In yesterday’s post, I showed that if an open-futurist is impressed by a certain plausible-sounding logical fatalism argument based on bivalence, and hence opts for truth gaps, then they should also be impressed by another logical fatalism argument based not on bivalence but on truth gaps.
However, there was a weakness to my logical fatalism argument. It was based on the principle:
- If something true now is incompatible with it’s being true that p, then p is not within your power.
But perhaps our open futurist will deny (1) on the grounds that a present action can be within our power, even though it is presently true that we will do it. (I think this is a problematic concession for the open futurist to make, but let’s bracket that.) Such an open futurist will instead run arguments based on:
- If q is a past-tensed truth, and q is incompatible with p, then p is not within your power.
Well, here is perhaps a truth value gap counterexample to (2).
Alice freely ϕs at 5 pm.
At 1 pm it is true that no indeterministic events will happen between 2 and 4 pm.
(To get the second part, we can suppose that the laws of nature are such that they only allow indeterministic events after 4:30 pm each day, or maybe God just promises not to allow any indeterministic events between 2 and 4 pm.)
So, consider the following complicated past-tensed statement, which is true at 3 pm:
- q: Two hours ago [i.e., at 1 pm], it was true that no indeterministic events would happen between an hour ago [2 pm] and an hour from now [4 pm], while half an hour ago [2:30 pm], it was neither true nor false that Alice freely ϕs at 5 pm.
Now, on the open futurist’s view, time-indexed propositions can only gain truth value as the result of indeterministic events. It logically follows from the ban on indeterministic events between 2 and 4 pm that any time-indexed proposition that was neither true nor false at 2:30, is also neither true nor false at 3 pm. Or to put it in a tensed way, q entails:
- It is neither true nor false that Alice ϕs at 5 pm.
But (3) is logically incompatible with Alice ϕing at 5 pm, since, necessarily, if Alice ϕs at 5 pm, then it’s true that Alice ϕs at 5 pm. Since q entails (3), it follows that:
- q is logically incompatible with Alice ϕing at 5 pm.
Hence it follows from (2) (since q is a past tensed truth) that at 3 pm it is true to say:
- It is not within Alice’s power that Alice ϕs at 5 pm.
Now, I said that “perhaps” this was a counterexample to (2). Besides objecting to the Tarski T-schema, there is one powerful response an open futurist can make. They can just embrace (5) and say: it’s only at 5 pm, or shortly prior to it, that it comes to be within Alice’s power to ϕ.
But I think the open futurist’s intuitions behind (2) also support:
- If q is a past-tensed truth and p is time-indexed, and q is incompatible with p, then p will never be within your power.
(The reason for the restriction to time-indexed p is to avoid this counterexample. Let q be the proposition that there was no wine in the world a minute ago. Let p be the proposition that you are drinking well-aged wine. Then p and q are incompatible. But if you make wine, and age it, then it can come to be the case that drinking well-aged wine is in your power.)
And now (4) and (6) imply:
- It will never be within Alice’s power that Alice ϕs at 5 pm,
which is just false in our story, since she does ϕ at 5 pm! (Alternate phrasing: replace “within Alice’s power” with “up to Alice”.)
What about open futurists who instead of supposing a truth value gap think that statements about contingent future events are all false? Well, such open futurists will not accept q (at 3 pm). But they will accept:
- q′: Two hours ago [i.e., at 1 pm], it was true that no indeterministic events would happen between an hour ago [2 pm] and an hour from now [4 pm], while half an hour ago [2:30 pm], it was false that Alice freely ϕs at 5 pm.
Again, on their view, time-indexed propositions only change truth value when indeterministic events happen. Thus, q′ entails that presently (i.e., at 3 pm) it is still false that Alice freely ϕs at 5 pm. And the rest of my argument goes through.
So it pretty much seems like I’ve shown that the only person who can accept a principle like (6) is someone who doesn’t believe in the possibility of free will.
Maybe what this is really an argument for is that the open futurist needs to deny the T-schema, which I had used to argue that if something is incompatible with it’s being true that Alice will ϕ at 5 pm, then it’s incompatible with Alice ϕing at 5 pm. Some open futurists do do that (Keith DeRose, for instance; I wonder now: do they do it because of an argument like this one?)
I have to confess a nagging suspicion of an error somewhere. I already found one that I just corrected—I had to restrict (6) to time-indexed truths, which forced me to remove an argument that would work even without the T-schema.
