Linked bibliography for the SEP article "The Frege-Hilbert Controversy" by Patricia Blanchette
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Primary Sources
- Frege, Gottlob, 1879, Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle: Louis Nebert. Translated as Concept Script, A Formal Language of Pure Thought Modeled Upon that of Arithmetic, by Stefan Bauer-Mengelberg in From Frege to Gödel, Jean van Heijenoort (ed.), Cambridge, MA: Harvard University Press, 1967, pp. 5–82. (Scholar)
- –––, 1881, “Booles rechnende Logik und die
Begriffsschrift”, unpublished manuscript in Frege 1969:
9–52 [1979: 9–46]. (Scholar)
- –––, 1884, Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl, Breslau: W. Koebner. Translated as The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, by J. L. Austin, Oxford: Oxford University Press, 1950. Reprinted Evanston, IL: Northwestern University Press, 1978. (Scholar)
- –––, 1903, “Über die Grundlagen der
Geometrie” (On the Foundations of Geometry) – First
Series. Jahresbericht der Deutschen Mathematiker-Vereinigung,
English translation in Frege 1984: 273–284.
- –––, 1906, “Über die Grundlagen der
Geometrie” (On the Foundations of Geometry) – Second
Series, Jahresbericht der Deutschen Mathematiker-Vereinigung,
English translation in Frege 1984: 293–340.
- –––, 1969 [1979], Nachgelassene Schriften und Wissenschaftlicher Briefwechsel, Hans Hermes, Friedrich Kambartel, and Friedrich Kaulbach (eds.), Hamburg: Felix Meiner Verlag, volume 1. English translation of some selections as Posthumous Writings, translated by Peter Long and Roger White, with the assistance of Raymond Hargreaves, Chicago: University of Chicago Press. (Scholar)
- –––, 1971, On the Foundations of Geometry and Formal Theories of Arithmetic, Eike-Henner W. Kluge (trans.), New Haven, CT: Yale University Press. (Scholar)
- –––, 1980, Philosophical and Mathematical
Correspondence, Gottfried Gabriel, Hans Hermes, Friedrich
Kambartel, Christian Thiel, Albert Veraart, Brian McGuinness, and Hans
Kaal (eds.) Oxford: Blackwell Publishers. (Scholar)
- –––, 1984, Collected Papers on Mathematics, Logic and Philosophy, Brian F. McGuinness (ed.), Oxford: Blackwell Publishers. (Scholar)
- Hallett, Michael and Ulrich Majer (eds.), 2004, David
Hilbert’s Lectures on the Foundations of Geometry
1891–1902, Berlin: Springer. (Scholar)
- Hilbert, David, 1899, Grundlagen der Geometrie, Leipzig:
Teubner. An English translation of the 10th edition is
available as Foundations of Geometry, Leo Unger (trans.), La
Salle, IL: Open Court Press, 1971. (Scholar)
- Huntington, Edward V., 1902, “A Complete Set of Postulates
for the Theory of Absolute Continuous Magnitude”,
Transactions of the American Mathematical Society, 3(2):
264–279. (Scholar)
- Padoa, Alessandro, 1900, “Essai d’une théorie
algébrique des nombres entiers, précédé
d’une introduction logique à une theorie déductive
quelconque” in Bibliothèque du Congrès
International de Philosophie, Paris, 1900, Paris: Armand Colin,
1901, Volume 3, pp. 309–365; partial English translation as
“Logical introduction to any deductive theory” in From
Frege to Gödel, Jean van Heijenoort (ed.), Cambridge, MA:
Harvard University Press, 1967, pp. 118–123. (Scholar)
- Peano, Giuseppe, 1889, Principii di Geometria logicamente
esposti, Torino: Fratelli Bocca. (Scholar)
- Pieri, Mario, 1898, “I Principii della geometria di
posizione composti in sistema logico deduttivo”, Memorie
della Reale Accademia delle Scienze di Torino (Series 2), 48:
1–62. (Scholar)
- Veblen, Oswald, 1904, “A System of Axioms for
Geometry”, Transactions of the American Mathematical
Society, 5(3): 343–384. doi:10.2307/1986462 (Scholar)
Secondary Sources
- Antonelli, Aldo and Robert May, 2000, “Frege’s New Science”, Notre Dame Journal of Formal Logic, 41(3): 242–270. doi:10.1305/ndjfl/1038336844 (Scholar)
- Blanchette, Patricia A., 1996, “Frege and Hilbert on Consistency”, Journal of Philosophy, 93(7): 317–336. doi:10.2307/2941124 (Scholar)
- –––,2007, “Frege on Consistency and Conceptual Analysis”, Philosophia Mathematica, 15(3): 321–346. doi:10.1093/philmat/nkm028 (Scholar)
- –––, 2012, Frege’s Conception of
Logic, Oxford: Oxford University Press. See esp. Ch. 5.
doi:10.1093/acprof:oso/9780199891610.001.0001 (Scholar)
- –––, 2014, “Frege on Formality and the 1906 Independence Test”, in Formalism and Beyond: On the Nature of Mathematical Discourse, Godehard Link (ed.), Boston/Berlin: De Gruyter, pp. 97– 118. (Scholar)
- –––, 2017, “Models in Geometry and Logic: 1870–1920”, in Logic, Methodology and Philosophy of Science: Proceedings of the 15th International Congress, Leitgeb, Niiniluoto, Seppälä. and Sober (eds.), London: College Publications, pp. 41–61. (Scholar)
- Bernays, Paul, 1922, “Die Bedeutung Hilberts fur die
Philosophie der Mathematik”, Die Naturwissenschaften,
10(4): 93–99. English translation by Paolo Mancosu in From
Brouwer to Hilbert; The Debate on the Foundations of Mathematics in
the 1920s, Paolo Mancosu (ed.), New York: Oxford University
Press, pp. 189–197. doi:10.1007/bf01591620 (German) (Scholar)
- Currie, Gregory, 1982, Frege: An Introduction to His Philosophy, Sussex: Harvester. (Scholar)
- Dedekind, Richard, 1888 Was Sind und Was Sollen die Zahlen?. English translation as “The Nature and Meaning of Numbers” in Dedekind, Essays on the Theory of Numbers, edited and translated by Wooster Woodruff Beman, Chicago: Open Court, 1901. (Scholar)
- Demopoulos, William, 1994, “Frege, Hilbert and the Conceptual Structure of Model Theory”, History and Philosophy of Logic, 15(2): 211–225. doi:10.1080/01445349408837233 (Scholar)
- Dummett, Michael, 1975, “Frege on the Consistency of
Mathematical Theories”, in Studien zu Frege, Matthias
Schirn (ed.), Stuttgart/Bad Cannstatt: Fromann-Holzboog, pp.
229–242. (Scholar)
- –––, 1991, Frege: Philosophy of Mathematics, Cambridge, MA: Harvard University Press. (Scholar)
- Eder, Günther, 2013 “Remarks on Independence Proofs and Indirect Reference”, History and Philosophy of Logic, 34(1): 68–78. doi:10.1080/01445340.2012.702568">10.1080/01445340.2012.702568 (Scholar)
- –––, 2016 “Frege’s ‘On the Foundations of Geometry’ and Axiomatic Metatheory”, Mind, 125(497): 5–40. doi:10.1080/01445340.2012.702568 (Scholar)
- Eder, Günther and Georg Schiemer, 2018, “Hilbert, Duality, and the Geometrical Roots of Model Theory”, The Review of Symbolic Logic, 11(1): 48–86. doi:10.1017/s1755020317000260 (Scholar)
- Hallett, Michael, 2010, “Frege and Hilbert”, in The Cambridge Companion to Frege, Tom Ricketts and Michael Potter (eds.), Cambridge: Cambridge University Press, pp. 413–464. doi:10.1017/ccol9780521624282.011 (Scholar)
- –––, 2012, “More on Frege and
Hilbert”, Analysis and Interpretation in the Exact Sciences:
Essays in Honour of William Demopoulos, Melanie Frappier, Derek
Brown, and Robert DiSalle (eds.), Dordrecht, New York: Springer, pp.
135–162. doi:10.1007/978-94-007-2582-9_8 (Scholar)
- Hodges, Wilfrid, 2004, “The Importance and Neglect of
Conceptual Analysis: Hilbert-Ackermann iii.3”, in
First-Order Logic Revisited, Vincent F. Hendricks et
al. (eds.), Berlin: Logos Verlag, pp. 129–153. (Scholar)
- Korselt, Alwin, 1903, “Über die Grundlagen der
Geometrie”, Jahresbericht der Deutschen
Mathematiker-Vereinigung, 12: 402–407. English translation
by E-H. W. Kluge in Frege 1971.
[Korselt 1903 available online (German)] (Scholar)
- Mancosu, Paolo, Richard Zach, and Calixto Badesa, 2009, “The Development of Mathematical Logic from Russell to Tarski, 1900–1935” in The Development of Modern Logic, Leila Haaparanta (ed.), New York: Oxford University Press. doi:10.1093/acprof:oso/9780195137316.003.0029 (Scholar)
- Nagel, Ernest, 1939, “The Formation of Modern Conceptions of
Formal Logic in the Development of Geometry”, Osiris,
7: 142–224. doi:10.1086/368504 (Scholar)
- Resnik, Michael David, 1974, “The Frege-Hilbert Controversy”, Philosophy and Phenomenological Research, 34(3): 386–403. doi:10.2307/2107085 (Scholar)
- Ricketts, Thomas, 1997, “Frege’s 1906 Foray Into Metalogic”, Philosophical Topics, 25(2): 169–188. doi:10.5840/philtopics199725214 (Scholar)
- Shapiro, Stewart, 2005, “Categories, Structures, and the Frege-Hilbert Controversy: The Status of Meta-mathematics”, Philosophia Mathematica, 13(1): 61–77. doi:10.1093/philmat/nki007 (Scholar)
- Tappenden, Jamie, 2000, “Frege on Axioms, Indirect Proofs, and Independence Arguments in Geometry: Did Frege Reject Independence Arguments?” Notre Dame Journal of Formal Logic, 41(3): 271–315. doi:10.1305/ndjfl/1038336845 (Scholar)
- Wehmeier, Kai F., 1997, “Aspekte der Frege-Hilbert-Korrespondenz”, History and Philosophy of Logic, 18(4): 201–209. doi:10.1080/01445349708837289 (Scholar)