[Inquiry] Re: Utter Indetermination

[Jon Awbrey]

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UI.  Note 4

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CybCom, Peirce List,

The best that I can recall from the last time that I thought about this --
and I'm really hoping I can retrace my thoughts without a trip to the
basement to dig up some old box of notes -- I next asked myself what
would be a likely hypothesis as to what each state of the medium or
sign system might naturally mean to itself.  Here, I was thinking
along the lines of the ideas about terms and types that are used
in category theory and computer science, where a notation like
"t : T" means that a term t is interpreted under the type T.
To avoid confusion with other uses of the symbol ":", it is
frequently useful to write this in the alternative form:
"t <: T", read as "t of type T", or "t typed under T".

If we use the type indicator "en" to mark the entitative interpretation
and we use the type indicator "ex" to mark the existential interpretation,
then we can express their respective characters by means of the annotations:

   O <: en = false,
   | <: en = true.

   O <: ex = true,
   | <: ex = false.

A natural hypothesis seems to be that each symbol
is true to itself, that is, means truth to itself.
According to this understanding, we could use the
symbol for truth in each interpretation as a sort
of name or signature for that very interpretation.
Thus we have en = | and ex = O, and can now write:

   O <: | = false,
   | <: | = true.

   O <: O = true,
   | <: O = false.

Let's pause there and contemplate that.

Jon Awbrey

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