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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 11.8 https://inquiryintoinquiry.com/2014/05/06/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 11.8 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#C… All, Let’s take a closer look at the “numerical incidence properties” of relations, concentrating on the assorted regularity conditions defined in the article on Relation Theory ( https://oeis.org/wiki/Relation_theory ). For example, L has the property of being “c-regular at j” if and only if the cardinality of the local flag L_{x @ j} is equal to c for all x in X_j, coded in symbols, if and only if |L_{x @ j}| = c for all x in X_j. In like fashion, one may define the numerical incidence properties “(< c)-regular at j”, “(> c)-regular at j”, and so on. For ease of reference, a number of such definitions are recorded below. Display 1. Definitions https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-comment-11.… Clearly, if any relation is (≤ c)-regular on one of its domains X_j and also (≥ c)-regular on the same domain, then it must be (= c)-regular on that domain, in short, c-regular at j. For example, let G = {r, s, t} and H = {1, 2, 3, 4, 5, 6, 7, 8, 9} and consider the dyadic relation F ⊆ G × H bigraphed below. Figure 38. Dyadic Relation F https://inquiryintoinquiry.files.wordpress.com/2014/05/lor-1870-figure-38.j… We observe that F is 3-regular at G and 1-regular at H. Regards, Jon