When linguists talk mathematical logic. . .

. . .we screw it up, or so says David Lobina in an amusing critique of a paper by Watumull, Hauser, Roberts, and Hornstein.  Both articles were recently published in Frontiers in Psychology.  Since I am chiefly a linguist and only sort of a mathematician, I am always concerned about misunderstanding or misrepresenting the formal literature.  But the gaffes pointed out by Lobina are, I would hope, not the kinds of mistakes I would generally make.

For example, Watumull et al. seem to have gravely misunderstood Gödel's 1931 definition of the primitive recursive functions. While Lobina is too gentlemanly to say so, the misunderstanding that he describes reminds me of stuff I see in undergraduate term papers. Gödel began his definition by specifying a finite list of functions; Watumull et al. apparently took this to be part of the meaning of "recursive," so they attempt to paraphrase it by stating that a recursive function must specify a finite sequence.  Huh?  Perhaps Frontiers in Psychology should have considered using one or two referees with some of the pertinent logical background.

  

While the original article may have flaws, I do stand in favor of the general point that recursion is incredibly important in natural language. Such points would be better supported without laughably wrong things getting published in the same vein.