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.
Usage
The term is used in
philosophical
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...
theories of reference, and is to be contrasted with referentially transparent context.
In the opaque case, "Mary believes that
Cicero
Marcus Tullius Cicero ( ; ; 3 January 106 BC – 7 December 43 BC) was a Roman statesman, lawyer, scholar, philosopher, orator, writer and Academic skeptic, who tried to uphold optimate principles during the political crises tha ...
is a great orator" gives rise to an opaque context; although Cicero was also called 'Tully',
[Tully is anglicised historic name from Tullius, source: ] we can't simply substitute 'Tully' for 'Cicero' in this context ("Mary believes that Tully is a great orator") and guarantee the same truth value, for Mary might not know that the names 'Tully' and 'Cicero' refer to one and the same thing. Of course, if Mary does believe that Cicero is a great orator, then there is a sense in which Mary believes that Tully is a great orator, even if she does not know that 'Tully' and 'Cicero' ''corefer''. It is the sense forced on us by "direct reference" theories of proper names, i.e. those that maintain that the meaning of a proper name just is its referent.
In the transparent case, "Cicero was a Roman orator" gives rise to a transparent context; there is no problem substituting 'Tully' for 'Cicero' here: "Tully was a Roman orator". Both sentences necessarily express the same thing if 'Cicero' and 'Tully' refer to the same person. Note that this element is missing in the opaque contexts, where a shift in the name can result in a sentence that expresses something different from the original.
Similar usage of the term applies for
artificial languages such as
programming language
A programming language is a system of notation for writing computer programs.
Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually def ...
s and
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
s. The Cicero–Tully example above can be easily adapted. Use the notation