Abstract

Do children understand how different numbers are related before they associate them with specific cardinalities?We explored how children rely on two abstract relations – contrast and entailment – to reason about the meaningsof ‘unknown’ number words. Previous studies argue that, because children give variable amounts when asked togive an unknown number, all unknown numbers begin with an existential meaning akin to some. In Experiment1, we tested an alternative hypothesis, that because numbers belong to a scale of contrasting alternatives,children assign them a meaning distinct from some. In the “Don’t Give-a-Number task”, children were shownthree kinds of fruit (apples, bananas, strawberries), and asked to not give either some or a number of one kind(e.g. Give everything, but not [some/five] bananas). While children tended to give zero bananas when asked to notgive some, they gave positive amounts when asked to not give numbers. This suggests that contrast – plusknowledge of a number’s membership in a count list – enables children to differentiate the meanings of unknownnumber words from the meaning of some. Experiment 2 tested whether children’s interpretation of unknownnumbers is further constrained by understanding numerical entailment relations – that if someone, e.g. has three,they thereby also have two, but if they do not have three, they also do not have four. On critical trials, childrensaw two characters with different quantities of fish, two apart (e.g. 2 vs. 4), and were asked about the number inbetween– who either has or doesn’t have, e.g. three. Children picked the larger quantity for the affirmative, andthe smaller for the negative prompts even when all the numbers were unknown, suggesting that they understoodthat, whatever three means, a larger quantity is more likely to contain that many, and a smaller quantity is morelikely not to. We conclude by discussing how contrast and entailment could help children scaffold the exactmeanings of unknown number words.