John, All: For the record, I checked with Gary Richmond before sending this response, not only as the List moderator but also as the primary addressee of the post to which I am replying. Of course, he may still have something to say about it himself.
JFS: The primary claim of this thread is that Peirce's 1911 version of EGs, which he sent in the letter L231 to Mr. Kehler (a member of LadyWelby's significs group) is the one which he intended as a definitive statement of EGs. I have already acknowledged that this is a plausible interpretative hypothesis, but I have also pointed out that the text of the letter itself neither states nor implies any such purpose on Peirce's part, and I have urged that we should always be cautious about treating *anything *that he wrote as "definitive." As he warned, "The last philosophical obstacle to the advance of knowledge which I intend to mention is the holding that this or that law or truth has found its last and perfect formulation" (CP 1.140, EP 2:49, 1898). Besides, immediately before giving the "tutorial" on EGs in RL 231, he presents an equation using Boole's algebra that affirms "the principle that every assertion is either true or false" (NEM 3:161-162). In this context, having already affirmed excluded middle, he evidently chooses not to go into the details of how "if A then B" is not *strictly *equivalent to "not (A and not-B)." In fact, he does not express *any *conditional propositions in the "tutorial" itself (NEM 3:162-169), sticking entirely with categorical propositions until *using *EGs to make two specific points about the logic of probability many handwritten pages later (NEM 3:178&185). JFS: The issues copied after my signature below were discussed and shown to be irrelevant. On the contrary, no *substantive *rebuttal was offered; rather, those issues were just summarily dismissed. JFS: The phrase "as analytical as possible" without any examples is hopelessly vague. I have carefully and thoroughly explained how I am interpreting and applying that phrase in this specific context. It corresponds directly to Peirce's statement in the RL 231 "tutorial" that "the real purpose [of the syntax of EGs] is to dissect the reasoning into the greatest possible number of distinct steps and so to force attention to every requisite of the reasoning" (NEM 3:168). In my view, this pertains not only to the permissions for *transforming *EGs, but also to how EGs *represent *propositions in the first place, including the derivation of negation from the logically simpler (i.e., primitive) relation of consequence. JFS: Peirce's 1906 version of EGs is the one he rejected in the strongest possible terms in the months following L231: This is false, or at least misleading. As the provided quotes from RL 378 and RL 376 (also cataloged as R 500) clearly indicate, what Peirce rejects in 1911 is not any previous *version* of EGs, but rather the lengthy and complicated *explanation *of them that he presented in "Prolegomena to an Apology for Pragmaticism" (CP 4:530-572, 1906). Moreover, he also states in RL 376, "In this I made an attempt to make the syntax cover Modals; but it has not satisfied me. ... The better exposition of 1903 divided the system into three parts, distinguished as the Alpha, the Beta, and the Gamma, parts; a division I shall here adhere to, although I shall now have to add a *Delta *part in order to deal with modals" (R 500:2-3). What further insights might we glean from these remarks? First, Peirce does not hold up what he says about the system of EGs in R 670, RL 231, or even RL 376 itself--in which, by the way, he proposes to "describe its latest state of development for the first time" (R 500:1)--as a "better exposition" than what he provides in "Prolegomena." Instead, he refers all the way back to the Lowell Lectures and accompanying Syllabus of 1903, where he initially uses scrolls rather than nested cuts and explicitly derives negation from a scroll with a filled-up inner close ( http://gnusystems.ca/Lowell2.htm and CP 4:399-402). Hence he clearly has not *abandoned *that approach in 1911; after all, he *includes *it in R 669, written just days and weeks before R 670 and RL 231. Second, the unsatisfactory attempt to "cover Modals" in "Prolegomena" calls for twelve different tinctures--four each for the three modes of "Possibility," "Intention," and "Actuality" (CP 4.554), because "four tinctures are necessary to break the continuity between any two parts of any ordinary surface" (R 295:44, 1906). However, recall Peirce's "discovery" the very same year that oddly enclosed areas represent a universe of possibility, not just the denial of actuality, prompted by his introduction of "blue tint." As he reveals in a paragraph that I omitted when excerpting R 490 previously, this changed his conception of the Gamma part. CSP: In my former exposition of Existential Graphs, I said that there must be a department of the System which I called the Gamma part into which I was as yet able to gain mere glimpses, sufficient only to show me its reality, and to rouse my intense curiosity, without giving me any real insight into it. The conception of the System which I have just set forth is a very recent discovery. I have not had time as yet to trace out all its consequences. But it is already plain that, in at least three places, it lifts the veil from the Gamma part of the system. (CP 4.576) I have previously commented at length on the third such clarification, which is that not every consequence whose antecedent does not happen to be realized is true. The second is "that a *reference *would be represented by a graph which should cross a cut" (CP 4.579). The first and most pertinent here is that "the cut may be imagined to extend down to one or another depth into the paper, so that the overturning of the piece cut out may expose one stratum or another, these being distinguished by their tints; the different tints representing different kinds of possibility" (CP 4.578). Peirce then adds, "This improvement gives substantially, as far as I can see, nearly the whole of that Gamma part which I have been endeavoring to discern" (ibid). In other words, he seems to decide in 1906 that the Gamma part simply *is *the Beta part with the addition of "blue tint" (later shading) in oddly enclosed areas to represent "a kind of possibility." However, his reach exceeds his grasp in "Prolegomena" as he unsuccessfully tries to accommodate *different *kinds of possibility with different tinctures, which he calls "nonsensical" in a November 1913 letter to F. A. Woods (RL 477); and he misidentifies the third mode as "Intention" rather than necessity, which is really "of the same mode [as possibility] since ... Negation being outside the category of modality cannot produce a variation in Modality" (CP 5.459, EP 2:358, 1905). Hence there now would need to be "a *Delta *part in order to deal with modals," but Peirce apparently never develops it. JFS: I consider this summary to be the end of the thread. Every objection to the original claim has been analyzed and shown to be irrelevant. With the possible exception of the moderator, no one has the unilateral authority to cut off a List discussion; and again, merely brushing off objections is not *showing *them to be irrelevant. In any case, this post obviously demonstrates that there *was *more to say of *considerable *relevance. "Do not block the way of inquiry" (CP 1.135, EP 2:48, 1898). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Aug 7, 2020 at 5:59 PM John F. Sowa <s...@bestweb.net> wrote: > Gary R, > > The primary claim of this thread is that Peirce's 1911 version of EGs, > which he sent in the letter L231 to Mr. Kehler (a member of LadyWelby's > significs group) is the one which he intended as a definitive statement of > EGs. For Peirce's text and some commentary, see > http://jfsowa.com/peirce/eg1911.pdf > > The issues copied after my signature below were discussed and shown to be > irrelevant. Since you weren't involved in the earlier stages of the > discussion, I'll summarize them briefly: > > 1. Nearly all words, when taken out of context, have a wide range of > senses. The primary way to pin down their meaning in any particular > application is to cite specific examples. > > 2. The phrase "as analytical as possible" without any examples is > hopelessly vague. Taking it from one context in 1902 and applying it to > another context in 1906 is dubious at best. > > 3. Peirce's 1906 version of EGs is the one he rejected in the strongest > possible terms in the months following L231: > > CSP L378, Sept. 1911: "I use a diagrammatic syntax, which I described > very badly and at an intolerable length in the Monist of October 1906." > > CSP L376, Dec. 1911: "in the Monist of Oct. 1906... The description was, > on the whole, as bad as it well could be." > > To take a vague term from 1902 and apply it to a version of 1906, which > Peirce rejected, is not a convincing argument. It does not deserve a QED. > > I consider this summary to be the end of the thread. Every objection to > the original claim has been analyzed and shown to be irrelevant. > > John > > ______________________________ > JAS: [Peirce's] primary objective in developing both his logical algebras > and EGs is *not *"making a calculus which would turn out conclusions by a > regular routine." It is "simply and solely the investigation of the > theory of logic," which requires "that the system devised for the > investigation of logic should be as analytical as possible" (CP 4.373, > 1902). > JAS: EGs with shading, rather than cuts, satisfy this criterion as long as > the *derivation *of negation from the primitive of consequence, > reflecting the fundamental asymmetry of all semeiosis, is kept firmly in > mind. Accordingly, I agree with Peirce's "confession" that it is an > "error" to assume that "because the blackened Inner Close can be made > indefinitely small, therefore it can be struck out entirely like an > infinitesimal" (CP 4.564n, c. 1906). Instead, *when a shaded area is > intended to represent negation--not the antecedent of a consequence--it > should have a darkened circle within it, "however small, to represent > iconically, the blackened Inner Close"* (ibid).[emphasis added by GR] > QED (more or less), >
_ _ _ _ _ _ _ _ _ _ ► 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.
