## Gellmans argument for oneness and omnipotence

Jerome Gellman (2000) has offered a clever argument from the claim that in every possible world there is a necessarily existing cause that explains all contingent truths (perhaps a different one in different worlds) to the claim that there is a necessarily existing cause that is omnipotent and that explains all contingent truths in every world. The argument is intricate, and here I shall give a variant that I think is in some ways superior.

If N is a necessary being that explains all the contingent truths of a world w, I shall call N "a creator in w." I shall assume the Iterativeness Postulate (IP):

(IP) If x has the power to gain the power to do A, then x already has the power to do A, although x might have to take two steps to do A (first acquire a power to directly do A, and then exercise the power).

It follows from IP that if N is a creator in w, then the powers of N are necessary properties of N. To see this, for a reductio suppose that w is actual and N contingently has the power to do A. Then N's causal activity explains why N has the power to do A, since N's causal activity explains all contingent truths. But then explanatorily prior to N's causal activity, N had the power to bring it about that it had the power to do A. But by IP, N had the power to do A explanatorily prior to Ns causal activity, which contradicts the claim that this causal activity explains the power.

Next, we show that a creator N1 in w1 and a creator N2 in w2 must be the same individual. Suppose first that w1 and w2 are distinct worlds. Let p be some contingent proposition true in w1 but not true in w2. Beings N1 and N2 exist necessarily, and hence both exist in w1. Let q be the proposition that N2's causal activity does not explain not-p. This proposition is true at w1 since not-p is false at w1 and only true propositions have explanations; on the other hand, q is false at w2. Since N1 is a creator in w1, N1's causal activity explains q. Therefore, N1 in w1 has the power to make q true, a power it exercises. By what we have already shown, N1 essentially has the power to make q true, and hence it also has this power in w2. Call this power P1. We can now ask why it is the case at w2 that N1 fails to exercise this power. Since N2 is a creator in w2, we must be able to explain N1's contingent failure to exercise P1 in terms of N2's causal activity. Therefore, N2 at w2 has the power to prevent N1 from exercising P1. Call this power P2. By what has already been shown, N2 has P2 essentially.

Moreover, N2 does not exercise P2 at w1, since at w1 N1 does exercise P1. Why does N2 fail to exercise P2 at w1? This must be explained in terms of N1's causal activity, just like all other contingent facts about w1. Hence, at w1 N1 has the power, P3, of preventing N2 from exercising P2. Hence, N1 has that power essentially and is prevented at w2 from exercising it by N2. Therefore, arguing as before, N2 essentially has the power, P4, of preventing N1 from exercising P3. And so on.

This regress seems clearly vicious, and so we conclude that N1 cannot be distinct from N2 (if N1 = N2, we can say that what explains N2's not bringing it about that p at w1 is simply that N2 brings it about that not-p at w1, and then we can reference our previous discussions of libertarian explanations in Section 2.3.2.3, above). But perhaps we can make the argument work even without going through with the regress. What explains at w1, we may ask, why it is that N2 exercised none of its powers to prevent N1 from engaging in the kind of activity it engages in in w1? It must be that the explanation lies in the exercise of some power P by N1 in w1. But then N1 also had this power in w2 and did not exercise it, and its failure to exercise it must be explained by N2's exercise of some preventative power Q. But Q is one of the powers whose exercise in w1 is prevented by N1's exercise of P. Repeating the argument with the two entities and worlds swapped, we conclude that each of N1 and N2 has the power to prevent the other from its preventing the other. But that is, surely, absurd! (It might not be absurd if N1 = N2 since in having the power to do A, I have the power to prevent myself from not doing non-A, but that is likely just because my doing A is identical with my refraining from doing non-A.)

So, if N1 is a creator in w1 and N2 is a creator in w2, then N1 = N2. It also follows that each world has only one creator. For if N1 and N2 were each a creator in w1, then we could choose any second world w2, let N3 be a creator in w2, and use the said argument to show that N1 = N3 and N2 = N3, so that it would also follow that N1 = N2.

Thus, there is a unique being that essentially has the power to explain every contingent truth in every world via its causal activity. But, surely, having the power to explain every possible contingent truth via one's causal activity implies omnipotence. (We can stipulate this if need be, and the stipulation will not be far away from ordinary usage.)

There are two difficulties in this line of argument. The first is that it requires that each world have one being that by itself explains all contingent truth. What if one takes the cos-mological argument only to establish the weaker claim that there is at least one necessary being and the necessary beings collectively explain all contingent truths? In that case, the said argument can still be applied, with "a creator" being allowed to designate a collective and not just an individual. The conclusion would be that the very same omnipotent collective explains contingent truth in every world. Can there be an omnipotent collective? It is tempting to quip that there is a conceptual impossibility in a committee's being omnipotent, since committees always suffer from impotence, say, due to interaction issues within the committee. There may be something to this quip. How, after all, could a collective collectively be omnipotent? How would the powers of the individuals interact with one another? Would some individuals have the power to prevent the functioning of others? These are difficult questions. It seems simpler to posit a single being.

The second difficulty is that on this argument, the creator's causal activity explains all contingent activity, including, presumably, any free choices by creatures. This problem infects other Leibnizian cosmological arguments. Probably, the way to handle it is to give a subtler and more careful definition of what it is to be a creator in w. Maybe the First Cause's activity does not have to explain all free choices made by everybody; it may simply have to explain both the prerequisites for all free choices made by any contingent beings, and everything that does not depend on the free choices of contingent beings? This is probably all we need for the crucial uniqueness argument.