Jon, List
I am now busy preparing slides for a Zoom talk on Feb 28, sponsored by Ontolog Forum. (I'll forward a copy of the announcement to P-List, if anyone is interested.) But first, I'll respond to some of your doubts.
JFS> The entire letter L376 is about Delta graphs and applications of Delta graphs.
JAS> This conjecture is quite a leap, considering that--as you acknowledged--Peirce mentions Delta exactly once in that entire 19-page letter, which he left unfinished...
The primary subject of L376 is Delta graphs. That is the only interpretation that unifies every part. In the following excerpt from L376, the word 'here' refers to the content of L376. For emphasis, certain passages in this excerpt are printed in bold.
"This syntax, which I have hitherto called the "system of Existential Graphs" . . . An account of slightly further development of it was given in the Monist of Oct. 1906. In this I made an attempt to make the syntax cover Modals; but it has not satisfied me. . . 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. A cross division of the description which here, as in that of 1903, is given precedence over the other is into the Conventions, the Rules, and the working of the System."
Note that Peirce had made various attempts to go beyond the 1903 version of modals, but he was not satisfied with them. Since he never used the 1903 version of modals, except for a few pages of the Logic Notebook, there is strong evidence that he was looking for a replacement. When he mentioned the division into Alpha, Beta, and Gamma, he did not say what each part included. He had that same division with his algebra of 1885, in which the third part was second-order predicate calculus (quantifiers that range over relations). Since he planned to keep that division, but with a new version of modals, it seems unlikely that he would have kept a version of modals that he had never used for any purpose in the previous eight years.
In the remainder of L376, note the paragraphs that begin with the phrases "The Conventions." and "the Phemic Sheet." The paragraphs that follow describe a version of logic that is different from any that Peirce had previously specified. Can you suggest any reason why he might be specifying a logic other than Delta graphs?
Note that he also mentions probabilities. That suggests another important innovation: The use of multiple "papers" for specifying both possible and probable parts of the phemic sheet. That would be a unification that goes beyond most logics of the 21st C. In fact, it would make a valuable contribution to the latest R & D in artificial intelligence. That is a topic I mentioned in Section 7 of my recent article on phaneroscopy, and it would put Peirce into the forefront of ongoing issues in AI. See the copy of Section 7 I sent to both Peirce and CG lists.
The 2006 version of logic that I have in mind is called IKL, which could be adapted to the specifications Peirce mentioned in R514, L231, and R376. Since I don't have time to pare down and discuss the references, I'll cite all of them.
The first version, which suggests, but doesn't specify a modal logic, is from a conference in Denmark in 2002, and published in a book in 2003: Laws, Facts, and Contexts: Foundations for Multimodal Reasoning, https://jfsowa.com/pubs/laws.htm . At the bottom of the text is a photograph of the participants. Hintikka and I are in the center, both wearing rain coats. We had a long conversation during the conference, and that influenced the directions I took in the published version and in the following articles.
In that article, I discuss, among other issues, Peirce's logic of 1906 with heraldic tinctures. But the complexity of the tinctures is irrelevant. I later moved to a much simpler version of modal logic that is similar to the logic of L376. But note Figure 1 of this article, which cites a graph from RLT (1898). Figure 1 is exactly equivalent to the "papers" in R514 and L376. That operator, when added to the first-order EGs of 1911, is sufficient for a modal logic that would be similar to or perhaps identical to what Peirce is writing about Delta graphs.
Next, see an article published in 2006, but written in 2005: Worlds, Models, and Descriptions, https://jfsowa.com/pubs/worlds.pdf . I wrote this article while I was collaborating on the development of the IKL logic, which was also published in 2006. For a list of references to IKL and the IKRIS project that sponsored the development of IKL, see https://jfsowa.com/ikl .
Then. look at Five Questions on Epistemic Logic, https://jfsowa.com/pubs/5qelogic.pdf . That article, which was published in 2010, discusses how a logic such as IKL or Peirce's delta graphs could represent various issues in modal logic with an emphasis on epistemic logic -- that is also a consideration for my recent article about phaneroscopy.
There is much more that could be said, and I plan to write it in the article on Delta graphs. And by the way, I wonder how you would explain the three questions I asked: Why did Juliette wash and scrub the floor in Deceber? Why were there papers on the floor? Why did Peirce slip on them in a very complex way?
John
From: "Jon Alan Schmidt" <jonalanschmidt@gmail.com>
Sent: 2/21/24 1:25 PM
To: Peirce-L <peirce-l@list.iupui.edu>
Subject: Re: [PEIRCE-L] Delta Existential Graphs (was The Proper Way in Logic)
JFS: The entire letter L376 is about Delta graphs and applications of Delta graphs.
This conjecture is quite a leap, considering that--as you acknowledged--Peirce mentions Delta exactly once in that entire 19-page letter, which he left unfinished unless additional pages somehow disappeared from the manuscript folder at Harvard's Houghton Library decades ago. Again, here is that lone sentence.
CSP: 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.
In the remaining text that we currently have, Peirce never gets around to discussing any of the individual parts of EGs and their differences, despite stating plainly that he was going to maintain them as "the better exposition" of the system as a whole. He also says nothing whatsoever about dealing with modals, which is his only stated purpose for adding a Delta part to the other three.
JFS: 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.
That is not what Peirce wrote in his letter to Risteen. Again, here is the exact quotation.
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.
Again, there is no mention here of Delta, nor of modals. In fact, there is no mention here of any of the different parts of EGs, because Peirce is describing the phemic sheet as employed in every part. He also does not say that the different "papers" correspond to different possibilities, he says that they correspond to different subjects--different universes of discourse--to which the utterer and interpreter together pay attention at different times. So I ask again, how exactly would the use of multiple "papers" and/or the "red pencil" operation of R 514 facilitate implementing formal systems of modal logic with EGs? Which specific one, "invented in 2006," do you have in mind?
JFS: Meanwhile, there are some questions to ponder:
Any answers to such questions about the details of Peirce's unfortunate accident are pure speculation. It seems to me that if it had happened while he was "laying out a diagram of papers" for a new version of EGs, then he likely would have said so somewhere.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Structural Engineer, Synechist Philosopher, Lutheran Christian
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