Sign Relations • 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 \mathrm{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, variously written in any of the forms, \mathrm{proj}_{OS} L,  L_{OS},  \mathrm{proj}_{12} L,  and L_{12}, is defined as follows.

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

Tables 3a and 3b show the denotative 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, s) in the corresponding projections, \mathrm{Den}(L_\mathrm{A}), \mathrm{Den}(L_\mathrm{B}) \subseteq O \times S.

Denotative Components Den(L_A) and Den(L_B)

Looking to the denotative aspects of L_\mathrm{A} and L_\mathrm{B}, various rows of the Tables specify, for example, that \mathrm{A} uses {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} to denote \mathrm{A} and {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} to denote \mathrm{B}, while \mathrm{B} uses {}^{\backprime\backprime} \mathrm{i} {}^{\prime\prime} to denote \mathrm{B} and {}^{\backprime\backprime} \mathrm{u} {}^{\prime\prime} to denote \mathrm{A}.

Resources

cc: FB | SemeioticsLaws of FormMathstodonAcademia.edu
cc: Conceptual GraphsCyberneticsStructural ModelingSystems Science

This entry was posted in C.S. Peirce, Inquiry, Logic, Mathematics, Relation Theory, Semiosis, Semiotics, Sign Relations, Triadicity and tagged , , , , , , , , . Bookmark the permalink.

4 Responses to Sign Relations • Denotation

  1. Pingback: Survey of Semiotics, Semiosis, Sign Relations • 5 | Inquiry Into Inquiry

  2. Pingback: Survey of Semiotics, Semiosis, Sign Relations • 5 | Inquiry Into Inquiry

  3. Pingback: Survey of Semiotics, Semiosis, Sign Relations • 6 | Inquiry Into Inquiry

  4. Pingback: Survey of Semiotics, Semiosis, Sign Relations • 6 | Systems Community of Inquiry

Leave a comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.