John, I'm inserting my (brief) responses. (This is probably the kind of conversation that would work better in "real time" than email .)
Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 30-Oct-17 10:21 Gary F, JFS: The issues are far deeper than notation or computer processing. GF: Yes, that's why I was disappointed that your post didn't address the issues I see as deeper! JFS: 1903 was a critical year in which Peirce began his correspondence with Lady Welby. That led him to address fundamental semiotic issues. GF: Yes, and as late as 1909 Peirce was still trying (apparently without success) to get Lady Welby to study Existential Graphs. And the graphs he sent her to study look pretty much the same as the graphs he introduced in the Lowell Lecture 2: nested cuts, areas defined by the cuts, and no shading. JFS: Last week, Ontolog Forum sponsored a telecon, in which I presented slides on "Context in Language and Logic". It addressed complex semiotic issues, and I mentioned Peirce at various points. Following are the slides. Slide 2 also has the URL for the audio: <http://jfsowa.com/ikl/contexts/contexts.pdf> http://jfsowa.com/ikl/contexts/contexts.pdf GF: I'll have a look when I have a chance. > the elementary phenomena of reasoning, that I'd like to understand better. JFS: I agree that 's important, and I also agree that Peirce was seeking the most fundamental methods he could discover. But I also believe that he abandoned the recto/verso system because (a) the questions raised by Lady Welby led him to more significant problems, and (b) those low-level ideas paled in comparison to his goal of representing "a moving picture of the action of the mind in thought." GF: This is irrelevant to the discussion of Lowell 2, and the Lowell Lectures as a whole, because Peirce had not introduced "the recto/verso system" in 1903. His earliest use of these terms in reference to EGs is in 1906, as far as I know, and he introduced it in order to improve the gamma graphs. > 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. JFS: For his EGs of 1903, they are logically equivalent. In fact, that is why his recto/verso description and his "magic blot" have no real meaning: they have no implications on the use of the graphs in perception, learning, reasoning, or action. But the 1911 system can be generalized to modal logic, 3-valued logic, and probability. GF: This too is irrelevant to the study of reasoning that Peirce was attempting in 1903. Also, in the Kehler letter (dated 1911), Peirce himself did not apply EGs to modal logic, 3-valued logic, or probability; he discussed probability and induction in the letter after using EGs to explicate deduction or "necessary reasoning." I can see (vaguely) how the 1909-11 version of EGs serves your purposes, but that doesn't help me to see how EGs serve Peirce's purposes - which by the way he stated in almost exactly the same way in the Kehler letter as he did in the Lowell lectures. We owe you thanks, by the way, for showing us how to find the Kehler letter in Google Books. And by the way, that letter of 1911 was addressed to Mr. Kehler, one of Lady Welby's correspondents, and the main topic was probability and induction. That's also significant. Implications of his 1911 system: 1. The rules come in 3 symmetric pairs, and each pair consists of an insertion rule (i) and an erasure rule (e), each of which is the inverse of the other. This feature supports some important theorems, which are difficult or impossible to prove with other rules of inference. GF: This is equally true of Lowell 2, as we'll see further on. 2. The rules are *notation independent*: with minor adaptations to the syntax, they can be used for reasoning in a very wide range of notations: the algebraic notation for predicate calculus (Peirce, Peano, or Polish notations); Kamp's discourse representation structures; many kinds of diagrams and networks, and even natural languages. GF: This does not explain why Peirce was dissatisfied with algebraic notations (including his own) and invented EGs for the sake of their optimal iconicity (as Stjernfelt calls it). And to cut things shorter, all of the points you've listed below are also irrelevant to that iconicity, and to Peirce's purpose in creating EGs as a replacement - not just another notation - for other systems of formal logic. That purpose, as far as I can see, has nothing to do with proving theorems. 3. They can be adapted to theorem proving with arbitrary icons inside an EG. I demonstrated that with Euclid's diagrams inside the ovals of EGs. But they can also be used with icons of any complexity -- far beyond Euclidean-style diagrams. 4. The psycholinguist Philip Johnson-Laird observed that Peirce's notation and rules are sufficiently simple to make them a promising candidate for a logic that could be supported by the neural mechanisms of the human brain. That is true of his later system, but not the recto/verso system. For an overview of these issues, see my slides on visualization: <http://jfsowa.com/talks/visual.pdf> http://jfsowa.com/talks/visual.pdf To show that Kamp's DRS notation is isomorphic to a subset of EGs, see slides 20 to 27 of visual.pdf. To see the application to English, see slides 28 to 30. (But this is true only for that subset of English or other NLs that can be translated to or from Kamp's DRS notation.) For the option of including icons inside the areas of EGs, see slides 31 to 42 of visual.pdf. For more detail about Euclid, see slides 19 to 39 of <http://www.jfsowa.com/talks/ppe.pdf> http://www.jfsowa.com/talks/ppe.pdf Note: There is considerable overlap between visual.pdf and ppe.pdf, but slides 19 to 39 of ppe.pdf go into more detail about Euclid. For theoretical issues, see slides 43 to 53 of visual.pdf. For the theoretical details, see <http://jfsowa.com/pubs/egtut.pdf> http://jfsowa.com/pubs/egtut.pdf I'm working on another paper that goes into more detail about Peirce's "magic lantern of thought". The 1911 system can support it. But the recto/verso system cannot. John
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