ONT Re: Model Theory Unplugged
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MTU. Note 2
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Taking the broad view once again, formal semantics and model theory
connect up with two other subjects that take up overlapping domains
of study, if perhaps from slightly different points of view, namely,
semiotics, or the theory of signs, and the mathematical perspective
that is commonly known as "representation theory".
The next thing that I say will be so obvious to some people that
they will wonder why I bother to mention it at all, and yet so
shocking to other people that they must wonder that I dare to
say it in the first place.
Some of the earliest and still the most powerful theorems in
model theory were discovered by Benjamin and Charles Peirce.
I have to give the father and the son joint credit because
the basic ideas seem to go back to the elder's germinal
work in algebra and because their eventual flowering
in logical form stems from a phase in time when
we still cannot be sure who exactly did what.
The thing that makes my attribution totally unremarkable is the
fundmental unity between model theory and representation theory,
which is quite well known, if not always remarked in this context.
Consequently, one of the tasks ahead of us is to form a stereoscopic view --
perhaps more like a mosaic eye view -- of the common objects of semiotics,
formal semantics, model theory, and representation theory. I am guessing
that the bridge to the mathematical theory of representations is probably
the most uncertain one in most minds at the present juncture, and so I'll
begin by working on that.
Jon Awbrey
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