[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

SR.  Commentary Note 5

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

There are systems whose states and developments of states
bear witness to objective realities and real objectives
that transcend the mere immediacy of those states and
developments.  How is this possible?  When it happens
we say that some aspects of state codify or denote
the elements and properties of an object system,
which may well be the system itself or perhaps
yet another system.  The study of such cases
is the subject matter of semiotics, as cast
in the focus of a system-theoretic light.

Surprisingly enough, the advance of an abstract science like
logic, mathematics, or semiotics depends on the accumulation
of a large stock of well-studied concrete examples.  We have
lots of those in logic and math, but not so many non-trivial
examples as yet in semiotics.  It will be necessary to begin
with some very elementary, but not quite trivial examples of
sign relations, that we may anticipate as affording us clues
to more complex examples down the line.

In this spirit, let me revive once more the "Story of A and B",
where we fix on those aspects of sign use between two people,
say, Ann and Bob, that concern their use of their own proper
names, "Ann" and "Bob", along with the pronouns "I" and "you".
For the sake of brevity, I abbreviate these four signs to the
set {"A", "B", "i", "u"}.  A maximally abstract consideration
of how A and B use these signs to refer to themselves and to
each other leads to the contemplation of two sign relations,
L(A) and L(B), as employed by A and B, respectively.

The 3-adic sign relations, L(A) and L(B), each consist of eight triples
of the form <x, y, z>, where the object x belongs to the object domain
!O! = {A, B}, where the sign y belongs to the sign domain !S!, where
the interpretant sign z belongs to the interpretant domain !I!, and
where it happens in this case that !S! = !I! = {"A", "B", "i", "u"}.
In general, it is convenient to refer to the union !S! |_| !I! as
the "syntactic domain", but in this case !S! = !I! = !S! |_| !I!.

Tables 1 and 2 present the triples of L(A) and L(B), respectively.

Table 1.  Sign Relation of Interpreter A
o---------------o---------------o---------------o
| Object        | Sign          | Interpretant  |
o---------------o---------------o---------------o
| A             | "A"           | "A"           |
| A             | "A"           | "i"           |
| A             | "i"           | "A"           |
| A             | "i"           | "i"           |
| B             | "B"           | "B"           |
| B             | "B"           | "u"           |
| B             | "u"           | "B"           |
| B             | "u"           | "u"           |
o---------------o---------------o---------------o

Table 2.  Sign Relation of Interpreter B
o---------------o---------------o---------------o
| Object        | Sign          | Interpretant  |
o---------------o---------------o---------------o
| A             | "A"           | "A"           |
| A             | "A"           | "u"           |
| A             | "u"           | "A"           |
| A             | "u"           | "u"           |
| B             | "B"           | "B"           |
| B             | "B"           | "i"           |
| B             | "i"           | "B"           |
| B             | "i"           | "i"           |
o---------------o---------------o---------------o

Jon Awbrey

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o