Laws and Explanations; Theories and Modal Possibilities

The book has two parts: In the first, after a review of some seminal classical accounts of laws and explanations, a new account is proposed for distinguishing between laws and accidental generalizations (LAG). Among the new consequences of this proposal it is proved that any explanation of a contingent generalization shows that the generalization is not accidental. The second part involves  physical  theories, their modality, and their explanatory power. In particular, it is shown that (1) Each theory has a theoretical implication structure associated with it, such that there are new  physical  modal operators  on  these structures and also special modal entities that are  in  these structures. A special subset of the physical modals, the  nomic  modals are associated with the laws of theories. (2) The familiar idea that theories always explain laws by deduction of them has to be seriously modified in light of the fact that there are a host of physical theories (including for example, Newtonian Classical mechanics, Hamiltonian, and Lagrangian theory, and probability theory) that we believe are  schematic  (they do not have any truth value). Nevertheless, we think that there is a kind of non-deductive explanation and generality that they achieve by subsumtion under a schema.