It’s worth mentioning, firstly, that this principle underlies diagonal argumentation in general (cf. Gaifman 2006). Even venerable examples such as Post’s informal argument that there is a recursively enumerable set of positive integers whose complement is not recursively enumerable, rely in essence on CL (Davis 1965: 312). A slight variant of CL is frequently found in the literature on undecidability (cf. Shoenfield 1967: 131). Secondly, the proof of CL does not rely essentially on any axiom