David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Philosophy 83 (01):117-28 (2008)
In a recent article (‘The Continuum: Russell’s Moment of Candour’), Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably inﬁnite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable inﬁnity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-deﬁned’ real numbers as proper objects of study. In practice, this means excluding as inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis.
|Keywords||continuum Cantor's diagonal argument realism philosophy of mathematics Bertrand Russell real numbers infinity|
|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
Christopher Ormell (1993). Is the Uncertainty of Mathematics the Real Source of its Intellectual Charm? Journal of Philosophy of Education 27 (1):125–133.
Philip Ehrlich (2012). The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small. Bulletin of Symbolic Logic 18 (1):1-45.
Brian Rotman (1996). Counting Information: A Note on Physicalized Numbers. [REVIEW] Minds and Machines 6 (2):229-238.
Roger Straughan (1993). Are Values Under‐Valued? A Reply to Christopher Ormell. Journal of Moral Education 22 (1):47-50.
Daesuk Han (2011). Wittgenstein and the Real Numbers. History and Philosophy of Logic 31 (3):219-245.
Anne Newstead (2001). Aristotle and Modern Mathematical Theories of the Continuum. In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
Michael Dummett (2000). Is Time a Continuum of Instants? Philosophy 75 (4):497-515.
Christopher Ormell (2006). The Continuum: Russell’s Moment of Candour. Philosophy 81 (4):659-668.
Added to index2009-01-28
Total downloads26 ( #77,973 of 1,679,397 )
Recent downloads (6 months)4 ( #59,947 of 1,679,397 )
How can I increase my downloads?