Times that never become present

Could there be times that are never present? At first sight, this seems a contradiction: surely, each time t is present at itself. Given the B-theory of time, this indeed is automatically true.

Not so, however, for A-theories. There is no contradiction in the growing block growing by leaps and bounds. Imagine that suddenly a whole minute is added to the growing block. The times in the middle of that minute never got to be at the leading edge of reality, and hence never got to be present, since to be present is to be at the leading edge of reality, given growing block. Or consider the moving spotlight: the spotlight could jump ahead in the spacetime manifold by a minute or an hour or a year, skipping over the intervening bits of the manifold. It's less clear whether it is possible to have times that aren't ever present given presentism. Still, Dean Zimmerman has considered an eccentric version of presentism on which there still is a four-dimensional spacetime manifold. On such a view, times could be identified with hypersurfaces in some preferred foliation, and there might be some such hypersurfaces that never become present.

So, apart from the B-theory and many versions of presentism, we have a possibility of times that are never present. Why would we want to countenance such a nutty option, though?

I can think of two reasons. The first would be to reconcile Aristotle's theory of time with many physical theories. According to Aristotle, times are endpoints of changes, and any interval of time contains at most finitely many changes, so that time is discrete. (Causal finitism might be a reason to adopt such a theory.) But in many modern physical theories, from Newton at least through Einstein, time is a continuous coordinate. One can try to reconcile the two views by supposing that time is continuous, as Newton and Einstein suppose, but that only those times which are the endpoints of changes are ever present. Aristotle then may be right that times are discrete, as long as we understand him to be speaking only about the times that matter, namely those that ever become present. The second motivation would be to have a flash ontology--an ontology on which physical things exist only during the discrete moments of quantum collapse--while softening the counterintuitive consequence that at most times the universe is empty. For we could identify the times that ever become present with the times at which a flash occurs. Then even if at most times, in the broad sense of the word "times", the universe is empty, still the universe is non-empty at all the times that matter, namely at all the times that become present.

Neither a B-theorist nor a standard presentist can suppose times that are never present. But she might still suppose something that plays a similar functional role. She could think of abstract times as numbers or as hypersurfaces in an abstract continuous manifold. Then real time could be discrete, while abstract time is continuous.