What Is “Presuppositional” Apologetics? by David Wright, AiG–U.S.
Presuppositions are simply beliefs that everyone has that affect how they think, view the world, interpret evidence, and read the Bible. Apologetics is a reasoned defense of beliefs. So presuppositional apologetics is a reasoned defense of Christian beliefs based on recognizing our presuppositions.
For instance, my presupposition is that God exists and He has given us His Word (the Bible) that is absolute truth. So I use the Bible as the basis for how to think, interpret evidence, explain the world around me, and read the Bible. An atheist’s presupposition will most likely be that there is no God and that truth is relative. An atheist believes that man decides truth, and so he thinks, interprets evidence, and views the world and Bible accordingly.
If we start off believing the Bible is the Word of God (2 Timothy 3:16; Psalm 18:30; Proverbs 30:5), then we use it as our axiom. An axiom (often used in logic) is a proposition that is not susceptible to proof or disproof; its truth is assumed. The Bible takes this stance, assuming God’s existence to be true and not something to be proven (Genesis 1:1; Exodus 3:14; Revelation 1:8).
The battle is not over evidence but over philosophical starting points: presuppositions. As Christians, we should never put away our axiom—the Bible—when discussing truth with others. This would be like a soldier going into battle without any armor or weapons. Asking a Christian to abandon the Bible for the sake of discussion is like asking an atheist to prove there is no God by using only the Bible. You would be asking the atheist to give up his axiom.
The prophets and the apostles never tried to prove God’s existence. They started by assuming God’s existence, and they always reasoned from Scripture (Acts 17:2, 17; 18:4, 19). By using the Word of God, we are actually pitting the unbeliever against God and not our own fallible thinking.
http://www.answersingenesis.org/articles/am/v2/n4/presuppositional-apologetics