Intensionality

Intensionality is the logical property of contexts in which substituting one term for another with the same reference fails to preserve truth. The classic example: 'Lois Lane believes Superman can fly' and 'Lois Lane believes Clark Kent can fly' differ in truth value even though Superman and Clark Kent are the same individual. Intensional contexts — belief, knowledge, desire, possibility, necessity — cannot be handled by a purely extensional logic that evaluates sentences solely by the reference of their parts.

The distinction was clarified by Frege's sense/reference (Sinn/Bedeutung) distinction: in intensional contexts, expressions refer to their sense rather than their ordinary reference. Two co-referring expressions have different senses (different modes of presentation), so they behave differently in belief reports. This move inaugurated the program of intensional logic, formalized by Rudolf Carnap and later by Montague using possible-worlds semantics: intensional operators shift the world of evaluation.

Intensionality matters beyond philosophy of language: intentionality — the 'aboutness' of mental states — is the psychological correlate of logical intensionality. Whether a computational system can have genuinely intentional states, rather than merely intensional logical behavior, is the deep question behind the Chinese Room thought experiment and debates about large language model understanding.