FOM: Cantor'sTheorem & Paradoxes & Continuum Hypothesis
twilson at csufresno.edu
Mon Feb 12 12:44:34 EST 2001
On Sat, 10 Feb 2001, Robert Tragesser wrote:
> The logical moves in the "diagonal argument" in the RAA parts of the
> usual proof of Cantor's Theorem (that the cardinal number of the set
> of all subsets of a set is greater than the cardinal of the set)
> exploit a variation on the trick yielding Russell's Paradox, the
> Barber Paradox, etc. [...] I'm curious about the provenance and
> evolution of this style of argument.
It may be worth mentioning, in this context, a old paper of Bill
F. William Lawvere, "Diagonal arguments and cartesian closed
categories", in Dold, Eckmann (eds.), Category Theory, Homology
Theory, and their Applications II, Springer Lecture Notes in
Mathematics 92, 1969.
The first two sentences of this paper read:
The similarity between the famous arguments of Cantor, Russell,
G"odel and Tarski is well-known, and suggests that these arguments
should all be special cases of a single theorem about a suitable
kind of abstract structure. We offer here a fixed-point theorem
in cartesian closed categories which seems to play this role.
Todd Wilson A smile is not an individual
Computer Science Department product; it is a co-product.
California State University, Fresno -- Thich Nhat Hanh
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