Robert Schwartzkopff

In natural language, number-words can be used in two different syntactic ways: adjectivally, i.e., with the syntactic status of an adjective, as in (1) ‘Mars has two moons,’ and nominally, i.e., with the syntactic status of a noun phrase, as in (2) ‘Two is even.’ This syntactic difference is often taken to correspond to a difference in semantic function: adjectival number-words function as predicables, whereas nominal number-words function as singular terms. The view that nominal number-words function as singular terms is typically supported by appeal to certain tests for singular-termhood, tests that stem from the (neo-)Fregean tradition. In this paper, I argue that these tests do not support the view of nominal number-words as singular terms.

Number and Count Sentences like ‘The number of Martian moons is two’ and ‘Mars has two moons’ give rise to a puzzle. How can they be equivalent if only the truth of Number but not that of Count Sentences requires the existence of numbers? Proponents of Linguistic Deflationism seek to resolve this puzzle by arguing that on their correct linguistic analysis the truth of Number Sentences does not require the existence of numbers. In this paper, I argue that Katharina Felka’s recent attempt to vindicate this strategy by analysing Number Sentences as so-called specificational sentences is philosophically dissatisfying and sketch a promising alternative.

Frege proposed that sentences like ‘The number of planets is eight’ be analysed as identity statements in which the number words refer to numbers. Recently, Friederike Moltmann argued that, pace Frege, such sentences be analysed as so-called specificational sentences in which the number words have the same non-referring semantic function as the number word ‘eight’ in ‘There are eight planets’. The aim of this paper is two-fold. First, I argue that Moltmann fails to show that such sentences should be analysed as specificational sentences. Second, I show that even if they are to be analysed in this way, Moltmann’s proposed specificational analysis is unsatisfactory.

Adherents of Ockham’s fundamental razor contend that considerations of ontological parsimony pertain primarily to fundamental objects. Derivative objects, on the other hand, are thought to be quite unobjectionable. One way to understand the fundamental vs. derivative distinction is in terms of the Aristotelian distinction between ontologically independent and dependent objects. In this paper I will defend the thesis that every natural number greater than 0 is an ontologically dependent object thereby exempting the natural numbers from Ockham’s fundamental razor.

Neo-Fregeans take their argument for arithmetical realism to depend on the availability of certain, so-called broadly syntactic tests for whether a given expression functions as a singular term. The broadly syntactic tests proposed in the neo-Fregean tradition are the so-called inferential test and the Aristotelian test. If these tests are to subserve the neo-Fregean argument, they must be at least adequate, in the sense of correctly classifying paradigm cases of singular terms and non-singular terms. In this paper, I pursue two main goals. On the one hand, I show that the tests’ current state-of-the-art formulations are inadequate and, hence, cannot subserve the neo-Fregean argument. On the other hand, I propose revisions that are adequate and, hence, can subserve this argument.