Ironically, it is really hard for Christian intellectuals to answer the question, “What is a Christian intellectual?”  Dr. Anthony Bradley posted this quote on his blog to answer the question:

An intellectual is one who loves ideas, is dedicated to clarifying them, developing them, criticizing them, turning them over and over, seeing their implications, stacking them atop one another, arranging them, sitting silent while new ideas pop up and old ones seem to rearrange themselves, playing with them, punning with their terminology, laughing at them, watching them clash, picking up the pieces, starting over, judging them, withholding judgment about them, changing them, bringing them into contact with their counterparts in other systems of thought, inviting them to dine and have a ball but also suiting them for service in workaday life. A Christian intellectual is all of the above to the glory of God. -James Sire, Habits of the Mind: Intellectual Life as a Christian Calling