John, List: Well over a year ago, I noted on-List that R 514 is correctly dated 1909 but mistakenly included some pages from Peirce's 1911 letter to Risteen ( here <https://list.iupui.edu/sympa/arc/peirce-l/2019-05/msg00010.html>). I also pointed out that R 669-670 were written during the weeks immediately prior to that letter, and that they record his switch from cuts to shading ( here <https://list.iupui.edu/sympa/arc/peirce-l/2019-04/msg00111.html>). As we had discussed a few weeks earlier (here <https://list.iupui.edu/sympa/arc/peirce-l/2019-03/msg00033.html>), shading is *more iconic* than cuts for representing oddly enclosed graphs as being scribed on a different *surface *from evenly enclosed graphs, with a natural boundary rather than a thin line as the discontinuity between them. However, I suggest that this comes with a trade-off relative to one of Peirce's other stated objectives.
CSP: [The] purpose of the System of Existential Graphs ... [is] to afford a method (1) as *simple *as possible (that is to say, with as small a number of arbitrary conventions as possible), for representing propositions (2) as *iconically*, or diagrammatically and (3) as *analytically *as possible. (CP 4.561n, 1908) Technically a scroll is not "just a way of drawing two cuts." These are indeed equivalent in *classical *logic, such that "if A then B" entails "not (A and not-B)" and vice-versa. However, Peirce recognized that "there is but one primary and fundamental logical relation, that of illation" (CP 3.440, 1896), which is what the scroll signifies when drawn as a *single *continuous cut that crosses itself so that the inner close touches the outer close at a node (CP 4.435-436, 1903; CP 4.564, 1906; R 669:16, 1911). By contrast, negation is *derived *by blackening the entire inner close of such a scroll to represent absurdity as the consequent, and then shrinking it down to infinitesimal size (CP 4.454-456, 1903; CP 4.564n, c. 1906; R 669:17-18, 1911). That being the case, from a strictly *philosophical *standpoint, I suggest that the scroll is *more analytical* than shading. As we discussed a few months later (here <https://list.iupui.edu/sympa/arc/peirce-l/2019-09/msg00016.html>), this is important when adapting existential graphs to *intuitionistic *logic as Arnold Oostra has outlined. Here a scroll is *not *equivalent to nested cuts; "if A then B" still entails "not (A and not-B)," but "not (A and not-B)" *does not* entail "if A then B." In other words, it remains permissible to detach the inner close of a scroll from its outer close to become a nested cut, but a nested cut cannot be attached to the outer close to create a scroll. Nevertheless, from a strictly *practical *standpoint, I continue to agree that NEM 3:162-169 is Peirce's simplest and clearest explanation of existential graphs, especially in conjunction with R 669-670 providing helpful background and context. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Jul 17, 2020 at 11:23 PM John F. Sowa <[email protected]> wrote: > I have often said that the excerpt of L231 published in NEM 3:162-169 is > Peirce's best and final version of existential graphs. For a copy and some > brief comments, see http://jfsowa.com/peirce/eg1911.pdf > > Following are some objections to the claim that eg1911 is definitive: > > 1. In his 1973 book, Don Roberts cited L231, but he did not mention its > notation (shaded ovals for negation instead of cuts) or its rules of > inference (three symmetric pairs). He also cited R514, which contains a > version that is almost identical to the version in L231. But he did not > discuss the notation or terminology in either one. Apparently, he did not > consider them important. > > 2. During the years between R514 (estimated date 1909) and L231 (1911), > Peirce continued to use the notation and terminology of his earlier > writings on EGs. Therefore, he didn't consider the R514-L231 version a > replacement for the earlier versions. > > 3. The text of L231 ignores a large amount of Peirce's terminology and > writings about EGs. It says nothing about Gamma graphs or the many complex > issues they represent. The 1911 version seems to be a brief summary rather > than a definitive presentation. > > I recently discussed these issues with Martin Irvine (on cc list above). > He mentioned some related MSS from 1911 and said that the date of 1909 for > R514 was wrong. It is a highly marked-up draft of L231, and it is now > grouped with L231. He also mentioned other MSS, also from 1911, which use > the same notation. He said that no later MSS with examples or discussion > of EGs have been found. > > About a month before L231 (dated 1911 June 22), Peirce wrote R669 (May 25 > to June 2) and a revised version R670 (June 7 to 17). For negation, Peirce > used a black area with the enclosed graph in white. > > But Peirce added "It is needless to say that the process of making a > black surface with a diagram upon it in white is insufferably > inconvenient." For that reason, he used his earlier notation, but he said > that the "bounding ovals", which he called 'cuts', "have no meaning at > all... It is only the color of the area itself which has the force of > affirming if it be white or evenly enclosed ... or of denying if it be > shaded or oddly enclosed." For a copy of R670, as transcribed by Ahti > Pietarinen, see http://jfsowa.com/peirce/r670.pdf > > A few days later, when Peirce wrote L231, he found a simpler solution: > shade the negated areas in pencil. That elimminated any use for the > meaningless word 'cut' or its synonym 'sep'. He also dropped the word > 'scroll' because a scroll is just a way of drawing two cuts. He dropped > the word 'spot' because no line of identity is ever attached to a rhema or > predicate that has no name; it's always attached to a word or other > symbol. He did keep the word 'peg', but dropped the synonym 'hook'. The > words 'spot', 'blot', and 'dot' are English words that have no obvious > translations to other languages. Fortunately, there is no need for them in > English. > > On 29 September 1911, Peirce wrote L378, a letter in French to A. Robert. > In it, he included a brief introduction to existential graphs with the same > notation as L231. In French, he made the following comment: "I use a > diagrammatic syntax, which I described very badly and at an intolerable > length in the Monist of October 1906, even though I was in possession of > this syntax since December 1896." > > For the original French of L378, see http://jfsowa.com/peirce/L378.pdf . > This is a PDF of the microfiche, in which the pencil shading was lost, but > it can be inferred from the descriptions. For a brief summary in English, > see http://jfsowaa.com/peirce/L378.htm . > > From L376 (December 6-9, 1911), Letter to Alan Douglas Risteen, p. 1: "I > gave an oral account of [the System of Existential Graphs], soon after, to > the National Academy of Sciences; and in 1903 for my audience of a course > of Lectures before the Lowell Institute, I printed a brief account of it. > An account of slightly further development of it was given in the Monist of > Oct. 1906. In this I made an attempt to make the syntax cover Modals; but > it has not satisfied me. The description was, on the whole, as bad as it > well could be, in great contrast to the one Dr. Carus rejected. For > although the system itself is marked by extreme simplicity, the description > fills 55 pages, and defines over a hundred technical terms applying to it. > The necessity for these was chiefly due to the lines called 'cuts' which > simply appear in the present description as the boundaries of shadings, or > shaded parts of the sheet. The better exposition of 1903 divided the > system into three parts, distinguished as the Alpha, the Beta, and the > Gamma, parts; a division I shall here adhere to, although I shall now have > to add a Delta part in order to deal with modals. A cross division of the > description which, here, as in that of 1903, is given precedence over the > other is into the Conventions, the Rules, and the working of the system." > > L376 breaks off at the end of p. 19. Unless anything further is found, > L231 is the most complete version of Peirce's 1911 EGs that survives. The > MSS before and after L231 are consistent with it, and they provide > additional detail about Peirce's opinions about earlier versions and his > motivation for the version that may be called eg1911. > > Conclusions: The 55 pages of 1906 and the 100+ technical terms > are definitely not Peirece's preferred version. Any technical terms that > do not occur in L231, L376, or L378 should be avoided, except in textual > criticism or biographical studies. > > Since no details about Delta graphs have been found, no definitive > conclusions about Peirce's intentions can be assumed. However, two points > seem reasonable: (1) Peirce's 1906 writings about the semantics of > modality cannot be trusted; (2) semantic developments in the 20th century > by logicians who had been strongly influenced by Peirce may be adapted to > some version of Peirce's syntax. First among them is C. I. Lewis, who had > studied Peirce's writings in detail before writing his famous axioms for > modal logic. > > John
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