Question: "What is presuppositional apologetics?"
Answer: Presuppositional apologetics is an approach to apologetics which aims to present a rational basis for the Christian faith and defend it against objections by exposing the logical flaws of other worldviews and hence demonstrating that biblical theism is the only worldview which can make consistent sense of reality.
Presuppositional apologetics does not discount the use of evidence, but such evidences are not used in the traditional manner—that is, an appeal to the authority of the unbeliever’s autonomous reason. Presuppositional apologetics holds that without a theistic worldview there is no consistent basis upon which to assume the possibility of autonomous reason. When the materialist attempts to refute Christianity by appeal to deductive reason, he is, in fact, borrowing from the Christian worldview, hence being inconsistent with his stated presuppositions.
The presuppositional approach to apologetics calls for the Christian and non-Christian to engage in an internal examination of their respective worldview and thus determine whether or not they are internally consistent. The essence of presuppositional apologetics is an attempt to demonstrate that the non-Christian’s worldview forces him to a state of subjectivity, irrationalism, and moral anarchy.
Since the unbeliever’s worldview is objectively false, it of necessity contains demonstrable contradictions (e.g., he makes moral judgments, but he cannot account for moral absolutes without the theistic worldview). The believer, within the Christian framework, can account for things like rationality, logic, uniformity of nature, morality, science, etc., because the Christian worldview conforms to a transcendent reality.
In summary, the presuppositional apologist engages in an internal critique of a given worldview in order to demonstrate that it is arbitrary, inconsistent within itself, and lacks the preconditions for epistemology. The presuppositional apologist can thus take a given value which is held by the unbeliever and demonstrate to him that if his own worldview were true, that very belief would be incoherent and/or meaningless. Presuppositional apologetics seeks to prove Christianity with reference to the impossibility of the contrary. In other words, unless the Christian worldview is presupposed—whether at a conscious or subconscious level—there is no possibility for proving anything.