Abstract
In his paper ‘History of Mathematics: Why and How’ for the 1978 International Congress of Mathematicians in Helsinki, André Weil makes the following statement:
»Some universities have established chairs for ‘the history and philosophy of mathematics’; it is hard for me to imagine what those two subjects can have in common.» (Weil, 1980, p. 230.)
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Bibliography
Agassi, J., Towards a Historiography of Science, Mouton, The Hague, 1963.
Barwise, J., ‘Axioms for Abstract Model Theory’, Annals of Mathematical Logic 7 (1974), 221–265.
Benacerraf, P. and Putnam, H. (eds.), Philosophy of Mathematics: Selected Readings, Blackwell, Oxford, 1964.
Beth, E.W., The Foundations of Mathematics, North-Holland, Amsterdam, 1959.
Bishop, E., Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.
Defletsen, M. and Luker, M., ‘The Four-Color Theorem and Mathematical Proof’, The Journal of Philosophy 77 (1980), 803–820.
Dummett, M., Elements of Intuitionism, Oxford University Press, Oxford, 1977.
Dummett, M., Truth and Other Enigmas, Duckworth, Oxford, 1978.
Feyerabend, P., Against Method, NLB, London, 1975.
Fine, A., ‘Conceptual Change in Mathematics and Science: Lakatos’ Stretching Refined’, in P. Asquith and I. Hacking (eds.), PSA 1978, vol. 2, Philosophy of Science Association, East Lansing, 1981, pp. 328–341.
Hacking, I., The Emergence of Probability, Cambridge University Press, Cambridge, 1975.
Hadamard, J., The Psychology of Invention in the Mathematical Field, Dover, New York, 1954.
Hallett, M., ‘Towards a Theory of Mathematical Research Programmes I—II’, The British Journal for the Philosophy of Science 30 (1979), 1–25, 135–159.
Henkin, L. et al. (eds.), Proceedings of the Tarski Symposium, American Mathematical Society, Providence, 1974.
Heyting, A., Intuitionism, North-Holland, Amsterdam, 1956.
Hintikka, J., ‘Surface Information and Depth Information’, in J. Hintikka and P. Suppes (eds.), Information and Inference, D. Reidel, Dordrecht, 1970.
Hintikka, J. and Remes, U., The Method of Analysis, Reidel, Dordrecht, 1974.
Hintikka, J., Gruender, D. and Agazzi, E. (eds.), Proceedings of the 1978 Pisa Conference on the History and Philosophy of Science, vol. II, D. Reidel, Dordrecht, 1981.
Howson, C. (ed.), Method and Appraisal in the Physical Sciences, Cambridge University Press, Cambridge, 1976.
Howson, C., ‘Methodology in Non-Empirical Disciplines’, in G. Radnitzky and G. Andersson (eds.), The Structure and Development of Science, Reidel, Dordrecht, 1979, pp. 257–266.
Knorr, W., The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry, D. Reidel, Dordrecht, 1975.
Kuhn, T.S., The Structure of Scientific Revolutions, 2nd ed., University of Chicago Press, Chicago, 1970.
Kuhn, T.S., The Essential Tension, The University of Chicago Press, Chicago, 1977.
Lakatos, I., ‘History of Science and Its Rational Reconstructions’, in Howson (1976), pp. 1–39.
Lakatos, I., Proofs and Refutations: The Logic of Mathematical Discovery,Cambridge University Press, Cambridge, 1976. (Published first in 1963–64.)
Lakatos, I., Philosophical Papers vol. 2: Mathematics, Science and Epistemology, Cambridge University Press, Cambridge, 1978.
Lehti, R., ‘Matemaattisen ajattelutavan kehitys’, in Logiikka ja matematiikka, WSOY, Porvoo, 1971, pp. 75–97.
Lindström, P., ‘On Extensions of Elementary Logic’, Theoria 35 (1969), 1–11.
MacLane, S., Categories for the Working Mathematician, 1971.
Maistrov, L.E., Probability Theory: A Historical Sketch, Academic Press, New York, 1974.
Moulines, C.U., ‘Theory-Nets and the Evolution of Theories: The Example of Newtonian Mechanics’, Synthese 41 (1979), 417–439.
Musgrave, A., ‘Logicism Revisited’, The British Journal for the Philosophy of Science 28 (1977), 99–127.
Nola, R., ’»Paradigms Lost, or the World Regained» — An Excursion into Realism and Idealism in Science’, Synthese 45 (1980), 317–350.
Paris, J. and Harrington, L., ‘A Mathematical Incompleteness in Peano arithmetic’, in J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 1133–1142.
Polya, G., How to Solve It, Princeton University Press, Princeton, 1945.
Popper, K.R., Conjectures and Refutations, Routledge and Kegan Paul, London, 1963.
Price, D. de Solla, Little Science, Big Science, Columbia University Press, New York, 1963.
Rescher, N., Scientific Progress: A Philosophical Essay on the Economics of Research in Natural Science, Blackwell, Oxford, 1978.
Sarton, G., The Study of the History of Mathematics and the Study of the History of Science, Dover, New York, 1957.
Simon, H., Langley, P. and Bradshaw, G., ‘Scientific Discovery as Problem Solving’, Synthese 47 (1981), 1–27.
Struik, D., A Concise History of Mathematics, Dover, New York, 1967.
Teller, P., ‘Computer Proof’, The Journal of Philosophy 77 (1980), 797–803.
Todhunter, I., A History of the Theory of Probability from the Time of Pascal to that of Laplace,Cambridge, 1865. (Chelsea, New York, 1965.)
Tymoczko, T., ‘The Four-Color Problem and Its Philosophical Significance’, The Journal of Philosophy 76 (1979), 57–83.
Weil, A., ‘History of Mathematics: Why and How?’, in O. Lehto (ed.), Proceedings of the International Congress of Mathematicians, Helsinki, 1978, Helsinki, 1980, pp. 227–236.
Wright, C., Wittgenstein on the Foundations of Mathematics, Duckworth, London, 1980.
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Niiniluoto, I. (1984). The Growth of Knowledge in Mathematics. In: Is Science Progressive?. Synthese Library, vol 177. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1978-0_8
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DOI: https://doi.org/10.1007/978-94-017-1978-0_8
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