In Ancient Greek, two terms meaning ‘man’ (anēr and anthrōpos) combine with common nouns referring to human occupations, ethnic groups, and ranks in a generic-specific construction (e.g. anēr hiereus ‘priest’ [lit. ‘man priest’]; anēr Spartiatēs ‘Spartan’ [lit. ‘man Spartan’]). This construction is used to refer to male human referents in a clearly identifiable set of discourse contexts, including (i) numeral expressions, (ii) non-assertive contexts, and (iii) presentative sentences in which a character is introduced at the beginning of a more or less lengthy story about him. In all these contexts, the function of the two terms may be thought of as similar to the function of the indefinite article, i.e. the construction always introduces indefinite referents, which may be both specific (anēr hiereus = ‘a [certain] priest’) and non-specific (anēr hiereus = ‘a priest, any priest’). The pairing of a generic and a specific noun resembles the well-known pattern by which generic superordinate terms such as ‘man’, ‘woman’, ‘animal’, ‘vegetable’, ‘bird’, ‘tree’, etc. grammaticalize into noun classifiers, accompanying more specific nouns with a more restricted meaning. Besides classifying discourse referents, the main function of noun classifiers is determination/reference, i.e. they generally play a determinerlike role, marking the discourse status of their referents. Based on the available typological evidence on noun classifiers, in this paper I will argue for an interpretation of the construction anēr/anthrōpos + common noun as an incipient with an identifiable set of discourse situations, in which a free-form lexeme with superordinate semantics is combined with a more specific noun. Classifier constructions are considered to be the first stage in the grammaticalization path leading from generic superordinate nouns to noun classifiers. Similar uses of other superordinate terms such as gynē ‘woman’ and ornis ‘bird’ are also discussed. These uses are suggestive of a rudimentary system of nominal classification in Ancient Greek. In the conclusions, I will provide some speculative thoughts on why this system has not eventually developed into a full system of noun classifiers.