[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 29

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Before we set out in quest of the SPICON, there are
a few other ground rules that come to mind that are
probably necessary to articulate as best that I can.

First, we need to understand that we're looking for a sign relation,
a collection of 3-tuples of the form <x, y, z> in a cartesian space
X x Y x Z, for suitable choices of the sets X, Y, Z, to be known as
the "object domain", the "sign domain", the "interpretant domain"
respectively.  The choice of these three domains, along with the
choice of a subset L c X x Y x Z, are choices that are up to us
to make in our tries at constructing a sign relation L that'll
fit all of the conditions that we find ourselves led by the
accumulated definitions to lay on it.

Second, though it's possible to make a big fuss about the
distinction between axioms and definitions, I will not be
doing that in this setting.  I am more used to the way of
talking that says, for example, "a mathematical object of
type T is 'defined' by the following set of 'axioms' ...",
and that is the manner of speaking that I'll have in mind.

Third, depending on how one states ones axioms or definitions,
there may be many sorts of trivial examples of the concept in
question.  For instance, some people will allow the empty set
to be counted as a graph or a group -- I have seen some silly
fights break out at conferences, and there's actually a paper
somewhere entitled "Is the Empty Graph a Pointless Concept?" --
but sensible people will usually just stipulate "nonempty set"
as part of the definition of whatever it is they have in mind.

Fourth, I am taking it for granted that we are limiting our
interest to "non-trivial" sign relations.  This rules out,
for instance, the empty sign relation, L = {} c X x Y x Z,
and singleton sign relations, L = {<x, y, z>} c X x Y x Z.

Acronymic accuracy would probably demand that I nomenclate it as
a "smallest possible un-trivial iconic sign relation" (SPUTICON),
but that sounds too medicinal.

Jon Awbrey

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