[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 31

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Peirce List,

Perhaps one other preliminary comment on the character of determination,
as it is characterized in Peirce's and in formally akin writings, would
be in order.  Our biologically evolved natural languages are apparently
not yet evolved enough to handle relations in general with any facility.
They avail us with forms of syntax that can be patched together more or
mostly less well to handle many particular situations, to be sure, else
we would not have evolved far enough to reflect on the issue, but there
is the tendency of these languages to focus our attention on the single
case rather than the systems ruled, and, what amounts to their greatest
aberrancy of continged coloring and distorted shaping, the liability to
which they expose us of confounding the forms of objects with the forms
of syntax.  This is one of the reasons that Peirce found himself forced
by the task of understanding how science works to create a new language
for talking about sign relations, and found himself forced by this task
in turn to create a new language for talking about relations in general,
that he was well on the way to doing by the "Logic of Relatives" (1870).

As we have discussed on many occasions, determination is not a property
of single cases, single pairs of elements, or single tuples in relation.
It is a concept that only makes sense with regard to whole systems that
are affected by or participate in systematic relations of the type that
we call determinate.

Determination is not just a property of 2-adic relations, as "x determines y",
but is a concept that can be applied to arbitrary relations, even those which
do not have a definable arity or adicity.  Without going to those extremes of
generality just yet, however, we can say for the present that it also applies
to k-adic relations, as "x_1 determines x_2, ..., x_k".  We're naturally very
focused on the present application to sign relations, in the case where k = 3.

With these generalities sufficiently covered for now,
it will perhaps be helpful to concoct a few examples.

After another hit of coffee ...

Jon Awbrey

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