Re: Greg Chaitin on incompleteness and other wonders
Would it make sense to say:
(a) Mathematics is a sub-set of language
(b) Language is a sub-set of mathematics
(c) Neither
Z
On Tue, 8 Jun 2004, John F. Sowa wrote:
> Last week, there was a lot of discussion about completeness
> and related topics. I don't want to reopen the discussion,
> but I would like to recommend a very readable paper by
> Greg Chaitin on some related topics:
>
> http://www.umcs.maine.edu/~chaitin/lowell.html
> Chaitin, Conversations with a Mathematician
>
> Greg is the founder of algorithmic information theory,
> and he is notable for publishing many readable papers
> and books that explain the implications of his much less
> readable research publications.
>
> The above paper is a transcription of a lecture entitled
> "A Century of Controversy over the Foundations of Mathematics",
> in which he summarizes in a very readable way some of the
> implications of Cantor's set theory, Russell's logical paradoxes,
> Goedel's incompleteness theorem, Turing's Halting problem, and
> his own work on algorithmic information theory.
>
> For other readable papers (and books) by Chaitin, most of which
> are on the web, see the web site
>
> http://www.umcs.maine.edu/~chaitin/
> G J Chaitin Home Page
>
> Many of the topics we have been discussing on CG and SUO lists
> touch on these issues, and Chaitin's papers provide some good
> background for clarifying the problems and how to approach them.
>
> John Sowa
>