83:2 April 2000
Philosophy of Applied Mathematics 

Advisory Editor: Penelope Maddy, Irvine

The philosophy of applied mathematics begins with the age-old problem of how mathematics comes to be so strikingly useful in science. Contemporary investigators address issues at various levels, from metaphysical debates to more focused questions about particular uses of mathematics. Examples of the former include debates over what the successful application of mathematics tells us about mathematical ontology, over the relations between various levels of mathematized science (e.g., between fundamental theory and engineering), over the nature of mathematical idealizations and over the question whether the apparent omnipresence of such idealizations pushes us inevitably toward some form of anti-realism in the philosophy of science. Examples of the latter include questions about the extent to which we can insist that our treatments of physical phenomena use only 'well-behaved' mathematical representations, about which applications of continuum mathematics are really 'smoothed out' versions of something else, about the meaning of differential equations at various types of 'boundaries', and about renormalization and related problems in classical and quantum theories. Both philosophers of mathematics and philosophers of science are invited to contribute papers that will open up new perspectives on these and other issues in the philosophy of applied mathematics.

Table of Contents:

Frank Arntzenius 

Are There Really Instantaneous Velocities?

Jody Azzouni 

Applying Mathematics: An Attempt to Design a Philosophical Problem

Robert W. Batterman 

A ‘Modern’ (= Victorian?) Attitude towards Scientific Understanding

Lawrence Sklar 

Topology versus Measure in Statistical Mechanics

Sheldon R. Smith 

Resolving Russell’s Anti-Realism about Causation: The Connection between Causation and the Functional Dependencies of Mathematical Physics

Mark Wilson 

The Unreasonable Uncooperativeness of Mathematics in the Physical Sciences