholar 

  • Geach, Peter and Black, Max (eds.) 1966: Translations from the philosophical writings of Gottlob Frege. Oxford: Basil Blackwell.

    Google Scholar 

  • George, Alexander (ed.) 1994: Mathematics and mind. (Proceedings of the Conference on Mathematics and Mind held at Amherst College, Massachusetts in April, 1991.) New York: Oxford University Press.

    Google Scholar 

  • Gödel, Kurt 1929: Über die Vollständigkeit des Logikkalküls. Doctoral dissertation, University of Vienna. Published, with an English translation, in Gödel 1986, 60–101. Page numbers in the text refer to this reprinting.

    Google Scholar 

  • Gödel, Kurt 1986: Kurt Gödel: Collected works, volume 1. Oxford: Clarendon Press.

    Google Scholar 

  • Hallett, Michael 1984: Cantorian set theory and limitation of size. Oxford: Clarendon Press.

    Google Scholar 

  • Hallett, Michael 1900: ‘Physicalism, reductionism and Hilbert’ in Irvine (ed.) 1990, 183–257.

    Google Scholar 

  • Hallett, Michael 1994: ‘Hubert’s axiomatic method and the laws of thought’ George, Alexander (ed.): Mathematics and mind. (Proceedings of the Conference on Mathematics and Mind held at Amherst College, Massachusetts in April, 1991.) New York: Oxford University Press in George (ed.) 1994, 158–200.

    Google Scholar 

  • Heijenoort, Jean van 1979: ‘Absolutism and relativism in logic’ in van Heijenoort 1985, 75–83. Previously unpublished.

    Google Scholar 

  • Heijenoort, Jean van 1985: Selected essays. Naples: Bibliopolis.

    Google Scholar 

  • Heijenoort, Jean van (ed.) 1967: From F rege to Göde I: a source book in mathematical logic. Cambridge, Mass.: Harvard University Press.

    Google Scholar 

  • Helmholtz, Hermann von 1868: ‘Über die Tatsachen, die der Geometrie zum Grunde liegen’, Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen, 1868, 193–221. Reprinted in Helmholtz 1927.

    Google Scholar 

  • Helmholtz, Hermann von 1927: Schriften zur Erkenntnistheorie, edited by Paul Hertz and Moritz Schlick. Berlin: Julius Springer. English translation, Cohen and Elkana (eds.) 1977.

    Google Scholar 

  • Hilbert, David *1894: Die Grundlagen der Geometrie. Sommersemester 1894: Hilberts eigene Manuskript. Niedersächsische Staats- und Universitätsbibliothek, Göttingen. Cod. Ms. 541.

    Google Scholar 

  • Hilbert, David 1899: ‘Grundlagen der Geometrie’, in Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, 1899. Leipzig: B. G. Teubner.

    Google Scholar 

  • Hilbert, David 1900a: ‘Über den Zahlbegriff’, Jahresbericht der deutschen Mathematiker-Vereinigung, 8, 180–4. English translation in Ewald (ed.) 1996.

    Google Scholar 

  • Hilbert, David 1900b: ‘Mathematische Probleme’, Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen, mathematisch-physikalische Klasse, 1900, 253–96. English translation in Ewald (ed.) 1996.

    Google Scholar 

  • Hilbert, David 1905a: ‘Über die Grundlagen der Logik und Arithmetik’ in Krazer (ed.) 1905, 174–85. English translation in van Heijenoort (ed.) 1967, 129–38.

    Google Scholar 

  • Hilbert, David *1905b: Logische Principien des mathematischen Denkens. Sommersemester 1905: Ausgearbeitet von Ernst Hellinger. Mathematisches Institut, Georg-August Universität, Göttingen. 277 pages, handwritten.

    Google Scholar 

  • Hilbert, David *1905c: Logische Principien des mathematischen Denkens. Sommersemester 1905: Ausgearbeitet von Max Born. Niedersächsiche Staats- und Universitätsbibliothek, Göttingen, Göttingen: Cod. Ms. Hilbert, 558a. 188 pages, handwritten.

    Google Scholar 

  • Hilbert, David *1908: Prinzipien der Mathematik. Sommersemester 1908: Ausarbeitung unbekannt. Mathematisches Institut, Georg-August Universität, Göttingen. 206 pages, handwritten.

    Google Scholar 

  • Hilbert, David *1910: Elemente und Prinzipienfragen der Mathematik. Sommersemester 1910: Ausgearbeitet von Richard Courant. Mathematisches Institut, Georg-August Universität, Göttingen. 163 pages, handwritten.

    Google Scholar 

  • Hilbert, David *1917: Mengenlehre. Sommersemester 1917: Ausgearbeitet von Margarethe Loeb. Mathematisches Institut, Georg-August Universität, Göttingen. 166 + IV pages, typewritten.

    Google Scholar 

  • Hilbert, David *1917–18: Prinzipien der Mathematik. Wintersemester 1917–18: Ausgearbeitet von Paul Bernays. Mathematisches Institut, Georg-August Universität, Gōttingen, vii + 246 pages, typewritten.

    Google Scholar 

  • Hilbert, David 1978: ‘Axiomatisches Denken’, Mathematische Annalen, 78, 405–15. Reprinted in Hilbert 1935, pp. 146–56. English translation in Ewald (ed.) 1995, volume 2.

    Google Scholar 

  • Hilbert, David *1919: Natur und mathematisches Erkennen. Herbstsemester 1919: Ausgearbeitet von Paul Bernays. Mathematisches Institut, Georg-August Universität, Göttingen. Vi + 165 pages, typewritten. Retyped and published in a limited edition by the Mathematisches Institut, Göttingen, 1989, 117 pages.

    Google Scholar 

  • Hilbert, David *1920a: Probleme der mathematischen Logik. Sommersemester 1920: Ausgearbeitet von N. [sie] Schönfinkel and Paul Bernays. Mathematisches Institut, Georg-August Unviersität, Gōttingen, i + 46 pages, typewritten.

    Google Scholar 

  • Hilbert, David *1920b: Logik-Kalkül. Wintersemester 1920–21: Ausgearbeitet von Paul Bernays. Mathematisches Institut, Georg-August Universität, Göttingen. 62 pages, typewritten.

    Google Scholar 

  • Hilbert, David *1921–22: Die Grundlagen der Mathematik. Wintersemester 1920–21: Ausgearbeitet von Paul Bernays. Mathematisches Institut, Georg-August Universität, Göttingen. 100 + 9 + 38 pages, typewritten.

    Google Scholar 

  • Hilbert, David 1922: ‘Neubegründung der Mathematik. Erste Mitteilung’, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, 1, 157–77. Reprinted in Hilbert 1935, pp. 157–78. English translation in Ewald (ed.) 1996.

    Google Scholar 

  • Hilbert, David *1922–23a: Logische Grundlagen der Mathematik. Wintersemester 1922–23: Ausarbeitung unbekannt, vermutlich von Paul Bernays. Niedersächsische Staats- und Universitätsbibliothek, Göttingen, Cod. Ms. 567. 33 pages typewritten (pages 21–22 are missing), plus 25 sheets in Hubert’s hand.

    Google Scholar 

  • Hilbert, David *1922–23b: Wissen und mathematisches Denken. Wintersemester 1922–23; Ausgearbeitet von Wilhelm Ackermann. Mathematisches Institut, Georg-August Universität, Göttingen, iii + 138 pages, typewritten. Retyped and published in a limited edition by the Mathematisches Institut, Göttingen, 1988, 99 pages.

    Google Scholar 

  • Hilbert, David 1923: ‘Die logischen Grundlagen der Mathematik’, Mathematische Annalen, 88, 151–85. Reprinted in Hilbert 1935, pp. 178–91. English translation in Ewald (ed.) 1996.

    Google Scholar 

  • Hilbert, David *1924–25: Über das Unendliche. Wintersemester 1924–25: Ausgearbeitet von Lothar Nordheim. Mathematisches Institut, Georg-August Universität, Göttingen. 136 pages, typewritten.

    Google Scholar 

  • Hilbert, David 1926: ‘Über das Unendliche’, Mathematische Annalen, 95, 161–90. English translation in van Heijenoort (ed.) 1967, 367–92.

    Google Scholar 

  • Hilbert, David 1928: ‘Die Grundlagen der Mathematik’, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, 6, 65–85. English translation in van Heijenoort (ed.) 1967, 464–79.

    Google Scholar 

  • Hilbert, David 1929: ‘Probleme der Grundlegung der Mathematik’ in Atti del Congresso Internationale dei Matematici, Bologna 3–10 Settembre 1928, volume 1, Bologna: Nicola Zanichelli, 1929, 135–41. Reprinted, with omissions, as Hilbert 1930.

    Google Scholar 

  • Hilbert, David 1930: ‘Probleme der Grundlegung der Mathematik’, Mathematische Annalen, 102, 151–65. Reprint, with omissions, of Hilbert 1929.

    Google Scholar 

  • Hilbert, David 1933: Gesammelte Abhandlungen. Zweiter Band. Berlin: Julius Springer.

    Google Scholar 

  • Hilbert, David 1935: Gesammelte Abhandlungen. Dritter Band. Berlin: Julius Springer.

    Google Scholar 

  • Hilbert, David: Cod. Ms.: 600, I, II, III, ‘Aufzeichnungen zu allgemeinen und besonderen Problemen der Mathematik’. (3 Hefte.) Niedersächsische Staats- und Universitätsbibliothek, Göttingen, Hilbert Nachlass.

    Google Scholar 

  • Hilbert, David: Cod. Ms.: 685,3, ‘Bernays: Weyls Kritik der Analysis’, in Bernays’s handwriting. Niedersächsisches Staats- und Universitätsbibliothek, Göttingen, Hilbert Nachlass.

    Google Scholar 

  • Hilbert, David and Ackermann, Wilhelm 1928: Grundzüge der theoretischen Logik. Berlin: Julius Springer.

    Google Scholar 

  • Hilbert, David and Bernays, Paul 1934: Grundlagen der Mathematik. Band I. Berlin: Julius Springer.

    Google Scholar 

  • Hilbert, David and Bernays, Paul 1939: Grundlagen der Mathematik. Band II. Berlin: Julius Springer.

    Google Scholar 

  • Husserl, Edmund 1902: ‘Notiz einer mündlicher Mitteilung Zermelos an Husserl’ Rang, Bernhard (ed.): Edmund Husserl: Aufsätze und Rezensionen (1890–1910). Husserliana: Edmund Husserls Gesammelte Werke, Band XXII. Den Haag: Martinus Nijhoff. in Rang (ed.) 1979, 399, translated by Dallas Willard as ‘Memorandum of verbal communication from Zermelo to Husserl’, in Willard (ed.) 1994, 442.

    Google Scholar 

  • Irvine, Andrew (ed.) 1900: Physicalism in mathematics. Dordrecht, Holland: D. Reidel Publishing Co.

    Google Scholar 

  • Kleene, S. C. 1952: Introduction to metamathematics. New York: Van Nostrand. Also published by North-Holland: Amsterdam, and Noordhoff: Groningen.

    Google Scholar 

  • Klein, Felix 1890: ‘Zur Nicht-Euklidischen Geometrie’, Mathematische Annalen, 37, 544–72. Reprinted in Klein 1927, 353–83.

    Google Scholar 

  • Klein, Felix 1927: Gesammelte mathematische Abhandlungen, Erster Band. Berlin: Verlag von Julius Springer.

    Google Scholar 

  • Kluge, E-H. W (ed.) 1971: Gottlob Frege on the foundations of geometry and formal theories of arithmetic. New Haven and London: Yale University Press.

    Google Scholar 

  • Krazer, A. (ed.) 1905: Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg, 1904. Leipzig: B. G. Teubner.

    Google Scholar 

  • Mendelson, Elliot 1964: Introduction to mathematical logic. New York: D. Van Nostrand Company. (Third edition, Monterey, California: Wadsworth and Brooks, 1987.)

    Google Scholar 

  • Patzig, Günther (ed.) 1986: Gottlob Frege: Funktion, Begriff, Bedeutung. Sechste Auflage. Göttingen: Vandenhoeck und Ruprecht.

    Google Scholar 

  • Poincaré, Henri 1905: ‘Les mathématiques et la logique’, Revue de métaphysique et de morale, 13, 815–35.

    Google Scholar 

  • Poincaré, Henri 1906: ‘Les mathématiques et la logique’, Revue de métaphysique et de morale, 14, 294–317. Reprinted with some changes in Poincaré 1908, 192–214.

    Google Scholar 

  • Poincaré, Henri 1908: Science et méthode. Paris: Ernest Flammarion.

    Google Scholar 

  • Post, Emil 1921: ‘Introduction to a general theory of elementary propositions’, American journal of mathematics, 43, 163–85. Reprinted in van Heijenoort (ed.) 1967, 264–83.

    Google Scholar 

  • Purkert, Walter and Ilgauds, Hans Joachim 1987: Georg Cantor 1845–1918. Basel, Boston and Stuttgart: Birkhäuser.

    Google Scholar 

  • Rang, Bernhard (ed.) 1979: Edmund Husserl: Aufsätze und Rezensionen (1890–1910). Husserliana: Edmund Husserls Gesammelte Werke, Band XXII. Den Haag: Martinus Nijhoff.

    Google Scholar 

  • Reid, Constance 1970: Hilbert. New York, Heidelberg, Berlin: Springer-Verlag.

    Google Scholar 

  • Richard, Jules 1905: ‘Les principes de mathématiques et le problème des ensembles’, Revue générale des sciences pures et appliquées, 16, 541. English translation by Jean van Heijenoort as ‘The principles of mathematics and the problem of sets’ in van Heijenoort (ed.) 1967, 142–9.

    Google Scholar 

  • Russell, B. A. W. 1897: An essay on the foundations of geometry. Cambridge: Cambridge University Press. Republished by Dover Publications, Inc. in 1937, with a new introduction by Morris Kline.

    Google Scholar 

  • Russell, B. A. W. 1899: ‘Sur les axiomes de la géometrie’, Revue de métaphysique et de morale, 7, 685–707.

    Google Scholar 

  • Russell, B. A. W. 1900: A critical exposition of the philosophy of Leibniz. London: George Allen and Unwin. Second edition, 1937.

    Google Scholar 

  • Russell, B. A. W. 1907: ‘Recent work in the philosophy of mathematics’, The international monthly, 1901, reprinted as ‘Mathematics and the metaphysicians’ in Russell 1977.

    Google Scholar 

  • Russell, B. A. W. 1903: The principles of mathematics. Volume 1. Cambridge: Cambridge University Press. Second edition published as The principles of mathematics, with a new introduction, by George Allen and Unwin, London, 1937.

    Google Scholar 

  • Russell, B. A. W. 1906: ‘On some difficulties in the theory of transfinite numbers and order types’, Proceedings of the London mathematical society, 4 (second series), 29–53. Reprinted in Russell 1975, 135–64.

    Google Scholar 

  • Russell, B. A. W. 1972: The problems of philosophy. The Home University Library of Modern Knowledge. Oxford: Oxford University Press.

    Google Scholar 

  • Russell, B. A. W. 1977: Mysticism and Logic. London: George Allen and Unwin.

    Google Scholar 

  • Russell, B. A. W. 1918–19: ‘Lectures on logical atomism’, The Monist, 28 (1918), 495–527

    Google Scholar 

  • Russell, B. A. W. 1918–19: ‘Lectures on logical atomism’, The Monist, 29 (1919), 33–63

    Google Scholar 

  • Russell, B. A. W. 1918–19: ‘Lectures on logical atomism’, The Monist, 29 190–222

    Google Scholar 

  • Russell, B. A. W. 1918–19: ‘Lectures on logical atomism’, The Monist, 29 345–80. Reprinted in Russell 1956, 177–281. Also reissued as The philosophy of logical atomism, edited and introduced by D. F. Pears, Open Court Publishing Co., LaSalle, Illinois, 1985.

    Google Scholar 

  • Russell, B. A. W. 1979: Introduction to mathematical philosophy. London: George Allen and Unwin.

    Google Scholar 

  • Russell, B. A. W. 1956: Logic and Knowledge. Edited by R. C. Marsh. London: George Allen and Unwin.

    Google Scholar 

  • Russell, B. A. W. 1957: ‘Mr. Strawson on referring’, Mind, 66, 385–9. Reprinted in Russell 1973, 120–6. Page numbers in the text refer to this reprinting.

    Google Scholar 

  • Russell, B. A. W. 1975: Essays in analysis. Edited by Douglas Lackey. London: George Allen and Unwin.

    Google Scholar 

  • Scharlau, Winfried (ed.) 1986: Rudolf Lipschitz: Briefwechsel mit Cantor, Dedekind, Helmholtz, Kronecker, Weierstrass und anderen. Braunschweig: Vieweg und Sohn.

    Google Scholar 

  • Schlick, Moritz 1978: Allgemeine Erkenntnislehre. Berlin: Julius Springer.

    Google Scholar 

  • Schröder, Ernst 1890–1905: Vorlesungen über die Algebra der Logik (exacter Logik). 3 Bände. Leipzig: B. G. Teubner.

    Google Scholar 

  • Sinaceur, M.-A. 1974: ‘L’infini et les nombres. Commentaires de R. Dedekind à «Zahlen». La correspondence avec Keferstein’, Revue d’histoire des sciences, 27, 251–78.

    Google Scholar 

  • Skolem, Thoralf 1923: ‘Einige Bermerkungen zur axiomatischen Mengenlehre’. Reprinted in Skolem 1970, 137–52. English translation in van Heijenoort (ed.) 1967, 290–301.

    Google Scholar 

  • Skolem, Thoralf 1930: ‘Einige Bemerkungen zu der Abhandlung von Ernst Zermelo „Über die Definitheit in der Axiomatic“’, Fundmenta mathematicae, 15, 337–41. Reprinted in Skolem 1970, 275–9.

    Google Scholar 

  • Skolem, Thoralf 1970: Selected papers in logic. Edited by Jens Erik Fenstad. Oslo: Universitetsforlaget.

    Google Scholar 

  • Tarski, Alfred 1936: ‘Über den Begriff der logischen Folgerung’, Actes du Congrès International de Philosophie Scientifique, 7, 1–11. English translation by J. H. Woodger in Tarski 1956, 409–420.

    Google Scholar 

  • Tarski, Alfred 1956: Logic, semantics, metamathematics: papers from 1923–1938, translated by J. H. Woodger. Oxford: Clarendon Press. Second, corrected edition, with a new introduction by John Corcoran, published by Hackett Publications, Indianoplis, 1983.

    Google Scholar 

  • Tijdeman, R. 1976: ‘Hubert’s seventh problem: on the Gel’fond — Baker method and its applications’ Browder, Felix (ed.): Mathematical developments arising from Hilbert problems. Proceedings of symposia in pure mathematics, volume 28, parts 1 and 2. Providence, Rhode Island: American Mathematical Society. in Browder (ed.), 241–68.

    Google Scholar 

  • Toepell, Michael-Markus 1986: Über die Entstehung von David Hilberts „Grundlagen der Geometrie“. (Studien zur Wissenschafts- Sozial- und Bildungsgeschichte, Band 2.) Göttingen: Vandenhoeck and Ruprecht.

    Google Scholar 

  • Weyl, Hermann 1910: ‘Über die Definition der mathematischen Grundbegriffe’, Mathematisch-naturwissenschaftliche Blätter, 7, 93–5

    Google Scholar 

  • Weyl, Hermann 1910: ‘Über die Definition der mathematischen Grundbegriffe’, Mathematisch-naturwissenschaftliche Blätter, 7, 109–13. Reprinted in Weyl 1968, volume 1, pp. 298–304.

    Google Scholar 

  • Weyl, Hermann 1917: Das Kontinuum. Reprinted by Chelsea Publishing Co., New York.

    Google Scholar 

  • Weyl, Hermann 1919: ‘Der circuius vitiosus in der heutigen Begründung der Analysis’, Jahresbericht der deutschen Mathematiker-Vereinigung, 28, 85–92. Reprinted in Weyl 1968, volume 2, 43–50.

    Google Scholar 

  • Weyl Hermann 1944: ‘David Hilbert and his mathematical work’, Bulletin of the American mathematical society, 50, 612–54. Reprinted in Weyl 1968, volume 4, 130–72; page numbers in the text refer to this reprinting. Also partially reprinted in Reid 1970, 245–83.

    Google Scholar 

  • Weyl, Hermann 1968: Gesammelte Abhandlungen. Volumes 1–4. Berlin, Heidelberg, New York: Springer-Verlag.

    Google Scholar 

  • Whitehead, A. N. and Russell, B. A. W. 1910–13: Principia mathematica. Volumes 1–3. Cambridge: Cambridge University Press.

    Google Scholar 

  • Willard, Dallas (ed.) 1994: Edmund Husserl: early writings in the philosophy of logic and mathematics. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Zermelo, Ernst 1908: ‘Untersuchungen über die Grundlagen der Mengenlehre, I’, Mathematische Annalen, 65, 261–81. English translation in van Heijenoort (ed.) 1967, 199–215.

    Google Scholar 

  • Zermelo, Ernst 1930: ‘Über Grenzzahlen und Mengenbereiche’, Fundamenta mathematicae, 16, 29–47. English translation in Ewald (ed.) 1996.

    Google Scholar 

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  1. McGill University, Canada

    Michael Hallett

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  1. Michael Hallett
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  1. University of Ottawa, Canada

    Mathieu Marion

  2. Boston University, USA

    Robert S. Cohen

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© 1995 Kluwer Academic Publishers

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Hallett, M. (1995). Hilbert and Logic. In: Marion, M., Cohen, R.S. (eds) Québec Studies in the Philosophy of Science. Boston Studies in the Philosophy of Science, vol 177. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1575-6_10

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