[Inquiry] Re: Futures Of Logical Graphs -- Discussion

[Jon Awbrey]

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FOLG.  Discussion Note 35

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JA = Jon Awbrey
JR = Joe Ransdell

Re: FOLG 32.  http://stderr.org/pipermail/inquiry/2005-November/003206.html
In: FOLG.     http://stderr.org/pipermail/inquiry/2005-November/thread.html#3165

In part:

JA: Now it's true that Peirce's definition of a sign relation requires that
    every sign in a sign relation creates or determines an interpretant sign
    that serves as a sign in the very same sign relation, and which therefore
    creates or determines its own interpretant sign, and so on, 'ad infinitum'.
    But there is nothing that keeps this "infinite semiosis" from being bounded
    in the nutshell of a finite sign relation, because nothing says that all of
    the signs must be distinct, and nothing says that this formal determination
    has to be extended in a temporal sequence, though of course that may happen.

JA: In sum, we may view the sign relation as a generative structure,
    as a matrix that funds the generation of many possible semioses.

JR remarks:

JR: I agree, with one qualifications, namely, that
    although the formal determination need not be
    extended in a temporal sequence, the fact that
    semeiosis is a materially based process (it is
    not simply a material process, of course, but
    it must be embodied in some sense) would seem
    to imply that any objectionable infinities of
    interpretation in actual semeiosis processes
    are not to be accounted for in this way.
    For that you have to go beyond purely
    formal conceptions of semeiotic.

Joe, Cybernetics List, Peirce List,

Right.  I probably did not make it clear enough that I do not consider
infinite sequences of signs to be objectionable in and of themselves --
when the underlying sign relation generates them they are perfectly
valid examples of semiotic trajectories -- I am only pointing out
that they are not necessary consequences of Peirce's definition.
One of the features of a 3-adic relation is that the object is
formally present in every moment of sign to interpretant sign
transition, in other words, the object need not be assigned
a place in the temporal sequence of signs, and therefore
denotative or referent meaning is not at all deferred
or postponed simply due to the circumstance that the
semiosis might in fact be indefinitely prolonged.

JR: I should add, too, that none of this is revealed by
    the formalism you are constructing for some purpose
    not yet clear to me, but maybe you weren't intending
    to suggest that you derived these conclusions from
    that as your basis.

Since I'm ultimately interested in systems theoretic models of semiotic processes,
including things like communication, computation, inference, inquiry, and so on,
the dynamics of material processes is never far from mind, but the complexity
of such processes has to be organized in a conceptual scheme of many layers
and taken up in stages.

The types of structure that I'm laying out now have a dual purpose.
They show how semiotic processes of logical evaluation and proof
can be embedded in a sign relational matrix, and they meanwhile
provide us with a selection of simple but not entirely trivial
examples of semiotic processes to play with.

Jon Awbrey

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