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GÖDEL’S NOTRE DAME COURSE

Published online by Cambridge University Press:  30 December 2016

MILOŠ ADŽIĆ  and
KOSTA DOŠEN
MILOŠ ADŽIĆ
Affiliation:
FACULTY OF PHILOSOPHY UNIVERSITY OF BELGRADE ČIKA LJUBINA 18-20 11000 BELGRADE, SERBIAE-mail: milos.adzic@gmail.com
KOSTA DOŠEN
Affiliation:
MATHEMATICAL INSTITUTE SERBIAN ACADEMY OF SCIENCES AND ARTS KNEZ MIHAILOVA 36, P.F. 367 11001 BELGRADE, SERBIAE-mail: kosta@mi.sanu.ac.rs
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Abstract

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This is a companion to a paper by the authors entitled “Gödel’s natural deduction,” which presented and made comments about the natural deduction system in Gödel’s unpublished notes for the elementary logic course he gave at the University of Notre Dame in 1939. In that earlier paper, which was itself a companion to a paper that examined the links between some philosophical views ascribed to Gödel and general proof theory, one can find a brief summary of Gödel’s notes for the Notre Dame course. In order to put the earlier paper in proper perspective, a more complete summary of these interesting notes, with comments concerning them, is given here.

Keywords

01A6003-0103-03propositional logicpredicate logic
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 22 , Issue 4 , December 2016 , pp. 469 - 481
Copyright
Copyright © The Association for Symbolic Logic 2016 

References

REFERENCES

Bernays, P., Axiomatische Untersuchung des Aussagen-Kalkuls der “Principia Mathematica” . Mathematische Zeitschrift, vol. 25 (1926), pp. 305–320.Google Scholar
Carroll, L., What the Tortoise said to Achilles . Mind, vol. 4 (1895), pp. 278–280.Google Scholar
Cassou-Noguès, P., Gödel’s introduction to logic in 1939 . History and Philosophy of Logic, vol. 30 (2009), pp. 69–90.Google Scholar
Dawson, J. W. Jr., Logical Dilemmas: The Life and Work of Kurt Gödel, Peters, Wellesley, 1997.Google Scholar
Dawson, J. W. Jr., Kurt Gödel at Notre Dame. Logic at Notre Dame , pp. 4–10, available at https://math.nd.edu/assets/13975/logicatndweb.pdf.Google Scholar
[6] Dawson, J. W. Jr. and Dawson, C. A., Future tasks for Gödel scholars, this Bulletin, vol. 11 (2005), pp. 150–171.Google Scholar
Došen, K. and Adžić, M., Gödel on deduction, preprint, available at http://www.mi.sanu.ac.rs/∼kosta/DAgoedded.pdf; http://arXiv.org.Google Scholar
Došen, K. and Adžić, M., Gödel’s natural deduction, preprint, available at http://www.mi.sanu.ac.rs/∼kosta/DAgoednatded.pdf; http://arXiv.org.Google Scholar
Dummett, M. A. E., A propositional calculus with denumerable matrix . The Journal of Symbolic Logic, vol. 24 (1959), pp. 97–106.Google Scholar
Gentzen, G., Untersuchungen über das logische Schließen . Mathematische Zeitschrift, vol. 39 (1935), pp. 176–210, 405–431 (English translation: Investigations into logical deduction, The Collected Papers of Gerhard Gentzen , M. E. Szabo, editor and translator, North-Holland, Amsterdam, 1969, pp. 68–131, 312–317).Google Scholar
Gödel, K., Zum intuitionistischen Aussagenkalkül . Anzeiger der Akademie der Wissenschaften in Wien, vol. 69 (1932), pp. 65–66 (reprinted with an additional comment: Ergebnisse eines mathematischen Kolloquiums , vol. 4(1933), p. 40; reprinted with an English translation: On the intuitionistic propositional calculus, in [13], pp. 222–225).Google Scholar
Gödel, K., Eine Interpretation des intuitionistischen Aussagenkalküls . Ergebnisse eines mathematischen Kolloquiums, vol. 4 (1933), pp. 39–40 (reprinted with an English translation: An interpretation of the intuitionistic propositional calculus, in [13], pp. 296–303).Google Scholar
Gödel, K., Collected Works, Volume I, Publications 1929–1936 (Feferman, S., Dawson, J. W. Jr., Kleene, S. C., Moore, G. H., Solovay, R. M., and van Heijenoort, J., editors), Oxford University Press, New York, 1986.Google Scholar
Gödel, K., Collected Works, Volume V, Correspondence H-Z (Dawson, J. W. Jr., Goldfarb, W., Parsons, C., and Sieg, W., editors), Oxford University Press, New York, 2003.Google Scholar
Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, Springer, Berlin, 1928 (English translation: Principles of Theoretical Logic , Chelsea, New York, 1950).Google Scholar
Jaśkowski, S., On the rules of suppositions in formal logic . Studia Logica, vol. 1 (1934), pp. 5–32 (reprinted in: Polish Logic 1920–1939 , S. McCall, editor, Oxford University Press, Oxford, 1967, pp. 232–258).Google Scholar
Kalmár, L., Über die Axiomatisierbarkeit des Aussagenkalküls . Acta litterarum ac scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, sectio scientiarum mathematicarum, vol. 7 (1935), pp. 222–243.Google Scholar
Kant, I., Logik: Ein Handbuch zu Vorlesungen , Friedrich Nicolovius, Königsberg, 1800 (English translation: The Jäsche logic , Lectures on Logic, Young, J. M., editor and translator, Cambridge University Press, Cambridge, 1992).Google Scholar
Lawvere, F. W., Adjointness in foundations . Dialectica , vol. 23 (1969), pp. 281–296.Google Scholar
Łukasiewicz, J., Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic, Oxford University Press, Oxford, 1950 (second edition, 1957).Google Scholar
Shepherdson, J. C., On the interpretation of Aristotelian syllogistic . The Journal of Symbolic Logic, vol. 21 (1956), pp. 137–147.Google Scholar
[22] The ASL Committee on Logic and Education, Guidelines for logic education, this Bulletin, vol. 1 (1995), pp. 4–7.Google Scholar
Wajsberg, M., Ein erweiteter Klassenkalkül . Monatshefte für Mathematik und Physik, vol. 40 (1933), pp. 113–126.Google Scholar
Whitehead, A. N. and Russell, B., Principia Mathematica, Volume I, Cambridge University Press, Cambridge, 1910.Google Scholar
Wittgenstein, L., Logisch-philosophische Abhandlung . Annalen der Naturphilosophie, vol. 14 (1921), pp. 185–262 (English translation by C. K. Ogden: Tractatus logico-philosophicus , Routledge, London, 1922; new translation by D. F. Pears and B. F. McGuinness, Routledge, London, 1961).Google Scholar
[26] Zach, R., Completeness before Post: Bernays, Hilbert, and the development of propositional logic, this Bulletin, vol. 5 (1999), pp. 331–366.Google Scholar