Philosophy Lexicon of Arguments

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Universal quantification: an operator, which indicates that the following expression is a statement about all the objects in the considered domain. Notation "(x)" or "∀x". Ex. E.g. (x) (Fx ∧ Gx) everyday language "All Fs are Gs." .- Antonym
 
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II 348
Everything/absolutely everything/Universal Quantification/Truth-Theory/Field: the object-language quantifiers of a Truth-theory cannot go beyond everything. - ((s) Otherwise the theory becomes circular).
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II 353
Universal Quantification/indeterminacy/McGee/Field: McGee: we must exclude the hypothesis that a person's apparently unrestricted quantifiers only go via entities of the type F if the person has a concept of F. This excludes the normal attempts to show the indeterminacy of universal quantification. - FieldVsMcGee: that does not work. - Question: do our own quantifiers have any particular area? - It is not clear what it means to have the concept of a restricted area, because if universal quantification is indeterminate, then also the terms that are used to restrict the area.

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

Fie III
H. Field
Science without numbers Princeton New Jersey 1980


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Ed. Martin Schulz, access date 2017-05-23