A Tale of Two Vectors

Why (according to classical physics) do forces compose according to the parallelogram of forces? This question has been controversial; it is one episode in a longstanding, fundamental dispute regarding which facts are not to be explained dynamically. If the parallelogram law is explained statically, then the laws of statics are separate from and (in an important sense) "transcend" the laws of dynamics. Alternatively, if the parallelogram law is explained dynamically, then statical laws become mere corollaries to the dynamical laws. I shall attempt to trace the history of this controversy in order to identify what it would be for one or the other of these rival views to be correct. I shall argue that various familiar accounts of natural law (Lewis's Best System Account, laws as contingent relations among universals, and scientific essentialism) not only make it difficult to see what the point of this dispute could have been, but also improperly foreclose some serious scientific options. I will sketch an alternative account of laws (including what their necessity amounts to and what it would be for certain laws to "transcend" others) that helps us to understand what this dispute was all about.