Re: The RM, Newtonian mechanics, algrebra and incompleteness
Date: Wed, 02 Jun 2004 12:23:44 GMT
"mAsterdam" <mAsterdam_at_vrijdag.org> wrote in message
> mountain man wrote:
> > Paul wrote:
> >>No, I think in this analogy Newton's model does correspond to a specific
> >>database design. The possibility that the relational theory itself is
> >>wrong corresponds to the possibility that algebra is wrong.
> > Or incomplete, as has been formally demonstrated
> > at least 30 years prior to the emergence of the RM.
> What do you mean? Do you mean that incomplete is wrong?
> Or that the Goedel-incompleteness somehow implies that
> any specific database design/relational theory must be
> incomplete/wrong? What are you saying?
http://www.mountainman.com.au/GIF/logic_space_1.jpg In reference to the above diagram:
Starting with a given set of axioms (yellow), one can derive a specific set of formalised "provable truths" (green). This logic space of provable truth however is not all there is to the notion of truth.
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. More recently Chaitin showed that there exists "random truths", which are valid and tue, but which require no reference to any axioms. (purple)
Here is a recent (2000) transcript of a talk given by Chaitin on the relevant details of the history of these developments: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/cmu.html entitled Historical Introduction --- A Century of Controversy Over the Foundations of Mathematics
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.
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.
I believe that an example of this is:
The intelligence (ie: data) that is encoded in (application level)
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.
Oz Received on Wed Jun 02 2004 - 14:23:44 CEST