 The languages to which Tarski’s semantics applied were extensional; Carnap’s semantics extends Tarski’s by assigning compositionally to each singular term, each predicate, and each sentence both an intension and an extension. The intension of an expression explicates what we understand when we understand it, and Carnap’s treatment of this is again “minimalist” in the sense that nothing subjective or psychological is involved; “understanding” is entirely schematic, i.e., determined solely by semantic rules. The extension of an expression at a state-description is determined by applying the semantic rules (or the expression’s intension) to the state-description. In the words of David Lewis (1970: 23): 