One of the difficulties with questions about logic is that in the course of history there has been more than one conception of "logic." Even though many people would agree that the proper kind of logic is universal to the human race, they do not agree as to what exactly logic is.
The Bible gives us a clear starting point by indicating that God is the absolute source for his creation and for its order. That includes us. That includes also not only the physical objects around us, but God's order, his governance of the world.
So God is the source of logical order as well. The world is not just a chaos. The order in the world goes back to the fact that God is a faithful God (Ex. 34:6). Logic, therefore, belongs to God even before there was a world. God is consistent with himself. He is always faithful to who he is.
The Bible indicates that God made human beings "in the image of God" (Gen. 1:26-27). We are like God in several respects. One is that we think like him. So we are in touch with logic. But we must make a distinction between God's knowledge and ours. Our knowledge is derivative knowledge, finite knowledge. So we can sometimes be mistaken. We can make mistakes also in the area of logic.
The Christian view is that there are two levels for logic. First, there is God's perfect level of understanding. He understands all of logic by understanding himself and his own internal self-consistency and faithfulness. Second, there is the level of human understanding, which is derivative, finite, and partial.
By contrast to this view, most of the history of Western philosophy has ignored the two levels. With few exceptions, philosophers have tried to answer the big questions about existence, and the big questions about logic as well, by just using their own resources, and not relying on God or on his word, the Bible. This route is the route of autonomy, that is, trying to make yourself into the final ruler. So logic gets reduced to one level--the human level.
The result is that a flaw runs through the entire conception of logic. This flaw is not utterly disastrous because, in spite to intentions to the contrary, no human being can in actuality escape the presence of God. People end up relying on him and on his consistency, even when they desire to be independent. But the flaw makes a difference, all the way through the discipline of logic. To trace the difference is a challenge.
Vern Poythress, Ph.D. is distinguished professor of New Testament, Biblical Interpretation, and Systematic Theology at Westminster Theological Seminary.
For Professor Poythress' full treatment of this question:
Vern S. Poythress, Logic: A God-Centered Approach to the Foundation of Western Thought (Wheaton, IL: Crossway, 2013).