[Inquiry] Re: Purpose Of Scientific Inquiry -- Discussion

[Jon Awbrey]

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POSI.  Discussion Note 4

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John,

Continuing to work my way backward through your last message:

JW: Anyway in looking at George J. Friedman's
    constraint theory where he uses bipartite
    graphs to show that variables are connected
    through relationships, and is able to find
    a very wide variety of structural features
    enabling consistency to be determined by the
    structural features alone without resorting
    to the details of the relationships, I have
    urged him many times to consider the concept
    of tying the interpretation to the underlying
    lattice, where I felt the whole of constraint
    theory could be seen in its simplest point of
    view.  George either did not agree, or had too
    much else to do.

I will have to take your word for it on Friedman's constraint theory,
but the definition of information in terms of constraints, gleaned from
Ashby, McCulloch, Wiener, the early "human information processing" (HIP)
tradition, the "structural models" paradigm in statistics, and others,
is one that is constantly on my mind, if that forms some part of what
we're talking about here.

Still, as useful as they are, bigraphs are models of 2-adic relations,
and that is too reductive a formalism to cover what is needed in the
theory of sign relations.  Even if you put weights on the edges you
still only get a very special case of 3-adic relations, probably
not enough for semiotics, and thus insufficiently complex for
the analysis of logical inference and information processing.
And lattices, too, as fond as I am of them, are but special
sorts of 2-adic relations, not enough to preserve all of
the pertinent structure in domains where irreducibly
3-adic relations come into play.  We eventually run
into the problem that many overlapping lattices or
partial orders will be required to capture the
complex of relationships in a complex domain.

Jon Awbrey

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