Why content must be a matter of truth conditions

It is argued that if, with Dummett, we see assertion as an act governed by conditions of correctness which makes a claim to the effect that these conditions are met, then the conditions of correctness that determine its content must have the impersonal character of a requirement of truth, rather than the speaker-relative character of a requirement of justification or assertibility. For otherwise it would be impossible for different speakers to use the same words to make an assertion with the same content.