Jim, List, No, I think that is incorrect.
"A non-relative term may be called a term of singular reference." I don't 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 On 2/13/2015 5:15 PM, Jim Willgoose wrote:
Jon, Jerry, list. Not to interfere here. But it can get more complicated since both non-relatives and relatives are terms of singular reference. So, the term "A" and the term "A:B" are both individuals with singular reference. Yet Peirce says that "every term of singular reference is general." How to resolve this! How to get generality out of both? 1) The non-relative term "A" as well as "A:B" could both be treated as Boolean classes; universal classes. Thus, singular reference is to a class. 2) As a "system of objects," however, the non-relative might be the logical sum of the term with itself. This would give a singleton A. ( or maybe A:A with respect to the next n+1 arity. "A:B" is easier in that the logical sum is four. But the degenerate case "A:A" is part of the system of objects. How to get generality? Maybe try Induction along with the assumption that the universe is greater than one. Jim WDate: Fri, 13 Feb 2015 00:48:44 -0500 From: jawb...@att.net To: jerry_lr_chand...@me.com; peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 4 Inquiry Blog http://inquiryintoinquiry.com/2015/01/30/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-preliminaries/ http://inquiryintoinquiry.com/2015/02/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-1/ http://inquiryintoinquiry.com/2015/02/03/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-2/ http://inquiryintoinquiry.com/2015/02/11/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-3/ http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-4/ Peirce List JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15566 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15607 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15608 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15616 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15624 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15634 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15636 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15639 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15641 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15646 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15657 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15659 JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15660 JW:http://permalink.gmane.org/gmane.science.philosophy.peirce/15664 JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15665 Jerry, List, When in doubt, please refer to my blog versions where I can use the appropriate math formatting and typefaces. Peirce uses roman (non-italic) typeface for constants or individuals, that is, proper names of individual entities. So I use LaTeX \mathrm{A}, \mathrm{B}, \mathrm{C}, etc. for these. Think "Ann", "Bob", "Cal", etc. for these. Math style sheets dictate italics for variables, so this is the default in LaTeX math settings. The only variable used in CP 3.220 is ''x''. A general term is one that denotes any and all the elements of a set. Peirce uses terms like "aggregate" or "logical sum" to refer to sets. General terms and variables are not exactly the same thing, although there is a relation between them in some contexts since a variable ranges over the members of a set. So if Bob and Cal and Don each love only Ann, but Ann loves only Don, then the dual relative ℓ = lover of = B:A + C:A + D:A + A:D. I think the problem is that "member" has two meanings. It can mean "member of a set" or "member of a tuple". Regards, Jon On 2/12/2015 11:55 PM, Jerry LR Chandler wrote: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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