[CG] Re: Sign Relations

Cf: Sign Relations • Discussion 12 http://inquiryintoinquiry.com/2022/07/16/sign-relations-discussion-12/ Re: Cybernetics https://groups.google.com/g/cybcom/c/TpRK4fxguD0 ::: Cliff Joslyn https://groups.google.com/g/cybcom/c/TpRK4fxguD0/m/8mh1CC18EQAJ Dear Cliff, From a purely speculative point of view, any triadic relation L ⊆ X×X×X on any set X might be capable of capturing aspects of objective structure immanent in the conduct of logical reasoning. At least I can think of no reason to exclude those possibilities à priori. When we turn to the task of developing computational adjuncts to inquiry there is still no harm in keeping arbitrary triadic relations in mind, as entire hosts of them will turn up on the “universe” side of many universes of discourse we happen to encounter, if nowhere else. Peirce's use of the word “definition” understandably leads us to anticipate a strictly apodictic development, say, along the lines of abstract group theory or axiomatic geometry. In that light I often look to group theory for hints on how to go about tackling a category of triadic relations such as we find in semiotics. The comparison makes for a very rough guide but the contrasts are also instructive. More than that, the history of group theory, springing as it did as yet unnamed from the ground of pressing mathematical problems, from Newton's use of symmetric functions and Galois' application of permutation groups to the theory of equations among other sources, tells us what state of development we might reasonably expect from the current still early days of semiotics. To be continued … Regards, Jon