 For this application of plural quantification to work, PFO must be applicable to all kinds of concrete objects, and it must be ontologically innocent, or at least not committed to any entities that share those features of abstract objects that are found to be nominalistically objectionable. Moreover, in order to simulate quantification over relations, we will need not just PFO but a theory more like monadic third-order logic (Sections  2.2  and  2.4).