This essay will survey various considerations that arise when a branch of physics requires formulation in terms of partial differential equations (or some facsimile thereof). My examples will derive almost exclusively from classical continuum (=smeared out matter) mechanics. Although the relevant formal facts are well known, it is difficult to find coherent discussions of how the underlying phenomena ought to be viewed. In this paper, I will give an introduction to some of the issues, although I will confess at the outset that I am not certain how these matters should be finally adjudicated. Certainly it would be helpful if philosophy paid more attention to the underlying issues.

Some of the points I will discuss bear upon some of Professor Sklar’s observations. Although my attention will be largely directed towards the status of boundary conditions (and related forms of singular surface), many of my examples can be adapted, mutatis mutandis, to initial conditions as well.