Technical Correction to my message: strike "complete" and replace with "bipartite"
After closer look at Jim's graph, I now believe that the figure was intended as a bipartite graph; the pairs of parentheses in the diagram appear to denote collections of symbols, as well as individuals related to other individual symbols. Thus, the symbols for "a" appear to me to be part of two different notational systems. Was that your intent, Jim? Cheers Jerry On Feb 14, 2015, at 10:30 PM, Jerry LR Chandler wrote: > Jim, List: > > Your diagram captures the essence of what I was seeking to communicate. > > If one addresses the notion of an individual, then a singular individual, > then a singular symbol, is interpreted as a logical correspondence > relationship with a single line that signifies the exact numerical > correspondence of a one-one relation. > > Your diagram shows the meaning of a symbol when a population of symbols, each > with the same identity is logically interpreted with respect to a proposition > engaging the entire population. > > Since each symbol has the same meaning, the complete graph you show > illustrates the the algebra very nicely. There is no difference that makes a > difference among the enumerated set of symbols that you present. > > The meaning of your alignment of the complete graph must be contrasted with > the alignment of points along a line. > All points of the domain correspond with all points of the range and vice > versa in your diagram. > (This is not the case for a mathematical function for a variable, except for > the special case of a constant.) > > The difference then becomes readily apparent in the two diagrams. > > This difference of interpretation also becomes readily apparent in the > constructions of chemical structures where symbols may represent different > valences / handedness. > > Excellent insight! > > Do you consider your diagram to be an icon or a symbol? (It's indexicality > is obvious (I hope!)) > How would you relate your diagram to Shannon information theory? Does it > infer perfect transmission of information when A is an identity of a Shannon > bit? > > Cheers > > Jerry > > > > On Feb 14, 2015, at 2:40 PM, Jim Willgoose wrote: > >> Jon,list >> >> Here is a picture of the idea of non-relative term generality. (Boole class) >> >> Jim W >> >> > Date: Fri, 13 Feb 2015 23:02:17 -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 >> > >> > 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: 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 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 >> <IMG_0197.JPG> >> ----------------------------- >> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> PEIRCE-L to this message. PEIRCE-L posts should go to >> peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but >> to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of >> the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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