Say that an entity E has age T at t if and only if E began to exist exactly at t-T[note 1] Observe that the age of an entity can be positive, zero, or negative. What kind of property of E is the having of a particular age?
Here is the problem. An entity continues to change in respect of age even when it no longer exists. But when an entity does not exist, the only change it can engage in is pure Cambridge change—the sort of "change" that Napoleon "experiences" when he changes from not being thought about by the Duke of Wellington or Bill Clinton to being thought about. I will assume that the age is the same kind of property during a substance's lifetime as afterwards.[note 2]
Now, Cambridge change is in the end grounded in something else undergoing non-Cambridge change. The Duke of Wellington or Bill Clinton change from not thinking to thinking about Napoleon, and thus Napoleon "changes" from being not thought about by them to being thought about by them. So the change in the age of an entity must be grounded in an something else's undergoing a genuine, non-Cambridge change. But what is that something else? And what does that something else change in respect of?
One intuitive thing to say is that "the time changes". E comes to have age T when the time changes from not being equal to t0+T, where t0 is the time E first came to exist, to being equal to t0+T. But what kind of a change is that? Time surely isn't literally some enduring entity that has a succession of temporal properties like "being noon", "being 3pm", etc. Maybe what we want to say is that reality itself or the cosmos changes in respect of time: it changes from being such that it is not t0+T to its being such that it is t0+T.
Suppose that our ontology includes moments of time, and that if t is a moment of time, then t exists at t and only at t. We can then say that the age of E changes to T precisely when reality changes so as to include the moment t0+T. If our ontology does not include moments of time, but, say, is relational, we may need to do some more work, but I do not see any obvious in-principle bar to defining the time.
We now have a seemingly well-defined property of age, defined in terms of reality's inclusion of a particular moment of time. Now, here is an oddity. This property of age can be equally well defined on a B-theory as on an A-theory. Indeed, I alluded to nothing A-theoretical in the account. A first consequence—Dean Zimmerman has a paper that among many other interesting things says something like this—is that it won't do to define the difference between the A- and B-theories in terms of the objective futurity, presentness and pastness of events, since such properties can be defined in terms of age, and both the A- and B-theories can define the property of age, and the definition seems mind-independent. Nor will it do to define the distinction between the A-theory and the B-theory in terms of an A-theorist's being committed to age being a non-Cambridge property. For the above argument shows that age is a Cambridge property (and by the same token, so are futurity, presentness and pastness), so it would be grossly unfair to the A-theorist thus to define the A-theory. A third consequence is that a reductio, like McTaggart's, of the very idea of futurity, presentness and pastness properties is apt to equally attack the B-theory as the A-theory, since both the B-theory and the A-theory can define such properties.
How, then, to define the A-theory, if not in terms of objective futurity, presentness and pastness of events? I see only one way at present: in terms of the idea that propositions change in truth value. The A-theorist, then, is one who gives up on the eternity of truth: p can be true at t0 but false at t1. This Aristotelian theory of propositions is, I think, false (on this theory, tomorrow I will no longer believe the same things as I believed today about my actions from today, even in cases where I have not forgotten these actions), but it is not clearly absurd.