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: jawb...@att.net > To: jimwillgo...@msn.com; jerry_lr_chand...@me.com; peirce-l@list.iupui.edu > 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 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 W > > > >> Date: 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> > >>>> > >> > > -- > > 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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