Always-false open-futurism and the end of time

On always-false open-futurism, reports of future contingents are always false.

Now, imagine that it is contingent whether the time continues past t₁. Perhaps God sustains the world in existence, and has promised to sustain it until t₁ inclusive, but is free to stop sustaining it right then.

Suppose it is now t₁. Thus, now is potentially the last moment of time, but potentially not. What does the previous sentence mean? It seems to mean the conjunction of these two claims:

1. How things are now is compatible with its not being the case that there will be time.

2. How things are now is compatible with its being the case that there will be time.

But on always-false open-futurism, when the very existence of future time is contingent in light of how things are now, all will-claims have to be false. Thus, how things are now necessitates that its not the case that there will be time. In other words, we don’t have (2).

If this is correct, then on always-false open-futurism there cannot be a moment which is both potentially the last moment of time and potentially not the last moment of time. Each moment of time either is necessarily not last or necessarily last. This is a bit of a burden for the theory.

On trivalent open-futurism on which will-claims about future contingents are neither true nor false, the problem disappears. That now is potentially the last moment of time but potentially not can be taken to be equivalent to:

3. It is neither true nor false that there will be time.