[Inquiry] Re: Utter Indetermination

[Jon Awbrey]

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UI.  Note 2

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All that being said, I did one time try to figure out if bringing
the interpreter back into the picture, in a Peircean way, and thus
embedding the usual sort of 2-adic approximation to interpretation
within a more adequate 3-adic context, might just suggest a natural
hypothesis, worth trying before the alternatives at any rate, as to
how a logical graph might interpret itself, that is to say, incline,
shift, swerve, or weigh in favor of some interpretations over others.

Let's start with the simplest logical graphs:

   O

and

   o
   |
   O

Here for the sake of my current archiver,
I will use a capital "O" for a root node,
and a lower case "o" for a non-root node.
The edge graph that appears second above
can be written in-line as "|", or by way
of its parenthetical expression, as "()".

In the entitative interpretation, the one that Peirce tried first
and that George Spencer Brown leaned toward in the 'Laws of Form',
we have the reading O = false and | = true.  In the existential
interpretation, that Peirce developed extensively in his later
systems of existential graphs, we have O = true and | = false.

Taking the old Greco-Latin concept of analogy, proportion, or ratio as
our first approach to the generalized-to-the-max notion of isomorphism,
we need to observe a couple of features of analogies.  First, they are
always grounded in a certain context.  Second, they are typically only
approximate relations.

For instance, we can state the analogy, Canada : USA :: USA : Mexico,
in the context of North-South geographic neighboring relations, but
this is a global approximation that ignores many local exceptions,
like Alaska and Hawaii and the circumstance that folks in my part
of Michigan more usually drive East or South to get to Canada.

The context-dependence of analogies means that changing the context
will tend to motivate different analogies between the same elements.

For instance, we can even say that true : false :: false : true
in the context of logical opposition.  Clearly, this is not the
same thing as saying that true = false.

Bringing it back to the present application, we can give
a rough first description of what the logical graphs are
iconic of by stating the analogy, true : false :: O : |.
We could've written equally well, true : false :: | : O,
since it is only a matter of preserving the distinction,
not the direction of orientation, which is the duty of
the precise interpretation, entitative or existential.

To be continued ...

Jon Awbrey

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