John, responses inserted below as GF:
Gary f. -----Original Message----- From: John F Sowa [mailto:[email protected]] Sent: 13-Dec-17 16:39 Gary F, I changed the title to focus on the more specific issues. Gary > I dug out my copy of The Meaning of Meaning, and found no triangle > diagram in it; I found the triangle on page 11 of my copy of the 8th edition (1946). I scanned that page as the attached MofMp11.jpg. GF: OK, that may be the one Mary was referring to. It's not an example of what I was referring to, which is very simple: either a triangle labelled "sign" (or "representamen"), "object" and "interpretant" at the vertices, or a 3-spoke diagram with those labels at the ends of the spokes. Whether the diagram you scanned is equivalent to that is a matter of interpretation; it could have inspired such diagrams in later publications, but that's not a question I'm concerned about. JFS: The labeling on the triangle is different from Peirce's, but one could relabel it with words from Peirce's writings. It's also possible to draw a triangular EG with relation labels (rhemes) taken from Peirce's own words: 1. At each corner of the triangle, place the label of a monadic predicate taken from Peirce's writings. Example: Mark, Interpretant, Object. 2. Remove a small line segment from each side of the triangle. In its place, insert the name of a dyadic predicate that relates the two corners. 3. In the center pf the triangle, place the label 'Sign', which would serve as the name of a triadic relation. Then draw a line of identity from that label to each of the three corners. The result of this exercise is an EG. Each corner is a ligature of three lines of identity that represents one of the three entities related by a sign. Each side represents a dyad that is implied by the triad in the middle. Then it's possible to represent an open-ended variety of semiotic relationships by linking two or more triangles at their corners. Each link is a ligature that connects two corners that are assumed to represent the same entity. For examples of such triangles, see Figure 1 (p. 4) and Figure 3 (p. 8) of "The role of logic and ontology in language and reasoning": <http://jfsowa.com/pubs/rolelog.pdf> http://jfsowa.com/pubs/rolelog.pdf In those examples, it would be possible to draw the triangles as EGs. But the added detail would make them less readable. And by the way, this is an example of my claim that diagrams of any kind -- or more generally, icons of any kind -- can be used in "generalized EGs". See the slides <http://jfsowa.com/talks/ppe.pdf> http://jfsowa.com/talks/ppe.pdf GF: This is all quite ingenious, but I don't see its relevance to the simple point I was making. I never said that triangles in general are useless in diagrams; and I haven't questioned your claim that icons of any kind can be used in "generalized EGs." I just don't find that fact informative about what Peirce was trying to accomplish with his EGs. > If someone can point to such a diagram anywhere in Peirce's writings > (either triangular or three-spoked), I will thank them profusely, for > refuting my claim that neither of those diagramming habits started > with Peirce. But the triadic sign relation (as expressed in writing) is as old as Aristotle, and it was developed in detail by the Scholastics. GF: No argument there, but Why the "But"? My claim was about whether Peirce drew a diagram of that relation as described above. For some discussion, see pp. 4 to 8 of rolelog.pdf. Peirce had studied those authors, and he had written extensively about diagrams. > Peirce himself says that 'genuine triadic relations can never be built > of dyadic relations'... and writes: 'You may think that a node > connecting three lines of identity Y is not a triadic idea. But > analysis will show that it is so". GF: Of course; Peirce explains this fully in Lowell 3.4, giving a narrative example to flesh out the diagram, and I pointed this out in my comment on 3.4. But perhaps you didn't read that. To illustrate that principle, see the attached giveEG.jpg. On the left is an EG that asserts the existence of three things, which are linked by a triadic relation named Gives. It says that something described as Sue, gives something described as Child something described as Book. On the right is an EG with three dyadic relations. But it also has a ligature, which Peirce described as a teridentity. That ligature represents something that is linked by three dyadic relations to the things described as Sue, Child, and Book. You could, if you wish, call that something an act of giving. But no matter how you describe it, the teridentity causes it to serve as a triadic relation. Dyads, by themselves, can never create a triad. But a combination of dyads with a teridentity can indeed create a triad. That's why Peirce considered teridentities important. GF: All of this is affirmed in my commentary on Lowell 3.4. But again, it's irrelevant to the simple claim I made about what diagrams of the S-O-I triad Peirce actually drew, or rather didn't draw. It's a pity that Peirce didn't draw more diagrams. He claimed that all his thought was diagrammatic, and he could have made his prose more convincing if he had drawn more diagrams. GF: You may be right about that - but we'll never know! John
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