Abstract Even though languages are capable of expressing very complex generalized quantifiers such as all but seven and an even number of, the range of possible meanings for monomorphemic determiners seems to be limited to every, no, some, and numerals. In this talk, I argue that this is not an accident. Borrowing insights from the semantic automata approach, I identify generalized quantifiers with string languages and show that all the monomorphemic quantifiers fall into the class of tier-based strictly local (TSL) languages. TSL has independently been argued to play a central role in phonology, morphology, and syntax. This suggests that the semantic limitations of monomorphemic quantifiers are connected to general computational properties of language.