What does Luke 1:4 mean?

The certainty which Luke wants to inspire is not a matter of wishful thinking, blind faith, or preference. His entire purpose for writing this gospel is to collect truth, in the form of eyewitness accounts, facts, and evidence (Luke 1:1–3). Luke was present for many crucial events in the early church, as a co-worker with the apostle Paul (Acts 1:1–3; 16:10). In his travels, he likely met many key figures in Jesus' earthly ministry. For this reason, Luke feels confident that his work can be of use.

Biblical faith has always placed great emphasis on truth and reason (Acts 17:11; 1 John 4:1; 2 Corinthians 13:5; Colossians 2:8). It is because of known events, and established truths, that Christians should be confident in God's promises (Hebrews 12:1; 2 Peter 1:16). We don't know who Theophilus is, exactly. What do know Luke seeks to strengthen his faith in the truths being taught about Jesus Christ. That greatly benefits modern readers, as well.