[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 28

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Formal reasoning of the sort that they do in mathematics, for all
its abstraction, would make very little headway without the benefit
of lots and lots of concrete examples.  And so the student who could
not provide examples of algebras, geometries, graphs, groups, spaces,
topologies, or whatever that exemplify this or that set of properties
would hardly get past the first quiz in whatever course he or she took.
The spectrum of shades from abstract to concrete is relative, of course.

Thus it presents something of a problem in trying to understand Peirce that
concrete examples, fleshed out to the level of detail that it takes to fully
exemplify his more abstract concepts, are few and far between in his writings.
They are slightly more prevalent in his earliest lectures and especially in his
mathematical papers, which is one of the reasons that I find myself eternally
returning to them for the clarification of his ideas.  So we have to do as
they commonly do in math courses, which is to make the most of the sparse
examples that are doled out to us, to work through the proofs ourselves,
often to fill in their gaps and correct their gaffes, and to recognize
the times when we have encountered, as teachers and textbook writers
frequently say, an "exercise for the reader".  In the present cases
the exercises require us to construct objects to specifications.

With all that in mind, let us return to the quest for something
nigh unto the "smallest possible iconic sign relation" (SPICON).
I think that many of the difficulties that we find in reasoning
about the relations of signs in general to the assorted species
of signs, like icons and indices, would be greatly eased by the
examination of such concretely detailed examples, if we can but
find a few.

Jon Awbrey

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