Sufficiency, Necessity, and Authority. Colossians 1:18. June 19, 2011. www.deanbible.org Jesus is sufficient and necessary. He provides all we need, and He alone can provide all we need. The first line of evidence is that He is the Creator with all that implies. The second line of evidence is that He is the head of the church, the authority over the church. Authority is a crucial concept involved in headship. What does it mean that Jesus is head over the church? What does it mean that Christ is the head of man, and man the head of woman? These are just some of the questions answered in this lesson.