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From: Chris Simmons <cps102.domain.name.hidden>

Date: Mon, 15 May 2000 19:41:53 +0100 (BST)

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
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*> 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
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*> 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

Date: Mon, 15 May 2000 19:41:53 +0100 (BST)

On Fri, 12 May 2000, Russell Standish wrote:

[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

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