John,
Summing up your detailed explanation, I gather that your reason for concluding that the 1909/11 rendition of EGs was “preferred” by Peirce is that he knew that his letter to Kehler would be widely circulated among Lady Welby’s circle and thought that they could gain more recognition in that way. I have my doubts whether he could have assumed that, but in any case, that is circumstantial evidence. Your reasons for preferring it yourself are clear enough, but I see nothing that convinces me that Peirce preferred the 1909/11 version for those reasons. You have a preference for “positive (unshaded) and negative (shaded) regions” as opposed to “evenly and oddly enclosed areas” (respectively), but as far as I can see in the Kehler letter, the boundaries of shaded regions are precisely and operationally equivalent to cuts. You are right that the shaded versions are easier to read at a glance, especially when the enclosures are deeply nested; but there’s also a physical problem with implementing that notation, because if you have occasion to erase or deiterate a graph in a shaded area, you have to do it without erasing the shading and thus negating the negation. There is also something of logical importance lost in substituting shading for cuts, and that will (I hope) become clear when we look at the next section of Lowell 2 (17), so I won’t go into it now. What I will say is, first, Thanks for directing my attention to MS L 231; I don’t have access to NEM 3 (except by doing a Google search for an unusual phrase in the letter), but now that I’ve found a copy of the manuscript online I’ve been reading it with great interest. Second, based on that reading, I think you’ve exaggerated the differences between the Lowell presentation of EGs and the 1911 presentation in that letter. Almost all the differences are due to changes in terminology, such as the change from “hooks” to “pegs”; the features named by those terms perform exactly the same functions in both versions. In fact, I would say that after some complex experimentation with the gamma graphs around 1906, Peirce “simplified” his EGs by simply returning to the 1903 version (with very minor changes) and leaving out most of the rationale for it. But we can argue that point as we move on with Lowell 2. One remark I found interesting in the Kehler letter after Peirce had taken several pages to explain the syntax of the graphs: on p. 23 he wrote, “By the space that I have occupied in explaining this syntax, you will surely think it is my chief work. On the contrary, it is one of the smallest, but it is the only one of which I could put you in a position to gain some understanding without writing a book about it.” That certainly alters my impression of the importance Peirce ascribed to his existential graphs. And just when I’m beginning to take them more seriously myself! Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 29-Nov-17 14:28 To: peirce-l@list.iupui.edu Cc: Dau, Frithjof <frithjof....@sap.com> Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 and 2.14 Gary, Please look at the attached diagram egprim.gif. EGs are truly diagrammatic: Every syntactic feature can be shown without any use of language. This is slide 4 of <http://jfsowa.com/talks/egintro.pdf> http://jfsowa.com/talks/egintro.pdf . I apologize for the mistake about 'spot'. I checked Don Roberts' book, which I first read almost 40 years ago. Don dutifully noted that Peirce had used the word 'spot' for the place where the name of a rhema was written. But it just seemed weird to say that the spot, not the name, represented a rhema or predicate. I also checked Don's glossary, which contains over 50 terms for talking about EGs. Many of them are about semantics. But to talk about the syntax, you only need 6 terms: line of identity, relation, enclose, shaded area, unshaded area, and peg. All other terminology is about notation-independent logical issues. > [GF] I must apologize to the list for introducing the term “dot” > into this discussion, as Peirce actually uses that term not in Lowell > 2, but in some of his other explanations of existential graphs, > notably CP 4.438: > > [CSP] Let a heavy dot or dash be used in place of a noun which has > been erased from a proposition. A blank form of proposition produced > by such erasures as can be filled, each with a proper name, to make a > proposition again, is called a rhema, or, relatively to the > proposition of which it is conceived to be a part, the predicate of > that proposition.” By the way, this operation is equivalent to Church's lambda abstraction about 30 years later. See slide 15 of <http://jfsowa.com/egintro.pdf> http://jfsowa.com/egintro.pdf . It's important to show the equivalence, but it's irrelevant Whether you use a blank, a dot, an underscore, or the Greek letter λ. > It could be argued that Peirce’s terminology in referring to a graph > as a “word” is rather sloppy, but after all, this is a personal letter > from a self-described “garrulous old man” to a new acquaintance. That statement is wrong for several reasons: 1. Peirce had said that every part of an EG asserts something. The line asserts existence, the predicate named 'man' asserts a type of entity, and the connection asserts the type of the existing thing. I admit that modern terminology does not say that a predicate, by itself, makes an assertion. But Peirce did so on various occasions. 2. Peirce wrote that letter in reply to "Mr. Kehler", who was a member of Lady Welby's Significs group. We don't have the original letter by Kehler, but it probably began with a flowery introduction to the esteemed professor Peirce. In response, Peirce deliberately described himself very modestly, and he used the word 'garrulous' as an apology for the length of the letter. 3. This letter is far more important than a casual note to a friend. Lady Welby had circulated Peirce's letters among the members of her group, which included many prominent British intellectuals. Note that Ogden & Richards included copies of some of Peirce's letters in the appendix of their book, _The Meaning of 'Meaning'_. > It is not an explanation of EGs intended for publication. I’d like to > know your reasons for claiming that this presentation is Peirce’s > “preferred” version of EGs. By 1911, Peirce had given up hope of getting further writings published. The length of the letter (52 printed pages in NEM vol. 3) indicates its importance. The practice of sharing letters in Lady Welby's group was his best chance of getting a prominent group of scholars to read it. The length of the letter and the amount of technical detail in it shows that he copied material from various manuscripts. I had discovered the EG content in 2000 from a transcription of MS 514 by Michel Balat. That MS was dated 1909, when Peirce might have had some hopes of publication. The fact that he chose that MS to copy for his letter of 1911 indicates (a) its importance, and (b) its value as a tutorial about the essential features of EGs. Finally, any EG from RTL (1898) or later could be redrawn with the conventions of 1911, and any proof by any earlier rules could be translated line-by-line to an equivalent proof by the later rules. But the later version has important advantages: 1. The shading makes the graphs more readable *and* more iconic: it directly shows which rules of inference are applicable. 2. The syntax is described with fewer words, and the rules of inference are shorter and more general. There is no need to distinguish Alpha and Beta graphs, since they use exactly the same rules of inference. 3. The generality of the 1909/1911 rules may be the result of Peirce's thinking about moving pictures and stereoscopic imagery. They are no longer tied to a "sheet" and they could be applied without change to 3D images or even 3D+time for movies. 4. As a result of that generality, the rules can be applied to any notation for logic that allows a distinction between positive (unshaded) and negative (shaded) regions. For examples, see egintro.pdf, slide 23 ff. In summary, the system of 1909/1911 is superior in every way. There is no philosophical or practical reason for Peirce to prefer any of the older versions. For Peirce's own tutorial, see <http://jfsowa.com/peirce/ms514.pdf> http://jfsowa.com/peirce/ms514.pdf . If anybody can find anything better in any of the older versions, I would love to see it. John
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