We now argue that CLAIM is true. The argument is nine steps. First, (1) The definition of an “omnipotent being” entails that an omnipotent
being could make any logically possible, contingent state of affairs ob-tain.
(1) does not assume that an omnipotent being exists, so it does not beg the question. (1) merely claims that if there is an omnipotent being, then it could make any logically possible, contingent state of affairs obtain.
difficulties with omnipotence, a pattern emerges: we are told that there is something that an omnipotent being both can and cannot do. But upon further inspection, it looks like the objection to omnipotence makes the mistake of trying to place an activity or a state of affairs in more than one “category”; for example, a given state of affairs is assumed to be contingent and necessary, or contingent and impossible.
And when one recognizes this mistake, the difficulty with omnipotence disappears. For instance, we are told that an omnipotent being can both make itself obtain and cannot make itself obtain. But when we recognize that an omnipotent being is necessary, and that it can only make contingent states of affairs obtain, the difficulty vanishes. This is a case of a state of affairs (the being’s existence) being mistakenly placed in the contingent category and the necessary category. Or we are told that an omnipotent being both can and cannot run a marathon: there is a contingent state of affairs that is impossible to bring about for an omnipotent being. But once we see that running a marathon is impossible for the being, the difficulty disappears. This time, a claim is mistakenly being placed in both the contingent category and the impossible category.
Or we are told that there must be something an omnipotent being cannot do: either it cannot make a stone it cannot lift or it cannot life the stone. But again, either it can make the stone or it cannot. If it cannot, then making the stone is in the impossible category, so there is no problem. And if it can make the stone – so making the stone is in the contingent category, then lifting the stone is in the impossible category, so again, there is no difficulty. It is only when we implicitly posit the impossible situation that, say, lifting the stone is in multiple categories (e.g., contingent and impossible) that the illusion of a difficulty with omnipotence arises.
Note that (1) is true even if there is not an omnipotent being, just as the definition of “unicorn” entails that “a unicorn will have a horn” is true even though there are no unicorns. (1) is true by definition.
The second step is,
(2) Any random logically possible world is a logically possible, contingent state of affairs.
(2) is innocuous. Consider a random logically possible world. This world can be thought of as a logically possible, contingent state of affairs; it might be an immensely complex state of affairs, but it can be thought of as a state of affairs.9 Furthermore, given (1) and (2), we can infer that, (3) The definition of an “omnipotent being” entails that an omnipotent
being could make any random logically possible world obtain.
If the definition of an “omnipotent being” entails that an omnipotent being could make all P ’s obtain, and any random Q is a P , then the definition of an “omnipotent being” entails that an omnipotent being can make any random Q obtain. Just as we saw above with (1), (3) does not assume that an omnipotent being exists; it merely claims that if one does, then it could make any random logically possible world obtain.
Step (4) is the following claim:
(4) If ((the definition of an “omnipotent being” entails that an omnipo-tent being could make it the case that any random logically possible world obtains) AND an omnipotent being is logically possible), then an omnipotent being could coexist with any random logically possible world.
This claim is very plausible. It is very plausible because it is a specific instance of a more general principle, and the general principle itself is very plausible. The principle is,
9Note that the argument will be consistent with any stance on the ontological status of possible worlds, from modal realism (see, e.g., Lewis [12]) to any form of
“ersatzism”. We are describing this (random) world as a logically possible “state of affairs”, but this does not entail that it is not concrete (it does not entail that it is concrete either). In short, the argument is agnostic about the ontological status of possible worlds.
PRINCIPLE : If ((the definition of an “x” entails that an x could make it the case that some logically possible state (or states) of affairs S obtains) AND an x is logically possible), then an x could “coexist”
with S (in, e.g., a logically possible world).
So, for example, if the definition of “carpenter” entails that a carpenter could make it the case that there is a cabinet, and the existence of a cabinet is a logically possible state of affairs, and the existence of a carpenter is logically possible as well, then a carpenter and a cabinet could coexist. If the definition of “arsonist” entails that an arsonist could make it the case that there is a fire, and the existence of a fire is a logically possible state of affairs, and the existence of an arsonist is logically possible as well, then an arsonist and a fire could coexist. PRINCIPLE essentially claims that if a being and a given state of affairs are both logically possible, so if there is a world W that contains the being and there is a world W∗ that contains the state of affairs, and if the being could bring about the state of affairs, then they could coexist. PRINCIPLE is obvious, if not outright trivial: to deny it, one would have to claim that a given being (is possible) and can bring about a given state of affairs (that is also possible), but it is not possible for the two to coexist (together in, say, a logically possible world). This is not coherent, for if they cannot coexist, then clearly the being cannot bring the state of affairs about, as we have supposed.10 But again, (4) is simply a specific instance of PRINCIPLE. PRINCIPLE is true, so (4) is true as well. We can then consider a particular omnipotent being; call it
“a”.
10Note that for a given x, there might be two (or more) states of affairs – S and S0 – that x could bring about, and S and S0 might not be compossible. For example, perhaps there is a logically possible carpenter that could make it the case that there are only brown cabinets or only red cabinets. What (4) entails in this case is that there is a possible world with the carpenter and only brown cabinets, and there is a different possible world with the carpenter and only red cabinets, but the principle does not entail that there is a single possible world with only brown cabinets and only red cabinets.
One might try positing the following counterexample to (4): suppose that x is a suicidal person and S is the state of affairs in which x is dead. x could bring S about, but x cannot coexist with S, because then x would be both alive and dead. This counterexample does not succeed, however, because x and S can coexist in, e.g., the same possible world, and this is the sense of “coexist” that the principle is concerned with.
(5) If ((a could make it the case that any random logically possible world obtains) AND a is logically possible), then a could coexist with any random logically possible world.
Step (5) follows from (4) with universal elimination, though this will be-come clearer in the following section when we give a formal version of the argument.
Step (6) is the antecedent of (5).
(6) (a could make it the case that any random logically possible world obtains) AND a is logically possible.
To establish (6), we must establish two claims: (A). we must show that a could make it the case that any random logically possible world obtains.
But (A) easily follows from step (3) (with universal elimination), which we have already established; and (B). we must show that a is logically possible, i.e., we must show that an omnipotent being is logically possible.
But we have already argued for this claim in section two.
So, with modus ponens and (5) and (6) we can infer that, (7) a could coexist with any random logically possible world.
But note that the following claim is true,
(8) If a could coexist with any random logically possible world, then there is a possible world in which an omnipotent being coexists with all logi-cally possible worlds.
Prima facie, this premise might not be obvious, but it can easily be shown to be true. Suppose (for conditional introduction) that an omnipotent be-ing could coexist with any random logically possible world. But if some-thing could be the case, then it is possibly the case.11 And if something is possibly the case, then given the meaning of “possibility” in possible worlds semantics, there is a possible world in which it is the case. So, if an omnipotent being could coexist with any random logically possible world, then there is a possible world in which an omnipotent being coexists with any random logically possible world. Furthermore, if an omnipotent being
11To deny this, one would have to claim that some P could be the case, but it is not possible that P , and with transposition, that some P is possible, but P couldn’t be the case. This is nonsense. For example, if something could be the case, then it must be possible.
can coexist with any random possible world, then it can coexist with all logically possible worlds.12 We have assumed the antecedent of (8) and derived the consequent; (8) is true.
We can now infer, with modus ponens on (7) and (8), that,
(9) There is a possible world in which an omnipotent being coexists with all logically possible worlds. But if something “coexists with all logically possible worlds”, it is necessary, for all that “necessary” means (in possible world semantics) is to exist in all possible worlds. That is, an omnipotent being is possibly necessary.
And (9) is simply CLAIM, so CLAIM is true. Given S5, an omnipotent being necessarily exists.
Call the argument the “modal theistic argument”, or the “MTA”. Even though the MTA is different from traditional ontological arguments, be they modal or not, the MTA is arguably a version of the modal ontological argument. Just as the traditional ontological argument held that we can infer that God exists from the idea of “God” (a being that is allegedly perfect etc), the MTA claims that we can infer that an omnipotent being exists from the idea (or from the definition of) “omnipotence”.