[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 23

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Jim,

One incidental point.  When I constructed the sign relations L(A) and L(B),
I cast them in the "object-oriented" form to which I had become accustomed,
that is, taking the Object, Sign, Interpretant domains in just that order.
It has since become clear to me, having focussed on Peirce earliest papers
for the last few years, that Peirce began with a parallelism, that I think
he eventually outgrew, between the sign relational domains and the three
categories that would take them in the order Sign, Object, Interpretant.
In honor of Kant, who I see as the prevailing influence in this way of
looking at the world, I will call these conversions K(A) and K(B):

Table 1.  Sign Relation K(A) of Interpreter A
o---------------o---------------o---------------o
| Sign` ` ` ` ` | Object` ` ` ` | Interpretant` |
o---------------o---------------o---------------o
| "A" ` ` ` ` ` | A ` ` ` ` ` ` | "A" ` ` ` ` ` |
| "A" ` ` ` ` ` | A ` ` ` ` ` ` | "i" ` ` ` ` ` |
| "i" ` ` ` ` ` | A ` ` ` ` ` ` | "A" ` ` ` ` ` |
| "i" ` ` ` ` ` | A ` ` ` ` ` ` | "i" ` ` ` ` ` |
| "B" ` ` ` ` ` | B ` ` ` ` ` ` | "B" ` ` ` ` ` |
| "B" ` ` ` ` ` | B ` ` ` ` ` ` | "u" ` ` ` ` ` |
| "u" ` ` ` ` ` | B ` ` ` ` ` ` | "B" ` ` ` ` ` |
| "u" ` ` ` ` ` | B ` ` ` ` ` ` | "u" ` ` ` ` ` |
o---------------o---------------o---------------o

Table 2.  Sign Relation K(B) of Interpreter B
o---------------o---------------o---------------o
| Sign` ` ` ` ` | Object` ` ` ` | Interpretant` |
o---------------o---------------o---------------o
| "A" ` ` ` ` ` | A ` ` ` ` ` ` | "A" ` ` ` ` ` |
| "A" ` ` ` ` ` | A ` ` ` ` ` ` | "u" ` ` ` ` ` |
| "u" ` ` ` ` ` | A ` ` ` ` ` ` | "A" ` ` ` ` ` |
| "u" ` ` ` ` ` | A ` ` ` ` ` ` | "u" ` ` ` ` ` |
| "B" ` ` ` ` ` | B ` ` ` ` ` ` | "B" ` ` ` ` ` |
| "B" ` ` ` ` ` | B ` ` ` ` ` ` | "i" ` ` ` ` ` |
| "i" ` ` ` ` ` | B ` ` ` ` ` ` | "B" ` ` ` ` ` |
| "i" ` ` ` ` ` | B ` ` ` ` ` ` | "i" ` ` ` ` ` |
o---------------o---------------o---------------o

Here are the sign relations K(A) and K(B)
written in the "sets as sums" formulation:

K(A) = "A":A:"A" + "A":A:"i" + "i":A:"A" + "i":A:"i" +
       "B":B:"B" + "B":B:"u" + "u":B:"B" + "u":B:"u"

K(B) = "A":A:"A" + "A":A:"u" + "u":A:"A" + "u":A:"u" +
       "B":B:"B" + "B":B:"i" + "i":B:"B" + "i":B:"i"

These forms should assist comparison with Peirce's early papers,
where he speaks of the sign, the object, and the interpretant
as the relate, the correlate, and the correspondent of the
sign relation in question.

Jon Awbrey

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