[CG] Re: Sign Relations

Cf: Sign Relations • Discussion 14 https://inquiryintoinquiry.com/2022/07/17/sign-relations-discussion-14/ Re: Cybernetics https://groups.google.com/g/cybcom/c/TpRK4fxguD0 :: Cliff Joslyn https://groups.google.com/g/cybcom/c/TpRK4fxguD0/m/iNl_yoqEAQAJ Dear Cliff, Let me see if I can illustrate the problem of definition with a few examples. First, to clear up one point of notation, in writing L ⊆ O × S × 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 then 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 a previous post of this series. Sign Relations • Examples https://inquiryintoinquiry.com/2022/07/02/sign-relations-examples-2/ Tables 1a and 1b. Sign Relation Tables L_A and L_B https://inquiryintoinquiry.files.wordpress.com/2020/05/sign-relation-twin-t… We have the following data. O = {A, B} S = {“A”, “B”, “i”, “u”} I = {“A”, “B”, “i”, “u”} 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. Regards, Jon