Universals are putative objects like wisdom, morality, redness, etc. Although we believe in properties (which, we argue, are not a kind of object), we do not believe in universals. However, a number of ordinary, natural language constructions seem to commit us to their existence. In this paper, we provide a fictionalist theory of universals, which allows us to speak as if universals existed, whilst denying that any really do.

Standard Type Theory, STT, tells us that b^n(a^m) is well-formed iff n=m+1. However, Linnebo and Rayo have advocated the use of Cumulative Type Theory, CTT, has more relaxed type-restrictions: according to CTT, b^β(a^α) is well-formed iff β > α. In this paper, we set ourselves against CTT. We begin our case by arguing against Linnebo and Rayo’s claim that CTT sheds new philosophical light on set theory. We then argue that, while CTT ’s type-restrictions are unjustifiable, the type-restrictions imposed by (...) STT are justified by a Fregean semantics. What is more, this Fregean semantics provides us with a principled way to resist Linnebo and Rayo’s Semantic Argument for CTT. We end by examining an alternative approach to cumulative types due to Florio and Jones; we argue that their theory is best seen as a misleadingly formulated version of STT. (shrink)

Frege’s rejection of singular reference to concepts is centrally implicated in his notorious paradox of the concept horse. I distinguish a number of claims in which that rejection might consist and detail the dialectical difficulties confronting the defense of several such claims. Arguably the least problematic such claim—that it is simply nonsense to say that a concept can be referred to with a singular term—has recently received a novel defense due to Robert Trueman. I set out Trueman’s argument for this (...) claim, identifying and remedying some omissions and errors of formulation therein. I then develop a response to the argument by showing, pace Trueman, that it is possible—and how it is possible—to express identities between objects and concepts. (shrink)

In Word and Object, Quine proposed that names be treated as the predicate elements of covert descriptions, expressing the property of being identical to the named individual. More recently, many theorists have proposed a predicativist view according which a referential name expresses the property of being called by that name. Whereas this Being-Called Predicativism has received much attention in the recent literature, Quinean Predicativism has not. This neglect is undeserved. In this paper, I argue, first, that close appositive constructions suggest (...) that names can function as predicates expressing identifying properties of the sort proposed by Quine, and, second, that a predicativist analysis which extends this view to referential names overcomes some of the central objections that have been raised against Being-Called Predicativism. (shrink)

The Reference Principle states that co-referring expressions are everywhere intersubstitutable salva congruitate. On first glance, looks like a truism, but a truism with some bite: transforms difficult philosophical questions about co-reference into easy grammatical questions about substitutability. This has led a number of philosophers to think that we can use to make short work of certain longstanding metaphysical debates. For example, it has been suggested that all we need to do to show that the predicate ‘ is a horse’ does (...) not refer to a property is point out that ‘ is a horse’ and ‘the property of being a horse’ are not everywhere intersubstitutable salva congruitate. However, when we understand ‘substitution’ in the simplest and most straightforward way, is no truism; in fact, natural languages are full of counterexamples to the principle. In this paper, I introduce a new notion of substitution, and then develop and argue for a version of that is immune to these counterexamples. Along the way I touch on the following topics: the relation between argument forms and their natural language instances; the reification of sense; the difference between terms and predicates; and the relation between reference and disquotation. I end by arguing that my new version of cannot be used to settle metaphysical debates quite as easily as some philosophers would like. (shrink)

In this paper I argue that Frege’s concept horse paradox is not easily avoided. I do so without appealing to Wright’s Reference Principle. I then use this result to show that Hale and Wright’s recent attempts to avoid this paradox by rejecting or otherwise defanging the Reference Principle are unsuccessful.

Frege's strict alignment between his syntactic and ontological categories is not, as is commonly assumed, some kind of a philosophical thesis. There is no thesis that proper names refer only to objects, say, or that what refers to an object is a proper name. Rather, the alignment of categories is internal to Frege's conception of what syntax and ontology are. To understand this, we need to recognise the pride of place Frege assigns within his theorising to the notion of truth. (...) For both language and the world, the Fregean categories are logical categories, categories, that is, of truth. The elaboration of this point makes clear the incoherence of supposing that they might not align. (shrink)

This paper uses the resources of higher-order logic to articulate a Fregean conception of predicate reference, and of word-world relations more generally, that is immune to the concept horse problem. The paper then addresses a prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright.