Full Text

vicious circle

Subject Philosophy

DOI: 10.1111/b.9781405106795.2004.x


L ogic, philosophy of mathematics Circular reasoning, also called begging the question or petitio principii , makes use of the conclusion to be proved as a premise, and hence renders the argument invalid. A circular definition explains the definiens in terms of the definiedum and renders the definition empty. Circularity in these cases is vicious. According to Russell, paradoxes in the foundations of mathematics are due to vicious circularity, for they violate the vicious circle principle that “whatever involves all of a collection must not be one of the collection.” His theory of types is established on the basis of this principle and attempts to avoid all paradoxes of this sort. Not all circularities in argument or definition, however, are vicious. All deductions mean to derive the conclusion from the premises and hence the conclusion must have been implied in the premises. If the circle is large enough, and the argument or definition can still provide new knowledge , it is considered to be a virtuous circle. “The vicious circles in question all arise from supposing that a collection of objects may contain members which can only be defined by means of the collection as a whole.” Russell, Collected Papers of Bertrand Russell , vol. VI ... log in or subscribe to read full text

Log In

You are not currently logged-in to Blackwell Reference Online

If your institution has a subscription, you can log in here:


     Forgotten your password?

Find out how to subscribe.

Your library does not have access to this title. Please contact your librarian to arrange access.

[ access key 0 : accessibility information including access key list ] [ access key 1 : home page ] [ access key 2 : skip navigation ] [ access key 6 : help ] [ access key 9 : contact us ] [ access key 0 : accessibility statement ]

Blackwell Publishing Home Page

Blackwell Reference Online ® is a Blackwell Publishing Inc. registered trademark
Technology partner: Semantico Ltd.

Blackwell Publishing and its licensors hold the copyright in all material held in Blackwell Reference Online. No material may be resold or published elsewhere without Blackwell Publishing's written consent, save as authorised by a licence with Blackwell Publishing or to the extent required by the applicable law.

Back to Top