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
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
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
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-
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-
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
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
hi,
--- Jim Choate [EMAIL PROTECTED] wrote:
hi,
On Sat, 30 Nov 2002, Peter Fairbrother wrote:
Godel didn't invent the term though, and may not
have said this is the/my
definition of completeness. I haven't read them
for some time, and can't
remember. He may well have assumed his
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
hi,
How ever how do you 'precisely' define
completeness?
There were a couple of examples in the message
you replied to. There
are different sorts of completeness as well. You
might also look into some
of the references I provided.
Okay,I ask a legitimate question,how do you argue
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
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
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