Jon, I admit that I was looking at the printed book, Reasoning and the logic of things. In that book, the transcription shows a clearly drawn line that connects the oval to the word 'is'. That is an excellent notation. I admit that the MS copies below are ambiguous. But the two sentences enclosed in ovals are equivalent to what Peirce proposed in R514: Draw a line around the proposition(s) about which the text outside the oval is making assertions.
Nevertheless, those assertions outside the oval are examples of METALANGUAGE about the proposition(s) inside the oval. Although Tarski and Carnap introduced that word and developed the theory and applications in some detail, Peirce's writings as early as 1898 showed that he had anticipated some of the issues, which he developed further in R514 and L376. Later in the 20th c, Carnap wrote quite a bit about both modal logic and metalanguage. He had also become a close friend and colleague of Quine, and they had years of correspondence about these issues. Carnap was strongly in favor of modal logic, but Quine said that modal logic was just metalanguage about logic. I admit that I had preferred Carnap's position to Quine's before the 1970s. But a book of collected papers in 1973 had several papers on modal logic by Dana Scott, Jakko Hintikka, and Michael Dunn which sold me on the new ways of thinking about modal logic. That led to the IKL work of 2005, which was published in 2006. When I studied Peirce's L376 in detail, it was obvious that he was thinking along the same lines. And his description of the phemic sheet as a collection of papers was in line with the specification of papers in R514. The IKL project (2004-2006) and the applications for the larger IKRIS project were very impressive. And the topics Peirce was discussing in L376 were so close to the topics we discussed that it almost seemed as if he had been a member of the project. I suggest the references in https://jfsowa.com/ikl . You don't have to believe anything I said. Just browse through the documents about IKRIS and IKL. That project was funded from 2004 to 2006, and the reports were very impressive. But Congress was in one of its wrangling moods about funding and threatened to shut down everything. And research is the first thing that gets cut. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> John, List: JFS: I already answered these points. I could say the same thing, but I will likewise give it another try. JFS: Please look at the example in RLT. A line of identity by itself is a complete, fully formed EG. There is no line of identity in that one-of-a-kind EG. The line connecting "is much to be wished" to the oval is lightly drawn, just like the oval itself; and in the very next EG, there is no line at all connecting the oval with "is false." At this point in the lecture, Peirce has not even introduced the line of identity yet. When he subsequently does so, he calls it "a heavy line" (RLT 153) and then consistently draws it accordingly. Here are the relevant manuscript images so that you can see the difference for yourself. [image.png] [image.png] [image.png] JFS: According to the way Peirce defined that notation and translated it to English, he chose the word 'that' as the English word that represents that construction (an oval with an attached line of identity). Please look at the actual text of RLT 151. Again, Peirce himself does not provide an English translation of that one-of-a-kind EG; and again, the line attached to the oval is lightly drawn, not a heavy line of identity. Why do you keep claiming otherwise? JFS: I am not asking you to believe anything I say. But I am asking you to look at the references I cited. I am asking you to look carefully at Peirce's own texts, and to set aside your preconceptions about what they say and show. JFS: The postulates of geometry are asserted to be true of whatever version of geometry they define. Peirce explicitly states in R 514 that "in the margin outside the red line, whatever is scribed is merely asserted to be possible. Thus, if the subject were geometry, I could write in that margin the postulates, and any pertinent problems stated in the form of postulates ..." Geometry falls within pure mathematics, which is a strictly hypothetical science that draws necessary conclusions about pure possibilities, as you yourself have observed on multiple occasions. JFS: All the evidence shows that L376 is the definition of Delta graphs. He is clearly defining a new version of modal logic in the same document in which he said that he needed to define a new version of modal logic. To deny that he was defining Delta graphs just does not make any sense of what he was writing. Peirce never says or implies in R L376 (1911) or elsewhere that he needs "to define a new version of modal logic." He simply states, "I shall now have to add a Delta part in order to deal with modals," because he was dissatisfied with his earlier attempts--first broken cuts in Gamma (1903), then tinctures (1906). To claim that he was defining Delta graphs in the 19 manuscript pages that are extant goes far beyond anything that he actually wrote on them. Perhaps he did go on to define Delta graphs in the subsequent pages that are missing, but unless and until someone finds them, we can only speculate. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
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