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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 8.5 https://inquiryintoinquiry.com/2014/02/20/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 8.5 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] Since multiplication by a dyadic relative term is a logical analogue of matrix multiplication in linear algebra, all the products computed above can be represented by “logical matrices”, that is, by arrays of boolean {0, 1} coordinate values. Absolute terms and dyadic relatives are represented as 1-dimensional and 2-dimensional arrays, respectively. The equations defining the absolute terms are given again below, first as logical sums of individual terms and then as n-tuples of boolean coordinates. Display 1. Othello Universe https://inquiryintoinquiry.files.wordpress.com/2021/12/lor-1870-othello-uni… Since we are going to be regarding these tuples as column arrays, it is convenient to arrange them into a table of the following form. Display 2. Othello Column Array https://inquiryintoinquiry.files.wordpress.com/2021/12/lor-1870-othello-col… Here are the dyadic relative terms again, followed by their representation as coefficient matrices, in this case bordered by row and column labels to remind us what the coefficient values are meant to signify. Display 3. ℓ = B:C +, C:B +, D:O +, E:I +, I:E +, O:D https://inquiryintoinquiry.files.wordpress.com/2021/12/lor-1870-othello-log… Display 4. s = C:O +, E:D +, I:O +, J:D +, J:O https://inquiryintoinquiry.files.wordpress.com/2021/12/lor-1870-othello-log… To be continued ... Regards, Jon