SUO: Re: Examples! Examples! Examples!
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EEE. Note 9
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What's Your Semiotic Quotient?
We are about to undertake the practice of two "forms of ignorance" (FOI's) --
now "Ignoring Stuff" is everybody's information management tool of choice,
at least quasi modo infantes, but like every faith that entertains service
to a duplicity of masters it is crucial to observe, with all due constancy
and fidelity, exactly which is which.
FOI 1. There's the stuff that we ignore because we just can't help it.
We are faced with, entangled by a situation of data overload --
I don't call it information overload, because information,
if we really had it, would be the cure. In the picture
of TLC that I drew in Figure 4, this is represented
by the ellipses "..." that are drawn in lieu of the
big middle regions of the extensional lattices.
FOI 2. There are the distinctions that we have deliberately decided to
collapse, ignore, neglect, or quotient out of mind, out of sight,
for the time being, or for the sake of the immediate end in view.
The latter more discerning form of ignorance is what we need to take up next.
I will approach the syntactic and theoretical domains of the TLC example in
a series of stages, using the few pieces of scaffolding that I usually use
for these types of problems, as indicated in the next couple of Figures.
o-----------------------------o-----------------------------o
| Object Domain | Syntactic Domain |
o-----------------------------o-----------------------------o
| |
| o-----------o |
| o~~~~~~~~~~~~~~~~~~~~~~~~/| s s s ... |\ |
| / \ / o-----------o \ |
| / \ / \ |
| / \ o-----------o \ |
| o~~~~~~~~~~~~~~~~~~~~~~~~~| s s s ... | \ |
| \ \ o-----------o \ |
| \ \ \ \ |
| \ \ \ o-----------o |
| \ o~~~~~~~~~~~~~~~~\~~~~~~~~| s s s ... | |
| \ / \ o-----------o |
| \ / \ / |
| \ / \ o-----------o / |
| o~~~~~~~~~~~~~~~~~~~~~~~~\| s s s ... |/ |
| o-----------o |
| |
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Figure 5. Lattice of Objects Inducing a Partition of Signs
Figure 5 depicts the generic situation, where we form a quotient
in a space of signs, that is, any species of syntactic elements,
in a way that corresponds to the elements in a space of objects,
in this case organized in the structure of a lattice ordering.
o--------------------------o---------------o--------------------------o
| Syntactic Domain 1 | Object Domain | Syntactic Domain 2 |
o--------------------------o---------------o--------------------------o
| |
| o-----------o o-----------o |
| /| s s s ... |\~~~~~~~~~~~~~o~~~~~~~~~~~~~/| s s s ... |\ |
| / o-----------o \ / \ / o-----------o \ |
| / \ / \ / \ |
| o-----------o \ / \ o-----------o \ |
| | s s s ... |~~~~~~~~\~~~~~o~~~~~~~\~~~~~~| s s s ... | \ |
| o-----------o \ \ \ o-----------o \ |
| \ \ \ \ \ \ |
| \ o-----------o \ \ \ o-----------o |
| \ | s s s ... |~~~~~~\~~~~~~~o~~~~~\~~~~~~~~| s s s ... | |
| \ o-----------o \ / \ o-----------o |
| \ / \ / \ / |
| \ o-----------o / \ / \ o-----------o / |
| \| s s s ... |/~~~~~~~~~~~~~o~~~~~~~~~~~~~\| s s s ... |/ |
| o-----------o o-----------o |
| |
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Figure 6. Lattice of Objects Inducing a Diversity of Sign Partitions
Figure 6 illustrates one potential direction of thickening plot,
where we have two different languages or systems of signs, each
of them falling into equivalence classes of signs according to
their separate notions of equivalence. If these equivalence
classes correspond to objects of the relevant object domain,
the way that I have drawn them in the Figure, then they are
called "referential equivalence classes" (REC's). However,
it would also be possible to form up equivalence classes
of signs according to any plan that strikes one's fancy,
whether it was modeled on objective reality or not, and
these more capricious sorts of equivalence classes are
referred to as "semiotic equivalence classes" (SEC's).
Jon Awbrey
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