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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. A prominent style of expressibility problem for views of broadly this kind, versions of which are due to Linnebo, Hale, and Wright, is then addressed. Central to an account of the relationship between language and reality is an account of that between predicates and reality. Frege’s problem of the concept horse (§1) threatens one prominent style of account, on which predicates refer to extra-linguistic entities fundamentally different in kind from those to which singular term refer. Here, I explore the interaction between this classic problem in the analytic tradition’s history and a contemporary view about the interpretation of higher-order logic, developing a higher-order Fregean semantics and metaphysics that is immune to the problem. At the heart of my approach is a seemingly anti-Fregean semantic framework that appears to withhold reference from predicates. I argue (§ 2) that this appearance is misleading: from a higher-order perspective, this seemingly anti-Fregean semantics can be seen to treat predicates referentially. After articulating the conception of higher-order logic on which this argument depends (§3), I show how to combine this approach with other central principles of Fregean semantics and metaphysics without giving rise to the concept horse problem (§4). I then (§5) address a prominent style of objection to views of broadly this kind, versions of which are due to Oystein Linnebo, Bob Hale, and Crispin Wright. The lesson is that the concept horse problem for Fregean conceptions of predicate reference—and of the language-reality relationship more generally—and their apparent conflict with non-referential treatments of predicates, both stem from a failure to take seriously the existential import of higherorder quantification alongside unwarranted insistence on formulating Fregean semantics in first-order terms.

A Higher-Order Solution to the Problem of the Concept Horse