n-Conclusive n-Substantial Postscripts

The discussion in progress is extremely stimulating --
and I find myself constantly flashing on many ideas that
I'd forgotten anyone still cared about.  But flashbacks are
not always conducive to coherent dialogue, so let me just
post a few pointers to places where I had the spacetime
and the presence of mind to work through the issues
in a more substantive way.

There is a field of study, _semiotics_, devoted to the ways
that "marks on paper" and other modulations of other media
relate their various kinds of meaning to the agents who
interpret those signs.

Some parts of semiotics have gotten pretty wild and woolly in post*modern times,
but the pre-modern founder of the subject, C.S. Peirce, thought it was important
enough to define "logic" as "formal semiotics".  Now, he may have purloined that
idea from Locke, but he added enough value of his own to make a good case for
the claim.

Semiotics of the Peircean variety is pursued by means of
<a href="http://ncatlab.org/nlab/show/triadic+relation">triadic relations</a>
called <a href="http://ncatlab.org/nlab/show/sign+relation">sign relations</a>.

I had been studying sign relations for many years, in contexts where the
domains of signs are the kinds of formal languages that arise in logic,
and had never really thought all that much about the finite case, when
my systems engineering advisor at the time asked me to come up with a
simple, finite, but still non-trivial example.  I included a couple
of such examples in the articles just linked, and I think their
study repays many dividends when it comes to grasping the
essentials in vastly more complex situations.

Jon Awbrey

[Re*cycled from a discussion at the n-Category Cafe]

cc: Arisbe, Inquiry

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