If Logic, Definitions and the Vicious Circle Principle

Journal of Philosophical Logic 41 (2):505-517 (2012)
In a definition (∀ x )(( x є r )↔D[ x ]) of the set r, the definiens D[ x ] must not depend on the definiendum r . This implies that all quantifiers in D[ x ] are independent of r and of (∀ x ). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious Circle Principle was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if ( b є a ) or ( b ⊆ a ). Likewise, the truth of an ordinary first-order sentence with the Gödel number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r
Keywords (In)dependence  IF logic  Definitions  Vicious circle principle  Truth-definition
Categories (categorize this paper)
DOI 10.1007/s10992-011-9184-4
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,780
Through your library
References found in this work BETA
The Principles of Mathematics Revisited.Jaakko Hintikka - 1996 - Cambridge University Press.
Principia Mathematica. [REVIEW]Morris R. Cohen - 1912 - Philosophical Review 21 (1):87-91.
Predicativity.Solomon Feferman - 2005 - In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford: Oxford University Press. pp. 590-624.

View all 6 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Ontology and the Vicious-Circle Principle.Charles S. Chihara - 1973 - Ithaca [N.Y.]Cornell University Press.
A Semantical Account of the Vicious Circle Principle.Philip Hugly & Charles Sayward - 1979 - Notre Dame Journal of Formal Logic 20 (3):595-598.
Russell, Presupposition, and the Vicious-Circle Principle.Darryl Jung - 1999 - Notre Dame Journal of Formal Logic 40 (1):55-80.
Sets and Plural Comprehension.Keith Hossack - 2014 - Journal of Philosophical Logic 43 (2-3):517-539.
Russell and the Vicious Circle Principle.Philippe Rouilhan - 1992 - Philosophical Studies 65 (1-2):169 - 182.
The Linguistic Hierarchy and the Vicious-Circle Principle.Arthur Pap - 1954 - Philosophical Studies 5 (4):49 - 53.
Ontology and the Vicious Circle Principle.Michael Corrado - 1974 - International Philosophical Quarterly 14 (3):375-378.
Review: Ontology and the Vicious Circle Principle. [REVIEW]Tom Richards - 1975 - Philosophical Quarterly 25 (98):68 - 79.
Ontology and the Vicious-Circle Principle.J. van Heijendort - 1974 - International Studies in Philosophy 6:204-205.
The Vicious Circle Principle: Comments on Philippe de Rouilhan.Peter Hylton - 1992 - Philosophical Studies 65 (1-2):183 - 191.
Added to PP index

Total downloads
70 ( #82,600 of 2,214,651 )

Recent downloads (6 months)
1 ( #408,895 of 2,214,651 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature