 Rigidity is most straightforwardly applied to proper names of concrete objects. There is general agreement that ‘Hesperus’ and ‘Biden’ refer rigidly. The debate about which expressions in natural languages are rigid designators is typically set up with a background assumption that proper names are singular terms. This assumption is challenged by predicative accounts of names (think of ‘every Biden’:  Fara 2015).  Whether such alternatives can “explain why names are rigid” (Lee 2020, p. 253; Schoubye 2018), perhaps in recognizing singular reference or denotation for some uses of names tacitly equivalent to demonstratives or definite descriptions (categories discussed below), remains a matter of controversy. 