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

Cf: Peirce’s 1870 “Logic of Relatives” • Comment 8.3 https://inquiryintoinquiry.com/2014/02/18/peirces-1870-logic-of-relatives-c… Peirce’s 1870 “Logic of Relatives” • Comment 8.3 ================================================ https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#C… All, I continue with my commentary on CP 3.73, developing the “Othello” example as a way of illustrating Peirce’s formalism. It is critically important to distinguish a “relation” from a “relative term”. • The “relation” is an object of thought which may be regarded “in extension” as a set of ordered tuples known as its “elementary relations”. • The “relative term” is a sign which denotes certain objects, called its “relates”, as these are determined in relation to certain other objects, called its “correlates”. Under most circumstances the relative term may be taken to denote the corresponding relation. Returning to the “Othello” example, let us consider the dyadic relatives “lover of____” and “servant of____”. The relative term ℓ equivalent to the rhematic expression “lover of____” is given by the following equation. ℓ = B:C +, C:B +, D:O +, E:I +, I:E +, O:D In the interests of simplicity, let’s put aside all distinctions of rank and fealty, collapsing the motley crews of servant and subordinate under the heading of a single service, denoted by the relative term s for “servant of____”. The terms of this unified service are given by the following equation. s = C:O +, E:D +, I:O +, J:D +, J:O The elementary relation I:C under s might be implied by the plot of the play but since it is so hotly arguable I will leave it out of the toll. One thing more we need to watch out for: There are many conventions in the field regarding the ordering of terms in their applications and different conventions are more convenient under different circumstances, so there’s little chance any one of them can be canonized once and for all. In our current reading we apply relative terms from right to left and our conception of relative multiplication, or relational composition, needs to be adjusted accordingly. Regards, Jon