Gary R, My remarks were ad rem, not ad hominem. Mathematics is like music. A mathematician or a musician thinks only in terms of the patterns, the operations on those patterns, and their relationship to whatever notation is used to represent them. The words used to describe those patterns are useful for communication among teachers, students, and critics. But those words are absent from the minds of the artists (musical or mathematical) who are imagining and creating novel patterns. Peirce was a great mathematical/logical artist. In June 1911, he had a new insight into the melodies of logic. Any logician can "hear" an exciting new melody in R670 and L231 that was not present in R669 or the Monist article of 1906. Peirce didn't have to write a "note to self" about the change. He just did it. And any logician can "hear" it. But I realize that many people can't feel or hear the difference. I plan to post the 1906 version and the 1911 version on my web site, and I'll point out exactly where the differences occur and their implications. I'll post that in the next two days. And I won't refer to any other person's comments or opinions on the subject. Meanwhile, I recommend the following slides and their quotations of mathematicians, logicians, and linguists about their subject: http://jfsowa.com/talks/ppe.pdf . The application of Peirce's EGs to Euclidean diagrams is easy with the 1911 EGs, but not with the earlier versions. That application is one of the strongest arguments in support of Peirce's claim that EGs represent "the action of the mind in thought." John
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