The Combinatorics of Falsification and Hypothesis Testing

Abstract: The present paper is concerned with the question of how falsifiable a single proposition is in the short and long run. Formal Learning theorists such as Schulte and Juhl have argued that long-run falsifiability is characterized by the topological notion of nowhere density in a suitable topological space. I argue that the short-run falsifiability of a hypothesis is in turn characterized by the VC finiteness of the hypothesis. Crucially, VC finite hypotheses correspond precisely to definable sets in NIP structures. I end the chapter by giving rigorous foundations for Mayo's conception of severe testing by way of a combinatorial, non-probabilistic notion of surprise. VC finite hypotheses again appear as the hypotheses with guaranteed short-run surprise bounds. Therefore, NIP theories and VC finite hypotheses capture the notion of short-run falsifiability.