List, Jon: If read from a technical perspective, this passage (CP 3.220) can be interpreted as nearly self-contradictory or utterly ambiguous. It appears that CSP is unable to distinguish between nouns as Proper Nouns and nouns as generals. But this can be a perplex gloss.
Contrast: > Every relative, ..., is general; (seemingly inferring that a relative is a general, that is, a mathematical variable.) > An individual relative refers > to a system all the members of which are individual. (seemingly inferring that and INDIVIDUAL relative is not a general (!) and further, requiring that the concept of "an individual relative" also makes necessary a system of relations such that only individuals (that is, perhaps non-generals? ) are the only members allowed.) > The expressions > > (A : B) > > (A : B : C) > > may denote individual relatives. are expressions of pairings of symbols that are not to be interpreted as variables, at least as I read it. (The notation is NOT the usual notation for variables for multiplication or addition. Nor is the subsequent table of extensions...) Nevertheless, I find the meaning of CP3.220 to clear and straight forward. It is analogous to the meaning of natural relations among atomic relatives. "Individual relative" may refer to the Proper Name of an individual chemical element. It is also consistent with his later paper on the logic of relatives in relation to graph theory: C. S. Peirce (1897 Jan.), "The Logic of Relatives", The Monist, v. VII, n. 2 pp. 161-217. In short, in CSP's terminology, the nature of addition and of multiplication, differ for general relatives and individual relatives, vaguely similar to Boolean notions. Cheers Jerry On Feb 12, 2015, at 3:28 PM, Jon Awbrey wrote: > Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Selection 4 > http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-selection-4/ > Posted : February 12, 2015 at 4:00 pm > > <blockquote> > > Chapter 3. The Logic of Relatives (cont.) > > §2. Relatives (cont.) > > 220. Every relative, like every term of singular reference, is general; > its definition describes a system in general terms; and, as general, it > may be conceived either as a logical sum of individual relatives, or as > a logical product of simple relatives. An individual relative refers > to a system all the members of which are individual. The expressions > > (A : B) > > (A : B : C) > > may denote individual relatives. Taking dual individual relatives, > for instance, we may arrange them all in an infinite block, thus, > > A:A A:B A:C A:D A:E etc. > B:A B:B B:C B:D B:E etc. > C:A C:B C:C C:D C:E etc. > D:A D:B D:C D:D D:E etc. > E:A E:B E:C E:D E:E etc. > etc. etc. etc. etc. etc. etc. > > In the same way, triple individual relatives may be arranged > in a cube, and so forth. The logical sum of all the relatives > in this infinite block will be the relative universe, ∞, where > > x ─< ∞, > > whatever dual relative x may be. It is needless to distinguish > the dual universe, the triple universe, etc., because, by adding > a perfectly indefinite additional member to the system, a dual > relative may be converted into a triple relative, etc. Thus, for > ''lover of a woman'', we may write ''lover of a woman coexisting > with anything''. In the same way, a term of single reference is > equivalent to a relative with an indefinite correlate; thus, > ''woman'' is equivalent to ''woman coexisting with anything''. > Thus, we shall have > > A = A:A + A:B + A:C + A:D + A:E + etc. > > A:B = A:B:A + A:B:B + A:B:C + A:B:D + etc. > > </blockquote> >
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