Any theory of person features must account for known typological patterns (including the inventory of persons and generalizations about syncretism), but also provide a handle on the person morphology of individual languages. In this paper, we develop an analysis of person based on the following core assumptions. (i) Person features represent functions that operate on an initial set of possible discourse referents, or on the output of other person functions. Which combinations of person features are well-formed follows from the properties of the functions they represent (compare Harbour 2011b, 2011c). (ii) There are two such person features. Their semantic specification implies that one is shared by first and second person, while the other is shared by second and third person (see Kerstens 1993; Halle 1997; Bennis and MacLean 2006; Aalberse and Don 2011). (iii) Rules that operate on features (including rules of impoverishment and spell-out rules) are sensitive to the order in which the functions represented by person features apply. The main results of the proposed theory are (a) an explanation of the typological inventory of persons (first, second and third in the singular; first inclusive, first exclusive, second and third in the plural); (b) an explanation of the typological observation that syncretism between first and third person is much rarer than syncretism between either first and second, or second and third person (see Baerman et al. 2005; Baerman and Brown 2011); (c) a descriptively adequate analysis of person agreement in Dutch where two person endings arrange themselves in such a way that there is a 2-3 syncretism in the regular case, a 1-2 syncretism under subject-verb inversion, and an optional 1-3 syncretism with a particular lexical class of verbs (modals).