Re: Attempts to Refute Cantor's Uncountability Proof?

Hatto von Aquitanien wrote:

I'm interested to know what attempts have been made to refute
Cantor's proof that the real numbers are not denumerable?
Quite honestly, I find the second diagonal method unconvincing.
There are a few directions from which one might attempt to
refute his argument. But before I spend a lot to time trying
to formulate my own argument, it seems reasonable to seek
prior art. Can anybody suggest a source which examines
this topic?

Extensive excerpts from: Uri Fidelman, "Hemispheric basis for
paradoxes and diagonal processes in mathematics", International
Journal of Mathematical Education in Science and Technology
18 #1 (1987), 61-66.
http://groups.google.com/group/sci.math/msg/22105794d2c59429

William Dilworth, "A correction in set theory", Transactions
of the Wisconsin Academy of Sciences, Arts and Letters 62
(1974), 205-216. [MR 58 #16089]
http://digital.library.wisc.edu/1711.dl/WI.WT1974

Excerpt from Underwood Dudley's 1992 book "Mathematical Cranks"
where Dudley discusses Dilworth's paper.
http://groups.google.com/group/sci.math/msg/bcb253de1b6043fb

Usenet posts about the lawsuit Dilworth filed against Dudley.
One of these posts is by Dudley himself (Nov, 15, 2003),
and Dudley describes the lengths at which Dilworth (now dead,
by the way) tried to attack him through the court system.
http://tinyurl.com/cffrn

Circuit Opinion for Dilworth vs. Dudley. (Dilworth lost.)
http://www.law.emory.edu/7circuit/jan96/95-2282.html

Wilfrid Hodges, "An editor recalls some hopeless papers",
Bulletin of Symbolic Logic 4 (1998), 1-16.
[MR 99c:03007; Zbl 979.03002]
http://www.emis.de/cgi-bin/MATH-item?0979.03002 [Zbl review]
http://www.math.ucla.edu/~asl/bsl/04-toc.htm [.ps file of paper]
http://groups-beta.google.com/group/sci.math/msg/f0ab89956d4591f3
[The above is a text-only copy posted in sci.math by Bill Dubuque.]

Dave L. Renfro

.

Loading