Chapter

The Vicious Circle Principle<sup>1</sup>

Peter Hylton

in Propositions, Functions, and Analysis

Published in print September 2005 | ISBN: 9780199286355
Published online May 2010 | e-ISBN: 9780191713309 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199286355.003.0006
The Vicious Circle Principle1

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The vicious-circle principle (VCP) is, according to Russell, a central and unifying idea in the type theory that is the basis of Principia Mathematica. Russell takes the principle from the work of the great French mathematician, Henri Poincaré. It is by no means obvious exactly how one should understand the principle. In the work of Poincaré and Russell there are a number of distinct formulations, and it is not clear which one should take as representing the VCP. This chapter focuses on the issue of the formulation of the principle — or, in fact, on one aspect of this issue. It seeks to show how this relatively narrow issue leads to a general understanding of Russell's use of the VCP.

Keywords: Bertrand Russell; vicious-circle principle; Principia Mathematica; Henri Poincaré

Chapter.  3663 words. 

Subjects: History of Western Philosophy

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