Cf: Triadic Relations • 2
At: http://inquiryintoinquiry.com/2020/05/24/triadic-relations-%e2%80%a2-2/
Examples from Semiotics
=======================
The study of signs — the full variety of significant forms of expression — in relation to all the affairs signs are
significant of, and in relation to all the beings signs are significant to, is known as “semiotics” or the theory of
signs. As described, semiotics treats of a 3-place relation among signs, their objects, and their interpreters.
The term “semiosis” refers to any activity or process involving signs. Studies of semiosis focusing on its abstract
form are not concerned with every concrete detail of the entities acting as signs, as objects, or as agents of semiosis,
but only with the most salient patterns of relationship among those three roles. In particular, the formal theory of
signs does not consider all the properties of the interpretive agent but only the more striking features of the
impressions signs make on a representative interpreter. From a formal point of view this impact or influence may be
treated as just another sign, called the “interpretant sign”, or the “interpretant” for short. A triadic relation of
this type, among objects, signs, and interpretants, is called a “sign relation”.
For example, consider the aspects of sign use involved when two people, say Ann and Bob, use their own proper names,
“Ann” and “Bob”, along with the pronouns, “I” and “you”, to refer to themselves and each other. For brevity, these four
signs may be abbreviated to the set {“A”, “B”, “i”, “u”}. The abstract consideration of how A and B use this set of
signs leads to the contemplation of a pair of triadic relations, the sign relations L_A and L_B, reflecting the
differential use of these signs by A and B, respectively.
Each of the sign relations L_A and L_B consists of eight triples of the form (x, y, z), where the “object” x belongs to
the “object domain” O = {A, B}, the “sign” y belongs to the “sign domain” S, the “interpretant sign” z belongs to the
“interpretant domain” I, and where it happens in this case that S = I = {“A”, “B”, “i”, “u”}. The union S ∪ I is often
referred to as the “syntactic domain”, but in this case S = I = S ∪ I.
The set-up so far is summarized as follows:
• L_A, L_B ⊆ O × S × I
• O = {A, B}
• S = {“A”, “B”, “i”, “u”}
• I = {“A”, “B”, “i”, “u”}
The relation L_A is the following set of eight triples in O × S × I.
{ (A, “A”, “A”), (A, “A”, “i”), (A, “i”, “A”), (A, “i”, “i”),
(B, “B”, “B”), (B, “B”, “u”), (B, “u”, “B”), (B, “u”, “u”) }
The triples in L_A represent the way interpreter A uses signs. For example, the presence of (B, “u”, “B”) in L_A says A
uses “B” to mean the same thing A uses “u” to mean, namely, B.
The relation L_B is the following set of eight triples in O × S × I.
{ (A, “A”, “A”), (A, “A”, “u”), (A, “u”, “A”), (A, “u”, “u”),
(B, “B”, “B”), (B, “B”, “i”), (B, “i”, “B”), (B, “i”, “i”) }
The triples in L_B represent the way interpreter B uses signs. For example, the presence of (B, “i”, “B”) in L_B says B
uses “B” to mean the same thing B uses “i” to mean, namely, B.
The triples in the relations L_A and L_B are conveniently arranged in the form
of relational data tables, as shown below.
L_A = Sign Relation of Interpreter A
https://inquiryintoinquiry.files.wordpress.com/2020/05/sign-relation-la-interpreter-a.png
L_B = Sign Relation of Interpreter B
https://inquiryintoinquiry.files.wordpress.com/2020/05/sign-relation-lb-interpreter-b.png
Resources
=========
• Semiotics ( 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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