John, All: JFS: My guess: He reviewed his earlier writings on EGs, especially the ones from 1903 and 1906. The content of R670 and L231 shows what he rejected.
No, it shows what he chose to *emphasize *in June 1911. He did not explicitly *reject *anything that he had written previously about EGs until December 1911, and even then he *endorsed *"the better exposition of 1903" for distinguishing the *Alpha*, *Beta*, and *Gamma* parts. JFS: The writings prior to June 1911 have some useful insights mixed with some obsolete material. It's necessary to evaluate them in terms of L231. This straightforwardly begs the question, since at issue is whether RL 231 is Peirce's *definitive *treatment of EGs. It is also necessary to evaluate RL 231 in terms of his earlier writings about EGs. JFS: All those quotations are prior to June 1911. They're irrelevant and obsolete. The first sentence states a fact. The second sentence states an opinion, and I obviously disagree. JAS: In R 669 (May 1911), he notes--just three weeks before composing RL 231--that necessary reasoning is possible without the concept of falsity, while negation is shorthand for implying the absurdity that "every proposition is true." JFS: No, for several reasons: (1) That is not an exact quotation, since Peirce knew that affirmation and negation are fundamental to every version of logic from Aristotle onward. Okay, here is the exact quotation. CSP: It was forced upon the logician’s attention that a certain development of reasoning was possible before, or as if before, the concept of *falsity *had ever been framed, or any recognition of such a thing as a false assertion had ever taken place. Probably every human being passes through such a grade of intellectual life, which may be called the state of paradisaical logic, when reasoning takes place but when the idea of falsity, whether in assertion or in inference, has never been recognized. But it will soon be recognized that not every assertion is true; and that once recognized, as soon as one notices that if a certain thing were true, every assertion would be true, one at once rejects the antecedent that lead to that absurd consequence. (R 669:18-19[16-17], May 31, 1911) I stand by my summary accordingly. JFS: (2) Peirce had forgotten his 1884 point that all reasoning can be done with just insertions and deletions (W 5:107). I find this highly implausible, unless we are likewise going to entertain the possibility that he also somehow had forgotten his c. 1906 "confession" that omitting the blackened inner close from a cut (or shading) for negation was an "error" (CP 4.564n). It seems much more likely that he deliberately *decided *to simplify his explanation of *Beta *EGs in R 670 and then RL 231, accepting the trade-off of making it less analytical by omitting the step of deriving negation from consequence. JFS: Although Peirce said that the version of 1903 was better than the version of 1906, it still has obsolete passages, such as the comments about the scroll. Again, whether those passages are "obsolete" is a matter of opinion, unless the missing pages from Peirce's December 1911 letter to Risteen turn up someday and shed further light on his views about EGs at that later date. JFS: With that explanation and further confirmation in L231, every previous comment about scrolls is obsolete and irrelevant. Repeating the same assertion over and over is not a persuasive argument. Besides, here is a relevant remark by Peirce from his entry for "negation" in Baldwin's *Dictionary of Philosophy and Psychology*. CSP: Out of the conceptions of non-relative deductive logic, such as consequence, coexistence or composition, aggregation, incompossibility, negation, etc., it is only necessary to select two, and almost any two at that, to have the material needed for defining the others. What ones are to be selected is a question the decision of which transcends the function of this branch of logic. (CP 2.379, 1902) For "non-relative deductive logic," which corresponds to *Alpha *EGs, we can choose just about any two of consequence (scroll), coexistence (blank), aggregation (multiple nested cuts), incompossibility (multiple graphs inside a cut), and negation (cut) as the primitives, then derive the other two. The same is true of first-order predicate logic, which corresponds to *Beta *EGs, with identity (line) as the third primitive. It makes little (if any) difference *within *those classical systems which two we choose, so we are free to prioritize either making EGs *simpler *as Peirce did in 1911 or making them *more analytical* as he did in most of his earlier treatments. I prefer the latter because it facilitates taking a further step toward *Gamma *EGs with tinctures as in R 490 (1906), or toward *Intuitionistic *EGs with no excluded middle as Arnold Oostra has outlined. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Aug 21, 2020 at 11:47 PM John F. Sowa <s...@bestweb.net> wrote: > Jon AS, List > > This thread began with my note of August 2nd, which I include below in > the file 2aug20.txt. All the points in that note are based on the > citations included in it. But I changed the subject line of this note to > emphasize Peirce's fundamental insight of 2 June 1911 shortly after 7:40 > pm. > > That was when Peirce finished writing two of his three "Illative > Permissions" in R669. He then wrote a short paragraph with a few lines at > the top of a new page. And he stopped. > > He did not write the third permission (about double negations), he left > most of the sheet blank, and he never resumed R669. Three questions: Why > did he stop when he had enough paper to write the third permission? Why > did he begin a completely new version of EGs in R670 with different > notation and terminology? And what did he do in the time between June 2 > and June 7? > > My guess: He reviewed his earlier writings on EGs, especially the ones > from 1903 and 1906. The content of R670 and L231 shows what he rejected. > His comments in L378 and L376 show that he considered the presentation in > 1906 "as bad as it could be". But his comments in R670 show that he > considered some combination of shading with tinctured areas as possible. > That would be an option for Delta graphs, as I mentioned in an earlier > note. > > JAS> understanding the entire system of EGs requires familiarity with all > his different writings about them. > > Familiarity does not imply agreement. The writings prior to June 1911 > have some useful insights mixed with some obsolete material. It's > necessary to evaluate them in terms of L231. > > JFS> There is no need to derive negation from anything else. > > JAS> Peirce repeatedly says otherwise, as I have repeatedly demonstrated.. > > All those quotations are prior to June 1911. They're irrelevant and > obsolete. > > JAS> In R 669 (May 1911), he notes--just three weeks before composing RL > 231--that necessary reasoning is possible without the concept of falsity > > No, for several reasons: (1) That is not an exact quotation, since Peirce > knew that affirmation and negation are fundamental to every version of > logic from Aristotle onward. (2) Peirce had forgotten his 1884 point that > all reasoning can be done with just insertions and deletions (W 5:107). > And Peirce's discovery of 2 June 1911 makes the earlier quotations > irrelevant. > > JAS> This (R 466:18-19, 1903) comes from one of Peirce's notebooks for the > Lowell Lectures, which in RL 376 (December 1911) he calls "the better > exposition" of EGs than "Prolegomena to an Apology for Pragmaticism" > (1906). The three primitives are thus consequence (scroll), coexistence > (blank), and identity (line) > > Although Peirce said that the version of 1903 was better than the version > of 1906, it still has obsolete passages, such as the comments about the > scroll. > > In R670, he writes "There are but three peculiar signs that the Syntax of > Existential Graphs absolutely requires." The first is the line of > identity. The, the second is the spot, which may be a medad or it may have > one or more pegs. "The third is one that shall deny a Graph instance, or > scribed assertion." With that explanation and further confirmation in > L231, every previous comment about scrolls is obsolete and irrelevant. > > At this point, I rest my case. I stand by the attached 2aug20.txt and the > additional comments above. Any relevant evidence to the contrary would > have to come from documents later than June 1911. > > John > >
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