[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 7

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It is well to observe that the form of determination that we find
in an abstract sign relation is not of necessity an "absolute" or
a "functional" determination.  For example, given the object B in
the sign relation L(A), there two possible signs for it, namely,
"B" and "u".  This amounts to a non-trivial constraint, since
the set of signs {"B", "u"} is a proper subset of !S!, but
it does not amount to an absolute determination, since
the corresponding 2-adic relation between !O! and !S!
is not a function from !O! to !S!, there being more
than one relational image of some objects in !O!.
In fact, this is true for every object in !O!.
In contrast, given any sign in the domain !S!
of L(A), there is exactly one object in the
domain !O! that that corresponds to it, and
so the corresponding 2-adic relation from
!S! to !O! is a function.  Thus we may
write it in the form f : !S! -> !O!.
This relation is the "denotation"
relation, and it happens in this
case to be a function for both
sign relations L(A) and L(B).

Jon Awbrey

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