A problem with this top-down approach to scientific theorizing is that it can run into conflict with experience. In the case of the conservation law, it was soon recognized that it is empirically false. What is conserved is not quantity of motion, but quantity of directed motion. This fact sank Descartes's clever attempt to inject mind into the physical world by having it merely deflect motions in the brain: this would violate the correct conservation law.
In contrast to the top-down approach, a bottom-up or inductive approach was championed by English philosophers. The approach consists of three steps:
The method just broadly sketched was also adopted by Sir Isaac Newton. He is perhaps most famous for promulgating universal gravitation, that all bodies of any mass attract each other with a force which is a function of the mass and the square of the distance. Newton is said to have been inspired by noticing the fall of an apple when the moon was in his line of sight. These two seemingly different cases exhibit the same pattern, namely, a falling toward the earth. This, the story goes, Newton generalized to all behavior of massive bodies, in the heavens and on earth.
We now think of Newton's generalization as one of the great achievements in the history of science, but in his day, Newton was reviled for having perpetuated a fraud. (Leibniz was one of his most bitter critics.) His critics asked the same sort of question Socrates asked of Euthyphro. If bodies really attract one another, what is it that makes them do so? Failure to answer the question betrays ignorance about what attraction is. If you answer that it is a force, the critics respond that this is no more than to say that bodies attract one another, i.e., to say nothing more. One of the most significant philosophical breakthroughs made by Newton was to convince people that attraction exists, whether he could explain it or not. In fact he could not give the sort of explanation the critics called for (in terms of impact), lamented the fact, and asserted that attraction is proved to exist anyway.
John Locke set about to show in a general way how our knowledge is based on experience. However, he did not get as far as one would like, and he ended up being a limited skeptic. Locke passed over the rationalistic claims of Descartes. He believed that we do not have the kind of rational insight Descartes had claimed, because what is in our mind is only what has come into it as sense impressions. So the role of reason is restricted to manipulation of sensory data, and this does not take us very far.
Generally, Locke was concerned about the ability of the senses to penetrate into the nature of things. He thought them to be very crude, so that even with the aid of instruments, they could provide only limited information about the nature of objects. Having adopted the philosophy of atomism (which claims that material objects are swarms of tiny atoms), he thought that the fundamental particles and processes are out of our reach. Further, he held that we know nothing of what our senses are not currently perceiving or have perceived before.
One would think that this largely negative result would be a low point for empiricism, but it was to be dealt a still heavier blow by David Hume. Hume finished the job of undermining the reliability of the senses and reason. So great was the damage, that Hume found himself in despair. He likened himself to a monster, unfit for human companionship. Then he decided not to take it so hard, and to go ahead and do philosophy in a loose and casual manner.