John,
I'll have to confess at this point that I have no interest in learning EGs for the sake of learning a new notation system, or for the sake of knowledge representation in automated systems. This is probably the reason why I found your tutorial, and the Peirce text it is based on, uninformative, as an introduction to EGs. All I managed to learn from them was how to translate back and forth between EGs and three or four logical algebra systems, none of which I have any use for ... i.e. from one set of meaningless symbols to another. I can't speak for others, but what I've been hoping to learn from Lowell 2, aside from the role of EGs in the larger context of the Lowell lectures (including the Syllabus), is how they suit the purpose which Peirce explicitly designed them for, namely "to enable us to separate reasoning into its smallest steps so that each one may be examined by itself . to facilitate the study of reasoning" (and not to facilitate reasoning itself). In other words, I'm trying to get a clearer view not of EGs as a mathematical system but of the process that their transformations are supposed to represent. It's not just the signs but their objects, the elementary phenomena of reasoning, that I'd like to understand better. The three pairs of rules you attached (from NEM) are essentially the same as the three pairs he gives later on in Lowell 2, except for the shading and the absence of lines of identity. But if one doesn't see how the spots, lines and areas of EGs represent propositions, including conditional propositions, what's the point of knowing these rules? That, I take it, is why Peirce doesn't start with them, but works up to them from a starting point which is the universe represented by the sheet of assertion and the individual "subjects" which make up that universe. From there he proceeds to the logical form which conveys "the most immediately useful information," and eventually works his way from that ground up to the code of permissions or "rules." Having said that, I have to say also that some of the statements in your post are even more confusing than Peirce's presentation in Lowell 2. You wrote, "Peirce said that a blank sheet of assertion is a graph. Since it's a graph, you can draw a double negation around it." - Eh? How can you draw anything around the sheet of assertion, which (by Peirce's definition) is unbounded?? Can you show us a replica? Then you wrote, "The blank is Peirce's only axiom, which is always true." GF: No, in Peirce the blank sheet of assertion does not represent a proposition, and it takes at least a proposition to be true or false. What he says is that anything made determinate by being scribed on the sheet of assertion is assumed to be true. And Peirce does not say that the "blank" is an "axiom" in any presentation of EGs that I've seen. Can you cite a reference for that? JFS: "If you draw just one oval around it [any area?], you get a graph that negates the truth. Therefore, it is always false." GF: What Peirce says in Lowell 2 is quite different: If you draw a closed line around a graph on the sheet of assertion, it makes that graph false of the universe represented by the sheet of assertion. JFS: "Peirce called it the pseudograph." GF: No, "pseudograph" in Peirce is another name for the "blot," which is the inner close of a scroll when it is completely filled, so it is the opposite of blank. A mere empty cut, or empty area, is not a pseudograph. In Lowell 2, the pseudograph represents an absurd consequent, which by its presence has the effect of negating the antecedent. It doesn't "negate the truth." If you don't think Lowell 2 is worth a close look, you're entitled to that opinion, but if we're going to refer to it at all, or to the Lowell lectures, then we should do so accurately. I'm trying to do that here, even when I question the clarity and value of Peirce's arguments, because I'm hoping others can clarify them better than I've been able to do so far. Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 29-Oct-17 13:17 To: peirce-l@list.iupui.edu Cc: Dau, Frithjof <frithjof....@sap.com> Subject: Re: [PEIRCE-L] Lowell Lecture 2.6 Jon A and Gary F, Peirce's way of presenting EGs in his Lowell lectures and his publications of 1906 is horrendously complex. The best I could say for it is "interesting". But I would never teach it, use it, or even mention it in an introduction to EGs. I would only present it as a side issue for advanced students. The version I recommend is the 8-page summary that he wrote in a long letter (52 pages) in 1911. The primary topic of that letter is "probability and induction" (NEM v 3, pp 158 to 210). When he got to 3-valued logic and probabilities, the recto/verso idea is untenable. Instead of talking about cuts, seps, and scrolls, he just talks about *areas* on the sheet of assertion. To represent negation, he uses a shaded oval, which he calls an area, not a cut. The shading makes his notation much more readable. An implication (the old scroll) becomes a shaded area that encloses an unshaded area. His rules of inference are much clearer, simpler, and more symmetric: just 3 pairs, each of which has an exact inverse. See the attached NEM3p166.png. (URLs below) Jon > Peirce's introduction of the "blot" at this point is I would continue that sentence with the word 'confusing'. Peirce said that a blank sheet of assertion is a graph. Since it's a graph, you can draw a double negation around it. The blank is Peirce's only axiom, which is always true. If you draw just one oval around it, you get a graph that negates the truth. Therefore, it is always false. Peirce called it the pseudograph. In a two-valued logic, the pseudograph implies everything. But when you get to probabilities or N-valued logic, you can't make that assumption. I believe that's why Peirce dropped his earlier explanations. For the semantics, he adopted endoporeutic, which is a version of Hintikka's Game Theoretical Semantics. Gary > At this point the "experiment" resorts to a kind of magic trick: > Peirce makes the blot disappear (gradually but completely) - yet > falsity remains Yes. But it's just another confusing way of explaining something very simple: The pseudograph is always false. If you draw it in any area, it makes the entire area false. John ___________________________________________________________________ I first came across this version of Peirce's EGs from a copy of a transcription of MS514 by Michel Balat. (By the way, I thank Jon for sending me the copy. I still have his email from 14 Dec 2000.) For my website, I added a commentary with additional explanation and posted it at <http://jfsowa.com/peirce/ms514.htm> http://jfsowa.com/peirce/ms514.htm In 2010, I published a more detailed analysis with further extensions: <http://jfsowa.com/pubs/egtut.pdf> http://jfsowa.com/pubs/egtut.pdf For the published version in NEM (v3 pp 162-169), see <https://books.google.com/books?id=KGhbDAAAQBAJ&pg=PA163&lpg=PA163&dq=%22fal se+that+there+is+a+phoenix%22&source=bl&ots=LKYw9nZEKh&sig=LEaTyTSTGiEuT-P_- 9a6XHEVwWQ&hl=en&sa=X&ved=0ahUKEwi509vA9pPXAhWEOSYKHcDQBZQQ6AEIJjAA#v=onepag e&q=%22false%20that%20there%20is%20a%20phoenix%22&f=false> https://books.google.com/books?id=KGhbDAAAQBAJ&pg=PA163&lpg=PA163&dq=%22fals e+that+there+is+a+phoenix%22&source=bl&ots=LKYw9nZEKh&sig=LEaTyTSTGiEuT-P_-9 a6XHEVwWQ&hl=en&sa=X&ved=0ahUKEwi509vA9pPXAhWEOSYKHcDQBZQQ6AEIJjAA#v=onepage &q=%22false%20that%20there%20is%20a%20phoenix%22&f=false Note: I found that volume of NEM by searching for the quoted phrase "false that there is a phoenix" -- which Peirce used as an example. The attached excerpt is from a screen shot.
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