 Montague (1970, 1974) showed that these mismatches do not preclude systematic connections of natural language sentences with the corresponding propositional structures. Abstracting from the technical details, one can specify an algorithm that pairs each natural language sentence that contains one or more quantificational expressions like ‘every doctor’ with one or more Fregean logical forms. This was a significant advance. Together with subsequent developments, Montague’s work showed that Frege’s logic was compatible with the idea that quantificational constructions in natural language have a systematic semantics. Indeed, one can use Frege’s formal apparatus to study such constructions. Montague maintained that the syntax of natural language was, nonetheless, misleading for purposes of (what he took to be) real semantics. On this view, the study of valid inference still suggests that grammar disguises the structure of propositional thought. But in thinking about the relation of logic to grammar, one should not assume a naive conception of the latter.