Omniscience and vagueness

Suppose there is metaphysical vagueness, say that it’s metaphysically vague whether Bob is bald. God cannot believe that Bob is bald, since then Bob is bald. God cannot believe that Bob is not bald, since then Bob is not bald. Does God simply suspend judgment?

Here is a neat solution for the classical theist. Classical theists believe in divine simplicity. Divine simplicity requires an extrinsic constitution model of divine belief or knowledge in the case of contingent things. Suppose a belief version. Then, plausibly, God’s beliefs about contingent things are partly constituted by the realities they are about. Hence, it is plausible that when a reality is vague, it is vague whether God believes in this reality.

Here is another solution. If we think of belief as taking-as-true and disbelief as taking-as-false, we should suppose a third state of taking-as-vague. Then we say that for every proposition, God has a belief, disbelief or third state, as the case might be.

Omniscience, timelessness, and A-theory

I’ve been thinking a lot this semester, in connection with my Philosophy of Time seminar, about whether the A-theory of time—the view that there is an objective present—can be made consistent with classical theism. I am now thinking there are two main problems here.

1. God’s vision of reality is a meticulous conscious vision, and hence if reality is different at different times, God’s consciousness is different at different times, contrary to a correct understanding of immutability.

2. One can only know p when p is true; one can only know p when one exists; thus, if p is true only at a time, one can only know p if one is in time. On an A-theory of time, there are propositions that are only true in time (such as that presently I am sitting), and hence an omniscient God has to be in time. Briefly: if all times are the same to God, God can’t know time-variable truths.

I stand by the first argument.

However, there may be a way out of (2).

Start with this. God exists at the actual world. Some classical theists will balk at this, saying that this denies divine transcendence. But there is an argument somewhat parallel to (2) here. If all worlds are the same to God, God can’t know world-variable truths, i.e., contingent truths.

Moreover, we can add something positive about what it is for God to exist at world w: God exists at w just in case God actualizes w. There is clearly nothing contrary to divine transcendence in God’s existing at a world in the sense of actualizing it. And of course it is only the actual world that God actualizes (though it is true at a non-actual world w′ that God actualizes w′; but all sorts of false things are true at non-actual worlds).

But given the A-theory, reality itself includes changing truths, including the truth about what it is now. If worlds are ways that all reality is, then on A-theory worlds are “tensed worlds”. Given a time t, say that a t-world is a world where t is present. Argument (2) requires God to exist at a t-world in order for God to know something that is true only at a t-world (say, to know that t is present).

Now suppose we have an A-theory that isn’t presentism, i.e., we have growing block or moving spotlight. Then one does not need to exist at t in order to exist at a t-world: on both growing block and moving spotlight our 2025-world has dinosaurs existing at it, but not in 2025, of course. But if one does not need to exist at t in order to exist at a t-world, it is not clear that one needs to exist in time at all in order to exist at a t-world. The t-world can have a “locus” (not a place, not a time) that is atemporal, and a being that exists at that atemporal locus can still know that t is present and all the other A-propositions true at that t-world.

Next suppose presentism, perhaps the most popular A-theory. Then everything that exists at a t-world exists at t. But that God exists at the t-world still only consists in God’s actualizing the t-world. This does not seem to threaten divine transcendence, aseity, simplicity, immutability, or anything else the classical theist should care about. It does make God exist at t, and hence makes God in time, but since God’s existing in time consists in God’s actualizing a t-world, this kind of existence in time does not make God dependent on time.

I still have some worries about these models. And we still have (1), which I think is decisive.

Perfect vision

One of the major themes in modern philosophy was concerns about the way that our contact with the world is mediated by our “ideas”. Thus, you are looking at a tree. But are you really seeing the tree, or are you just seeing your sense-impression, which doesn’t have much in common with the tree? Even direct realists like Reid who say you are seeing the cat still think that your conscious experience involves qualia that aren’t like a tree.

Thinking about this gives us the impression that an epistemically better way to relate to the tree would be if the tree itself took the place of our sense-impressions or qualia. Berkeley did that, but at the cost of demoting the tree to a mere figment of our perception. But if we could do that without demoting the tree, then we would be better kinds of perceivers.

However, that on some theory we would be better kinds of perceivers is not a strong reason to think that theory is true! After all, we would be better perceivers if we could see far infrared, but we can’t. It’s not my point to question the orthodoxy about our perceptions of trees.

But now think about beatitude, where the blessed see God. If seeing God is like seeing a tree in the sense that there is something like a mediating supersense-impression in us, then something desirable is lacking in the blessed. And that’s not right. Such a mediated vision of God is not as intimate as we could wish for. Would it not be so much more intimate if it were a direct vision of God in the fullest sense, where God himself takes the place of our qualia? We shouldn’t argue from “it would be better that way” to “it is that way” in our earthly lives, but in beatitude it does not seem such a terrible argument.

But where this kind of argument really comes into its own is when we think of what the epistemic life of a perfect being would be like. The above considerations suggest that when God sees the tree (and it is traditional to compare God’s knowledge of creation to vision), the vision is fully direct and intimate, and the tree itself plays the role of sense-impressions in us. We would expect a perfect being’s vision to be like that.

Now notice, however, that this is an account of God’s vision of the world on which God’s vision is partly extrinsically constituted: the tree partly constitutes God’s conscious experience of the tree. This is the extrinsic constitution model of how a simple God can know. We have thus started with us and with considerations of perfection, and have come to something like this model without any considerations of divine simplicity. Thus the model is not an ad hoc defense of divine simplicity. It is, rather, a model of the perfect way to epistemically relate to the world.

Divine attributes

In previous posts I’ve noted piecemeal that standard definitions of omniscience and omnipotence are incomplete. God’s omnipotence isn’t just that God knows everything—it has to be that he knows it certainly and consciously. We might even say: with maximal certainty and vividness. God’s omnipotence isn’t just that God can do everything—he does it all effortlessly.

It has now occurred to me that both devotionally and philosophically it is fruitful to think about divine attributes by asking what is left out by the rather thin and colorless analytic accounts of them.

Take a flat account of God’s moral perfection as saying that God always does the morally right thing. Well, first, we have to add: and for the right reasons (indeed all the right reasons). Second, we should add that God does this with the perfect attitude—with the appropriate alacrity, without inappropriate regrets, etc.

Or consider the account of God’s being a creator on which God creates everything other than himself. We probably should minimally add that he does this with perfect freedom.

At the moment, this is all I have in the way of clear examples. But I think it’s a worthwhile avenue for exploration and devotion.

From three or four problems of omniscience down to one

The three most influential problems of omniscience are:

1. Boethius’ problem of foreknowledge: What is known is necessarily so, and thus if God knows what you will do, you will necessarily do it.

2. Pike’s problem of foreknowledge: If you can act otherwise, you can thereby make it be that either God didn’t exist or that God wasn’t omniscient or that God had believed otherwise than God actually did, and you just can’t do that.

3. The simplicity and knowledge of contingents problem: If the world had been different, God’s beliefs would have been different, which implies that God’s beliefs are accidents of God, contrary to divine simplicity.

Of these, (1) is fully solved by Boethius/Aquinas by distinguishing between necessity of consequence and necessity of consequent. The problem in (1) is just a simple matter of a fallacy of modal scope ambiguity. It’s a non-problem.

I now want to argue that the most widely accepted solution to (3) also solves (2).

This solution, likely already known to Aquinas, is that God’s belief in contingent facts is partly extrinsically constituted by creatures, and all the contingency is on the created side. For instance, God’s belief that there are zebras is grounded in essential facts about God that do not vary between possible worlds and the actual existence of zebras, which only obtains in some possible worlds.

Suppose we apply this solution to (3). Then God’s belief that you will ϕ at t is partly grounded in your ϕing at t and partly in essential facts about God. At this point it is obvious that:

4. If you were not to ϕ at t, God wouldn’t have believed you would ϕ at t.

For the contingent part of the grounds of God’s believing that you would ϕ at t is your actually ϕing at t, so when you take that away, God’s belief goes away. And if instead you ψ at t, your action thereby constitutes the contingent part of the grounds of God’s believing that you would ψ at t, and so:

5. If you were to ψ at t, God would have believe you would ψ at t.

If God’s past belief is partly constituted by our actions, it is no surprise that there is counterfactual dependence between our actions and God’s past belief. In other words, the classical theist who accepts divine simplicity has a way out of Pike’s argument that is motivated completely independently of considerations of time and freedom, namely by embracing counterfactuals like (4) and (5) that Pike considers absurd.

Of course the extrinsic constitution of divine beliefs is somewhat hard to swallow, notwithstanding excellent work by people like W. Matthews Grant to make it more plausible (I myself have swallowed it). But once we do that, problem (2) is gone, and problem (1) was never there as it was based on a fallacy.

There is a fourth problem, a more recondite one, which is about the incompatibility between God’s knowledge of what time is objectively present (assuming the A-theory of time) and divine immutability. Probably the most extensive pressing of this problem is in Richard Gale’s On the Nature and Existence of God. But Aquinas (according to the very plausible interpretation by Miriam Pritschet in an excellent paper I heard yesterday at the ACPA) responds to the fourth problem precisely by using the extrinsic constitution of God’s knowledge of continent facts (indeed this is why I said that the solution to the simplicity problem was likely known to Aquinas). So even that fourth problem reduces to the third—or just doesn’t get off the ground if the B-theory of time is true.

Aquinas on God's knowledge of propositions

Does God know that the sky is blue?

That seems like a silly question. It’s not like we’re asking whether God knows future contingents, or counterfactuals of freedom. That the sky is blue is something that it is utterly unproblematic for God to know.

Except that it is tempting to say that God has no propositional knowledge, and knowing that the sky is blue is knowing a proposition.

It seems that Aquinas answers the question in Summa Theologiae I.14.14: “God knows all the propositions that can be formulated” (that’s in Freddoso’s translation; the older Dominican translation talks of “enunciable things”, but I think that doesn’t affect what I am going to say). It seems that God does have propositional knowledge, albeit not in the divided or successive way that we do.

But what he is up to in I.14.14 is not what it initially sounds like to the analytic philosopher’s ear.

For consider Thomas’s argument in I.14.14 that God knows all formulable propositions:

Since (a) to formulate propositions lies within the power of our intellect, and since (b), as was explained above (a. 9), God knows whatever lies within either His own power or the power of a creature, it must be the case that God knows all the propositions that can be formulated.

But now notice an ambiguity in “God knows the proposition that the sky is blue.” In one sense, which I will call “alethic”, this just means God knows that the sky is blue. In another sense, the “objectual”, it means that God knows a certain abstract object, the proposition that the sky is blue. In the objectual sense, God also knows the proposition that the sky is green—God fully knows that proposition, just as he knows other objects, like the person Socrates. But God does not, of course, have the alethic knowledge here—God does not know that the sky is green, because the sky is not green.

If it was the alethic sense that Thomas was after, his argument would be invalid. For in article 9, the discussion clearly concerns objectual knowledge. Exactly the same argument establishes that God knows the proposition that the sky is green as that he knows the proposition that the sky is blue. Furthermore, the Biblical quote Thomas gives in support of his view is “The Lord knows the thoughts of men” (Psalm 93:11). But the Lord doesn’t know all of them to be true, doesn’t know all of them alethically, because not all of the thoughts of humans are true.

Furthermore, if it was alethic knowledge that Aquinas was after, it would be inaccurate to say God knows all propositions. For only “half” of the propositions can be known alethically—the true ones!

All that said, I think we can still bootstrap from the objectual to the alethic knowledge. God’s knowledge of objects is perfect (Aquinas relies on this perfection multiple times in Question 14) and hence complete. If God knows something, God also knows all of its properties, intrinsic and relational. Thus, if God knows a proposition objectually, and that proposition has a truth value, God knows that truth value. In particular, if that proposition is true, God knows that it is true. And that seems to suffice for counting as knowing the proposition alethically.

So, it looks like Aquinas is committed to God objectually knowing both the propositions that the sky is green and that the sky is blue, and also knowing that the former is false and the latter is true—which seems to be enough for God to count as knowing that the sky is blue. (Though I could see this last point getting questioned.)

More on A-theory and divine timelessness

Argument One:

1. If from x’s point of view there is an objective fact about what time it presently is, then x is in time.

2. If x knows an objective fact about something, then from x’s point of view there is an objective fact about it.

3. If the A-theory of time is true, then there is an objective fact about what time it presently is.

4. God knows all objective facts.

5. So, if the A-theory of time is true, then God knows an objective fact about what time it presently is. (3 and 4)

6. So, if the A-theory of time is true, from God’s point of view there is an objective fact about time it presently is. (2 and 5)

7. So, if the A-theory of time is true, God is in time. (1 and 6)

Note that no claim is made that if the A-theory of time is true, God changes.

Argument Two:

1. God is actual.

2. Everything actual is in the actual world.

3. If the A-theory of time is true, the actual world is a temporally-centered world (one where there is a fact as to what time is present).

4. Anything that is in a temporally-centered world is in time.

5. So, if the A-theory of time is true, God is in time.

Many will dispute 3, but if we think of worlds as ways for everything to be, then I think it is hard to dispute 3.

I wonder if a classical theist who is an A-theorist might be able to respond that, yes, God is in time but God is not a temporal being. Compare that by doctrine of omnipresence, God is in space, but God is not a spatial being. Still, I think there is a difference. For as the above arguments show, the claim that God is in time is more limiting than the claim that God is spatially omnipresent—it is a claim that God is at the one objectively present point of time (he was and will be at others, of course).

God's timelessness, the A-theory of time, and two kinds of Cambridge change

Classical theism holds that God is timeless and knows all objective truths. According to A-theories of time, objective truths change (e.g., what exists simpliciter changes on presentism, and on other A-theories at least what time is objectively present changes). There is a prima facie conflict here, which leads some classical theists to reject the A-theory of time.

But there is also a widely accepted reply. Classical theism also holds that God is simple. One of the consequences of divine simplicity is that if God had created a different world, he wouldn’t have been any different intrinsically—and yet he would know something different, namely that he created that world rather than this one. Seemingly the only good solution to this problem is to suppose that God’s knowledge is in part extrinsically constituted—that facts about what God knows about contingent things are partly constituted by these contingent things.

But the same move seems to save timelessness and the A-theory. For if God’s knowledge is partly extrinsically constituted, then as the created world objectively changes, as the A-theory holds, God’s knowledge can change without any intrinsic change in God. Basically, the change of God’s knowledge is only a Cambridge change in God—a purely relational change.

I have always been pulled two ways here. Since I accepted divine simplicity, the response seemed right. But it also seemed right to think there is a tension between God’s timelessness and the A-theory of time, thereby yielding an argument against the A-theory.

I haven’t settled this entirely to my satisfaction, but I now think there may well be an argument from classical theism against the A-theory.

First, note that the extrinsic constitution move is aimed not specifically at a tension between God’s timelessness and the A-theory, but at a tension between God’s immutability and the A-theory. The move shows how an immutable being could have changing knowledge, because of extrinsic constitution. But while any timeless being is immutable, the other implication need not hold: timelessness is a stronger condition than immutability, and hence there could be a tension between divine timelessness and the A-theory even if there isn’t a tension between immutability and the A-theory.

Here is why I see a tension. The crucial concept here is of a merely relational change, a Cambridge change. The most common example of a Cambridge change is something like:

1. Bob became shorter than his daughter Alice.

Here, we’re not supposed to think that Bob changed intrinsically, but simply that Alice got taller!

But there is another kind of change that I used to lump in with (1):

2. Dinosaurs became beloved of children around the world.

Both are, I suppose, Cambridge changes. But they are crucially different. The difference comes from the fact that in (1), the change is between the slightly younger Bob being taller than Alice was then and the slightly older bob being sorter than Alice was then. While the change was due to Alice’s growth, rather than Bob’s shrinkage, nonetheless it is crucial to this kind of Cambridge change that we be comparing the subject at t₁, considered relationally, with the subject at t₂, again considered relationally. It is, say, the 2018 Bob who is taller than Alice, while it is the 2023 Bob who is shorter than Alice. I will call this kind of thing strong Cambridge change.

But when dinosaurs become beloved of children around the world, as they did over the course of the 20th century, this wasn’t a change between earlier and later dinosaurs. Indeed, the dinosaurs were no longer around when this Cambridge change happened. I will call this kind of thing weak Cambridge change.

Strong Cambridge change requires an object to at least persist through time: to be one way (relationally) at one time and another way (again, relationally) at another. Weak Cambridge change does not require even that. One can have weak Cambridge change of an object that exists only for an instant (think of an instantaneous event that becomes notorious).

A timeless being can “undergo” weak Cambridge change, but not strong Cambridge change. And I suspect that change in knowledge, even when the knowledge is extrinsically constituted, is strong Cambridge change.

Here is a piece of evidence for this thesis. Knowledge for us is partly extrinsically constituted—if only because (I am grateful to Christopher Tomaszewski for this decisive point) what we know has to be true, and truths is typically extrinsic to us! But now suppose that I have a case where the only thing lacking to knowledge is truth—I have a belief that is justified in the right way, but it just happens not to be true. Now suppose that at noon the thing I believe comes to be true (here we are assuming the A-theory). If we set up the case right, I come to know the thing at noon, though the change is a strong Cambridge change. But suppose that at noon I also cease to exist. Then I don’t come to know the thing! To come to know something, I would have to persist from not knowing to knowing. Prior to noon I was such that if the thing were true, I’d know it, but the thing isn’t true. After noon, I don’t know the thing, even though it isn’t true, because I don’t exist after noon. Change in extrinsically constituted knowledge seems to be at least strong Cambridge change.

Further, think about this. When God knows p in one world and not-p in another, this transworld difference is a difference between how God is in the one world and how God is in the other world, even if it is a relational difference. Similarly, we would expect that if God changes from knowing p at t₁ to knowing not-p at t₂, God exists at t₁ and also at t₂. And this does not seem to fit with God’s timelessness. (But don’t classical theists say God is omnipresent, and shouldn’t that include omnitemporal presence? Yes, but omnitemporal presence is not omnitemporal existence.)

In other words, I think for God to change in knowledge in lockstep with the objective facts changing, God has to exist in lockstep with these objective facts. To change from knowing to not knowing some fact due to the change in these facts, one needs to be a contemporary of these changing facts. And a timeless being is not (except should there be an Incarnation) a contemporary of anything.

In summary: A timeless being can only undergo weak Cambridge change, while it is strong Cambridge change that would be needed to maintain knowledge through a change in objective truths, even if that change is extrinsically constituted. One can uphold the A-theory with a changeless God, but not, I think, a timeless God.

Or so I suspect, but I am far from sure, because the distinction between weak and strong Cambridge change is still a bit vague for me.

And even if my specific arguments about God aren't right, I think the weak/strong Cambridge change distinction is worth thinking about.

Anthropomorphism about God

Consider an anthropomorphic picture of God that some non-classical theists have:

1. God is not simple, and in particular God’s beliefs are proper parts of God.

2. God’s beliefs change as the reality they are about changes.

Putting these together, it follows that:

3. I can bring about the destruction of a part of God.

How? Easy. I am now sitting, and God knows that. So, a part of God is the belief that I am sitting. But I can destroy that belief of God’s by standing up! For as soon as I stand up, the belief that I am sitting will no longer exist. But on the view in question, God’s beliefs are parts of him. So by standing up, I would bring it about that a part of God doesn’t exist.

But (3) is as absurd as can be.

And of course by standing up, I bring it about that a new divine belief exists. So:

4. I can bring about the genesis of a part of God.

Which is really absurd, too.

Yet another formulation of my argument against a theistic multiverse

Here’s yet another way to formulate my omniscience argument against a theistic multiverse, a theory on which God creates infinitely concretely real worlds, and yet where we have a Lewisian analysis of modality in terms of truth at worlds.

1. Premise schema: For any first order sentence ϕ: Necessarily, ϕ if and only if God believes that ϕ.

2. Premise schema: For any sentence ϕ: Possibly ϕ if and only if ∃w(at w: ϕ).

3. Premise: Possibly there are unicorns.

4. Premise: Possible there are no unicorns.

5. Necessarily, there are unicorns if and only if God believes that there are unicorns. (Instance of 1)

6. Possibly, God believes that there are unicorns. (3 and 5)

7. Possibly God believes that there are unicorns if and only if ∃w(at w: God believes that there are unicorns). (Instance of 2)

8. ∃w(at w: God believes that there are unicorns). (6 and 7)

9. ∃w(at w: God believes that there are no unicorns). (from 1, 2, 4 in the same way 8 was derived from 1, 2, 3)

So, either there is a world at which it is the case that God both believes there are unicorns and believes that there are no unicorns, or what God believes varies between worlds. The former makes God contradict himself. The content of God’s beliefs varying across worlds is unproblematic if the worlds are abstract. But if they are concrete, then it implies a real disunity in the mind of God.

Premise schema (1) is restricted to first order sentences to avoid liar paradoxes.

Divine simplicity and divine knowledge of contingent facts

One of the big puzzles about divine simplicity which I have been exploring is that of God’s knowledge of contingent facts. A sloppy way to put the question is:

1. How can God know p in one world and not know p in another, even though God is intrinsically the same in both worlds?

But that’s not really a question about divine simplicity, since the same is often true for us. Yesterday you knew that today the sun would rise. Yet there is a possible world w₂ which up to yesterday was exactly the same as our actual world w₁, but due to a miracle or weird quantum stuff, the sun did not rise today in w₂. Yesterday, you were intrinsically the same in w₁ and w₂, but only in w₁ did you know that today the sun would rise. For, of course, you can’t know something that isn’t true.

So perhaps the real question is:

2. How can God believe p in one world and not believe p in another, even though God is intrinsically the same in both worlds?

I wonder, however, if there isn’t a possibility of a really radical answer: it is false that God believes p in one world and not in another, because in fact God doesn’t have any beliefs in any world—he only knows.

In our case, belief seems to be an essential component of knowledge. But God’s knowledge is only analogical to our knowledge, and hence it should not be a big surprise if the constitutive structure of God’s knowledge is different from our knowledge.

And even in our case, it is not clear that belief is an essential component of knowledge. Anscombe famously thought that there was such a thing as intentional knowledge—knowledge of what you are intentionally doing—and it seems that on her story, the role played in ordinary knowledge by belief was played by an intention. If she is right about that, then an immediate lesson is that belief is not an essential component of knowledge. And in fact even the following claim would not be true:

3. If one knows p, then one believes or intends p.

For suppose that I intentionally know that I am writing a blog post. Then I presumably also know that I am writing a blog post on a sunny day. But I don’t intentionally know that I am writing a blog post on a sunny day, since the sunniness of the day is not a part of the intention. Instead, my knowledge is based in part on the intention to write a blog post and in part on the belief that it is a sunny day. Thus, knowledge of p can be based on belief that p, intention that p, or a complex combination of belief and intention. But once we have seen this, then we should be quite open to a lot of complexity in the structure of knowledge.

Of course, Anscombe might be wrong about there being such a thing as knowledge not constituted by belief. But her view is still intelligible. And its very intelligibility implies a great deal of flexibility in the concept of knowledge. The idea of knowledge without belief is not nonsense in the way that the idea of a fork without tines is.

The same point can be supported in other ways. We can imagine concluding that we have no beliefs, but we have other kinds of representational states, such as credences, and that we nonetheless have knowledge. We are not in the realm of tineless forks here.

Now, it is true that all the examples I can think of for other ways that knowledge could be constituted in us besides being based on belief still imply intrinsic differences given different contents (beyond the issues of semantic externalism due to twinearthability). But the point is just that knowledge is flexible enough concept, that we should be open to God having something analogous to our knowledge but without any contingent intrinsic state being needed. (One model of this possibility is here.)

A Biblical argument for epistemicism

1. If God knows the exact number of hairs we have on our head, then there is a definite number of hairs we have on our head.

2. If there is a definite number of hairs we have on our head, vagueness is at most epistemic.

3. God knows the exact number of hairs we have on our head. (Luke 12:7)

4. So, vagueness is at most epistemic.

Premise 2 is based on observing that the number of hairs we have on our heads involves similar kinds of vagueness to more paradigmatic cases of vagueness. Think here about these questions:

• What’s the cut-off between hairs on the head and hairs on the upper neck?

• How much keratin needs to come out of a hair follicle before that keratin counts as a hair?

• How far must the molecules of a hair separate from the molecules of the skin before the hair counts as no longer attached?

One might worry that Premise 3 relies on biblical data too literalistically. Jesus is emphasizing the impressiveness of God’s knowledge. Suppose that instead of God knowing the exact number of hairs on my head, God knew the exact vagueness profile for the hairs on my head. That would be even more impressive. I see some force in this objection, but it implies that epistemicism holds at the level of vagueness profiles, and it seems (but perhaps isn’t?) ad hoc to go for epistemicism there rather than everywhere.

On reflection, I think premise 1 might be the most questionable premise. Perhaps God’s knowledge definitely matches the number of hairs: for every natural number n, it’s definitely true that: God believes I have n hairs if and only if I have n hairs, but there is no natural number n such that God definitely believes I have n hairs. In other words, the vagueness profile concerning God’s beliefs exactly matches the vagueness profile in reality. I am sceptical of this solution. It doesn’t feel like knowledge to me if it’s got this sort of vagueness to it.

An odd argument for an omniscient being

Here’s a funny logically valid argument:

1. The analytic/synthetic distinction between truths is the same as the a priori / a posteriori distinction.

2. The analytic/synthetic distinction between truths makes sense.

3. If 1 and 2, then every truth is knowable.

4. So, every truth is knowable. (1–3)

5. If every truth is knowable, then every truth is known.

6. So, every truth is known. (4–5)

7. If every truth is known, there is an omniscient being.

8. So, there is an omniscient being. (6–7)

I won’t argue for 1 and 2: those are big-picture substantive philosophical questions. I am sceptical of both claims.

The argument for 3 is this. If the analytic/synthetic distinction makes sense, then the two concepts are exclusive and exhaustive among truths: a truth is synthetic just in case it’s not analytic. So, every truth is analytic or synthetic. But if 1 is true and the analytic/synthetic distinction makes sense, then it follows that every truth is a priori or a posteriori. But these phrases are short for a priori knowable and a posteriori knowable. Thus, if 1 is true and the analytic/synthetic distinction makes sense, then every truth is knowable.

The argument for 5 is the famous knowability paradox: If p is an unknown truth, then that p is an unknown truth is a truth that cannot be known (for if someone know that p is an unknown truth, then they would thereby know that p is a truth, and then it wouldn’t be an unknown truth, and no one can’t know what isn’t so).

One argument for 7 is an Ockham’s Razor argument: it is more plausible to think there is one being that knows all things than that the knowledge is scattered among many. A sketch of a deductive argument for 5 that skirts over some important technical issues is this: if you know a conjunction, you know all the conjuncts; let p be the conjunction of all truths; if every truth is known, then p is known; and someone who knows p knows all.

Omniscience

The following account of the doctrine of propositional omniscience is incomplete:

1. x is omniscient iff x knows every truth and believes no falsehood.

For suppose that x believes no falsehood and knows every truth but is suffering from retrieval problems for the truths that x believes, in such a way that it takes x a minute to recall what is the capital of China. That’s not omniscience—it’s not sufficiently perfect as knowledge. This suggests to me that omniscience requires occurrent knowledge of every truth: a total contemplation of all of reality.

Moreover, suppose x knows every truth but some of these truths x is not sure of. Again, that’s not omniscience. Nor would it be omniscience if x were sure of every truth and believed no falsehood, but there was some falsehood to which x assigned a small degree of belief—say, a credence of 0.2. (For one, such a being would have probabilistically inconsistent credences, as it would assign credence 1 to the negation of that falsehood.)

So, propositional omniscience should at least be:

2. x is omniscient iff x occurrently knows every truth for sure and has no degree of belief in any falsehood.

And, of course, propositional omniscience is unlikely to be all of omniscience.

Guessing and omniscience

Suppose that yesterday you guessed that today I’d freely mow the lawn, and today I did freely mow the lawn. Then, the correctness of your guess is a doxastic good you possessed.

(Note: If the future is open, so that there was no truth yesterday that today I’d mow the lawn, it’s a little tricky to say when you possessed it. For when you guessed, it wasn’t true that you possessed the doxastic good of guessing correctly. Rather, now that it has become the case that this doxastic good is attributable to you.)

Now no one can have a doxastic good that God lacks. Thus, God had to have at least guessed the same thing yesterday. And God has no doxastic bads. So, God never gets anything wrong. But the only plausible way it can be true that

1. God always gets right the things we guess right, and

2. God never gets things wrong

is if God has comprehensive knowledge of the future.

If classical theism rules out open theism, then classical theism rules out presentism

If presentism and most, if not all, other versions of the A-theory are true, then propositions change in truth value. For instance, on presentism, in the time of the dinosaurs it was not true that horses exist, but now it is true; on growing block, ten years ago the year 2019 wasn't at the leading edge of reality, but now it is. The following argument seems to show that such views are incompatible with classical theism.

1. God never comes to know anything.

2. If at t₁, x doesn’t know a proposition p but at t₂ > t₁, x knows p, then x comes to know p.

3. If propositions change in truth value, then there are times t₁ < t₂ and a proposition p such that p is not true at t₁ and p is true at t₂.

4. It is always the case that God knows every true proposition.

5. It is never the case that anyone knows any proposition that isn’t true.

6. So, if propositions change in truth value, then there are times t₁ < t₂ and a proposition p such that God doesn’t know p at t₁ but God does know p at t₂. (by 3-5)

7. So, if propositions change in truth value, God comes to know something. (by 2 and 6)

8. So, propositions do not change in truth value. (by 1 and 7)

I think the only controversial proposition is (1). Of course, some non-classical theists—say, open theists—will deny (1). But non-classical theists aren’t the target of the argument.

However, there is a way for classical theists to try to get out of (1) as well. They could say that the content of God’s knowledge changes, even though God and God’s act of knowing are unchanging. The move would be like this. We classical theists accept divine simplicity, and hence hold that God would not have been intrinsically any different had he created otherwise than he did. But had God created otherwise than he did, the content of his knowledge would have been different (since God knows what he creates). So the content of God’s knowledge needs to be partially constituted by created reality. (This could be a radical semantic externalism, say.) Thus, had God created otherwise than he did, God (and his act of knowledge which is identical to God) would have been merely extrinsically different.

But exactly the same move allows one to reconcile the denial of (1) with immutability. The content of God’s knowledge is partially constituted by created reality, and hence as created reality changes, the content of God’s knowledge changes, but the change in God is merely extrinsic, like a mother’s change from being taller than her daughter to being shorter than her daughter solely due to her daughter’s growth.

I agree that denying (1) is compatible with God’s being intrinsically unchanging. For a long time I thought that this observation destroyed the argument (1)-(8). But I now think not. For I am now thinking that even if (1) is compatible with immutability, (1) is a part of classical theism. For it is a part of classical theism that God doesn’t learn in any way, and coming to know is a kind of learning.

Here is one way to see that (1) is a part of classical theism. Classical theists want to reject any open theist views. But here is one open theist view, probably the best one. The future is open and propositions reporting what people will freely do tomorrow are now either false or neither-true-nor-false, but tomorrow they come to be true. An omniscient being knows all true propositions, but it is no shortcoming of omniscience to fail to know propositions that aren’t true. Then, our open theist says, God learns these propositions as soon as they become true. This is all that omniscience calls for.

Now, classical theists will want to reject this open theist view on the grounds of its violating immutability. But they cannot do so if they themselves reject (1). For the presentist (say) classical theist can reject (1) without violating immutability, so can our open theist. Indeed, our open theists can say exactly the same thing I suggested earlier: God changes extrinsically as time progresses, and the content of God’s knowledge changes, but God remains intrinsically the same.

So, what do I think the classical theist should say to our open theist? I think this: that God doesn’t come to know is not just a consequence of the doctrine of immutability, but is itself a part of the doctrine of immutability. A God who learns is mutable in an objectionable way even if this learning is not an intrinsic change in God. But if we say this, then of course we are committed to (1), and we cannot be presentists or accept any other of the theories of time on which propositions change in truth value.

I think the best response on the part of the classical theist who is an entrenched presentist would be to deny (1) and concede that classical theism does not rule out open theism. Instead, open theism is ruled out by divine revelation, and revelation here adds to classical theism. But it seems very strange to say that classical theism does not rule out open theism.

God and the B-theory of time

1. All reality is such that it can be known perfectly from the point of view of God.

2. The point of view of God is eternal and timeless.

3. Thus, all reality is such that it can be known perfectly from an eternal and timeless point of view.

4. If all reality is such that it can be known perfectly from an eternal and timeless point of view, then the B-theory of time is true.

5. So, the B-theory of time is true.

I am not sure of premise (4), however.

Supervenience and omniscience

Problem: It seems that if God necessarily exists, then the moral automatically supervenes on the non-moral. For, any two worlds that differ in moral facts also differ in what God believes about moral facts, and presumably belief facts are non-moral. This trivializes the mechanism of supervenience for theists.

Potential Solution: Divine simplicity makes God’s beliefs about God-external facts be externally constituted. Thus, a part of what makes it true that God believes that there are sheep are the sheep. If so, then perhaps a part of what makes it true that God believes a moral fact is that very moral fact. Thus, God’s beliefs about moral facts are partly constituted by the moral facts, and hence are not themselves non-moral.

Evil, omniscience, and other matters

If God exists, there are many evils that God doesn’t prevent, even though it seems that we would have been obligated to prevent them if we could.

A sceptical theist move is that God knows something about the situations that we don’t. For instance, it may seem to us that the evil is pointless, but God sees it as interwoven with greater goods.

An interesting response to this is that even if we knew about the greater goods, we would be obligated to prevent the evil. Say, Carl sees Alice about to torture Bob, and Carl somehow knows (maybe God told him) that one day Alice will repent of the evil in response to a beautiful offer of forgiveness from Bob. Then I am inclined to think Carl should still prevent Alice from torturing Bob, even if repentance and forgiveness are goods so great that it would have been better for both Alice and Bob if the torture happened.

Here is an interesting sceptical theist response to this response. Normally, we don’t know the future well enough to know that great goods would arise from our permitting an evil. Because of this, our moral obligations to prevent grave evils have a bias in them towards what is causally closer to us. Moreover, this bias in the obligations, although it is explained by the fact that normally we don’t know the future very well, is present even in the exceptional cases where we do know the future sufficiently well, as in the Carl, Alice and Bob case.

This move requires an ethical system where a moral rule that applies in all circumstances can be explained by its usefulness in normal circumstances. Rule utilitarianism is of course such an ethical system. Divine command theory is as well: God can be motivated to issue an exceptionless rule because of the fact that normally the rule is a good one and it might not be good for us to be trying to figure out whether a case at hand is an exception to the rule (this is something I learned from Steve Evans). And St. Thomas Aquinas in his argument against nonmarital sex holds that natural law is also like that (he argues that typically nonmarital sex is bad for the offspring, and concludes that it is wrong even in the exceptional cases where it’s not bad for the offspring, because, as he says, laws are made with regard to the typical case).

Historically, this approach tends to be used to derive or explain deontic prohibitions (e.g., Aquinas’ prohibition on nonmarital sex). But the move from typical beneficiality of a rule to its holding always does not require that the rule be a deontic prohibition. A rule that weights nearer causal consequences more heavily could just as easily be justified in such a way, even if the rule did not amount to a deontic prohibition.

Similarly, one might use typical facts about our relationships with those closer to us—that we know what is good for them better than for strangers, that they are more likely to accept our help, that the material benefits of our help enhance the relationship—to explain why helping those closer to us should be more heavily weighted in our moral calculus than helping strangers, even in those cases where the the typical facts do not obtain. Once again, this isn’t a deontic case.

One might even have such typical-case-justified rules in prudential reasoning (perhaps a bias towards the nearer future is not irrational after all) and maybe even in theoretical reasoning (perhaps we shouldn’t be perfect Bayesian agents after all, because that’s not in our nature, given that normally Bayesian reasoning is too hard for us).

Socratic perfection is impossible

Socrates thought it was important that if you didn't know something, you knew you didn't know it. And he thought that it was important to know what followed from what. Say that an agent is Socratically perfect provided that (a) for every proposition p that she doesn't know, she knows that she doesn't know p, and (b) her knowledge is closed under entailment.

Suppose Sally is Socratically perfect and consider:

1. Sally doesn’t know the proposition expressed by (1).

If Sally knows the proposition expressed by (1), then (1) is true, and so Sally doesn’t know the proposition expressed by (1). Contradiction!

If Sally doesn’t know the proposition expressed by (1), then she knows that she doesn’t know it. But that she doesn’t know the proposition expressed by (1) just is the proposition expressed by (1). So Sally doesn’t know the proposition expressed by (1). So Sally knows the proposition expressed by (1). Contradiction!

So it seems it is impossible to have a Socratically perfect agent.

(Technical note: A careful reader will notice that I never used closure of Sally’s knowledge. That’s because (1) involves dubious self-reference, and to handle that rigorously, one needs to use Goedel’s diagonal lemma, and once one does that, the modified argument will use closure.)

But what about God? After all, God is Socratically perfect, since he knows all truths. Well, in the case of God, knowledge is equivalent to truth, so (1)-type sentences just are liar sentences, and so the problem above just is the liar paradox. Alternately, maybe the above argument works for discursive knowledge, while God’s knowledge is non-discursive.