Abstract
Hatcher’s main theme (Hatcher, 1972), that a pragmatic approach to foundational problems is the most salutary one, is, I hope, nowadays generally agreed. I will examine instead his two other main proposals: that the most fruitful, or useful way to view mathematics is as the exact part of our thinking, and that naturalness is an important intuitive criterion in elaborating foundational systems. Both proposals are meant to be taken intuitively and pragmatically, that is, Hatcher gives no substantial explanation of what he means by ‘exact’ and ‘natural’, and gives no argument for the desirability of his proposals other than that they account, in his opinion, for certain facets of mathematical practice. I hold both proposals to be unacceptable, for the (not ‘ultimate’, but largely pragmatically inspired) reasons which follow.
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Bibliography
Beth, E. W. and Piaget, J., 1961, Epistémologie mathématique et psychologie, Presses Universitaires de France, Paris. English translation (1966): Mathematical Epistemology and Psychology, Gordon and Breach, N.Y.
Bunge, M., 1962, Intuition and Science, Prentice-Hall, Englewood Cliffs, N.J.
Cleave, J. P., 1971, ‘Cauchy, Convergence and Continuity’, Brit. J. Phil. Sci. 22, 27–37.
Gonseth, F., 1970, ‘Mon itinéraire philosophique’, Revue internationale de philosophie, Nos. 93-94, Fasc. 3–4.
Hatcher, W. S., 1972, this volume, pp. 349–358.
Lakatos, I., 1963, ‘Proofs and Refutations (I)-(IV)’ Brit. J. Phil. Sci. 14 (1963-4), 1-25, 120-39, 221-45, 296–342.
Wang, H., 1958, ‘Eighty Years of Foundational Studies’, Dialectica 12, 466–97.
Wittgenstein, L., 1922, Tractatus Logico-Philosophicus, Routledge and Kegan Paul, London.
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© 1973 D. Reidel Publishing Company, Dordrecht, Holland
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Castonguay, C. (1973). Naturalism in Mathematics. In: Bunge, M. (eds) Exact Philosophy. Synthese Library, vol 50. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2516-4_7
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DOI: https://doi.org/10.1007/978-94-010-2516-4_7
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