Jerry, I was not talking about translating natural languages. I was talking about translating one mathematical or logical notation to another. The question whether two mathematical structures are isomorphic (have precise one-to-one translations to and from each other) is determined by a formal proof. The translations of existential graphs to and from predicate calculus are very simple and easy to verify. See, for example, my commentary in http://jfsowa.com/peirce/ms514.pdf . And by the way, I discussed this commentary with people who are very familiar with Peice's EGs, including Jay Zeman and Don Roberts. and they found no problems with it. Some mathematical structures are so complex that the proof may be difficult to find. But the proofs that all the versions of Peirce's first-order EGs (Alpha and Beta graphs) are isomorphic to every version of FOL in Peirce's algebraic notation and FOL notations by Frege, Schroeder, Peano, Whitehead, Russell... are trivial: you cam just state some simple rules. For a discussion by an independent authority, see "Peirce the Logician" by Hilary Putnam: http://jfsowa.com/peirce/putnam.htm . For the article in question, see http://jfsowa.com/talks/ppe.pdf . Then click on the URL on slide 2, which points to the Journal of Applied Logic from 2018, which contains my 72-page article among others. Fernando Zalamea, a Peirce scholar who is also an excellent mathematician and logic, invited me to present a version of those slide at a workshop in Bogota. Two people who attended were John Woods and Woosuk Park, who are on the editorial board of that journal -- just check the front matter. They invited me to submit the article to that journal. It was reviewed and accepted by very competent mathematicians and logicians. I am certain that the issues in that book you cited are unrelated to what I was doing. If you have any doubt, please write to the author of that book, send the URL of my article, and ask whether I am guilty of any of the errors she was discussing. I am certain that she'll say that the issues she was talking about are unrelated to what I was doing. John
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