Sampling for possibilities

This paper views empirical research as a search for illustrations of interesting possibilities which have occurred, and the exploration of the variety of such possibilities in a sample or universe. This leads to a definition of "illustrative inference" (in contrast to statistical inference), which, we argue, is of considerable importance in many fields of inquiry – ranging from market research and qualitative research in social science, to cosmology. Sometimes, it may be helpful to model illustrative inference quantitatively, so that the size of a sample can be linked to its power (for illustrating possibilities): we outline one model based on probability theory, and another based on a resampling technique.