Re: The RM, Newtonian mechanics, algrebra and incompleteness

From: Paul <>
Date: Thu, 03 Jun 2004 16:41:54 +0100
Message-ID: <xFHvc.10431$>

mountain man wrote:
>> Not exactly, Godel's Incompleteness Theorem only applies to
>> theories or systems that are above a certain complexity. See here
>> for example:
>> 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: 

I'm fairly sure I'm right. The axioms of number theory or Peano arithmetic are more complicated than those for the theories of real numbers or Euclidean geometry. I think the important ones are probably the "inductive" ones (every number has a successor, and different numbers have different successors). Although it seems intuitively that the theory of real numbers must somehow be a superset of the Peano arithmetic, that's not the case. In the theory of real numbers, you don't have the concept of a successor function, they're all on a continuum and (maybe paradoxically) this makes it simpler.

Here is something about Tarski's completeness proof for Euclidean geometry:

>> 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: 

I still don't quite see what the killer point is here. Is it that your application just has a single form to display all data? And the form knows what views to use by consulting a table? How is this different to the "Switchboard Manager" functionality that comes with Access for example?

> 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.

Isn't this the same as what is done by any of the front-end GUIs you get with most DBMSs? For example SQL Server's Enterprise Manager? It's totally general, all the information it needs is in relations in the database. In theory you could just give every database user a copy of Enterprise Manager and it would suffice for any database, for any purpose. It just wouldn't be very user-friendly.

I don't think that applications store any essential business knowledge, they are just there to make things easier for the user. If you like they are non-essential business knowledge. For example "Users of the accounting form 53(a) don't need to see the 'foobar' column". I'm assuming here that the foobar column isn't actually restricted for security purposes; it's just not useful for some particular task.

Paul. Received on Thu Jun 03 2004 - 17:41:54 CEST

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