[CG] Re: Sign Relations

Sign Relations • Denotation • https://inquiryintoinquiry.com/2024/02/12/sign-relations-denotation-b/ All, 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, variously written in any of forms, proj_{OS} L, L_OS, proj₁₂ L, and L₁₂, 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-t… 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. Resources — Sign Relations • https://oeis.org/wiki/Sign_relation Denotation • https://oeis.org/wiki/Sign_relation#Denotation Document History • https://oeis.org/wiki/Sign_relation#Document_history Regards, Jon cc: https://www.academia.edu/community/VXKKxG cc: https://mathstodon.xyz/@Inquiry/111891382765624469