Sign Relations • 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 $\mathrm{Con}(L).$  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 $L,$ variously written in any of the forms, $\mathrm{proj}_{SI} L,$  $L_{SI},$  $\mathrm{proj}_{23} L,$  and $L_{23},$ is defined as follows.

$\begin{matrix} \mathrm{Con}(L) & = & \mathrm{proj}_{SI} L & = & \{ (s, i) \in S \times I ~:~ (o, s, i) \in L ~\text{for some}~ o \in O \}. \end{matrix}$

Tables 4a and 4b show the connotative components of the sign relations associated with the interpreters $\mathrm{A}$ and $\mathrm{B},$ respectively.  The rows of each Table list the ordered pairs $(s, i)$ in the corresponding projections, $\mathrm{Con}(L_\mathrm{A}), \mathrm{Con}(L_\mathrm{B}) \subseteq S \times I.$

References

• Charles S. Peirce (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.  Online.
• 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.  ArchiveJournal.  Online (doc) (pdf).

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