Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-28T09:15:11.199Z Has data issue: false hasContentIssue false

Is Russell's Paradox Genuine?

Published online by Cambridge University Press:  25 February 2009

James Moulder
Affiliation:
Rhodes University, Grahamstown, South Africa

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
Copyright
Copyright © The Royal Institute of Philosophy 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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. 320Google Scholar; and van Heijenoort, J., ‘Logical Paradoxes’ in The Encyclopedia of Philosophy, Vol. 5, ed. Edwards, P. (London, 1968) pp. 4551Google Scholar. I will refer to these three discussions as C, Q, and H, respectively.