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Full Idea
Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities.
Gist of Idea
Quantifiers for domains and for inference come apart if there are no entities
Source
Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §6.3)
Book Ref
-: 'Philosophical Review 114' [Phil Review 2005], p.218
A Reaction
This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008.
Related Ideas
Idea 10008 Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]
Idea 13818 If we allow empty domains, we must allow empty names [Bostock]
| 17743 | De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan, by Walicki] |
| 9991 | For Frege the variable ranges over all objects [Frege, by Tait] |
| 10536 | Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett on Frege] |
| 9871 | Frege always, and fatally, neglected the domain of quantification [Dummett on Frege] |
| 10656 | With 'extensive connection', boundary elements are not included in domains [Whitehead, by Varzi] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
| 10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
| 18914 | Davidson controversially proposed to quantify over events [Davidson, by Engelbretsen] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 13818 | If we allow empty domains, we must allow empty names [Bostock] |
| 10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| 10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |