“First, all men know God, regardless of what they may say about this. Even unbelievers have direct and compelling evidence that warrants their (unacknowledged) belief not only that God exists, but also that He is all-powerful, holy, the Creator and sovereign determiner of all events, etc. This evidence is supplied to all men by the clear revelation of God in nature and to many men by the self-attesting revelation of God in Scripture.
Second, because all men know God from His works of creation and providence, even those who will not profess and glorify Him are able, and actually do, gain considerable knowledge about themselves and about the world. Their knowledge of God justifies their logical and empirical reasoning. It provides the needed philosophical context and the personal operational basis for their coming to know anything else. Thus, unbelievers actually do possess a knowledge of God (His sovereign power, holy character, etc.) and extensive knowledge of the world (history, science, art, etc.).
Third, because unbelievers personally deny knowing God (that is, they repudiate the first point above), they are unable to give an epistemological or philosophical account of their knowledge of the world and of themselves that is intelligible. The knowledge of God is necessary in order to justify any knowledge of the world. The unbelieving philosophical assumptions and systems of thought that non-Christians profess to follow render their reasoning and interpretations unintelligible (lacking meaning, coherence, etc.). Unbelievers have no cogent explanation for their ability to know the things they actually know.
When Van Til discussed matters pertaining to the third point, he said he was speaking about the unbeliever “epistemologically.” Epistemology is the theory of knowledge. In terms of their professed theories, unbeliever’s cannot provide a cogent justification of the truths that they believe. Of course, the inadequacies of the unbeliever’s reflective theories about himself as a knower or about knowing itself do not cancel, deny, or preclude the actual knowledge that he happens to possess. A ten-year old child may very well be able to swim the length of the pool – and actually do it over and over again – without being able to offer an adequate scientific account of how this is possible (with respect to body densities, buoyancy, friction, displacement, propulsion in a medium, coordination of limbs, etc.).”
(Bahnsen, Van Til’s Apologetic, 405-406)