David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Philosophia Mathematica 18 (2):193-226 (2010)
There is an apparent tension between the open-ended aspect of the ordinal sequence and the assumption that the set-theoretical universe is fully determinate. This tension is already present in Cantor, who stressed the incompletable character of the transfinite number sequence in Grundlagen and avowed the definiteness of the totality of sets and numbers in subsequent philosophical publications and in correspondence. The tension is particularly discernible in his late distinction between sets and inconsistent multiplicities. I discuss Cantor’s contrasting views, and I conclude that his account of that distinction is only tenable if the definiteness of the set-theoretical universe is rejected. Partially supported by the Spanish CICYT, grant MTM 2008–03389. Earlier versions of this paper were presented at the VIII International Ontology Congress in San Sebastian, and at the Seminar in Logic and the Philosophy of Mathematics of the University of Bristol. I wish to thank the participants for their comments. I am also grateful to Joan Bertran, Joan Climent, and one anonymous referee for their careful reading of the paper and their helpful remarks and suggestions. CiteULike Connotea Del.icio.us What's this?
|Keywords||No keywords specified (fix it)|
|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
Øystein Linnebo (2013). The Potential Hierarchy of Sets. Review of Symbolic Logic 6 (2):205-228.
Salvatore Florio & Stewart Shapiro (2014). Set Theory, Type Theory, and Absolute Generality. Mind 123 (489):157-174.
Similar books and articles
L. H. Kauffman (2012). The Russell Operator. Constructivist Foundations 7 (2):112-115.
J. Ferreiros (2004). The Motives Behind Cantor’s Set Theory: Physical, Biological and Philosophical Questions. Science in Context 17 (1/2):1–35.
Mary Tiles (1989). The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. Dover Publications.
Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
Edward G. Belaga, Halfway Up To the Mathematical Inﬁnity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transﬁnite Design.
Edward G. Belaga, From Traditional Set Theory – That of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension.
I. Jane (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
Added to index2010-06-05
Total downloads44 ( #94,270 of 1,902,047 )
Recent downloads (6 months)4 ( #205,572 of 1,902,047 )
How can I increase my downloads?