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Any god who needs to submit himself to an external system of proof to validate his existence is of little interest to me. The God I worship is the very source of all such systems of proof, whether they be logical, mathematical, scientific, archaeological, or historical. How will these systems prove that my God exists, when they cannot even prove that they themselves are true? When they owe even their own existence to the existence of God?

Very well, then. The existence of God cannot be proven. Not because his existence is tenuous or uncertain, but because there is no system beyond God with which God can be judged to exist. Does that mean that all the efforts of Christendom, from Biblical times to the 21st century, directed at finding the proofs of God are futile?

Certainly not. They show us that God, taken together with the world that he created, is self-consistent. And self-consistency is the highest level of verification which can be expected from the truth of the highest order. Furthermore, beyond demonstrating the consistency of Christianity, they are also useful for assaulting the inconsistent paradigms which raise themselves up against God.

I intend to show that God, as revealed in Jesus Christ, is the one axiom that generates all other truths in the world. That he is the perfect explanation for all that exists in the universe. That is how you "prove" a postulate. Postulates are unproven by definition - you may say that they are "taken on faith" - but if a result of a postulate agrees with a fact that we observe in the world, then those two things taken together are self-consistent. I then repeat this process for every fact in the world.

For my God is the one Father of all, who is above all, and in all, and through all. All of creation was made by him and for him, and therefore all things can be found in him, as he can be found in all things.

You may next want to read:
Science as evidence for Christianity (Summary and Conclusion)
The word "If" does not apply to God
Another post, from the table of contents