One problem for a moving present

Suppose that we think that the present moves, ever pushing into the future. Now the present is within a Friday. Tomorrow the present will be within a Saturday. On this theory, it is the same thing, the present, that today is within a Friday and tomorrow it will be within a Saturday.

It follows that the present is something that has always existed and will always exist. After all, if a rock will tomorrow be found in one cave, and today is present in another cave, then the rock exists both today and tomorrow. The present on this view has the same temporal extent as whole time sequence.

But this is absurd. Clearly, the present does not extend back to the Battle of Waterloo. Hence an A-theory on which the present relentlessly moves forward must be rejected.

Moving spotlight theorists should, thus, not reify the spotlight. So what should they do? Well, maybe they can say that events that are presently occurring have a special property, let's say L, for being lit up. And which events have this special property changes with time. Right now the writing of this post has L. In an hour, the writing of this post will no longer have L. This, I think, leads to the McTaggart paradoxes. Here's how. Let's ask: Is having L intrinsic or extrinsic to the writing of this post? If extrinsic, then there will be something else that has an L-like property in a more basic way, and we have failed to account for the present in terms of events having L. Let W be the event of the writing of this post. Suppose then that W intrinsically has L. But in an hour, W will not intrinsically have L. I think this is what triggers the McTaggart paradoxes: the idea that events change in respect of what intrinsic properties they have. Anyway, in an hour, the writing of this post will have L₁, the property of having been lit up an hour ago. The writing of this post will gain L₁ only at a time when W no longer exists. Hence, while L is intrinsic to W, L₁ is not intrinsic, since only extrinsic properties can be gained when one does not exist. Therefore, we need to define L₁ in terms of L and a B-relation of some sort.

OK, that's all I want to do in the way of helping moving spotlight theories.