[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 6

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Let us now discuss the way in which the sign relations
L(A) and L(B) satisfy the definition of sign relations
that was given earlier.  This involves us in detailing
the forms of correspondence and determination that are
exemplified by L(A) and L(B).  At the present level of
abstraction, we are dealing with sign relations simple,
with no parameters of time and causality yet specified,
and thus we have no specification of the corresponding
sign processes, though it can be said that these forms
produce all of the sign processes that conform to them.

As it happens, all of the various aspects of correspondence
and determination can be subsumed under the general concept
of "constraint", as it is understood in information theory.
For example, the fact that the sign relations L(A) and L(B)
are proper subsets of the cartesian product !O! x !S! x !I!
implies that a non-trivial constraint is present, and such
a constraint can generally be exploited somehow or another
for the sake of conveying information.  More specifically,
we can say that the object A constrains or determines the
sign and the interpretant within the sign relation L(B) in
that the set of pairs from the SI plane !S! x !I! that are
compatible with having A in the object role, in other words,
that form triples of L(B) when combined with A as an object,
is a proper the subset of the SI plane, namely, the set of
four pairs {<"A", "A">, <"A", "u">, <"u", "A">, <"u", "u">}.
This is "determination" in a formal or mathematical sense,
as when we treat of algebras, geometries, or combinatorial
designs of various sorts.  Thus we can speak of how signs
determine objects and interpretants, or how interpretants
determine objects and signs, all with equal facility.

Jon Awbrey

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