Editing Gödel's incompleteness theorems (section)

=== Translations, during his lifetime, of Gödel's paper into English ===
None of the following agree in all translated words and in typography. The typography is a serious matter, because Gödel expressly wished to emphasize "those metamathematical notions that had been defined in their usual sense before . . ." {{harv|van Heijenoort|1967|p=595}}. Three translations exist. Of the first John Dawson states that: "The Meltzer translation was seriously deficient and received a devastating review in the ''Journal of Symbolic Logic''; "Gödel also complained about Braithwaite's commentary {{harv|Dawson|1997|p=216}}. "Fortunately, the Meltzer translation was soon supplanted by a better one prepared by Elliott Mendelson for Martin Davis's anthology ''The Undecidable'' . . . he found the translation "not quite so good" as he had expected . . . [but because of time constraints he] agreed to its publication" (ibid). (In a footnote Dawson states that "he would regret his compliance, for the published volume was marred throughout by sloppy typography and numerous misprints" (ibid)). Dawson states that "The translation that Gödel favored was that by Jean van Heijenoort" (ibid). For the serious student another version exists as a set of lecture notes recorded by Stephen Kleene and J. B. Rosser "during lectures given by Gödel at to the Institute for Advanced Study during the spring of 1934" (cf commentary by {{harvnb|Davis|1965|p=39}} and beginning on p.&nbsp;41); this version is titled "On Undecidable Propositions of Formal Mathematical Systems". In their order of publication:
* B. Meltzer (translation) and [[R. B. Braithwaite]] (Introduction), 1962. ''On Formally Undecidable Propositions of Principia Mathematica and Related Systems'', Dover Publications, New York (Dover edition 1992), {{ISBN|0-486-66980-7}} (pbk.) This contains a useful translation of Gödel's German abbreviations on pp.&nbsp;33–34. As noted above, typography, translation and commentary is suspect. Unfortunately, this translation was reprinted with all its suspect content by
:* [[Stephen Hawking]] editor, 2005. ''God Created the Integers: The Mathematical Breakthroughs That Changed History'', Running Press, Philadelphia, {{ISBN|0-7624-1922-9}}. Gödel's paper appears starting on p. 1097, with Hawking's commentary starting on p. 1089.
* [[Martin Davis (mathematician)|Martin Davis]] editor, 1965. ''The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable problems and Computable Functions'', Raven Press, New York, no ISBN. Gödel's paper begins on page 5, preceded by one page of commentary.
* [[Jean van Heijenoort]] editor, 1967, 3rd edition 1967. ''From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931'', Harvard University Press, Cambridge Mass., {{ISBN|0-674-32449-8}} (pbk). van Heijenoort did the translation. He states that "Professor Gödel approved the translation, which in many places was accommodated to his wishes." (p.&nbsp;595). Gödel's paper begins on p.&nbsp;595; van Heijenoort's commentary begins on p.&nbsp;592.
* Martin Davis editor, 1965, ibid. "On Undecidable Propositions of Formal Mathematical Systems." A copy with Gödel's corrections of errata and Gödel's added notes begins on page 41, preceded by two pages of Davis's commentary. Until Davis included this in his volume this lecture existed only as mimeographed notes.