 Standard second-order logic allows for predicate variables bound by quantifiers. Hence, to the extent that these variables are taken to range over properties, this system could be seen as a formal theory of properties. Its expressive power is however limited, since it does not allow for subject terms that stand for properties. Thus, for example, one cannot even say of a property \(F\) that \(F = F\). This is a serious limitation if one wants a formal tool for a realm of properties whose laws one is trying to explore. Standard higher order logics beyond the second order obviate this limitation by allowing for predicates in subject position, provided that the predicates that are predicated of them belong to a higher type. This presupposes a grammar in which predicates are assigned types of increasing levels, which can be taken to mean that the properties themselves, for which the predicates stand for, are arranged into a hierarchy of types. Thus, such logics appropriate one version or another of the type theory concocted by Russell to tame his own paradox and related conundrums. If a predicate can be predicated of another predicate only if the former is of a type higher than the latter, then self-predication is banished and Russell’s paradox cannot even be formulated. Following this line, we can construct a type-theoretical formal property theory. The simple theory of types, as presented, e.g., in Copi (1971), can be seen as a prototypical version of such a property theory (if we neglect the principle of extensionality assumed by Copi). The type-theoretical approach keeps having supporters. For example, it is followed in the property theories embedded in Zalta’s (1983) theory of abstract objects and more recently in the metaphysical systems proposed by Williamson (2013) and Hale (2013).