On All-False Open Futurism (AFOF), any future tensed statement about a future contingent must be false. It is false that there will be a sea battle tomorrow, for instance.
Suppose now I realize that due to a bug, tomorrow I will be able to transfer ten million dollars from a client’s account to mine, and then retire to a country that won’t extradite me. A little angel says to me:
- Your freely taking your client’s money without permission tomorrow entails your being a thief tomorrow.
I don’t want to be a thief, tomorrow or ever, so I am about to decide not to do it. But now a little devil convinces me of AFOF and says that while (1) is true, so is:
- Your freely taking your client’s money without permission tomorrow entails your being a saint tomorrow.
Perhaps I am not very good at modal logic and the devil needs to explain. Given AFOF, it is necessarily false that I will freely take my client’s money without permission tomorrow, and a necessary falsehood entails everything. So, the devil adds, I might as well buy my plane tickets now.
The angel, however, grants AFOF for the sake of argument, but says that notwithstanding (2), the following holds:
- Tomorrow it will be the case your taking your client’s money without permission entails your being a thief.
For the entailment holds always.
At this point, we have an interesting question. Given AFOF, should I guide my actions by the entailment between future-tensed claims in (2) or by the future-tensed entailment claim in (3)? The angel urges that the devil’s reasoning undercuts all rationality, while the angel’s reasoning does not, and hence is superior.
But the devil has one more trick up his sleeve. He notes that it is a contingent question whether there will be a tomorrow at all. For God might freely decide to end time before tomorrow. Thus, that there will be a tomorrow is false on AFOF. But (3) implies that there will be a tomorrow, and so (3) is false as well. I try to argue on the basis of Scripture that God has made promises that entail a future eternity, but the devil is a lot better at citing the Bible than I, and convinces me that God might transfer us to a timeless state or maybe eternal life is a supertask lasting from 8 to 9 pm tonight. And in any case, surely it should not depend on revelation whether the angel has a good argument not to take the client’s money. This is a problem for AFOF.
Maybe this is the way out. The angel could say this:
- Necessarily, if there will be a tomorrow, then it will be true tomorrow that taking your client’s money without permission entails your being a thief.
But while this conditional is true on AFOF, if the devil has made his case that God hasn’t promised there will be a tomorrow, he can respond with:
- Necessarily, if God hasn’t promised there will be a tomorrow and there will be a tomorrow, then it will be true tomorrow that taking your client’s money without permission entails your being a saint.
For the antecedent of the conditional here is necessarily false on AFOF, it being contingent that there will be a tomorrow absent a divine promise. And it seems that (5) is even more relevant to guiding action than (4), then.
Maybe the defender of AFOF can insist that the future must be infinite. But this does not seem plausible.
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I think proponents of AFOF like Patrick Todd and Amy Seymour would say that the devil’s reasoning relies on a fundamental scope mistake. The devil’s arguments only work if one misinterprets "will" as a simple indicative.
The devil’s claim is that because "I will freely take my client’s money tomorrow" is a future contingent, AFOF renders it a necessary falsehood, from which anything follows.
This misunderstands what AFOF actually claims is false. Both Seymour and Todd argue that "will" should be understood as a modal operator that functions like a universal quantifier over all possible or "available" futures.
The proposition that is false is: "In all possible futures, I take the money". The proposition that is contingent is the content itself: "I take the money." The falsity of the first claim does not make the second a necessary falsehood. It just means that there is at least one possible future where I do not take the money. Since the action itself is not a necessary falsehood, the principle of explosion does not apply, and it does not entail "your being a saint tomorrow."
If anything, the angel's reasoning is the proper way to deliberate on an AFOF model. The angel's claim, "Tomorrow it will be the case your taking your client’s money without permission entails your being a thief," is a statement about a necessary connection that holds in every possible future.
So the devil’s final move (that the angel's claim (3) is itself false because "there will be a tomorrow" is a future contingent) is also mistaken. The existence of a "tomorrow" is a structural feature of the branching-time models that undergird these theories. The set of "available futures" are the tomorrows.
As Seymour's framework shows, a proposition like WILL: (p ∨ ~p) is true. This means it is settled that something will happen tomorrow or not happen tomorrow, which presupposes the existence of a tomorrow for events to unfold in. Therefore, "there will be a tomorrow" is not a future contingent in the same way as a sea-battle. It is a future necessity and therefore true, unless one posits a specific, contingent world-ending event, which changes the model but doesn't save the devil's original logical error.
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