 Frege famously distinguished two mutually exclusive ontological domains, functions and objects. According to his view, a function is an ‘incomplete’ entity that maps arguments to values, and is denoted by an incomplete expression, whereas an object is a ‘complete’ entity and can be denoted by a singular term. Frege reduced properties and relations to functions and so these entities are not included among the objects. Some authors make use of Frege’s notion of ‘object’ when discussing abstract objects (e.g., Hale 1987). But though Frege’s sense of ‘object’ is important, it is not the only way to use the term. Other philosophers include properties and relations among the abstract objects. And when the background context for discussing objects is type theory, properties and relations of higher type (e.g., properties of properties, and properties of relations) may be all be considered ‘objects’. This latter use of ‘object’ is interchangeable with  ‘entity.’[1]  Throughout this entry, we will follow this last usage and treat the expressions ‘object’ and ‘entity’ as having the same meaning. (For further discussion, see the entry on  objects.)