The error is located in the very first premise, i.e. in the notion that theological assumptions or presuppositions lie behind every claim or position or theory or philosophy. Why do they think that? In order to understand why, we need to consider a distinction made by Aristotle. Aristotle pointed out that for humans, the order of being and the order of knowing are not the same, but are opposite. We are animals. As animals, we start (in the order of knowing) with sense knowledge, with what is closest to the senses. Gradually we penetrate more deeply into the being of things, with greater abstractive power. Eventually, if we think deeply and carefully enough, we may arrive at the idea of being qua being, and even Being per se. But the order of Being is exactly the opposite from the order of [human] knowing. Everything comes ultimately from God; He is thus first in the order of being. What is most proximate to the senses is not first in the order of being, just as accidents are not prior (in the order of being) to substances. God is first in the order of being, but last in the order of natural [human] knowing.
Now, fast-forward to Descartes. Descartes tosses out all sense knowledge, and tries to start with an epistemically certain foundation, the cogito. But what about that evil demon? Descartes has to deal with the evil demon possibility by immediately positing a good God. So God comes in right away (epistemologically). For Descartes, in order to know anything about the world, one has to make a theological assumption. That is early presuppositionalism. For Descartes, the order of knowing is made the same as the order of being. (This is no accident, because Descartes in his philosophical anthropology is guilty of what Maritain calls "angelism", disregarding our humanity, and 'raising' us to the status of angels, where in fact the order of being and the order of knowing is much more aligned.) Presuppositionalists (for the same reason as Descartes) mistake the order of being (or the order of authority) for the order of knowing. They think that the order of knowing must be the same as the order of being (or the order of authority), when in fact it is our materiality that requires the two orders to be the opposite.
For the Calvinists, reason is fallen; it is totally depraved. Therefore, reason must build on no other foundation than the Scriptures. Calvinist presuppositionalists replaced Descartes's positing of a good God with the presupposition of the truth and authority of God's Word (i.e. the Bible), or with Christianity. Their claim that Christianity (or the Bible) must be presupposed as the foundation for all other knowledge, is itself based (not on the Bible, ironically) on Cartesian skepticism regarding the reliability of our senses and reason and intellect.
I have had Calvinistic presuppositionalists tell me the following:
"You cannot even call the experience of your senses knowledge without making theological assumptions."
Notice the [Cartesian] skepticism presupposed in that claim. Here was my response to a fellow who made that claim to me:
"This is fideism built on [philosophical] skepticism. The problem with this position is that if one cannot trust one's senses without first making theological assumptions, then one has no non-arbitrary grounds to trust one's reason without making theological assumptions. Then since one cannot trust one's senses and reason, one has no way of knowing which theological assumptions to make, whether such assumptions are true, and therefore whether such assumptions actually shore up one's senses and reason. One cannot appeal to Scripture (or anything else in the world) to acquire these theological assumptions, because one cannot trust one's senses to perceive Scripture or one's reason to interpret Scripture. Therefore, once one digs a skeptical hole, there is no boot-strapping one's way out of it, apart from a purely fideistic leap, [or from reversing the process by which one dug the skeptical hole]. Fideistic leaps can go in any direction (e.g. Allah, Buddha, Krishna, Gaia, Elvis, atheism, polytheism, pantheism, etc.). Fideism is the great equalizer. Given fideism, no leap is any better or worse than any other leap. The evaluative faculty (i.e. reason) has been stripped away by skepticism."
Another presuppositionalist claimed that "all positions start with equally unprovable assumptions and suppositions." Such a claim is a form of skepticism. It entails (though it itself could not acknowledge this) that nothing can be known at all. It entails that positions cannot even be tested on the grounds of coherence, since even the principles of logic are just assumptions and suppositions.
Presuppositionalism is especially attractive to those who either deny that philosophical knowledge is possible, and/or are ignorant of the possibility of philosophical knowledge. I've heard presuppositionalists say something like this: "Since every position starts with mere assumptions and presuppositions, you might as well build on the foundation of the Word of God." Other times they say that starting with any other foundation is idolatry, for it puts something other than God at the foundation. Notice there the mistake of failing to distinguish between the order of being and the order of knowing, and thus assuming that what comes first in the order of knowing is first in the order of being/authority. By claiming that they start with Scripture, presuppositionalists make themselves highly susceptible to being unaware of the presuppositions that they bring to Scripture. If you are explicitly claiming to start with Scripture, you cannot allow yourself to believe or recognize that you are actually starting with something that you are bringing to Scripture.
Often presuppositionalists mistakenly assume that what is highest in authority must be epistemologically foundational, as if the two are the same. That is why they insist you start with the Bible, not with sense knowledge and reasoning. (Of course, they are glossing over the problem of how we know that the Bible is the Word of God, and how we interpret the Bible, without presupposing the reliability of our sense knowledge and reason.) In actuality, the supreme authority of the Bible does not mean that all knowledge and reasoning must be built on the Bible. For example, we don't have to build our mathematics on the Bible (as some presuppositionalists claim). The supreme authority of the Bible means rather that we must strive to make all our knowledge in agreement with (i.e. compatible with) the teachings of the Bible.
Once sense knowledge and reason are knocked out (by skepticism), then the only kind of religious expression possible is some form of fideism. And that's precisely what presuppositionalism is. It is fideism, built on [Cartesian] skepticism. One way to show the problems with presuppositionalism to a presuppositionalist is to show its philosophical presuppositions, especially its skepticism. Presuppositionalists typically do not realize they have any presuppositions other than explicitly Christian ones. Presuppositionalism suffers from two irremediable contradictions: it starts with a presupposed foundation (e.g. Scripture) to which its own epistemic condition (e.g. skepticism) allows no access. (That is the first contradiction.) It then attempts to evaluate other 'worldviews' according to a standard found in its own (e.g. coherence), as if it were not fideistic (and thus relativistic) at its core. (That is the second contradiction.)
Presuppositionalists are typically highly suspicious of philosophy. See, for example, here. But true philosophy does not undermine the gospel, because truth cannot contradict truth.
When I was in seminary (Covenant Theological Seminary), at one point I naively believed that all doctrinal disagreements between Bible-believing Christians could be resolved (in principle) by exegesis. That was one of the reasons I worked very hard at exegesis, and at graduation received the American Bible Society Award for excellence in the field of Biblical exegesis. But it was already very clear to me not only that exegesis and interpretation are two distinct arts, but also that interpretation depends in large part on philosophical assumptions that one brings to the interpretive process. That is one of the reasons that I decided to continue my graduate studies in philosophy. If we do not realize that we are even bringing philosophical presuppositions to the interpretive process, we will not be getting to the fundamental causes of our interpretive disagreements. The first step for the presuppositionalist is to begin to realize that he is bringing philosophical assumptions to the interpretive process. Only then will he realize that he needs some way of evaluating these assumptions. (Claiming to evaluate them by way of Scripture simply ignores the fact that he would be using these assumptions to interpret Scripture, so the evaluation would be question-begging, and thus worthless.)
Here's an example from the "Joint Federal Vision Statement" of the tacit presupposition that we initially bring no philosophical assumptions to the interpretive process:
"We deny that the Bible can be rightly understood by any hermeneutical grid not derived from the Scriptures themselves."
If that statement is true, then either there is a missing exception clause for the first hermeneutical grid one uses to interpret Scripture (in which case the statement is ad hoc), OR the Bible cannot be rightly understood. (This is not a pedantic criticism; it is precisely this kind of sloppiness that makes it hard for presuppositionalists to see the inconsistency in their own position.)
Philosophical ignorance or error is another stumbling block to unity. What is more, it typically leads to debates that do not address the fundamental points of disagreement that divide us. So I pray that this post might be helpful in showing what is wrong with presuppositionalism, in order that this stumbling block might be removed from the path toward unity.