Opaque context is a context in which substitution of two expressions with the same reference salva veritate (i.e. keeping the truth value constant) is impossible. The verb hope in (ia) creates an opaque context. This can be seen by replacing the murderer of Smith with an expression which is assumed to have the same reference (in this case John's brother). The result in (ic) is a sentence which does not need to have the same truth value as (ia). One has only to imagine a situation in which John does not know that his beloved brother is the unknown murderer.
(i) a John hopes that the murderer of Smith will be hanged b The murderer of Smith is his (i.e. John's) brother c John hopes that his brother will be hanged
Many different elements may create opaque contexts: words that express propositional attitudes (like know and believe, fear and hate), verbs like seek and want, temporal and modal expressions. Contexts of direct and indirect speech may also be opaque contexts. The pattern in (i) can be explained by making a distinction between extension and intension. The murderer of Smith and John's brother may have the same extension in a particular situation, but their intension, their meaning is different. A context which not opaque is called a transparent context.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.