Cf: Sign Relations • Connotation
http://inquiryintoinquiry.com/2020/06/24/sign-relations-%e2%80%a2-connotation/
Another aspect of a sign's complete meaning concerns the reference a sign has to its interpretants, which interpretants
are collectively known as the “connotation” of the sign. In the pragmatic theory of sign relations, connotative
references fall within the projection of the sign relation on the plane spanned by its sign domain and its interpretant
domain.
In the full theory of sign relations the connotative aspect of meaning includes the links a sign has to affects,
concepts, ideas, impressions, intentions, and the whole realm of an interpretive agent's mental states and allied
activities, broadly encompassing intellectual associations, emotional impressions, motivational impulses, and real
conduct. Taken at the full, in the natural setting of semiotic phenomena, this complex system of references is unlikely
ever to find itself mapped in much detail, much less completely formalized, but the tangible warp of its accumulated
mass is commonly alluded to as the connotative import of language.
Formally speaking, however, the connotative aspect of meaning presents no additional difficulty. The dyadic relation
making up the connotative aspect of a sign relation L is notated as Con(L). Information about the connotative aspect of
meaning is obtained from L by taking its projection on the sign-interpretant plane. We may visualize this as the
“shadow” L casts on the 2-dimensional space whose axes are the sign domain S and the interpretant domain I. The
connotative component of a sign relation L, alternatively written in any of forms, proj_SI L, L_SI, proj_23 L, and L_23,
is defined as follows.
• Con(L) = proj_SI L = {(s, i) ∈ S × I : (o, s, i) ∈ L for some o ∈ O}.
Tables 4a and 4b show the connotative components of the sign relations
associated with the interpreters A and B, respectively. The rows
of each Table list the ordered pairs (s, i) in the corresponding
projections, Con(L_A), Con(L_B) ⊆ S × I.
Tables 4a and 4b. Connotative Components Con(L_A) and Con(L_B)
https://inquiryintoinquiry.files.wordpress.com/2020/06/sign-relation-twin-tables-con-la-con-lb.png
References
==========
• Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75),
in Carolyn Eisele (ed., 1976), The New Elements of Mathematics
by Charles S. Peirce, vol. 4, 13–73.
https://arisbe.sitehost.iu.edu/menu/library/bycsp/L75/l75.htm
• Awbrey, J.L., and Awbrey, S.M. (1995),
“Interpretation as Action : The Risk of Inquiry”,
Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.
https://web.archive.org/web/20001210162300/http://chss.montclair.edu/inquiry/fall95/awbrey.html
https://www.pdcnet.org/inquiryct/content/inquiryct_1995_0015_0001_0040_0052
https://www.academia.edu/1266493/Interpretation_as_Action_The_Risk_of_Inquiry
Resources
=========
• Semeiotic ( https://oeis.org/wiki/Semeiotic )
• Logic Syllabus ( https://inquiryintoinquiry.com/logic-syllabus/ )
• Sign Relations ( https://oeis.org/wiki/Sign_relation )
• Triadic Relations ( https://oeis.org/wiki/Triadic_relation )
* Relation Theory ( https://oeis.org/wiki/Relation_theory )
Regards,
Jon
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