Re: [ontolog-forum] Axiomatic ontology

[Pat Hayes <phayes@xxxxxxx>]

At 2:05 PM +0100 2/7/08, Jakub Kotowski wrote:

> Hi Rob,
>
> Rob Freeman napsal(a):
> > I probably used the words "not empty" because I had
> just read Ramsey's
> > Theorem stated in terms of systems with objects "within"
> them in this
> > definition I found on the Web:
> >
> > "No matter how jumbled and chaotic you try to arrange
> certain objects,
> > you will find yourself creating a very highly organized and
> structured
> > object within it."
> > (http://www.math.uchicago.edu/~mileti/museum/ramsey.html)
> >
> >  
> The highly organized objects, they refer to, correspond exactly to
> the
> complete subgraphs I was talking about. In this sense perhaps yes -
> the
> chaotic are not empty sometimes in a precise sense :)

Are you guys using 'chaotic' here in the technical sense from chaos theory, or in some looser sense? Because Ramsey Schmamsey, chaos-theory-type chaotic systems certainly do *exist*.

> > I don't know how chaos is regarded
> in information theory.
> >  
> I unfortunately do not have much background in information or
> chaos
> theory but I am interested in it too. I googled a paper that may be
> of
> interest to you because except chaos and information theory it
> also
> refers to Kolmogorov's algorithmic complexity (algorithmic
> entropy).
> However, they are more concerned with measuring information and
> entropy
> of finite strings (with a possible application to data
> compression):

Yes, quite. Remember that information theory is all about measuring information-bearing capacity. Its like a theory of the volume of buckets: it says nothing about what kind of liquid is actually in the bucket. So according to Kolmogoroff theory, a random sequence has maximum information (capacity). True: but the only information it can bear is information about itself. One gets a kind of informational rigidity, where the possible content is reduced to zero when the capacity is at a theoretical maximum. If I knew more about QED I might suggest an analogy with Bohr/Heisenberg complementarity, but I don't so I won't.

Pat

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