Re: In an RDBMS, what does "Data" mean?
Date: Fri, 04 Jun 2004 17:43:01 +0100
Message-ID: <7E1wc.11238$NK4.1467178_at_stones.force9.net>
Anthony W. Youngman wrote:
>>> I'm not sure a database is a finite set of axioms. >> >> Why not? A databases is just a finite set of tuples from which you >> derive other truths.
>
> In which case, your database is arbitrarily complex ...
I don't understand.
Suppose my database just has one tuple:
('John', 'Smith', 23, 5, 'Cedar Avenue')
That corresponds to the real-life statement: "John Smith is age 23 and
lives at 5 Cedar Avenue."
Then I can derive other truths such as:
"There is a person whose surname is Smith"
"Everyone is under the age of 50".
These are my "theorems" if you like.
How does this differ from a conventional theory where you start with some axioms and prove theorems?
> The whole point of axioms is that YOU DON'T WANT THEM! The aim of
> logicians, mathematicians, and scientists is always to simplify things.
> If you can derive an axiom from other axioms, it ceases to be an axiom
> and becomes a theorem, and makes your fundamental theory simpler.
OK, I agree with all of that, I don't see how it contradicts what I said though.
> To define "axiom == tuple" is, I think, a major mistake. I can't explain
> why, it just feels COMPLETELY wrong.
Well it seems completely right to me :)
I guess it would be come under "Proof Theory"
http://en.wikipedia.org/wiki/Proof_theory
which is really just the study of different formal logics.
Note that I'm not saying you can't also look at databases another way where you regard something else as axioms instead.
>> There's a big (though maybe subtle) difference between "infinite" and >> "unbounded but finite". Even though there is no theoretical limit to >> the size of a database, we do know that any given database is of >> finite size. >>
> Yep. But as any scientist will tell you, an unbounded axiom set is a
> crap theory. That's why it feels wrong.
Peano's axioms:
http://en.wikipedia.org/wiki/Peano_axioms
which are the basis for the whole of arithmetic are usually given as
five axioms. BUT the induction axiom isn't actually expressible in
first-order logic, so really it is an "axiom schema" which is an
infinite number of axioms masquerading as one axiom. See the above link
for details.
But anyway I'm not saying a database has an infinite number of axioms. In fact my point was the exact opposite: that because a database only has a finite axiom set, and things like arithmetic really have an infinite axiom set, Godel's theorems might be irrelevant anyway.
Paul. Received on Fri Jun 04 2004 - 18:43:01 CEST