Uniformitarianism has had two separate meanings, both more prevalent in 19th-century discourse:
Within religious philosophy, Uniformitarianism ("with a capital U") is the belief that the Universe has existed as it is now for an infinite time and will continue to exist for ever. This is not considered a very fruitful philosophical stance, opposed as it is to traditional theology and modern science.
Within scientific philosophy, uniformitarianism ("with a small u") refers to the principle that the same processes that shape the universe occurred in the past as they do now, and that the same laws of physics obtain in all parts of the knowable universe. This axiomatic principle, not often referred to as an "-ism" in modern discussions, is particularly relevant to geology and other sciences on a long timescale such as astronomy and paleontology.
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Example Usage of Uniformitarianism
MysteryOnward: @Adam4004 If u look at your tweets, you'll notice u 1st brought term Uniformitarianism up & insinuated i'd ask for citations -> I didn't.
MysteryOnward: @Adam4004 I haven't asked u to cite info on Uniformitarianism for many months. Are u bringing this up as diversion for lack of citations?
Adam4004: @MysteryOnward By the way. I don't need u to cite info on Uniformitarianism bc I know what it is.