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Full Idea
For the substitutional interpretation of quantifiers, a sentence of the form '(∃x) Fx' is true iff there is some closed term 't' of the language such that 'Ft' is true. For the objectual interpretation some object x must exist such that Fx is true.
Gist of Idea
On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true
Source
Charles Parsons (A Plea for Substitutional Quantification [1971], p.156)
Book Ref
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.156
A Reaction
How could you decide if it was true for 't' if you didn't know what object 't' referred to?
| 17447 | Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck] |
| 18201 | General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C] |
| 9469 | Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C] |
| 9468 | On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C] |
| 9470 | Modal logic is not an extensional language [Parsons,C] |
| 13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
| 13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
| 13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |