David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
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
|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
Joseph W. Dauben (1977). Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the Infinite. Journal of the History of Ideas 38 (1):85-108.
Citations of this work BETA
No citations found.
Similar books and articles
Mary Tiles (1989/2004). The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise. Dover Publications.
Edward G. Belaga, From Traditional Set Theory – That of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension.
J. Ferreiros (2004). The Motives Behind Cantor’s Set Theory: Physical, Biological and Philosophical Questions. Science in Context 17 (1/2):1–35.
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.
Ignasi Jané (2010). Idealist and Realist Elements in Cantor's Approach to Set Theory. Philosophia Mathematica 18 (2):193-226.
Added to index2010-08-11
Total downloads21 ( #86,490 of 1,102,036 )
Recent downloads (6 months)4 ( #91,864 of 1,102,036 )
How can I increase my downloads?