The Combinatorics of Falsification and Hypothesis Testing

Reid Dale

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arXiv · 2209.12066

The Combinatorics of Falsification and Hypothesis Testing

Reid Dale

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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.

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Reid Dale. 2022-09-24. The Combinatorics of Falsification and Hypothesis Testing. https://arxiv.org/abs/2209.12066

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