[CG] Re: Peirce's 1870 “Logic of Relatives”

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 11.9 https://inquiryintoinquiry.com/2014/05/07/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 11.9 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#C… All, Among the variety of regularities affecting dyadic relations we pay special attention to the c-regularity conditions where c is equal to 1. Let P ⊆ X × Y be an arbitrary dyadic relation. The following properties can be defined. Definitions 1 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… We previously examined dyadic relations exemplifying each of these regularity conditions. Then we introduced a few bits of terminology and special-purpose notations for working with tubular relations. Definitions 2 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… We arrive by way of this winding stair at the special cases of dyadic relations P ⊆ X × Y variously described as “1-regular”, “total and tubular”, or “total prefunctions” on specified domains, X or Y or both, and which are more often celebrated as “functions” on those domains. If P is a pre-function P : X ⇀ Y that happens to be total at X then P is known as a “function” from X to Y, typically indicated as P : X → Y. To say a relation P ⊆ X × Y is “total and tubular” at X is to say P is 1-regular at X. Thus, we may formalize the following definitions. Definitions 3 https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… For example, let X = Y = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and let F ⊆ X × Y be the dyadic relation depicted in the bigraph below. Figure 39. Dyadic Relation F https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-39.j… We observe that F is a function at Y and we record this fact in either of the manners F : X ← Y or F : Y → X. Regards, Jon