## Sign Relations • Discussion 14

Re: Cybernetics • Cliff Joslyn (1) (2) (3) (4)

Dear Cliff,

A few examples of sign relations and triadic relations may serve to illustrate the problem of their demarcation.

First, to clear up one point of notation, in writing $L \subseteq O \times S \times I,$ there is no assumption on my part the relational domains $O, S, I$ are necessarily disjoint.  They may intersect or even be identical, as $O = S = I.$  Of course we rarely need to contemplate limiting cases of that type but I find it useful to keep them in our categorical catalogue.  (Other writers will differ on that score.)  On the other hand, we very often consider cases where $S = I,$ as in the following two examples of sign relations discussed in Sign Relations • Examples. We have the following data. $\begin{array}{ccl} O & = & \{ \mathrm{A}, \mathrm{B} \} \\[6pt] S & = & \{ \mathrm{A}", \mathrm{B}", \mathrm{i}", \mathrm{u}" \} \\[6pt] I & = & \{ \mathrm{A}", \mathrm{B}", \mathrm{i}", \mathrm{u}" \} \end{array}$

As I mentioned, those examples were deliberately constructed to be as simple as possible but they do exemplify many typical features of sign relations in general.  Until the time my advisor asked me for cases of that order I had always contemplated formal languages with countable numbers of signs and never really thought about finite sign relations at all.

### Reference

• Charles S. Peirce (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73.  Online.

### Sources

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