Maryland in Philosopher's Annual top ten of 2023

Psychological evidence for restricted quantification.

The Philosopher's Annual has selected its ten best articles in philosophy from 2023, and among them is one by a team of our local philosophers and linguists, including Paul and Alexander: "Psychological evidence for restricted quantification," by Tyler Knowlton, Paul Pietroski, Alexander Williams, Justin Halberda and Jeff Lidz. The paper argues that we do not understand every as it is represented in the currently standard semantics, as a relation between the Fs and either the Gs or the FGs (that is, the Gs among the Fs). Rather we understand it as a unary quantifier over the Gs, restricted to the Fs, a view with ancient precedents. The evidence comes from a suite of studies suggesting that, when asked to evaluate sentences of the form every F is G, participants mentally group the Fs, but group neither the Gs nor the FGs. The complete abstract is below.

Knowlton was an undergraduate student with Halberda at Johns Hopkins. He then came to College Park to work with Pietroski and Lidz in Linguistics, joining Alexander, Valentine Hacquard and others on various projects in semantics, language acquisition and psycholinguistics. His 2021 dissertation was The Psycho-Logic of Universal Quantifiers. Currently he is a MindCORE Postdoctoral Research Fellow at the University of Pennsylvania.

Psychological evidence for restricted quantification

Quantificational determiners are often said to be devices for expressing relations. For example, the meaning of every is standardly described as the inclusion relation, with a sentence like every frog is green meaning roughly that the green things include the frogs. Here, we consider an older, non-relational alternative: determiners are tools for creating restricted quantifiers. On this view, determiners specify how many elements of a restricted domain (e.g., the frogs) satisfy a given condition (e.g., being green). One important difference concerns how the determiner treats its two grammatical arguments. On the relational view, the arguments are on a logical par as independent terms that specify the two relata. But on the restricted view, the arguments play distinct logical roles: specifying the limited domain versus supplying an additional condition on domain entities. We present psycholinguistic evidence suggesting that the restricted view better describes what speakers know when they know the meaning of a determiner. In particular, we find that when asked to evaluate sentences of the form every F is G, participants mentally group the Fs but not the Gs. Moreover, participants forego representing the group defined by the intersection of F and G. This tells against the idea that speakers understand every F is G as implying that the Fs bear a relation (e.g., inclusion) to a second group.