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An Editor Recalls Some Hopeless Papers

Published online by Cambridge University Press:  15 January 2014

Wilfrid Hodges
Wilfrid Hodges*
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, England, U.K.E-mail: [email protected]
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Extract

§1. Introduction. I dedicate this essay to the two-dozen-odd people whose refutations of Cantor's diagonal argument (I mean the one proving that the set of real numbers and the set of natural numbers have different cardinalities) have come to me either as referee or as editor in the last twenty years or so. Sadly these submissions were all quite unpublishable; I sent them back with what I hope were helpful comments. A few years ago it occurred to me to wonder why so many people devote so much energy to refuting this harmless little argument—what had it done to make them angry with it? So I started to keep notes of these papers, in the hope that some pattern would emerge.

These pages report the results. They might be useful for editors faced with similar problem papers, or even for the authors of the papers themselves. But the main message to reach me is that there are several points of basic elementary logic that we usually teach and explain very badly, or not at all.

In 1995 an engineer named William Dilworth, who had published a refutation of Cantor's argument in the Transactions of the Wisconsin Academy of Sciences, Arts and Letters, sued for libel a mathematician named Underwood Dudley who had called him a crank ([9] pp. 44f, 354).

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 4 , Issue 1 , March 1998 , pp. 1 - 16
Copyright
Copyright © Association for Symbolic Logic 1998

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References

REFERENCES

[1] Aristotle, , Metaphysics X–XIV, Loeb Classical Library, Harvard University Press, Cambridge, Mass., 1935.Google Scholar
[2] Barrow, John D., Theories of everything: the quest for ultimate explanation, Oxford University Press, Oxford, 1990.Google Scholar
[3] Barwise, Jon and Etchemendy, John, The liar, Oxford University Press, New York, 1987.Google Scholar
[4] Benacerraf, Paul, What numbers could not be, Philosophy of mathematics, Selected readings (Benacerraf, Paul and Putnam, Hilary, editors), Cambridge University Press, Cambridge, 2nd ed., 1983, pp. 272–294.Google Scholar
[5] Beth, E.W., Semantic entailment and formal derivability, The philosophy of mathematics (Hintikka, Jaakko, editor), Oxford University Press, 1969, pp. 9–41.Google Scholar
[6] Cantor, Georg, Über eine Eigenschaft des Inbegriffes aller reellen algebraischen Zahlen, Journal für die reine und angewandte Mathematik, vol. 77 (1874), pp. 258–262.Google Scholar
[7] Cantor, Georg, Über eine elementare Frage der Mannigfaltigkeitslehre, Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. I (1891), pp. 75–78.Google Scholar
[8] Carroll, Lewis, What the tortoise said to Achilles, Mind, vol. 4 (1895), pp. 278–280.Google Scholar
[9] Dudley, Underwood, Mathematical cranks, Mathematical Association of America, Washington, DC, 1992.Google Scholar
[10] Dummett, Michael, Frege, philosophy of language, Duckworth, London, 1973.Google Scholar
[11] Fisher, Alec, The logic of real arguments, Cambridge University Press, Cambridge, 1988.Google Scholar
[12] Fraenkel, Abraham A., Abstract set theory, 4th ed., North-Holland, Amsterdam, 1976, revised by Azriel Lévy.Google Scholar
[13] Gelernter, H., Realization of a geometry theorem-proving machine, Proceedings of international conference on information processing, UNESCO House, Paris, 1959, pp. 273–282.Google Scholar
[14] Gödel, Kurt, Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Collected works (Feferman, S. et al., editors), vol. II, Oxford University Press, Oxford, 1990, pp. 240–251.Google Scholar
[15] Hodges, Wilfrid, Critical commentary on P. Johnson-Laird and R. Byrne, ‘Deduction’, Behavioral and Brain Sciences, vol. 16 (1993), p. 353f.Google Scholar
[16] Johnson-Laird, P. N. and Byrne, Ruth M. J., Deduction, Lawrence Erlbaum, Hove, 1991.Google Scholar
[17] Kamp, Hans and Reyle, Uwe, From discourse to logic, Kluwer, Dordrecht, 1993.Google Scholar
[18] Kleene, Stephen Cole, Introduction to metamathematics, North-Holland, Amsterdam, 1952.Google Scholar
[19] Rips, Lance J., The psychology of proof, MIT Press, Cambridge, Mass., 1994.Google Scholar
[20] Russell, Bertrand, The principles of mathematics, George Allen and Unwin, London, 1903.Google Scholar
[21] Smith, D. E., History of mathematics, vol. II, Dover, New York, 1958.Google Scholar
[22] Wittgenstein, Ludwig, Remarks on the foundations of mathematics, Blackwell, Oxford, 1956.Google Scholar