In his Short Treatise and his Commentary on the Peri hermeneias, al-Fārābī offers two different but related accounts of indefinite terms and the propositions that contain them. In both works he presents a series of different senses that an indefinite term may have, commencing with a sense in which such a term would be equivalent to a privative term, and concluding with a sense in which it would determine the logical complement of the corresponding definite term. I offer an interpretation of this series according to which they reveal the workings of a fine analytical mind and a subtle teacher.