Article PDF
Avoid common mistakes on your manuscript.
References
Arai, T.: 1990, ‘Derivability Conditions on Rosser's Provability Predicates’, to appear in the Notre Dame Journal of Formal Logic.
Detlefsen, M.: 1986, Hilbert's Program, D. Reidel Publishing Co., Dordrecht.
Feferman, S.: 1960, ‘The Arithmetization of Metamathematics in a General Setting’, Fundamenta Mathematicae 49, 35–92.
Gentzen, G.: ‘The Consistency of Elementary Number Theory’, in M. E. Szabo (trans. and ed.), The Collected Works of Gerhard Gentzen, North-Holland Publishing Co., Amsterdam, 1969.
Gentzen, G.: 1938, ‘The Present State of Research into the Foundations of Mathematics’, in M. E. Szabo (trans. and ed.), The Collected Works of Gerhard Gentzen, North-Holland Publishing Co., Amsterdam, 1969.
Guaspari, D. and R.Solovay: 1979, ‘Rosser Sentences’, Annals of Mathematical Logic 16, 81–99.
Hilbert, D.: 1901, ‘Mathematical Problems’, Bulletin of the American Mathematical Society 8, 437–479.
Hilbert, D.: 1925, ‘On the Infinite’, in J. van Heijenoort (ed.), From Frege to Gödel, Harvard Univ. Press, Cambridge, 1967.
Hilbert, D.: 1927, ‘The Foundations of Mathematics’, in J. van Heijenoort (ed.), From Frege to Gödel, Harvard Univ. Press, Cambridge, 1967.
Hilbert, D.: 1930, Grundlagen der Geometrie, Teubner, Leipzig and Berlin, 7th. ed.
Hilbert, D.: 1931, ‘Die Grundlegung der elementaren Zahlenlehre’, in Gesammelte Abhandlungen, vol. 3, Julius Springer-Verlag (dy1935), Berlin.
Jeroslow, R.: 1975, ‘Experimental Logics and 377-1’, Journal of Philosophical Logic 4, 253–267.
Kreisel, G.: 1971, ‘A Survey of Proof Theory II’, in J. E. Fenstad (ed.), Proceedings of the Second Scandinavian Logic Symposium, North-Holland Publishing Co., Amsterdam.
Kreisel, G. and G.Takeuti: 1974, ‘Formally Self-Referential Propositions for Cut-Free Analysis and Related Systems’, Dissertationes Mathematicae 118, 4–50.
Kreisel, G.: 1976, ‘What Have We Learnt from Hilbert's Second Problem?’, AMS Proceedings of Symposia in Pure Mathematics 28, American Mathematical Society, Providence.
Kreisel, G.: 1980, ‘Kurt Gödel’, Biographical Memoirs of the Fellows of the Royal Society 26, 149–224.
Prawitz, D.: 1981, ‘Philosophical Aspects of Proof Theory’, in Contemporary Philosophy: A New Survey, vol. 1, Martinus Nijhof Publishers, The Hague.
Rosser, J. B.: 1936, ‘Extensions of Some Theorems of Gödel and Church’, Journal of Symbolic Logic 1, 87–91.
Sieg, W.: 1985, ‘Fragments of Arithmetic’, Annals of Pure and Applied Logic 28, 33–71.
Simpson, S.: 1988, ‘Partial Realizations of Hilbert's Program’, Journal of Symbolic Logic 53, 349–363.
Smorynski, C.: 1977, ‘The Incompleteness Theorems’, in J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland Publishing Co., Amsterdam.
Smorynski, C.: 1985, Self-Reference and Modal Logic, Springer-Verlag, New York.
Smorynski, C.: 1988, ‘Hilbert's Programme’, CWI Quarterly 1, 3–59.
Visser, A.: 1989, ‘Peano's Smart Children: A Provability Logical Study of Systems with Built-in Consistency’, Notre Dame Journal of Formal Logic 30, 161–196.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Detlefsen, M. On an alleged refutation of Hilbert's Program using Gödel's First Incompleteness Theorem. J Philos Logic 19, 343–377 (1990). https://doi.org/10.1007/BF00263316
Issue Date:
DOI: https://doi.org/10.1007/BF00263316