Reading the Rock Record

In this video, we look at some of the way of dating rocks. What principles are used to interpret the history of rocks and the world?
For clarity, at the end, when I say that we cannot judge between the two points of view, what I mean is that we cannot judge between the two points of view using objective reasoning. We certainly can make a judgement, but it cannot be objective reasoning, since every viewpoint is colored by presumptions.
Note: The geologic column used in this video was modified from a column produced by Cornerstone Educational Supply.