One common objection is circular reasoning, on my blog, I put together
a collection of quotes from Dr. Van Til pertaining to this objection. There's also a helpful article by Dr. Richard Pratt to be found where he answers common objections.
Here are a few short but to the point quotes without the greater context:
"The only alternative to “circular reasoning” as engaged in by Christians, no matter on what point they speak, is that of reasoning on the basis of isolated facts and isolated minds, with the result that there is no possibility of reasoning at all. Unless as sinners we have an absolutely inspired Bible, we have no absolute God interpreting reality for us, and unless we have an absolute God interpreting reality for us, there is no true interpretation at all.
This is not to deny that there is a true interpretation up to a point by those who do not self-consciously build upon the self-conscious God of Scripture as their ultimate reference point. Non-believers often speak the truth in spite of themselves. But we are not now concerned with what men do in spite of themselves. We are concerned to indicate that the absolute distinction between true and false must be maintained when a self-consciously adopted monotheistic and a self-consciously adopted theistic point of view confront one another.
We may now first show what the Scripture says about personal revelation, then what it says about scriptural revelation, in order to see that plenary inspiration is involved in these two.” – Cornelius Van Til, Systematic Theology Chapter 12 The Inspiration of Scripture
"To admit one’s own presuppositions and to point out the presuppositions of others is therefore to maintain that all reasoning is, in the nature of the case, circular reasoning. The starting-point, the method, and the conclusion are always involved in one another.” – Cornelius Van Til, Apologetics, Chapter 4 The Problem of Method
"The charge is made that we engage in circular reasoning. Now if it be called circular reasoning when we hold it necessary to presuppose the existence of God, we are not ashamed of it because we are firmly convinced that all forms of reasoning that leave God out of account will end in ruin. Yet we hold that our reasoning cannot fairly be called circular reasoning, because we are not reasoning about and seeking to explain facts by assuming the existence and meaning of certain other facts on the same level of being with the facts we are investigating, and then explaining these facts in turn by the facts with which we began. We are presupposing God, not merely another fact of the universe. If God is to come into contact with us at all it is natural that the initiative must be with him. And this will also apply to the very question about the relation of God to us. Accordingly, it is only on God’s own testimony that we can know anything about him." Cornelius Van Til, A Survey of Christian Epistemology, Chapter 15 The Method of Christian Theistic Epistemology
Not sure what you've read up on, but wanted to mention a couple of important terms, autonomy and theonomy. A Christian worldview accounts for both, while a consistent Atheist worldview is autonomous through and through, in theory at least, it is supposed. Dr. Frame put together a nice glossary of terms helpful to any presuppositional discussion, it's found here.
