John, List, All: JFS: 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.
This conveniently establishes a position that is effectively unfalsifiable. The fact that Peirce never explicitly rejects his earlier writings about EGs is deemed irrelevant, because "any logician" can simply "hear" the "new melody" that he supposedly composed in June 1911. Anyone who cannot likewise "feel or hear" it is apparently *not *a logician and should be ignored accordingly. Descriptive words are ultimately inadequate since one must allegedly perceive the patterns directly. As I have pointed out before, in his late 1911 letters to Robert (RL 378) and Risteen (RL 376), Peirce does not criticize the *patterns *of the 1906 EGs; he only criticizes his *description *of them at that time in "Prolegomena," which uses lots and lots of words. He now recognizes that shading is a much better alternative to thin oval lines for distinguishing oddly enclosed areas from evenly enclosed areas, and that it is sufficient in Gamma EGs for shaded/unshaded areas to represent the universes of possibility/actuality rather than having multiple tinctures corresponding to different kinds of each, along with the third modality of intentions. He further simplifies his presentation of EGs for the uninitiated, including these two men along with the National Academy of Sciences (R 670) and Kehler (RL 231), by omitting the derivation of negation from consequence and treating it as a primitive instead, even though this is "philosophically inaccurate" (Bellucci and Pietarinen). We really should be able to agree about all this. We should also then be able agree that for many *practical *purposes, such as teaching classical logic or using it to prove theorems, negation ovals are the "best" choice for a third primitive along with the blank sheet and line of identity; while for many *philosophical *purposes, such as studying logic more deeply including non-classical alternatives, implication scrolls are the "best" choice instead. Why be unreasonably adamant that one is superior to the other for any and every conceivable purpose? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Jan 29, 2021 at 9:38 PM John F. Sowa <s...@bestweb.net> wrote: > 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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