[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 8

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Let us now discuss another issue that often comes up in discussing
sign relations, the question of their possible cardinalities.  The
recursive form of the usual definition of a sign relation may lead
one to think that sign relations are necessarily infinite, but the
definition is in fact perfectly consistent with the existence of
finite sign relations, that is, those that have a finite number
of triples.  For example, L(A) and L(B) each have eight triples.

The definition of a sign relation does require that each sign of
a given object requires the existence of another sign of the same
object to fill the role of its interpretant, which in turn requires
the existence of a further sign of the same object to fill the role
of its interpretant, and so on, 'ad infinitum', one might say, but
this does not necessitate that all of these signs are different or
even that they succeed one another in time.  At this highest level
of abstraction the sign relation demands no more than a purely
formal or logical determination, not a causal or temporal one.
Accordingly, it is best to view this form of determination as
a form of closure, one that can be filled by a finite number
of signs, interpretant signs, and sign relational triples.

Jon Awbrey

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