Three understandings of propositional omniscience
Suppose that God exists and is propositionally omniscient. How should we best understand the exact meaning of His propositional omniscience?Footnote 1 Consider these three different understandings of the scope of God's propositional knowledge:Footnote 2
Full Propositional Omniscience (FPO): God knows all true propositions.
Moderately Restricted Propositional Omniscience (MPO): God knows all true propositions that are knowable to someone. Equivalently, God knows all true propositions that someone can know.
Strictly Restricted Propositional Omniscience (SPO): God knows all true propositions that are knowable to Him. Equivalently, God knows all true propositions that God can know.
Many philosophers have accepted FPO, or something very similar to it, as the standard interpretation of God's propositional omniscience.Footnote 3 Given the factiveness of knowledge, the objects of a knowing agent's propositional knowledge can only be true propositions. Therefore, FPO attributes the widest possible scope of propositional knowledge to God and describes the maximum expectation we might have from Him as a propositionally omniscient being. If FPO is true, then there is no true proposition that God does not know. Some theists, however, believe that FPO is false and that the scope of God's propositional knowledge is restricted in some manner. It has been claimed that there are true propositions which are in principle unknowable to any possible knowing agent, including God. Suppose, for example, that the following proposition is true:
(F) Alvin Plantinga will mow the lawn tomorrow.
Some philosophers hold that God's having knowledge of F is incompatible with Alvin Plantinga's being free in mowing the lawn tomorrow. More generally, they argue that although there are true propositions about future actions of free agents, no one – not even God – can know those propositions.Footnote 4 It is logically impossible for everyone to know them. This claim, if true, falsifies FPO. We should therefore adopt a more conservative description of the scope of God's propositional knowledge. God at best knows all knowable true propositions. If so, MPO, contrasted with FPO, provides a more precise understanding of God's propositional omniscience.
The main motivation for replacing FPO with MPO is the possibility that there are true propositions that no one can know. However, regardless of whether or not there are such propositions, MPO is no less defensible than FPO. In the case that there is no necessarily unknowable proposition, the domain of all true propositions and the domain of all true propositions that someone can know are identical. Therefore, FPO and MPO are logically equivalent and attribute the same scope of knowledge to God. So it seems that, compared to FPO, MPO provides a more, or at least equally, accurate understanding of God's propositional omniscience. But even MPO has been challenged. Consider the following proposition:
(D) I am in the Ashby Library of Clare Hall.
D is a de se (or first-person) proposition that I know. A de se proposition expresses something that a person conceives, from an internal perspective, about herself. Some philosophers have argued that since no one can conceive a person in the same way (i.e. from the same point of view) as that person conceives herself, no one can grasp a de se proposition except the person the proposition is about. According to these philosophers, I cannot share my knowledge of D with anybody. Therefore, although other people can know D*, no one other than me can know D:
(D*) Mohammad Saleh Zarepour is in the Ashby Library of Clare Hall.
If I delusionally think that I am Avicenna, not Mohammad Saleh Zarepour, then I might know D without knowing D*. If, in addition to not knowing who I am, I do not know that the building I am in is the Ashby Library of Clare Hall, then I might know D* without knowing D. Therefore, it is possible that I know D without knowing D* and vice versa.Footnote 5 This shows, the adherents of this view believe, that these two propositions are neither identical nor even reducible to each other.Footnote 6 D is a perspectival proposition that no one other than me can know. By contrast, D* is a non-perspectival proposition that someone can know without having access to my privileged first-person perspective.
Some philosophers have appealed to the unshareability of de se propositions to argue against the idea of God's propositional omniscience in the sense not only of FPO but also of MPO. For example, Patrick Grim has argued that God cannot know de se propositions that His creatures know, from a first-person point of view, about themselves.Footnote 7 According to Grim, although God can know D*, He cannot know D. For every knowing agent a, a knows D only if a has access to my first-person perspective. But owing to the unshareability of de se propositions, a has no access to my first-person perspective unless a is me. Thus, a does not know D unless a is me. But, given the traditional picture of God's ontological relation to His creatures, He is necessarily non-identical to me. It is metaphysically impossible for Him to be (or to become) identical to me.Footnote 8 Therefore, God cannot know D.Footnote 9 This conclusion, if soundly derived, makes MPO – and, a fortiori, FPO – false. D is a true proposition (by assumption) that I know but God does not. So there is a true proposition that someone knows but God does not. Ergo, MPO is false and we should revise our understanding of God's propositional omniscience.Footnote 10 SPO is our next option. God can then be considered as propositionally omniscient in the sense that He knows all true propositions that are possible for Him (not merely someone) to know.
If there are true propositions that someone can know but God cannot, then while both FPO and MPO are false, SPO is still true. This indicates that, in this case, SPO provides a better description of the scope of God's propositional knowledge than the two other interpretations. But even if there is no such proposition, SPO is not less defensible than MPO. In this latter case, the domain of all true propositions that someone can know and the domain of all true propositions that God can know are identical. As a result, MPO and SPO express the same thing. They entail each other. This reveals that, in any case, compared to MPO, SPO provides a more, or at least equally, accurate understanding of God's propositional omniscience. Coupling this fact with the preferability of MPO over FPO, which I argued for earlier, we can conclude that, among these three analyses of the scope of God's propositional knowledge, SPO is preferable. There is no possible scenario in which SPO is false but FPO or MPO is true.
In sum, FPO entails MPO and the latter itself entails SPO. But MPO entails FPO only when there is no true proposition that no one can know. Similarly, SPO entails MPO only when there is no true proposition that someone can know but God cannot. So among these three, SPO provides the most cautious and most accurate description of the scope of God's propositional knowledge. In other words, regardless of whether or not there are true propositions that God cannot know because they are either unknowable to anyone or knowable to someone but not to God, God's propositional omniscience can be best understood in terms of SPO. God is propositionally omniscient because for every true proposition p that is possible for Him to know, He actually knows p. It seems plausible, therefore, to accept SPO as the standard analysis of God's propositional omniscience, at least from a theistic point of view. However, it might be too early to embrace this conclusion safely.
Pruss's objection: an easy way from strictly restricted to full omniscience
A consequence of the above line of argument is that SPO entails FPO only when we can show that there are neither true propositions that are necessarily unknowable to everyone nor true propositions that are in principle knowable but only to someone other than God. To infer FPO from SPO, we must therefore show that the arguments for the unknowability to God of propositions like F and D fail. However, Alexander Pruss has proposed an ingenious argument to reject this seemingly indisputable idea.Footnote 11 He argues – without presupposing either that all true propositions are knowable to someone or that all knowable true propositions are knowable to God – that God's strictly restricted propositional omniscience, when conjoined with two uncontroversial claims, entails His full propositional omniscience. If Pruss's argument is sound, there is no significant difference between those three interpretations of God's propositional omniscience. In any case (e.g. regardless of whether or not the arguments for the unknowability of F and D to God are sound), from each of these three interpretations you can easily arrive at the others.Footnote 12
Pruss's argument is proposed in his criticism of Peter van Inwagen's account of God's propositional omniscience.Footnote 13 Van Inwagen has been understood by Pruss to be committed to MPO as the correct interpretation of the scope of God's propositional knowledge. Pruss puts forward an argument to show that, contrary to van Inwagen's view and to what I showed above, there is no justification for replacing FPO with MPO. He first argues that SPO conjoined with two uncontroversial theses entails FPO. But, as Pruss says, ‘if the weaker claim [i.e. SPO], together with uncontroversial theses, entails full omniscience [i.e. FPO], obviously so does the stronger [i.e. MPO]’.Footnote 14 The conclusion is that given those uncontroversial theses, SPO, MPO, and FPO are equivalent to each other and they all attribute the same scope of propositional knowledge to God. So it is better to keep the simplest interpretation, i.e. FPO, as the standard analysis of God's propositional omniscience.
In order to explain Pruss's argument, we should first illustrate his interpretation of the notion of knowability. In the above discussion, it is implicitly supposed that these three propositions are equivalent to each other and express the same notion:
(1) p is knowable to a.
(2) a can know p.
(3) It is possible for a to know p.
Pruss seems to have the same supposition, but he further analyses the notion of possibility mentioned in the third proposition based on a possible world semantics and considers the above propositions as equivalent to the following proposition:
(4) There is a possible world w in which a knows p.
Adopting this construal of the knowability of a proposition, Pruss interprets (SPO) as follows:
(SPO-1) God knows a proposition p if and only if p is true and there is some possible world in which God knows p.
Put otherwise, God knows a proposition if and only if it is true and there is a possible world in which he knows that proposition. Pruss argues that (SPO-1) together with two other theses entails (FPO). These theses can be articulated as follows:
God's Knowledge of Contingencies (T1): There is at least one proposition such that God knows it in the actual world and its negation in some other possible world.
Closure of God's Knowledge (T2): Necessarily, if God knows two propositions, He knows all logical consequences of their conjunction.
Both of these theses indisputably seem to be true. Consider the proposition that Donald Trump is now President of the United States. In the actual world, God knows this proposition. But in a possible world where Hilary Clinton won the 2016 election, God knows the negation of this proposition; i.e. God knows that Donald Trump is not now President of the United States. So T1 is uncontroversial. T2 states that, in all possible worlds, God's propositional knowledge is in some sense closed under logical consequence. As Pruss clarifies, although T2 is false if God is replaced with a finite knower, it does not seem to be controversial in the case of God, who has supposedly infinite cognitive power. It seems plausible to think that God knows all the logical consequences of what he knows. But if we accept both T1 and T2 then it is straightforward to show that SPO-1 implies FPO. Let me explain how.
Consider an arbitrary true proposition p. Moreover, consider a proposition q such that although God knows q in the actual world, He knows ~q in another possible world w*. The existence of such a proposition is guaranteed by T1. Since p is true, ~q ∨ p is true. On the other hand, God knows ~q ∨ p in w*. This is because God knows ~q in w* and ~q ∨ p is one of its logical consequences. Therefore, it is guaranteed by T2 that God knows ~q ∨ p in w*. So ~q ∨ p is true and there is a possible world – i.e. w* – in which God knows this proposition. By SPO-1, we can conclude that God knows ~q ∨ p. But if God knows both q and ~q ∨ p, then He surely knows p (as T2 confirms). This indicates that given SPO-1, T1, and T2, God knows all true propositions. In other words, given T1 and T2, SPO-1 implies FPO. So if we accept, as Pruss does, that SPO-1 provides a plausible interpretation of SPO, we can conclude that the conjunction of SPO with T1 and T2 entails FPO. In less formal language, if God knows all true propositions that are knowable to Him, as well as all of their logical consequences, then He knows all true propositions.Footnote 15
Pruss's project fails: no easy way from strictly restricted to full omniscience
Although Pruss's argument seems powerful, at the end of the day it does not work. I agree with him that T1 and T2 are uncontroversial and I do not challenge these theses. I argue, instead, that SPO-1 cannot provide a defensible construal of SPO. As a result, although the argument for deducing FPO from the conjunction of SPO-1 with T1 and T2 is formally valid, it does not show that SPO entails FPO. In order to see why SPO-1 is problematic, we should reconsider the role of this thesis in the dialectic of Pruss's argument. There is only one step of the argument in which we must appeal to SPO-1. To establish that God knows ~q ∨ p, Pruss shows, on the one hand, that ~q ∨ p is true, and, on the other hand, that God knows ~q ∨ p in w*. So by employing SPO-1, we can conclude that God knows ~q ∨ p, since not only is this proposition true, but there is also a possible world in which God knows it. ~q ∨ p is a disjunctive proposition whose truth and knowability come from two distinct sources. On the one hand, ~q ∨ p is true, since its second disjunct, i.e. p, is so. On the other hand, ~q ∨ p is knowable to God, since its first disjunct, i.e. ~q, is so. More precisely, ~q is knowable to God in the sense that there is a possible world w* in which God knows this proposition. From this we can conclude, by T2, that God knows ~q ∨ p in w*. So ~q ∨ p is knowable to God. This shows how knowability has been transmitted, by T2, from ~q to ~q ∨ p. So the disjunctive proposition under discussion has a conjunctive property – i.e. being true in the actual world and being known to God in some possible world – that none of its disjuncts has been argued to have. SPO-1 implies that God knows such a disjunctive proposition. This indicates that if we espouse SPO-1, then we have to accept that even if there is no independent reason showing that God knows a particular proposition, He knows the disjunction of that proposition with some false proposition. This sounds immensely counterintuitive and provides strong evidence against the plausibility of SPO-1.
To see better why SPO-1 is implausible, replace p and q with the following propositions respectively:
(F) Alvin Plantinga will mow the lawn tomorrow.
(Q) Donald Trump is now President of the United States.
Suppose that F is true and Alvin Plantinga will actually mow the lawn tomorrow. This fact makes the disjunctive proposition ~Q ∨ F true. Since Donald Trump is now President of the United States, ~Q is not true in the actual world. So God does not know this proposition. However, in a possible world in which Hilary Clinton won the 2016 election God knows that Donald Trump is not now President of the United States; i.e. He knows ~Q. Furthermore, since God's knowledge is closed under logical consequence He knows ~Q ∨ F in a possible world in which Hilary Clinton won the 2016 election. So ~Q ∨ F is true and there is a possible world in which God knows this proposition. SPO-1 therefore necessitates that God knows ~Q ∨ F; i.e. that God knows that either Donald Trump is not now President of the United States or Alvin Plantinga will mow the lawn tomorrow. And this means that even without having any independent justification for the belief that God knows that Alvin Plantinga will mow the lawn tomorrow, we can prove that He knows the disjunction of this proposition with a false proposition. This seems to be highly controversial. If we do not have independent evidence for the belief that there is a way of knowing a proposition, then obviously we are not justified in believing that there is a way of knowing the disjunction of that proposition with a false proposition.Footnote 16 The burden of proof is on those who understand SPO as SPO-1 to show that God can actually know a disjunction that neither of its disjunct has been argued to be known to Him in the actual world. They might say that we should accept the conclusion that God knows such disjunctions because it is entailed by SPO-1. But this is just begging the question of the correct understanding of SPO. From the perspective of some friends of SPO (such as van Inwagen, against whom Pruss argues) who thinks that there is no way for God to know the proposition that Alvin Plantinga will mow the lawn tomorrow, there is no way for Him to know the disjunction of this proposition with a false proposition. Therefore, they would simply reject SPO-1. Indeed the main problem with SPO-1 is that, according to this thesis, God's knowledge of a disjunctive proposition in the actual world can be drawn from the conjunction of (1) the truth of one of the disjuncts of that proposition in the actual world, and (2) God's knowledge of the other disjunct in a non-actual possible world. But, evidently, (1) and (2) do not present sufficient grounds for God's knowledge of such a disjunctive proposition. Therefore SPO-1, like any other thesis which clashes with this conclusion, should be rejected.Footnote 17
SPO-1 cannot provide an accurate interpretation of SPO as understood by the defenders of this thesis. As a result, Pruss's argument that SPO entails FPO relies on an indefensible reading of the former thesis.Footnote 18 The argument is accordingly unsound. Now an immediate question arises: how should we interpret SPO? An alternative interpretation of SPO which might naturally come to mind could be proposed as follows:
(SPO-2) God knows a proposition p if and only if p is either a true atomic proposition that God knows in some possible world or a logical consequence of the atomic propositions that God knows.
In other words, for every atomic proposition p, God knows p if and only if p is true and there is a possible world in which God knows p. Moreover, for every non-atomic proposition p, God knows p if and only if p is logically entailed by some other instances of God's propositional knowledge. The closure of God's knowledge is embedded in this interpretation. This means that SPO-2, by contrast with SPO-1, entails T2. But the more significant advantage of SPO-2 over SPO-1 is that it excludes the aforementioned controversial disjunctive propositions from the scope of God's knowledge. According to SPO-2, God knows a disjunctive proposition if and only if God knows at least one of its disjuncts. So to show that God knows that either Donald Trump is not now President of the United States or Alvin Plantinga will mow the lawn tomorrow, we have to show either that God knows that Donald Trump is not now President of the United States or that God knows that Alvin Plantinga will mow the lawn tomorrow. That Donald Trump is not now President of the United States is false and it is impossible to know a false proposition. Therefore the only way to establish that God knows the disjunctive proposition is to prove that God can actually know that Alvin Plantinga will mow the lawn tomorrow. So Pruss cannot follow his previous strategy to conclude FPO from SPO-2. His argument is intended to challenge the idea that SPO is preferable to FPO as the standard interpretation of God's propositional omniscience. However, this idea is immune to Pruss's criticism if SPO is understood in the sense of SPO-2, rather than SPO-1.
There is, however, an important concern about SPO-2. This thesis excludes all the problematic disjunctive propositions from the scope of God's knowledge. But it might also exclude some other disjunctive propositions which, intuitively, should be part of God's knowledge. Put otherwise, the main concern regarding SPO-2 is whether it actually includes all instances of God's knowledge. All theists seem to agree that God knows (1) every true atomic proposition that He knows in some possible world and (2) every non-atomic proposition that is logically entailed by the other propositions He knows. Thus, there seems to be no complaint that the scope of God's propositional knowledge is more restricted than SPO-2 suggests. But one might worry that there are some instances of God's propositional knowledge that cannot be accommodated by SPO-2. If so, the scope of God's propositional knowledge is more extended than what SPO-2 expresses. Indeed, it seems that Pruss himself has exactly the same concern. He says:Footnote 19
[S]uppose that the laws of nature determine it to be the case that tomorrow Alvin Plantinga will freely choose whether to mow the lawn or bake a cake (or that an electron will go up or go down in the magnetic field). Then an omniscient being had better know that tomorrow Alvin Plantinga will choose to mow the lawn or tomorrow Alvin Plantinga will choose to bake a cake. But this is a disjunction, and the definition of [strictly] restricted omniscience constrained to exclude [the aforementioned] disjunctions [i.e. SPO-2] does not appear sufficient to guarantee that an omniscient being will know this.Footnote 20
Interestingly, the success of this objection contradicts the main aim of Pruss's argument, which is to establish FPO as the standard definition of God's propositional omniscience. To see why, consider the following propositions:
(F) Alvin Plantinga will mow the lawn tomorrow.
(F*) Alvin Plantinga will bake a cake tomorrow.
Supposedly, it is determined by the laws of nature that F ∨ F* is true. Since F ∨ F* is true, then either F or F* is true. Otherwise, classical logic (to which both Pruss and van Inwagen are committed) is undermined.Footnote 21 In fact, F ∨ F* is supposed to be a deterministically true proposition such that although at least one of its disjuncts is true,Footnote 22 neither of them is deterministically true. Now there are two possibilities: either (a) God knows (at least one of) the true disjunct(s) of F ∨ F*, or (b) although at least one of the disjuncts of F ∨ F* is true, God knows neither of them. In the former case, contrary to what Pruss claims, SPO-2 guarantees that God knows F ∨ F*, since it is a logical consequence of the disjunct(s) God knows. Thus in this case SPO-2 is completely compatible with the intuition that if a proposition is determined to be true by the laws of nature, then God knows it by knowing those laws. Now, we can turn to the latter case in which God does not know the true disjunct(s) of F ∨ F*. On this horn, although at least one of the disjuncts of F ∨ F* is true, God knows neither of them. So it is confirmed that there is at least one true proposition that God does not know. This horn is therefore built upon the rejection of God's full propositional omniscience; i.e. FPO. Admittedly, in this case, SPO-2 does not suffice to guarantee that God knows F ∨ F* and Pruss's objection seems to be successful. But this success is due to the rejection of FPO. This indicates that Pruss can reject SPO-2 as a plausible understanding of SPO only if he accepts that FPO is rejected. If he does so, he has undermined the whole motivation behind his own argument – which was establishing FPO as the standard interpretation of God's propositional omniscience. In sum, if Pruss does not give up FPO, then he seems to have no way of refuting SPO-2. But if he interprets SPO as SPO-2, then he would fail to show that SPO entails FPO. If, on the other hand, he rejects SPO-2 at the expense of rejecting FPO, then he has already rejected what he is trying to establish.Footnote 23 So it seems that his project fails.
A plausible construal of SPO
Although Pruss's project fails, it raises an important concern regarding SPO. It seems intuitively correct that God must know all propositions whose truth is determined by the laws of nature. So if there are such disjunctive propositions, then God must know them. But this cannot be guaranteed by SPO-2, at least if we accept that there are deterministically true disjunctive propositions such that God does not know neither of their disjuncts. So the advocates of SPO must look for another interpretation which both includes such seemingly unproblematic disjunctive propositions (e.g. F ∨ F*) and excludes the problematic disjunctive propositions (e.g. ~Q ∨ F). SPO-1 fails to satisfy the latter condition. By contrast, SPO-2 satisfies the latter, but not the former. So we must find a reading of SPO which satisfies both of these conditions. Here is my proposal:
(SPO-3) God knows a proposition p if and only if p is true and God knows p in some possible world in which p has the same truth-maker(s) as the actual world.Footnote 24
Recall that the main concern about the problematic disjunctive propositions was that their truth and knowability come from two distinct sources. In other words, although there is some possible world in which God knows that proposition, this knowledge is transmitted from God's knowledge of a truth-maker of that proposition that does not exist in the actual world.Footnote 25 Reconsider the problematic proposition ~Q ∨ F, i.e. the proposition that either Donald Trump is not now President of the United States or Alvin Plantinga will mow the lawn tomorrow. God knows this proposition in a possible world in which Hilary Clinton won the 2016 election. God's knowledge of the disjunctive proposition in that possible world is, by assumption, based on his knowledge of Clinton's victory. Indeed, Clinton's victory is a truth-maker of the disjunctive proposition that does not exist in the actual world. So the knowability of the disjunctive proposition comes from God's knowledge of a truth-maker of this proposition that does not exist in the actual world. Thus there is no guarantee of God's knowledge of the disjunctive proposition in the actual world. Generally, if God's knowledge of a proposition p in a possible world w is implied by His knowledge of a truth-maker of p that does not exist in the actual world, then the fact that p is known to God in w is not evidence for that p can be known by God in the actual world. This is a robust intuition that is well accommodated by SPO-3. So this interpretation of SPO successfully excludes all the problematic disjunctive propositions.
Now, reconsider the seemingly unproblematic proposition F ∨ F*, i.e. the proposition that either Alvin Plantinga will mow the lawn tomorrow, or Alvin Plantinga will bake a cake tomorrow. By assumption, although this disjunctive proposition is determined by the laws of nature to be true, neither of its disjuncts is deterministically true. So according to this assumption the disjunctive proposition seems to have a truth-maker M (which is some fact that can be expressed by some of the laws of nature) that is not identical to the truth-makers of either F or F*.Footnote 26 By contrast with SPO-2, there is nothing in SPO-3 which excludes F ∨ F* from the domain of God's knowledge. According to SPO-3, knowing the disjuncts of a disjunctive proposition is not a necessary condition for knowing the disjunctive proposition. God can know F ∨ F* through knowing M without knowing either F, or F*, or their truth-makers. Indeed, it seems quite plausible to think that there are infinitely many possible worlds other than the actual one in which F ∨ F* has the same truth-makers as the actual world and God knows this disjunctive proposition through knowing the laws of nature and consequently M. So the inclusiveness of SPO-3 cannot be objected to in this way.
Pruss does not discuss SPO-3 at all, but he warns that excluding all ‘shifty’ propositions from the scope of God's knowledge is implausible:Footnote 27
If one believes in truth-makers, one might try the following trick. Say that a proposition p is ‘shifty’ provided that there are two worlds w 1 and w 2 at each of which p is true, but p has a truth-maker at w 1 which does not exist in w 2. For instance, the proposition that I will mow the lawn tomorrow or Trump is President is shifty, since in some worlds it has the event of my mowing the lawn tomorrow as a truth-maker, while in other worlds it is still true, even though that event does not exist. Then one simply excludes all shifty propositions. I do worry, though, that excluding all shifty propositions will exclude just about every interesting proposition. For instance, take the proposition that George greeted Sarah. In one world this is made true by George's saying ‘Hello’ to Sarah while in another this is made true by his saying ‘Hi’ to her.
SPO-3 is not vulnerable to the above objection, however. SPO-3 does not allow us to exclude a proposition from the scope of God's knowledge merely because of its shiftiness. The only thing SPO-3 implies about shifty propositions is that God's knowledge of a shifty proposition in a possible world provides sufficient evidence for God's knowledge of this proposition in another possible world only if this proposition has the same truth-makers in these worlds. This condition guarantees that these two worlds are similar enough to each other in all respects that matter for knowing that proposition. It is quite tenable that if there is no non-actual possible world in which God knows a proposition p and this proposition has the same truth-maker as the actual world, then God cannot know p in the actual world either.
Suppose that the shifty proposition that George greeted Sarah is made true by George's saying ‘Hello’ to Sarah in w 1 and by his saying ‘Hi’ to her in the actual world. God's knowledge of this proposition in w 1 is obtained through his knowledge of George's saying ‘Hello’ to Sarah. But this fact does not exist in the actual world. So the mere fact that God knows that proposition in w 1 does not provide sufficient evidence that He knows this proposition in the actual world. Nonetheless, this does not mean, on its own, that God cannot know this proposition in the actual world. There are many possible worlds other than w 1 in which God knows that George greeted Sarah through his knowledge of George's saying ‘Hi’ to Sarah. In such worlds, the proposition under discussion has the same truth-maker as the actual world. If so, it is guaranteed by SPO-3 that God knows that proposition in the actual world too.
The core content of SPO-3 is that the necessary and sufficient condition for God's knowledge of a proposition p in the actual world is the existence of a possible world w in which God knows p and, moreover, w is similar to the actual world in all aspects relevant to knowing p. Therefore SPO-3 seems to be a bona fide interpretation of SPO.
Concluding remarks
I have discussed three accounts of God's propositional omniscience from a theistic point of view: (1) the full account (i.e. FPO) according to which God is propositionally omniscient in the sense that He knows all true propositions; (2) the moderately restricted account (i.e. MPO) according to which God is propositionally omniscient in the sense that He knows all true propositions that someone can know; and (3) the strictly restricted account (i.e. SPO) according to which God is propositionally omniscient in the sense that He knows all propositions that He can know. I argued that SPO is preferable to the two other candidates regardless of whether or not there are true propositions that God cannot know because they are either unknowable to anyone or knowable to someone but not to God.
I also discussed Pruss's argument that SPO entails FPO and showed that it is based on a flawed construal of SPO. By appealing to the notion of truth-making, I defended an alternative interpretation of SPO according to which God knows a proposition p if and only if p is true and God knows p in some possible world in which p has the same truth-maker(s) as in the actual world. This understanding of SPO blocks the inference of FPO from SPO and accommodates defensible intuitions we have about God's cognitive power. God knows a true proposition p if and only if there is a logically possible and relevantly similar world in which God knows p. If there is some conceivable mechanism through which God can know p in such a possible world, then God knows p in the actual world. This might be a conservative and restricted understanding of God's propositional omniscience, but it is definitely more precise than FPO and MPO in demarcating the scope of God's propositional knowledge.
There might still remain a final concern about my approach. One might wonder whether the proposed understanding of God's omniscience is vulnerable to McEar-like objections.Footnote 28 Suppose that McEar is a knowing agent who essentially can know nothing except a single proposition R (whatever it is). In other words, in all logically possible worlds in which McEar exists, s/he can know nothing except R. Now, if we replace ‘God’ with ‘McEar’ in SPO-3, we get a description of the scope of McEar's knowledge which is still true. Nonetheless, McEar is trivially not an omniscient being. So SPO-3, the critic might conclude, cannot be counted as a plausible description of God's omniscience. I do not think, however, that this objection is tenable. Similar to the debate between Pruss and van Inwagen, my discussion is presented in a theistic framework wherein it is supposed from the outset that God is omniscient. So my aim was not primarily to give a definition of the notion of omniscience, but rather to provide a description of the scope of God's knowledge on which all theists can concur, regardless of the various limitations they consider for God's cognitive power. I think, for the reasons discussed in the article, that SPO-3 well satisfies this expectation. Providing a general definition of omniscience can be postponed to a future project.Footnote 29