Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...) number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

One puzzling feature of talk about properties, propositions and natural numbers is that statements that are explicitly about them can be introduced apparently without change of truth conditions from statements that don't mention them at all. Thus it seems that the existence of numbers, properties and propositions can be established`from nothing'. This metaphysical puzzle is tied to a series of syntactic and semantic puzzles about the relationship between ordinary, metaphysically innocent statements and their metaphysically loaded counterparts, statements that explicitly mention (...) numbers, properties and propositions, but nonetheless appear to be equivalent to the former. I argue that the standard solutions to the metaphysical puzzles make a mistaken assumption about the semantics of the loaded counterparts. Instead I propose a solution to the syntactic and semantic puzzles, and argue that this solution also gives us a new solution to the metaphysical puzzle. I argue that instead of containing more semantically singular terms that aim to refer to extra entities, the loaded counterparts are focus constructions. Their syntactic structure is in the service of presenting information with a focus, but not to refer to new entities. This will allow us to spell out Frege's metaphor of content carving. (shrink)

Ontology and the Ambitions of Metaphysics By HofweberThomasOxford University Press, 2016. xvi + 366 pp. £50.00.