The wisdom of "might": How children come to know what possibilities are

Abstract

Some representations have a special structure: a recursive structure. This structure is most easily seen in human languages. Some complete sentences have parts that are themselves complete sentences. For example, any English sentence can be embedded under a negation operator (“it is not the case that...”), a disjunction (“... or ...”), or a possibility modal (“Perhaps...”). Since the result of appending a logical operator to a sentence or set of sentences is a new, more complex sentence, the process can be repeated. This yields an infinite hierarchy of increasingly complex sentences. This hierarchy is important for logical inference: every valid inference involves a logical operator.

This infinite hierarchy is not unique to human languages. The mental representations that adults draw on when they generate and interpret these sentences must have the same expressive power. But it is an open question whether recursive operations structure the thoughts of nonlinguistic animals and prelinguistic humans. Descartes (1988) argued that animal thought has no such structure, and contem- porary philosophers like Donald Davidson (1982) have agreed. Jerry Fodor (1986) has offered reasons to think there are structured representations in nonlinguistic thought. But this question is not one to be settled by philosophy alone. We must undertake empirical studies to evaluate the differences between the thoughts of creatures with and without language. Developmental psychology offers useful avenues for developing these empirical methods: we can trace how behavior changes as a function of age of the acquisition of a recursively structured language. This problem can be broken up into case studies. This dissertation takes up the ontogenesis of possibility concepts, mental symbols that are expressed in English by words like ‘maybe’, ‘perhaps’, ‘might’, ‘can’, and so on. These words allow English speakers to coher- ently describe incompatible possibilities, to treat incompatible possibilities as equally good candidates for a single reality: It might rain today, and it might not. It’s incoherent to say that it will both rain and not rain, but there’s nothing incoherent about saying it might do both.

Possibility concepts also participate in logical inferences. There’s a good case to be made that nec- essarily x entails possibly x; contrapositively, the non-possibility of x, entails the non-necessity of x. Accepting this logical relationship has implications, for example, in moral philosophy: If it’s not possible for you to do something, you cannot be obligated to do that thing. This is a version of the dictum that ‘ought’ implies ‘can’.

How does the ability to deploy these concepts emerge over ontogenesis? This first paper of this dissertation describes a problem-solving situation where many 3-year-olds fail to deploy possibility concepts. Rather, they deploy a process that I call “minimal representation of possibility”. Faced with multiple open possibilities, they use simulation to establish one state that is possible, and take that possibility to be the fact of the matter. They represent a possibility in the minimal sense that the represented state is merely possible; it might turn out false. But they do not deploy a symbol that marks that state as merely possible, one member of a range of open candidates. The child does not distinguish this mere possibility from a necessity.

The second paper asks why children deploy minimal representations of possibility. It rules out three task-demand explanations for why they deploy this strategy. One of the open hypotheses is that children deploy minimal representations of possibility because they do not have possibility concepts to deploy.

The third paper turns around the question of the first two. The first two papers tested whether children could tell the difference between a mere possibility and a necessity. The third tests whether children can tell the difference between possibilities and impossibilities, and yields converging evidence. The emerging ability to contrast the possible with the impossible tracks the emerging ability to contrast the possible with the necessary.

Over the course of these studies, a developmental trajectory appears. No 2-year-olds, about 20% of 3-year-olds, and perhaps half of 4-year-olds deploy possibility concepts in their problem solving, even over substantial variation in the problems they must solve. Throughout the dissertation, the hypothesis that young children lack possibility concepts remains open. This leaves open the possibility that this logical operator is not available to nonlinguistic thought.