A central question for ontology is the question of whether numbers really
exist. But it seems easy to answer this question in the affirmative The truth of a
sentence like (1) ‘Seven students came to the party’ can be established simply by
looking around at the party and counting students. A trivial paraphrase of (1) is (2)
‘The number of students who came to the party is seven’. But (2) appears to entail
the existence of a number and so it seems that we must conclude that numbers exist.
This is sometimes called the puzzle of how we can get something from nothing.
Most extant attempts to solve the puzzle take it for granted that (1) is ontologically
innocent and focus their attention either on (2) or on the transition from (1) to (2).
We argue that both attempts go wrong at the first step the assumption that (1) is
ontologically innocent is undermined by a highly attractive and independently wellmotivated
degree-based account of number word constructions Thus the degreebased
account provides a straightforward linguistic resolution of the puzzle of how
we can get something from nothing But the paper also has a second aim The
semantics we present treats seven as a referring expression that refers to a degree
of a certain sort. But what are degrees? We consider various anti-platonist proposals
that seek to account for degrees in terms of relations between concrete entities, and
argue that they are incompatible with the Universal Density of Measurement
hypothesis (UDM) of Fox and Hackl (Linguist Philos 29:537–586, 2006). While the
UDM cannot yet claim to be the consensus view among degree-based semanticists

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• Number word constructions, degree semantics and the metaphysics of degrees