Question: "What does the Bible say about uniformitarianism vs. catastrophism?"
Answer: Geologically speaking, uniformitarianism is the idea that geological processes (rates of erosion and uplift, etc.) are essentially the same today as they were in the unobservable past. We can, therefore, make accurate determinations about the past simply by observing the present. This principle is often summed up aphoristically in the phrase “the present is the key to the past.” A strict uniformitarian would look at a canyon with a river running through the bottom and see millions of years of slow, gradual erosion caused by that river.
Catastrophism is the idea that natural disasters (floods, earthquakes, etc.) can dramatically alter the surface of the Earth very quickly and that we can be certain that at least some of the geological features we see today were formed rapidly during past catastrophes rather than by the slow, gradual processes of uniformitarianism. We must, therefore, take the possible effects of unknown catastrophes into consideration when studying the history of the Earth’s surface. A catastrophist would look at the same canyon with the river running through the bottom and wonder if it was the result of gradual uniformitarian or rapid catastrophic erosion (like the canyon rapidly formed by the Toutle River washing out a mudslide following the Mt. St. Helens eruption in Washington State).
The uniformitarianism-versus-catastrophism debate is essentially this: how much can geologists rely on extrapolations of present-day geological processes when postulating the history and age of geological phenomena?
While you won’t find the words “uniformitarianism” or “catastrophism” anywhere in the Bible, it is abundantly clear which side it takes in the debate. According to the Bible, the Earth was inundated in a global deluge not many thousands of years ago (Noah’s flood). Thus, any geological phenomena caused by gradual uniformitarian processes prior to that catastrophe were either eroded by the flood’s waters or else lost under the massive amounts of sedimentation deposited during the flood. We cannot, therefore, rely upon uniformitarian reasoning to take us any further back in time than to the flood of Noah’s day. The only canyons we see now are those that were carved out either during the flood or after its waters receded.