## Semiotics, Semiosis, Sign Relations • Discussion 12

RM:
I persist in the idea that in your six combinations [O, S, I] only one is relevant for semiotics, the others being out of the field […] On the projections, there is also matter for discussion … but to discuss well one must reserve a rather large agenda … I thus wait for your reply dealing with semiosis to resume a debate well-centered on the essential …

Dear Robert,

A bit of calm today — and feeling slaked after a day spent minding Voltaire’s advice and pulling weeds from our garden — I’ll take up one of your last problems first as it may be the one most quickly resolved.

I take it you are referring to the section of the Sign Relation article titled “Six Ways of Looking at a Sign Relation” which begins as follows.

In the context of 3-adic relations in general, Peirce provides the following illustration of the six converses of a 3-adic relation, that is, the six differently ordered ways of stating what is logically the same 3-adic relation:

So in a triadic fact, say, for example

$A ~\text{gives}~ B ~\text{to}~ C$

we make no distinction in the ordinary logic of relations between the subject nominative, the direct object, and the indirect object.  We say that the proposition has three logical subjects.  We regard it as a mere affair of English grammar that there are six ways of expressing this:

These six sentences express one and the same indivisible phenomenon.
(C.S. Peirce, “The Categories Defended”, MS 308 (1903), EP 2, 170–171).

“These six sentences express one and the same indivisible phenomenon.”

It’s a statement telling of the difference between affairs of grammar and affairs of logic, mathematics, and phenomena.

To be continued …

cc: Category Theory • Cybernetics (1) (2)
cc: Ontolog ForumStructural ModelingSystems Science
cc: FB | SemeioticsLaws of Form • Peirce List (1) (2) (3) (4) (5) (6)

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