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5. Theory of Logic / G. Quantification / 2. Domain of Quantification

[specifying the objects from which quantifiers select]

16 ideas
De Morgan introduced a 'universe of discourse', to replace Boole's universe of 'all things' [De Morgan ,by Walicki]
For Frege the variable ranges over all objects [Frege ,by Tait]
Frege always, and fatally, neglected the domain of quantification [Dummett on Frege]
With 'extensive connection', boundary elements are not included in domains [Whitehead ,by Varzi]
Reference to a totality need not refer to a conjunction of all its elements [Gödel]
Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)]
Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)]
Frege's domain for variables is all objects, but modern interpretations first fix the domain [Dummett]
Davidson controversially proposed to quantify over events [Davidson]
The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
If we allow empty domains, we must allow empty names [Bostock]
'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry]
Quantifiers for domains and for inference come apart if there are no entities [Hofweber]
We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]