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Why Russell's Paradox Won't Go Away

Published online by Cambridge University Press:  30 January 2009

Francis Moorcroft
Francis Moorcroft
Affiliation:
University of Hull
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Extract

In ‘The Mind's I is Illiterate’, G. S. Miller discusses several paradoxes and paradoxical sentences which Miller claims are related by a common abuse of language. The Whiteley sentence ‘Lucas cannot consistently believe this sentence’ fails to be meaningful for want of a referent outside of the sentence for the phrase ‘this sentence’; the Liar Paradox when formulated as ‘I am lying’ is similarly disposed of when it is seen that the verb is defective and the sentence fails to refer to anything outside of itself. The same point is made concerning the Russell Paradox of the set of all sets that do not belong to themselves. The moral made is that philosophers are simply to be more careful about the laneuaee that thev are usine and then the paradoxes will go away.

Type
Discussion
Information
Philosophy , Volume 68 , Issue 263 , January 1993 , pp. 99 - 103
Copyright
Copyright © The Royal Institute of Philosophy 1993

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References

1 Miller, G. S., ‘The Mind's I is Illiterate’, Philosophy, 01 1992.Google Scholar

2 Cantor, G.Gesammelte Abhandlungen Mathematischen und philoso-phishen Inhalt. Zermelo, E. (ed.), (Berlin: Springer 1932), 238.Google Scholar

3 Cantor, ibid., 204.

4 Miller, ibid., 111.

5 Ibid.

6 Thanks are due to A. J. Dale for discussing matters raised in this paper.