Jon, I am preparing slides for a Zoom talk on 2/28. (I'll send the abstract and link tomorrow.) This is my last note on this thread until 2/29 or later.
JAS> Even in the printed book, the line attached to the first oval on page 151 is thinly drawn, exactly like the oval itself, while the lines of identity on pages 153ff... That's too bad for an elegant notation. But it reinforces the point that Peirce was using the same methods for representing metalanguage in 1898 as in 1911. Metalanguage is the only feature required to define modality. Please read my brief summary about the IKRIS project in https://jfsowa.com/ikl . You don't have to believe anything I wrote. There are many, many references on that page to IKRIS reports written by other authors (almost all of whom have a PhD in logic, computer science, or some other branch of science or philosophy). JAS> I suspect that you were reading back into his text what you had already decided for yourself when you changed your mind regarding Carnap vs. Quine, namely, that modal logic is "just metalanguage about logic." Peirce never states nor implies this--not in R L376, and as far as I know, not anywhere else. It's not something I decided for myself. It's something I learned from professional logicians from 1973 onwards. Please read the references. That fact is not a debatable issue. As for Peirce not realizing some of the issues, he can't be blamed for not discovering methods that logicians adopted 60 years after he died. JAS> he anticipates the future formalization of modal logic when he states, "The quantified subject of a hypothetical proposition is a possibility, or possible case, or possible state of things" (CP 2.347, c. 1895). Even more specifically, he anticipates C. I. Lewis's development and advocacy of strict implication in... [see below] The axioms Lewis states for modal logic are true for an open-ended variety of modalities, including every version Peirce described in his tinctured graphs of 1906. The fact that Peirce was thinking of such things in 1906 shows that he had reasons for moving beyond the modal version of 1903 (which he never used after 1903). That sentence "The quantified subject of a hypothetical proposition is a possibility, or possible case, or possible state of things" (CP 2.347, c. 1895)." does not imply that the postulates in the margin of a sheet are inside a negation. It simply means that the postulates are true of a possible world described in the nested statements on that sheet. And there is no negation of the nested statements. The text in the margin is metalanguage asserted about the nested text. (Please excuse my use of a term that Peirce had not invented, but he frequently used metalanguage when he talked about quotations by other people. We are also using metalanguage when we are talking about writings by Peirce, by ourselves, or by each other. And there are no implicit negations. The only negations are explicit.) And note that he never rejected the KINDS of modalities he described with the tinctures of 1906. What he rejected is the complexity of the specifications in that article. With his notation of R514, he can state any kind of modality with an appropriate choice of postulates in the margin of the sheet. In fact, he could put postulates in the margin to say that the possible world of "You are a good girl" is much to be wished. He could even go back to the medieval Modistae and put postulates in the margin that specify a world described in Holy Scriptures. Whether he might consider that world possible, actual, necessary or impossible is independent of the fact that it was described in Holy Scriptures. The postulates in the margin of a paper may specify anything in any scientific theory or anything described in Alice in Wonderland. The postulates on any paper are not inside a negation because they are asserted to be true only of the nested propositions in the part of the phemic sheet on that same paper. Other parts of the phemic sheet on other papers may have very different propositions in the margin. I thank you for raising all those objections. With the answers I have stated (or minor variations thereof) plus the material in the many references about metalanguage and modal logics from 1973 onward, I now have everything I need for a solid article about what Peirce had written about his Delta graphs and how they are related to the modal logics of the 21st C. For any material I have not mentioned, please read the references. As I keep saying, you don't have to believe me. Just read the references. If you have questions about how those references are related to what Peirce wrote, I'll answer them. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> John, List: JFS: 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'. Even in the printed book, the line attached to the first oval on page 151 is thinly drawn, exactly like the oval itself, while the lines of identity on pages 153ff are unambiguously heavy; and again, there is no line attached to the second oval on page 151. Here are those images. [image.png] [image.png] [image.png] JFS: 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. According to R 514, the text in the margin is not making assertions about the propositions inside the red line, it consists of "postulates" that are "merely asserted to be possible," i.e., the hypothetical antecedent from which those propositions would follow necessarily as the consequent. This is a completely different notation from the unique EGs on RLT 151, where the proposition written inside the oval fills the blank in the rheme written outside the oval. JFS: When I studied Peirce's L376 in detail, it was obvious that he was thinking along the same lines. I suspect that you were reading back into his text what you had already decided for yourself when you changed your mind regarding Carnap vs. Quine, namely, that modal logic is "just metalanguage about logic." Peirce never states nor implies this--not in R L376, and as far as I know, not anywhere else. On the contrary, he anticipates the future formalization of modal logic when he states, "The quantified subject of a hypothetical proposition is a possibility, or possible case, or possible state of things" (CP 2.347, c. 1895). Even more specifically, he anticipates C. I. Lewis's development and advocacy of strict implication in the following passage. CSP: The consequence de inesse [material implication], "if A is true, then B is true," is expressed by letting i denote the actual state of things, Ai mean that in the actual state of things A is true, and Bi mean that in the actual state of things B is true, and then saying "If Ai is true then Bi is true," or, what is the same thing, "Either Ai is not true or Bi is true." But an ordinary Philonian conditional [strict implication] is expressed by saying, "In any possible state of things, i, either Ai is not true, or Bi is true." (CP 3.444, 1896) Peirce might have changed his mind about this (like you did) sometime over the next 15 years, but only an exact quotation to that effect from his later writings could warrant such a claim. Can you provide one? JFS: And his description of the phemic sheet as a collection of papers was in line with the specification of papers in R514. What "specification of papers in R 514"? Peirce says nothing in that text about multiple sheets. If you are simply affirming that the "red pencil" operation of R 514 could be applied to each of the "many pages" of R L376, then we agree about that. However, I now advocate shading the margin instead of marking its boundary with a red line, consistent with Peirce's other writings about EGs in 1911 that you have often emphasized. Again, it is a more iconic way of conveying that the margin is a different surface from the interior--it "represents a universe of possibility" (CP 4.579, 1906), while "the main part of the sheet represents existence or actuality" (CP 4.577). In my updated candidate for Delta EGs as outlined last night, there is a separate sheet for each possible state of things (PST), with its law-graphs in the shaded margin and its fact-graphs in the unshaded interior. After all, Goble refers to laws for a possible world as "the fundamental postulates of that world" (https://projecteuclid.org/journalArticle/Download?urlId=10.1305%2Fndjfl%2F1093890890, p. 153), and the fact-graphs on a PST sheet represent what would be fact-propositions if that PST were actualized. By the way, a few paragraphs before the "red pencil" discussion in R 514--the fragmented 1909 manuscript itself, not the misfiled June 1911 letter to J. H. Kehler with its EG tutorial (R L231)--Peirce states, "So much, to explain in the second mode of clearness the three Modalities. The May be, The Actually is, The Would be." In other words, he explicitly reaffirms his definition of modality as possibility/actuality/necessity, although we do not have the preceding pages that presumably provide more details. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sun, Feb 25, 2024 at 10:05 PM John F Sowa <s...@bestweb.net> wrote: 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
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