Van Tillian/Clarkian Presuppositional Apologetics.

[Ryft]

Statler's our only posterboy for this, by the way (that I'm aware of, though Frodo has made some remarks that would qualify; have to ask him for clarity).

As a matter of fact, Statler is not your only poster boy for this.

[Presuppositional apologetics is] the ultimate fingers-in-the-ears defense.

Hrmm, cramming your fingers in your ears is about refusing to hear your opponent's argument. That is exactly the opposite of what presuppositional apologetics does. You could not have missed the mark any worse if you had tried. But hey, it is delightfully fun rhetoric, I will give you that (although I would be embarrassed for anyone who found such rhetoric intellectually compelling).

The WMD of disagreements.

You do not win a debate by disagreeing. You have to break the argument. Presuppositional apologetics invests nothing in disagreements, and everything in breaking God-denying arguments. (Disagreeing is an autobiographical matter and therefore irrelevant.)

Is God's character the way it is because it is good, or is God's character good simply because it is God's character?

The latter; i.e., the nature and character of God is what defines good.

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And they seriously believe that Atheists are going to buy into this...

Quite the opposite, rather. They seriously believe that atheists will NOT buy into this, an expectation that arises from the Reformed theology upon which it is based.

At any rate, here's an article by Jonathan Sarfati which "explains" this ideology, and RationalWiki's rebuttal calling him out on his bullshit.

Sarfati? Oh please. The man is a joke. If you want to reference someone who "explains this ideology," cite from the men indicated in the thread title, Cornelius Van Til or Gordon H. Clark. However, while I have exegetical disputes with the presuppositionalism of Clark, I would highly recommend the fourth edition of Van Til's Defense of the Faith edited by K. Scott Oliphint (P&R Publishing, 2008) and Greg Bahnsen's Presuppositional Apologetics: Stated and Defended (American Vision, 2009).

Neither Creation Ministries International nor Answers in Genesis should be consulted on presuppositional apologetics. It is not their area. Sarfati and his ilk (e.g., Carl Wieland) embarrass themselves even on that which is their area, young-earth creationism, never mind this in-depth subject.