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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 11.14 https://inquiryintoinquiry.com/2014/05/15/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 11.14 https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2#C… All, Let’s now look at a more familiar example of a morphism J, say, one of the mappings of reals into reals commonly known as logarithm functions, where you get to pick your favorite base. Here we have K(r, s) = r + s and L(u, v) = u ⋅ v and the formula J(L(u, v)) = K(Ju, Jv) becomes J(u ⋅ v) = J(u) + J(v), where ordinary multiplication and addition are indicated by a dot (⋅) and a plus sign (+), respectively. Figure 49 shows how the multiplication, addition, and logarithm operations fit together. Figure 49. Logarithm Arrow J : {+} ← {⋅} https://inquiryintoinquiry.files.wordpress.com/2022/03/lor-1870-logarithm-a… Thus, where the “image operation” J is the logarithm map, the “source operation” is the numerical product, and the “target operation” is the numerical sum, we have the following rule of thumb. • “The image of the product is the sum of the images.” • J(u ⋅ v) = J(u) + J(v) Regards, Jon