Re: Military time (whoops!)

[David Auerbach auerbach@xxxxxxxx]

On Jun 19, at 2:47 PM, Harry Binswanger wrote:
> > No, they just ended up linking the various invocations of Cantor's
> > Theorem, about which I *was* going to have a footnote but then
> > ellipsis happened and....
> Re Cantor's proof: are you referring to (but not mentioning!)
> diagonalization?
Yep. (Although that's not the only proof, the general method Cantor
used has gained the honorific "diagonalization". In latter guises,
it re-emerges (Patricia, do I need a hyphen there?) as various fixed
point theorems. These range from the Burali-Forti Theorem (or
paradox, depending on how you take it) to various Tarski theorems (on
the definability of the semantic notion of truth) to the Gödel
Theorems (on the essential incompleteness of formal systems); it has
a quite lovely history.
 For those who want incredibly fun but still accurate entrée to the
above there are some wonderful puzzle books by Raymond Smullyan that
cover the territory. I'm thinkin particularly of "What is the Name of
This Book", "The Lady or the Tiger" and "Forever Undecided". (Reading
suggestion (is anyone still reading?) is one of the first two and
then the last.)
Warning: Do not surf newsgroups and the unmoderated web for info on
the above matters. It attracts cranks. Almost exactly the same
cranks who don't like it that .999...=1.  There's a sociology
thesis waiting about which mathematical are crank fodder. In past
centuries it was squaring the circle; Hobbes was a prominent crank in
that arena.


David Auerbach
Department of Philosophy & Religion
Box 8103
Raleigh, NC 27695-8103                  http://
slowfoodusa.org
auerbach@xxxxxxxx                  http://
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