horizō

The verb is formed on ὅρος, the boundary marker, and in classical and Hellenistic usage it covers marking off territory, defining a term, and settling a question; LSJ records the concrete territorial use alongside the logical one, plus a middle sense of resolving on something for oneself. None of the eight New Testament occurrences is territorial. BDAG sorts them into determining or fixing a thing (Luke 22:22; Acts 2:23; 17:26; Hebrews 4:7), appointing or designating a person (Acts 10:42; 17:31; Romans 1:4), and, with an infinitive, resolving on a course of action (Acts 11:29). K. L. Schmidt's TDNT article notes how heavily the usage clusters in Luke and Acts, where it belongs to the vocabulary of God's settled plan and stands beside βουλή and πρόγνωσις in Acts 2:23; Barrett makes the same observation for the Acts speeches, where ὡρισμένος functions almost as a technical marker of what God has fixed. The lexical value of the verb is not in doubt. The exegetical crux is Romans 1:4: ὁρισθέντος υἱοῦ θεοῦ ἐν δυνάμει has been taken either as an appointment or installation of the Son into a new phase of sonship at the resurrection (so Dunn and Jewett, with BDAG classing the verse under the appointment sense) or as a public declaration of what was already true (Cranfield, defending the older English rendering and concerned that appointment language implies adoptionism). Fitzmyer observes that the formula Paul is quoting does not by itself settle the christological question, and that ἐν δυνάμει may qualify the title rather than the verb.