First, let’s agree to reject dialetheic logics out of hand; it will be taken as a non-starter for me, and, I hope, for you, if any argument were to proceed on the assumption that a proposition can be both true and false at the same time and in the same sense. It may be useful, at times, to proceed as though this were the case (I’m not denying the usefulness of paraconsistent logics), but it certainly cannot be literally correct. Such logical systems do not (and, by implication granting S5, cannot) describe the extra-mental structure of modality.
Can God know the future on open theism? It is typically assumed that open theism involves a commitment to Presentism about time (according to which future events are not real, and so propositions about the future are not literally true). I am not sure that this is correct, since they may, perhaps, accept the growing-block theory of time instead, but that will land them in precisely the same predicament as Presentism will as far as my following objections are concerned. In any case, the open theist must accept some version of the A-theory other than the moving-spotlight theory of time (or other more esoteric theories of time which will allow for the reality of future events or states of affairs). God, on the open theist view, shouldn’t be able to know the future because there is no future to know.
It seems undeniable that if “P” is true, and if “P⊃Q” is true, then “Q” is true; that’s just good old Modus Ponens. Now, let’s take P to represent the tripartite conjunction: “the state of affairs S1 in the world will entail the subsequent state of affairs S2 just in case God does not intervene in the world at some time between S1 and S2 (inclusive of S1, not inclusive of S2) and God will not intervene in the world at any time between S1 and S2, and S1 describes the current state of affairs.” Let Q represent the proposition “in the future, S2 will be the case.”
Let us say that God knows P, and God knows that P⊃Q. Does God know Q? If not, He has a deficient grasp of logic. If so, then He knows at least some fact(s) about the future.
- If open theism is true, God cannot know the future.
- Possibly, God can know propositions like “P” and “P⊃Q.”
- If God can know propositions like “P&(P⊃Q),” then God can know propositions like Q.
- If God can know propositions like Q, then God can know propositions about the future.
- If God can know propositions about the future, then God can know the future.
- Therefore, open theism is false.
What will the open theist say? The most plausible response open to them, I think, is to deny premise 5. Generally we think of propositions about the future as having truth-makers which are future states of affairs, but it is conceivable that there be true propositions about the future which have, as their truth-makers, nothing beyond present truth-makers. Perhaps P is presently true, while Modus Ponens and P⊃Q are true presently (they may be timeless truths, so we avoid saying that they are ‘presently’ true, even if they are true presently). That might be a sufficient response. A second response might go like this: premise 1 should be restated as 1*: “if open theism is true, God cannot know the whole future,” and premise 5 should be restated as 5*: “If God can know propositions about the future, then God can know at least some of the future.” Obviously 6 does not logically follow from 1*-5*.
Here’s a second argument:
- If a proposition is meaningful, then it cannot fail to be true or false (where the ‘or’ is exclusive).
- There are meaningful propositions about the future which are not entailed by any presently available truths.
- Therefore, there are true propositions about the future which are not entailed by any presently available truths (they cannot all be false, for if P is false, then “P is false” is true).
- God is omniscient.
- A being is not omniscient if there are truths (i.e., meaningful true propositions) it fails to know.
- If open theism is true, there are meaningful true propositions about the future which God fails to know.
- Therefore, open theism is false.
The best responses to this argument which I have heard include (i) denying premise 2 altogether, or (ii) denying premise 1. The denial of premise 1 (given our assumed rejection of dialetheic logics) amounts to a rejection of the law of excluded middle (LEM), and that, my friends, is as good as a reductio against open theism. Rather, it is a reductio of open theism! Alternatively, to deny premise 2 (by denying the meaningfulness of propositions about future states of affairs not entailed by presently available truths), seems implausible given the fact that we all apprehend the meaning of sentences like “tomorrow Julie will eat worms in the playground again.” So, we have at least one relatively good, though simple, argument against open theism.
… Maybe there’s time for a quick third: suppose that epistemic justification means something like ‘true justified belief’ (and let’s, for the moment, ignore Gettier cases, just for simplicity). Now it looks like I can know propositions like P:”tomorrow I will finally propose to her,” even though it looks like God cannot know P! That’s another reductio ad absurdam to add to our growing list of reasons to reject open theism.
My mistake; obviously this last argument presupposes the ‘truth’ of propositions like P, but that’s the very object of contention, so my argument runs in, as they say, a circle of embarrassingly short diameter.
As to whether either of the former arguments will work, it seems to me that if the open theism is too deeply entrenched then the open theist will simply bite the bullet and accept the consequences of my arguments while maintaining open theism. However, at least the arguments can act as a warning to others to avoid the philosophical pit that is open theism.