Rigid designation is a concept in philosophy and linguistics that refers to terms that consistently refer to the same object or entity in all possible worlds. For example, the name H2O rigidly designates the substance water, meaning that wherever water exists, it is referred to as H2O, regardless of the context.
This idea contrasts with non-rigid designators, which can refer to different objects in different situations. For instance, the term "the tallest building" can refer to different buildings depending on the time and place, making it a non-rigid designator. Rigid designation helps clarify discussions about identity and reference in various contexts.