Jon, Every statement about a thought expresses a possibility. Every statement about a claim, a wish, a fear, etc, expresses a possibility. That is why metalanguage is a more explicit method for expressing and reasoning about possibility. Quine said that in the 1960s, and other logicians have been developing methods for doing that since the 1970s. Today, nobody uses the Lewis-style of modal logic for any practical purpose.
JAS: how would you scribe the graph for "A thinks that B is possibly true"? I'm sorry that I forgot to answer that question. I was commenting on other points, and I forgot to state the translation for the EG you drew. For my recommended version of metalevel EGs, I would first replace the dotted line of your EG with a solid line. That would express the sentence "A is thinking the proposition that there exists a B." Then I would connect that solid line by a ligature to the word 'possible'. Literally, that new EG could be read "A is thinking the possible proposition that there exists a B." But it could be read more simply "A thinks it's possible that there is a B." Exactly the same procedure can be used to attach any other adjective or phrase, such as 'necessary', 'impossible', 'probable', 'useful', 'desirable', 'feared', 'doubted', 'lawful', 'illegal' or 'written in Holy Scriptures". That is the reason why the version of modality that C. I. Lewis specified in 1932 is a dead end. Anything you can express with it can be expressed more clearly and generally with metalanguage. I believe that Peirce recognized the need for more expressive power. And metalanguage adds that power without losing anything that might be expressed with the 1903 EGs. Some people dabbled with methods for computing with a Lewis-style of reasoning, but they have never been used for any practical applications. Metalanguage is simpler and more general. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> John, List: JFS: In both graphs in your note below, the thin line may be read as "that"' Yes, of course; that is obvious from the syntax of the English sentences that I translated into those two graphs--although, as I said in that post, it is a dotted line, not a thin line. JFS: But neither of those two sentences can be translated to any version of modal logic based on the modal logics by C. I. Lewis or later variations of it. No, of course not; that is obvious from the fact that neither of those two sentences expresses a modal proposition, i.e., one that involves possibility or necessity. JFS: They can also be translated to and from Peirce's Delta graphs No, this is incorrect; that is obvious from the fact that such propositions about propositions can already be represented by Gamma EGs using the dotted oval/line notation that Peirce introduced in 1903 (LF 2/1:166), which is isomorphic with the thinly drawn oval/line notation that he used in 1898 (RLT 151). In 1911, he did not need a new Delta part of EGs in order to deal with metalanguage; according to his own explicit statement in R L376, he needed a new Delta part of EGs in order to deal with modals, due to his dissatisfaction with the cuts (including broken cuts) of 1903 and the tinctures of 1906. With that in mind, in your candidate for Delta EGs, how would you scribe the graph for "A thinks that B is possibly true"? Or will you continue refusing to provide any examples of how you would represent (and reason about) even very simple modal propositions, despite my multiple requests? By contrast, I am happy to show you how I would scribe that graph in my candidate for Delta EGs based on R 339:[340r] (1909). [image.png] Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Wed, Mar 13, 2024 at 4:51 PM John F Sowa <s...@bestweb.net> wrote: Jon, In both graphs in your note below, the thin line may be read as "that"' A thinks THAT C is a good girl. A is claiming THAT A is thinking THAT C is a good girl. Both of those sentences and both of those EGs can be translated to and from the IKL logic of 2006, which uses the symbol "that" to represent metalanguage. They can also be translated to and from Peirce's Delta graphs, which can be translated to and from the IKL logic. But neither of those two sentences can be translated to any version of modal logic based on the modal logics by C. I. Lewis or later variations of it. John
_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at https://www.cspeirce.com . It'll take a while to repair / update all the links! ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
