Abstract

I examine the prospects for extending Hartry Field's instrumental account of how mathematics is applied in physical theories by looking at obstacles to extending his account beyond classical field theories and into the realms of classical particle mechanics and classical equilibrium statistical mechanics . ;I first define a broader notion of intrinsic formulation than that Field uses in Science Without Numbers; based on this definition and some work of Brent Mundy in measurement theory, I provide a definition of the intrinsic content of a physical theory. I then argue that serious obstacles to extending Field's account to CPM and CESM arise. Most of these obstacles arise in the fundamental mathematical frameworks used in these theories, namely, configuration spaces, phase spaces and probability distributions defined on phase spaces. A further obstacle arises in a kind of approximation used in some derivations, in particular, a derivation of the Maxwell-Boltzmann distribution law used in CESM. ;I claim these obstacles have a common source, a serious flaw in Field's account: to apply Field's account to a physical theory T it must be the case that, without any coding, some of the mathematical structures used in T be physically exemplified in the subject matter of T. In many cases, however, these structures will be too rich. Using this analysis of why the obstacles to Field's account arise, I close by tentatively sketching ideas for alternative accounts of applied mathematics