God’s household: The earliest churches were churches that met in homes (Romans 16:5; 1 Corinthians 16:19; Colossians 4:15; Philemon 1:2). They followed similar rules of behavior to Greek and Roman households (see study note on 1 Tim 3:4–5). Breaking the rules brought shame to the whole household and its leader. The same applies to the church (compare Ephesians 2:19–22; Hebrews 3:6; 10:21; 1 Peter 4:17).
the pillar and foundation of the truth: This idea may be looking forward to the change from the time of the apostles to the period after their deaths (compare Galatians 2:9; Revelation 3:12). The church must be more active, not just defensive, to uphold the truth in the world (compare 2 Corinthians 10:3–6).