Suppose that the future is not open, so that there are non-trivial truths about what people will freely do. (If we want more precision, we may suppose unrestricted bivalence, excluded middle and the rule: (exists(t) & t>now & ~will-hold-at(p,t)) → will-hold-at(~p,t).) According to ot, God does not know all such truths. Thus, according to non-open-future open theism (nofot), God knows some but not all truths. If one accepts nofot (as van Inwagen and Hasker seem to), then when defining the range of omniscience (there are several aspects to omniscience: the range aspect specifies what truths are known by the omniscient being; but there is also the inerrance aspect, the justification aspect, and maybe a modal aspect), we cannot simply say that God knows all truths. Something else needs to be said.
Some have said things like this:
- God knows p iff p is true and in some possible world p is known by somebody (cf. van Inwagen).
Anyway, Bill Hasker and I have had an extended email discussion on the question of how to define the range of omniscience, and Bill kindly let me comment on that discussion in public, as long as I included "the statement that [Hasker's] personal concern is primarily with the question, 'What truths must God know, if God is omniscient?'" I take this to mean that Bill's focus is on the issue of the range of omniscience.
As an initial move, Hasker pointed out that (1) is not a fair statement of what nofot proponents have meant by statements like "God knows everything that can be known." Rather than saying that God knows every truth which is such that God knows it in some world, they meant that God knows every kind of truth that it is possible for God to know. Our correspondence focused on refining this intuition.
One worry I've had from the beginning was that if omniscience is defined by saying that x is omniscient iff x knows any truth that isn't of a kind that it is impossible for x to know, then some very limited beings will count as omniscient. For instance, every kind of truth is impossible of being known by an electron, perhaps, and so electrons will count as omniscient. Hasker pointed out, however, that his project is not defining omniscience in general, but defining God's omniscience. He was looking for a definition that would apply to an (otherwise) divine being.
After much back and forth, we provisionally (and Bill emphasized the provisionalness of this when he allowed me to share the notion) agreed on the following as expressing Bill's intuition:
- A being that is divine is omniscient if and only if essentially: (a) x Knows all the truths of classes U1, . . . Un, (b) x's Knowledge is closed under entailment, and (c) x Knows every truth that does not fall in a kind L of truths such that it can be proved from necessary truths that x does not Know any member of L.
The notion of a "kind" or "class" (I think the terms are synonymous in our discussion) is modally shifty--a kind or class isn't a set that has its membership essentially. For instance, empirical truths are a kind of truths, but of course what propositions are empirical truths is different between worlds. Moreover, the "proofs from necessary truths" are supposed to be non-trivial. Thus, it won't do to trivialize (c) by considering the kind L of truths "truths that x does not know", since the proof that x doesn't know any truths from L is trivial.
Hasker's idea, then, is that if the arguments for the incompatibility of foreknowledge and free will succeed, then because their premises all are necessary truths, it follows that, roughly, the class of truths reporting future free actions will be one of the exceptional kinds in (c). On the other hand, if the arguments fail, then (c) still requires God to know truths reporting future free actions. Thus, (2) is something that all parties to the debate should be able to accept.
Objection 1: Suppose that the arguments for the incompatibility of foreknowledge and free will all fail. Then an omniscient being has to know future free actions. But now imagine Fred who is divine, and who essentially has properties (a) and (b), and who essentially has two additional properties: (d) he does not Know any future free actions and (e) he does not believe anything he does not Know. Then, Fred satisfies (a) and (b). Moreover, he satisfies (c) trivially if we let L be the kind truths that Fred does not believe. For it can be non-trivially proved from necessary truths that Fred does not Know any truths of kind L (Knowledge, just like knowledge, requires belief, and this is a non-trivial thesis), and hence (c) at most requires of Fred that he Know all the truths that he believes, which is guaranteed by (e). So, Fred counts as omniscient. But he shouldn't, if the arguments for the incompatibility of foreknowledge and free will all fail.
As of the end of our conversation, Hasker thinks this problem is not "very significant" because it is an "arbitrary assumption" that Fred doesn't know future free actions, given the failure of the arguments. I do not fully understand the significance of this objection. Maybe the force of the objection is that the definition is supposed to apply only to non-gerrymandered beings (maybe that's a part of being divine)? To be honest, here there is a methodological question to which I have no answer. Quite possibly, counterexamples to (2) are going to be impossible beings, since quite possibly, the only possible divine being is God, and he is presumably no counterexample to (2). However, it seems to me that gerrymandered impossible beings can still be useful tools for showing that the definition is inadequate. But perhaps commenters will have something wiser to say on this point.
Objection 2: Suppose that JITB+ is the correct account of Knowledge (justified, infallible, true belief, plus any needed anti-Gettier condition). This fact about Knowledge is non-trivial. Then, consider the classes L1, L2, L3 and L4 of truths: L1 is the class of truths that x is not justified in believing; L2 is the class of truths that x is not infallible in believing; L3 is the class of truths that x does not believe; L4 is the class of truths that x believes Gettieredly. Then, if it is a necessary truth that Knowledge = JITB+, it follows that each of the classes L1, L2, L3 and L4 has the property that it can be proved from necessary truths that God doesn't believe any member of the class. But then (c) requires x to Know a certain subclass of the truths that are not in the union of L1, L2, L3 and L4. But the union of L1, L2, L3 and L4 is all the truths that x does not Know. Hence, (c) requires x to Know a certain subclass of the truths that x Knows, a requirement that is always trivially satisfied. Hence, condition (c) holds of every x, and does so necessarily, as long as there is a correct and non-trivial account of Knowledge (JITB+ was just an example). Now, maybe, there is no correct and non-trivial account of Knowledge. But it would be odd if a definition of omniscience required that supposition for its non-triviality. (Neither this nor the next objection were put by me to Bill after we formulated (2), so I don't know what he would say.)
Objection 3: Consider the following class L5 of truths: all truths p such that either x does not Know p or Fermat's Last Theorem is false. Then, we can prove that x does not Know any truth in L5. But the proof is non-trivial, because it depends on the non-trivial fact that Fermat's Last Theorem is true. Now any x Knows all the truths that aren't in L5, since a truth is in L5 iff x doesn't Know it. So, if L5 is an admissible kind, then (c) trivially holds for all x and can be dropped.
Perhaps this objection can be avoided by requiring the kinds in (c) to be natural enough. But now the problem is whether open theism is compatible with (c). Maybe the kind L6 truths reporting future free actions is natural. But given the closure of divine knowledge under entailment, that's not enough. An open-theist God also can't know truths like Obama is not president or I will freely mow the lawn. We could try to rule those out by introducing some kind like L7: truths that have as their only true disjuncts a future free action. But of course the example can be varied indefinitely: It's not the case that both Obama is president and I will not freely mow the lawn. And not all the cases will yield "natural enough" exceptional kinds. Perhaps, instead, one includes as an exceptional kind L8: truths that include a report of a future free action. But that's too big an exception: an omniscient deity should be required to know that I either will or will not freely mow. So maybe we want L9 truths that when combined with other things x Knows entail a report of a future free action. It's not clear that this is natural enough, though. Moreover, L9 isn't quite enough, either. For an open-theist deity not only doesn't Know that I will freely mow the lawn tomorrow and doesn't Know that you will freely mow the lawn tomorrow, but also doesn't know that either I or you will freely mow the lawn tomorrow. So: L10 truths that when combined with other things x Knows entail a non-trivial disjunction of future free actions ("I will or will not freely mow" counts as a trivial disjunction). But the more wrinkles we put on, the less natural the kind. Maybe we can try this: L11 truths every truthmaker of which includes a future free action. That's more natural than L10, but has truthmaker commitments. Moreover, it's too strong. For even an open-theist deity can know some truths whose truthmaker includes a future free action. For instance, it might be determined that if I don't freely mow the lawn tomorrow, I will be compelled to mow the lawn. But in fact I freely mow the lawn tomorrow. In that case the proposition that I will mow the lawn tomorrow is made true only by my future free action of mowing the lawn, but it is a proposition that an omniscient deity should have to know. (Maybe though it is included in U1,...,Un. Still, in that case, it is condition (a) that is doing the brunt of the work, I think.)
Does anyone have a better nofot-compatible definition of omniscience?