Jon, I looked at the notation from DNLR. (1870) Peirce uses small letters for generals and capital letters for individuals. The small case "a" is understood as "every a." So, the expression: a= A1 + A2 + A3 + A4 + A5.....etc. would be understood as the logical sum of individuals with (should-be subscript) representing the cardinal number. (either one or two or three individuals etc.) This use of small and Capital letters is similar to Boole. Peirce gives a key in 1870 where absolute terms are: f-frenchman h-horse t-tree and so on. They are absolute terms that denote individuals (or non-relatives if you prefer) The size is measured by the subscript number. (the "+" could be reinterpreted as numerical sum with subscripts functioning as names plus a counting rule) f,h,t denote a frenchman. a horse, a tree etc. Now what is interesting is that a degenerate relation a:a would assign "every a to every a" thus setting up a universal class by assigning individual A's to each other. So, there is generality here. Jim W > Date: Fri, 13 Feb 2015 23:02:17 -0500 > From: [email protected] > To: [email protected]; [email protected]; [email protected] > Subject: Re: [PEIRCE-L] Peirce’s 1880 “Algebra Of Logic” Chapter 3 • > Selection 4 > > Re: Jim Willgoose > At: http://permalink.gmane.org/gmane.science.philosophy.peirce/15677 > > Jim, List, > > These are some of the reasons that I prefer > "elementary relative" to "individual relative" > and "absolute", "monadic", or "non-relative" to > "term of singular reference", since the words > "individual" and "singular" have too many > meanings in too many different contexts. > > Regards, > > Jon > > On 2/13/2015 10:21 PM, Jim Willgoose wrote: > > Jon, > > > > Yes. You are right. I should have stayed out of that one on reference. > > The question of generality is open though. > > > > Jim W > > > >> Date: Fri, 13 Feb 2015 18:04:13 -0500 > >> From: [email protected] > >> To: [email protected]; [email protected]; [email protected] > >> Subject: Re: [PEIRCE-L] Peirce’s 1880 “Algebra Of Logic” Chapter 3 • > >> Selection 4 > >> > >> Jim, List, > >> > >> No, I think that is incorrect. > >> > >> "A non-relative term may be called a term of singular reference." > >> > >> I don't think that leaves any room for A:B to be a term of singular > >> reference. > >> > >> The series singular, dual, plural here describes the arities 1, 2, ≥ 3. > >> > >> A non-relative term is also known as an absolute term. > >> > >> The letters A, B, C here refer to individuals, not classes. > >> > >> All the concepts and distinctions treated in this chapter, modulo the usual > >> variations in notation and terminology, are discussed in much greater > >> detail > >> in the 1870 Logic of Relatives. See the following article, where I added > >> much > >> in the way of illustrative examples: > >> > >> http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives > >> > >> Regards, > >> > >> Jon > >> > > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache
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