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Proof by reductio ad absurdum*

Published online by Cambridge University Press:  03 November 2016

R.L. Goodstein
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Extract

If, like David Copperfield, you are on the road to Dover, for the first time and with no one to guide you, and you come to a point where the road forks, then of all your mathematical knowledge, only the method of reductio ad absurdum can help you. For if you choose the wrong turning, and find yourself in Folkestone, you may be quite sure you ought to have taken the other road.

Type
Research Article
Information
The Mathematical Gazette , Volume 32 , Issue 300 , July 1948 , pp. 198 - 204
Copyright
Copyright © The Mathematical Association 1948

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Footnotes

*

Lecture delivered to the General Meeting of the Mathematical Association, 10th April, 1947.

References

Brouwer, L.E.J. “Intuitionism and Formalism,” Bull. Amer. Math. Soc., 20, 1913.Google Scholar
Gentzen, G. “Die Widerspruchsfreiheit der reinen Zahlentheorie,” Math, Ann., 112, 1936.Google Scholar
Gödel, K. “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I.” Monatsheft f. Math. Phys., 38, 1931.Google Scholar
Goodstein, R.L. “Function theory in an axiom-free equation calculus,” Proc. of the London Math. Soc, Ser. 2, 48, 1945.Google Scholar
Goodstein, R.L. “Mathematical Systems,” Mind, 48, N.S., 189, 1939.Google Scholar
Heyting, A. “Mathematische Grundlagenforshung, Intuitionismus, Bewistheorie,” Erg. d. Math., 3, 4, Berlin, 1934.Google Scholar
Hilbert, D. “Über das Unendliche,” Math. Ann., 95, 1926.CrossRefGoogle Scholar
Lucasiewicz, J. “Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls,” C. R. Soc Sciences Varsovie, 23, 1930.Google Scholar
Post, E.L. “Introduction to a General Theory of Elementary Propositions,” Amer. Journ. Math., 43, 1921.Google Scholar
Reichenbach, H. Philosophic Foundations of Quantum Mechanics, University of California Press, 1946.Google Scholar