Re: The Theoretical Foundations of the Relational Model

James wrote:

>>The whole exercise culminated in an attempt to place all of mathematics >>upon a foundation of logic (until one M. Goedel put the kybosh on that!)

I think that was Kurt Godel (where that should be an o-umlaut).

> Could you elaborate on this?
> Did someone propose that all mathematics can be founded upon logic?

Gingerly dipping a toe into waters wherein lie sharks...

Mathematicians in general around the turn of the 19th-20th century were working towards that goal, yes. And Bertrand Russell (two l's I think) was one of the chief protagonists as I understand it.

> What did Goedel do to discount that theory?

Produced his Incompleteness Theorem.

Roughly, he demonstrated that any mathematical system complicated enough to be interesting is inherently incomplete - meaning roughly that there are true statements that can be expressed in the system that cannot be proved true by the system.

See Douglas R Hofstadter's book "Godel, Escher, Bach: the Eternal Golden Braid" for a lengthy but eventually comprehensible (and quite enjoyable) explanation of Goedel's incompleteness theorem. It's been quite a while since I last read it.

>>Carnap, Rudolph. _Introduction_to_Symbolic_Logic_and_its_Applications_.
>>Russel, Bertrand. _Introduction_to_Mathematical_Philosophy_.
>>Langer, Susanne. _An_Introduction_to_Symbolic_Logic_ (This is the best.)

What do you mean by 2-D and 3-D (and n-D) in relation to systems of logic? I'm not sure the question has meaning; certainly, I can't see what you might be getting at.

> Do you have a recommendation?

With due respect, catch up on some homework.

Valid question: which homework?

For databases, I'd suggest either C J Date "Introduction to Database Systems" (7th Edn) or Elmasri and Navathe "Fundamentals of Database Systems". I'm not qualified to suggest books on mathematical logic; I've not yet found one that I understood as well as I'd like to.

-=JL=-   Received on Mon Jun 17 2002 - 02:40:56 CDT