Full Idea
The Geach-Kaplan sentence 'Some critics admire only one another' provably has no singular first-order paraphrase using only its predicates.
Gist of Idea
'Some critics admire only one another' cannot be paraphrased in singular first-order
Source
Øystein Linnebo (Plural Quantification [2008], 1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.2
A Reaction
There seems to be a choice of either going second-order (picking out a property), or going plural (collectively quantifying), or maybe both.