Quantifiers are elements of quantity that are used to define the selection (essentially, all or some) of tokens within the set of the abstract target object type (e.g., a noun such as 'rock'). For instance, quantifiers allow the referent of a certain type of object (e.g., table, turtle, rock) to point to all tokens of that type (e.g., "all rocks") or some tokens of that type (e.g., "some rocks").
Kinds of Quantifiers
- Universal Quantifier (∀): given some object x, ∀x can be interpreted as: "for all x...", "all x...", "any x..."
- Existential Quantifier (∃x), given some object x, ∃x can be interpreted as: "for some x...", "some x...", "there exists (at least one) x..."
Partee, B., A. ter Meulen, and R. E. Wall. (1990) Mathematical Methods in Linguistics. Springar.