I think a more precise wording than "recursive" would be objecting to impredicative definitions; those which quantify over (something containing or pertaining t

I think a more precise wording than "recursive" would be objecting to impredicative definitions; those which quantify over (something containing or pertaining to) themselves. For example, it's fine to define an arithmetic function recursively; it's not so fine to define a set based on whether it contains itself.