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

Cf: Peirce's 1870 “Logic of Relatives” • Comment 12.2 (part 3 of 3) https://inquiryintoinquiry.com/2014/06/11/peirces-1870-logic-of-relatives-c… Peirce's 1870 “Logic of Relatives” • Comment 12.2 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#C… All, Finally, let's see how operations on boolean values induce the corresponding operations on sets and terms. The term ℓ^w determines a selection of individuals from the universe of discourse X which may be computed via the corresponding operation on coefficient matrices. If the terms ℓ and w are represented by the matrices L = Mat(ℓ) and W = Mat(w), respectively, then the operation on terms which produces the term ℓ^w must be represented by a corresponding operation on matrices, L^W = Mat(ℓ)^Mat(w), which gives the matrix Mat(ℓ^w). In short, the involution operation on matrices must be defined in such a way that the following equation holds. Equation 1. Matrix Involution L^W https://inquiryintoinquiry.files.wordpress.com/2022/03/lor-1870-matrix-invo… The fact that ℓ^w denotes individuals in a subset of X tells us its matrix representation L^W is a 1‑dimensional array of coefficients in B indexed by the elements of X. The value of the matrix L^W at the index u in X is written (L^W)_u and computed as follows. Equation 2. Matrix Computation L^W https://inquiryintoinquiry.files.wordpress.com/2022/03/lor-1870-matrix-comp… Regards, Jon