John, List: JFS: This is my last note on this thread until 2/29 or later.
Understood, and at this point, I doubt that there is much more for either of us to say without further repeating ourselves anyway. JFS: Metalanguage is the only feature required to define modality. Peirce never said anything about needing a Delta part of EGs to *define* modality, he said only that he needed it to *deal with* modals, i.e., modal propositions. Accordingly, I am primarily interested in developing a version of EGs for *reasoning about* modality--possibility and necessity, or analogous concepts like permission and obligation--by implementing the now-standard formal systems of modal logic. JFS: 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. A hypothetical proposition is a *conditional *proposition (e.g., see CP 3.374, 1885), which is represented in all parts of EGs by nested cuts until Peirce introduces shading in June 1911. The postulates in the margin are not "inside a negation," they are inside the outer close--the red line of R 514 (1909) is the inner cut, and the physical edges of the page constitute the outer cut. Hence, the postulates are not asserted to be false, but they are also not asserted to be true--they are "merely asserted to be possible." The nested statements are also not asserted to be true or false in the *actual *state of things; instead, what is asserted is that *if *the postulates in the margin are true, *then *the nested statements are also true. In other words, the postulates in the margin and the nested statements *together *describe a possible state of things--the postulates are its law-propositions, and the nested statements are its fact-propositions. JFS: The text in the margin is metalanguage asserted about the nested text. ... With his [Peirce's] notation of R514, he can state any kind of modality with an appropriate choice of postulates in the margin of the sheet. That is *not *how postulates work. As an obvious example, Euclid's five postulates are not metalanguage asserted *about *the theorems that follow from them, they are pure possibilities (antecedent) from which those theorems are derived as deductively necessary conclusions (consequent). In accordance with R 514 but adopting Peirce's 1911 notation, we can write the five postulates in the *shaded *margin of a sheet and the theorems inside its *unshaded *area, thus asserting the conditional proposition that *if *the postulates are true, *then *the theorems are also true. The postulates and theorems *together *describe the possible world of Euclidean geometry, with the postulates as its law-propositions and the theorems as its fact-propositions. JFS: I thank you for raising all those objections. Likewise, I thank you for the exchange. As I acknowledge in the other thread, it is what prompted me to develop an interesting extension of my candidate for Delta EGs. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Mon, Feb 26, 2024 at 3:58 PM John F Sowa <s...@bestweb.net> wrote: > 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 >
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