If I say that Alice is everything Oscar hopes to be (healthy, wealthy, wise etc.), I seem to be quantifying over properties. That suggestion faces an immediate difficulty, however: though Alice may be wise, she surely is not the property of being wise. This problem can be framed in terms of a substitution failure: if a predicate like 'happy' denoted a property, we would expect pairs like 'Oscar is happy' and 'Oscar is the property of being happy' to be equivalent, which they clearly are not. I argue that a Fregean response that draws a distinction between objects and concepts faces serious difficulties, and that a syntactic solution to the substitution problem likewise fails. I propose to account for the substitution failure by instead distinguishing different ways that expressions can stand for properties: whereas the 'the property of being happy' refers to a property, 'happy' expresses or ascribes that property. I go on to compare this view to proposals made by Wright (1998) andLiebesman (2014), and end by drawing out a consequence my proposal has for a debate about the ontological commitments of predicatively quantified sentences.One reaction to this problem would be to jump ship to the nominalist camp. Predicates, one might insist, let us describe things as being this way or that, but not by way of denoting properties, or anything else for that matter. An immediate hurdle confronting this view is that it threatens to rob us of the resources needed to make sense of the possibility of quantifying into predicate position. For if predicates do not denote anything, there looks to be nothing for predicative quantifiers to quantify over, and so no obvious way to understand the semantics of such quantifiers. 2 Moving forward, I will set the nominalist view aside. The question I want to consider is how to deal with substitution failures like the above while holding on to the idea that there are things that predicates denote, and that predicative quantifiers can accordingly be construed as quantifying over. I will consider three competing answers to that question, and argue that we should opt for the third.The first option is to adopt a Fregean approach, and to hold that the postcopular expressions in (1a) and (1b) must denote different things. Properties, the Fregean will say, are objects of a certain sort, in the sense that they are denoted by certain nominal expressions and quantified over in certain nominally quantified sentences. Predicates like 'happy', he will insist, denote things of a fundamentally different kind -what Frege termed concepts. The Fregean would thus have us abandon the property-based view: the things denoted by predicates and quantified over by predicative quantifiers are not properties, but things of this fundamentally different kind.A second option is to look for a syntactic solution. Truth conditions, we should remind ourselves, are determined by both syntax and semantics. We might therefore seek a syntactic explanation of the change in truth conditions that we observe in our substitution p...