Quantifiers and Psycholinguistic Teamwork

Not long after Jeff Lidz joined the linguistics department at the University of Maryland, back in 2005, he introduced me to Justin Halberda. The three of us started talking about meaning, concepts, representations of number(s), quantification, lexical acquisition, vision, Paris, food, and so on. Over the years, we convinced a series of terrific young colleagues to join us and do the real work that is required to convert lab meetings into published papers. Here is a series of papers--with the most recent work at the top--that emerged as we went along.

Linguistic Meanings As Cognitive Instructions.
Authors: Tyler Knowlton, Tim Hunter, Darko Odic, Alexis Wellwood, Jeff Lidz, Paul Pietroski, and Justin Halberda
(Annals of the New York Academy of Sciences, 2021, early version published online.)
The sentences Most of the dots are blue and More of the dots are blue are equivalent as descriptions of scenes in which all the non-blue dots are the same color (e.g., red). But across a range of experimental settings--involving picture-sentence matching, scene creation, memory for visual features, and accuracy on judgments of truth/falsity under time pressure--the more/most contrast has significant effects, in ways which suggest that the meanings of more and most are mental representations that provide (different) detailed instructions to conceptual systems.
The Mental Representation Of Universal Quantifiers.
Authors: Tyler Knowlton, Paul Pietroski, Justin Halberda, and Jeff Lidz
(forthcoming in Linguistics and Philosophy)
The sentences Each of the dots is blue and Every one of the dots is blue and All of the dots are blue illustrate distinct ways of expressing universal generalizations. But do the meanings of the words for universal quantification differ? And if so, is the difference between first-order and second-order quantification relevant? Answers: yes and yes.

Individuals and Non-Individuals in Cognition and Semantics: the Mass/Count Distinction and Quantity Representation.
Authors: Darko Odic, Paul Pietroski, Tim Hunter, Jeff Lidz, and Justin Halberda
(Glossa 3:1-20, 2018.)
The sentences Most of the dots are blue and Most of the paint is blue differ significantly: dots is a plural count noun, while paint is a "mass" noun. It can be tempting to think that count-nouns are somehow how more basic, semantically, and that mass-nous involve some extra layer of complexity. But we find evidence that pushes in the other direction.

Young Children's Understanding of 'more' and Discrimination of Number and Surface Area.
Authors: Darko Odic, Paul Pietroski, Tim Hunter, Jeff Lidz, and Justin Halberda
(Journal of Experimental Psychology: Learning, Memory, and Cognition 39: 451-461, 2013.)

Interface Transparency and the Psychosemantics of most: Jeff Lidz, Paul Pietroski, Tim Hunter, and Justin Halberda
(Natural Language Semantics, 19: 227-56, 2011).
This paper extends the initial results obtained in the paper listed below. Here, we offer experimental evidence that adult speakers of English understand sentences like 'Most of the dots are blue' in a quite specific way that involves representing the cardinality of the blue dots, the cardinality of the dots, and subtracting the former from the latter--as opposed to, say, representing the cardinalities of the blue dots and the nonblue dots (as such). We also argue that this finding, together with independent studies of the visual system, provides some empirical support for a more general view about how meaningful expressions generated by the language faculty interface with other cognitive systems.

The Meaning of 'Most': semantics, numerosity, and psychology: Paul Pietroski, Jeff Lidz, Justin Halberda, and Tim Hunter
(Mind and Language, 24:554-85, 2009). The title is descriptive. We offer experimental evidence in support of a certain view about how the meaning of the English determiner 'most' is related to various psychological capacities potentially relevant to human capacities for counting and quantifying. In this first installment of an ongoing project, we offer experimental evidence that adult speakers of English do indeed understand sentences like 'Most of the dots are blue' in terms of cardinality comparison (as opposed to, say, one-to-one correspondence). We also make some tentative suggestions about how the meaning of 'most' is related to potential verification procedures and the "analog magnitude system" that humans share with other animals.

Seeing What you Mean, Mostly.
Authors: Paul Pietroski, Jeff Lidz, Justin Halberda, Tim Hunter, and Darko Odic
(Syntax and Semantics: Experiments at the Interfaces, edited by J. Runner, 37:187-224, 2011).
Another paper in the same vein, stressing that while our proposal is not a form of verificationism, meanings are related to verification strategies in empirically testable ways--at least with regard to "logical" vocabulary.