John, List: 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.
JFS: Peirce is not saying that he is preserving the details of the 1903 logics. He is saying that he is preserving that DIVISION into Alpha (propositional logic), Beta (predicate logic), and Gamma (something beyond Alpha and Beta). Please do not put words in Peirce's mouth. Preserving the division without also preserving the details of "the better exposition of 1903" would make no sense. Going straight into a specification for the new Delta part without saying anything at all about the Alpha, Beta, and Gamma parts, having just stated the intention to "adhere to" that division, would likewise make no sense. Again, can you identify even *one sentence* from the entire extant letter to Risteen that is about EGs but *not *applicable to those other three parts, i.e., unique to Delta? JFS: Quine correctly said that modal logic was just a version of metalanguage about logic. That is Quine's opinion, apparently one that you share. However, it is by no means universal, even among logicians today, and there is no basis for claiming that *Peirce *would agree unless you can provide an exact quotation to that effect. Again, having made up your own mind, I suspect that you are reading that position back into his texts, including R L376. JFS: All the useful applications are based on some version of metalanguage, along the lines of the December 1911 article. It is a letter, not an article, and as far as I can tell, it neither states nor implies anything about the use of metalanguage instead of formal modal logic. Please provide an exact quotation to support your claim. JFS: Logics that use the two operators for necessary and possible, have no practical applications of any kind. Again, I would caution against making such sweeping and dismissive pronouncements. After all, there might very well be practical applications of formal modal logic that have not yet come to your attention or that get discovered in the future. In any case, according to Peirce, "True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men" (CP 1.76, c. 1896). JFS: Peirce has an unusually large percentage of successful revivals. His Delta graphs are among them. I recognized their importance, because I have used and worked with similar logics from the late 20th and early 21st C. No one can say for sure what Peirce had in mind for Delta EGs since he never spelled it out himself, unless there are more pages of R L376 somewhere out there, waiting to be discovered. I still see no evidence in the extant text of that letter nor elsewhere (including R 514) to support your conjecture that it was about adding metalanguage to Beta EGs, given that his only stated reason for needing "a *Delta *part" at all is "in order to deal with modals." It seems much more plausible that he was considering a new notation for representing and reasoning about modal propositions to replace his unsatisfactory broken cuts (1903) and tinctures (1906), such as the one that he introduces on R 339:[340r] (1909 Jan 7). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Mon, Mar 11, 2024 at 10:14 PM John F Sowa <s...@bestweb.net> wrote: > Jon, > > I'll go into much more detail in the preview article, which I am now > working on. I'll just respond to the following point: > > JAS: Your quotation here omits the crucial first part of the only > sentence in R L376 that mentions Delta--"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." > > I answered that before: Peirce is not saying that he is preserving the > details of the 1903 logics. He is saying that he is preserving that > *DIVISION* into Alpha (propositional logic), Beta (predicate logic), and > Gamma (something beyond Alpha and Beta). > > The most significant Gamma graphs are the the ones that represent the > second-order version of his 1885 Algebra of Logic. He had reviewed > Russell's logic of 1903, and he must have heard about (but didn't have time > to study) Whitehead & Russell's logic of 1910. Both of them discussed > higher-order logic (second order and higher), but not modal logic. > > During the years after 1903, Peirce mentioned the modal words in English > many, many times. And he experimented with new notations for modality, but > he never used or even mentioned his 1903 modal logic for any purpose. In > fact, he had only used it for a few examples in 1903. > > But the most important evidence is to look at the developments in the > years after Peirce. C. I. Lewis introduced a new version of propositional > modal logic in 1932, which had been inspired by Peirce's 1903 modal logic. > It was different from Peirce's version, but equivalent in expressive power > to the propositional subset of his modal logic of 1903. During the 30 or > 40 years after 1932, many logicians built on that logic. But many others > (Quine among them) rejected it. Quine correctly said that modal logic was > just a version of metalanguage about logic. Other logicians criticized it > or ignored it altogether. Very few did much with it after the 1960s. From > the 1970s and later, new versions of logic were developed to handle modal > issues, but (a) they did not use the box and diamond operators for > modality; (b) they used different words. such as contexts, situations, or > domains; and (c) they combined predicate calculus with metalanguage, as > Peirce did in L376. > > In my preview of the Delta graph article, I'll explain these issues in > more detail and discuss the directions taken in 1973 and later. Short > summary: All the useful applications are based on some version of > metalanguage, along the lines of the December 1911 article. Logics that > use the two operators for necessary and possible, have no practical > applications of any kind. > > Peirce had good taste and good insights into the kind of logic required > for problems in philosophy, science, and engineering. Metalanguage is the > foundation for all useful modal reasoning in the 21st C. Textbooks still > mention the Lewis-style of modal logic, but there are no applications to > any kind of practical applications. > > Summary: Any version of mathematics and/or logic that has no applications > is. literally, useless. There are many such versions in the many years of > published tomes. And most of them have few or no citations. > > On rare occasions, something from the distant past is revived and becomes > a big success. Peirce has an unusually large percentage of successful > revivals. His Delta graphs are among them. I recognized their importance, > because I have used and worked with similar logics from the late 20th and > early 21st C. > > John >
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