Omnipotence and Omniscience

I don’t think anything could simultaneously have the property of being omnipotent and omniscient. Whatever consequences this yields are what they are, but what follows is why I believe it is the case. I first provide necessary conditions for omnipotence and omniscience. Then I sketch a state of affairs that displays how a contradiction is brought on by assuming something (B) is both omnipotent and omniscient.

We call something (B) omnipotent only if, if for any contingent event or state of affairs E, B can make it the case that ~E. So B can’t make it the case that ‘2+2=4’ is false, nor can B make it the case that ‘It is not the case that Hesperus is Phosphorus’ is true. However, B could make it the case that ‘Abraham Lincoln was the 16th President of the United States’ is false, and B could make it the case that ‘It is not the case that New York City is the most populous city in the United States in 2016’ is true.

We call something (B) omniscient only if, for any proposition P, B knows the truth value of P. A further condition is that B is able to determine the proposition P expressed by any given utterance U of any sentence S at any context C.

Let us assume something (B) is both omnipotent and omniscient. Let us also assume there is some contingent state of affairs E that is the case. Let us finally assume there is some proposition P, where P =def ‘The fact that E is an eternal fact’. As an example, if  E =def ‘There is more Hydrogen than Francium’, then P =def ‘The fact that there is more Hydrogen than Francium is an eternal fact’. I do not mean anything deep by the term ‘eternal fact’. I mean just this. Let F be a state of affairs. Let Q be a proposition, where Q =def ‘The fact that F is an eternal fact’. Let R be a proposition where R =def ‘F is the case’. We express (using the Tense Logic (TL) due to Arthur Prior) that:

(1) Q ≡def (G (R) ^ H (R) ^ R)

This reads as: the fact that F is an eternal fact if and only if it will always be the case that F is the case and it has always been the case that F is the case and F is the case.

Here is the problem. Assume we ask B, regarding some contingent state of affairs E that is the case, whether the proposition P stating that the fact that E is an eternal fact is true or not true. As we saw in (1), P can be made logically equivalent to a propositional formula in propositional logic, meaning that P must either be true or not true (since all formulae in propositional logic have truth values of true or not true). Following our definition of omniscience, B must be able to give the correct truth value for P. Since B knows whether or not P is true or not true, B also knows whether or not the fact that E is an eternal fact. However, this contradicts B’s omnipotence. If B is omnipotent, B should be able to at some time(s) make it the case that ~E, where this modifies the eternality of the fact that E (or the inverse, see footnote). However, if B were to do this after answering that the fact that E is/(isn’t) an eternal fact, B would not have actually known that it was/(wasn’t) an eternal fact (since it then wouldn’t be and hence never was/(was and hence never wouldn’t be)). That is why I think nothing can be both omnipotent and omniscient simultaneously.

I anticipate two objections to my central claim. The first is that eternal facts might simply not exist regarding contingent states of affairs. Let us assume that this is true. It is either necessarily true or contingently true. I do not think it is necessarily true. A universe in which there is eternal recurrence might have one contingent event repeat every recurrence cycle, and thus the truth that that particular event occurs once per recurrence cycle is an eternal contingent truth. This situation seems intuitively plausible. If the claim is contingently true, then by our definition of omnipotence B should be able to make it the case that is it false, and the problem re-emerges. The second objection is that I have not defined omnipotence and omniscience adequately. However, recall that I did not give exhaustive definitions of either term, rather, I just provided necessary conditions for calling anything either omniscient or omnipotent. While there is a wide-ranging debate about what it means to be either omnipotent or omniscient, I do think there is a strong intuition that something that could not meet the criteria I have established could not be called either, regardless of what other criteria there exists for ‘true’ omnipotence and omniscience.

I do not believe I have even come close to settling this problem entirely. There are still serious issues, for instance, regarding the temporality of B, and whether the antecedence of B’s judgment of P to B’s potential modification of E (or ~E) is necessarily temporal or purely logical. All this is of course complicated by the fact that there is also a non-trivial case for an omniscient and omnipotent being existing in some way outside time. However, I do think my problem is a genuine one that creates some theoretical tension between the two properties, and hopefully puts some pressure on the pre-theoretical sense that they can be unproblematically conjoined in one being.

 Strictly speaking, we add that this must be true in all models.

 I could claim that it must be either true or false, but I leave the question open.

 If the fact that E is an eternal fact, any negation changes its eternality. If E is not an eternal fact, negating ~E at all times where it obtains makes the fact that ~~E (and hence the fact that E) an eternal fact.