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Published online by Cambridge University Press: 05 June 2012
INTRODUCTION
Consider the statement
(1) Necessarily 9 = 9.
(1) is believed by most philosophical logicians to be non-extensional according to each of two prominent conceptions of extensionality. First, it fails the salva veritate substitution test when ‘9’ is replace by the co-referential singular term ‘the number of planets’. Second, in possible world semantics, its truth is regarded as dependent on the reference-in-all-possible-worlds of ‘9’, or, alterntively, on the intension of ‘9’ conceived as a function from possible worlds to individuals.
More generally, a statement is SV-Extensional according to the salva veritate substitution conception just in case singular terms co-referential with a statement's constituent singular terms, predicates co extensive with the statement's constituent predicates, and statements co-valent with a statement's constituent statement(s), substitute in that statement salva veritate. A statement is not SV- Extensional if there is at least one failure of salva veritate substitution. (This is close to the characterization in Quine's Word and Object.)
A statement is TD-Extensional according to the truth-value dependence conception just in case its truth value depends only on the extensions simpliciter, if any at all, of its constituent singular terms, predicates and statements. A statement is not TD-Extensional if entities other than extensional entities areinvolved in the computation of its truth value.
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