I'll have a try at this one. But since Affable Geek gave a Great answer to the direct question, I allow myself to tackle the question on a broader spectrum. Is neurology a threat to Christianity? Assumes that science and Christianity is opposed to science or vice versa.
But if you that a look in history you will find that the same question was asked during the enlightenment. Could rational reasoning replace God? But rational reasoning proved that it could not save the human being. Then modernity came along? Science or technology would save us. But that also failed in the end. Now we live in post-modernity, and what next.
My point is simply that the next kid on the block is neurology, where is used to be psychology. The problem is not the new scientific discovery but the premises behind the study. For the atheist neurologist that is the greatest threat to any kind of belief system. For the believer just an other way to praise God the creator. (Understand that all of the philosophy come with some good in them. They are not a total affront to Christianity. And the good part in them should be redeem.)
My answer is greatly influence by Ravi Zacharias' book Deliverus from evil.
Is neutrology a threat to Christianity? that really depends on the premises you hold.
EDIT
How does rational reasoning try to save us? If I take the first point of the westminster confession of faith the shorter catechism:
Q. 1. What is the chief end of man?
A. Man's chief end is to glorify God, and to enjoy him forever.
source
The way some thinkers have looked at the rational reasoning was to bring them a purpose in life and a joy in life. That could be compared has the salvation in Christianity René Descartes used rational reasoning to get to God, because of is Catholic premises. But Voltaire on the other end express the following :
The world embarrasses me, and I cannot dream that this watch exists and has no watchmaker
Voltaire / 1694-1778 / Les Cabales, 1772 source
The both of them look to rational reasoning, but they only proved their thesis or premises. Therefore, rational reasoning failed to bring everlasting joy, eternal life and all the questions.
What to I mean that science and technology failed in the end?
A bit like rational reasoning, if one look into it for everlasting joy, eternal life and the answer to all the questions, well I believe that the old saying : the more I learn the more I learn how little I know (Socrates ?)
The problem with the human heart is that it tries to be free from God. Our hearts create all kind of divinity to worship. (Jean Calvin idea of our heart as a idol factory, Tim Keller Counterfeit Gods).
This being said, I am in no way implying that Christianity have all the answer, and at is core it understand human limitations. How could a finite being understand fully an infinite one.
- Ps 115.3
- Isaiah 55:8 and following
Note : I am in no way saying the christian most switch off their brains. We should push in science and technology, and thinking hard about all the issues of life. Think by John Piper would express that though more. But we should not look in to those field has a place to receive everlasting joy, freedom from sin, peace, everlasting life. Our final hope must be in our Lord and Savior Jesus-Christ.
Edit 2
I left the previous post unchanged to allow you to follow the discussion. After talking with @Marc Gravell. The idea in this post what to present that the philosophy of the time could not dismiss the idea of God. Not the technical/scientific method. Thanks Marc for the discussion.