Jon, List, Before I read your note below, I had just sent an off-list note to you and Gary R. to recommend that you make very important revisions to your article. It's a pity that you had sent the article to the publisher so long ago. It's probably too late to stop the publication and make the necessary revisions.
Basic point: Peirce added the notation for metalanguage to EGs in 1898 (RLT). That is 5 years before the Gamma graphs of 1903. That addition is sufficient to support modality. It makes the modal features of Gamma graphs irrelevant. But modality alone is not sufficient for a proof of pragmatism (a major goal of Peirce's last decade). Metalanguage is a prerequisite, but much more is necessary. I have been urging you (and other subscribers to P-list) to read the developments of the IKRIS project of 2004 to 2006, which uses a metalanguage feature added to the ISO standard for Common Logic. See https://jfsowa.com/ikl . I was just one of a committee of 9 who defined the IKL logic. But that logic, by itself, was not sufficient to support the major developments needed for a proof of pragmatism. The critical additions are closely related to what Peirce specified in L376. I call that material a specification of Delta graphs. I don't care what you call it. The specifications are important. The names are irrelevant. Allan Risteen was also highly influential in discussing the issues with Peirce before he started to write L376. Please read the references to Risteen in EP2 -- they're all listed in the index. And one of Risteen's areas of expertise was his study of the mathematics by Arthur Cayley (see his Wikipedia page). I realize that you insist in ignoring everything but the first two paragraphs of L376. I believe that is a serious mistake. You are deliberately putting blinders on your eyes. I think that we can all agree that it's unwise to reject anything Peirce wrote just because of some preconceived notion that it's irrelevant. I have a strong background in mathematics and logic and their applications to computer systems. By working with a logic similar to the one Peirce developed (IKL), I learned how such a logic is important for scientific and engineering applications. The IKRIS project is an important example. That is one reason why I have been so enthusiastic about L376. Modern technology is more advanced, but the principles of pragmatism are just as important. In summary, the specifications in L376, supplemented with R514, L231, and the kinds of topics Peirce would have discussed with Risteen, are essential for a proof of pragmatism. The iKRIS project of 2004-2006 shows the value of a very similar logic, but much more is needed beyond the metalanguage Peirce knew that, and the full IKRIS project (much more than just the logic) demonstrated that. What you or Peirce or I may call it is irrelevant. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> Subject: Re: [PEIRCE-L] Modal EGs in Delta vs. Gamma John, List: JFS: Since your article has just been accepted for publication, you probably still have time to make a few corrections. Actually, my paper was accepted for publication (after review and revision) six months ago, and I see no need to correct anything at this point anyway--I stand by everything that I wrote in it. JFS: More precisely, Peirce had a notation for metalanguage in 1898, which is simpler and does not need the useless baggage of Gamma graphs. Simpler than what? Peirce explicitly incorporated the 1898 notation for metalanguage into Gamma EGs in 1903, only changing the oval/line from thinly drawn to dotted. Consequently, any EG with that notation is a Gamma EG. JFS: But metalanguage, by itself, is not sufficient for a proof of pragmatism. There is an open-ended variety of ways for using metalanguage. Peirce never states nor implies in R L376 that he needs to add a Delta part to EGs in order to use metalanguage or provide a proof of pragmatism. Instead, he says that he needs to add a Delta part to EGs "in order to deal with modals," i.e., he needs a new notation for representing and reasoning about propositions involving possibility or necessity to replace the unsatisfactory (broken) cuts of 1903 and the nonsensical tinctures of 1906. Accordingly, ascribing any other purpose whatsoever to Delta EGs is utterly unwarranted. As you stated not long ago, "Any attempt to say anything beyond what Peirce wrote is an opinion of the person who does the writing. ... Nobody can claim that their opinion is what Peirce intended" (https://list.iupui.edu/sympa/arc/peirce-l/2024-01/msg00098.html). JFS: Please note that EGs that refer to "circumstances" can be translated to ordinary statements in Peirce's algebraic notion for first-order logic. There is nothing special about circumstances, by themselves, that makes them modal. As I have explained repeatedly, the EGs scribed on R 339:[340r] cannot be properly interpreted as Beta EGs. The heavy lines for "circumstances" or "times" do not denote indefinite individuals, they represent possible states of things--exactly what is needed for modal logic but missing from previous versions of EGs. The attached letters "p" and "q" do not denote general concepts being attributed to individuals, they denote propositions that would be true in those possible states of things--i.e., modal propositions. The additional modal axioms added to classical propositional logic do not correspond to valid theorems in first-order predicate logic as implemented with Beta EGs. There are no counterparts in the latter for propositions that are non-modal (no attached heavy lines) or that include iterated modalities (multiple attached heavy lines). JFS: Those topics would explain why Delta graphs (as described in L376) have much more structure than just a notation for metalanguage. Peirce used that structure to support a phemic sheet that has multiple "papers". Nothing in the extant 19 pages of R L376 describes Delta EGs. Everything in that letter is applicable to the other three parts, as confirmed by your ongoing refusal/inability to provide any exact quotations from it to the contrary, despite my repeated requests. The "many papers" are neither new nor unique to Delta EGs--they correspond to different subjects that attract "the common attention" of the utterer and interpreter at different times, such that the collection of all of them represents the entire universe of discourse. Accordingly, nothing precludes them from being employed with Alpha, Beta, and Gamma EGs; in fact, Peirce was simply reiterating in 1911 what he had already written previously (R 280, c. 1905; CP 4.561n, 1908; https://list.iupui.edu/sympa/arc/peirce-l/2024-03/msg00004.html). JFS: And the remainder of L376 describes how they may be used in an "investigation". That is necessary to support a logic of pragmatism. Why did you put "investigation" in quotation marks? That word never appears in R L376. Can you provide an exact quotation from that letter where Peirce describes how the "many papers" may be used in an "investigation"? I am not seeing it. JFS: That additional structure is what makes Delta graphs the fourth kind of logic that goes beyond Gamma graphs. You say that as if you somehow know exactly what Peirce had in mind for Delta graphs. Perhaps you meant to say, "That additional structure is what would make my [John Sowa's] candidate for Delta graphs the fourth kind of logic that goes beyond Gamma graphs." Even so, as I already pointed out, the "many papers" are equally applicable to Alpha, Beta, and Gamma EGs; there is nothing about them that specifically deals with modals or would otherwise be unique to Delta EGs. JFS: And by the way, when you make these additions to your article, you can include an acknowledgment to thank me for all this help in explaining what Peirce was doing. I am glad to see that you are maintaining a sense of humor. Again, I have appreciated the stimulating exchange and have learned quite a bit from it about how Peirce anticipated the use of metalanguage in logic, even though we continue to disagree on whether it has anything to do with Delta EGs. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sun, Mar 17, 2024 at 2:06 PM John F Sowa <s...@bestweb.net> wrote: Jon, List, Since your article has just been accepted for publication, you probably still have time to make a few corrections. Following are some suggestions. JAS: Indeed, given that Peirce already had a notation for metalanguage in his 1903 Gamma EGs--in fact, five years earlier--how could that be what he had in mind for the new Delta part that he added in 1911? What exactly are you proposing to add that goes beyond the dotted (or thinly drawn) oval and line for asserting propositions about propositions? What must be added is all of L376. More would be better, but we can look to the future to see what is needed. More precisely, Peirce had a notation for metalanguage in 1898, which is simpler and does not need the useless baggage of Gamma graphs. There is no need for them when you adopt the notation for metalanguage. But metalanguage, by itself, is not sufficient for a proof of pragmatism. There is an open-ended variety of ways for using metalanguage. I also copied page 340r from the logic notebook (see attached). Please note that EGs that refer to "circumstances" can be translated to ordinary statements in Peirce's algebraic notion for first-order logic. There is nothing special about circumstances, by themselves, that makes them modal. You should make that correction in your article. Did you read the Wikipedia article about Arthur Cayley and the comments about Risteen in EP2? Those topics would explain why Delta graphs (as described in L376) have much more structure than just a notation for metalanguage. Peirce used that structure to support a phemic sheet that has multiple "papers". And the remainder of L376 describes how they may be used in an "investigation". That is necessary to support a logic of pragmatism. That additional structure is what makes Delta graphs the fourth kind of logic that goes beyond Gamma graphs. I suggest that you include all of L376 in an appendix to your article. That is what I'm doing. In summary, Peirce was years ahead of his time, and it's essential to give him full credit for his accomplishments. It would be insulting to claim that he didn't realize that his logic of 1892, by itself, was sufficient. And by the way, when you make these additions to your article, you can include an acknowledgment to thank me for all this help in explaining what Peirce was doing. John
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