RE: How about Self-Inconsistency
Hi, Rob:
We cannot deduce that a system may be greater than itself from what
Goedel has said since he has thrown away self-referencing.
Whether a system or a part of it may understand itself is rather a
philosophical problem. In dialectics, a system may understand itself from its
opposite. Anyway, what we are concerned is whether it may affect our practices.
Yang
> -----Original Message-----
> From: owner-standard-upper-ontology@LISTSERV.IEEE.ORG
> [mailto:owner-standard-upper-ontology@LISTSERV.IEEE.ORG] On Behalf Of Rob
> Freeman
> Sent: Wednesday, March 09, 2005 6:49 AM
> To: Yang
> Cc: 'SUO WG'
> Subject: Re: How about Self-Inconsistency
>
>
> Hi Yang,
>
> On Tuesday 08 March 2005 17:01, Yang wrote:
> > Hi, Rob,
> > Sorry for later reply since I have some other things.
> > I just cannot agree with your opinion that the sum of the parts may
> > be sometimes greater than the whole.
> > First we may realize that integration is really a fuzzy concept not
> > only in the concept itself but also in the ways of integration.
> > There may be different kinds of integration and integration ways.
> > As for the Escher print, or the pictures given by Chris, we may just say
> > that the print or the pictures themselves are some kind of integration
> > since they have included what we have suspected from different viewpoints.
> > I think we should realize that self-inconsistency occurs very often
> > and perhaps it may be the main tune of the world. And what is more
> > important is that we should find a common mechanism of integration.
> > And can we find it?
>
> This is perhaps at the crux of the issue, and reflects broader problems of
> knowledge. One might regard it as the "fundamental paradox of science": how
> can a part of the universe hope understand the whole universe?
>
> By the same token you might regard it as suggesting a solution for that
> paradox: if you can project many new patterns out of any given pattern, then
> perhaps it is reasonable that the mind might conceive something greater than
> itself.
>
> Consciousness presents the same dilemma. How can the mind be aware of itself.
>
> The philosophy of it is interesting. It is Douglas Hofstadter who suggests to
> me Goedel might have something to do with it. He claims Goedel found that
> "any sufficiently powerful formal system specifies an infinite number of
> other formal systems." (P-7 from the preface to the 20th anniversary edition
> of GEB: "any formal system as powerful as PM does in fact contain models not
> just of itself but of an infinite number of other formal systems, some like
> it, some very much unlike it. That is essentially what Goedel realized.")
>
> If that is so then it does seem fair to say, in some way, that the system is
> greater than itself.
>
> The only thing I know for sure is that Goedel proved there are propositions p
> from which it follows that p and ~p are true.
>
> But this whole completeness issue is interesting. I would like to know because
> I would like to prove that it is more efficient to keep examples and find the
> order, than it is to find all the order and throw away the examples. The
> simple analogy of lining up a group of people in two ways seems to indicate
> that it is. But a mathematical proof would be nice.
>
> -Rob