Jon, The entire letter L376 is about Delta graphs and applications of Delta graphs. Since Peirce began the letter to Risteen shortly after his visit, he was assuming that Risteen knew a great deal about the material they had discussed. Therefore, he plunged into examples without much of an intro.
As Peirce wrote, the phemic sheet of a Delta graph contains multiple "papers", each of which represents one possibility specified by "postulates" that govern the remaining content of the sheet. There are many ways of partitioning a sheet of paper to distinguish the postulates from the content they govern. The excerpt from R514 is one method, and it happens to fill an entire sheet of paper. He may have thought of some other notation for partitioning the paper, but the logical result would be equivalent. There is much more to say, and I'll send the full preview later this week. Meanwhile, there are some questions to ponder: Why did Juliette scrub and polish the floor in December? Spring cleaning is rarely done in December. Why was there some paper on the floor? Why did Peirce slip n it? Didn't he see it? Why was his accident so serious? If he had been walking in a straight line, he might have fallen on his rear. That might have been painful, but it wouldn't cause a serious injury that took 6 months to heal. Such a serious accident might have occurred if Peirce had been walking fast while turning or twisting. But why would he be doing that? Possible answer: Charles had asked Juliette to wash the floor because he wanted to build a diagram with multiple papers. He was laying out a diagram of papers with a large example of what he was writing about. As he turned to lay our another layer, he turned and slipped. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> Sent: 2/20/24 2:00 PM To: Peirce-L <peirce-l@list.iupui.edu> Subject: Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic) John, List: Here is an exact quotation of what Peirce actually says in R L376 (letter to Risteen) about the phemic sheet consisting of multiple "papers." CSP: I provide my system with a phemic sheet, which is a surface upon which the utterer and interpreter will, by force of a voluntary and actually contracted habit, recognize that whatever is scribed upon it and is interpretable as an assertion is to be recognized as an assertion, although it may refer to a mere idea as its subject. If “snows” is scribed upon the Phemic Sheet, it asserts that in the universe to which a special understanding between utterer and interpreter has made the special part of the phemic sheet on which it is scribed to relate, it sometime does snow. For they two may conceive that the “phemic sheet” embraces many papers, so that one part of it is before the common attention at one time and another part at another, and that actual conventions between them equivalent to scribed graphs make some of those pieces relate to one subject and part to another. There is no mention of Delta, nor anything that would "deal with modals," which again is Peirce's only stated purpose for adding a Delta part to EGs. Instead, the different papers correspond to different subjects that attract "the common attention" of the utterer and interpreter at different times--i.e., different universes of discourse; not different times, aspects, or modalities of the same universe of discourse. There is also nothing about the new "red pencil" operation that Peirce describes in R 514 (as quoted below), and based on his specific example in that text--postulates in geometry--it likewise does not "deal with modals." Instead, it treats the edges of the sheet and the red line drawn a short distance inside them as two cuts, the latter nested within the former, such that what is being represented overall is a conditional--if the propositions in the margin (outer close) are true, then the graphs within the red line (inner close) are also true. In other words, the universe of discourse is made more explicit instead of being entirely taken for granted, and it might be strictly hypothetical--"merely asserted to be possible." In summary, it remains unclear to me what the content of your new article has to do with Delta graphs. How would the use of multiple "papers" and/or the "red pencil" operation facilitate implementing formal systems of modal logic with EGs? Which specific one, "invented in 2006," do you have in mind? Regards, Jon On Mon, Feb 19, 2024 at 10:30 PM John F Sowa <s...@bestweb.net> wrote: Jon, That's true: JAS> I am admittedly curious about the content of your new article. As you know, there is only one place in Peirce's entire vast corpus of writings where he mentions Delta. But note the following excerpt from R514, which also contains a rough draft of the EGs in L231: "Since my paper of 1906, I have improved the [EG] system slightly (at least), and the manner of exposition of it greatly, by first stating the force of the different signs without going into their deeper significance in the Since my paper of 1906, I have improved the [EG] system slightly (at least), and the manner of exposition of it greatly, by first stating the force of the different signs without going into their deeper significance in the least... One of my possibly slight improvements, is that I begin by drawing (preferably with a red pencil), a line all round my sheet at a little distance from the edge; and 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 such as, that "if on a plane, there be circle with a ray cutting it, and two be marked [end of R514] That operation is the way L376 represents multiple parts of the phemic sheet. And it is a way of saying the conditions for the nested graph to be possible. That doesn't say much more. But that operation when combined with a notation for first-order logic is a method for representing modality in various logics in the late 20th and early 21st C. There are also other hints that suggest ways of extending FOL. They don't prove that Peirce intended exactly the same kinds of applications. But it shows that his ways of thinking could lead in promising directions. Following is the abstract of the article I'm writing. Abstract. In December 1911, Peirce wrote an intriguing claim about existential graphs: “I shall now have to add a Delta part in order to deal with modals.” Although his unfinished draft does not specify the details, it explains how an utterer and an interpreter may use Delta graphs in an investigation. Further hints may be found in several manuscripts he wrote in the previous six months. As another hint, the intended recipient of the letter was Allan Risteen. When that letter is combined with information about Risteen’s expertise and Peirce’s work on a proof of pragmaticism, it suggests that the phemic sheet of a Delta graph consists of multiple “papers”, each of which represents a different time, aspect, or modality of some universe of discourse. Although Peirce did not specify the details of Delta graphs, a combination of features mentioned in several 1911 manuscripts would satisfy the hints about Delta graphs. The result would be similar or perhaps equivalent to a logic for modality that was invented in 2006. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> Sent: 2/18/24 8:08 PM To: Peirce-L <peirce-l@list.iupui.edu> Subject: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic) John, List: JFS: I am now writing the article on Delta Graphs. That is an example where Peirce was on solid ground with his deep understanding of logic and mathematics. Next week, I'll send the abstract and preview of the new article, which shows how Peirce anticipated a version of logic that was developed in the 21st century (2006 to be exact). (https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00038.html) JFS: I'm moving on to the the article on Delta graphs. I'll send a note with a preview of that article later this week. (https://list.iupui.edu/sympa/arc/peirce-l/2024-02/msg00104.html) I am admittedly curious about the content of your new article. As you know, there is only one place in Peirce's entire vast corpus of writings where he mentions Delta. CSP: In this ["Prolegomena to an Apology for Pragmaticism," CP 4.530-572, 1906] I made an attempt to make the syntax [of Existential Graphs] 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 [in 1897]. 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. (R L376, R 500:2-3, 1911 Dec 6) For EGs as described in "the better exposition of 1903," modal logic is implemented with broken cuts in Gamma. However, by the time Peirce wrote this letter to Allan Douglas Risteen, he had abandoned cuts in general, having replaced them with more iconic shading for negation. Consequently, he needed a new way to "deal with modals," and this is the sole purpose that he states for adding a Delta part. 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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