Modal Arguments for Atheism (2012)
One can put forth different kinds of arguments to defend atheism. One kind is an evidential argument, where some contingent fact about the world is cited as evidence against God's existence. Perhaps the most popular of such arguments is the evidential argument from evil, which cites the large amount of severe evil or suffering in the world as strong evidence against God's existence. Other evidential arguments for atheism include: the argument from scale, which cites the scale of the universe as evidence against God's existence; the argument from nonbelief, which cites the scope of nonbelief in God as evidence against his existence; and the argument from physical minds, which cites the overwhelming evidence that minds have a physical basis (or are physically realized) as evidence against God's existence. These arguments have the probabilistic conclusion that God does not exist, and thus do not conclusively demonstrate the truth of atheism.
There are also more ambitious logical arguments for atheism, which attempt to show that either (a) the proposition that God exists is logically inconsistent with some contingent fact about the world, or (b) the concept of God is logically incoherent in some way. The first kind of logical argument resembles evidential arguments because it is based on some contingent fact about the world. But unlike evidential arguments, this kind of logical argument purports to conclusively demonstrate the truth of atheism based on a logical incompatibility between the cited contingent fact about the world and the proposition that God exists. The second kind of logical argument is the most ambitious of them all. Unlike the first kind of logical argument, which concludes with the contingent truth of atheism, the second kind concludes with the necessary truth of atheism.
In addition to the better-known evidential and logical arguments for atheism, there is a third kind of argument that will be the focus of this paper: modal arguments for atheism. Unlike the other two kinds, modal arguments begin with a possibility claim—that some proposition is possibly true. But like the second kind of logical argument, modal arguments conclude with the necessary truth of atheism. Thus modal arguments appear to be very strong, for they deliver the necessary truth of atheism on the basis of a mere possibility claim.
In order to show how they contribute to the philosophical defense of atheism, in this paper I formulate modal arguments for atheism and then examine the ways a critic might respond to them. Specifically, I aim to show that modal arguments for atheism either (a) positively support atheism or (b) at least undermine modal arguments for theism.
2. The General Structure of Modal Arguments for Atheism
Laying out the general structure of modal arguments for atheism makes it easier to generate concrete examples. With that in mind, their general structure is as follows:
- It is possible that p.
- Necessarily, if it is possible that God exists, then it is necessary that God exists.
- Necessarily, if God exists, then it is not the case that p.
- Therefore, it is not possible that God exists. (from A, B, & C)
Premise A is the formula for generating the possibility claims that underlie the modal arguments. Premise B follows from the conception of God as a necessary being: if God is a being that, conceptually speaking, exists necessarily, then it is necessarily true that he will exist in every possible world if he exists in any possible world. Premise C asserts a logical incompatibility between God's existence and the object or state of affairs held to be possible in premise A. With these premises in place we can deduce our conclusion in the following manner. First, from C it follows that "if it is necessary that God exists, then it is necessary that it is not the case that p." Next, since A is logically equivalent to "it is not necessary that it is not the case that p," it follows from A and the above consequence of C, via modus tollens, that "it is not necessary that God exists." Then from this and B it follows, again via modus tollens, that "it is not possible that God exists."
3. Generating Modal Arguments for Atheism
With the general structure of these arguments in place, we can now generate specific arguments by substituting an actual proposition for p. But how do we determine what proposition to use in place of p? How do we know if a given proposition will work? Here we must find a proposition that is logically inconsistent with the proposition "God exists"—that is, a proposition that, when plugged in for p, will give us a true C-premise. One way to do this is to look at evidential arguments for atheism. For example, recall that the evidential argument from evil cites the large amount of severe evil or suffering in the world as evidence against God's existence. This is cited as evidence for atheism because it is probably gratuitous—that is, there is probably no morally sufficient reason for God to permit or create it. And that is precisely the kind of evil that God, as a morally perfect being, will not permit or create. Consequently, God and gratuitous evil cannot possibly coexist. Thus, our first instance of p could be:
- Gratuitous evil exists.
Plugging this proposition in for p would give us the modal argument from gratuitous evil.
Another evidential argument to look at here is the one from physical minds. Since God is necessarily a minded, nonphysical being, he could not exist if all minds were physically realized. And if God did exist, then it could not be the case that all minds are physically realized. So God's existence and the physical realization of all minds are logically incompatible things. Thus, our second instance of p could be:
- All minds are physically realized.
Plugging this proposition in for p would then give us the modal argument from physical minds.
Now let's look at the evidential arguments from nonbelief and scale. Unfortunately, neither will help us to construct more modal arguments for atheism because there is a crucial difference between them and the evidential arguments from evil and physical minds. To see this difference, first note that these arguments each involve (basically) two claims: an incompatibility claim asserting a logical incompatibility between God's existence and some state of affairs S, and an evidence claim asserting that S obtains. Again, all of these arguments have atheism as their probabilistic conclusion. However, when it comes to the arguments from evil and physical minds, it is the evidence claim that is probabilistic, whereas the incompatibility claim is not. But when it comes to the arguments from nonbelief and scale, it is the incompatibility claim, and not the evidence claim, that is probabilistic. Since their incompatibility claims are only probabilistic, these two arguments do not help us here: they would not provide airtight C-premises, and thus would not generate airtight modal arguments for atheism.
Fortunately, other bases for strong modal arguments for atheism can be found without looking at evidential arguments. For example, since God is morally perfect, he will not allow a state of affairs to obtain in which every free person besides himself always does the morally wrong thing. So our third instance of p could be:
- Every metaphysically free, non-God person always does the morally wrong thing.
Plugging this proposition in for p would then give us what I will call the modal argument from super depravity. Now if (3) is objectionable for some reason, we could use a similar, more modest claim for our third instance of p. This is:
3'. The world's metaphysically free, non-God creatures produce more moral evil than moral goodness such that their freedom is not worth the cost.
Plugging this proposition in for p instead of (3) would give us what I will call the modal argument from depravity.
There are at least two other bases for generating good modal arguments for atheism. Let's say that something is a maltheistic deity if and only if it has the properties of being omniscient, omnipotent, and perfectly evil. Any being that qualifies as a maltheistic deity cannot possibly coexist with God. For suppose that God and such a maltheistic deity coexist. Since both are omniscient, omnipotent beings, it is impossible for either to thwart the will of the other, for it is logically impossible to thwart the will of a being that is omniscient and omnipotent. Moreover, their wills will be in complete conflict with each other since God is perfectly good and a maltheistic deity is perfectly evil. Now let's say that God wills something. Since he is omniscient and omnipotent, it is impossible for his will to be thwarted; so God will succeed in his willing. However, since the maltheistic deity is also omniscient and omnipotent, it is impossible for its will to be thwarted; so it will succeed in thwarting God's will. Therefore, God will also not succeed in his willing, which obviously contradicts that God will succeed in his willing. The same kind of contradiction can be generated by supposing first that the maltheistic deity wills something. Since the supposition that both God and a maltheistic deity exist leads to logical contradictions, these beings cannot possibly coexist. We thus have a fourth instance of p with:
- A maltheistic deity exists.
Plugging this in for p would give us the modal argument from a maltheistic deity. In fact, this argument could actually be a template for several such arguments since there appears to be more than one possible being that qualifies as a maltheistic deity. An easy way to generate multiple possible maltheistic deities is by adding a single property at a time. For instance, we can get a unique maltheistic deity by adding the property of necessary existence to omniscience, omnipotence, and perfect evilness; and a different one by adding the property of contingent existence instead.
Finally, there is another basis for modal arguments for atheism that is more like a template for several such arguments—perhaps even an infinite number of them. First of all, it is necessarily true that if God exists, then he is the creator of the universe. In other words, God's existence necessarily precludes any other being from creating the universe. So we have a fifth instance of p with:
- Some other being besides God created the universe.
Plugging this in for p would then give us the modal argument from a different creator. Of course, there are numerous possible beings besides God—perhaps an infinite number of them—that could have created the universe. So for each proposition asserting that one particular non-God being created the universe—or that several particular non-God beings did so—we could generate a good modal argument for atheism. Thus there are several (if not infinitely many) modal arguments from a different creator.
4. Responding to Modal Arguments for Atheism
So, what are we to make of arguments that deliver the necessary truth of atheism from a mere possibility claim? Surely such a strong atheistic conclusion cannot be delivered so easily and cheaply—as well as an infinite number of times! There must be something fishy going on here.
But what is it about these arguments that stinks? There is no obvious culprit here. Since the arguments are all deductively valid, the problem must lie with one or more of the premises themselves. But even then there is still no obvious culprit. The A-premises are all quite strong: besides their intuitive plausibility, the objects or states of affairs that they assert to be possible are all conceivable, coherent things. Moreover, at least (1) and (2) are very plausible in their own right. For the horrific evil we face in this world certainly appears, upon philosophical reflection, to be gratuitous—there is no discernible justification for God to permit or create it. And it is, of course, very plausible for this evil to really be how it appears to be. Our best evidence also suggests that all minds with which we are acquainted are physically realized, which in turn suggests that all minds are physically realized. Though this evidence could be deceiving, it is again very plausible that things really are as they appear here. But since (1) and (2) are very plausible in their own right, surely the mere possibility of them being true is as strong as possibilities come.
Then there is B and the C-premises. As mentioned above, the former follows from the conception of God as a necessary being, which is popular among philosophers. The latter are all airtight incompatibility claims; so they are beyond dispute. What, then, are the possible options for contesting these arguments? Well, one can contest the A-premises or contest B. Let's begin with the first one. Even though the A-premises are all quite strong, there are nevertheless two strategies (that I know of) for contesting them. One is to directly contest them by trying to show that the objects or states of affairs that they assert to be possible are really incoherent things. However, this is not a viable strategy: not only would this be an endless task in virtue of the countless non-God beings that could have created the universe, but it is surely false that all of the seemingly possible objects or states of affairs are really incoherent things. The more promising strategy is to contest the A-premises indirectly by putting forth some theistic counterargument that specifically delivers the conclusion that:
- It is necessary that God exists.
Armed with this proposition, an imagined critic can deduce the falsity of the A-premises from Q and the C-premises. But how should one go about getting Q?
Not just any theistic argument will work here. In order to give our imagined critic what he or she needs to deduce the falsity of the A-premises, the argument must specifically conclude with Q—that is, it must point specifically to a necessarily existing God. However, most theistic arguments do not do so, such as those that appeal to the existence, order, complexity, "fine-tuning," or apparent design of the universe, or to the existence of minds, reason, miracles, religious experiences, and so on. The bases of these arguments do not even point specifically towards God, let alone to a necessarily existing one. And even if they did offer some support for the existence of God (which I think is false), they would still offer no support for a necessarily existing God over a contingently existing one.
One exception here is the modal cosmological argument, which invokes a necessarily existing God as the one necessary being needed to explain why contingent beings exist. But as I have shown elsewhere, this argument is invalid: it does not point specifically to God, or even to only one necessary being. It is also based on the rather dubious principle of sufficient reason, and so will not give our imagined critic what he or she needs to deduce the falsity of the A-premises.
As far as I can tell, the only viable option left is to use an ontological argument. Now the classic ontological argument will not work because it is clearly invalid. But a modal version of the ontological argument will work, and it can be formulated quite simply as:
- It is possible that God exists.
- Necessarily, if it is possible that God exists, then it is necessary that God exists.
- Therefore, it is necessary that God exists. (from B & P)
In fact, this argument works very well in the present context. Unlike most theistic arguments, it is clearly valid (as a straightforward example of modus ponens) and does not contain any premise that embodies an invalid inference. Furthermore, it essentially tries to beat modal arguments for atheism at their own game. For besides using premise B just as modal arguments for atheism use it, it too rests on a possibility claim that can be defended on similar grounds as our A-premises: not only is it intuitively plausible, but God is a conceivable, coherent thing. Thus, putting forth the modal ontological argument is the best way for our imagined critic to contest the A-premises.
In response, we could point out that there are numerous arguments that P is false because the concept of God is actually an incoherent concept. However, we must ignore such arguments, for although they cause problems for theism, falling back on them to contest P would render modal arguments for atheism superfluous. Namely, if we can provide independent grounds to doubt the coherence of the concept of God, then we do not need modal arguments for atheism. In fact, if any incoherence argument works, then atheism is established and theism is destroyed—any other atheistic argument, or demonstration of the failure of theistic arguments, would be unnecessary. Thus, we must ignore incoherence arguments in order for modal arguments for atheism to have the merit that I attribute to them in this paper.
But even if we ignore incoherence arguments, contesting our A-premises by appealing to the modal ontological argument fails to defeat modal arguments for atheism. First of all, P and any given A-premise are, at best, equally plausible—it would be absurd to claim that P is more plausible than any of the A-premises. For even if P is intuitively plausible, and God is a conceivable, coherent thing, the same can be said of the objects or states of affairs said to be possible in the A-premises. Now the equal plausibility of P and any given A-premise implies that the modal ontological argument and any given modal argument for atheism are on an equal footing—that the soundness of one argument is as plausible as the soundness of the other. But since the soundness of one argument implies the unsoundness of the other, the soundness of any given modal argument for atheism is as plausible as its unsoundness. Therefore, at best the modal ontological argument undermines any given modal argument for atheism considered by itself.
However, even if the modal ontological argument undermines any given modal argument for atheism taken alone, the modal ontological argument certainly does not undermine the entire set of modal arguments for atheism. To see why, consider first the disjunction of the A-premises:
(DA) A1 or A2 or A3 or A4 or A5.
Since the truth of this proposition only requires that one of its disjuncts be true, and since each one is just as plausible as P, it has a much higher probability of being true than P—especially if DA has an infinite number of disjuncts. So DA is more plausible than P. Consequently, it is more plausible that at least one of the modal arguments for atheism is sound and that the modal ontological argument is unsound than that the modal ontological argument is sound while the modal arguments for atheism are unsound. Thus the modal ontological argument does not undermine the entire set of modal arguments for atheism.
Suppose that P is somehow more plausible than any given A-premise. While this would defeat the claim that P and any given A-premise are equally plausible, it would not necessarily undermine the higher probability of DA. For suppose that DA does have an infinite number of disjuncts, and that each one has some chance of being true. If so, then the probability of DA, regardless of the probability of each individual disjunct, approaches 1. So no matter how much more plausible P is than any of DA's disjuncts, DA is still more plausible than P.
Furthermore, even if DA has only a finite number of disjuncts, it is still more likely to be true than P. For given the conservative assumptions that (a) either DA or P must be true, (b) each disjunct again has some chance of being true, and (c) there are only 5 disjuncts, each disjunct only needs to have a probability of at least .14 in order for DA to have a higher probability than P. However, an estimated probability of .14 for each A-premise is not only absurdly low in its own right, but results in P having a probability of .47—almost 3.5 times as likely as each A-premise! This is absurdly generous. We should therefore estimate the probability of each A-premise to be higher than .14, which means that we should estimate DA to be more probable than P. So once again, DA is more plausible than P.
In a final attempt to contest the set of modal arguments for atheism by contesting their A-premises, our imagined critic could argue that the modal ontological argument is not the only counterargument to be considered. In addition to P, there are several other possibility claims that, when combined with B, entail Q, and thus the falsity of the A-premises. More specifically, our imagined critic could generate a new possibility claim, and hence a new theistic counterargument, by removing the proposition "God exists" from P and replacing it with any of the following:
- God created the universe.
- Jesus was the son of God.
- God spoke to Abraham.
- There is eternal communion with God.
- The Ten Commandments were given by God.
- The Bible is the word of God.
- The Koran is the word of God.
- Satan rebelled against God.
- God loves everyone.
There are countless other examples that could work here—perhaps even an infinite number of them. So in place of a single modal theistic argument, there is actually a set of such arguments comparable to the set of modal arguments for atheism. Consequently, even if the modal ontological argument by itself does not undermine the entire set of modal arguments for atheism, the set of modal theistic arguments does undermine it (or so our imagined critic would argue).
As clever as it may be, this response does not work. The problem here is that taking "God exists" out of P and replacing it with anything like (7) through (15) above would not really generate a new modal argument for theism. In fact, the above procedure would not really involve taking the proposition "God exists" out of P at all, but would instead involve adding something to this proposition that does not do any independent work. For instance, consider the possibility claim generated from (7): it is possible that God created the universe. This amounts to the claim that "it is possible that God exists and created the universe." Now it is true that this claim can be substituted in for P in the modal ontological argument, and that the argument will still remain valid. However, it is the proposition "God exists" that is still doing all of the work—adding that he created the universe is completely superfluous. What our imagined critic needs to do is generate modal arguments for theism in the same way that I generated modal arguments for atheism. After finding the first instance of p with "gratuitous evil exists," I did not try to find other instances by tacking on superfluous additions to gratuitous evil (e.g., specific victims). Since it is the evil that would be doing all of the work here, such a procedure would not have delivered truly new instances of p, and thus would not have delivered new modal arguments for atheism. Instead, this procedure would have delivered only a single modal argument for atheism presented in different ways. I therefore found other objects or states of affairs that are completely independent of gratuitous evil, and it is because they worked on their own that I was able to use them to generate new modal arguments for atheism. By following the faulty tacking-on procedure, our imagined critic has merely found different ways to present the modal ontological argument; and until he or she can apply the procedure that I followed to theism, the modal ontological argument is the only modal theistic argument available to be pitted against the set of modal arguments for atheism.
Since contesting the A-premises failed to refute modal arguments for atheism, contesting B—which amounts to contesting the conception of God as a necessary being—is the only option left. Luckily for theists, this is a good response to such arguments. For starters, B is suspicious since it is the only premise in these modal arguments (the ontological argument and those for atheism) that asserts the entailment of a necessity from a mere possibility. It is ultimately responsible for the fishiness of deducing the necessary truth of atheism from mere possibility claims.
There are also grounds for thinking that B is false. For one thing, B implies that P and the A-premises are logically inconsistent with each other. But this inconsistency is suspect: as stated above, P and the A-premises are all intuitively plausible, and their objects or states of affairs are conceivable, coherent things. Since there seems to be no logical inconsistency between P and the A-premises, B appears to be false. Furthermore, it is trivially true that if it is necessary that God exists, then it is possible that God exists. But from this and B it follows that "it is necessary that God exists" and "it is possible that God exists" are logically equivalent propositions. However, such a consequence seems false—claims of possibility and necessity are on opposite sides of the modal spectrum. So again, B appears to be false.
Finally, there appears to be no good reason to conceive of God as a necessary being, and thus no grounds for thinking that B is true. As I have argued elsewhere, neither the need for God to exist independently of all else, nor the idea that necessary existence is a perfection, constitute a good reason for conceiving of God as a necessary being. Instead, God seems to be (conceptually speaking) a logically contingent being—one that exists in some, though not all, possible worlds.
On the other hand, Alvin Plantinga offers some very promising grounds for conceiving of God as a necessary being. While necessary existence is not itself a perfection, perhaps it is a necessary condition of perfection. First, consider that the goodness of a being in a world W may not be a function of the being's properties in that world alone; it may also depend upon its properties in other worlds. If so, then a truly perfect being must have the set of traditional, perfect-making divine attributes (let's call this set T) in the world in which it exists, as well as in every other possible world. But since existence is a necessary condition of having properties (things that do not exist do not have properties, according to Plantinga), a being must exist in order to have T. So if a perfect being must have T in every possible world, and having T in every possible world requires existing in every possible world, then a perfect being must exist in every possible world. And since God is, by definition, a perfect being, he must be conceived of as a being that exists in every possible world—that is, as a necessary being.
Despite its brilliance, I think this attempt to vindicate the necessary beinghood of God fails. To see why, consider first the following observation made by Plantinga:
Those who worship God do not think of him as a being that happens to be of surpassing excellence in this world but who in some other worlds is powerless or uninformed or of dubious moral character.
But why do people not think of God in this way? Well, if God had T in this world and had properties that fell short of T in others, then God would have T accidentally. But if God had T accidentally, then God could fail to have T, which in turn implies that God is not perfect—he would be a better being if he could not fail to have T. However, God is perfect by definition; so he could not fail to have T, or have T accidentally. Instead, God must have T essentially, or in every possible world in which he exists. The upshot here is that God's perfection requires that he have T essentially and not accidentally, which means that God's goodness is a function of his having T essentially instead of accidentally. This can then be generalized: the goodness of any being is a function of whether it has its properties essentially, or accidentally.
The idea that a being's goodness is a function of whether it has its properties essentially or accidentally seems to be what Plantinga is driving at when he suggests that the goodness of a being in a world W depends on its properties in other worlds. If so, then Plantinga seems to be correct. However, he has not established that a perfect being must have T in every possible world. Instead, he has established that a perfect being must have T essentially, which is consistent with this being's logical contingency. Put another way, Plantinga has established that a being's perfection requires that it have T in every world it happens to grace, not that it must instantiate T in every possible world.
On the other hand, isn't the claim that a perfect being must have T in every possible world still plausible? That depends on whether a necessary being that has T essentially is a better being than a logically contingent being that has T essentially. I don't think that such a being would be better, for if it were, then maximal exemplification of T would have to contribute to perfect beinghood—having T essentially would not be sufficient for perfect beinghood. But why should we think this? We would not think, for example, that a soccer player with the best possible soccer skills is a better soccer player than another with the same skills just because the former played in every game of the season while the latter played in only some of them. Here the rate at which a perfect skill is exemplified is irrelevant to being a perfect soccer player—all it takes is the possession of certain skills. Likewise, a necessary God does not seem to be a better being than a logically contingent God just because the former's essential T-properties are exemplified in every possible world, while the latter's essential T-properties are only exemplified in some. All it takes to be a perfect being is having T essentially, and this is true of both Gods. So it does not seem to be true that a perfect being must have T in every possible world. Consequently, Plantinga has not provided good grounds for conceiving of God as a necessary being.
At this point, then, we seem to have no good reason to conceive of God as a necessary being, and thus no grounds for thinking that B is true. On the other hand, we do seem to have good grounds for thinking that B is false. So until it can be shown otherwise, rejecting B is a viable way—indeed, the only viable way—to reject modal arguments for atheism.
5. Modal Arguments for Atheism and the Philosophical Defense of Atheism
I have shown that premise B is the only viable place to contend modal arguments for atheism. But no matter what B's epistemic status, modal arguments for atheism make a contribution to the philosophical defense of atheism. For suppose that B is true, or at least more plausible than its negation. If so, then the only threat to modal arguments for atheism is the modal ontological argument. However, the set of modal arguments for atheism is stronger than the modal ontological argument: because DA is more plausible than P, it is more plausible that at least one of the modal arguments for atheism is sound and that the modal ontological argument is unsound than that all of the modal arguments for atheism are unsound and that the modal ontological argument is sound. So if B is true or more plausible than its negation, then atheism is positively supported by modal arguments for atheism.
Now suppose that B is false, or at least no more plausible than its negation. If so, then modal arguments for atheism thereby fail, but the modal ontological argument and modal cosmological argument also fail, for they too rely upon the conception of God as a necessary being. Put another way, even if modal arguments for atheism fail in virtue of relying on the conception of God as a necessary being, they take the modal ontological argument and modal cosmological argument down with them. So even if modal arguments for atheism do not positively support atheism, they still make a contribution to the philosophical defense of atheism.
 Nicholas Everitt, The Non-Existence of God (New York, NY: Routledge, 2004), Chapter 11.
 Ted Drange, Nonbelief and Evil: Two Arguments for the Nonexistence of God (Amherst, NY: Prometheus Books, 1998).
 See Richard Gale, "Freedom Versus Unsurpassable Greatness," International Journal for the Philosophy of Religion, Vol. 23, No. 2 (1988): 65-75, and Richard Gale, On the Nature and Existence of God (New York, NY: Cambridge University Press, 1991), Chapter 6. Gale neither uses the phrase "modal argument from gratuitous evil" nor formulates such an argument, but "the modal problem of evil" he refers to (p. 229) in his excellent book is another way to describe the argument.
 Again, see "Freedom Versus Unsurpassable Greatness" and On the Nature and Existence of God. Here, too, Gale does not use the phrase "modal argument from super depravity" or formulate such an argument, but he does provide the basis for this argument.
 Michael Tooley, "Plantinga's Defence of the Ontological Argument," Mind, Vol. 90 (1981): 422-427.
 Of course, the intuitive plausibility of the A-premises, as well as the conceivability and coherence of their contents, does not guarantee their truth. But it does provide defeasible justification for them. Perhaps the objects or states of affairs are not really coherent, the A-premises are defeated by competing possibility claims, or the A-premises are false for some other reason. However, until such defeat is forthcoming, the intuitive plausibility of the A-premises, as well as the conceivability and coherence of their contents, provides good epistemic grounds for them. For although intuitions can certainly be mistaken, undefeated ones carry some epistemic weight. Moreover, a thing could be conceivable without being possible, but its conceivability at least suggests that it is possible, insofar as our imaginative and rational powers give us epistemic access to modal space. Finally, incoherent things are automatically impossible; so a thing's coherence suggests its possibility at least in the sense that it is not automatically rendered impossible.
 See my "Questions of Existence and the Modal Cosmological Argument" (2011) on the Secular Web. In that paper I argue that one reason why the modal cosmological argument is not rationally acceptable is that invoking God as the necessary being that explains contingent beings has the wildly implausible result that gratuitous evil is impossible. It is now evident that I could have offered several reasons—perhaps an infinite number of them—for why the modal cosmological argument is not rationally acceptable: asserting that God is the necessary being that explains contingent beings results in the impossibility of every object or state of affairs contained in the instances of p mentioned above, and each such consequence is an implausible result.
 A not viable option would be a moral argument for theism that is something like:
- Necessarily, if God does not exist, then moral realism is false.
- Necessarily, moral realism is true.
- Therefore, necessarily, God exists
This is not a viable option because not only are both premises highly controversial, but the first seems patently false. In fact, it smacks of being an article of faith. So no one would be justified in simply putting forth this argument as something that can be unproblematically relied upon for another purpose, like blunting the force of modal arguments for atheism.
 Since the invalidity of this argument is old news, I will be brief in explaining it here. Its first premise is the conceptual claim that "God is the greatest possible being," and its second premise is that "existence is a great-making property." Now these premises at best establish what God is conceptually—the first premise asserts what the concept of God amounts to at the most general level, and the second premise allows us to fill in one of the great-making properties (existence) contained in this concept. But it does not follow from what God is conceptually that there is a God. Like the concept of any other concrete being, the concept of God does not guarantee its own instantiation. So the argument is invalid.
 A bad way to argue for P is the following modus ponens argument:
- God ought to exist.
- If God ought to exist, then it is possible that God exists.
- Therefore, it is possible that God exists.
Since God is a perfect being, it would be very good if he existed. So N is plausibly true (assuming, of course, that ought-statements can be true). However, O is probably false because God could be an incoherent thing even if he ought to exist. For instance, a clean-shaven man with a beard that is very powerful, knowledgeable, benevolent, and deeply concerned with the well-being of cats certainly ought to exist because it would be very good if such a being existed. But this being is obviously an incoherent one, and thus cannot possibly exist; so the fact that it ought to exist does not imply that it is possible for it to exist. Furthermore, it would be misguided to defend O by claiming that it is an instance of the widely accepted "ought-implies-can" principle; for the widely accepted version of this principle pertains to action, not the existence of objects or states of affairs. For example, it is unreasonable or false to maintain that Jack ought to jump over the moon or bench press his car because Jack cannot do these things—a necessary condition of saying that Jack ought to do something is that he can do it. But even if the ought-implies-can principle is acceptable with respect to action, this does not generalize to the existence of God and other things. For as I have already shown, a thing ought to exist in virtue of it being very good if that thing existed, and this is no guarantee that it is possible for the thing to exist.
This argument is part of Carl Kordig's ontological argument. See Carl Kordig, "A Deontic Argument for God's Existence," Nous, Vol. 15 (1981): 207-208.
 One could argue that the A-premises (or at least some of them) are more intuitively plausible, and thus stronger, because they involve objects or states of affairs that are simpler than God. However, it is common among theologians and philosophers to maintain that God is a simple object; so it may not be the case that God is more complex than the objects or states of affairs that the A-premises assert to be possible. Though the claim that God is simple seems absurd, considerations of simplicity are themselves complex and turbid; so I will ignore them in the present context.
 Of course, the reverse also holds: since the soundness of the modal ontological argument is as plausible as the soundness of any modal argument for atheism, and the soundness of the latter implies the unsoundness of the former, the soundness of the modal ontological argument is as plausible as its unsoundness. Thus any modal argument for atheism taken alone undermines the modal ontological argument. Colloquially, the arguments "cancel each other out." This is an important result for the philosophical defense of atheism since it shows that the modal ontological argument does not provide rational justification for theism.
 The probability estimates for DA and P when the former has only 5 disjuncts and each disjunct has a probability of .14 are calculated as follows. Since DA and P are mutually exclusive, the probability of P is equivalent to the probability of DA's falsity, which in turn is equivalent to the probability of the conjunction of the negations of the A-premises. That is, the probability of P is equivalent to the probability of the following proposition:
(CA) Not-A1 and Not-A2 and Not-A3 and Not-A4 and Not-A5.
But since the probability of each A-premise is assumed to be .14, the probability of each negation of an A-premise is .86. So the probability of CA, and hence P, is given by (.86)5, which is approximately .47. The probability of DA is then 1 - P, which is approximately .53.
 I would like to thank an anonymous reviewer for pointing out this possible objection.
 See my "Questions of Existence and the Modal Cosmological Argument" on the Secular Web.
 Alvin Plantinga, The Nature of Necessity (New York, NY: Oxford University Press, 1974), p. 214.
 The Nature of Necessity, p. 214.
 Beings seem similar to cars: those that could have less than maximal value could be better and thus are not perfect. In other words, a car is not perfect if it could fall short of maximal car value; and a being is not perfect if it could fall short of maximal being value.
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