[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 32

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Cybernetics List, Peirce List,

Earnest contemplation of the relationship between semiotic trajectories
and the infrastructure of sign relations that is needed to support them
may bring the seeker to a state of enlightenment about a motley crew of
old knots in the semiotic web of maya, most pointedly the one that goes
about raveling and reveiling the world in the name of infinite semiosis.

To see how the variety of misunderstandings
about infinite semiosis got started, it may
help to refresh our memories with regard to
one of Peirce's last, best definitions of
a sign relation:

| A sign is something, A, which brings something, B,
| its interpretant sign determined or created by it,
| into the same sort of correspondence with something,
| C, its object, as that in which itself stands to C.
|
| C.S. Peirce, NEM 4, pp. 20-21, cf. p. 54 (1902).
|
| C.S. Peirce, [Application to the Carnegie Institution], L 75, pp. 13-73 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by Charles S. Peirce,
| Volume 4, Mathematical Philosophy', Mouton, The Hague, 1976.  Available here:
| Arisbe Website, http://members.door.net/arisbe/menu/library/bycsp/l75/l75.htm

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.

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

Jon Awbrey

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