 Addressing this question brings out the need to have it clear at which level of granularity one is testing for equivalence. Take for example the classical extensional notion of logical equivalence. This is a coarse equivalence, in that informationally different claims such as 2 is even and 2 is prime cannot be distinguished, as their extensions will coincide. Take instead an equivalence given by identity at the level of representations (say syntactic equality). This is on the contrary too fine-grained in some cases: to a bilingual speaker, the information that the shop is closed would be equally conveyed by a sign saying “Closed” as by a sign saying “Geschlossen”, even if the two words are different. 