John,
Unfortunately you've added to the rampant confusion by saying that "a spot is just a very short line of identity.” This is not true of Peirce’s “final preferred version” of EGs because, as you point out yourself, he does not use the term “spot” in that version. And it is not true of Lowell 2, because in that text, a “line of identity” (however short) is not a “spot”: rather the end of that line must be attached to a “spot” (rheme, predicate) at one of its “hooks” or “pegs” in order to form a complete graph representing the subject-and-predicate (-and-copula, if you like). See the new commentary on 2.14 which I posted just now. Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 27-Nov-17 02:06 To: peirce-l@list.iupui.edu Cc: Dau, Frithjof <frithjof....@sap.com> Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14 Gary F, Mary L, Kirsti, Jerry LRC, and list, In 1911, Peirce presented his clearest and simplest version of EGs. He explained the essentials in just 8 pages of NEM (3:162 to 169). I believe that it is his final preferred version, and I'll use it for explaining issues about the more complex 1903 version. Gary > [Mary's] question about the “blot” has me thinking again about “the > two peculiar graphs” which are “the blank place which asserts only > what is already well-understood between us to be true, and the blot > which asserts something well understood to be false” Kirsti, > instead of warning against confusing SPOT, DOT and BLOT, it would have > been most interesting to hear how they are related. In his 1911 terminology, Peirce did not use the words 'spot', 'dot', or 'blot'. Instead, a spot is just a very short line of identity. The line represents an existential quantifier, and there is no reason to distinguish long lines from short lines (spots). He used the word 'peg' instead of 'dot'. Each relation has zero or more pegs, to which lines of identity may be attached. He also shaded negative areas (nested in an odd number of negations) and left positive areas unshaded (nested in an even number, zero or more, negations). A blot is just a shaded area that contains nothing but a blank. Gary > [The blank place and the blot] are peculiar in several ways, and each > is in some sense the opposite of the other. Each is the negation of the other. The blank place is unshaded, and the blot is a shaded blank. Gary > For instance, the blank cannot be erased, but any graph can be added > to it on the sheet of assertion; while the blot can be erased, but > nothing can be added to it, because it “fills up its area.” One reason why the "the blank place" is "peculiar" is that Peirce had talked about it in two different ways. He called the sheet of assertion the universe of discourse when it contains all the EGs that Graphist and Grapheus agree is true. But the blank, by itself, is true before anything is asserted. In modern terminology, the blank is Peirce's only axiom. Any EG that can be proved without any other assumptions is a theorem. In 1911, Peirce clarified that issues by using two distinct terms: 'the universe' and 'a sheet of paper'. The sheet is no longer identified with the universe, and there is no reason why one couldn't or shouldn't shade a blank area of a sheet. Gary, quoting Peirce > [A blot] "fills up its area." In 1911, Peirce no longer used this metaphor. With the rules of 1903 or 1911, a blot or a shaded blank implies every graph. To prove that any graph g can be proved from it: 1. Start with a sheet of paper that contains a shaded blank. 2. By the rule of insertion in a shaded area, insert the graph for not-g inside the shaded area. All the shaded areas of not-g then become unshaded, and the unshaded areas become shaded. 3. The resulting graph consists of g in an unshaded area that is surrounded by a shaded ring that represents a double negation. 4. Finally, erase the double negation to derive g. Another important point: In 1911, Peirce allowed any word, not just verbs, to be the name of a relation. From NEM, page 3.162: > Every word makes an assertion. Thus ——man means "There is a man" > in whatever universe the whole sheet refers to. The dash before "man" > is the "line of identity." This EG is Peirce's first example in 1911. And note that he begins with a Beta graph. In fact, he does not even mention the distinction between Alpha and Beta. The same rules of inference apply to both. For Peirce's version of 1911 with my commentary, see <http://jfsowa.com/peirce/ms514.htm> http://jfsowa.com/peirce/ms514.htm Jerry, > CSP’s genius [etc.] make it difficult for anyone to project his > thoughts into rarefied logical, mathematical, scientific or > philosophical atmospheres. Yes. He wrote volumes of insights that we still need to explore. But you can't put words in his mouth. If you can't find where he stated something explicitly, you can't claim him as the source. Note my discussion above. Every one of my claims is based on something that Peirce explicitly wrote. John
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