Title: RE: CDR: Re: ...(one of them about Completeness)
Mathametics is incomplete,other wise we would have
known every thing about every thing. From our
Popping in without the relevant background, I'm afraid, but I'll
give my view on this long lasting thread anyway:
Mathematics do
Jim Choate wrote:
Complete means that we can take any and all -legal- strings within that
formalism and assign them -one of only two- truth values; True v False.
Getting much closer.
Complete means we can, within the formalism, _prove_ that all universally
valid statements within the
Jim Choate says:
Godel's does -not- say mathematics is incomplete, it says we can't prove
completeness -within- mathematics proper. To do so requires a
meta-mathematics of some sort.
You are mixing up what Godel says about proving consistency within a system,
and his incompleteness theorem.
On Tue, 3 Dec 2002, Tyler Durden wrote:
Well, this is quite a post, and I agree with most of it.
As for the Godel stuff, there's a part of it with which I disagree (or at
least as far as I take what you said).
-I- didn't say this stuff, the people who did the original work did. Go
read
On Wed, 4 Dec 2002, Ken Hirsch wrote:
Jim Choate says:
Godel's does -not- say mathematics is incomplete, it says we can't prove
completeness -within- mathematics proper. To do so requires a
meta-mathematics of some sort.
You are mixing up what Godel says about proving consistency
On Mon, 2 Dec 2002, Tyler Durden wrote:
That any particular string can be -precisely- defined as truth or false
as required by the definition of completeness, is what is not possible.
Here we come down to what appears to be at the heart of the confusion as far
as I see it. True, depending
Well, this is quite a post, and I agree with most of it.
As for the Godel stuff, there's a part of it with which I disagree (or at
least as far as I take what you said).
If you want
to compare something mathematically you -must- use the same axioms and
rules of derivation. The -only-
hi,
Thanks for the replies,a few more queries.
Complete means that we can take any and all -legal-
strings within that
formalism and assign them -one of only two- truth
values; True v False.
The fundamental problem is axiomatic. The rules
define -all- statements as
being -either true or
On Sun, 1 Dec 2002, Sarad AV wrote:
By principle of what?
By the principles of mathematics.
Godel used Principia Mathematica as a starting point. You might also.
Isn't that the reason we call it 'undecidable',put it
in an undeciable list which is the truth.
The problem description doesn't
That any particular string can be -precisely- defined as truth or false
as required by the definition of completeness, is what is not possible.
Here we come down to what appears to be at the heart of the confusion as far
as I see it. True, depending on who's saying it (even in a discussion of
On Sun, 1 Dec 2002, Sarad AV wrote:
--- Jim Choate [EMAIL PROTECTED] wrote:
On Sun, 1 Dec 2002, Sarad AV wrote:
We can't define completeness.
We can define it, as has been done.
okay,I get what you mean,thank you.
How ever how do you 'precisely' define completeness?
There
On Sun, 1 Dec 2002, Sarad AV wrote:
We can't define completeness.
We can define it, as has been done.
What we can't do is -prove- any set of rules of arrangement that describe
symbol manipulation as -complete- -within the rules of arrangement-.
Complete means that we can take any and all
Jim Choate wrote:
With regard to completeness, I have Godel's paper (On Formally
Undecidable Propositions of Principia Mathematica and Related Systems, K.
Godel, ISBN 0-486-66980-7 (Dover), $7 US) and if somebody happens to know
the section where he defines completeness I'll be happy to
Howdy,
I just picked up The Future of the Electronic Marketplace by D. Leebaert
(ISBN 0-262-62132-0). Anybody who has read it care to comment? It's a MIT
Press book and the little bit of skimming I've done it seems pretty
interesting. Published in '99.
With regard to completeness, I have
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