On Fri, 12 May 2000, Russell Standish wrote:
> Dear Chris,
> Your ideas are mostly uncontentious, but don't really raise
> new issues. Most of these concepts have been discussed, not only on
> this list, but also in papers by myself (the Occam paper), Bruno
> Marchal, Juergen Schmidhuber and Max Tegmark, as well as Alistair
> Malcolm's website.
>
> Bruno has raised the issue that the "whole of mathematics" is actually
> undefinable. In my work, I take this statement to mean recursively
> enumerable axiomatic systems, which is strictly a subset of
> mathematics. I believe when you use the term "finite", you actually
> mean "recursively enumerable". But if someone can resolve this issue
> in a different way, then that would be a new and interesting
> contribution.
>
[snip]
No, I really meant finite. Think about it. I'm not saying 'every piece
of mathematics which can exist' nor even 'every possible description of
every piece of mathematics done to date'. I'm assuming we could have some
set alphabet, and could translate (ie represent) every piece of maths done
to date over this alphabet. We only need *one* instance of every proof
done to date, I'm only really assuming that everything's written in the
same alphabet. We could simplify some things by, say, including the
english, greek, etc alphabets, and new symbols for 'newline' 'newpage' (or
just copy each text *once* using latex). The point is, each text can then
be considered a string over some alphabet. There's finitely many texts
(of course...) so there's finitely many strings. So the language of all
maths *written down to date* is finite.
So what's so special about it, if anything, was what I was saying.
Chris Simmons.
Don't bother, the web page is crap ;)
http://www.york.ac.uk/~cps102
Received on Mon May 15 2000 - 11:44:49 PDT