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Remarks on finitism

from PART IV - PHILOSOPHY OF MODERN MATHEMATICAL AND LOGICAL THOUGHT

Published online by Cambridge University Press:  31 March 2017

Wilfried Sieg
Affiliation:
Carnegie Mellon University, Pennsylvania
Richard Sommer
Affiliation:
Stanford University, California
Carolyn Talcott
Affiliation:
Stanford University, California
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Reflections on the Foundations of Mathematics
Essays in Honor of Solomon Feferman
, pp. 410 - 419
Publisher: Cambridge University Press
Print publication year: 2002

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References

[1] P., Bernays, Die Philosophie der Mathematik und die Hilbertsche Beweistheorie, Blätter für deutsche Philosophie, vol. 4 (1930-31), pp. 326-367. Reprinted in [2]. A translation by P., Mancosu appears in[22], pp. 234-265.Google Scholar
[2] P., Bernays, Abhandlungen zur philosophie der mathematik, Darmstadt: Wissenschaftliche Buchgesellschaft, 1976.
[3] G., Gentzen, Die Widerspruchfreiheit der reinen Zahlentheorie, Mathematische Annalen, vol. 112 (1936), pp. 493-565.Google Scholar
[4] K., Gödel, Über formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme I, Monatshefte für Mathematik und Physik, vol. 38 (1931), pp. 173-198.
[5] K., Gödel, The present situation in the foundations of mathematics, [11], *1933o.
[6] K., Gödel, Lecture at Zilsel's, [11], *1938a
[7] K., Gödel, Über eine bisher noch nicht benutzte Erweiterung des finiten Standpunktes, Dialectica, vol. 12 (1958), pp. 280-287. Reprinted with an Englsh translation in [10]. [8] is a revised version.Google Scholar
[8] K., Gödel, On an extension of finitary mathematics which has not yet been used, [10], 1972.Revised version of [7].Google Scholar
[9] K., Gödel, Collected works, vol. I, Oxford: Oxford University Press, 1986.
[10] K., Gödel, Collected works, vol. II, Oxford: Oxford University Press, 1990.
[11] K., Gödel, Collected works, vol. III, Oxford: Oxford University Press, 1995.
[12] D., Hilbert, Über das Unendliche, Mathematische Annalen, vol. 95 (1926), pp. 161-90. Translated by Stefan Bauer-Mengelberg in [29, 367-92].Google Scholar
[13] D., Hilbert, Die Grundlagen derMathematik, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität 6 (1928), (1927). Translated in [29] pp. 464-479.
[14] D., Hilbert, Die Grundlegung der elementaren Zahlenlehre, Mathematische Annalen, vol. 104 (1930), pp. 485-494. Reprinted in part in [15].Google Scholar
[15] D., Hilbert, Gesammelte Abhandlungen, vol. 3, Berlin: Springer, 1935.
[16] D., Hilbert and P., Bernays, Grundlagen derMathematik I, Berlin: Springer-Verlag, 1934, The second edition was published in 1968.
[17] D., Hilbert, Grundlagen der Mathematik II, Berlin: Springer-Verlag, 1939, The second edition was published in 1970.
[18] A., Ignjatovic, Hilbert's program and the omega rule, The Journal of Symbolic Logic, vol. 59 (1994), pp. 322-343.Google Scholar
[19] A., Kino, J., Myhill, and R., Vesley (editors), Intuitionism and proof theory, Amsterdam: North- Holland, 1970.
[20] G., Kreisel, Ordinal logics and the characterization of informal notions of proof, Proceedings of the International Congress of Mathematicians, Edinburgh, (1958), pp. 289-299.
[21] G., Kreisel Principles of proof and ordinals implicit in given concepts, [19], (1970), pp. 489-516.
[22] P., Mancosu (editor), From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920's, Oxford: Oxford University Press, 1998.
[23] K-G., Niebergall and M., Schirn, Hilbert's finitism and the notion of infinity, [24], (1998), pp. 271-306.
[24] M., Schirn (editor), The philosophy of mathematics today, Oxford: Clareendon Press, 1998.
[25] W., Sieg, Calculations by man and machine, Technical report, Carnegie Mellon, 2000.
[26] W.W., Tait, Nested recursion, Mathematische Annalen, vol. 143 (1961), pp. 236-250.Google Scholar
[27] W.W., Tait, Constructive reasoning, [30], (1967), pp. 185-199.
[28] W.W., Tait, Finitism, Journal of Philosophy, vol. 78 (1981), pp. 524-556.Google Scholar
[29] J., van Heijenoort (editor), From Frege to Gödel: A source book in mathematical logic, Cambridge: Harvard University Press, 1967.
[30] B., van Rootselaar and J.F., Staal (editors), Logic, methodology and philosophy of science III, Amsterdam: North-Holland, 1968.
[31] R., Zach, Numbers and functions in Hilbert's finitism, Taiwanese Journal for Philosophy and History of Science, vol. 10 (1998), pp. 33-60.Google Scholar

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