David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
The Monist 67 (1):92-107 (1984)
In studying the early history of mathematical logic and set theory one typically reads that Georg Cantor discovered the so-called Burali-Forti (BF) paradox sometime in 1895, and that he offered his solution to it in his famous 1899 letter to Dedekind. This account, however, leaves it something of a mystery why Cantor never discussed the paradox in his writings. Far from regarding the foundations of set theory to be shaken, he showed no apparent concern over the paradox and its implications whatever. Against this account, I will argue here that in fact Cantor never saw any paradox at all, but that his conception of set at that time, and already as far back as 1883, was one in which the paradoxes cannot arise.
|Keywords||Burali-Forti paradox Georg Cantor proper classes|
|Categories||categorize this paper)|
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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Julián Garrido Garrido (2002). Las Paradojas De La Teoria De Conjuntos. Theoria 17 (1):35-62.
G. Hellman (2011). On the Significance of the Burali-Forti Paradox. Analysis 71 (4):631-637.
Loïc Colson (2007). Another Paradox in Naive Set-Theory. Studia Logica 85 (1):33 - 39.
Nicholas J. J. Smith (2000). The Principle of Uniform Solution (of the Paradoxes of Self-Reference). Mind 109 (433):117-122.
Barkley Rosser (1942). The Burali-Forti Paradox. Journal of Symbolic Logic 7 (1):1-17.
Irving M. Copi (1958). The Burali-Forti Paradox. Philosophy of Science 25 (4):281-286.
A. Hazen (1986). Logical Objects and the Paradox of Burali-Forti. Erkenntnis 24 (3):283 - 291.
Stewart Shapiro (2007). Burali-Forti's Revenge. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Marcus Rossberg & Philip A. Ebert (2010). Cantor on Frege's Foundations of Arithmetic : Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik. History and Philosophy of Logic 30 (4):341-348.
Gregory Landini (2009). Russell's Schema, Not Priest's Inclosure. History and Philosophy of Logic 30 (2):105-139.
Laureano Luna & William Taylor (2010). Cantor's Proof in the Full Definable Universe. Australasian Journal of Logic 9:11-25.
Kevin C. Klement (2010). Russell, His Paradoxes, and Cantor's Theorem: Part I. Philosophy Compass 5 (1):16-28.
Claire Ortiz Hill (1997). Did Georg Cantor Influence Edmund Husserl? Synthese 113 (1):145-170.
Added to index2010-12-22
Total downloads40 ( #43,551 of 1,103,048 )
Recent downloads (6 months)10 ( #21,045 of 1,103,048 )
How can I increase my downloads?