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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
Øystein 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.
| 10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
| 10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
| 10635 | Second-order quantification and plural quantification are different [Linnebo] |
| 10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
| 10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
| 10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
| 10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
| 10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
| 10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
| 10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |