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Re: In an RDBMS, what does "Data" mean?

From: Anthony W. Youngman <wol_at_thewolery.demon.co.uk>
Date: Mon, 7 Jun 2004 23:29:24 +0100
Message-ID: <zHiLa9IExOxAFw1d@thewolery.demon.co.uk>


In message <c9of1n$7rt$1_at_news.netins.net>, Dawn M. Wolthuis <dwolt_at_tincat-group.com> writes
>"Anthony W. Youngman" <wol_at_thewolery.demon.co.uk> wrote in message
>news:FhLmDnFZR7vAFwQU_at_thewolery.demon.co.uk...
>> In message <Comvc.4724$n65.4145_at_newssvr33.news.prodigy.com>, Eric Kaun
>> <ekaun_at_yahoo.com> writes
>> >> This theory will then be the equivalent of Kepler and Newton
>discovering
>> >> ellipses and calculus, or of Einstein realising that mass and energy
>> >> were interchangeable. Basically, pretty much ALL of relational theory's
>> >> axioms are taken as given by the mathematicians, and no thought is
>given
>> >> as to whether they actually match the real world.
>> >
>> >Which axioms don't match? I wasn't really aware there were axioms per se.
>>
>> BLOODY HELL ...
>>
>> I don't mean to sound stunned, but this takes the biscuit ...
>>
>> ALL mathematical theories are based on axioms.
>>
>> Science is basically the search for experimental proof that the axioms
>> correctly describe the real world.
>>
>> If you can't describe relational theory in terms of axioms and logical
>> deductions, then it isn't maths and can't be science!
>
>By George, you've got it., Wol!!! Perfect!
>
>Relational theory, once some choice axioms are added in (without being
>stated as axioms and without being obvious that they out to be axiomatic
>when measured by any map to reality) does then proceed with mathematics, but
>there is a lot of "tossing stuff in and out" going on because there is not
>that match with reality at each point.
>

Fine. This seems as good a place as any to say what I thought of after that previous post.

This is for all those people who think "if I don't understand it, then it must be wrong" (is Tony listening :-)

Now. It's not words of one syllable, I'm afraid, but I'm trying to explain something very heavy as simply as I can.

Let's start by defining what the words mean.

A "theory", a "model" and an "axiom" are ALL things that have not been proven correct. BUT - and here we hit our first point of confusion - with the exception of a "mathematical theory", they are all things that CANNOT be proven correct. Once proven, a mathematical theory become a "theorem", but a mathematical axiom by definition cannot be proven true, scientific theories and models can only be shown to be false, and a mathematical model cannot be proven to be true because it relies on axioms which cannot be proven true.

Okay. Now ALL models (scientific or mathematical) belong to the set "IF {axioms} THEN {theorems}". Read C&D's twelve rules. Ask yourself which rules are axioms, which rules are convenient constraints, and what else? Basically, what fundamental mathematical category does each rule fall into?

I think Codd (maybe Date) is even on record as saying that various rules were "convenient constraints". In other words, they are axioms with as much validity as Euclid's "parallel lines never meet" - they make the maths easy with no real grounding in reality.

Once you've identified those axioms, ask yourself "what proof do we have in favour of them?" and DON'T FORGET that you CANNOT use logic! "if/then" is NOT TRANSITIVE"! Just because the theorems are true doesn't mean you can conclude the axioms are true - indeed - it's the exact opposite - you can only prove the theorems are true BECAUSE you have ASSUMED the axioms are true.

LOOK at the subject of this thread again. It is an AXIOM of relational theory that data comes in tuples. Show me that that's true! And because it's an axiom, mathematics itself tells you that logic CAN not give you an answer!

Cheers,
Wol

-- 
Anthony W. Youngman - wol at thewolery dot demon dot co dot uk
HEX wondered how much he should tell the Wizards. He felt it would not be a
good idea to burden them with too much input. Hex always thought of his reports
as Lies-to-People.
The Science of Discworld : (c) Terry Pratchett 1999
Received on Mon Jun 07 2004 - 17:29:24 CDT

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