Mike, List: I agree that the interchange was (generally) enjoyable and enlightening, and I am sorry that it ultimately became contentious and tiresome--I am not interested in "slugging it out" further. I also agree that John Sowa has much of value to say about EGs and logic, especially as applied in computer science and artificial intelligence research, from which we all can learn. I would not be surprised if combining the "many papers" concept from R L376 with the use of metalanguage has all the important practical applications that he anticipates--but it is *his own *idea, not Peirce's. Accordingly, my only major objection to his article-in-progress is the unqualified claim in its title and proposed content that it describes what *Peirce *had in mind for Delta EGs, which indeed is "not backed sufficiently by Peirce's own statements."
As far as I know, no other Peirce scholar has ever suggested that his December 1911 letter to Risteen presents a "specification" of Delta EGs, presumably because there is no basis in the text itself for such an interpretation. In fact, there is nothing in its extant 19 pages that deals with modals or is otherwise unique to the new Delta part. As Peirce himself says up-front, "the Conventions, the Rules, and the working of the System" are "a cross division"--*orthogonal *to the division into the Alpha/Beta/Gamma parts in "the better exposition of 1903," and thus applicable to *all *of them. This includes the "many papers" concept for the phemic sheet, where different pages contain graphs about different subjects that the utterer and interpreter give their "common attention" at different times, which is not novel in 1911--it reiterates something that Peirce had stated at least twice previously. Moreover ... - Peirce's 1898 and 1903 notations for metalanguage are *identical*, except that the oval and line are lightly drawn in the former and dotted in the latter. - Peirce never again uses *either *of these notations in manuscripts after 1903, so it is equally unlikely that he would have revived *either *of them in 1911. - Peirce's "red pencil" notation in R 514 has nothing to do with metalanguage--it turns an entire sheet into nested cuts for implication, with the antecedent (postulates) in the margin and the consequent (theorems) inside the red line. - Those pages in R 514 are among the "Fragments on Existential Graphs" that properly belong there and are dated 1909, not from the misfiled letter to Kehler of June 1911 (R L231) that includes a "tutorial" on EGs (NEM 3:162-169). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Tue, Mar 19, 2024 at 10:16 PM Mike Bergman <m...@mkbergman.com> wrote: > Hi All, > > As many have noted, I, too, have learned much and have (generally) enjoyed > this interchange between JAS and JFS. Further, I have no dog in this hunt > and certainly do not claim any special understanding about Peirce's > existential graphs. > > So, as a voting matter, my impression of this interchange is that I would > have no problems with a thesis put forward such as, "Sowa has studied > Peirce's EGs for many decades and believes that 'metalanguage' helps > exposit . . . " > > Where I concur with JAS is that these assertions are not backed > sufficiently by Peirce's own statements. Further, now from my own > perspective, I think these kind of minutiae arguments are deflective from > understanding the more important points of what Peirce was trying to do, > what he was striving for, what his mindset and thought process and logical > rigor were striving to achieve. Much has changed in the six score decades > since Peirce but his ultimate objective of trying to reason about the > nature of things remains. That is a conversation I welcome, and may > initiate at some point myself. > > If the protagonists want to keep slugging it out, I say, OK, go for it. > But the fight from my perspective is growing tiresome. > > Best, Mike > On 3/19/2024 9:04 PM, John F Sowa wrote: > > To refresh my memory, I reread Peirce's Lowell Lectures about Gamma > graphs. And the following passage from Lecture V (NEM 3, p. 365) explains > what he meant in L376 when he said that he would keep the Gamma division: > > "I must begin by a few words concerning gamma graphs; because it is by > means of gamma graphs that I have been enabled to understand these > subjects... In particular, it is absolutely necessary to representing the > reasoning about these subjects that we should be able to reason with graphs > about graphs and thus that we should have graphs of graphs." > > That explains the issues we have been debating recently. Peirce had > recognized > the importance of graphs of graphs when he wrote "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", > > That division would require some version of metalanguage for specifying > modality and higher-order logic. But it does *NOT *imply all (or any) > details that he happened to specify in 1903. Since he had earlier > specified a version of metalanguage in 1898 (RLT), he had previously > recognized the importance of metalanguage. The examples in the Lowell > lectures are similar to his 1898 version. Since he never again used the > details he specified in 1903 in any further MSS, it's unlikely that he > would revive them in 1911. > > The only feature he was reviving was the use of metalanguage. The 1898 > version was just as good as anything he specified in 1903. Since it was > simpler than the Gamma graphs, that would make it better. In fact, Peirce > mentioned another version of metalanguage in R514 (June 1911) that was > logically equivalent and syntactically similar to what he was writing in > L376 (December 1911). > > The novel features of L376 are sufficiently advanced to qualify as a > fourth branch of EGs. But they require a bit more explanation. As I said > before, they depend critically on the expertise of Allan Risteen. For that > information, see the references to Risteen that are listed in the index to > EP2. And the applications discussed in L376 have strong resemblances to > the applications of the very similar IKL logic in 2006. For those, see the > brief discussion and detailed references in https://jfsowa.com/ikl . > > I'll write more about these topics in another note later this week. > > John > > -- > __________________________________________ > > Michael K. Bergman > 319.621.5225http://mkbergman.comhttp://www.linkedin.com/in/mkbergman > __________________________________________ > >
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