A Christian argument against eternalism, with some remarks on "finite" and "infinite"

1. We have an infinite future.

2. If eternalism is true, then anything that has an infinite future is infinite.

3. We are finite.

4. So, eternalism is not true.

The crucial premise is 2. One thought behind 2 is that our best version of eternalism holds that we four-dimensional, and if we have an infinite future, that makes us infinite in the fourth dimension.

But I think we can do better than that. Plausibly, part of what we mean by “We have an infinite future” is that we will have infinitely many token future mental states (if not, add that to the premises). On eternalism, all these mental states exist. And they are clearly all ours. So if we have an infinite future, we have an infinite mental life, and that is a way of being infinite.

I am an eternalist, and I want to affirm 1 and 3. What can I do? One move is this. The relevant sense of “finite” in 3 is not a mathematical sense, but something more “metaphysical” like limited. Now, to be limited is to have one or more limits. This is quite compatible with there being respects in which we lack a limit. Thus, the charged infinite rod that sometimes figures in physics homework has limits: not limits of length, but limits of width and height (and others). In the metaphysical sense, then, the rod is finite. Likewise, then, even if we are temporally infinite or infinite in the number of mental states, we are still limited in other ways.

If we go for this move, we have to make a choice what to mean by “infinite”. We could say that something is infinite provided there is some respect in which it is unlimited. If we did that, then one thing could be finite and infinite—as long as it is limited in one way and unlimited in another. The “infinite rod” would then be both finite and infinite. And, if eternalism is true and there is an eternal afterlife, we are finite and infinite. On this take, the argument is invalid, because it is missing the assumption that nothing is both finite and infinite.

A second otion is to make “infinite” mean unlimited in all respects. In that case, we are finite and not infinite. Indeed, only God is infinite then. A set with what the mathematician calls “infinite cardinality” is limited by not having a greater cardinality than the one it has.

A third option would be to take “finite” to mean limited in every way, “infinite” to mean unlimited in all respects, and then allow for the possibility of things that are neither finite or infinite—perhaps us.