[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 31

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Cybernetics List, Peirce List,

Let's take another look at the semiotic sequence
associated with a logical evaluation and the
corresponding sample of a sign relation
that we were looking at last time.

o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` o o o ` ` ` ` ` ` o o ` ` ` ` ` ` ` o ` ` ` ` ` ` ` ` ` |
| ` `\| | ` ` ` ` ` ` | | ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| ` ` o o o ` ` ` ` ` o o o ` ` ` ` ` ` o o ` ` ` ` ` ` o ` |
| ` ` `\|/` ` ` ` ` ` `\|/` ` ` ` ` ` ` |/` ` ` ` ` ` ` | ` |
| ` ` ` O ` ` ` = ` ` ` O ` ` ` = ` ` ` O ` ` ` = ` ` ` O ` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| (()())(())()` = ` (())(())()` = ` ` (())()` ` = ` ` `( )` |
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
o-----------------------------------------------------------o

o-------------------o-------------------o-------------------o
| Object` ` ` ` ` ` | Sign` ` ` ` ` ` ` | Interpretant` ` ` |
o-------------------o-------------------o-------------------o
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(()())(())()"` ` | "(())(())()"` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())(())()"` ` ` | "(())()"` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())()"` ` ` ` ` | "()"` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
o-------------------o-------------------o-------------------o

The sign of equality "=", interpreted as logical equivalence "<=>",
that marked our steps in the process of conducting the evaluation,
is evidently intended to denote an equivalence relation, and this
is a 2-adic relation that is reflexive, symmetric, and transitive.
If we then pass to the reflexive, symmetric, transitive closure
of the <s, i> pairs that occur in our initial sample, attaching
the constant reference to Falsity in the object domain, we will
sweep out a more complete selection of the sign relation that
inheres in the definition of the primary logical arithmetic.

o-------------------o-------------------o-------------------o
| Object` ` ` ` ` ` | Sign` ` ` ` ` ` ` | Interpretant` ` ` |
o-------------------o-------------------o-------------------o
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(()())(())()"` ` | "(()())(())()"` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(()())(())()"` ` | "(())(())()"` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(()())(())()"` ` | "(())()"` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(()())(())()"` ` | "()"` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
o-------------------o-------------------o-------------------o
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())(())()"` ` ` | "(()())(())()"` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())(())()"` ` ` | "(())(())()"` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())(())()"` ` ` | "(())()"` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())(())()"` ` ` | "()"` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
o-------------------o-------------------o-------------------o
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())()"` ` ` ` ` | "(()())(())()"` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())()"` ` ` ` ` | "(())(())()"` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())()"` ` ` ` ` | "(())()"` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "(())()"` ` ` ` ` | "()"` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
o-------------------o-------------------o-------------------o
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "()"` ` ` ` ` ` ` | "(()())(())()"` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "()"` ` ` ` ` ` ` | "(())(())()"` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "()"` ` ` ` ` ` ` | "(())()"` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
| Falsity ` ` ` ` ` | "()"` ` ` ` ` ` ` | "()"` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` |
o-------------------o-------------------o-------------------o

Jon Awbrey

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