Statistical model selection criteria and the philosophical problem of underdetermination

I discuss the philosophical significance of the statistical model selection criteria, in particular their relevance for philosophical problems of underdetermination. I present an easily comprehensible account of their simplest possible application and contrast it with their application to curve-fitting problems. I embed philosophers' earlier discussion concerning the situations in which the criteria yield implausible results into a more general framework. Among other things, I discuss a difficulty which is related to the so-called subfamily problem, and I show that it has analogies in all legitimate applications of the model selection criteria, and that an analogy of Goodman's new riddle of induction can be formulated in only some of their applications.