"But then Galileo made the troubling discovery that the heavier stone does not fall any faster than the lighter one."<p>It does fall faster, if you drop both stones in the atmosphere; the heavier stone has more mass per unit of surface area, to better overcome a constant level of air resistance.<p>Aristotle's physics were based on pretty accurate observation of the pre-industrial world, although they're surprisingly short on first principles. The really serious shortcomings were mostly related to impetus, the Aristotelian theory of motion -- it accidentally models friction well for objects in continuous contact with the ground, but it's very hard for Aristotelian physics to explain why an arrow keeps flying after it leaves the bowstring, and even gains speed after its apogee.