Patricia is a person with a strange defect. She has tensed beliefs that she fails to update. For instance, she believes that the Battle of Waterloo was two hundred years ago, and she does not change in respect of this belief—she believed twenty years ago that the Battle of Waterloo was then two hundred years ago, and in twenty years she will believe that the Battle of Waterloo will then be two hundred years ago. Presentists tend to think that the objects of beliefs are tensed propositions, and if so, then it is very plausible that her mind is intrinsically in the very same state with respect to the Battle of Waterloo in 1988, in 2028 and in 2015.[note 1] Interestingly, her belief about the Battle of Waterloo was false in 1988, is false now, will be false in 2028, but on June 18, 2015, her belief will be true.
If Patricia's believings about the Battle of Waterloo do not change intrinsically while they change from false to true to false again, it follows that this change from false to true to false is a Cambridge change. But Cambridge changes are relational. Now in the case of a Cambridge change in x, there is a y distinct from x which changes intrinsically and the change in x is a change relative to y, and x has the changing extrinsic property in virtue of y's having the changing intrinsic property. Thus, what makes Patricia's believings change in a Cambridge way from false to true to false is that something else changes intrinsically.
So what is it that changes intrinsically in virtue of the change in which Patricia's believing changes from false to true to false? Well, the only plausible candidate for an answer to this is that the object of the belief changes intrinsically. When someone falsely believes it is raining and continues to believe it until it becomes true, the belief changes in truth value in virtue of the weather changing from, say, sunshine to rain. But then Patricia's beliefs must be about something in reality. In particular, presentisms like those of Merricks on which there are no truth grounds for facts about the past are going to be falsified by these considerations.
What about presentisms like those of Bigelow and Crisp on which there are past-tensed presently existing states of affairs? Do those do better? I think not. For when a belief changes in truth value without intrinsically changing, I think it must change in virtue of a change in that which the belief is about. But the belief that the Battle of Waterloo was 200 years ago is plainly not about any present state of affairs.
One way out for the presentist is to say that believings change in correctness in virtue of a change in the truth value of the proposition that forms their content. This is intuitively wrong—believings should change in virtue of a change in that which they are about and except in higher order cases they are not about a proposition—but let us pass on that objection. But now the problem reappears in respect of the change in the truth value of the proposition (see also this past post). It does not appear that there is any intrinsic change in the proposition when it changes in truth value. For suppose that the proposition that it is raining changes in truth value with the weather. Surely, then, it changes because of the weather. But how can changes in the weather, changes in the physical world, explain intrinsic changes in the Platonic realm of propositions? (And we need to be realists about propositions for the present suggestion to have any force.) That seems very much implausible. So the proposition changes in truth value in an extrinsic, indeed Cambridge, way. But now the same problem we had with believings reappears at the level of propositions.