Galileo was not mor precise than Ptolemy. Actually the opposite. But Copernicus and Galileo had the imagination to infer the best physical model for the data.
In the long run it is not mathematical logic that makes for consensus in science. It is the ability to move research forward.
My, what a champion of inference and circumstantial evidence you seem to be, until it comes to inferences regarding how matter becomes organized and performs specific functions. Seems only certain types of inference and circumstantial evidence suit your fancy, namely those that suit your personal philosophy regarding objective reality.