[In Presuppositionalism,] the apologist presupposes the truth of Christianity and then reasons from that point. One basic presupposition is that the non-Christian also has presuppositions that color everything he or she [believes] about God. (Encyclopedia of Christian Apologetics by Norman L. Geisler)
Presuppositionalism is a school of Christian apologetics that believes the Christian faith is the only basis for rational thought. It presupposes that the Bible is divine revelation and attempts to expose flaws in other worldviews. (Wikipedia)
Presuppositionalists believe that one must presuppose the Christian worldview and the Scriptures in order to dispel the worldview of the unbeliever. (reclaimingthemind.org)
Presuppositionalists [believe that] the content of Scripture must serve as his ultimate presupposition. It merely applies the doctrine of scriptural infallibility to the realm of knowing. (Wikipedia)
Presuppositionalism is the predominant apologetic of contemporary conservative Calvinist and Reformed churches. (Wikipedia)
Presuppositional apologetics is opposed to evidentialism and classical apologetics. It differs from classical apologetics in that presuppositional apologetics rejects the validity of traditional proofs for the existence of God. Further, the presuppositional apologist differs with both classical and historical apologetics in its use of historical evidence. The historical apologist, in agreement with the classical apologist, argues in favor of beginning with reason and evidence to demonstrate the truth of Christianity. The presuppositionalist, on the other hand, insists that one must begin with presuppositions [from the Bible, and not try and use reason and evidence to prove Christianity]. The historical apologist believes that the historical facts “speak for themselves.” They are “self-interpreting” in their historical context. The pure presuppositionalist, on the other hand, insists that no facts are self-interpreting, that all facts are interpreted and can be properly understood only within the context of an overall [biblical] worldview. (Encyclopedia of Christian Apologetics by Norman L. Geisler)
Presuppositionalists criticize “evidentialists” for seeking to give credence to the unbelievers worldview by meeting them on neutral ground. The presuppositionalist believes that there is no such thing as neutral ground. As well, while the evidentialist will attempt to give arguments to increase the probability of their beliefs, presuppositionalist believe that one must have absolute certainty, not merely probability. (reclaimingthemind.org)
Presuppositionalists assert that any system of belief is built on certain foundational presuppositions (unprovable assertions that must be believed to make [their belief system] meaningful). As a result, the best means of Christian apologetics is not to prove certain specific assertions such as the existence of God, the historicity of the resurrection or the authority of the Bible, [but rather to] explore the foundational presuppositions of competing belief systems with the goal of showing that human experience makes sense most clearly when viewed in the light of the foundational teachings of the Christian faith. (apologetics315.com)
Presuppositionalists describe Thomistic (also “Traditional” or “Classical”) apologetics as concentrating on the first aspect of apologetics with its logical proofs for the existence of God, [and that it is] simply assuming common ground with the non-Christian and utilizing a piece-by-piece methodology. In this scheme, the common foundation of neutral brute facts leads to a generic concept of deity, then to the various characteristics of the Christian God as revealed in Scripture, and so forth. Piece-by-piece, Christian theology is built up from a neutral common ground. (Wikipedia)
Presuppositionalism is often accused of circular reasoning, e.g., “You should believe the Bible is God’s word because it authoritatively says it is God’s word.” (reclaimingthemind.org)
Depending on how one is defined, there are three or four basic kinds of presuppositionalism: (1) revelational presuppositionalism (Cornelius Van Til); (2) rational presuppositionalism (Gordon Clark); and (3) systematic consistency (Edward Carnell). Some view Francis Schaeffer’s apologetic as an example of a fourth variation that might be called practical presuppositionalism. Each approach differs in the way in which a worldview is judged for truth.
According to revelational presuppositionalism, one must begin any rational understanding of truth by presupposing the truth of the Christian faith. One must posit that the Triune God has revealed himself in Holy Scriptures, the divinely authoritative Word of God. Without this presupposition one cannot make any sense out of the universe, life, language, history, or anything else.
The Rational Presuppositionalist begins with the Trinity revealed in the written Word of God. But the test for whether this is true is simply the law of noncontradiction. That is, one knows that Christianity is true and all opposing systems are false because all of them have internal contradictions and only Christianity is internally consistent. Thus, a rational principle, the law of noncontradiction, is used as the test for truth.
The Systematic Consistency [view agrees with the need for the belief system to be rationally consistent; but also sees the need for it to include all the facts, and meet life’s basic needs.] The only system, they believe, that measures up to all three is Christianity.
.The Practical Presuppositionalistic (Francis Schaeffer) [approach’s] chief feature is that all non-Christian systems are unlivable. Only Christian truth is livable. In this sense, it uses unlivability as a test for the falsity of non-Christian systems and livability as a test for the truth of Christianity.
(Encyclopedia of Christian Apologetics by Norman L. Geisler)