Now, the ancient people (many of them) used simple logic when they came up with the idea that the sun rotates around the Earth. They used their powers of observation, and logically concluded that the sun was moving around the Earth each day from east to west, and that was logically sensible...given their lack of further information or scientific instruments of observation. They did the best they were able to, using logic, given their limited powers of observation at the time and their limited technical education.

THEN it became a basic assumption and a matter of faith that the sun moved around the Earth. It was an incorrect assumption, but it had been arrived at using observation of natural phenomena and simple logic.

It required the development of much more advanced instruments and methods of observation to allow a more sophisticated and well-informed use of logic to supercede what had gone before. We now know that the Earth rotates around the Sun, and we know it again by using observation coupled with logic. And we have reached a new point of belief (commonly accepted knowledge) about it.

Most human belief is something that initially develops out of the use of someone's observation and logic. That doesn't mean that it's necessarily correct, but that's how a belief gets started: by observation and deduction. The observation may be inadequate. The deduction may prove faulty. The assumptions may prove incorrect.