Religion and Historical Methods

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I have recently been reading “Muhammad and the Empires of Faith” by Dr Sean W Anthony. Dr Anthony is a historian of the early Islamic period who attempts to apply critical historical methods to beginning of Islam and, in particular, the life of Prophet Muhammad (SAW). To understand this material better I have listened to some of his interviews. He has compared his project to the work of Western historians to apply these same methods to the founding of Christianity. I am curious, what do Christians make of these methods and investigations?