Cf: Sign Relations • Denotation
http://inquiryintoinquiry.com/2020/06/23/sign-relations-%e2%80%a2-denotation/
One aspect of a sign's complete meaning concerns the reference a sign has to its objects, which objects are collectively
known as the “denotation” of the sign. In the pragmatic theory of sign relations, denotative references fall within the
projection of the sign relation on the plane spanned by its object domain and its sign domain.
The dyadic relation making up the “denotative”, “referent”, or “semantic” aspect of a sign relation L is notated as
Den(L). Information about the denotative aspect of meaning is obtained from L by taking its “projection” on the
object-sign plane. We may visualize this as the “shadow” L casts on the 2-dimensional space whose axes are the object
domain O and the sign domain S. The denotative component of a sign relation L, alternatively written in any of forms,
proj_OS L, L_OS, proj_12 L, and L_12, is defined as follows.
• Den(L) = proj_OS L = {(o, s) ∈ O × S : (o, s, i) ∈ L for some i ∈ I}.
Tables 3a and 3b show the denotative components of the sign relations
associated with the interpreters A and B, respectively. The rows
of each Table list the ordered pairs (o, s) in the corresponding
projections, Den(L_A), Den(L_B) ⊆ O × S.
Tables 3a and 3b. Denotative Components Den(L_A) and Den(L_B)
https://inquiryintoinquiry.files.wordpress.com/2020/06/sign-relation-twin-tables-den-la-den-lb.png
Looking to the denotative aspects of L_A and L_B,
various rows of the Tables specify, for example,
that A uses “i” to denote A and “u” to denote B,
while B uses “i” to denote B and “u” to denote A.
Regards,
Jon
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