The author of "What Gödel Discovered" has a good point that Gödel numbers are not a convenient representation of a proposition of Russell's Principia Mathemat

The author of "What Gödel Discovered" has a good point that Gödel numbers are not a convenient representation of a proposition of Russell's Principia Mathematica (PM). (Nor are Gödel numbers adequate because they omit the order of a proposition.) Lisp expressions are an improvement. However, a Lisp expression, as used in the article, is also not adequate because it also omits the order of the proposition. See the following for a high-level representation of propositions of PM that includes the crucial orders on proportions: https://papers.ssrn.com/abstract=3459566 https://papers.ssrn.com/abstract=3459566