Jon AS, List, For anyone who is not familiar with Peirce's 1911 EGs, see my introduction to EGs, which is based on the 1911 version. The first 10 slides are sufficient for an overview. The remaining slides show features of the 1911 EGs that make a major advance over the logics of the 20th century: http://jfsowa.com/talks/egintro.pdf The following comment shows why Peirce rejected R669 and replaced it with R670 and L231: JAS> Peirce had a very good reason for not writing a third rule at the end of R 669, and it was not because "he suddenly realized" something at that moment in time and "abruptly" abandoned his previous train of thought. It was simply because he had already stated the third rule a few paragraphs earlier, and had explicitly pointed out that it is not an illative permission; i.e., it is not a rule of inference. After reading that comment, I realized that Peirce's insight on 2 June 1911 was that the adjective 'illative' is irrelevant and misleading for all three permissions (rules of inference). The rules depend only on negation. They do not depend on a "sign of illation", such as a scroll or other symbol for if-then. In L231, Peirce called all three rules permissions (without the adjective 'illative'). I believe that R669 is the *last* MS in which he wrote the words 'illative' or 'illation'. I have not read all his extant MSS, but I very strongly doubt that he would continue using a word he had rejected. See slides 11 and 12 of egintro.pdf for an explanation in terms of the 20th c logics. For the details about Peirce's five MSS that document his development of the 1911 EGs and his rejection R669, see the attached file eg1911x,pdf.JAS> The final sentences [of R669] note the inadequacy of automated reasoning to apply "the two illative permissions," since they require "a living intelligence" (R 669:23-24[21-22], LoF 1:584). No. Modern theorem provers can use Peirce's rules (and other rules derived from them) quite efficiently. For an overview of the issues, see the slides in http://jfsowa.com/talks/ppe.pdf . For more detail, slide2 of ppe.pdf has a link to a 76-page article in the Journal of Applied Logics, JAS> Unlike "Prolegomena" (CP 4.569), none of these manuscripts includes a "4th Permission" expressing "the strange rule" that Peirce deemed to be inconsistent with "the reality of some possibilities" as affirmed by his pragmatism (CP 4.580-581, 1906), such that he was ultimately "sceptical as to the universal validity of" it (RL 477:33[13], 1913). That gets into his modal logic, which he intended to replace with Delta graphs. Any comment about modal issues in 1913 should be evaluated in terms of the Delta graphs, for which we don't have any MSS. JAS> deriving negation from... a scroll with a blackened inner close... is more analytical because it preserves the fundamental asymmetry of reasoning and can thus be easily adapted for intuitionistic/triadic logic without excluded middle, which "is universally true" (R 339:515[344r]). No. In R670, negation is a primitive. The scroll is nothing but a way of drawing a nest of two negations without raising the pen. Since negation is a primitive in R670, it would be absurd to derive negation from a nest of two negations plus a pseudograph. In structure, motivation, and applications, intuitionistic and 3-valued logic are totally different from each other and from any version of Peirce's EGs. Oostra's choice of the scroll as a marker for intuitionistic rules has no similarity to Peirce's use for any version of EGs. There is much more to say about these issues, and I'll write another note about them. John
eg1911x.pdf
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