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Single Idea 10791

[from 'Nominalism and Substitutional Quantifiers' by Ruth Barcan Marcus, in 5. Theory of Logic / G. Quantification / 2. Domain of Quantification ]

Full Idea

On a substitutional semantics of a first-order language, a domain of objects is not specified. Variables do not range over objects. They are place markers for substituends (..and sentences are true-for-all-names, or true-for-at-least-one-name).

Clarification

'Substituends' are things that can inserted for the place markers

Gist of Idea

Substitutional semantics has no domain of objects, but place-markers for substitutions

Source

Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.165)

Book Reference

'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.165