Jon, We have discussed this issue many times before. R669 was the end of the line for Peirce's old specification of EGs. In the next MS, R670, he deleted the complex encrustations that made it impossible to generalize EGs beyond two dimensions, and he began to replace them with a more precise and general foundation -- the polished and perfected specification in L231 a few weeks later.
In my article for the Semiotica issue on EGs (2011), I made the mistake of calling the version in R514 a tutorial, because it had been mistakenly dated 1909 -- prior to the version of R669 dated May 1911. Peirce's undated draft in R514 and the final version in L231 (dated June 1911) is his best specification of EGs, Please read or reread that article: https://jfsowa.com/pubs/egtut.pdf And please read the section on advanced topics, which show innovations that are superior to later developments by other logicians, including Gerhard Gentzen (1935). In that section, I showed how Peirce's version in R514 can prove an unsolved research problem from 1988 that was still unsolved in 1910. Since I made a mistake of calling it a tutorial, that article didn't get the attention it deserved. But I presented a more complete version in Reasoning with diagrams and images, Journal of Applied Logics 5:5, 2018, pp. 987-1059. That article got a huge amount of attention and citations. In the letter L231, which Peirce sent to Lady Welby's group, he presented a clean, general foundation that incorporates the innovations of R670. In that same letter, he summarized issues related to his proof of pragmaticism, which he had been working on since 1904. In it, he also wrote that he was trying to develop a method for reasoning about "stereoscopic moving images". In today's terminology, he was anticipating virtual reality (VR). The old method with cuts cannot be generalized beyond two dimensions. But the new method of shading can be extended to any number of dimensions -- including everything being done today with virtual reality. Please stop advertising an obsolete system that Peirce had abandoned. It's important to give him credit for anticipating some of the latest and greatest innovations of the 21st century. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> List: When explaining his system of Existential Graphs (EG), Peirce typically identifies five standard transformation rules--erasure, insertion, iteration, deiteration, and double cut. Sometimes he groups the first four into two pairs, erasure/insertion and iteration/deiteration. At the end of R 669 (1911), he calls these "illative permissions" and claims that they "will suffice to enable any valid deduction to be performed," while the double cut rule "ought to be reckoned as a permission, but it is not an illative permission, i.e. a permission authorizing a species of inference." Instead, he suggests that "since a scroll [double cut] both of whose closes are empty asserts nothing, it is to be imagined that there is an abundant store of empty scrolls on a part of the sheet that is out of sight, whence one of them can be brought into view whenever desired." Any graph already scribed on the sheet may then be iterated into the inner close of that empty double cut, followed by erasure of the original instance. What about the reverse operation of removing a double cut with an empty outer close? Peirce offers a clever theoretical justification for this about five years earlier, in a manuscript that will be published in its entirety for the first time in volume 3 of Logic of the Future (R S-30[Copy T], 1906). Whereas "a Scroll is not a Graph and its removal is neither the Insertion nor the Deletion of any Graph," the blank is a graph--a continuous graph, "the essential property of which is that any portion of an Instance of such a Graph is itself an Instance of the same Graph." Since the blank is always present on the unenclosed sheet, it may be deiterated from any empty outer close of a double cut, effectively collapsing it. The inner close is now no more enclosed than the double cut itself, thus allowing the graph in the inner close to be iterated to the area just outside the double cut and then deiterated along with the blank that remains in the inner close, which likewise collapses. This approach is even more perspicuous when shading of oddly enclosed areas replaces cuts/scrolls, as Peirce ultimately advocates--any empty ring-shaped area, shaded or unshaded, is an instance of the blank that may be iterated or deiterated at will. In short, the only "undeduced permissions" in EG are "under defined conditions either to delete an indecomposable Graph or to insert an indecomposable Graph in a defined place," namely, erasing in unshaded areas, inserting in shaded areas, and deiterating from or iterating to equally or more enclosed areas. Moreover, "the Graphs of Coëxistence (the Blank) and of Identity are 'indecomposable,' i.e. partless, in the sense of the maxim, although they and their Instances can be separated into parts of any multitude we like, whenever we like, and with such boundaries as we choose to impose." Hence, in Beta EG, a line of identity that crosses an otherwise empty ring-shaped area may be iterated or deiterated along with the blank. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt
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