Class nominalists analyze a particular's having of a property in terms of that particular's membership in a class of things that all share that property.

Finally, D.M. Armstrong (1979) has stated a regress argument similar to Bradley’s, as a threat to class nominalists. The thought is that since class nominalists analyze particulars’ having of properties in terms of particulars’ membership in a class of things that all have those properties, they would incur a regress when trying to define a membership relation. However, class nominalists like Lewis (2002), have been adamant about not being committed to a membership relation of any sort; indeed,