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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 10.8 https://inquiryintoinquiry.com/2014/04/22/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 10.8 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#C… All, Our progress through the 1870 Logic of Relatives brings us in sight of a critical transition point, one which turns on the “teridentity” relation. The markup for Peirce’s “giver of a horse to an owner of it” is shown again in Figure 22. Figure 22. Giver of a Horse to an Owner of It https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-goh.png The hypergraph picture of the abstract composition is given in Figure 23. Figure 23. Anything that is a Giver of Anything to an Owner of It https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-e280a2goe28… If we analyze this in accord with the spreadsheet model of relational composition then the core of it is a particular way of composing a triadic “giving” relation G ⊆ X × Y × Z with a dyadic “owning” relation O ⊆ Y × Z in such a way as to determine a specialized dyadic relation (G ◦ O) ⊆ X × Z. Table 24 schematizes the associated constraints on tuples. Table 24. Relational Composition G ◦ O https://inquiryintoinquiry.files.wordpress.com/2022/02/lor-1870-relational-… So we see the notorious teridentity relation, which I left equivocally denoted by the same symbol as the identity relation 1, is already implicit in Peirce’s discussion at this point. Regards, Jon