Opaque context

An opaque context or referentially opaque context is a linguistic context in which it is not always possible to substitute 'co-referential' expressions (expressions referring to the same object) without altering the truth of sentences. The expressions involved are usually grammatically singular terms. So, substitution of co-referential expressions into an opaque context does not always preserve truth. For example, 'Lois believes x is a hero' is an opaque context because 'Lois believes Superman is a hero' is true while 'Lois believes Clark Kent is a hero' is false, even though 'Superman' and 'Clark Kent' are co-referential expressions. An opaque context or referentially opaque context is a linguistic context in which it is not always possible to substitute 'co-referential' expressions (expressions referring to the same object) without altering the truth of sentences. The expressions involved are usually grammatically singular terms. So, substitution of co-referential expressions into an opaque context does not always preserve truth. For example, 'Lois believes x is a hero' is an opaque context because 'Lois believes Superman is a hero' is true while 'Lois believes Clark Kent is a hero' is false, even though 'Superman' and 'Clark Kent' are co-referential expressions. The term is used in philosophical theories of reference, and is to be contrasted with 'referentially transparent context'. In rough outline: Similar usage of the term applies for artificial languages such as programming languages and logics. The Cicero-Tully example above can be easily adapted. Use the notation [ t ] {displaystyle } as a quotation that mentions a term t {displaystyle t} . Define a predicate L {displaystyle L} to the effect that the letters making up a term number six. Then [ x ] {displaystyle } induces an opaque context, or is referentially opaque, because L ( [ C i c e r o ] ) {displaystyle L()} is true while L ( [ T u l l y ] ) {displaystyle L()} is false. Programming languages often have richer semantics than logics' semantics of truth and falsity, and so an operator such as [ x ] {displaystyle } may fail to be referentially transparent for other reasons as well.