Only reasoning

Abstract

Four experiments were carried out to investigate how people reason with “only” as a quantifier. An assertion such as “only artists are beekeepers” has the same truth conditions as “all beekeepers are artists,” but we argue that it makes explicit both the relation between the two sets and the relation between their complements, i.e., an individual who is not an artist is not a beekeeper. Experiment 1 confirmed our expectation that this additional complexity would lead subjects to draw fewer logically correct conclusions from pairs of premises containing “only” than from equivalent pairs containing “all.” We outline a putative representation of “only” in terms of a theory of reasoning based on mental models. Experiment 2 confirmed this theory's predictions about the most frequent errors and the relative difficulty of different sorts of inferences from a premise containing “only” and another premise in a mood based on “all,” “some,” “no,” or “some—not.” Experiment 3 corroborated the prediction that modus tollens would occur more often with an “only” premise than with an “all” premise, because of the former's explicit representation of the negative relation. Experiment 4 showed that the presence or absence of a definite article in the quantified noun phrase, e.g., “only the artists are beekeepers” had no marked effect on the interpretation of premises.