The quality of philosophical diagnosis within the philosophy of science will be greatly improved if the original distinctions of applied mathematics are employed instead of the inadequate substitutes provided by the logical empiricists. The problem of evaluating counterfactual claims is examined from this point of view.

The concept of emergence is commonly invoked in modern physics but rarely defined. Building on recent influential work by Jeremy Butterfield, I provide precise definitions of emergence concepts as they pertain to properties represented in models, applying them to some basic examples from space-time and thermostatistical physics. The chief formal innovation I employ, similarity structure, consists in a structured set of similarity relations among those models under analysis—and their properties—and is a generalization of topological structure. Although motivated from physics, this (...) similarity-structure-based account of emergence applies to any science that represents its possibilia with models. (shrink)