  Major advances have recently been made in merging language and vision
representations. But most tasks considered so far have confined themselves to
the processing of objects and lexicalised relations amongst objects (content
words). We know, however, that humans (even pre-school children) can abstract
over raw data to perform certain types of higher-level reasoning, expressed in
natural language by function words. A case in point is given by their ability
to learn quantifiers, i.e. expressions like 'few', 'some' and 'all'. From
formal semantics and cognitive linguistics, we know that quantifiers are
relations over sets which, as a simplification, we can see as proportions. For
instance, in 'most fish are red', most encodes the proportion of fish which are
red fish. In this paper, we study how well current language and vision
strategies model such relations. We show that state-of-the-art attention
mechanisms coupled with a traditional linguistic formalisation of quantifiers
gives best performance on the task. Additionally, we provide insights on the
role of 'gist' representations in quantification. A 'logical' strategy to
tackle the task would be to first obtain a numerosity estimation for the two
involved sets and then compare their cardinalities. We however argue that
precisely identifying the composition of the sets is not only beyond current
state-of-the-art models but perhaps even detrimental to a task that is most
efficiently performed by refining the approximate numerosity estimator of the
system.
