Abstract
An argument has been in progress for some time between those who claim that mathematics is a discovery and those who insist that it is an invention: between, in other words, proponents of the theory that mathematics is independent of our knowledge of it until we explore the field of mathematics and proponents of the theory that mathematics is a creation of the human mind. The argument of course is one about mathematics, not in it,though the mathematicians themselves do occasionally get involved.
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F.P. Ramsey, The Foundations of Mathematics (New York 1931, Harcourt Brace), p. 2.
John von Neumann, “The Mathematician,” reprinted in James R. Newman (ed.), The World of Mathematics (New York 1956, Simon and Schuster), 4 vols., vol. 4, pp. 2053–2063
Stephen C. Kleene, Introduction to Mathematics (New York 1952, Van Nostrand), p. 45.
Philip E.B. Jourdain, “The Nature of Mathematics,” reprinted in Newman (ed.), The World of Mathematics (New York 1956, Simon and Schuster, 4 vols., vol. 1, pp. 67–8.
Alonzo Church, Introduction to Mathematical Logic, (Princeton 1956, University Press), n. 31
Frank P. Ramsey, The Foundations of Mathematics (New York 1931, Harcourt Brace), p. 14.
J.J. Sylvester, “The Study that Knows Nothing of Observation,” part of an Address to the British Association, 1869, reprinted in The World of Mathematics (New York 1962, Simon and Schuster), vol. 3, pp. 1758–1766.
David Hilbert, “The Foundations of Mathematics” in Jean van Heijnoort (ed.), From Frege to Gödel ( Cambridge, Mass., 1967, Harvard University Press ), p. 464.
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© 1979 Martinus Nijhoff, Publishers bv, The Hague
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Feibleman, J.K. (1979). The Discovery Theory in Mathematics. In: Assumptions of Grand Logics. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9278-8_12
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DOI: https://doi.org/10.1007/978-94-009-9278-8_12
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