Authored by: Mitchell LeBlanc.

Robert Bass, a philosophy professor of Coastal Carolina University published an article in the Volume VII, Issue 1, Summer 2007 edition of the Florida Philosophical Review (pg. 85). The article presents an omniscience puzzle which is demonstrated as follows:

(1) Todd is omniscient

Of course, Todd’s being omniscient entails that for any proposition p, the following must be true:

(2) If p, then Todd knows that p

Basically, Todd knows any truth. Now, consider  hiders:

…whose defining property is that they are capable of perfectly concealing their existence from any other being. When a hider conceals its existence, it is in hiding.

Now, if there are hiders who are hiding, Todd’s omniscience is compromised because he would not know that there is at least one hider in hiding.

If it is even the case that hiders are merely possible, Todd’s omniscience is compromised because he would not be able to distinguish between a state of affairs in which hiders exist but are hiding, and a state of affairs in which hiders do not exist.

If it is the case that hiders are impossible, Todd must know that they are impossible, otherwise his omniscience is compromised since not knowing they are impossible, it will seem to him that they are possible and he would be subjected to the aforementioned problem.

Thus:

(3) If Todd does not know that hiders are impossible, then Todd is not omniscient

and the contraposition

(4) If Todd is omniscient, then Todd knows that hiders are impossible

Thus given (1):

(5) Todd knows that hiders are impossible

Bass states:

Of course, that argument can be run in reverse. If hiders are either possible, or else impossible in

some way that Todd doesn’t know, then Todd doesn’t know hiders are impossible. If he doesn’t

know that hiders are impossible, then Todd is not omniscient. The question that faces us here is

how Todd knows—if he does—that hiders are impossible.

Of course, that argument can be run in reverse. If hiders are either possible, or else impossible in some way that Todd doesn’t know, then Todd doesn’t know hiders are impossible. If he doesn’t know that hiders are impossible, then Todd is not omniscient. The question that faces us here is how Todd knows – if he does – that hiders are impossible.

So, how might hiders be impossible? They may be  intrinsically impossible, like a square circle or they might be extrinsically impossible, like irresistible forces are impossible in worlds containing immovable objects.

There can be no possible world in which hiders, if intrinsically impossible, exist. On the other hand, extrinsically impossible hiders are logically possible and would be present in some possible worlds (but not the ones where the conditions of that world render their existence impossible).

There are now two questions, are hiders intrinsically or extrinsically impossible, and how does Todd know? If Todd knows that hiders are impossible, his knowledge will be either inferential or non-inferential. Could Todd non-inferentially know that hiders are impossible?

Bass is suspicious:

There are two reasons for suspicion. First, so far as Todd’s non-inferential knowledge is being modeled upon ours, plausible cases of non-inferential knowledge typically yield less than certainty. I do not infer from premises that the person with the familiar profile and gait that I see walking across campus is my friend, David. But, upon catching up with him, I can be surprised to discover that it is someone else entirely. Further, even where non-inferential processes appear to yield certainty, as in the case of whether two straight lines can enclose a space, the certainty may turn out to be on certitude, the state of feeling certain that something is so, which may not in fact be so. If the normal products of non-inferential belief -forming mechanisms deserve to be called knowledge, that is due to the fact that those mechanism are generally reliable. General reliability is not enough for Todd to rule out the existence of hiders, however. For if he reaches the belief that hiders are impossible only through a generally reliable mechanism, and if he also knows, as he must if he is omniscient, that the way in which he comes to the belief is only generally reliable, it will remain possible that, though his belief that hiders are impossible was the product of a generally reliable belief-formation mechanism, it is still mistaken.

But what about extrinsic impossibility? Presume there are finders, beings from which no other being can successfully hide. It seems that the existence of finders render the existence of hiders impossible. Surely, if there are any omniscient beings, there can be no hiders. But, if Todd is to know that there are any finders or omniscient beings, it stands to reason that he has already ruled out the existence of hiders. Appealing to the existence of finders, or omniscient beings in an attempt to show that there are no hiders would obviously beg the question. So, as Bass states:

…the existence of something incompatible with the existence of hiders can only be known if it is already known that there are no hiders – which leaves us, in order to show that hiders are extrinsically impossible, trying to show that they are impossible in some other way – that is, presumably, that they are intrinsically impossible. But if that could have been shown, we would never have needed to explore the question of their extrinsic impossibility at all.

As such, Todd does not know that he is omniscient and therefore is not omniscience. But what if we consider God rather than Todd, that is to say, a being with the characteristics traditionally ascribed to God. Could this being rule out the possibility of hiders?

Bass states:

Much remains the same. There is still the fact that the conception of a hider appears consistent, and if it is, hiders are not intrinsically impossible. Perhaps, however, there is something God knows that would enable him to show that hiders are extrinsically impossible. One suggestions derives from consideration of God’s role as creator. The argument would be that there could be hiders only if God had created them, but since he did not, and knows that he did not, there are none. The problem with this is that, according to orthodox conceptions of God, there is at least one thing that exists without having been created by God, namely, God himself. God cannot argue that it is impossible for there to be anything uncreated by God because that would rule out his own existence. And that means that hiders might be beings uncreated by God and, being in hiding, unknown to God.

Perhaps a revision of this line of thought will succeed. God is self-existent – that is, does not depend for his existence upon anything else. If God had a proof that there could be only one self-existent being, he could argue that if hiders exist without being his creations, then they would have to either be self-existent or the creations of some other self-existent being. But since there are no other self-existent beings – which, ex hypothesi, has been proven – there is no way for hiders to exist.

Let’s set this attempt aside, for the moment, to consider another. Suppose that some (modal) version of the ontological argument is sound. Then, it will be necessarily true that God exists with the full set of theistic attributes. That being than which no greater can be conceived will be omniscient, omnipotent, perfectly good, self-existent and so on. But if the ontological argument is sound, God will understand that it is, and therefore will have proof that there is an omniscient being and hence that there are no hiders.

Both of the foregoing attempts depend upon proofs which have not actually been given, and in the absence of the proofs, it is difficult to be confident of the solution. In addition, however, they share another feature – both are susceptible to the identification problem. In each case, we are supposing that there is a proof of the existence of some being with one or more of the traditional attributes of God. Then, the conclusion of that proof is used as a premise for a further argument to rule out the existence of hiders. But what about the being considering the proof? What is to identify that being – call it the Arguer – as the one proved to exist?

Let’s call the being supposedly proved to exist a God-like being:

(a) There is a God-like being

(b) If there is a God-like being, it knows that it is omniscient

(c) If some being knows that it is omniscient, then it is omniscient

(d) The Arguer is the God-like being

(e) Therefore, the Arguer is omniscient.

The identification problem lies in (d). How would the Arguer know that he is the God-like being? If the Arguer does not know that, he does not know the conclusion and this renders the conclusion false. Even if the Ontological Argument is sound, what is to certify to the Arguer that he is the omniscient being proved to exist?

The problem can also be expressed in matters of omnipotence. How would an all powerful being know that it is all powerful? Having no problem in accomplishing anything it has set out to do does nothing to establish the conclusion that it is all-powerful, perhaps it just has not tried anything that exceeded its power. Similar problems apply to most, if not all, of the attributes of God.

So, it even seems that this provides evidence that the ontological argument is not sound. For it were sound, then there would be an omniscient being, and therefore hiders would be, and could be known to be, impossible. But any proposed omniscient being is faced with the identification problem, and has to acknowledge that they might not be the omniscient being proved to exist.

Conclusion

As such:

(1) If any being is omniscient, then it knows that it is omniscient

(2) No being knows that it is omniscient, because there is no being that knows hiders to be impossible and who can solve the identification problem

(3) Therefore, no being is omniscient

Justification for (2):

(2a) If hiders are not known to be impossible or if the identification problem is not solved, then no being knows that it is omniscient

(2b) Hiders are not known to be impossible, or the identification is not solved

And we therefore have:

(1) If any being is omniscient, then it knows that it is omniscient

(2a) If hiders are not known to be impossible or if the identification problem is not solved, then no being knows that it is omniscient

(2b) Hiders are not known to be impossible, or the identification is not solved

(3) Therefore, no being is omniscient

Objections and subsequent responses can be found in the linked paper.