Alonzo Church proposed a theory of sequences of functions and their arguments as surrogates for Russellian singular propositions and singular concepts. Church’s proposed theory accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell-Myhill antinomy is rebutted. Russell-Myhill is not a problem specifically for Alternative (0); it is a refutation of unrestrained concept comprehension. Criteria more lax than (0) are philosophically (...) inadequate. It is shown, however, that Church’s proposed theory is vulnerable under (0) to a version of Russell’s notorious Gray’s Elegy objection. Some amendments to Church’s proposal are proffered, including an amendment, first proposed in the author’s _Frege’s Puzzle_ (1986), that addresses Russell’s objection. Church’s response (personal correspondence) is considered. (shrink)