Translating Cornelius Van Til’s teaching that all unbelieving thought teeter-totters back and forth from rationalism to irrationalism to the language of atheism and idolatry, John Frame gives the following instructions:

Against atheistic relativism. When you find a nonbeliever who stresses the atheistic relativist side of unbelief, be persistent in asking these questions: (1) how can you be sure that relativism is right, when it itself rules out all Cherence? (2) How can you live as a relativist? Having no assurance of anything must be a terrible strain, rationally, emotionally, and volitionally, what basis do you have for making decisions? What basis do you have for criticizing the treatment you receive from others? How can you say anything is wrong, unfair, or unjust? What basis do you have for trusting logic – or, for that matter, your own mind?

Against idolatrous rationalism. When you meet someone who tends to stress the powers, rather than the limits, of what autonomous thought and action, you will likely be dealing with someone in the grip of an idol. Find out what his idol is and take aim by asking these questions: (1) What basis is there for thinking that this idol is absolute? (2) Does your god really do the job of a God? Did it create the world? Is it the ground of logic, mathematics, ethical value, and the universal judgments of science? Is it adequate as a final standard of meaning, truth, and right?

We know that an impersonal god can do none of these things. So the unbeliever will be tempted either to lapse into relativism or to grant that his god has some elements of personality. Once he does the latter, he’s granting part of our case, and we can pursue him further, especially by asking him, “How do you know this person?”

Against atheistic idolatry. Press the fundamental contradiction in this rationalistic – irrationalistic combination. A proof that there are no proofs, an absolute statement that there are no absolute statements. Then attack the original rationalistic and irrationalistic elements, as above. It will not be easy. The unbeliever will slide from one position to another, from rationalism to irrationalism and back again. Argument itself will not be enough; God must intervene. Thus, prayer is the ultimate apologetic weapon.

-John M. Frame, Apologetics to the Glory of God, 201-202.