Among philosophers of mind, it is common to assume that at least some mental properties are functional in nature, and that functional properties are second-order properties. In the functionalist literature, the notion of being a second-order property is cashed out in three different ways: (i) in terms of semantic features of characterizations or definitions of properties, (ii) in terms of syntactic features of second-order quantification, and (iii) in terms of a metaphysical criterion, according to which properties are second order if (...) they are properties of first-order properties. It is shown that in the context of functionalism reference to these interpretations is misguided, and it is suggested that the notion of an ordering of properties in this context is best understood as being tied to dependence-relations. (shrink)