Abstract
When Alice answered Humpty Dumpty’s query about the number of her unbirthdays by saying it results from taking 1 from 365 to yield 364, Humpty Dumpty’s demur that he’d rather see that done on paper, strikes us as ludicrous simply because 365 − 1 = 364 is a paradigm of certainty. Beyond the shadow of a doubt. Bertrand Russell reported that when he set out to find certainty he looked to mathematics because he thought it ‘more likely to be found there than elsewhere’.1 What he found was disappointing: demonstrations he was expected to accept were ‘full of fallacies’, instead of being ‘safe, beyond controversy, and final’.2 He thereupon devoted himself to laying a foundation which would make mathematics secure.
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Notes
Cf. B. Russell, Portraits from Memory and other Essays (London: George Allen & Unwin, 1956) p. 18ff.
G. Polya, Induction and Analogy in Mathematics (Oxford University Press, 1964) Preface.
D. J. O’Connor and Brian Carr, Introduction to the Theory of Knowledge (Brighton: Harvester Press, and University of Minnesota Press, 1982).
Imre Lakatos, ‘A Renaissance of Empiricism in the Recent Philosophy of Mathematics?’, in New Directions in the Philosophy of Mathematics. an anthology edited by Thomas Tymoczko (Boston; Basel; Stuttgart: Birkhäuser, 1986) It will be evident throughout how much I have gained from this excellent collection of essays.
W. V.O. Quine, ‘Two Dogmas of Empiricism’ in his From a Logical Point of View (Harvard University Press, 1964) p. 43.
John Stuart Mill, A System of Logic (New York: Harper & Brothers, 1856) p. 153.
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W. V.O. Quine, From a Logical Point of View (Harvard University Press, 1964) p. 13.
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R. Courant and H. Robbins, What is Mathematics? (Oxford University Press, 1941) p. 53.
H. P. Grice and P. F. Strawson, ‘In Defence of a Dogma’, in L. W. Sumner and J. Woods (eds), Necessary Truth (New York: Random House, 1969) p. 143.
L. Wittgenstein, Tractatus Logico-Philosophus (London: Routledge & Kegan Paul, 1961) 6.112.
D. S. Swayder, ‘Wittgenstein on Mathematics’ in Peter Winch (ed.) Studies in the Philosophy of Wittgenstein (London: Routledge & Kegan Paul, 1969) p. 103.
C. Adam and P. Tannery (eds), Descartes’ Oeuvres (Paris: 1897–1913), Vol. 10, (1901), (tr) G. Polya.
G. Polya, How to Solve It (Princeton University Press, 1945) p. 103.
K. Gödel, ‘Russell’s Mathematical Logic’, in P. Benacerraf and H. Putnam (eds), Philosophy of Mathematics (Eaglewood Cliffs: Prentice-Hall, 1964) p. 213.
L. Wittgenstein, Remarks on the Foundation of Mathematics (Oxford: Blackwell, 1956) p. 173.
L. Wittgenstein, Philosophical Investigations (Oxford: Basil Blackwell, 1953) p. 39.
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© 1991 Palgrave Macmillan, a division of Macmillan Publishers Limited
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Ambrose, A. (1991). On Certainty. In: Mahalingam, I., Carr, B. (eds) Logical Foundations. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-21232-3_6
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