I take it that the belief that Scripture is inerrant is the belief that a correct interpretation of Scripture is true.
Question: whether Scripture is inerrant.
Objection 1: That it is not, as there are places where Scripture contradicts itself.
Objection 2: That it is not, as there are places where Scripture disagrees with historical research.
Objection 3: That it is not, as various people disagree as to the meaning of Scripture.
Objection 4:That it is not, as it is unclear what it intends in various places.
I answer that: Scripture is inerrant, being inspired and preserved by God for our instruction in what is necessary for the spiritual life. This inerrancy is of no help to us, however, except insofar as we have a correct interpretation of it, and this is available most securely only through the illumining of our hearts by the Spirit of God, and often available not only most securely, but only truly in that way. I further take it that any effectiveness of Scripture on the hearer or reader is due to the illumining of the Spirit--which is not to say that any doctrine by which a person changes for the better is true, but that the change made in hearing the doctrine is by that truth which is contained in that doctrine (whatever that may be) being impressed on the heart by the Spirit so as to effect that change in the heart.
Answer to objection 1: Where Scripture contradicts itself, either the contradiction is itself meant to teach, or what is contradicted is not intended, in one or all places, as what we are to learn.
Answer to objection 2: Where Scripture disagrees with historical research, it is either correct--as in places where it is a matter of faith that Jesus Christ was born of the Virgin Mary, lived a perfect life, died on a cross, and rose again--or is not intended to instruct as to such things--as in places where the numbers in each army may disagree with historical research without altering the sense of the passage. The claim is that Scripture is accurate in what it teaches, but not all that it says is teaching in the sense we might take it to be. It may be difficult to say what a certain passage is meant to teach.
Answer to objection 3: The disagreement of people over the teachings of Scripture has no more relevance to the inerrancy of Scripture than does the disagreement of scientists have anything to do with whether the created order can be described. Nor do our disagreements over the sense of any passage have anything more to do with whether it has one, or what it is, than do similar disagreements over what is before our physical eyes have anything to do with whether there is anything there, or what it is.
Answer to Objection 4: The lack of clarity which is held to exist in Scripture is, variously, unimportant, nonexistent, meant in itself to teach, or to be worked through by the power of the Spirit of God. That a thing is unclear has no more to do with what it is in Scripture than in creation. It may be that a part of Scripture--even a great deal of it--is incomprehensible apart from the renewing of our minds. Indeed, I suspect that Scripture interpreted apart from the Spirit of God is almost always Scripture poorly and sinfully interpreted. If it is truth we are looking for, then we must rely on the mind of Christ, which we have through the Spirit, to enlighten us. Whether we interpret through the Spirit or not, though, Scripture remains, in itself, inerrant.