The earth revolving around the sun was also armchair reasoning, and refuted by empirical data like the lack of observable parallax of stars. Geocentrism is a pretty interesting historical example because of this: the Greeks reached the wrong conclusion with right arguments. Another example in the opposite direction: the Atomists were right about matter basically being divided up into very tiny discrete units moving in a void, but could you really say any of their armchair arguments about that were right?
It is not clear that the Greeks rejected heliocentrism at all, let alone any reason other than heresy. On the contrary, Hipparchus refused to choose, on the grounds of Galilean relativity.
The atomists got the atomic theory from the Brownian motion of dust in a beam of light. the same way that Einstein convinced the final holdouts thousands of years later.
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