Size Matters: Grounding Quantifiers in Spatial Perception
Simon Pauw

Abstract:
Words like many and few have a dual nature: though traditionally
analyzed as quantifiers (~many of the houses~), they also behave like
gradable adjectives (~few/fewer houses~). In fact, such terms pattern
syntactically and semantically with both quantifiers and
adjectives. Why aren't they confined to one grammatical class? What is
the cognitive basis for their dual behavior? And how might such
conceptual and linguistic duality have evolved?

Historical evidence suggests that the dual syntax of these terms
(henceforth, gradable quantifiers) might be the result of a
grammaticalization process where they originate as adjectives and
later become quantifiers, as illustrated by the quantifier few, based
on the Old English adjective feawe. This dissertation explores the
hypothesis that this grammaticalization path might be the result of
the cognitive relationship between size and number. Judgments of size
(underlying modifiers such as big and small) depend on perceptual
features of objects (or sets of objects) in the environment. Judgments
of approximate number (underlying terms like few and many) exploit a
combination of spatial features that apply exclusively to sets of
objects, such as their size and density. This cognitive overlap
between the concepts of size and number may account for the duality
observed in gradable quantifiers: the dependence on size motivates
their adjectival uses, while their exclusive application to sets of
objects motivates their quantificational uses.

This dissertation describes a series of experiments that captures the
insight above within an evolutionary language games framework, in
which robotic agents self-organize the means for describing objects
(or in this case, groups of objects) in their perceived
environment. The model allows the exploration of the specific
conditions under which the hypothesis might hold. In particular,
agents equipped with an approximate number sense that incorporates
size can be shown to develop linguistic terms with the dual functions
observed in gradable quantifiers.

A first set of experiments show that gradable quantifiers are indeed
likely to emerge as adjectives due to their cognitive overlap with
size predicates such as big and small. But, gradable quantifiers are
not only cognitively related to size predicates but also to
quantifiers such as all or three (they exclusively apply to sets). A
second set of experiments show that this cognitive overlap will invite
the (initially adjectival) gradable quantifiers to grammaticalize into
quantifiers. Overall, this dissertation shows that the syntactic
duality of gradable quantifiers might be reflecting an underlying
cognitive duality. More generally, it suggests how the inclusion of
cognitive constraints may illuminate the origins of both conceptual
and linguistic duality.

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