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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
Řystein Linnebo (Plural Quantification [2008], 1)
Book Ref
'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.
| 21699 | Russell offered a paraphrase of definite description, to avoid the commitment to objects [Quine] |
| 14227 | We could refer to tables as 'xs that are arranged tablewise' [Inwagen] |
| 8262 | How can a theory of meaning show the ontological commitments of two paraphrases of one idea? [Lowe] |
| 10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
| 18491 | The idea of 'making' can be mere conceptual explanation (like 'because') [Künne] |
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 18861 | Maybe number statements can be paraphrased into quantifications plus identities [Tallant] |