[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 9

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Cybernetics List, Peirce List,

Briefly if roughly put, icons are signs that denote their objects
by virtue of sharing properties with them.  To put it a bit more
fully, icons are signs that receive their interpretant signs on
account of possessing specific properties in common with them.

The family of related relationships that fall under the headings of
analogy, icon, metaphor, model, simile, simulation, and so on forms
an extremely important complex of ideas in mathematics, there being
recognized under the generic idea of "structure-preserving mappings"
and commonly formalized in the language of homomorphisms, morphisms,
or "arrows", depending on the operative level of abstraction that's
in play.

To consider how a system of logical graphs, taken together
as a semiotic domain, might bear an iconic relationship to
a system of logical objects that make up our object domain,
we will next need to consider what our logical objects are.

A popular answer, if by popular one means that both Peirce and Frege
agreed on it, is to say that our ultimate logical objects are without
loss of generality most conveniently referred to as Truth and Falsity.
If nothing else, it serves the end of beginning simply to go along with
this thought for a while, and so we can start with an object domain that
consists of just two objects or "values", to wit, !O! = B = {false, true}.

Given those two categories of structured individuals, namely,
!O! = B = {false, true} and !S! = {logical graphs}, the next
task is to consider the brands of morphisms from !S! to !O!
that we have might reasonably have in mind when we speak of
the "arrows of interpretation".

Jon Awbrey

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