Re: The Theoretical Foundations of the Relational Model
Date: 18 Jun 2002 08:05:48 +0200
Message-ID: <vcblm9djf43.fsf_at_beta13.sm.luth.se>
Jonathan Leffler <jleffler_at_earthlink.net> writes:
> I think that was Kurt Godel (where that should be an o-umlaut).
It is traditional in German to spell "ö" as "oe" when the letter "ö" is unavailable, so the spelling "Goedel" is also OK.
> Gingerly dipping a toe into waters wherein lie sharks...
Yes, but my teeth are made of rubber.
> 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.
Bertrand Russell and Gottlob Frege are indeed the two names chiefly associated with what is known as "logicism", but it isn't true to say that "mathematicians in general" were at all concerned with this program.
As for the relevance of Godel's theorem to logicism, this is not an uncontroversial issue. It is a common idea that Godel's theorem somehow disproved the claims of logicism, but in fact it's very difficult to find anything claimed by Russell that is incompatible with the incompleteness theorem. In particular, the concept of completeness is nowhere mentioned in Principia Mathematica.
> 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.
As an aside, it is by no means the case that complete systems are necessarily uninteresting. For example, an enormous amount of work has been done in computing on quantifier elimination in the elementary theory of the real field, which has manifold applications. Received on Tue Jun 18 2002 - 08:05:48 CEST