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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 9.5 https://inquiryintoinquiry.com/2014/03/04/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 9.5 ================================================ https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#C… All, I'm breaking the email version of this Comment into sections on account of the abundance of Figures and attachments in it. [Section 1] Peirce’s comma operation, in its application to an absolute term, is tantamount to the representation of that term’s denotation as an idempotent transformation, which is commonly represented as a diagonal matrix. Hence the alternate name, “diagonal extension”. An idempotent element x is given by the abstract condition that xx = x but elements like those are commonly encountered in more concrete circumstances, acting as operators or transformations on other sets or spaces, and in that action they will often be represented as matrices of coefficients. Let’s see how this looks in the matrix and graph pictures of absolute and relative terms. Absolute Terms ============== Display 1. Absolute Terms 1 M N W https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-othello-abs… Previously, we represented absolute terms as column arrays. The above four terms are given by the columns of the following table. Display 2. Othello Columns 1 M N W Large https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-othello-col… To be continued ... Regards, Jon