## Sign Relations • Ennotation

A third aspect of a sign’s complete meaning concerns the reference its objects have to its interpretants, which has no standard name in semiotics.  It would be called an induced relation in graph theory or the result of relational composition in relation theory.  If an interpretant is recognized as a sign in its own right then its independent reference to an object can be taken as belonging to another moment of denotation, but this neglects the mediational character of the whole transaction in which this occurs.  Denotation and connotation have to do with dyadic relations in which the sign plays an active role but here we are dealing with a dyadic relation between objects and interpretants mediated by the sign from an off-stage position, as it were.

As a relation between objects and interpretants mediated by a sign, this third aspect of meaning may be referred to as the ennotation of a sign and the dyadic relation making up the ennotative aspect of a sign relation $L$ may be notated as $\mathrm{Enn}(L).$  Information about the ennotative aspect of meaning is obtained from $L$ by taking its projection on the object-interpretant plane.  We may visualize this as the “shadow” $L$ casts on the 2-dimensional space whose axes are the object domain $O$ and the interpretant domain $I.$  The ennotative component of a sign relation $L,$ alternatively written in any of forms, $\mathrm{proj}_{OI} L,$ $L_{OI},$ $\mathrm{proj}_{13} L,$  and $L_{13},$ is defined as follows. $\begin{matrix} \mathrm{Enn}(L) & = & \mathrm{proj}_{OI} L & = & \{ (o, i) \in O \times I ~:~ (o, s, i) \in L ~\text{for some}~ s \in S \}. \end{matrix}$

As it happens, the sign relations $L_\mathrm{A}$ and $L_\mathrm{B}$ are fully symmetric with respect to exchanging signs and interpretants, so all the data of $\mathrm{proj}_{OS} L_\mathrm{A}$ is echoed unchanged in $\mathrm{proj}_{OI} L_\mathrm{A}$ and all the data of $\mathrm{proj}_{OS} L_\mathrm{B}$ is echoed unchanged in $\mathrm{proj}_{OI} L_\mathrm{B}.$

Tables 5a and 5b show the ennotative components of the sign relations associated with the interpreters $\mathrm{A}$ and $\mathrm{B},$ respectively.  The rows of each Table list the ordered pairs $(o, i)$ in the corresponding projections, $\mathrm{Enn}(L_\mathrm{A}), \mathrm{Enn}(L_\mathrm{B}) \subseteq O \times I.$ ### 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.  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.  ArchiveJournalOnline.

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Portions of the above article were adapted from the following sources under the GNU Free Documentation License, under other applicable licenses, or by permission of the copyright holders.

cc: CyberneticsOntolog • Peirce List (1) (2)Structural ModelingSystems Science

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