Journal of Philosophical Logic 48 (5):885-908 (2019)

Authors
Graham Leach-Krouse
Kansas State University
Abstract
Russell’s paradox is purely logical in the following sense: a contradiction can be formally deduced from the proposition that there is a set of all non-self-membered sets, in pure first-order logic—the first-order logical form of this proposition is inconsistent. This explains why Russell’s paradox is portable—why versions of the paradox arise in contexts unrelated to set theory, from propositions with the same logical form as the claim that there is a set of all non-self-membered sets. Burali-Forti’s paradox, like Russell’s paradox, is portable. I offer the following explanation for this fact: Burali-Forti’s paradox, like Russell’s, is purely logical. Concretely, I show that if we enrich the language \ of first-order logic with a well-foundedness quantifier W and adopt certain minimal inference rules for this quantifier, then a contradiction can be formally deduced from the proposition that there is a greatest ordinal. Moreover, a proposition with the same logical form as the claim that there is a greatest ordinal can be found at the heart of several other paradoxes that resemble Burali-Forti’s. The reductio of Burali-Forti can be repeated verbatim to establish the inconsistency of these other propositions. Hence, the portability of the Burali-Forti’s paradox is explained in the same way as the portability of Russell’s: both paradoxes involve an inconsistent logical form—Russell’s involves an inconsistent form expressible in \ and Burali-Forti’s involves an inconsistent form expressible in \.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10992-019-09500-4
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 62,268
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Logical Basis of Metaphysics.Michael Dummett - 1991 - Harvard University Press.
What Are Logical Notions?John Corcoran & Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38.

View all 24 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

An Order-Theoretic Account of Some Set-Theoretic Paradoxes.Thomas Forster & Thierry Libert - 2011 - Notre Dame Journal of Formal Logic 52 (1):1-19.
Las Paradojas De La Teoria De Conjuntos: Un Analysis Sistematico.Julián Garrido - 2002 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 17 (1):35-62.
Las Paradojas De La Teoria De Conjuntos.Julián Garrido Garrido - 2002 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 17 (1):35-62.
Logical Objects and the Paradox of Burali-Forti.A. Hazen - 1986 - Erkenntnis 24 (3):283 - 291.
Léments de Calcul Vectoriel. [REVIEW]Burali-Forti Burali-Forti - 1911 - Ancient Philosophy (Misc) 21:638.
Sur le paradoxe dit «de Burali-Forti».Manuel Rebuschi - 1996 - Philosophia Scientiae 1 (1):111-124.
Librationist Closures of the Paradoxes.Frode Bjørdal - 2012 - Logic and Logical Philosophy 21 (4):323-361.
Quantification and Paradox.Edward Ferrier - 2018 - Dissertation, University of Massachusetts Amherst
Another Paradox In Naive Set-Theory.Loïc Colson - 2007 - Studia Logica 85 (1):33-39.

Analytics

Added to PP index
2019-02-04

Total views
35 ( #307,322 of 2,444,875 )

Recent downloads (6 months)
1 ( #457,287 of 2,444,875 )

How can I increase my downloads?

Downloads

My notes