[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 8

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Cybernetics List, Peirce List,

In order to discuss the various forms of iconicity that might be
involved in the application of Peirce's logical graphs and their
kind to the object domain of logic itself, we will need to bring
out two or three "categories of structured individuals" (COSI's),
depending on how we count.  These are called the "object domain",
the "sign domain", and the "interpretant sign domain", which may
be written !O!, !S!, !I!, respectively, or X, Y, Z, respectively,
depending on the style that fits the current frame of discussion.

For the time being, I will be considering systems where the sign
domain and the interpretant domain are the same sets of entities,
although, of course, their roles in a given "sign relation", say,
L c !O! x !S! x !I! or L c X x Y x Z, remain as distinct as ever.
I will tend to use the term "semiotic domain" for the common set
of elements that constitute the signs and the interpretant signs
in any setting where the sign domain and the interpretant domain
are equal as sets.

At the "alpha level", "primary arithmetic", or "zeroth order" of
consideration that we have so far introduced, the sign domain is
any one of the several "formal languages" that we have placed in
one-to-one correspondence with each other, namely, the languages
of non-intersecting plane closed curves, well-formed parenthesis
strings, or rooted trees.  The interpretant sign domain will for
the present be taken to be any one of the same languages, and so
I'll refer to any of them indifferently as the "semiotic domain".

But that's enough for a Sunday afternoon ...

Jon Awbrey

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