Jon and Mike, The unfinished letter L376 has rarely been mentioned by Peirce scholars, and nobody has undertaken a serious study of it. If anybody can find anything more than a brief citation about it, please send a copy to P-List so that we can all see it and analyze it.
Please note the quotation by Peirce from Lowell lecture V: "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 quotation shows that Gamma graphs add one and only one NECESSARY feature to Alpha + Beta graphs: the same or equivalent metalanguage feature used in 1898 (RLT). When Peirce referred to the DIVISION of Gamma graphs, that is the only feature required. He later did much more talking about modality and with new notations. He never again used any of the notations that are unique to the 1903 Gamma graphs. Re the four branches of EGs: I take Peirce's words seriously. He admitted that he sometimes made mistakes, but it is exceedingly rare for him to make a major statement, such as stating that his Delta graphs are a fourth branch of EGs without solid evidence for it. JAS: In fact, there is nothing in its extant 19 pages that deals with modals or is otherwise unique to the new Delta part. In order to understand what Peirce wrote in those 19 pages, you need to understand why he believed that a totally new branch of EGs was necessary for a proof of pragmatism. Did you read the comments about Risteen in EP2? Did you read anything by or about Arthur Cayley? Did you read the citations to the IKRIS project and the IKL logic of 2004 to 2006? The future cannot influence the past, but developments in the future can show which developments in the past were going along the same track. JAS: 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. No, Peirce had an excellent notation for implication: A nest of two ovals. That example in R514 is an application of metalanguage. The pages classified as R514 were included in the same batch as L231, partly because they contained a first draft of Peirce's best and FINAL notation for EGs -- which he continued to use in every MS after June 1911 -- including L376 in which he mentioned shading for negation. In any case, R670, in which he finally dumped all previous notations for EGs, also contained a brief mention of a notation which appears to be similar to the example in R514. It's irrelevant whether the one in R514 is dated as 1909 or 1911. In any case, the L376 notation for metalanguage is different from either of those notations because the multiple pages are organized in a tree. And by the way, the IKRIS applications are also organized in a tree -- and for exactly the same reasons, There is much more to say about this. And it is not just "said by John Sowa". I admit that the incomplete L376 does not specify all necessary details. To a significant extent, the reconstruction resembles a kind of archaeology, in which the missing parts of an ancient fossil are compared to similar parts of a modern animal in order to determine their structure and function. In this case, the modern animal is the IKRIS project. For the reconstruction, there a huge amount of evidence from various writings by Peirce, from evidence of Risteen's expertise, and from future developments to demonstrate (a) what Peirce wrote in L376 is important for supporting a proof of pragmatism, (b) the new features of Delta graphs provide solid evidence that Peirce was on the right track for such a proof, and (c) evidence from the 21st C (IKRIS and IKL) use the same kind of logic and a closely related methodology for supporting research and developments in science and engineering. They IKRIS guys didn't call their work "a proof of pragmatism", but Peirce would have done so. I'm busy writing much more, which explains much more. And I'll send more info to P-List along the way. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> 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 319.621.5225 http://mkbergman.com http://www.linkedin.com/in/mkbergman __________________________________________
_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
