Clarkian presuppositionalismGordon Clark and his followers treat the truth of the Scriptures as the axiom of their system. The axiom cannot be proven or disproven; rather, the worldview that results from the axiom may be tested for consistency and comprehensiveness. Testing for internal contradiction exemplifies Clark's strict reliance on the laws of logic (He famously translates the first verse of the Gospel of John as "In the beginning was the Logic, and the Logic was with God, and the Logic was God.") Thus, in order to invalidate non-Christian worldviews, one must simply show how a different presupposition results in necessary logical contradictions, while showing that presupposing the Bible leads to no logical contradiction. By contrast, some Van Tillians have suggested that God as He has revealed Himself in Scripture reveals apparent paradoxes.
However, Clark allowed that presupposing axioms (or "first principles") themselves do not make a philosophical system true, including his own; the fact that all worldviews he examined other than Christianity had internal contradictions only made Christianity highly more probable as truth, but not necessarily so. Nonetheless, he believed that this method was effective in many practical cases (when arguing against, for instance, secular humanism or dialectical materialism) and that, in the end, each of us must simply choose (that is, make an informed selection) from among seemingly consistent worldviews the one that most adequately answers life's questions and seems the most internally coherent. (Some Van Tillian critics suggest that the concept of coherence itself must be defined in terms of Christian presuppositions but is instead being used by Clark as a "neutral" principle for discerning the truth of any proposition.)
Using this approach, Clark labored to expose the contradictions of many worldviews that were in vogue in his day and to defend the Christian worldview by proving its consistency over and against those who attacked it. His unflagging use of logic sometimes led him to what most Reformed theologians consider rather unorthodox ideas on such topics as the problem of evil — topics which are most often treated by theologians as paradoxes or apparent contradictions not resolvable by human logic. But Clark famously rejected the idea that Scripture teaches paradoxes and notion of "apparent contradiction", asking "apparent to whom?". He described an alleged biblical paradox as nothing more than "a charley-horse between the ears that can be eliminated by rational massage."
With regard to other schools of apologetics, Clark suggested that the cosmological argument was not just unpersuasive but also logically invalid (because it begged the question), and he similarly dismissed the other Thomistic arguments. As a staunch critic of all varieties of empiricism, he did not tend to make much use of evidential arguments, which yield likelihoods and probabilities rather than logical certainties (that is, either coherence or incoherence).
Taken from Wikipedia -- Note, if they can get it right to give Clark a mention, I am sure us reformed believers can at least do what Wikipedia has got right regarding the subject of presuppositionalism.