Philosophy 83 (1):117-28 (2008)
In a recent article, 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)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Is the Uncertainty of Mathematics the Real Source of its Intellectual Charm?Christopher Ormell - 1993 - Journal of Philosophy of Education 27 (1):125–133.
Aristotle and Modern Mathematical Theories of the Continuum.Anne Newstead - 2001 - In Demetra Sfendoni-Mentzou & James Brown (eds.), Aristotle and Contemporary Philosophy of Science. Peter Lang.
Wittgenstein and the Real Numbers.Daesuk Han - 2010 - History and Philosophy of Logic 31 (3):219-245.
Are Values Under‐Valued? A Reply to Christopher Ormell.Roger Straughan - 1993 - Journal of Moral Education 22 (1):47-50.
Counting Information: A Note on Physicalized Numbers. [REVIEW]Brian Rotman - 1996 - Minds and Machines 6 (2):229-238.
The Absolute Arithmetic Continuum and the Unification of All Numbers Great and Small.Philip Ehrlich - 2012 - Bulletin of Symbolic Logic 18 (1):1-45.
Added to index2009-01-28
Total downloads54 ( #96,375 of 2,163,987 )
Recent downloads (6 months)4 ( #84,084 of 2,163,987 )
How can I increase my downloads?