Consider two claims about God's knowledge.
- For all p, if p, then God knows p.
- For all p, if p, and possibly God knows p, then God knows p.
- Necessarily, God's knowledge is closed under conjunction and tautological implication (i.e., if God knows p and God knows q, then God knows (p and q), and if God knows p, and p tautologically implies q, then God knows q).
- There is at least one proposition p such that possibly God knows p and possibly God knows not-p.
Here is the argument that (2)-(4) entail (1). Fix any true p. By (4), let q be any proposition such that possibly God knows q and possibly God knows not-q. If q holds, then let r=q. If q does not hold, then let r=not-q. Note that r is true. Observe that possibly God knows not-r (if r=q, then this follows from the fact that God possibly knows not-p; if r=not-q, then this follows from the fact that God possibly knows q as well as (3), since q tautologically implies not-r). Let s be the proposition (p or not-r). Then, God possibly knows s. For God possibly knows not-r, and in any world where God knows not-r, God also knows (p or not-r) by (3). Now, s is true as p is true. Therefore, s is a proposition that is true and possibly known by God. Therefore, by (2), God knows s. Moreover, r is a true proposition, and God possibly knows r (since God possibly knows q and God possibly knows not-q). Therefore, God knows r, by (2). But s is (p or not-r). By (3), it follows that God knows p, since (s and r) tautologically implies p.
So if one attempts to limit omniscience by saying that omniscience only means that God knows things that God can know, or that God only knows things that possibly are known by someone (which also entails (2)), one hasn't limited omniscience at all: God still ends up knowing all true propositions, assuming (3) and (4). Is there some other way of non-arbitrarily limiting omniscience? I am not sure. But, fortunately, there is no need to limit omniscience. God knows all truths.
Alexander: I have a question. Does God know that 'God knows everything' is true? We can ask questions regarding knowing everything, or degrees of knowing, because we know we do not know everything. Consequently, the idea of knowing everything is an idea we would have. But if a being knows everything would that question even arise for that being? Do any questions ever arise for an all-knowing being? Does God know that He knows everything? If the question does not arise for God then there is one proposition that God does not know.
Hello Alex,
Open theists uniformly believe that God knows all truths. Who is your target here?
Even if the argument is correct (I am still thinking about it) there is a sense in which God's knowledge may be limited.
Consider the subjective consciousness of of finite beings. Assume that 'what it is like" to be one of these finite beings is itself a real feature of the universe.
Therefore a complete understanding of the universe would include an understanding of what it is like to be each of various finite conscious beings.
Now part of what it is like to be you or me or any finite consciousness is to be limited. But God of course is not limited in this way. Therefore God cannot know what it is like to be a finite conscious being.
Note that God having access to our inner states does not give God access to what it is like for us to live subjectively--just as a man who is somehow given awareness of the subjective states of a bat does not know what it is like to be a bat--he knows what it is like for a man to be given bat experiences.
One of the great things about the doctrine of the Incarnation is that it allows the Christian theist to bridge this ontological divide--at least on the kenotic understanding of the incarnation. But whatever insight the incarnation brings to God, it is plausibly not complete. To know what its like to be the human Jesus is not to know what its like to be a lobster
I said this would follow even if the argument Alex gives is true because I don't think "knowing what its like" constitutes propositional knowledge. But it is knowledge nontheless.
John Alexander:
Even if a question "does not arise" one may know the answer. In some sense, the question whether it is acceptable to murder someone by force feeding him cream puffs while one is wearing a blue and purple and gold striped swimsuit "does not arise". But we all know the answer.
Flavius:
Swinburne seems to be an open theist, and yet he thinks God doesn't know every true proposition. So he is a fit target.
As far as I can tell, Keith DeRose is committed to the denial of (1), though he accepts the weaker claim that for all p, if p is true, then God knows p. However, because Keith denies the axiom that if p, then it's true that p, the argument as I've put it will not move him, as it makes use of that axiom. Perhaps the argument could be tweaked not to need that axiom, however.
Gordon:
One might argue that this is the right place to make the claim that God knows everything that is knowable by God.
But I disagree. First, I am not sure "what it's like" knowledge is genuinely knowledge. Suppose I have never seen anything red, but I know that tomorrow at noon I will see a red tomato. Then, already I know what it is like to see red. I know that to see red is like that, where the "that" contextually points to my tomorrow noon-time experience. (Nothing wrong with demonstratives that point to things I haven't experienced.) And then tomorrow at noon I know that to see red is like that, where the "that" points to the same experience. It does not seem that I have learned anything.
Second, the principle that one cannot know what it is like to have an experience of A unless one has had an experience of A is false. It is enough to have a false memory of an experience of A, for instance. Of course, God doesn't have false memories, but the point that the principle is false remains. Maybe there is a way of reformulating the principle that avoids the counterexample, but I do not know it.
Alex,
Thanks, I was having a hard time understanding who you had in mind in your original post. Now that I see it's Swinburne, I would want to say that this is not the standard view among open theists today. For the vast majority, I would say that all sides agree that God knows all there is to be known. The difference has to do with what there is to be known. In other words, the question really isn't about omniscience; it's about metaphysics, especially the nature of time.
I'm new to this blog, but I doubt that any of this is news given that Alan Rhoda is a contributor.
Alexander
"Even if a question "does not arise" one may know the answer."
This is very counter-intuitive. How can one know that one knows the answer unless one knows the question? So my questions still remains; does God know that "God knows everything" is true? or, "Does God know that He knows everything?" It seems to me that simply stipulating that God knows everything does not settle anything. I am wondering what kind of explanation you can give that explains how God would know that He knows everything without Him asking the question as to the limits of what He knows. And asking the question, if indeed it is a question, implies that He does not know the answer. If He simply is immediately aware that He knows everything does He have to test this against the facts in order for it to count as a knowledge claim? In some sense is not testing an admission of doubt or the admission that it is possible that what is being claimed is wrong?
What about knowledge of future libertarian free actions?
Why can't someone argue that (2) doesn't entail (1) as follows? Suppose that my ordering a snow cone at noon in the actual world is a libertarian free action. It's possible that God knows that I order a cone at noon happens in a world where this _isn't_ a libertarian free action (e.g., God takes control of my mind) but doesn't know it in this world because God lacks the sort of grounds that would give knowledge.
[Disclaimer: I don't think libertarian free actions cause trouble for omniscience, per se, but those who think it causes trouble given further assumptions about God's time-bound perspective and the point that the principle needs to make reference to grounds of knowledge is the important one.]
Clayton:
Are you denying S5? It seems you are, since you are allowing that in one world something is possible which is impossible in another. By "possible" I meant "metaphysically possible", by the way.
John:
How God knows is a really tough question, but I don't see why it is more of a problem to figure out how God knows that he knows everything than, say, to figure out how he knows unprovable mathematical truths.
Flavius:
It may not be a common view, but I think it is a view that has something going for it as compared to standard open theism. "Standard" open theism has the advantage that it lets one say that God knows every true proposition. This version of open theism denies that. However, since both versions of open theism deny that God knows future contingents, both differ significantly from the theistic tradition. Moreover, the more standard open theism has the serious disadvantage of changing logic. Of course, best not to be an open theist of any sort.
Alex,
Your argument is interesting. It took me a while to get it clear in my mind. Here's how I translated the proof in my mind:
Let P be a true proposition that God supposedly cannot know, for example, P might be the proposition that Jones will choose to mow his lawn next Saturday.
Let Q be any true proposition that God could know, for example, the proposition that Obama is President, where God could also know that not Q.
Let S = the proposition that Q is not true or that P is true.
The argument then goes as follows:
1. God could know S [because God could know not Q, and not Q or P tautologically follows from not Q]
2. Therefore, God knows S [by (2)]
3. God knows Q [by (2)]
4. Q and S tautologically entails P.
5. Therefore, God knows P.
This is an interesting result. I will ask Peter van Inwagen about it during our next meeting, for he promotes a view of onniscience in which (2) but not (1) is true in his Problem of Evil. I wonder how he would reply to your argument.
I see two ways to try to get out of this argument. One way is to work with a modality other than metaphysical possibility.
The other is to play around with "true in virtue of" (or truthmakers). To do that, one tweaks the statement "possibly x knows p." The literal reading is: M(xKp), i.e., there is a world where xKp. But a better reading might place a restriction on that world--that has to be a world not only where p is true, but where p is true "in the same way" as it is in the actual world.
One way of starting to make this intuition precise is this. Start with the ternary relation V(p,q,w) which says that at w, p is true in virtue of q's being true. For instance, "Pigs fly and the sky is blue" is true in virtue of the sky being blue, and "If the Queen invites to McDonald's for dinner tomorrow, I will not be surprised", understood as a material conditional, is true in virtue of the proposition that the Queen will not invite me to McDonald's for dinner tomorrow. A single proposition may be true in virtue of multiple propositions. Thus, that there exists a human is true in virtue of the proposition that you exist and are human, but is also true in virtue of the proposition that I exist and am human.
Three formal properties of the V relation that might help clarify it:
(i) if V(p,q,w), then q entails p
(ii) if V(p,q,w), then p and q are true at w
(iii) if p has truthmaker T, and p is distinct from the proposition that T exists, then V(p,T exists,w).
Let v(p,w) be the set (actually it's not a set, so we need to do some technical mumbo-jumbo) of all propositions q such that V(p,q,w).
Now, replace "possibly x knows p" with this: "There is a world w1 such that v(p,w1) is a subset of v(p,@) and x knows p at w1", where @ is the actual world. This ensures that at w1, p isn't true for some aberrant reason. Maybe we even want the stronger requirement that v(p,w1)=v(p,@).
The variant of 2 is now:
2*. (p)(If p is (actually) true and there is a world w1 such that v(p,w1) is a subset of v(p,@) [or v(p,w1)=v(p,@)] and God knows p at w1, then God (actually) knows p).
I don't have an argument that 2* entails 1 (at least if one doesn't count arguments that 1 is a necessary truth!). Maybe you can find one?
Alex,
After discussing your argument with my wife last night (she's so smart), a truth-maker type reply occurred to me. But that reply isn't open to van Inwagen because he doesn't accept truth-makers (not yet...). I look forward to finding out what he thinks about this...
Joshua:
I think the suggestion in my preceding comment is a generalization of the truthmaker reply (assuming your truthmaker reply is the one I am thinking of--modifying (2) to say that if p is true and God possibly knows p in some world that contains only the actual world's truthmakers for p, then God knows p), but it is also available to those who do not accept truthmakers. Granted, some may balk at the "holds in virtue of" relation, but such a relation is clearly correct in a lot of cases (such as disjunctive ones), and all it needs is the uncontroversial claim that if p holds but q does not, then (p or q) holds in virtue of p's holding (maybe we need a qualification that we are not dealing with something gerrymandered). If I am right, the response in that comment completely sidesteps my argument, which is too bad, though it comes at a cost of making the doctrine more complex.
By the way, using the "in virtue of" tool would also help with making a plausible version of the Restricted PSR that normally says that if p can have an explanation, then p has an explanation. We could instead say: if p has an explanation in some world w such that v(p,w) is a subset of v(p,@), then p actually has an explanation. I think this would more easily sidestep some potential counterexamples to the RPSR, and would still be strong enough for a cosmological argument.
I've also wondered whether some version of the "in virtue of" reply can't be used to help with characterizing omnipotence, but couldn't find a way.
Alex,
I agree with what you said. (Another option is available to those who think there are complex propositions built up out of other propositions, but again it requires a revision to the open theist's claim in (2).)
On another note, in an earlier comment you suggested that an open theist who thinks that God knows all there is to know "has the serious disadvantage of changing logic." I'm not sure I see that (yet). Suppose I think that expressions purporting to say what creatures will freely do fail to express any propositions because there are no such propositions. Why can't I still accept classical logic as applied to propositions?
Josh:
I haven't interacted with any open theist who takes the line of saying there are no such propositions. In general, I am quite sympathetic to views on which some things that look like sentences don't express propositions. But there are costs to such solutions to problems. Let me point out some of these costs (some of which I think one should be willing to pay in other contexts).
1. "Jones freely mows the lawn tomorrow, then Jones mows the lawn tomorrow" seems perfectly true. But how can it be true, or even make sense, if its antecedent doesn't express a proposition? And if it is true, then classical logic fails if we grant that classical logic presupposes that the blanks in sentential operators express propositions.
2. Whether an apparent sentence expresses a proposition ends up depending on things that seem extraneous. Thus, normally, "Jones will mow the lawn tomorrow" on this view fails to express a proposition--and hence is nonsense. But if Jones has a certain kind of compulsive habit, or if God has promised Jones' wife that Jones will mow the lawn, then "Jones will mow the lawn tomorrow" does express a proposition, indeed a true one.
3. (This is the biggie, I think.) We have propositional attitudes towards future contingent propositions, some of which attitudes are surely appropriate. Fears, hopes and desires all have appropriate future-directed cases.
Alex,
Those are interesting costs. Perhaps someone could reply to cost 1 by suggesting that "Jones freely mows the lawn tomorrow, then Jones mows the lawn tomorrow" be translated as "If 'Jones freely mows the lawn tomorrow' expresses a truth, then 'Jones freely mows the lawn tomorrow' expresses a truth." But costs 2 and 3 do seem serious to me.
Josh:
Another cost is that it is a really weird idea that one would assign probabilities to nonsense. But we assign probabilities to claims about the future.
OK Alex,
I finally got to find out what Peter van Inwagen thinks about your argument. He said that his view is more nuanced than the one you critique. He then pointed me to his paper, "What Does an Omniscient Being Know about the Future?" There he says this:
"
A being x is omniscient (in the restricted sense) if and only if it satisfies the following three conditions at every moment t:
x is able at t to consider or hold before its mind 'simultaneously' and in complete detail every possible world. (Possible worlds are here understood as Plantinga understands them in The Nature of Necessity.)
For every set of possible worlds that contains the actual world and is such that it is possible (for any being) to know at t of that set that it contains the actual world, x knows at t of that set that it contains the actual world. (Here 'the actual world' is a definite description, a non-rigid designator of the world that happens to be actual. ...cut)
x's knowledge is closed under entailment (...) and x believes only what x knows (if x believes that p, x knows that p).
"
Peter's impression is that your argument doesn't pose a problem for his account.
What do you think?
Josh:
I think Peter's position is subject to the same argument. Let's be concrete. Let p be the proposition that tomorrow I will mow the lawn. Suppose for the sake of argument that p is in fact false. (If not, then run the argument with ~p.) I will show that Peter's position entails that x knows p. Let q be the contingently false proposition that yesterday I had pork chops for breakfast. Let s be the disjunction: p or q.
Let Wr be the set of worlds where r holds. Observe that Ws is the union of Wp and Wq. Observe that Wp and W~q contain the actual world. Let t be now.
Observe that it is possible for some being to know at t of Ws that it contains the actual world. Presumably, there are plenty of worlds where I now both know that yesterday I had pork chops for breakfast, and I understand set theory and successfully do some basic logic, and in those worlds I know that Ws contains the actual world. Therefore, the antecedent of Peter's second condition is satisfied. Hence, so is the consequent. Therefore, x knows of Ws that Ws contains the actual world.
Furthermore, I actually now know that W~q contains the actual world. Therefore, by the same second condition, x knows of W~q that W~q contains the actual world.
That Ws contains the actual world entails s.
That W~q contains the actual world entails ~q.
Thus, x knows s & ~q.
s & ~q entails p.
Thus, x knows p.
QED
Does Peter give his account in print? (P.s. give my best to him next time you see him.)
Correction: I should have supposed that p is in fact true. (I suppose the reason I wrote "false" is that p in fact has a low epistemic probability.)
Alex,
Peter's account is in "What Does an Omniscient Being Know about the Future" in Oxford Studies in Philosophy of Religion (p. 224).
I'll have to see what Peter thinks about this argument. I think you might be able to publish your argument in reply to Peter (if it's sound).
Actually, Peter can escape my argument as his definition stands. For he defines closure under entailment as follows: if x knows p, and p entails q, then x knows q. But this is compatible with the claim that x knows p and x knows q, but x doesn't know (p and q). I need the latter claim for my argument. Nonetheless, I kind of feel that it may have been an oversight for Peter to have omitted closure under conjunction from his definition of omniscience.
I wrote this up and send it off. Thanks to everybody who contributed to the discussion!
Wow! A week ago, I wrote this up and sent it off to Religious Studies, and this morning I got an acceptance. That was fast. My wife quipped that it was almost as good as a fast rejection.
Congratulations! (Bonus, it's nice to know RS has fast turn around time)