The logic in language: How all quantifiers are alike, but each quantifier is different

Abstract

Quantifier words like EACH, EVERY, ALL and THREE are among the most abstract words in language. Unlike nouns, verbs and adjectives, the meanings of quantifiers are not related to a referent out in the world. Rather, quantifiers specify what relationships hold between the sets of entities, events and properties denoted by other words. When two quantifiers are in the same clause, they create a systematic ambiguity. "Every kid climbed a tree" could mean that there was only one tree, climbed by all, or many different trees, one per climbing kid. In the present study, participants chose a picture to indicate their preferred reading of different ambiguous sentences -those containing EVERY, as well as the other three quantifiers. In Experiment 1, we found large systematic differences in preference, depending on the quantifier word. In Experiment 2, we then manipulated the choice of a particular reading of one sentence, and tested how this affected participants" reading preference on a subsequent target sentence. We found a priming effect for all quantifiers, but only when the prime and target sentences contained the same quantifier. For example, ALL-A sentences prime other ALL-A sentences, while EACH-A primes EACH-A, but sentences with EACH do not prime sentences with ALL or vice versa. In Experiment 3, we ask whether the lack of priming across quantifiers could be due to the two sentences sharing one fewer word. We find that changing the verb between the prime and target sentence does not reduce the priming effect. In Experiment 4, we discover one case where there is priming across quantifiers -when one number (e.g. THREE) is in the prime, and a different one (e.g. FOUR) is in the target. We discuss how these findings relate to linguistic theories of quantifier meaning and what they tell us about the division of labor between conceptual content and combinatorial semantics, as well as the mental representations of quantification and of the abstract logical structure of language.

The role of alternative salience in the derivation of scalar implicatures

“…Our response is to note that the priming effects we observed in Experiments 1 and 2 were extremely large and if a visual bias were to exist, we would have expected to observe priming effects of some degree in Experiment 3, even if they were smaller effects, but we observed nothing at all. Furthermore, other researchers using extremely similar paradigms (but with ambiguous sentences) also conclude that visual similarity alone cannot explain their priming effects (see Bott & Chemla, 2014;Feiman & Snedeker, 2016;and Raffray & Pickering, 2010).…”

Priming quantifier scope: Reexamining the evidence against scope inversion

“…Finally, scopal priming without predicate similarity has been found in another task. Feiman & Snedeker (2016) used more naturalistic sentences (e.g. Every boy climbed a tree) and manipulated whether the verbs in the prime and target were the same (e.g.…”

“…7 Critically, Feiman and Snedeker were able to rule out the possibility that priming in their task was based on visual similarity or checking strategies by showing that the priming effect disappeared if the prime and target mismatched on the quantifier (each vs. every vs. all), while the pictures stayed the same. Why wasn't the priming effect in Feiman and Snedeker (2016) based in checking strategies? We suspect that participants didn't need to rely on them.…”

Getting to No: Pragmatic and Semantic Factors in Two‐ and Three‐Year‐Olds' Understanding of Negation

“…Prior work with both adults and children has shown that the structure of one sentence affects how we process subsequent sentences. Specifically, constructing a particular syntactic structure or logical form appears to facilitate subsequent construction of the same form, even when the referents and lexical content changes (Bock, ; Feiman & Snedeker, ; Huttenlocher, Vasilyeva, & Shimpi, ; Raffray & Pickering, ; Thothathiri & Snedeker, ; see Pickering & Ferreira, for review). In the present study, the affirmative trials may have served as structural primes for the closely matched negatives.…”