It's really kind of amazing to watch.
Look, presuppositionalism is not, really, that big a deal. I am going to put the idea as simply as I can, in as small a space as I can, and maybe that will help the occasional person googling for the term out a bit.
Presuppositionalism is a variety of Christian apologetics--an approach, that is, that some Christians take to arguing for the truth of the Christian position. There are other varieties of apologetics. There is what some call evidentialism, which is, as you might have guessed, arguing from the available evidence--the evidence from the physical world, from history, and so forth. Then there is what some call Schaeffer's apologetics, which I think of as a variant of presuppositionalism. All have their uses, in my opinion. I can do the evidentialist thing. I have done it--done it well enough that I've left the people I was
The big idea in presuppositionalism is that we all make certain assumptions--presuppositions--in our thinking and that there are logical consequences to those presuppositions. For instance, in writing this post, I do so presupposing that someone might read it, that someone might understand it, and so forth. One opens one's eyes on the presupposition that, under normal circumstances, one will be able to see. To try to make someone happy is to operate on the presuppositions that happiness exists and that people can experience it, and so forth. You get the idea so far?
The same kind of thing applies to religious thinking. If you start with the idea that there is no God, or that God is of this nature or that nature, there are certain necessary logical consequences to those presuppositions. For instance, if the universe that exists today did not start intentionally, with a creator God, then it necessarily follows that it started unintentionally. If there is no creator, then there is no creator's plan; the universe and everything in it are unplanned. You are unplanned, a mere accident of existence, as is everything about you and around you. Likewise, if God is impersonal, or panentheistic, or there are multiple gods, each of those have certain necessary logical consequences.
Still with me? Good. I thought so.
As far as the Christian presuppositionalist is concerned, it is impossible for certain things--many presuppositionalists would say anything--to make decent sense without the presupposition that the material in the Bible is actually true. It is not possible to make a good case for personality arising from a godless, impersonal universe. In a godless, impersonal universe, there is logically no purpose for love; it merely happens to have arisen by accident and proven to be a successful adaptive behavior. It becomes extremely difficult to talk about good and evil without appealing to some transcendant standard like that found in the will of a God. And so forth. The Christian presuppositional apologist will do his best to note the logical consequences of his conversational partner's presuppositions and point them out. We argue that if you start with God and His revelation in the Bible, the universe makes sense; if you don't, it doesn't and you don't.
And there it is in a nutshell. There have been whole books written on the subject, and I have necessarily been brief and probably not done the subject justice, but that should be enough for you to see that presuppositionalism isn't quite the bogeyman that some people make it out to be.