It would seem that some statements like ‘There are exactly four moons of Jupiter’ and ‘The number of moons of Jupiter is four’ have the same truth-conditions and yet differ in ontological commitment. One strategy to resolve this paradoxical phenomenon is to insist that the statements have not only the same truth-conditions but also the same ontological commitments; the other strategy is to reject the presumption that they have the same truth-conditions. This paper critically examines some popular versions of these (...) two strategies, and defends a new solution according to which the statements have the same ontological commitments and yet differ in truth-conditions. (shrink)

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 ‘Seven students came to the party’ can be established simply by looking around at the party and counting students. A trivial paraphrase of is ‘The number of students who came to the party is seven’. But 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 is ontologically innocent, and focus their attention either on or on the transition from to. We argue that both attempts go wrong at the first step: the assumption that is ontologically innocent is undermined by a highly attractive and independently well-motivated degree-based account of number word constructions. Thus the degree-based 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 of Fox and Hackl. While the UDM cannot yet claim to be the consensus view among degree-based semanticists, our aim is to use it to illustrate how views about the nature of degrees can be evaluated by considering the properties degrees must have if they are to play the explanatory roles they are called upon to play in linguistics. In the present state of development of degree-based semantics there are difficult open questions about what these properties are. These questions need to be addressed if we are to develop a clear picture of what natural language semantics has to contribute to ontology and metaphysics. (shrink)

This paper contributes to the debate over the so-called “easy argument for numbers”, an argument that uses evidence from natural language to support the metaphysically significant claim that numbers exist. It presents novel data showing that critical examples in the literature are ambiguous between two readings, contrary to previous assumptions. It then accounts for these data using independently motivated linguistic theory. The account developed rescues the easy argument from the primary challenges leveled against it in the literature and sets the (...) agenda for future work to determine whether or not the argument is valid. (shrink)

In this paper, we outline and critically evaluate Thomas Hofweber’s solution to a semantic puzzle he calls Frege’s Other Puzzle. After sketching the Puzzle and two traditional responses to it—the Substantival Strategy and the Adjectival Strategy—we outline Hofweber’s proposed version of Adjectivalism. We argue that two key components—the syntactic and semantic components—of Hofweber’s analysis both suffer from serious empirical difficulties. Ultimately, this suggests that an altogether different solution to Frege’s Other Puzzle is required.