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Is Russell's Paradox Genuine?

Published online by Cambridge University Press:  25 February 2009

James Moulder
James Moulder
Affiliation:
Rhodes University, Grahamstown, South Africa
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Extract

Copi, Quine and van Heijenoort have each claimed that there are two fundamentally different kinds of logical paradox; namely, genuine paradoxes like Russell's and pseudo-paradoxes like the Barber of Seville. I want to contest this claim and will present my case in three stages. Firstly, I will characterize the logical paradoxes; state standard versions of three of them; and demonstrate that a symbolic formulation of each leads to a formal contradiction. Secondly, I will discuss the reasons Copi, Quine and van Heijenoort have given for the distinction between genuine and pseudo-paradoxes. Thirdly, I will attempt to explain why there is no such class as the class of all and only those classes which are not members of themselves.

Type
Articles
Information
Philosophy , Volume 49 , Issue 189 , July 1974 , pp. 295 - 302
Copyright
Copyright © The Royal Institute of Philosophy 1974

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References

1 Copi, I. M., The Theory of Logical Types (London, 1971)Google Scholar; Quine, W. V., ‘Paradox’ in The Ways of Paradox (Cambridge, Mass., 1963) pp. 3–20Google Scholar; and van Heijenoort, J., ‘Logical Paradoxes’ in The Encyclopedia of Philosophy, Vol. 5, ed. Edwards, P. (London, 1968) pp. 45–51Google Scholar. I will refer to these three discussions as C, Q, and H, respectively.