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

Cf: Peirce’s 1870 “Logic of Relatives” • Selection 10 https://inquiryintoinquiry.com/2014/03/09/peirces-1870-logic-of-relatives-s… All, We continue with §3. Application of the Algebraic Signs to Logic. Peirce’s 1870 “Logic of Relatives” • Selection 10 ================================================= https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#S… <QUOTE CSP> The Signs for Multiplication (cont.) The sum x + x generally denotes no logical term. But x,_∞ + x,_∞ may be considered as denoting some two x’s. It is natural to write [Display 1] x + x = 2.x and x,_∞ + x,_∞ = 2.x,_∞ https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-selection-1… where the dot shows that this multiplication is invertible. We may also use the antique figures so that [Display 2] https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-selection-1… Then 2 alone will denote some two things. But this multiplication is not in general commutative, and only becomes so when it affects a relative which imparts a relation such that a thing only bears it to one thing, and one thing alone bears it to a thing. For instance, the lovers of two women are not the same as two lovers of women, that is, [Display 3] ℓ2.w and 2.ℓw https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-selection-1… are unequal; but the husbands of two women are the same as two husbands of women, that is, [Display 4] https://inquiryintoinquiry.files.wordpress.com/2022/01/lor-1870-selection-1… (Peirce, CP 3.75) </QUOTE> Regards, Jon