 Another consideration Church offered in favor of second order logic was the more pragmatic one that a greater understanding of mathematical theories could be obtained by comparing their formulations in first and second order languages (1956a: chapter V). (Discussion of this topic is beyond the scope of this entry; but see Myhill (1953), Shapiro (1991, 2001), Button and Walsh (2018) and the citations therein. See also the entries on  model theory,  second and higher order logic, and  Skolem’s Paradox.)