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 
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}](https://s0.wp.com/latex.php?latex=%5Cbegin%7Barray%7D%7Bccl%7D++O+%26+%3D+%26+%5C%7B+%5Cmathrm%7BA%7D%2C+%5Cmathrm%7BB%7D+%5C%7D++%5C%5C%5B6pt%5D++S+%26+%3D+%26+%5C%7B+%60%60%5Cmathrm%7BA%7D%22%2C+%60%60%5Cmathrm%7BB%7D%22%2C+%60%60%5Cmathrm%7Bi%7D%22%2C+%60%60%5Cmathrm%7Bu%7D%22+%5C%7D++%5C%5C%5B6pt%5D++I+%26+%3D+%26+%5C%7B+%60%60%5Cmathrm%7BA%7D%22%2C+%60%60%5Cmathrm%7BB%7D%22%2C+%60%60%5Cmathrm%7Bi%7D%22%2C+%60%60%5Cmathrm%7Bu%7D%22+%5C%7D++%5Cend%7Barray%7D&bg=ffffff&fg=000000&s=0&c=20201002)
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
- C.S. Peirce • On the Definition of Logic
- C.S. Peirce • Logic as Semiotic
- C.S. Peirce • Objective Logic
cc: Conceptual Graphs • Cybernetics • Laws of Form • Ontolog Forum
cc: FB | Semeiotics • Structural Modeling • Systems Science
Inquiry Into Inquiry 
Pingback: Survey of Semiotics, Semiosis, Sign Relations • 3 | Inquiry Into Inquiry