Singular concepts

Abstract

Alonzo Church proposed a powerful and elegant 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 here rebutted. Russell–Myhill is not a problem specifically for Alternative (0); it is a refutation of unrestrained concept comprehension. Unrestricted comprehension is also inconsistent with facts about sets of properties. Criteria more lax than (0) are philosophically inadequate. In particular, the rival conception of propositions as classes of possible worlds is subject to a fatal philosophical collapse. It follows on that conception, given that each of us is fallible, that everyone believes everything. 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.