Re: In an RDBMS, what does "Data" mean?

Marshall Spight wrote:
> How might one falsify arithmetic? If arithmetic was falsified, would
> that mean it wasn't useful anymore?

It depends what you mean by "falsify arithmetic". There's a result by Tarski ( http://plato.stanford.edu/entries/tarski-truth/ ) that says essentially that no language can talk about the truth of sentences contained within itself without leading to things like the liar paradox.

You need to have a "meta-language" for arithmetic in order to talk about whether statements in arithmetic are true or not.

I guess the problem is where do you start? Set theory I suppose but then how do you talk rigorously about set theory?

All this stuff is very subtle but I think it is useful to know a bit about this kind of thing if you're interested in relational database theory.

If you mean that arithmetic is inconsistent i.e. there is a statement where you can prove both it and its negation, then that means *everything* in arithetic is both true and false.

Check out this though:
http://plato.stanford.edu/entries/mathematics-inconsistent/ Inconsistent Mathematics, where you have theories that use non-classical logic and can deal with inconsistencies without collapsing in on themselves.

Paul. Received on Sat May 22 2004 - 12:26:34 CEST