Abstract

Contemporary formalisations of Meinong's theory of objects prove that Russell's accusation of inconsistency of the theory is not valid. However, in the same formalisations there has appeared a new source of potential inconsistency. Theories of objects inspired by Meinong's ontology usually include, in addition to basic principles of the ontology, abstraction-axioms for defining objects and properties (relations). Although these axioms seem to be perfectly acceptable, they lead to paradoxes when adopted without any restrictions. These paradoxes may be understood as paradoxes of size (not of self-referentiality): too many objects or too many properfies are defined by the axioms. We can avoid them at the cost of counterintuifive stipulations, some of them similar to those applied in set theory or in higher-order logics (like a stratificafion of formulas). We need however to look for phenomenologically well grounded protecfions against paradoxes. This search can deepen our understanding of the nature of Meinongian objects.