Nonsense and Sensibility: Inferring Unseen Possibilities

How do we distinguish the sensible yet unlikely (blue bananas) from the nonsensical (hour-long bananas), given observations only of what is true in the world (e.g., yellow bananas)? Judgments like these may be supported by the M constraint: the assumption that ontological categories are organized into a predicability tree, and that properties apply to different subtrees within this hierarchy. We provide a computational theory that shows how the M constraint can be used to acquire predicability trees given observations only of what is true. We also suggest how the M constraint itself could be learned. A friend comes home from the market exclaiming that she has just seen the most interesting banana. She tells you to guess what was so interesting about it. Which of the following questions are you most likely to ask? “Was the banana blue?” “Was the banana the shopkeeper’s fault?” “Was the banana an hour long?” Probably you are more likely to ask the first question. You may never have seen or heard of a blue banana before, but it seems like one might exist somewhere, and such a banana would indeed be noteworthy. The other two questions, on the other hand, do not make sense. Bananas are not the kind of thing that can be someone’s fault or an hour long. How can we judge so quickly that it is far more sensible for bananas to be blue than an hour long, when we have seen no direct evidence in the world regarding either blue or hour-long bananas? We may never have seen a blue banana, but we have seen many other blue things—blueberries, bicycles, and bedspreads, for example—which share many properties with bananas. They are all visible objects, and we can touch them, move them, or give them to our friends. If these objects can sensibly be blue, then perhaps it would be sensible for bananas to be blue as well. None of the other blue objects is an hour long, however, which might make us more doubtful that bananas could sensibly have this property. Kinds such as physical objects and events are examples of ontological categories. The properties that apply to the members of the ontological categories (“blue,” “hour long”) are also known as predicates. When a predicate can sensibly be applied to an object, and a truth value can be assigned (“Bananas are usually blue” is sensible, though false), that predicate is said to span the object (Keil, 1979). Predicates do not appear to span objects arbitrarily. Instead, predicates seem to cluster together and apply to whole categories of objects. In addition, these categories do not overlap arbitrarily, but also seem to follow structural rules. Sommers (1971) proposed “the M constraint”: categories of objects are organized in a strict hierarchy, and predicates must span subtrees of the hierarchy (thus preventing any “Ms” within the tree). See Figure 1 for an example of such a predicability tree, and how it governs the set of pairs which are sensible together, which in turn governs which pairs may be true. This hierarchical constraint could be extremely useful in making inferences about what is sensible based on limited evidence. If we know that soccer games cannot sensibly be blue but can be an hour long, and bicycles can be blue but cannot sensibly be an hour long, then according to the M constraint, bananas cannot sensibly have both properties. Knowing this, all we need to do to make a quick inference is figure out whether bananas are more like bicycles or soccer games. Observations that bananas and bicycles can both be yellow and green, as well as sharing other properties, can help us infer that bananas could sensibly be blue, but not an hour long. Keil (1979) provided some evidence that people do follow the M constraint in reasoning about the world. When asked to judge which statements about predicateobject pairs were sensible, adults provided sets of answers which showed a strict hierarchical organization. This was true for children as well, though their predicability trees were far simpler than those of adults. Keil also showed that children can make quick inferences based on hierarchical relationships of categories and predicates. Most interestingly, Keil proposed that the M constraint is a part of the innate core knowledge that guides children in learning about the world. If the M constraint (or a weaker statistical bias) does exist as a psychological reality, how could we use it to learn what is sensible? We propose a formal model that incorporates the M constraint and can discover a predicability tree given limited evidence about what is true in the world. Our model takes the M constraint as given; however, we also describe how Bayesian model selection can be used to infer that a model with the M constraint accounts better for the observed data than an alternative model with no hierarchical constraint. We therefore suggest that the M constraint need not be innate. A Structured Approach to Sensibility Assume that we are working with a fixed collection of objects and predicates. We develop a computational theory that assumes that the objects and predicates are