This paper describes an alternative to the common view that explanation in the special sciences involves subsumption under laws. According to this alternative, whether or not a generalization can be used to explain has to do with whether it is invariant rather than with whether it is lawful. A generalization is invariant if it is stable or robust in the sense that it would continue to hold under a relevant if it is stable or robust in the sense that it (...) would continue to hold under a relevant class of changes. Unlike lawfulness, invariance comes in degrees and has other features that are well suited to capture the characteristics of explanatory generalizations in the special sciences. For example, a generalization can be invariant even if it has exceptions or holds only over a limited spatio-temporal interval. The notion of invariance can be used to resolve a number of dilemmas that arise in standard treatments of explanatory generalizations in the special sciences. (shrink)

The robust behavior of the patent citation network is a complex target of recent bottom-up models in science. This paper investigates the purpose and testing of three especially simple bottom-up models of the citation count distribution observed in the patent citation network. The complex causal webs in the models generate weakly emergent patterns of behavior, and this explains both the need for empirical observation of computer simulations of the models and the epistemic harmlessness of the resulting epistemic opacity.