The mind represents abstract magnitude information, including time, space, and number, but in what format is this information stored? We show support for the bipartite format of perceptual magnitudes, in which the measured value on a dimension is scaled to the dynamic range of the input, leading to a privileged status for values at the lowest and highest end of the range. In six experiments with college undergraduates, we show that observers are faster and more accurate to find the endpoints (i.e., the minimum and maximum) than any of the inner values, even as the number of items increases beyond visual short-term memory limits. Our results show that length, size, and number are represented in a dynamic format that allows for comparison-free sorting, with endpoints represented with an immediately accessible status, consistent with the bipartite model of perceptual magnitudes. We discuss the implications for theories of visual search and ensemble perception.

Odic, O., T. Knowlton, A. Wellwood, P. Pietroski, J. Lidz & J. Halberda. (2024). Observers efficiently extract the minimal and maximal element in perceptual magnitude sets: Evidence for a bipartite format. Psychological Science.

official link (open access)

A long-standing tension in semantic theory concerns the reconciliation of positive gradable adjective (GA) ascriptions and comparative GA ascriptions. Vagueness-based approaches derive the comparative from the positive, and face non-trivial challenges with incommensurability and non-GA comparatives. Classic degree-based approaches effectively derive the positive from the comparative, out of sync with the direction of evidence from morphology, and create some difficulties in accounting for GA scale-mates with differing thresholds (e.g., 'cold' ∼ 'warm' ∼ 'hot'). We propose a new reconciliation that capitalizes on recent proposals analyzing GAs as predicates of states. On our account, GAs lexically involve both a threshold property and a background state structure. Positive occurrences of GAs make use of the threshold property, while comparative occurrences make use of degrees representing elements of the background structure. Our approach preserves the virtues of classic degree-based approaches while offering a natural account of scale-mates, and without appeal to covert morphemes like POS or related devices. As we show, it is possible to inject our solution back into the classic degree-based approach, but we find reasons to prefer our states-based account.

Cariani, F., P. Santorio & A. Wellwood. (2023) Sinn und Bedeutung, 27, pp96-113.

official link (open access)

Jake Quilty-Dunn, Nicolos Porot, and Eric Mandelbaum’s Behavioral and Brain Sciences target article, “The Best Game in Town: The re-emergence of the language-of-thought hypothesis across the cognitive sciences”, focuses on evidence from nonlinguistic faculties to defend the claim that cognition generally traffics in language-of-thought (LoT)-type representations. This focus creates needed space to discuss the mounting accumulation of nonclassical evidence for LoT, but it also misses relevant work in linguistics that directly offers a perspective on specific hypotheses about candidate LoT representations.

Wellwood, A., and T. Hunter. (2023). Linguistic meanings in mind. Behavioral and Brain Sciences, 46.

publisher link

A prominent strand of theorizing in linguistics models meaning in language by specifying an "interpretation function" which relates morphosyntactic objects (i.e., those representations whose properties are uncovered by research in morphology and syntax) to elements of non-linguistic experience. Such theorizing has, for the most part, proceeded in relative isolation from developments in the other cognitive sciences. A recent body of experimental work growing out of this tradition has, however, pressed the question of precisely how linguistic representations relate to other faculties of mind. We present the beginnings of a two-step formal proposal for how to do this, specifying: (i) the co-domain of the linguistic interpretation function as the Language of Thought (LoT); (ii) what this mental language is like, (iii) which expression of this language is the semantic value of a sentence like 'Most of the dots are yellow', and (iv) how that LoT expression is interpreted by other cognitive faculties, in ways that produce the choices of verification procedure that have been empirically observed.

Hunter, T., and A. Wellwood. (2023). Linguistic meanings interpreted. Proceedings of the Annual Meeting of the Cognitive Science Society, 45, pp44-47.

official link (open access)

English-acquiring children before 4 years of age show a fine-grained understanding of how the meaning of more interacts with the lexical semantics of nouns: if the noun expresses a concept of objects, the comparison is based on number; if it expresses a concept of substance, it is based on volume or area. Is the meaning that children have acquired sufficiently general to support parallel semantic sensitivities when more combines with verbs? We probe this question with 4-5 year olds. Our expectation, based in semantic theory, is that more combined with an ‘event’ verb like jump should be quantified by number, but with a ‘process’ verb like walk it should be more flexible. Our Experiment 1 tests this with adults and Experiment 2 with children. We find children’s understanding to be broadly consistent with that of adults, providing initial support for an early-acquired, highly general meaning for more.

Wellwood, A. (2023). Children's understanding of verbal comparatives. Proceedings of the Annual Meeting of the Cognitive Science Society, 45, pp44-47.

official link (open access)

I ask what a small set of modification data requires of clausal event semantics. Classic Davidsonian semantics posits that modifiers like "in the hallway" express properties of events, and expects that iterations of such modifiers will simply contribute additional conjuncts at logical form. The data I consider challenges this view, and others cast in the Davidsonian spirit, at least so long as we hope to preserve an important and plausible semantic principle, Role Exhaustion (Williams 2015). As I show, preserving the principle and accounting for the facts can be accomplished by adopting two independently-motivated sets of claims: first, that verbs introduce existential closure over their event argument, and modifiers take verb meanings as semantic arguments (Champollion 2015); second, that simple clauses have two layers of event description, "framing" and "framed" (Schein 2016). In the end, I sketch two possible extensions of the approach, towards the interpretation of temporal modification and negative perceptual reports.

Wellwood, A. (2022). Framing events in the logic of adverbial modification. Semantics and Linguistic Theory (SALT) 32, 294-313.

official link (open access)

On standard analyses, indicative conditionals behave in a Boolean fashion when interacting with and and or. We test this prediction by investigating probability judgments about sentences of the form "If A, then B {and, or} if C, then D". Our findings are incompatible with a Boolean picture. This is challenging for standard analyses of ICs, as well as for several nonclassical analyses. Some trivalent theories, conversely, may account for the data.

Santorio, P. and A. Wellwood. (2023). Nonboolean conditionals. Experiments in Linguistic Meaning (ELM) 2.

official link (open access)

Some linguistic features are more readily learned than others, and are thereby more likely to be maintained in diachronic language change, giving rise to typological universals. Less readily learned features may give rise to typological gaps. We consider an apparent typological gap—that a morphologically superlative determiner (e.g., “gleebest” in “gleebest of the cows”) with a negative meaning is cross-linguistically unattested—and ask whether it reflects an underlying learning bias. We find 4-year-olds know that such determiners indicate quantity (replicating Wellwood, Gagliardi, & Lidz, 2016), but only when positive (‘most’), but not negative (‘least’). Importantly, the observed bias is not specific to the apparent typological gap: same-age children showed difficulty learning the negative meaning of a non-superlative determiner, though such meanings are attested. The data thus suggest that children are generally biased against negativity, consistent with much prior work on conceptual bias and language learning/processing.

He, A.X. and A. Wellwood. (2022). “Most” is easy but “least” is hard: Novel determiner learning in 4-year-olds. Proceedings of the annual meeting of the Cognitive Science Society.

official link (open access)

This paper investigates the semantics of implicit comparatives (Alice is tall compared to Bob) and its connections to the semantics of explicit comparatives (Alice is taller than Bob) and sentences with adjectives in plain positive form (Alice is tall). We consider evidence from two experiments that tested judgments about these three kinds of sentence, and provide a semantics for implicit comparatives from the perspective of degree semantics.

Castillo-Gamboa, J., A. Wellwood, and D. Rudin. (2021). Experiments in Linguistic Meaning 1.

official link (open access)

Natural languages like English connect pronunciations with meanings. Linguistic pronunciations can be described in ways that relate them to our motor system (e.g., to the movement of our lips and tongue). But how do linguistic meanings relate to our nonlinguistic cognitive systems? As a case study, we defend an explicit proposal about the meaning of most by comparing it to the closely related more: whereas more expresses a comparison between two independent subsets, most expresses a subset–superset comparison. Six experiments with adults and children demonstrate that these subtle differences between their meanings influence how participants organize and interrogate their visual world. In otherwise identical situations, changing the word from most to more affects preferences for picture–sentence matching (experiments 1–2), scene creation (experiments 3–4), memory for visual features (experiment 5), and accuracy on speeded truth judgments (experiment 6). These effects support the idea that the meanings of more and most are mental representations that provide detailed instructions to conceptual systems.

Knowlton, T., T. Hunter, D. Odic, A. Wellwood, J. Halberda, P. Pietroski, J. Lidz. (2021). Annals of the New York Academy of Sciences.

publisher link

In a degree semantics setting, comparative sentences express relations between degrees—formal objects representing extent along particular dimensions. Degrees and an ordering on them constitute 'scales', thought to be lexically specified by some adjectives (e.g., more intelligent) and adverbs (more quickly). Comparatives targeting nouns (more soup) and verbs (run more) work differently: here, scale selection depends in large part on the ontological implications of the NP or VP. Focusing on adverbial and verbal comparatives, we address three questions: (i) How well can speakers quantify and compare events (jump) versus activities (move) along different dimensions, as measured by their evaluation of adverbial comparatives?; (ii) To what extent does the event structure of a verb  determine the scale with bare more?; and, (iii) To what extent do features of the visual scene impact quantification when grammar leaves multiple dimensions open? Together, our four experimental studies show that speakers can easily quantify number, distance, and duration in dynamic scenes using more times, higher, and longer, and that dimensional selection for verbal more depends on the verb: given identical displays, our participants evaluated jump more (event verb) by number, but move more (activity verb) differently. So far, our results do not suggest that the dimension for move more depends on specific features of the visual scene. 

Farkas, H., and A. Wellwood. (2020). Quantifying events and activities. In P. Hallman (Ed.), Interactions of Degree and Quantification.

read pdf | publisher link

Contemporary research in compositional, truth-conditional semantics often takes judgments of the relative unacceptability of certain phrasal combinations as evidence for lexical semantics. For example, observing that completely full sounds perfectly natural whereas completely tall does not has been used to motivate a distinction whereby the lexical entry for full but not for tall specifies a scalar endpoint. So far, such inferences seem unobjectionable. In general, however, applying this methodology can lead to dubious conclusions. For example, observing that slightly bent is natural but slightly cheap is not (that is, not without a “too cheap” interpretation) leads researchers to suggest that the interpretation of bent involves a scalar minimum but cheap does not, contra intuition—after all, one would think that what is minimally cheap is (just) free. Such claims, found in sufficient abundance, raise the question of how we can support semantic theories that posit properties of entities that those entities appear to lack. This paper argues, using theories of adjectival scale structure as a test case, that the (un)acceptability data recruited in semantic explanations reveals properties of a two-stage system of semantic interpretation that can support divergences between our semantic and metaphysical intuitions.

Wellwood, A. (2020). Interpreting degree semantics. Frontiers in Psychology, 10.

official link (open access)

This book reimagines the compositional semantics of comparative sentences using words such as more, as, too, and others. The book's central thesis entails a rejection of a fundamental assumption of degree semantic frameworks: that gradable adjectives like tall lexicalize functions from individuals to degrees, i.e., measure functions.

I argue that comparative expressions in English themselves introduce “measure functions”; this is the case whether that morphology targets adjectives, as in taller or more intelligent; nouns, as in more coffee, more coffees; verbs, such as run more, jump more; or expressions of other categories. Furthermore, she suggests that expressions that comfortably and meaningfully appear in the comparative form should be distinguished from those that do not in terms of a general notion of "measurability": a measurable predicate has a domain of application with non-trivial structure. This notion unifies the independently motivated distinctions between, for example, gradable and non-gradable adjectives, mass and count nouns, singular and plural noun phrases, and telic and atelic verb phrases. Based on careful examination of the distribution of dimensions for comparison within the class of measurable predicates, I tie the selection of measure functions to the specific nature and structure of the domain entities targeted for measurement.

The book ultimately explores how, precisely, we should understand semantic theories that invoke the "nature" of domain entities: does the theory depend for its explanation on features of metaphysical reality, or something else? Such questions are especially pertinent in light of a growing body of research in cognitive science exploring the understanding and acquisition of comparative sentences.

Wellwood, A. (2019). The Meaning of More. Oxford, UK: Oxford University Press.

publisher site

Semantic theories predict that the dimension for comparison given a sentence like A gleebed more than B depends on what the verb gleeb means: if gleeb expresses a property of events, the evaluation should proceed by number; if it expresses a property of processes, any of distance, duration, or number should be available. An adequate test of theories like this requires first determining, independently of language, the conditions under which people will understand a novel verb to be true of a series of events or a single ongoing process. We investigate this prior question by studying people’s representation of two cues in simple visual scenes: a) whether some happening is interrupted by temporal pauses, and b) whether and how the speed of an object’s motion changes. We measured representation by probing people’s choice of verb in free-form descriptions of the scenes, and how they segment the scenes for the purposes of counting. We find evidence that both types of cues shape people’s representation of simple motions as events or processes, but in different ways.

A. Wellwood, A. X. He, and H. Farkas. (2019). Events and processes in language and mind. Baltic International Yearbook of Cognition, Logic and Communication, Vol. 13.

official link (open access)

I present a biased look at data relating to the form, meaning, understanding, and acquisition of comparative sentences with more. I highlight two major points: (i) comparatives provide a potentially unique case study for examining the interplay of current ideas in formal semantics, generative syntax, and cognitive psychology; (ii) we can give unified explanations for the otherwise disparate phenomena observed here only by interpreting our semantic theory along explicitly cognitive lines. The upshot is not so much a rejection of more traditional views as providing a window on their scientific limitations.

Wellwood, A. (2019). What more is. Philosophical Perspectives.

official link (open access)

Comparatives can invoke various dimensions for comparison, but not anything goes: more coffee invokes volume or weight, but not temperature, while more coffees invokes number, but not volume or weight. In general, the extant literature assumes that the difference between more coffee/coffees reflects a morphosyntactic ambiguity of more, such that it spells out MUCH-ER with bare nouns, and MANY-ER with plural nouns. Semantically, MUCH introduces a variable over measure functions, with constraints, whereas MANY introduces a cardinality function. I argue for an alternative, univocal theory based on the decomposition MUCH-ER, and account for the observed patterns of constrained variability by means of a stronger condition on the selection of measure functions than has previously been proposed.

Wellwood, A. (2018). Structure preservation in comparatives. Semantics and Linguistic Theory, 28.

official link (open access)

Comparative constructions like More people have been to Russia than I have are reported to be acceptable and meaningful by native speakers of English; yet, upon closer reflection, they are judged to be incoherent. This mismatch between initial perception and more considered judgment challenges the idea that we perceive sentences veridically, and interpret them fully. It is thus potentially revealing about the relationship between grammar and language processing. This paper presents the results of the first detailed investigation of these so-called 'comparative illusions'. We test four hypotheses about their source: a shallow syntactic parser, some type of repair by ellipsis, an incorrectly-resolved lexical ambiguity, or a persistent event comparison interpretation. Two formal acceptability studies show that speakers are most prone to the illusion when the matrix clause supports an event comparison reading. A verbatim recall task tests and finds evidence for such construals in speakers' recollections of the sentences. We suggest that this reflects speakers' entertaining an interpretation that is initially consistent with the sentence, but failing to notice when this interpretation becomes unavailable at the than-clause. In particular, semantic knowledge blinds people to an illicit operator-variable configuration in the syntax. Rather than illustrating processing in the absence of grammatical analysis, comparative illusions thus underscore the importance of syntactic and semantic rules in sentence processing.

Additional materials related to the published experiments and our preliminary experiments can be found on Github.

Wellwood, A., R. Pancheva, V. Hacquard, and C. Phillips. (2018). The anatomy of a comparative illusion. Journal of Semantics, 35(3).

read pdf | official link

Semanticists often assume an ontology for natural language that includes not only ordinary objects, but also events, as well as other entities. We link this ontology to how speakers represent static and dynamic entities. Specifically, we test how speakers determine whether an entity counts as "atomic" by using count vs. mass (e.g., some gleebs, some gleeb) and distributive vs. non-distributive descriptions (e.g., gleeb every second or so, gleeb around a little). We then seek evidence for atomic representation in a non-linguistic task. Ultimately we suggest that natural language ontology reveals properties of language-independent conceptualization.

Wellwood, A., S. J. Hespos, and L. Rips. (2018). How similar are objects and events? Acta Linguistica.

read pdf | official link

Beginning at least with Bach (1986), semanticists have suggested that the objects/events and substances/processes that nouns and verbs apply to are strongly parallel. We investigate whether these parallels can be understood to reflect a shared representational format in cognition, which in turn underlies aspects of the intuitive metaphysics of these categories. We hypothesized that a way of counting (atomicity) is necessary for object and event representations, unlike substance or process representations. Atomicity is strongly implied by plural language (some gorps, for novel gorp) but not mass language (some gorp). We investigate the language-perception interface across these domains using minimally different images and animations designed to encourage atomicity ('natural' spatial and temporal breaks), versus those that should not ('unnatural' breaks). Testing preference for matching such stimuli with mass or count syntax, our results support Bach’s analogy in perception, and highlight the formal role of atomicity in object and event representation.

Wellwood, A., S. J. Hespos, and L. Rips. (2018). The object : substance :: event : process analogy. In Oxford Studies in Experimental Philosophy, Volume 2, Oxford University Press.

read pdf | official link

Kotek et al. (2015) argue on the basis of novel experimental evidence that sentences like 'Most of the dots are blue' are ambiguous, i.e. have two distinct truth conditions. Kotek at al furthermore suggest that when their results are taken together with those of earlier work by Lidz et al. (2011), the overall picture that emerges casts doubt on the conclusions that Lidz et al. drew from their earlier results. We disagree with this characterization of the relationship between the two studies. Our main aim in this reply is to clarify the relationship as we see it. In our view, Kotek et al.'s central claims are simply logically independent of those of Lidz et al.: the former concern which truth condition(s) a certain kind of sentence has, while the latter concern the procedures that speakers choose for the purposes of determining whether a particular truth condition is satisfied in various scenes. The appearance of a conflict between the two studies stems from inattention to the distinction between questions about truth conditions and questions about verification procedures.

Hunter, T., J. Lidz, D. Odic, and A. Wellwood. (2017). On how verification tasks are related to verification procedures: a reply to Kotek et al. Natural Language Semantics, 25(2).

read pdf | official link