Revisiting Wittgenstein’s puzzle: hierarchical encoding and comparison facilitate learning of probabilistic relational categories

Kittur et al. (2004, 2006) and Jung and Hummel (2011, 2014) showed that people have great difficulty learning relation-based categories with a probabilistic (i.e., family resemblance) structure, in which no single relation is shared by all members of a category. Yet acquisition of such categories is not strictly impossible: in all these studies, roughly half the participants eventually learned to criterion. What are these participants doing that the other half are not? We hypothesized that successful participants were those who divided the nominal categories into two or more sub-categories, each of which individually had a deterministic structure. We report three experiments testing this hypothesis: explicitly presenting participants with hierarchical (category and sub-category) structures facilitated the acquisition of otherwise probabilistic relational categories, but only when participants learned the subordinate-level (i.e., deterministic) categories prior to learning the nominal (i.e., probabilistic) categories and only when they were permitted to view multiple exemplars of the same category simultaneously. These findings suggest that one way to learn natural relational categories with a probabilistic structure [e.g., Wittgenstein's (1953), category game, or even mother] is by learning deterministic subordinate-level concepts first and connecting them together under a common concept or label. They also add to the literature suggesting that comparison of multiple exemplars plays an instrumental role in relational learning.