Suppose you agree with Tom Morris that the doctrine of the Incarnation requires that there be no conflict in the essential properties of divinity and the essential properties of (full) humanity. Mere humans might have essential properties that a fully human person might not have, such as transworld depravity, but a fully human being is not barred in principle from also being divine.
If this is true, consider the knowability paradox, according to which it follows from the claim that all truths are knowable that all truths are known. The proof relies on two principles about knowledge that I won't defend here: that knowledge implies truth, and that knowledge distributes across conjunctions.
The proof is simple. Let K = it is known by some human at some time that. Then assume that some unknown truth is known: K(p & ~Kp). Distribute the K operator to get Kp & K~Kp, and then use the fact that knowledge implies truth to drop the K operator from the second conjunct, thus deriving: Kp & ~Kp. So by RAA, we get ~K(p&~Kp). Since this result is a theorem, by the rule of necessitation, it is necessary: []~K(p&~Kp). By the interdefinability rules for necessity and possibility, this claim implies that knowledge of an unknown truth is impossible: ~<>K(p&~Kp).
Now, if we assume that all truths are knowable, and since p & ~Kp is an arbitrarily chosen value for an unknown truth, it follows that the truth that p is an unknown truth is itself knowable, i.e., <>K(p&~Kp). Since this conclusion contradicts that of the last paragraph, we should conclude that it is false that all truths are knowable.
Now for the bite...
If Morris is correct, then an essential property of any fully human being is that all truths are knowable for such a being. Why? Because God is omniscient and essentially so, and since the knowability of all truth is itself a modal property, it is an essential property if it is a property of an individual. Similarly if there are unknowable truths for fully human individuals, then it is an essential property of a fully human being for there to be truths such a being can't know. But the essential property of being omniscient is incompatible with the essential property of there being unknowable truths for that person, and so nothing could be both divine and (fully) human without it being an essential property of fully human beings that all truths are knowable for them.
So, if Morris is right, Christians, unlike other theists, have a special stake in trying to solve the knowability paradox. The doctrine of the Incarnation threatens to saddle Christians with the knowability claim, and it is hard to see any other aspect of general theism that has that implication. So, it would appear, Christians have a stake with semantic anti-realists in needing to find a solution to the knowability paradox.
So, how might they proceed? Here's an outlandish reply: if you're merely human, not only are you non-omniscient, you couldn't be omniscient; but if you're fully human, not only can you know any truth, you in fact know all truths. That is, the lesson of the knowability paradox is that if you're fully human, you can't stop with the modal of property of being able to know any truth--you'll have to go all the way to holding that any fully human being actually knows all truths. Ain't that a kicker!
Haven't you already shown a contradiction when you derive Kp & ~Kp? I'm not sure why you need to go further.
I'm having trouble with the very starting point here. We're assuming that some unknown truth is known: K(p & ~Kp). This is a de dicto existential claim, really: 3p: K(p & ~Kp). It means there's some truth p such that the following de re claim is true about it: ~Kp. The problem I'm having is that when stating this you don't have any de re knowledge of p, because the overall claim is de dicto. I think that's where the problem lies. Have I completely misunderstood what's going on?
Jeremy, the contradiction you note depends on the initial assumption K(p&~Kp), and that assumption needs to be discharged. And once discharged, semantic realists are typically unmoved. Only people who think all truths are knowable will be bothered.
There are several ways to symbolize the paradox. The one I used here involves second-order quantification, with 'p' being a zero-place predicate. If one prefers fully explicit first-order presentations, that can (and has) been done, but it just makes the proof less intuitive.
If you buy the idea that the two-minds view is coherent, why would it not block this kind of problem. Morris grants that God the Son is non-omniscient in his human consciousness, but not in his divine consciousness. Morris also claims that Alvin Plantinga, in conversation, has suggested that the on a Social Trinitarian view the divine persons may differ in the modal status of their attributes; e.g. it could be that God the Father is essentially omniscient, and that God the Son exemplifies that property only contingently.
By the way I think Morris is on stronger footing when he says that mere humans have accidental properties that a fully human person might not have, instead of essential properties. At least on my understanding, the essential properties of the fully human are the minimum set for the kind humanity, and common accidental properties are attributed to the greater set of mere humans. It seems to me that the idea is to keep the divide between the merely and fully as small as possible. If your outlandish proposal were the case, then it seems that people would be inclined to think that Jesus Christ wasn't much like them at all.
Matt, the two minds view, and the social trinitarian view, won't help here unless it is an essential property of full humanity that all truths are knowable. The issue is not non-omniscience itself, nor is the issue whether omniscience is essential or accidental. The issue arises if the modal claim that truth is constitutively epistemic (i.e., knowable) is not true of full humanity.
You're right about the kinds in question: full humanity and mere humanity for Morris. But of course, if you take a fully human person and a merely human person, they'll have incompatible essential properties even if the kind properties are not incompatible. Part of the outlandishness of the last paragraph above is that the properties in question would have to trace to the individual, rather than kind, nature in order not to conflict with the essential properties of mere humanity (as long as we assume that an essential property of mere humanity is that there are unknowable truths for such).
I'm having Jeremy-style problems. We start with an assumption: K(p & ~Kp). But it's ambiguous. What is plausible is that
K 3p(p & ~Kp)
but then the conjunction distribution move won't work; while
3p K(p & ~Kp)
is obviously problematic: there is a truth that is known by someone and not known by anyone. Since this seems so obvious to me, I worry that I am missing the point somehow. So: what's the locus classicus of the knowability paradox? (I see that you, Jonathan, have an article in Nous on it too.)
Thanks!
Heath, the K operator embeds two existential quantifiers, and the assumption K(p&~Kp) has no quantifiers other than those embedded in the K operator.
In the usual presentations of the paradox, one assumes that there are unknown truths, and then takes an instance of that claim, p&~Kp. The above way is, I think, a more elegant proof, however.
My Nous piece explains the logic of the paradox in more detail than can be found anywhere, more detail than anyone is likely to have patience for! What I do is give the quick version as above, and then go into more and more detail for those who are worried about the logic. So, the proof can be done with first-order or second-order quantifiers, with or without truth-predicates, with or without burying quantifiers inside the K operator, etc.
So if I follow correctly, your solution would be that all fully human beings, who are not merely human, hold omniscience as a common individual essential property. Your first premise is that Morris's view is supposed to block all conflict between essential properties, which I think is correct. However, Morris blocks these properties in two ways. The first way that he does this is to deny that many properties that would conflict with divinity are necessary for humanity. The second way that he blocks the conflict is through mind reduplication. On Morris's view you have two essential properties omniscience and non-omniscience, that would appear to conflict, but are harmonized by the two minds reduplication. It seems to me that the knowability property would be a property of the mind, and it isn't clear to me why Morris's mind reduplication won't block this problem. Perhaps I'm just being dense about all of this... :)
The problem that arises for me on your suggested solution is that on Morris's view it seems to be necessary for the fully human person to be non-omniscient. That the fully human person be non-omniscient seems to be required to block the problem of Jesus Christ's temptation and self professions of a lack of knowledge. I suppose that if you are right, then you'll need a different story to solve these problems