How does the Greek verb in Acts 13:48 either support or refute predestination?
Acts 13:48 is indeed a strong verse on God's sovereign choice of those who would be saved. The verb TETAGMENOI does not occur in Acts 20:13, but the aorist form of it does occur in Acts 29:23. There, the middle voice is indeed used and is translated like an active verb. However, the aorist has a distinct middle form that is different from the passive form. The perfect tense, found in Acts 13:48, does not. Context, lexeme, and usage are key. In 1 Cor 16:15, an active voice verb is used. So, neither of these texts offers a real parallel to Acts 13:48. The problem with taking the verb in Acts 13:48 as a middle is that it would have to be a direct middle (the idea would be 'they appointed themselves'), which is nonsense in this context and is extremely rare of a usage overall. I know of no linguistic ground for overturning the traditional translation here.