Re: Domains as relations

From: Paul <pbrazier_at_cosmos-uk.co.uk>
Date: 8 Oct 2002 08:48:28 -0700
Message-ID: <51d64140.0210080748.1946dcc4_at_posting.google.com>


hidders_at_hcoss.uia.ac.be (Jan.Hidders) wrote in message news:<3da2b632$1_at_news.uia.ac.be>...
> >I guess Godel would imply that a totally relational
> >system would be "incomplete" in some sense - so at some point we'd
> >have to accept that the relational model is in fact embedded within a
> >larger "meta-model" which we'd have to use to answer some questions
> >about the system.
>
> That won't help. Goedels' incompleteness theorem says you cannot finitely
> axiomatize the natural numbers (or even do it with a recursively enumerable
> list of axioms) so building a bigger system cannot be a solution.

What I'm meaning is that you can answer the question by appealing to some higher authority or "intuition" - in essence you say it is true "because I say it is". The meta-model is kind of half inside the system in the sense that it can answer questions about the (internal) system, but outside of the system in the sense that it can't answer questions about itself.

e.g. from http://www.ddc.net/ygg/etext/godel/

"His Propostion XI states that the consistency of any formal deductive system (if it is consistent) is neither provable nor disprovable within the system. A quick leap of logic interprets this corollary as such: 'Any sufficiently complex, consistent logical framework cannot be self-dependent' - i.e., it must rely on intuition, or some external confirmation of certain propositions (specifically, one that proves internal consistency)."

So a totally relational system must have some kind of external "intuition" in order to be complete and consistent. i.e. it can't be self-consistent.

I think...

Paul. Received on Tue Oct 08 2002 - 17:48:28 CEST

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