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Unpacking Paradigmatic Gaps (UNPAG) is a project that aims to investigate paradigmatic gaps in expressions referring to individuals, times, and possible worlds, from a theoretical, experimental and typological perspective. The project is funded by an Advanced Grant awarded by the European Research Council to Professor Hedde Zeijlstra, in 2024. UNPAG is hosted by the English Department of the University of Göttingen.
The project can be found here.
Why can't we always say what we can think?
Why can't we always say what we can think?
Universal paradigmatic gaps are gaps in linguistic paradigms that appear across languages and across users of a given language. Up to now, only very few gaps of this kind have been discussed in the literature. The one gap that has received substantial discussion concerns the universal absence of a lexicalized negated form for the quantifiers all, every or always: There appears to be no language in the world that exhibits a single word (or lexical item) that means ‘not all’, ‘not every’ or ‘not always’. UNPAG will show that the landscape of universal paradigmatic gaps is in fact much richer and more varied than generally thought of.
It is deeply enigmatic that such words do not exist across languages and cultures. Any theory seeking to explain such missing lexicalizations, i.e. any theory of universal paradigmatic gaps, should be able to make clear predictions about what may or may not be lexicalized, and why that is the case. Such a theory has thus far not been developed. Such a theory should have a broad empirical foundation. However, to date, the pool of data has been heavily slanted toward well-studied, Western, Indo-European, adult spoken language, and negative quantifiers therein. No existing study has thus far come even close to targeting a richer empirical base.
Understanding the nature, distribution and behavior of universal paradigmatic gaps will have several profound implications for our understanding of human cognition, language and communication.
The pillars of the project
The pillars of the project
UNPAG consists in four pillars, which correspond to different empirical domains in which paradigmatic gaps have been attested.
Pillar 1
Negated Universal Quantifiers
Pillar 1
Negated Universal Quantifiers
Horn (1972, a.o.) famously observed that the absence of a word like nall, meaning ‘not all’, is part of a broader systematic absence of words with a particular logical footprint: words like noth (meaning 'not both'), or nand (meaning 'not and') also seem to be missing in the world's languages. However, Kuhn & Pasalskaya (2023) have recently argued that French Sign Language has a simplex sign for unnecessary, which suggests that the nall gap may not be as systematic as previously thought.
UNPAG will develop the hypothesis that negated universal quantifiers are rare, but not ruled out by the grammar. Instead, their meaning is so weak that it makes them poor candidates for lexicalization. This hypothesis will be investigated through extensive typological and experimental work.
Pillar 2
Existential NPIs and universal PPIs
Pillar 2
Existential NPIs and universal PPIs
Paradigmatic gaps can also be attested in the domain of Polarity-Sensitive Items (PSIs): there seems to be no language with a word like every that is either a Negative Polarity Item (NPI) or a Positive Polarity Item (PPI).
In order to understand these gaps, we first need to understand what renders some element an NPI or a PPI. According to many theories (Chierchia 2013, a.m.o.), NPIs are elements that obligatorily introduce subdomain alternatives, which must be exhaustified. Assigning this treatment of NPIs to universal quantifiers would render these items universal PPIs.
UNPAG will adopt the hypothesis that such universal PPIs do in fact exist, but are harder to identify than existential NPIs.
Pillar 3
Existential PPIs and universal NPIs
Pillar 3
Existential PPIs and universal NPIs
This pillar follows the same rationale as Pillar 2: theories that can explain the behavior of existential PPIs should also be applicable to universal NPIs.
In particular, the view developed by Zeijlstra (2022) for existential PPIs argues that certain quantifiers are lexically encoded with an (arguably presuppositional) condition that they cannot entail the non-existence of referents satisfying their description. Kamali & Zeijlstra (2023) extend this view to universal NPIs. Their theory predicts that such items should be licensed in positive sentences, but, when in negative contexts, have to take scope below negation. Kamali & Zeijlstra (2023) show that Turkish universal quantifiers do in fact exhibit this semantic footprint.
UNPAG will considerably extend this empirical domain by investigating the scopal behavior of both existential and universal quantifiers across a number of typologically distinct languages.
Pillar 4
Strong and weak neg-raising modals
Pillar 4
Strong and weak neg-raising modals
Universal modals come in two varieties: strong necessity (e.g.: have to, must) and weak necessity (e.g.: should, ought). Existential modals, however, seem to invariably express strong possibility. That is, despite their morphological similarity to weak necessity modals, could and might do not express weak possibility. One of the goals of UNPAG is to investigate to which extent the absence of weak possibility modals is cross-linguistic robust, and which factors contribute to this state-of-affairs.
Another goal of this pillar is to examine paradigmatic gaps in the domain of neg-raising predicates. There seems to be a correlation between modal strength and neg-raising: only weak necessity modals give rise to neg-raising inferences; strong necessity modals do not. Similarly, Newkirk (2022) observes that, in Kinande, possiblity modals can be strengthened into necessity modals, but only weak ones. Is this pattern replicable in other languages? And what explains this pattern?
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