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Towards a Re-Evaluation of Julius König's Contribution to Logic

  • Miriam Franchella (a1)
Abstract

Julius König is famous for his mistaken attempt to demonstrate that the continuum hypothesis was false. It is also known that the only positive result that could have survived from his proof is the paradox which bears his name. Less famous is his 1914 book Neue Grundlagen der Logik, Arithmetik und Mengenlehre. Still, it contains original contributions to logic, like the concept of metatheory and the solution of paradoxes based on the refusal of the law of bivalence. We are going to discover them by analysing the content of the book.

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References
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Bernays, P. (1935), Hilberts Untersuchungen über die Grundlagen der Arithmetik, D. Hilbert Gesammelte Abhandlungen, vol. 3, Springer, pp. 196216.
Boole, G. (1847), Mathematical Analysis of logic, Macmillan, Barclay and Macmillan / George Bell, Cambridge / London.
Brouwer, L.E.J. (1907), Over de grondslagen der wiskunde, Maas and van Suchtelen, Amsterdam, (English translation, On the Foundations of Mathematics, L.E.J. Brouwer Collected Works (A. Heyting editor), vol. 1 (1975), North-Holland, Amsterdam, pp. 11–101).
Brouwer, L.E.J. (1908), De onbetrouwbaarheid der logische principes, Tijdschrift voor Wijsbegeerte, vol. 2, pp. 152158, (English translation, The Unreliability of Logical Principles, L.E.J. Brouwer Collected Works (A. Heyting editor), vol. 1 (1975), North-Holland, Amsterdam, pp. 107–111).
Brouwer, L.E.J.(1912), Intuitionisme en formalisme; inaugurale rede, Clausen, Amsterdam, (English translation, Intuition and Formalism, L.E.J. Brouwer Collected Works (A. Heyting editor), vol. 1 (1975), North-Holland, Amsterdam, pp. 123–138).
Dedekind, R. (1888), Was sind und was sollen die Zahlen?, Vieweg, Wiesbaden.
Descartes, R. (1963), Œuvres et lettres, Pleiade, Paris.
Frege, G. (1879), Begriffsschrift, Nebert, Halle.
Frege, G. (1893), Grundgesetze der Arithmetik, Pohle, Jena.
Grassmann, H. (1861), Lehrbuch der Arithmetik für höhere Lehranstalten, Th. Chr. Fr. Enslin., Berlin.
Hallett, M. (1984), Cantorian Set Theory and Limitation of Size, Oxford University Press, Oxford.
Hilbert, D. (1905a), Über die Grundlagen der Logik und der Arithmetik, Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 17. August 1904, Teubner, Leipzig, (English translation, On the Foundations of Logic and Arithmetic, From Frege to Gödel: a Source Book in Mathematical Logic (J. van Heijenoort, editor), 1976, Harvard University Press, Cambridge, pp. 130–138).
Hilbert, D. (1905b), Logische Principien des mathematischen Denkens, Vorlesungen ausgearbeitet von Ernst Hellinger.
Hilbert, D. (1922), Neubegründung der Mathematik. Erste Mitteilung, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, vol. 1, pp. 157177.
Hilbert, D. (1926), Über das Unendliche, Mathematische Annalen, vol. 95, pp. 161190, (English translation, On the Infinite, From Frege to Gödel: a Source Book in Mathematical Logic (J. van Heijenoort, editor), 1976, Harvard University Press, Cambridge, pp. 369–392).
Hilbert, D. (1972), Historisches Wörterbuch der Philosophie, vol. Bd II, Schwabe, Basel.
Kneale, W. and Kneale, M. (1962), The Development of Logic, Oxford University Press, Oxford.
König, J. (1905a), Zum Kontinuum-Problem, Mathematische Annalen, vol. 60, pp. 177180.
König, J. (1905b), Über die Grundlagen der Mengenlehre und das Kontinuumproblem, Mathematische Annalen, vol. 61, pp. 156160.
König, J. (1906), Sur la théorie des ensembles, Comptes rendus de l'Académie des Sciences de Paris, pp. 110112.
König, J. (1907), Über die Grundlagen der Mengenlehre und das Kontinuumproblem, Mathematische Annalen, vol. 63, pp. 217221.
König, J. (1914), Neue Grundlagen der Logik, Arithmetik und Mengenlehre, Von Veit, Leipzig.
MacColl, H. (1897), Symbolical Reasoning, Mind, vol. 6, pp. 493510.
MacColl, H. (1906), Symbolic logic and Its Applications, Longmans, Green & Co., London, New York, Bombay.
Moore, G.H. (1978), The Origins of Zermelo's Axiomatization of Set Theory, Journal of Philosophical Logic, vol. 7, pp. 307329.
Moore, G.H. (1982), Zermelo's Axiom of Choice: its Origins, Development, and Influence, Springer, New York.
Neumann, J. von (1927), Zur Hilbertschen Beweistheorie, Mathematische Zeitschrift, vol. 26, pp. 146.
Peano, G. (1889), Arithmetices principia nova methodo exposita, Bocca & Clausen, Torino.
Peckhaus, V. (1990), Hilbertprogramm und kritische Philosophie, Vandenhoeck & Ruprecht, Göttingen.
Peckhaus, V. (1994), Logic in Transition: the Logical Calculi of Hilbert (1905) and Zermelo (1908), Logic and Philosophy of Science in Uppsala (Prawitz, D. and Westerstähl, D., editors), Kluwer, Amsterdam, pp. 311323.
Peckhaus, V. (1996), The influence of Hermann Günther Grassmann and Robert Grassmann on Ernst, Schröder's Algebra of Logic, Hermann Günther Grassmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar (Schubring, G., editor), Kluwer, Dordrecht, Boston, London, pp. 217227.
Poincaré, H. (1894), Sur la nature du raisonnement mathématique, Revue de métaphysique et de morale, vol. 2, pp. 371384.
Poincaré, H. (1902), La Science et l'Hypothèse., Bibliothèque de philosophie scientifique, Paris.
Poincaré, H. (1905), Les mathématiques et la logique, Revue de métaphysique et de morale, vol. 13, pp. 815835.
Poincaré, H. (1906), Les mathématiques et la logique, Revue de métaphysique et de morale, vol. 14, pp. 294317.
Poincaré, H. (1908), L'invention mathématique, vol. 10, pp. 357371.
Poincaré, H. (1909), La logique de l'infini, Revue de métaphysique et de morale, vol. 17, pp. 461482.
Post, E.L. (1921), Introduction to a General Theory of Elementary Propositions, American Journal of Mathematics, vol. 43, pp. 163185.
Rescher, N. (1969), Many-valued Logic, McGraw-Hill, New York.
Russell, B. and Whitehead, A.N. (1910), Principia Mathematica I, Cambridge University Press, Cambridge.
Russell, B. and Whitehead, A.N. (1911), Principia Mathematica II, Cambridge University Press, Cambridge.
Russell, B. and Whitehead, A.N. (1912), Principia Mathematica III, Cambridge University Press, Cambridge.
Schröder, E. (1890), Vorlesungen über die Algebra der Logik, vol. 1, Teubner, Leipzig.
Sigwart, C. (1873), Logik, 3rd ed., Taupp, Tübingen, (1904), (This was the edition to which König referred).
Szénássy, B. (1992), History of Mathematics in Hungary until the 20th century, Springer, Berlin.
Wang, H. (1957), The Axiomatization of Arithmetic, Journal for Symbolic Logic, vol. 22, pp. 145158.
Wittgenstein, L. (1921), Logisch-philosophische Abhandlung, Annalen der Naturphilosophie, vol. 14, pp. 185262.
Zermelo, E. (1904), Beweis, dass jede Menge wohlgeordnet werden kann, Mathematische Zeitschrift, vol. 59, pp. 514516.
Zermelo, E. (1908), Untersuchungen über die Grundlagen der Mengenlehre I, Mathematische Annalen, vol. 65, pp. 261281.
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Bulletin of Symbolic Logic
  • ISSN: 1079-8986
  • EISSN: 1943-5894
  • URL: /core/journals/bulletin-of-symbolic-logic
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