Sonia Ramotowska

Theories of counterfactuals agree on the use of a comparative similarity relation, but disagree about the quantificational force of counterfactual modals. This study reports findings from two experiments designed to evaluate the predictions of three prominent approaches: universal theories, homogeneity theories, and single-world selection theories (supplemented with supervaluations over selection functions). To differentiate the predictions of these theories, we examined counterfactual sentences embedded under various quantifiers and elicited graded truth-value judgments from speakers. The results provide empirical support for selection-based theories, while posing challenges to universal and homogeneity approaches. Additionally, we argue that a more recent implicature-based theory also fails to align with our findings. We discuss the broader implications of these results, including the similarities and differences between counterfactuals and plural definites. EARLY ACCESS

Plain disjunctive sentences, such as The mystery box contains a blue ball or a yellow ball, typically imply that the speaker does not know which of the two disjuncts is true. This is known as an ignorance inference. We can distinguish between two aspects of this inference: the negated universal upper bound part (i.e., the speaker is uncertain about each disjunct), which we call uncertainty, and the existential lower bound part (i.e., the speaker considers each disjunct possible), which we call possibility. In the traditional approach, uncertainty is derived as a primary implicature, from which possibility follows. In this paper, we report on two experiments using a sentence-picture verification task based on the mystery box paradigm that challenge the traditional implicature approach. Our findings show that possibility can arise without uncertainty, and we thus call for a reevaluation of the traditional view of disjunction and ignorance inferences. Our experimental findings are related to similar results involving disjunction in embedded contexts and pave the way for alternative theories that can account for the observed patterns of inference derivation in a unified fashion. We discuss how recent implicature and non-implicature theories can account for the derivation of existential lower bound inferences without the presence of negated universal upper bound inferences.

In this paper, we investigate, by means of a computational model, how individuals map quantifiers onto numbers and how they order quantifiers on a mental line. We selected five English quantifiers (few, fewer than half, many, more than half, and most) which differ in truth conditions and vagueness. We collected binary truth value judgment data in an online quantifier verification experiment. Using a Bayesian three-parameter logistic regression model, we separated three sources of individual differences: truth condition, vagueness, and response error. Clustering on one of the model’s parameter that corresponds to truth conditions revealed four subgroups of participants with different quantifier-to-number mappings and different ranges of the mental line of quantifiers. Our findings suggest multiple sources of individual differences in semantic representations of quantifiers and support a conceptual distinction between different types of imprecision in quantifier meanings. We discuss the consequence of our findings for the main theoretical approaches to quantifiers: the bivalent truth-conditional approach and the fuzzy logic approach. We argue that the former approach neither can explain inter-individual differences nor intra-individual differences in truth conditions of vague quantifiers. The latter approach requires further specification to fully account for individual differences demonstrated in this study.