[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 30

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Cybernetics List, Peirce List,

Now that we've seen a few -- very simple but still non-trivial --
examples of semiotic processes, namely, ones which fall under
the headings of logical computation, evaluation, and proof,
there are a number of questions that typically arise with
respect to the relationship between sign relations and
sign processes.

For concreteness, let's consider the example of
logical evaluation that we looked at in Note 15.

Cf: FOLG 15.  http://stderr.org/pipermail/inquiry/2005-October/003134.html
In: FOLG.     http://stderr.org/pipermail/inquiry/2005-October/thread.html#3104

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

What sorts of sign relation are implicated in this sign process?
For simplicity, let's answer for the existential interpretation.

In Ex, all four of the listed signs are expressions of Falsity,
and, viewed within the special type of semiotic procedure that
is being considered here, each sign interprets its predecessor
in the sequence.  Thus we might begin by drawing up this Table:

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

That much of a sign relation is enough to cover the case before us,
but of course it is only a small sample from the larger population
of triples of the form <o, s, i> that is implied by the definition
of the primary arithmetic.

Jon Awbrey

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