[jesuslop]

An ad fontes breadcrumb elucidation I think that passes through Gödel 1934, in §9 "General recursive functions". "...this leads to the question what one would mean by 'every recursive function'. One may attempt to define this notion as follows...", and remites to footnote 34: "This was suggested by Herbrand in private cummunication". Finally the note points to the article post scriptum where Gödel appraises (later) Turing work as settling what would become known Church's thesis, that Turing machines exhaust all 'mechanical procedures'. "In consequence of later advances, in particular of the fact that, due to A. M. Turing's work, a precise and unquestionably adequate definition of the general concept of formal system [by defining 'mechanical procedure'] can now be given..."