  Frege argued for the distinctness of sense from reference as follows. Suppose, for reductio, that the sole semantic value of the name ‘Mark Twain’ were its reference. Then, as the name ‘Samuel Clemens’ is coreferential, the two names would be identical in their semantic values. Given a plausible assumption of compositionality, the sentences ‘Mark Twain was a famous American author’ and ‘Samuel Clemens was a famous American author’ would then express the same proposition. But that is counterintuitive. It seems that fully competent speakers can believe what the one expresses without believing what the other expresses. (Imagine our agent had an American literature class, having read Huck Finn and Tom Sawyer, in which biographical facts were withheld. She will accept the first  sentence and reject the second.) If this is so, then the two sentences express different propositions. And if they express different propositions, there must be some semantically relevant difference between the names ‘Mark Twain’ and ‘Samuel Clemens’. As their references do not differ, sense is distinct from reference.