The paradox Lowe is referring to is the following. If P is the predicate "non-predicable', then if for any predicate there is a property, there is a property of non-predicability, but if P has this property, we can use P as a predicate and there is no property. We have a paradox, because P is such that in order to be a property it is not a property, which is self-contradictory. This version of Russell's paradox can therefore be used against the reduction of properties to predicates. But if properties are not identical to predicates, there is an "intimate connection' (Lowe) between them and a part of the difficulties caused by the formal treatment of properties is located in the subtlety of the relations between predicates and properties. We usually establish a correspondence between the two by means of formal transformations.
Nef, F. (2010)., Properties, in R. Poli & J. Seibt (eds.), Theory and applications of ontology, Dordrecht, Springer, pp. 135-151.
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