On the Reality of the Continuum Discussion Note: A Reply to Ormell, ‘Russell's Moment of Candour’, Philosophy: Anne Newstead and James Franklin

Philosophy 83 (1):117-127 (2008)
Download Edit this record How to cite View on PhilPapers
Abstract
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
PhilPapers/Archive ID
NEWOTR-9
Revision history
Archival date: 2019-02-24
View upload history
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2009-01-28

Total views
83 ( #25,602 of 39,659 )

Recent downloads (6 months)
6 ( #36,258 of 39,659 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.