 It appears that properties can have a double role that no other entities can have: they can occur in propositions and facts both as arguments and as attributed (Russell 1903: §48). For example, in truly saying that this apple is red and that red is a color, we express a proposition wherein red occurs as attributed, and another proposition wherein red occurs as argument. Correspondingly, there are two facts with red in both roles, respectively. This duplicity grounds the common distinction between different orders or types of properties: first-order ones are properties of things that are not themselves predicables; second-order ones are properties of first-order properties; and so on. Even though the formal and ontological issues behind this terminology are controversial, it is widely used and is often connected to the subdivision between first-order and higher-order logics (see, e.g., Thomason 1974; Oliver 1996; Williamson 2013; entry on  type theory).  It originates from Frege’s and Russell’s logical theories, especially Russell’s type theory, wherein distinctions of types and orders are rigidly regimented in order to circumvent the logical paradoxes (see  §6).