You noticed the thing about my article I'm the least comfortable with: the idea of a "Barendregt numeral."
The number encoding scheme I use in the article is from To Mock a Mockingbird. Near the end of the book, a character says: "Oh, there are many other [number encodings] that would work... but this particular one is technically convenient. I have adopted this idea from the logician Henk Barendregt."
But I couldn't find any other source that claims Barendregt invented it. Thanks for finding another source, I'll take a look at it and update the article!
For me, it was the thing about the article I found most interesting!
I'm not sure Barendregt is claiming to have invented it, and in your quote, Smullyan doesn't either. I've only skimmed the paper, but the paper is framed as an introduction to the λ-calculus and SKI-combinators, not as a presentation of novel results in the field. Its section "0. Preliminaries" (♥) does claim to present a novel representation of recursive functions, but doesn't bother to mention the numerals. In a journal paper published today, the absence of an endnote there would amount to a claim that the representation of numerals was novel, but I don't think that was necessarily true in that less-bibliometrics-plagued time. Though Barendregt does cite 18 sources in his endnotes, so maybe so.
The number encoding scheme I use in the article is from To Mock a Mockingbird. Near the end of the book, a character says: "Oh, there are many other [number encodings] that would work... but this particular one is technically convenient. I have adopted this idea from the logician Henk Barendregt."
But I couldn't find any other source that claims Barendregt invented it. Thanks for finding another source, I'll take a look at it and update the article!