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References
Benacerraf, P.: 1965, ‘What Numbers Could Not Be’, Philosophical Review 74, 47–73.
Benacerraf, P.: 1973, ‘Mathematical Truth’, The Journal of Philosophy 70, 661–79.
Benacerraf, P. and H. Putnam (eds.): 1984, Philosophy of Mathematics: Selected Readings, 2nd. edn., Cambridge University Press, Cambridge, Mass.
Carnap, R.: 1956, ‘Empiricism, Semantics, and Ontology’, Meaning and Necessity, 2nd. edn., University of Chicago Press, Chicago, reprinted in 3.
Chihara, C.: 1973, Ontology and the Vicious Circle Principle, Cornell University Press, Ithaca.
Dedekind, R.: 1888, Was sind und was sollen die Zahlend, Brunswick, Vieweg.
Dummett, M.: 1963, ‘The Philosophical Significance of Gödel's Theorem’, Ratio 5, 140–55, reprinted in 11, page references are to 11.
Dummett, M.: 1963, ‘Platonism’, first published in 11.
Dummett, M.: 1975, ‘The Philosophical Basis of Intuitionistic Logic’, H. E. Rose and J. C. Shepherson (eds.), Logic Colloquium '73, North-Holland, pp. 5–40, reprinted in 11, page references are to 11.
Dummett, M.: 1977, Elements of Intuitionism, Clarendon Press, Oxford.
Dummett, M.: 1978, Truth and Other Enigmas, Harvard University Press, Cambridge, Mass.
Field, H.: 1980, Science Without Numbers, Princeton University Press, Princeton, N.J.
Field, H.: 1981, ‘Realism and Anti-Realism About Mathematics’, Rice University Conference on Realism and Anti-Realism, unpublished.
Frege, G.: 1884, Die Grundlagen der Arithmetik, Verlag von Wilhelm Koebner, Breslau.
Gödel, K.: 1947, ‘What Is Cantor's Continuum Problem?’, American Mathematical Monthly 54, 515–25. A revised and supplemented version appears in 3. Page references are to 3. ‘Gödel 1964’ refers to the supplement in the later version (which first appeared in the 1st. edn. of 3 in 1964).
Jubien, M.: 1977, ‘Ontology and Mathematical Truth’, Nous 11.
Kitcher, P.: 1978, ‘The Plight of the Platonist’, Nous 12, 119–36.
Kitcher, P.: 1983, The Nature of Mathematical Knowledge, Oxford University Press.
Lawvere, W.: 1964, ‘An Elementary Theory of the Category of Sets’, Proceedings of the National Academy of Science 52, 1506–11.
Lear, T.: 1982, ‘Leaving the World Alone’, The Journal of Philosophy.
Maddy, P.: 1980, ‘Perception and Mathematical Intuition’, Philosophical Review 89, 163–96.
Parsons, C.: 1979–80, ‘Mathematical Intuition’, Proceedings of the Aristotelian Society pp. 145–68.
Putnam, H.: 1979, ‘Analyticity and Aprioricity: Beyond Wittgenstein and Quine’, Midwest Studies in Philosophy IV (Studies in Metaphysics).
Quine, W. V.: 1953, ‘On What There Is,’ From A Logical Point of View: Harvard University Press, Harvard.
Steiner, M.: 1975, Mathematical Knowledge, Cornell University Press, Ithaca.
Tait, W.: 1983, ‘Against Intuitionism: Constructive Mathematics Is a Part of Classical Mathematics’, The Journal of Philosophy 12, 173–95.
Wittgenstein, L.: 1953, Philosophical Investigations, Macmillan.
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Earlier versions of this paper were presented to the Philosophy Department of the University of Wisconsin at Madison in the Winter of 1984, at the Tarski Memorial Conference at Ohio State in the spring of 1984 and at the Pacific Division meeting of the APA in the spring of 1985. I received many valuable comments on all of these occasions and, in particular, from Paul Benacerraf and Clifton McIntosh, who commented on my paper at the APA meeting. I should also like to thank Michael Friedman for his comments on an earlier version and for our many discussions of its subject matter.
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Tait, W.W. Truth and proof: The Platonism of mathematics. Synthese 69, 341–370 (1986). https://doi.org/10.1007/BF00413978
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DOI: https://doi.org/10.1007/BF00413978