Proof vs Experience in Christianity

I believe in Christianity as I believe that the sun has risen: not only because I see it, but because by it I see everything else.  -C. S. Lewis, The Weight of Glory


Of course even before Lewis, G. K. Chesterton already acknowledged that concept when he said:

God is like the sun; you cannot look at it, but without it, you cannot look at anything else.

This would imply that the value of Christianity lies not in its irrefutable proof, but the lens it provides us to view our own existence. You do not try to prove Christianity, you accept it as true and see how through that everything else fits into place. "Taste and see that the Lord is Good" says the Psalmist. This is why we do not bring people to Christ by elaborate arguments, but testify how through Christ our lives have changed.  It requires not just convincing, but a total change in mindset of the person.

Of course logically speaking, Christianity works because it is true. It is not true because it works. It is unfortunate that due to our own limits, it seems that Christ can only be known through the latter.