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Single Idea 10536

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

Full Idea

For Frege there is no need to specify the domain of the individual variables, which is taken as the totality of all objects. This contrasts with the standard notion of an interpretation, which demands that we first fix the domain.

Gist of Idea

Frege's domain for variables is all objects, but modern interpretations first fix the domain

Source

comment on Gottlob Frege (Begriffsschrift [1879]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14

Book Ref

Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.475

A Reaction

What intrigues me is how domains of quantification shift according to context in ordinary usage, even in mid-sentence. I ought to go through every idea in this database, specifying its domain of quantification. Any volunteers?

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]