At least since Aristotle's Posterior analytics, mathematics has been the model of science, in which everything should be deduced from self-evident axioms and definitions. Indeed, mathematics was quite long considerably more advanced and certain than any other field of research. It is then no wonder that Descartes tried to fit physics and especially mechanics into this model. Even more, he suggested that basic laws of mechanics could be derived from mere geometrical considerations: after all, matter was defined by extension, so the characteristics of the motion of matter should be reducible to the extensional characteristics of matter, such as size and velocity.
What Descartes had failed to take into consideration was that the nature of matter is not exhausted by its extension and that it cannot be identified with mere space. Thus, one had to take into account also the mass of bodies, when considering e.g. how two bodies behaved in a collision. Recognizing this made it a necessity to empirically observe the actual movement of bodies and to look for regularities that could be generalized from these observations. Inconsistently, such studies were still often called mathematical and even a semblance of mathematical deduction was upheld.
Followers of Leibniz in Germany were more aware of the inability to reduce physics to mathematics. Hence, we see Christian Wolff admitting that his cosmological considerations had an empirical basis and that reliable experiences in general must supplement the inabilities of human understanding. In light of the empiricist tendencies of Wolff, it is interesting to see that Bilfinger supposed that it might be possible to derive basic laws of physics apriorically. I do not think Bilfinger is necessarily going against Wolff, but merely explicating the Wolffian position from a different angle: true, in practice we must use empirical method, but in principle we should be able to use deduction.
Bilfinger still doesn't advocate a return to supposedly geometrical demonstrations of Descartes. Instead, he supposes laws of physics should be derived from metaphysics. In other words, Bilfinger doesn't want to state that physical laws would be necessary like laws of logic and mathematics. Instead, they are based ultimately on the decision of God. According to the Wolffian position, God has created the best out of all the possible worlds. Hence, all the laws that the world follows must also be as perfect as they could be – and if we knew what is objectively best, we could know the laws chosen by God.
What Bilfinger's position makes clear is the contingency of physical laws. Specifically, the creator of the laws still holds the power to suspend these laws for a limited period and place. In common parlance such local suspensions of laws are called miracles. In effect, Bilfinger is saying that miracles are possible and that God has power to make them – another defense of Wolff against suggestions of atheism.
So much for physical laws, next time I shall deal with the difference between intuitive and symbolic cognition.