  The first objection is the irrelevancy of belief objection. Believing that you live in that time and possessing accurate descriptive information of the medieval age does not make your uses of ‘today’ about 1 August 1204, even though that is the date that best fits your conception of the date of your utterance. Uses of ‘today’ are about whatever day they occur on, whatever descriptions one associate with one's uses of the expression and however one conceives of the day of one's utterance. But if the sense of a use of a ‘today’ were determined by the beliefs of the speaker, and if sense determines reference, then it would seem that your utterance is about 1204. So, the beliefs of the speaker are irrelevant to the day an utterance of ‘today’ is about. 