This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on (...) to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation. (shrink)

According to the "experimenter's regress", disputes about the validity of experimental results cannot be closed by objective facts because no conclusive criteria other than the outcome of the experiment itself exist for deciding whether the experimental apparatus was functioning properly or not. Given the frequent characterization of simulations as "computer experiments", one might worry that an analogous regress arises for computer simulations. The present paper analyzes the most likely scenarios where one might expect such a "simulationist's regress" to surface, and, (...) in doing so, discusses analogies and disanalogies between simulation and experimentation. I conclude that, on a properly broadened understanding of robustness, the practice of simulating mathematical models can be seen to have sufficient internal structure to avoid any special susceptibility to regress-like situations. (shrink)