Linked bibliography for the SEP article "The Emergence of First-Order Logic" by William Ewald

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

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Awodey, Steve & Erich H. Reck, 2002, “Completeness and Categoricity, Part I: Nineteenth-century Axiomatics to Twentieth-century Metalogic”, History and Philosophy of Logic, 23(1): 1–30. doi:10.1080/01445340210146889 (Scholar)
Badesa, Calixto, 2004, The Birth of Model Theory: Löwenheim’s Theorem in the Frame of the Theory of Relatives, Princeton: Princeton University Press. (Scholar)
Bernays, Paul, 1918, “Beiträge zur axiomatischen Behandlung des Aussagen-Kalküls”, Habilitation Thesis, University of Göttingen; first published in Hilbert [LFL], pp. 231-268. (Scholar)
–––, 1926, “Axiomatische Untersuchung des Aussagen-Kalküls der Principia Mathematica”, Mathematische Zeitschrift, 25: 305–320. (Scholar)
–––, 1937, “A System of Axiomatic Set Theory”, Journal of Symbolic Logic, 2(1): 65–77. doi:10.2307/2268862 (Scholar)
Boole, George, 1847, The Mathematical Analysis of Logic: Being An Essay Towards a Calculus of Deductive Reasoning, Cambridge: Macmillan. Reprinted in Ewald 1996: vol. 1, pp. 451–509. [Boole 1847 available online] (Scholar)
Brady, Geraldine, 2000, From Peirce to Skolem: A Neglected Chapter in the History of Logic, (Studies in the History and Philosophy of Mathematics, 4), Amsterdam: Elsevier. (Scholar)
Carnap, Rudolf, “Die logizistische Grundlegung der Mathematik”, Erkenntnis, 2(1): 91–105. (References to the translation in Paul Benacerraf and Hilary Putnam, Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press, 1983, 41–52.) doi:10.1007/bf02028142 (de) doi:10.1017/CBO9781139171519.003 (en) (Scholar)
Church, Alonzo, 1956, Introduction to Mathematical Logic, Princeton: Princeton University Press. (Scholar)
–––, 1974, “Russellian Simple Type Theory”, Proceedings and Addresses of the American Philosophical Association, 47: 21–33. doi:10.2307/3129899 (Scholar)
De Morgan, Augustus, 1864, “On the Syllogism, No. IV, and on the Logic of Relations”, Transactions of the Cambridge Philosophical Society, 10: 173–230. (Read 8 Feb. 1858.) [De Morgan 1864 available online] (Scholar)
Dutilh Novaes, Catarina, forthcoming, “Axiomatizations of Arithmetic and the First-order/Second-order Divide”, Synthese, first online: 30 December 2014. doi:10.1007/s11229-014-0636-6 (Scholar)
Eklund, Matti, 1996, “On How Logic Became First-Order”, Nordic Journal of Philosophical Logic, 1(2): 147–167. [Eklund 1996 available online] (Scholar)
Ewald, William Bragg (ed.), 1996, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols., Oxford: Clarendon Press. (Scholar)
Ferreirós, José, 2001, “The Road to Modern Logic—An Interpretation”, Bulletin of Symbolic Logic, 7(4): 441–484. doi:10.2307/2687794 (Scholar)
Fraenkel, Abraham A., 1927, “Review of Skolem 1922”, Jahrbuch über die Fortschritte der Mathematik, 49: 138–139. (Scholar)
Frege, Gottlob, 1879, Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle: Nebert. Translated by Stefan Bauer-Mengelberg in van Heijenoort 1967: 1–82. (Scholar)
–––, 1884, Die Grundlagen der Arithmetik, eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau: Koebner. Translated by J. L. Austin as The Foundations of Arithmetic, A Logico-Mathematical Inquiry into the Concept of Number, Oxford: Blackwell, 1950. (Scholar)
–––, 1893, Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet, vol. 1, Jena: Pohl. (Scholar)
–––, 1895, “Kritische Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra der Logik”, Archiv für systematische Philosophie, 1: 433–456. [Frege 1895 available online] (Scholar)
–––, [PMC], Philosophical and Mathematical Correspondence, Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel, Albert Veraart, Brian McGuinness, and Hans Kaal (eds.), Chicago: University of Chicago Press, 1980.
Gabbay, Dov M. & John Woods (eds.), 2009, Handbook of the History of Logic, Vol. 5: Logic from Russell to Church, Amsterdam: Elsevier-North Holland. (Scholar)
Gödel, Kurt, 1929, Über die Vollständigkeit des Logikkalküls, Doctoral Dissertation, University of Vienna. Printed with translation in Sol Feferman et al. (eds), Kurt Gödel: Collected Works, Vol. 1: Publications 1929–1936, Oxford: Clarendon Press, pp. 60–101. (Scholar)
–––, 1931, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I”, Monatshefte für Mathematik und Physik, 38: 173–198; translated by S. Bauer-Mengelberg in van Heijenoort 1967: 596–616. (Scholar)
–––, 1940, The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory, Princeton: Princeton University Press. (Scholar)
Goldfarb, Warren D., 1979, “Logic in the Twenties: The Nature of the Quantifier”, Journal of Symbolic Logic, 44(3): 351–368. doi:10.2307/2273128 (Scholar)
Hilbert, David, 1905, “Über die Grundlagen der Logik und der Arithmetik”, in Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13. August 1904, Leipzig: Teubner, pp. 174–185; translated by S. Bauer-Mengelberg in van Heijenoort 1967: 130–138. (Scholar)
–––, 1917, “Axiomatisches Denken”, Mathematische Annalen 78(1–4): 405–415; translated by W. Ewald in Ewald 1996 (Volume 2), pp. 1105–1115. doi:10.1007/BF01457115 (de) (Scholar)
–––, 1917/18, Prinzipien der Mathematik, unpublished lectures held in Göttingen, Winter Semester, 1917/18 (lecture notes recorded by Paul Bernays). Reprinted in Hilbert 2013: 31–221.) (Scholar)
–––, 1928, “Probleme der Grundlegung der Mathematik”, (the “Bologna Lecture”), reprinted in Hilbert 2013: 954–966. (Scholar)
–––, [LFL], David Hilbert, Lectures on the Foundations of Logic, Mathematics and the Natural Sciences (Volume III: Foundations of Logic and Arithmetic, 1917–1933), William Ewald and Wilfried Sieg (eds.), Berlin: Springer Verlag, 2013. doi:10.1007/978-3-540-69444-1 (Scholar)
Hilbert, David & Wilhelm Ackermann, 1928, Grundzüge der theoretischen Logik, Berlin: Springer Verlag. (Scholar)
Hilbert, David & Paul Bernays, 1939, Prinzipien der Mathematik II, Berlin: Springer Verlag. (Scholar)
Landini, Gregory, 1998, Russell’s Hidden Substitutional Theory, Oxford: Oxford University Press. (Scholar)
Lindström, Per, 1969, “On Extensions of Elementary Logic”, Theoria, 35(1): 1–11. doi:10.1111/j.1755-2567.1969.tb00356.x (Scholar)
Linsky, Bernard, 2011, The Evolution of ‘Principia Mathematica’: Bertrand Russell’s Manuscripts and Notes for the Second Edition, Cambridge: Cambridge University Press. doi:10.1017/cbo9780511760181 (Scholar)
Löwenheim, Leopold, 1915, “Über Möglichkeiten im Relativkalkül”, Mathematische Annalen, 76(4): 447–470. Translation in van Heijenoort 1967: 228–251. doi:10.1007/bf01458217 (de) (Scholar)
–––, 1940, “Einkleidung der Mathematik im Schröderschen Relativkalkül”, Journal of Symbolic Logic, 5(1): 1–15. doi:10.2307/2269177 (Scholar)
Macintyre, Angus, 2011, “The Impact of Gödel’s Incompleteness Theorems on Mathematics”, in Kurt Gödel and the Foundations of Mathematics: Horizons of Truth, Matthias Baaz, Christos H. Papadimitriou, Dana S. Scott, Hilary Putnam, and Charles L. Harper (eds.), Cambridge: Cambridge University Press, pp. 3–26. doi:10.1017/cbo9780511974236.004 (Scholar)
Mancosu, Paolo (ed.), 1998, From Brouwer to Hilbert: The Debate on the Foundations of Mathematics in the 1920s, Oxford: Oxford University Press. (Scholar)
Mancosu, Paolo, Richard Zach, & Calixto Badesa, 2009, “The Development of Mathematical Logic from Russell to Tarski, 1900–1935”, in L. Haaparanta (ed.), The Development of Modern Logic, Oxford: Oxford University Press, pp. 318–470; reprinted in Paolo Mancosu (ed.), The Adventure of Reason: Interplay Between Philosophy of Mathematics and Mathematical Logic, 1900–1940, Oxford: Oxford University Press, pp. 5–120. (Scholar)
Moore, Gregory S., 1988, “The Emergence of First-Order Logic”, in William Aspray and Philip Kitcher (eds), History and Philosophy of Modern Mathematics, (Minnesota Studies in the Philosophy of Science, 11), pp. 95–135, Minneapolis: University of Minnesota Press. (Scholar)
Peano, Giuseppe, 1889, Arithmetices Principia, nova methodo exposita, Turin: Bocca. Translated in van Heijenoort 1967: 20–55. [Peano 1889 (it) available online] (Scholar)
Peirce, Charles S., 1867, Five Papers on Logic Presented to the American Academy; reprinted in Writings of Charles S. Peirce: A Chronological Edition (Volume 2), Edward C. Moore (ed.), Bloomington: Indiana University Press, 1984, pp. 12-86. (Scholar)
–––, 1870 [1873], “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences, 9(2): 317–378, communicated 26 January 1870, published 1873. doi:10.2307/25058006 (Scholar)
–––, 1881, “On the Logic of Number”, American Journal of Mathematics, 4(1): 85–95. Reprinted in Ewald 1996: vol. 1, pp. 598–608. doi:10.2307/2369151 (Scholar)
–––, 1883, “A Theory of Probable Inference”, in C. S. Peirce (ed.), Studies in Logic by Members of the Johns Hopkins University, Boston: Little Brown, pp. 126–181. [Peirce 1883 available online] (Scholar)
–––, 1885, “On the Algebra of Logic: A Contribution to the Philosophy of Notation”, American Journal of Mathematics, 7(2): 180–202. Reprinted in Ewald 1996: vol. 1, pp. 608–632. doi:10.2307/2369451 (Scholar)
Quine, Willard V., 1936, “Set-theoretic Foundations for Logic”, Journal of Symbolic Logic, 1(2): 45–57. doi:10.2307/2268548 (Scholar)
Reck, Erich H., 2013, “Developments in Logic: Carnap, Gödel, and Tarski”, in Oxford Handbook of the History of Analytical Philosophy, Michael Beaney (ed.), Oxford: Oxford University Press, pp 546–571. (Scholar)
Russell, Bertrand, 1903, The Principles of Mathematics, Cambridge: Cambridge University Press. [Russell 1903 available online] (Scholar)
–––, 1908, “Mathematical Logic as Based on the Theory of Types”, American Journal of Mathematics, 30(3): 222–262. Reprinted in van Heijenoort 1967: 150–182. doi:10.2307/2369948 (Scholar)
Schiemer, Georg & Erich H. Reck, 2013, “Logic in the 1930s: Type Theory and Model Theory”, Bulletin of Symbolic Logic, 19(4): 433–472. doi:10.1017/s1079898600010568 (Scholar)
Schröder, Ernst, 1890–95, Vorlesungen über die Algebra der Logik (exakte Logik), 3 volumes, Leipzig: Teubner. (Scholar)
Sieg, Wilfried, 1999, “Hilbert’s Programs: 1917–1922”, Bulletin of Symbolic Logic, 5(1): 1–44. doi:10.2307/421139 (Scholar)
–––, 2009, “Hilbert’s Proof Theory”, in Gabbay & Woods 2009: 321–384. doi:10.1016/s1874-5857(09)70012-3 (Scholar)
–––, 2013, Hilbert’s Programs and Beyond, Oxford: Oxford University Press. (Scholar)
Skolem, Thoralf, 1920, “Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem theoreme über dichte Mengen”, Kristiania. Partially translated by S. Bauer Mengelberg in van Heijenoort 1967: 252–263. (Scholar)
–––, 1922, “Einige Bemerkungen zur axiomatischen Begründung der Mengenlehre”, translated by S. Bauer Mengelberg in van Heijenoort 1967: 217–232. (Scholar)
–––, 1923, “Begründung der elementaren Arithmetik durch die rekurrierende Denkweise ohne Anwendung scheinbarer Veränderlichen mit unendlichem Ausdehnungsbereich”, Kristiania. Translated by S. Bauer Mengelberg in van Heijenoort 1967: 302–333. [Skolem 1923 (de) available online] (Scholar)
Tarski, Alfred, 1935, “Der Wahrheitsbegriff in den formalisierten Sprachen”, Studia Philosophica, 1: 261–405. Translated in Logic, Semantics, Metamathematics: Papers from 1923 to 1938, Oxford: Oxford University Press, 1956. (Scholar)
van Heijenoort, Jean, (ed.), 1967, From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, Cambridge, MA: Harvard University Press (Scholar)
von Neumann, John, 1927, “Zur Hilbertschen Beweistheorie”, Mathematische Zeitschrift, 26: 1–46. (Scholar)
Weyl, Hermann, 1910, “Über die Definitionen der mathematischen Grundbegriffe”, Mathematisch-Wissenschaftliche Blätter, 7: 93–95, 109–113. (Scholar)
–––, 1918, Das Kontinuum, Berlin: de Gruyter. (Scholar)
Whitehead, Alfred N. & Bertrand Russell, 1910–1913, Principia Mathematica, 3 volumes, Cambridge: Cambridge University Press. (Scholar)
Zach, Richard, 1999, “Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic”, Bulletin of Symbolic Logic, 5: 331–366. (Scholar)
Zermelo, Ernst, 1908, “Untersuchungen über die Grundlagen der Mengenlehre, I”, Mathematische Annalen, 65(2): 261–281. Translated by S. Bauer Mengelberg in van Heijenoort 1967: 199–215. doi:10.1007/bf01449999 (de) (Scholar)
–––, 1929, “Über den Begriff der Definitheit in der Axiomatik”, Fundamenta Mathematicae, 14: 339–344. doi:10.4064/fm-14-1-339-344 (Scholar)

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