The early natural philosophers aimed to “save the appearances” with their epicycles, and epicycles upon epicycles, because if Aristotle was right that a circle was the most perfect shape, and that the celestial sphere was perfect, then it all the celestial objects had to be perfect circles and spheres.
But there were some problems with the idea of all these perfect circles. Predictions of celestial motions were off if the supposed circular orbits of planets did not have other circular orbits built into them until the predictions matched the observations of the cosmos, so that is why we got epicycles to save the appearances of circular orbits in the celestial sphere.
Then Copernicus presented a new model of astronomy with his On The Revolutions of the Heavenly Spheres. The Catholic Church of 1543, when The Revolutions was published, was not very friendly to anything published against their religious dogma, however, so perhaps Rheticus did Copernicus a favor when he wrote in his preface that the Copernican model of the heavens was not meant to be ontologically true, only mathematically expedient. After all, Galileo would be subjected to house arrest for publishing his findings that the heavenly sphere really were not perfect, as evidenced by the sunspots he saw through his telescopes and craters on the moon.
Galileo’s house arrest even scared Descartes into turning from heresy to a more Church-appeasing view of the world; somehow Descartes’s ontological argument for God, whereby he clearly and distinctly perceives a god who is perfect, and that is existence is a perfection, therefore God exists, is seen as an ingenious observation, but to me it is a very vacuous form of reasoning, which may be logically consistent if the premises are true, but the premises themselves have huge flaws that make it possible to prove the existence of any absurd creature you can fancy up.
Be that as it may, Tycho Brahe dealt more damage to the Aristotelian view of a perfect heaven with his observation of a supernova; a supernova disrupted the idea of the fixed stars being perfectly incorruptible. So what Rheticus was saying in so many words in his preface to Copernicus is what William James, that brilliant father of American psychology and philosopher, would come to call Pragmatism. That is, we may not be able to see directly what is absolutely true in a purely metaphysical sense, but so long as our theories match up to our observations and predictions to the highest degree possible, then we have reached a practical, or pragmatic truth.
Really, can we hope to do any better than to be as pragmatic as possible? Is there really any other way of making truth statements? Or do our paradigm shifts get us no closer to either pragmatic or absolute truth, but only present the illusion of scientific progression?
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