[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 5

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Cybernetics List, Peirce List,

For some reason -- that I won't stop to examine right now --
I tend to think "category of structured individuals" when
the individuals in question have a whole lot of structure,
but "collection of structured items" when the individuals
have a minimal amount of internal structure.  For example,
any set is a COSI, so any relation in extension is a COSI,
but a 1-adic relation is just a set of 1-tuples, that are
in some lights indiscernible from their single components,
and so its structured individuals have far less structure
than the k-tuples of k-adic relations, when k exceeds one.
This spectrum of differentiations among relational models
will be useful to bear in mind when the time comes to say
what distinquishes relational thinking proper from 1-adic
and 2-adic thinking, that constitute its degenerate cases.

Still on our way to saying what brands of iconicity are worth buying,
at least when it comes to graphical systems of logic, it will useful
to introduce one more distinction that affects the types of mappings
that can be formed between two COSI's.

One type of structure-preserving map is a "system-wide iconic map" (SWIM).
The other is a type that we might call a "pointwise-restricted iconic map",
or a "pointedly rigid iconic map" (PRIM).  I tried to make this nomenclature
as self-explanatory as I could, but failing that I will explain it next time.

Jon Awbrey

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