Jon AS, List, The *opinion* that the EG version of June 1911 is Peirce's best is Peirce's own, as he stated in December, after six months of further consideration. The fact that he stated it in a lengthy letter to a member of Lady Welby's significs group is further evidence of its importance. That opinion is further supported by the development of logic in the following century. Please read beyond slide 12 of http://jfsowa.com/talks/egintro.pdf . See also http://jfsowa.com/talks/ppe.pdf . Slide 2 of ppe.pdf has a link to a 76-page article published in the Journal of Applied Logics that goes into all the details. One of the most important features of the 1911 version is its ability to serve as a foundation for Gerhard Gentzen's two systems of natural deduction and clause form (published in 1934). Those two system have had immense influence on modern proof procedures -- including the development of modern methods of computational theorem proving. But in 1988, Larry Wos, one of the pioneers in theorem proving methods, published an unsolved problem about relating Gentzen's two systems. This problem is important for automatically relating two different proof procedures. In 2011, I published the solution in Semiotica. For a quick outline, see egintro.pdf or ppe.pdf. For the details, see the article in the J. of Applied Logics. That proof is clean and clear in terms of the 1911 EGs. It's possible in terms of the earlier versions, but it is more complex and harder to discover. Another important point: The 1911 EGs can be generalized beyond two dimensions for "stereoscopic moving images". It's not an accident that Peirce mentioned them in L231, but he had not yet decided how to proceed with the details. ppe.pdf (and the JAL article) present a generalization. Whether that is what Peirce was thinking is not clear, but it shows that the 1911 EGs are sufficient to support something along the lines that Peirce was contemplating. As for the point that negation must be inferred, please reread slides 11 and 12 of egintro.pdf. Note that observing if-then is impossible (for a lengthy discussion, see Hume and the lengthy debates that followed). But the inference required for negation is quite simple: If you expect something and don't observe it, you can use the word 'not'. Children learn to use the word 'not' sometime after their second birthday -- around the same time that they learn to use the words 'I' and 'you' correctly. But they don't learn to use 'if-then' and 'or' until much later. And the idea that children (or even adults) would learn 'not' from the derivation that Peirce presented in 1906 or the one in R669 is absurd. There is much more to say about all these issues, but please read at least to the end of egintro.pdf. It also has many references for further study. John
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