Many people make a broad distinction between presuppositional and evidential (or classical) apologetics. The classical method enjoys a rich history (for instance B.B. Warfield would be considered a classical apologist), while the Presuppositional approach really came to fruition with Van Til and Greg Bahnsen (though I've read various things from different theologians in church history that have sounded very presuppositional).
I recall hearing Michael Horton say he was presuppositional, but really, whatever "worked" for a particular person is what he would use. He may be on to something- if understood in this sense: I believe that one must be attentive to where a non-believer “is at”. Presuppositional arguments might be good for a hardcore atheist or pseudo-intellectual type. For instance, a guy I work with is a left-wing liberal, and well educated. Presuppositional arguments are very effective to get him to think. An evidential approach though may be perfect for someone who assumes much of the Christian worldview already. Sharing the classical argument that Christ was either “liar, lunatic or Lord” might be very helpful in getting to the gospel, quickly, for someone who's ready. From my viewpoint, both methods are possible.
That being said, my real love in apologetics is the presuppositional approach. Probably the best example of this approach is the debate between the late Greg Bahnsen and the atheist Gordon Stein. “Does God Exist?”. It’s best to track down an audio copy of this debate. This is not "easy listening". It requires one's complete attention, and multiple listenings. It's not something one can put on and then "multi-task". It will be of tremendous benefit to anyone interested in presuppositional apologetics.
If you’ve only listened to it once, my opinion is that it gets better the more one listens to it- it really takes time to chew and digest the arguments from both sides. Quite frankly, the first time I listened to the debate years ago, a lot of it went over my head. I subsequently burned off a copy to CD in which I divided each segment up to individual tracks, and took the time to focus on each section. Sometimes driving to work, I’d listen to only Bahnsen’s segments, other times just Stein’s. If wasn't until I took a seminary-level class in presuppositional apologetics that it all really made sense to me. Presuppositional arguments are like dynamite. They are extremely powerful.
Bahnsen doesn’t deny the use of reason, argument, and evidence. His point though is that these only make “sense” and find meaning in the context of a theistic worldview.
In response to the question “Is God good?” Bahnsen responds he knows God is good because:
“He saved me. He created me. He made the world and He made it good. He sent His son into the world to die for my sins. Many of these evidences are quite convincing to me, but I don’t use them outside of a word-view in which they make sense, in which they would be taken as true. If you mean is God good in such a way, or can I give you evidence that you would accept? That would depend on what your presuppositions are.”
In response to the question, “What solid evidence do you have to maintain that the Christian faith is the only true religion with a god? There are religions far older, and more or just as wide spread which millions of people consider valid,” Bahnsen answers,
“I have not found the non-Christian religions to be philosophically defensible, each of them being either internally incoherent or undermining human reason and experience… I will give just a couple of illustrations. Obviously I’m not going to cover all of them.
For instance, Hinduism assumes that God, or Raman is the impersonal and universal soul of the unchanging one of which all things are part (for instance). And because of that particular outlook, Hinduism says that everything in terms of my normal experience of the world and thinking is Maya, or illusion. Because everything in experience and thinking presupposes distinctions. But that is contrary to the most fundamental metaphysical fact, and that’s that there are no distinctions, all is one. So basically, Hinduism tells me that all my thinking, all of my reasoning is illusion. In so doing, it undermines reason.
You can take religions such as Shintoism, it’s view of Commi, the forces that permeate the universe, or Taoism, the ordering force of the universe. And they are impersonal forces, and as such are even less than human beings because they don’t have volition or intelligence.”
I point these things out to enforce the fact that presuppositional arguments are not an appeal to fideism. The employ reason, argument, and evidence. Bahnsen says elsewhere (not in the debate):
"God wishes for us to be rational: to exercise and improve our reasoning ability in understanding, propounding and defending the truths of Scripture. And as Locke observed, this reasoning ability does not begin or end with the teaching of Aristotle. To be rational is a trait much broader than the use of syllogisms (although they certainly have their place). The kind of rationality or reasoning that we will employ in defending the Christian faith involves not only study of formal logic (patterns or abstract forms of inference), but also attention to informal fallacies in ordinary language, the use of inductive reasoning, the handling of empirical evidence in history, science, linguistics, etc., and especially reflection upon the demands of an adequate worldview in terms of which all such thinking makes sense."
Bahnsen was keen on exposing the prejudice of non-Christians in regards to the "facts." In evaluating arguments against Scripture, Bahnsen uses arguments very similar to Josh McDowell:
"The third indication of prejudice in the criticism of the unbeliever is that he or she has not taken account of the actual evidence which is publicly available regarding the text of Scripture. If the critic had taken time to look into this subject, he or she would not have offered the outlandish evaluation that the Biblical text is unreliable. This came home to me with great force after taking an advanced course on Plato in graduate school, a course which took account of the textual criticism of the literary corpus of Plato's works. Our earliest extant manuscript of a work by Plato dates from right before 900 A.D. ("Oxford B," found in a Patmos monastery by E. B. Clarke), and we must remember that Plato is thought to have written roughly 350 years before Christ -- thus leaving us with a gap of over twelve centuries. By contrast, the earliest fragments of the New Testament date less than fifty years after the original writing; the bulk of our most important extant manuscripts dates from 200-300 years after original composition. The text of the New Testament is remarkably uniform and well established. The reliability of the Old Testament text has been demonstrated by the discovery of the Dead Sea scrolls.
The overall authenticity and accuracy of the Biblical text is well known to scholars. Frederick Kenyon concluded: "The Christian can take the whole Bible in his hand and say without fear or hesitation that he holds in it the true Word of God, handed down without essential loss from generation to generation, throughout the centuries." Such assessments from competent scholars could be multiplied easily -- which only goes to show the prejudice that operates in the thinking of unbelievers who offhand criticize the Bible for "very likely" having a dubious text."
I point all these things out for any of you interested in learning about presuppositionalism. Sometimes those of us who spent years in evangelicalism will over-react to the multitudes of Arminian apologetics we've been exposed to, and wrongly embrace a form of presuppostionalism that is an over-reaction to folks like Strobel, Geisler, McDowell, Paul Little, etc. When I first gripped presuppositional apologetics, it was just one more weapon against Arminian theology. The more though I learned about it, the more I learned to employ some of the work from the Classical approach.