The Copernican Principle, especially as it has been applied by modern speculative physics, is evolutionist in its essence. The evolutionary worldview posits several paradigmatic foundational principles, all of which have their nascence and inception in the assumptions and theories of the heliocentrists/copernicans.
The first principle of evolutionism is that of material origin or first cause. Whereas both Natural Theology and Divine Revelation recognize One, Omnipotent, Uncreated, Eternal, Intelligent, Simple, and Good First Cause (Creator), In Whom there is no matter, no composition, no material extension, and no potency, Who is pure Act and Pure Spirit, and from Whom came forth the material, finite, created Universe; the evolutionary worldview posits a material first cause. Matter was, matter is, and matter will be. All things that exist are products of cosmological and biological material causes. Whatever form their existence might take at any moment of measurement, observation, or apprehension, owes all of its attributes to random physical causes, and not to the intelligently determined design of an omnipotent Creator.
The Copernican Principle (CP) underpins the Big Bang Theory (BBT) of the origin of the Universe. This theory posits a material first cause. Something - in some versions so small that it amounts to virtually nothing - exploded, cooled, and gelled. And then there was the Universe. And this took billions, and billions of years.
The next principle is perpetual change. In the evolutionary/copernican/relativist paradigm, there is no stable, immovable, absolutely at rest body. If absolutely nothing in the material Universe is at rest, then no motion whatsoever is capable of measurement; for all measurement requires a standard for comparison. Furthermore, if absolutely nothing in the material Universe is at rest, then there can be no objective direction. There is no up, no down, and no center. All motion is relative, i.e. subjective, i.e. based on perception and vantage point and nothing more. Indeed Big Bang Cosmology posits just this: an acentric universe with no objective direction and no objectively measurable motion.
According to Natural Philosophy and Divine Revelation, the Earth is a fixed, stable body at rest in the center of the spherical, finite Universe. A fixed Earth conforms to common sense, and, being fixed, provides the basis and foundation for all measurement of all motion. Copernicus, Galileo, Kepler, Einstein and the modern scientist establishment posited that the Earth is not fixed, but rather revolves around the sun and rotates on its own axis, in addition to hurtling through outer space with its sun, moon, planets, and galaxy. This destroys the objective existence of a body at rest in the created cosmos, destroys all true measurement of motion, and - not incidentally - destroys belief in the literal sense and inerrancy of Sacred Scripture.
Likewise biological evolutionism posits perpetual change in the matter-form composition of generic biological forms. Sacred Writ reveals that the Eternal Word created all things according to their kinds (genera). Sacred Theology and Scholastic Philosophy teach that the kinds of plants and animals made by God during the Six Days of Creation are immutable substances, which, though subject to the changes of growth and corruption, are not subject to transubstantiation or transmutation. Evolution holds for the absurd idea that a lower being has the power, through material causality, to transmute itself into a higher being, so that it gives what it never had. Amoeba has no lungs and no legs, but by some magic (called billions and billions of years), its offspring has lungs and legs. Ape has no rationality, but, by the power inherent in matter cum quasi-infinite magnitudes of time, can transmute itself into man.
Evolutionism gives to matter creative power OVER TIME. Matter creates OVER TIME. Because time is the essential requisite for the evolutionary system to have any possibility at all, the entire construct is qualified by the attribute of perpetual change, a function of time. In the case of man, matter is alleged to have created both a body and an immaterial soul. But this is absurd because there is no intellectual or spiritual power or capacity in matter. For this cause the evolutionary paradigm is constrained to categorize man, not as rational animal, but as just plain animal, and to deny the existence of his immaterial, rational, immortal soul. But this flies in the face of observable reality.
Evolution posits that the observable and measurable created kinds are not immutable forms, but rather transitional forms, always in the process of becoming, and therefore never actually participating in true existence according to a true essence or nature. Absurd consequences follow: True taxonomic measurement ceases to be possible because there are no immutable biological forms (no beings at rest, we might say) upon which to base a true branch of science. No category of living being can be anything other than a transitional, relative existence (relative to what, they never say); and this unmoors the entire science of taxonomy.
I don't want this reply to go on forever, wherefore I hope I have sufficiently addressed your question.
And yet for all this blather, if the Copernican Principle was disproved tomorrow, all the evidence for evolution would still be there; and if evolution was disproved tomorrow, then we'd still have no reason to assign our planet a special place in the universe. The two questions are completely independent. The one thing that links them together is that some religious people deny both of them. But they really have nothing to do with one another. It's like when Bush invented the "axis of evil" --- remember that? Consisting of three countries with no common factor except that he didn't like any of them.
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