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: [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 > <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 [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > 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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