There are only 5 types of evidence in this world. From the least reliable to the most reliable, they are:
-Replicated eyewitness evidence
-Personally Replicated eyewitness evidence
-Mechanically Replicated eyewitness evidence
If you eliminate all eyewitness evidence from your equation, you are left with only 1/5th what the world has to offer.
If you allow some types of eyewitness evidence but not others- you only have to go up two levels to reach the realm of theology rather than science.