Contrast and entailment: Abstract logical relations constrain how 2- and 3-year-old children interpret unknown numbers

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 meanings of 'unknown' number words. Previous studies argue that, because children give variable amounts when asked to give an unknown number, all unknown numbers begin with an existential meaning akin to some. In Experiment 1, 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 shown three 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 not give some, they gave positive amounts when asked to not give numbers. This suggests that contrast -plus knowledge of a number's membership in a count list -enables children to differentiate the meanings of unknown number words from the meaning of some. Experiment 2 tested whether children's interpretation of unknown numbers 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, children saw two characters with different quantities of fish, two apart (e.g. 2 vs. 4), and were asked about the number in-between -who either has or doesn't have, e.g. three. Children picked the larger quantity for the affirmative, and the smaller for the negative prompts even when all the numbers were unknown, suggesting that they understood that, whatever three means, a larger quantity is more likely to contain that many, and a smaller quantity is more likely not to. We conclude by discussing how contrast and entailment could help children scaffold their exact meanings of unknown number words.

Priming reveals similarities and differences between three purported cases of implicature: Some, number and free choice disjunctions

“…Children first learn number words in a fixed, ascending order by rote memorizing the count list like a nursery rhyme, creating associations between the sounds of different number words before they know any of their meanings (Wynn, 1990;Carey, 2009). When they later begin to learn numerical meanings, they start with intuitions about how the meanings of unknown number words relate to each other (Feiman et al, 2019), and rely on the meanings of smaller number words that they learn first to understand the meanings of words higher in the count list (Barner, 2017;Barner & Bachrach, 2010). Thus, on multiple accounts, access to numerical alternatives is necessary to construct numerical meanings.…”

Priming Reveals Similarities and Differences between Three Purported Cases of Implicature: Some, Number and Free Choice Disjunctions

“…Children first learn number words in a fixed, ascending order by rote memorizing the count list like a nursery rhyme, creating associations between the sounds of different number words before they know any of their meanings (Wynn, 1990;Carey, 2009). When they later begin to learn numerical meanings, they start with intuitions about how the meanings of unknown number words relate to each other (Feiman et al, 2019), and rely on the meanings of smaller number words that they learn first to understand the meanings of words higher in the count list (Barner, 2017;Barner & Bachrach, 2010). Thus, on multiple accounts, access to numerical alternatives is necessary to construct numerical meanings.…”