substitutional quantification

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A sentence containing a quantifier is usually interpreted by assigning values to the variable it contains. Values are thought of as ‘objects’; hence this is termed objectual quantification. By contrast, the quantifier is interpreted substitutionally if expressions are substituted for the variable, and the result evaluated according to whether any of the substitutions produce a true sentence. Substitutional quantifiers are frequently written Σ and Π. (Σx)(logicians are x) would be evaluated as true, with the quantifier interpreted susbstitutionally, if there is a sentence ‘logicians are…’ which is true.

Subjects: Philosophy.

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