John, List, All: JFS: Again, you have not cited any statements by Peirce after June 1911. Therefore, nothing in your note contradicts the evidence that the 1911 version of EGs is Peirce's best and last available version.
That it is his *last *version is a fact, as far as we know. That it is his *best *version is an opinion. By what criteria? Simplest and most iconic? Sure. Most analytical? Definitely not. JFS: Furthermore, Peirce's letters of Sept. and Dec. 1911 explicitly reject the version of 1906 on which R669 is based. This is false, and we have been over it before. What Peirce rejects in those two letters, as well as in another one that he wrote two years later, is not "the version of 1906" but his lengthy and convoluted *description *of EGs in "Prolegomena to an Apology for Pragmaticism." That is perfectly consistent with my hypothesis that in June 1911, Peirce merely decided to simplify his *presentation *of EGs for the uninitiated--the National Academy of Sciences (R 670), J. H. Kehler (RL 231), A. Robert (RL 378), A. D. Risteen (RL 376), and F. A. Woods (RL 477). Moreover, he tells Risteen that the badness of the "Prolegomena" description was "in great contrast to the one Dr. Carus rejected" way back in 1896-7, and that the 1903 Lowell Lectures with accompanying Syllabus was "the better exposition." He then tells Woods that the 1896-7 attempt was "the most lucid and interesting paper I have ever written." In other words, Peirce not only never *rejects *those earlier explanations, he explicitly *reaffirms *them. What he has come to recognize, as he mentions to Risteen, is that shading is vastly superior to cuts for distinguishing evenly and oddly enclosed areas--something that I have repeatedly acknowledged myself, and even implemented in my recently posted Synechistic EGs ( https://list.iupui.edu/sympa/arc/peirce-l/2021-01/msg00011.html). However, it would be more accurate to say that he *rediscovers *this utility, because he had already noticed it before. "The *blue *tint, however, of the area within the cut is a great aid to the understanding" (R 490:13, 1906). "Some slight shading with a blue pencil of the oddly enclosed areas will conduce to clearness" (CP 4.617, 1908). JFS: The most efficient theorem proving methods today do *not* depend on a sign for if-then. So what? Peirce was consistently adamant that the proper purpose of the *philosophical* science of logic is not efficiency in proving theorems, but thoroughness in analyzing the process of inference into its most basic constituents. Treating negation as a primitive makes EGs more useful to a mathematician as a calculus (minimum steps) but detracts from the primary reason why Peirce the logician created them in the first place (maximum steps). I have said it before, I will say it again--we have different purposes, so we reach different conclusions. JFS: By demoting the scroll to *nothing but* a nest of two negations, Peirce's methods are a major simplification and clarification of Gentzen's system. One more time--Peirce never "demotes" the scroll; on the contrary, he *explicitly denies* that a consequence can be reduced to two negations. CSP: Indeed, so far is the concept of *Sequence* from being a composite of two Negations, that, on the contrary, the concept of the Negation of any state of things, X, is, precisely, a composite of which one element is the concept of Sequence. Namely, it is the concept of a sequence from X of the essence of falsity. (R 300:50[51], 1908) Again, as your own slide 11 rightly affirms, "Even negation ~ must be inferred." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sat, Jan 23, 2021 at 4:42 PM John F. Sowa <s...@bestweb.net> wrote: > Jon, List, > > Again, you have not cited any statements by Peirce after June 1911. > Therefore, nothing in your note contradicts the evidence that the 1911 > version of EGs is Peirce's best and last available version. > > Furthermore, Peirce's letters of Sept. and Dec. 1911 explicitly reject the > version of 1906 on which R669 is based. That does not mean that every > statement he wrote about EGs prior to 1911 is obsolete, but it means that > everything he wrote prior to June 1911 must be evaluated in terms of his > 1911 version. > > Finally, an enormous amount of research on, with, and about logic has been > done during the century following Peirce. The claim that a "sign of > illation" is important or even useful for inference is false. The most > efficient theorem proving methods today do *not* depend on a sign for > if-then. > > I suggested slides 11 and 12 of http://jfsowa.com/talks/egintro.pdf in my > previous note. For further evidence why a sign for if-then can be an > *impediment* to inference, please read the slides about Gentzen's method of > natural deduction and Peirce's *improvement* on it. For more detail, see > the various references, especially http://jfsowa.com/talks/ppe.pdf . > > By demoting the scroll to *nothing but* a nest of two negations, Peirce's > methods are a major simplification and clarification of Gentzen's system. > Also note that Frege's proof procedure, which is the basis for the > Principia by Whitehead and Russell, puts the sign for if-then at the > center. But that results in a horribly complex proof procedure: 43 steps > to prove a theorem that takes 7 steps by Peirce's rules (which depend only > on negations). > > There is much more to say about all these issues. But the main point is > very clear: In June 1911, Peirce realized that all inferences depend on > inserting or erasing graphs or parts of a graph in positive or negative > areas. That's is the foundation for defining an open-ended variety of > derived rules of inference -- modus ponens is just one of many. > Aristotle's syllogisms are others. So are Gentzen's methods and many > versions used in computer systems. > > John >
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
