Notre Dame Journal of Formal Logic

Russell, Presupposition, and the Vicious-Circle Principle

Darryl Jung

Abstract

Prompted by Poincaré, Russell put forward his celebrated vicious-circle principle (vcp) as the solution to the modern paradoxes. Ramsey, Gödel, and Quine, among others, have raised two salient objections against Russell's vcp. First, Gödel has claimed that Russell's various renderings of the vcp really express distinct principles and thus, distinct solutions to the paradoxes, a claim that gainsays one of Russell's positions on the nature of the solution to the paradoxes, namely, that such a solution be uniform. Secondly, Ramsey, Gödel, and Quine have protested that the vcp's proscription against impredicative specification is incompatible with a realistic conception of the domain of quantification, a conception that Russell certainly held. I examine Russell's vcp and defend it against these objections.

Article information

Source
Notre Dame J. Formal Logic Volume 40, Number 1 (1999), 55-80.

Dates
First available: 5 December 2002

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1039096305

Mathematical Reviews number (MathSciNet)
MR1811203

Digital Object Identifier
doi:10.1305/ndjfl/1039096305

Zentralblatt MATH identifier
0968.03012

Subjects
Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 03-03: Historical (must also be assigned at least one classification number from Section 01)

Citation

Jung, Darryl. Russell, Presupposition, and the Vicious-Circle Principle. Notre Dame Journal of Formal Logic 40 (1999), no. 1, 55--80. doi:10.1305/ndjfl/1039096305. http://projecteuclid.org/euclid.ndjfl/1039096305.


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