[Inquiry] Re: Sign Relations -- Commentary

[Jon Awbrey]

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SR.  Commentary Note 3

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For ease of reference, I repeat here the explication
of the sign relation definition that I gave last time:

CSP: | A sign is something, 'A', which brings something, 'B',
     | its 'interpretant' sign, determined or created by it,
     | into the same sort of correspondence (or a lower implied
     | sort) with something, 'C', its 'object', as that in which
     | itself stands to 'C'.

JA: | It is immportant to note that the "correspondence" referred to here is
    | a "triple correspondence", what might be called a "3-place transaction"
    | in database terms.  Let us refer to this 3-place relation as L.  To say
    | that "A brings B to correspond with C in the same way that A corresponds
    | with C" is simply to say that A brings B into the same 3-place relation L
    | with something else B' and C, in that order, as A occupies in the 3-place
    | relation L with B and C, in that order.
    |
    | To make this clearer, I will draw out the inference over several steps:
    |
    | Using the acronym "SOC" for "sort of correspondence",
    | I form the following paraphrase of the main condition:
    |
    |    A brings something into the same SOC with C
    |    as the SOC in which A stands to C.
    |
    | In order to expand the expression correctly, one has to ask:
    |
    |    What is the SOC in which A stands to C?
    |
    | The SOC in which A stands to C is given by Formula 1.
    |
    |    1.  A brings something into some SOC with C,
    |        namely, the SOC in which A stands to C.
    |
    | If B enters into the same SOC with C as A stands in, that is to say,
    | if B takes up the same role that A had in Formula 1, then we obtain:
    |
    |    2.  B brings something into some SOC with C,
    |        namely, the SOC in which A stands to C.
    |
    | Let us suppose that B' is the something in Formula 2.
    | Now, B' can either be something old or something new.
    | If B' is something old, then it belongs to {A, B, C}.
    | If B' is something new, we leave it with the name B'.
    |
    | In any case, we have:
    |
    |    3.  B brings a thing B' into some SOC with C,
    |        namely, the SOC in which A stands to C.
    |
    | In sum, the bringing of a new, possibly old, thing
    | into the relation is part of being in the relation.

At this point it may be useful to remark that most of the
complexity of the above unpacking is due to the fact that
we put the burden of maintaining the entire sign relation
on the backs of the individual signs, as if it were their
job to carry the load all by themselves.  Perhaps this is
true in actual point of fact, but for the sake of logical
analysis it is much more convenient and achieves much the
same effect to think of the sign relation separately as a
structure that is preserved invariant under the allowable
processes of sign relational transformation, or semiosis.

Jon Awbrey

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