
I found this resource on the DG site, "Why We Believe the Bible - Appendix Five: Thoughts on How to Know If a Writing Is From God." I thought it was really good as I have been trying to study inerrancy and the related issues lately.
It's Piper's thoughts on how to know if God wrote the bible. His point here is that being convinced that God wrote the bible is not going to come about like conviction of most other things. Bahnsen referred to this in his famous debate with Stein, calling it the "crackers in the pantry" fallacy. If you wanted to look in the pantry to see if the crackers were really there, you would just open up the door and look. This is not so with God and his word. As finite, created, and sinful beings we cannot take God in hand and examine Him at will, rather God must reveal himself to us. There are a lot of other good statements in here about the inward witness of the Holy Spirit; and Piper even cites 2 Corinthians 4:-6 which are perfect verses for all this. The gist of those verses being that men do not need to pursue verifying the gospel presentation so as to find God, so much as have their eyes opened to what's right in front of them. God must shine into their heart. This is an inward work that must be done, and always happens through the Holy Spirit.
What I always think is helpful when talking to believers about this is to turn things personal and inward. Do you know God? How did you become convinced of his reality and the veracity of the gospel message? Was it by thoroughly researching all the historical issues? Or was it by considering all the philosophical ideologies and systems of thought? No. If you're a Christian, whatever your exposure to extra-biblical evidences may have been, you believe God to be who he is because of two things. One, you have heard the gospel in some form or fashion. And two, God has shone in your heart and revealed himself to you, convincing you of it's truth and glory.
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Actually, the whole set of notes and all of the appendices are really good. So scroll to the top and check them out if you have time. If nothing else, at least read the above mentioned appendix as it's very good and very short.