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Re: The RM, Newtonian mechanics, algrebra and incompleteness

From: mountain man <hobbit_at_southern_seaweed.com.op>
Date: Thu, 03 Jun 2004 03:20:04 GMT
Message-ID: <ENwvc.3363$rz4.1067@news-server.bigpond.net.au>


"Paul" <paul_at_test.com> wrote in message
news:bitvc.10290$NK4.1395886_at_stones.force9.net...
> mountain man wrote:
> > Godel showed that there exists "unprovable truths" in all
> > mathematical systems, which are valid and true, but which
> > are not capable of being referenced by the foundational
> > axioms.
>
> Not exactly, Godel's Incompleteness Theorem only applies to theories or
> systems that are above a certain complexity. See here for example:
> http://www.sm.luth.se/~torkel/eget/godel/complete.html
>
> There are certainly complete theories, for example the theories of real
> numbers, of complex numbers, and of Euclidean geometry. In these
> theories there are no truths that cannot be proved within the system.

I think you should double-check the above. Godel's incompleteness theorem was a statement in elementary number theory (arithmetic). Here is a reference:
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/cmu.html

> > IMO it implies that the complete notion of whatever-it-is-that
> > -is-truth cannot be encapsulated in any traditional mathematical
> > language using the traditional axiomatic methodology everyone
> > has been spoon fed the last few hundred years, and that another
> > approach is required, in the long run. This includes algebra.
>
> Are you sure? I can't find any definite links to a completeness result
> for algebra, but it's quite a simple system compared to the one for the
> whole of arithmetic, so I'd be surprised if it wasn't complete.

See above.

> > How does this apply to relational database theory and the
> > Relational Model, and tables and row values? There will
> > necessarily exist example truths such as those defined above
> > that exist independent of the relational model, and which are
> > not addressable by the model.
>
> Check out this article on Codd's 1972 paper "Relational Completeness of
> Data Base Sublanguages":
>

http://www.intelligententerprise.com/db_area/archives/1999/990501/online.jhtml
>
> Unfortunately I can't find an online version of Codd's original paper,
> but he appears to prove that relational algebra is complete. Whether
> this is "completeness" used in exactly the same sense as Godel's
> Incompleteness Theorem I'm not quite sure though.
>
> > I believe that an example of this is:
> >
> > The intelligence (ie: data) that is encoded in (application level)
> > SQL code captured in RDBMS stored procedures exists right
> > alongside the data, and the constraints, etc. While the RM and
> > theory address the data and constraints, etc, the intelligence
> > (which is data) of the application level processes cannot be
> > formally addressed by it, even though it consists of valid SQL
> > statements expressing manipulations of perfectly valid data
> > objects known to the model and theory.
>
> Do you have a simple concrete example of what you mean by this?
> What kind of stored procedures are you thinking of?
> Plain single SELECT statements?
> Or a series of INSERTs, UPDATEs and DELETEs that do some business
> process? In this latter case you've got procedural code and I think it
> should be possible to replace it with declarative code. It's difficult
> to talk about without an example though.

Well here is an example that goes to the extreme: http://www.mountainman.com.au/software/southwind/

The entire (100% of) application software suite is in the form of stored procedures. No intelligence specific to the organization is stored external to the RDBMS software layer.

The Relational Model of the data needs expansion to be able to address this configuration of organizational intelligence. It remains mute to this intelligence.

Pete Brown
Falls Creek
Oz Received on Wed Jun 02 2004 - 22:20:04 CDT

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