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Single Idea 13450

[filed under theme 5. Theory of Logic / G. Quantification / 2. Domain of Quantification ]

Full Idea

There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases.

Gist of Idea

Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals

Source

Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1)

Book Ref

'Absolute Generality', ed/tr. Rayo,A/Uzquiano,G [OUP 2006], p.4

The 16 ideas with the same theme [specifying the objects from which quantifiers select]:

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]