[Inquiry] Re: Kaina Stoicheia -- Commentary

[Jon Awbrey]

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KS.  Commentary Note 5

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Peirce List,

The venn diagram shown below presents a familiar way of picturing
the universe of discourse [p, q].  The propositional expressions
inscribed in the cells represent the four elements of <<p, q>>.
The 16 propositions of the form <<p, q>> -> B can be pictured
as all the ways of shading the cells of the diagram, given
the two colors that correspond to the boolean values in B.
One observes that 4 cells shaded in 2 colors produces
2^4 = 16 different patterns altogether.

o-------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` `o-----------o` `o-----------o` ` ` ` ` |
| ` ` ` ` / ` ` ` ` ` ` \ / ` ` ` ` ` ` \ ` ` ` ` |
| ` ` ` `/` ` ` ` ` ` ` `o` ` ` ` ` ` ` `\` ` ` ` |
| ` ` ` / ` ` ` ` ` ` ` / \ ` ` ` ` ` ` ` \ ` ` ` |
| ` ` `/` ` ` ` ` ` ` `/` `\` ` ` ` ` ` ` `\` ` ` |
| ` ` o ` ` ` ` ` ` ` o ` ` o ` ` ` ` ` ` ` o ` ` |
| ` ` | ` ` ` ` ` ` ` | ` ` | ` ` ` ` ` ` ` | ` ` |
| ` ` | ` ` p (q) ` ` | p q | ` ` (p) q ` ` | ` ` |
| ` ` | ` ` ` ` ` ` ` | ` ` | ` ` ` ` ` ` ` | ` ` |
| ` ` o ` ` ` ` ` ` ` o ` ` o ` ` ` ` ` ` ` o ` ` |
| ` ` `\` ` ` ` ` ` ` `\` `/` ` ` ` ` ` ` `/` ` ` |
| ` ` ` \ ` ` ` ` ` ` ` \ / ` ` ` ` ` ` ` / ` ` ` |
| ` ` ` `\` ` ` ` ` ` ` `o` ` ` ` ` ` ` `/` ` ` ` |
| ` ` ` ` \ ` ` ` ` ` ` / \ ` ` ` ` ` ` / ` ` ` ` |
| ` ` ` ` `o-----------o` `o-----------o` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` (p) (q) ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-------------------------------------------------o

Each way of coloring the universe of discourse [p, q]
may be thought of as an actual state of that universe
or a contingent realization of its inherent potential.
This is just another way of interpreting the abstract
elements of <<p, q>> -> B, which can now be conceived
as "possible universes" of type [p, q].

Suppose we walk into the gallery of possible universes of type [p, q]
and find ourselves in a condition of indeterminate choice that ranges
over a particular subset of the 16 possible pictures.  There are just
2^16 subsets of 16 things, in this case corresponding to the space of
propositions of type (<<p, q>> -> B) -> B, which are naturally enough
referred to as "higher order propositions" since they can be regarded
as propositions about propositions.

This brings us to the verge of the next higher order of indetermination.

Jon Awbrey

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