Re: godel-like incompleteness of relational model

Paul <paul_at_test.com> wrote in message news:<6%_qc.6458$NK4.656343_at_stones.force9.net>...
> mountain man wrote:
> >>>>And what is the problem with The Relational Model?
> >>>
> >>>It has a Godel-like incompleteness:
> >
> > http://www.mountainman.com.au/software/history/relational_model_incomplete.htm
>
> I don't quite understand what you mean here. Even if you think that
> relational theory is missing something, I don't think it is a
> "Godel-like" incompleteness.

I'm not entirely certain, but it seems to me that any logic model that is consistent (i.e. theorems derived from the axioms do not contradict the axioms or other theorems so derived) will be unable to find certain truths within the system. And that seems to be Godel's sword in the stone (you know, he's actually not the first to come up with the idea, but the first to apply it to number theory). In other words, pretty much everything is Godel-like, unless you adapt an informal system, but then when you do that, you lose the power of logic altogether.  

> >>I'm no mathematician, but didn't Godel prove that 'any' formal system
> >>is incomplete?
> >
> > Yes, he did. But I am being specific about provision of one specific
> > instance in which the incompleness of the RM is comprehendable.
>
> Well, Godel acually proved that first-order predicate logic (upon which
> the relational model is based) is complete in some sense. The
> Incompleteness theorem only applies to theories that are above a certain
> complexity. To add to the confusion, there are slightly different
> meanings of "complete" here. See this page for more details:
> http://www.sm.luth.se/~torkel/eget/godel/completeness.html

Good short article that touches on some key points of the theorem and its implications. But seriously, I'm a bit over my head here, since my only source on Godel is the book "Godel, Escher, Bach: a Golden Braid". I haven't read the actual Incompleteness proof.

Todd Received on Fri May 21 2004 - 00:05:31 CEST