A comment from a Reformed Forum comment wall giving a brief explanation of presuppositionalism.
“It seems that the atheist can admit the possibility that he is wrong on some fairly trivial things, but he will not and cannot willingly admit he is wrong when it comes to his being autonomous (Being a law unto himself). Because his autonomy is his anchor, his ultimate commitment. That is where the major struggle between Christian theism and atheism lies. If he is to be wrong, it is always (ultimately) because he says so. Anything deemed “Truth” must pass the test of his “autonomous cognitive filter” (detached from any external authority) he will not submit his intellect to another because he sees man as the ultimate arranger and unifier of the facts. That is, there is no God who defines what reality is. According to the atheist, it’s all up to him (his autonomous reason, sense experience, intuition etc.). This position of autonomy presupposes that there is no God who creates, knows all and defines His creation as he so chooses and requires all men to think His thoughts after Him. In that sense the atheist can’t admit that he might be wrong when it comes to his autonomy and be consistent with his own autonomy. So the atheist would have to say: “I might be wrong that there is no God who is the Lord of the universe and demands that my intellect be placed under his Lordship.” The very positing of the possibility of God’s non-existence means autonomous man is more ultimate than God and defines what is possible and impossible. This is the very thing that Christianity rejects. So agnosticism is really dogmatism in disguise.
The consistent Christian believes that God is the “all-conditioner”. He is the transcendental reality upon which the intelligibility of anything rests. We don’t come to Bible and say “Wow! there is a God, where has He been my whole life?” Everyone knows God, but not everyone honors Him as such. God is revealed through nature, ourselves and Scripture, but we suppress this knowledge in unrighteousness. We don’t want to submit to the Lord. Our innate knowledge of God is manifested in many ways. It is clear in the ways that people use the gifts that are only intelligible in a framework of this Triune God’s revelation. People try to fit the laws of logic, morality, laws science etc. into an autonomous framework that ends up destroying these realities failing to provide the necessary grounding for them. So it’s not that the unbeliever is stupid (by any means), often he is very intelligent, but this is because he relies on God’s revelation (though not giving honor to Him). The Christian understands that the basic reliability of our sense perception that we use when we read the Bible rests on the creative design of the God who reveals Himself through the Bible (and nature, conscious, along with all the facts of the universe). Also our rational faculties work because they were designed by this God whose very nature they are meant to reflect. The universe is rational because God is it’s rational Creator.”