Cf: Sign Relations • Examples
At: http://inquiryintoinquiry.com/2020/06/16/sign-relations-%e2%80%a2-examples/
Because the examples to follow have been artificially constructed to be as simple as possible, their detailed
elaboration can run the risk of trivializing the whole theory of sign relations. Despite their simplicity, however,
these examples have subtleties of their own, and their careful treatment will serve to illustrate many important issues
in the general theory of signs.
Imagine a discussion between two people, Ann and Bob, and attend only to the aspects of their interpretive practice
involving the use of the following nouns and pronouns:
"Ann", "Bob", "I", "you".
* The "object domain" of their discussion is the set of two people {Ann, Bob}.
* The "sign domain" of their discussion is the set of four signs {"Ann", "Bob", "I",
"you"}.
Ann and Bob are not only the passive objects of linguistic references but also the active interpreters of the language
they use. The "system of interpretation" (SOI) associated with each language user can be represented in the form of an
individual three-place relation known as the "sign relation" of that interpreter.
In terms of its set-theoretic extension, a sign relation L is a subset of a cartesian product O x S x I. The three sets
O, S, I are known as the "object domain", the "sign domain", and the "interpretant domain", respectively, of the sign
relation L as a subset of O x S x I.
Broadly speaking, the three domains of a sign relation may be any sets at all but the types of sign relations
contemplated in formal settings are usually constrained to having I as a subset of S. In that case it becomes
convenient to lump signs and interpretants together into a single class called the "sign system" or the "syntactic
domain". In the forthcoming examples S and I are identical as sets, so the same elements manifest themselves in two
different roles of the sign relations in question.
When it becomes necessary to refer to the whole set of objects and signs in the union of the domains O, S, I for a given
sign relation L, we will call this set the "World of L" and write W = W_L = O ∪ S ∪ I.
To facilitate an interest in the formal structures of sign relations and to keep notations as uncluttered as possible as
the examples become more complicated, it serves to introduce the following general notations:
* O = Object Domain
* S = Sign Domain
* I = Interpretant Domain
Introducing a few abbreviations for use in this Example, we have the following
data:
* O = {Ann, Bob} = {A, B}
* S = {"Ann", "Bob", "I", "you"} = {"A", "B", "i", "u"}
* I = {"Ann", "Bob", "I", "you"} = {"A", "B", "i", "u"}
In the present example, S = I = Syntactic Domain.
Tables 1a and 1b show the sign relations associated with the interpreters A and B, respectively. In this arrangement
the rows of each Table list the ordered triples of the form (o, s, i) belonging to the corresponding sign relations,
L_A, L_B as subsets of O x S x I.
Sign Relation Tables L_A and L_B
https://inquiryintoinquiry.files.wordpress.com/2020/05/sign-relation-twin-tables-la-lb.png
These Tables codify a rudimentary level of interpretive practice for the agents A and B and provide a basis for
formalizing the initial semantics appropriate to their common syntactic domain. Each row of a Table names an object and
two co-referent signs, making up an ordered triple of the form (o, s, i) called an "elementary relation", that is, one
element of the relation's set-theoretic extension.
Already in this elementary context, there are several different meanings that might attach to the project of a formal
semiotics, or a formal theory of meaning for signs. In the process of discussing these alternatives, it is useful to
introduce a few terms occasionally used in the philosophy of language to point out the needed distinctions. That is the
task we'll turn to next.
Regards,
Jon
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