This is a preview of subscription content, log in via an institution to check access.
References
Becker, O.: 1975,Grundlagen der Mathematik in geschichtlicher Entwicklung, Suhrkamp, Frankfurt.
Benacerraf, P., and H. Putnam (eds.): 1964,Philosophy of Mathematics: Selected Readings, 1st ed., Prentice-Hall, Englewood Cliffs.
Bernays, P.: 1964, ‘On Platonism in Mathematics’, in Benacerraf and Putnam (1964), pp. 274–86 (trans. of Bernays, 1934).
Bolzano, B.: 1950,The Paradoxes of the Infinite, trans. F. Prihonsky, Yale University Press, New Haven.
Brouwer, L. E. J.: 1964, ‘Intuitionism and Formalism’, in Benacerraf and Putnam (1964), pp. 66–77 (trans. of Brouwer, 1912).
Chihara, C.: 1990,Constructibility and Mathematical Existence, Clarendon Press, Oxford.
Dalen, D. van: 1979, ‘Brouwer: the Genesis of his Intuitionism’,Dialectica 32, 291–303.
Davis, P. J., and R. Hersh: 1981,The Mathematical Experience, Birkhauser, Boston.
Diamond, C. (ed.): 1976,Wittgenstein's Lectures on the Foundations of Mathematics. Cambridge 1939, Cornell University Press, Ithaca.
Dummett, M. A. E.: 1964, ‘Wittgenstein's Philosophy of Mathematics’, in Benacerraf and Putnam (1964), pp. 491–509.
Feferman, S. et al.: 1990,Kurt Gödel. Collected Works. Volume II, Oxford University Press, Oxford.
Føllesdal, D.: 1992, ‘Gödel and Husserl’, Lecture presented to the Boston University conference on the History of the Foundations of Mathematics, Boston Colloquium for the Philosophy of Science, 6 April 1992.
Gödel, K.: 1964a, ‘Russell's Mathematical Logic’, in Benacerraf and Putnam (1964), pp. 211–32 (repr. of Gödel, 1944).
Gödel, K.: 1964b, ‘What is Cantor's Continuum Problem?’, in Benacerraf and Putnam (1964), pp. 258–73 (version of Gödel, 1947).
Gödel, K.: 1990a, ‘On an Extension of Finitary Mathematics which has not yet been used (1972)’, in Feferman et al. (1990), pp. 271–80 (repr. of Gödel, 1972).
Gödel, K.: 1990b, ‘A Remark about the Relationship between Relativity Theory and Idealistic Philosophy’, in Feferman et al. (1990), pp. 202–07 (repr. of Gödel, 1949).
Heyting, A.: 1964a, ‘The Intuitionist Foundations of Mathematics’, in Benacerraf and Putnam (1964), pp. 42–49 (trans. of Heyting, 1931).
Heyting, A.: 1964b, ‘Disputation’, in Benacerraf and Putnam (1964), pp. 55–65 (repr. from Heyting, 1956).
Kreisel, G.: 1985, ‘Mathematical Logic: Tool and Object Lesson for Science’,Synthese 62, 139–51.
Maddy, P.: 1990,Realism in Mathematics, Clarendon Press, Oxford.
Molk, J.: 1885, ‘Sur une notion qui comprend celle de la divisibilité et sur la theorie de l'elimination’,Acta Mathematica 6, 1–166.
Norris, C.: 1987,Derrida, Harvard University Press, Cambridge.
Parsons, C.: 1983,Mathematics in Philosophy. Selected Essays, Cornell University Press, Ithaca.
Parsons, C.: 1990, ‘Introductory Note to Gödel 1944’, in Feferman et al. (1990), pp. 102–18.
Russell, B., and A. N. Whitehead: 1910, 1912, 1913,Principia Mathematica, Cambridge University Press, Cambridge (Vol. 1 (1910), Vol. 2 (1912), Vol. 3 (1913)).
Stein, H.: 1990, ‘Introductory Note to Gödel 1949a’, in Feferman et al. (1990), pp. 199–201.
Stigt, W. P. van: 1976, ‘The Rejected Parts of Brouwer's Dissertation on the Foundation of Mathematics’,Historia mathematica 6, 385–404.
Troelstra, A. S., and D. van Dalen: 1988,Constructivism in Mathematics: An Introduction, Vols. I and II, North-Holland, Amsterdam.
Wang, H.: 1987,Reflections on Kurt Gödel, MIT Press, Cambridge.
Rights and permissions
About this article
Cite this article
McCarty, D.C. On the failure of mathematics' philosophy. Synthese 96, 255–291 (1993). https://doi.org/10.1007/BF01306898
Issue Date:
DOI: https://doi.org/10.1007/BF01306898