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Philosophy Research Archives

Volume 1, 1975

James L. Hudson
Pages 135-140

Frege's Way Out

I show that Frege's statement (In the Epilogue to his Grundgesetze der Arithmetic v. II) of a way to avoid Russell's paradox is defective, in that he presents two different methods as if they were one. One of these "ways out" is notably more plausible than the other, and is almost surely what Frege really intended. The well-known arguments of Lesniewski, Geach, and Quine that Frege's revision of his system is inadequate to avoid paradox are not affected by the ambiguity of Frede's statement. But a rectnt argument by Linsky and Schumm (Analysis 82 (1971-72), 5-7), intended as a very simple derivation of a contradiction within Frege's revised system, is valid only for the less plausible of the two versions of Frege's way out, and thus is not an effective attack on the revision that Frege intended to make.

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