James White recently argued for presuppositional apologetics and against evidential apologetics. (link) He starts out with an analysis of Colossians 1:16-18, and Colossians 2:2-9, which focus on the Lordship of Christ. James White points out that the gospel is a radical claim, which unbelievers reject.
What caught my attention was James White's denial that unbelievers can have 'true knowledge' and his objection to the approach of starting from common ground between believers and unbelievers to show the reasonableness of believing in the God of the Bible and other Christian doctrines.
Presuppostionalism, as I understand it, has two distinct schools of thought; the Gordon Clark camp and the Cornelius Van Til camp. Clarinan presuppositionalism is not my cup of tea, but it's fairly innocuous. My main complaint against Clark's presuppositionalism is that he presupposes the truth of sola scripture, whereas I think the evidence for the truth of scripture and problems of other sources (Pope's, Councils, the Koran...) is very strong. While everyone has some presuppositions, I generally try to minimize what I presuppose and if something can be demonstrated, there's no need to presuppose it. On the other hand, Van Til's version of presuppositionalism is marked with antinomy and skepticism.
While James White didn't declare himself to be in either Gordon Clark's or Van Til's camp, and generally didn't get into much detail about presuppositionalism, but his denial that unbelievers can have 'true knowledge' and his objection to common ground between believers and unbelievers seems to show more influence from Van Til than Clark, since Van Til famously denied the same things.