Questions of Existence and the Modal Cosmological Argument (2011)
The cosmological argument is a very popular argument for the existence of God among both philosophers and laypersons. From St. Thomas Aquinas to William Lane Craig, theistic philosophers have utilized some version of it to defend belief in God, and the average believer on the street will often unknowingly appeal to similar kinds of justification. In fact, I used to believe in God based solely on the idea that God explains where everything came from. The explanatory role that God can fill is probably one of the most attractive features of theism, for it provides an anthropomorphic, easily understandable explanation for anything that seems to need one. For instance, consider the questions, "Why is there something rather than nothing?" and "Why is there this something instead of some other something?" Human beings have asked these so-called "questions of existence" for centuries, and it is not unusual for believers to assert that God is needed to answer them.
The idea that God is necessary to answer the questions of existence is the foundation of a modal version of the cosmological argument. Like other cosmological arguments, it begins with an existential fact and ends with God as the explanation of that fact. But what distinguishes the modal version from other such arguments is that this existential fact involves the existence of something that could have been nonexistent or replaced by a different something. The fact that this something does exist instead of nothing or another something cries out for an explanation, and God, the argument contends, is this explanation. This essay critically evaluates this argument, concluding that it does not constitute rational justification for belief in God.
II. A Formulation of the Modal Cosmological Argument
A modal cosmological argument (MCA) motivated by questions of existence might run as follows:
(P1) Contingent beings exist.
(P2) All beings that exist have an explanation for their existence.
(P3) There is an explanation for the existence of contingent beings (from P1 & P2).
(P4) Contingent beings are either explained by themselves or by some other
(P5) Contingent beings are not explained by themselves.
(P6) Contingent beings are explained by some other
(P7) The other being(s) that explain(s) the existence of contingent beings must be either contingent or necessary (from P6).
(P8) The other being(s) that explain(s) the existence of contingent beings cannot also be contingent because more contingency by itself will result in something existing inexplicably, which conflicts with P2.
(P9) There must exist at least one necessary being the explains the existence of contingent beings (from P7 & P8).
(C) God is the one necessary being that explains the existence of contingent beings (from P9).
The "contingent beings" cited are logically contingent in that they are capable of either existing or not existing. (In the language of possible worlds semantics, they are beings that exist in some possible worlds, but not in others.) This is not the same as being ontologically contingent, where an entity was caused to exist by something else, or otherwise depends on something else for its existence. While logically contingent beings can also be ontologically contingent, they need not be: entities that could have been nonexistent might exist without being dependent on or caused by something else. (In other words, even if something exists in some possible worlds and not in others, it still could exist independently of anything else.) Thus, among logically contingent beings we need to distinguish between those that are also ontologically contingent, and those that are ontologically noncontingent in virtue of existing independently of anything else. This distinction is very important for evaluating the MCA; for if ontologically contingent beings alone required an explanation, that explanation could be found in an ontologically noncontingent being that is nonetheless logically contingent—e.g., a big bang singularity, a quantum mechanical vacuum, or some other naturalistic grounding. And then one would not need to postulate the existence of at least one necessary being or anything supernatural. This is, of course, contrary to some theists' goal of providing rational justification for belief in God, so the argument requires that all contingency—even that of ontologically noncontingent beings that are logically contingent—have an explanation for its existence.
This brings us to "necessary beings." While contingent beings are capable of existing or not existing, necessary beings must exist because their nonexistence leads to a contradiction, and thus is impossible. In the semantics of possible worlds, a contingent being exists in some possible worlds but not in others, while a necessary being exists in all possible worlds. Promising candidates for necessary beings are abstract objects—e.g., propositions and numbers. Let's consider propositions. Assume that "There are no propositions" is true in some possible world P. If this proposition is true in world P, then it is also true in world P that "There is a true proposition." But if in world P it is true that there is a true proposition, then it is true in P that "There is a proposition," which contradicts the original proposition that denies the existence of propositions in world P. Because the supposition that there are no propositions is self-contradictory, the nonexistence of propositions is impossible—so there must be propositions. Consequently, propositions are self-explanatory; they do not need an external explanation for their existence.
Now that key terms have been clarified, let's discuss the premises of the argument. P1 is the existential fact that contingent beings exist. Just about everything we confront in daily life is a contingent being—houses, cars, books, computers, food, friends, ourselves—even the universe itself.
P2 is a weak version of the "Principle of Sufficient Reason" (PSR). It reflects the demand for an answer to the questions of existence because asking why something exists instead of nothing or something else is tantamount to demanding an explanation (or "sufficient reason") for the existence of anything that happens to exist. P2 is a weak version of this principle because it allows there to be brute facts or states of affairs, but rules out the possibility of beings that exist inexplicably. This distinction is important because a strong version of the PSR requires a sufficient reason for everything, including why certain facts are true or why certain states of affairs obtain. But that would negate all contingency, compromising the contingent nature of God's free choice to create the collection of contingent beings that he supposedly did. For even if God's free choice to create a collection of beings out of love provided an intelligible, complete explanation of why there is something rather than nothing, we would still be left with the unanswered question, "Why did God freely create this collection over some other collection?" A freely willed choice between different possibilities would require some contingent, brute fact or state of affairs pertaining to God's free choice of creating this particular collection of contingent beings. Consequently, the MCA reviewed here employs the tailor-made, weaker version of the PSR.
P3 is the entailment of P1 and P2: if there are contingent beings and all existent beings must have an explanation for their existence, then it follows that these contingent beings must have an explanation for their existence. P4 follows from P3: since contingent beings have an explanation for their existence, it must be the case that this explanation lies in themselves or in some other being(s)—there are no other options. P5 is a necessary truth because contingent beings are, by definition, not necessary; yet necessary beings are the only ones capable of explaining their own existence. P6 is the entailment of P4 and P5: if contingent beings are explained by themselves or by some other being(s), and they cannot be explained by themselves, then they must be explained by some other being(s). P7 follows from P6: given that contingent beings are explained by some other being(s), the other being(s) must be contingent or necessary—there are no other options.
P8 is the denial that the required explanation can be found in more contingency, and is based on the inability of more contingency to answer the questions of existence (or satisfy the PSR's explanatory demand). For even if we tried to explain the existence of contingent beings that we are well-acquainted with by making them members of (a) some finitely regressing collection of naturalistic, contingent beings with some eternally existing starting point that explains the others in the collection, or (b) an infinitely regressing collection of naturalistic, contingent beings in which each one is explained by one or many previous such beings, we can still ask the questions, "Why does this contingent starting point exist instead of nothing or a different starting point?" or "Why does this collection of contingent beings exist instead of nothing or some other collection?" However, neither a contingent starting point nor an infinite collection of contingent beings can explain their own existence in virtue of not being necessary, so in either case the question would be left unanswered and there would be something that exists inexplicably, contrary to the PSR.
P9 then follows from P7 and P8: because the other being(s) that explain(s) the existence of contingent beings must be either contingent or necessary, and the other being(s) cannot also be contingent, there must be at least one necessary being that explains the existence of contingent beings. And since necessary beings explain their own existence, the one(s) that explain(s) the existence of contingent beings provide(s) a complete or ultimate explanation of existence, which amounts to answering the questions of existence and satisfying the PSR's explanatory demand. Finally, because there must be at least one necessary being, some theists conclude that there is only one such being and that this being is God.
III. Evaluation of the Argument
A. The Gap Problem
Like all versions of the cosmological argument, the MCA suffers from what Richard Gale calls "the gap problem"—the logical gap between the premises and conclusion that renders the argument invalid. Specifically, even if the MCA's premises are true and so there must be at least one necessary being that explains the existence of contingent beings, there could be more than one necessary being or only one necessary being that is not the God of traditional theism that does this explaining (the one necessary being need not be all-knowing, all-powerful, or morally perfect). Indeed, the MCA's premises are compatible with deism, dystheism, polytheism, or any other kind of supernaturalism, so long as the deities or powers invoked are necessary beings that can account for the existence of contingent beings. Therefore, the conclusion that God is the one necessary being that explains contingency is an arbitrary non sequitur.
While this alone is sufficient to demonstrate that the argument fails as a proof of God's existence, could it nevertheless be rationally acceptable and thereby constitute rational justification for theism? For example, one might argue that although the MCA does not conclusively demonstrate the existence of God, it shows that there must be at least one necessary being to provide an ultimate explanation of existence, or at least that it is reasonable to believe this. Furthermore, the argument goes, atheism cannot provide this ultimate explanation of existence because any naturalistic
We could offer two counterarguments in response to this argument. First, we might argue that even if (a) the MCA demonstrates the existence of at least one necessary being or makes belief in one reasonable and (b) it is rational to postulate only one necessary being, the MCA is not rationally acceptable because God is but one option out of a giant pool of possible supernatural beings, any one of which could be the required necessary being. Put another way, because there are many supernatural beings (perhaps even an infinite number of them) that could be the necessary being in question, there is no reason to think that any particular candidate (like God) is this being rather than any other. Therefore, the MCA is not rationally acceptable. Second, we might argue that it is possible for atheism to provide an ultimate explanation of existence because the initial state or
For the sake of argument, let's reject the last counterargument and assume that atheism probably cannot provide an ultimate explanation for existence. Let's also consider two arguments for rejecting the first counterargument. The stronger of the two argues that even though there may be several possible supernatural beings that could be the necessary being we need, the MCA is nonetheless rationally acceptable because among those possible beings, God is the best candidate for the job. (I do not know what could plausibly support this claim, but let's ignore that issue.) The weaker of the two argues that even though there may be several possible supernatural beings that could equally be the necessary being we need, God is at least a good candidate for the job, and that makes the MCA rationally acceptable. Assuming that we can no longer rely on either counterargument from the previous paragraph, have we finally arrived at a rationally acceptable MCA? I think not.
First of all, notice that both responses to the first counterargument rely on the idea that God is a good candidate for the requisite necessary being. (This is of course implied by him being the best candidate.) This makes sense since the MCA could hardly be rationally acceptable if God was a poor candidate for the necessary being. What's more, the entire back-and-forth exchange assumes that the MCA demonstrates that there must be at least one necessary being to explain contingent beings, or at least makes it reasonable to believe this. This has been accepted by both sides of the debate and is crucial for the MCA's rational acceptability. Thus, the MCA can be rationally acceptable only if (1) it really does demonstrate or make it reasonable to believe that there must be at least one necessary being to explain contingent beings and (2) God really is a good candidate for this necessary being. In the remainder of this section, I will argue that neither option seems to be true, and thus the MCA is not rationally acceptable.
B. Running for Office
Is God a good candidate for the requisite necessary being? Before we can answer this question, we have to ask another: Do we have good reason to think of God as a necessary being in the first place? Simply stipulating that God is a necessary being begs the question. Moreover, God appears to be logically contingent because we can conceive of him existing in some possible worlds but not in others. (In other words, God appears to be capable of either existing or not existing.) The idea that God must exist in all possible worlds or none at all seems to be an unwarranted stipulation invented by some philosophers.
Of course, the prima facie presumption that God is a logically contingent being is subject to rational defeat. But then the onus is on the theist to show why God is really a necessary being. And what could someone say that would warrant this claim? One might defend an ontological argument that attempts to demonstrate that God does in fact necessarily exist, but this would (a) render the MCA moot and (b) require a defense that would be much more difficult to establish than the MCA. For the MCA, the theist only needs to show that necessary existence is essential to the conception of God in order for God to be a candidate for the requisite necessary being. In other words, the theist has to argue that, conceptually, God must exist necessarily if he exists at all, not that that God in fact necessarily exists.
One possibility for thinking that necessary existence must be included in the conception of God is that God must exist independently of everything else. But this is ontological non-contingency, which is compatible with logical contingency. For even if God's existence could not depend on anything else, he still could exist in some possible worlds but not in others. It would simply be the case that in the possible worlds in which he does exist, he exists independently of all else. But it does not follow that God must exist in every possible world if he exists in any possible world; and that is what we would need to establish God as a necessary being. Thus, ontological noncontingency does not justify the inclusion of necessary existence in the concept of God.
Another possibility open to the theist is the Cartesian idea that existence is a perfection. If existence increases a thing's perfection, perhaps necessary existence increases its perfection even more because a necessary being has a more secure claim to existence than a contingent one. Moreover, since God is perfect by definition, then he must have every perfection; and if necessary existence is a perfection, then God must be a necessary being. However, the idea that existence increases the perfection of something is both odd and arguably false. For instance, consider the concept of a "perfect life partner." You might conceive of this person as a partner who (a) you never fight with, become frustrated with, or turned off by; (b) always cares for you, supports you completely and appropriately (e.g., never reacts inappropriately or poorly to your needs), and otherwise provides adequate assistance for you; (c) spends the exact amount of time with you as you wish, engages with you in as much pleasurable activity as you wish, and always enjoys spending this time with you; and (d) wants to be your life partner and loves you for who you are. Now whether or not this person exists seems utterly irrelevant to our conception of what makes a perfect life partner; if a fictional character in a story happened to share these traits with a real person, we would not say that the latter is more perfect than the former. Instead, we would say that both are equally perfect life partners, though one is nonexistent and the other is not. Of course, we might say that the actual existence of this perfect life partner is better for you and even makes the world itself better, but this would not alter the equal perfection of the fictional character and the real person.
Furthermore, we can contest the idea that necessary existence increases the perfection of something even more than plain existence does in the same way that we contested the Cartesian premise on which it rests. Suppose that a necessarily existing life partner has a stronger claim to existence than a contingently existing one; even so, a necessarily existing life partner is not a better life partner than a contingently existing one. Instead, the modal status of existence seems utterly irrelevant to the perfection of these life partners; both are equally perfect, but one exists even though it could have been nonexistent, while the other exists and could not have been nonexistent. Since this amplified Cartesian idea is probably false, it does not justify the inclusion of necessary existence in the concept of God.
On the face of it, then, God is not a necessary being, and so cannot be a good candidate for the necessary being in question. Therefore, the MCA is not rationally acceptable.
But suppose I am mistaken and God should be conceived of as a necessary being. Even then there is an excellent, seemingly decisive reason to reject him as a good candidate for the necessary being needed to explain contingency. It begins with the logical incompatibility of God and gratuitous evil, which is evil that God does not have a morally sufficient reason to permit or create. The logical incompatibility of God and this kind of evil follows from God's moral perfection: it is simply part of what it means to be morally perfect that God would not permit or create evil without having a morally sufficient reason to do so. And since gratuitous evil is precisely the kind of evil which God does not have a morally sufficient reason to permit or create, he will not permit or create it. Thus, there will be no gratuitous evil if God exists; that is, God's existence entails the nonexistence of gratuitous evil. But conjoining this necessary truth with the claim that God is the necessary being that explains contingency (which would make him exist in all possible worlds) entails the falsity of the following proposition:
(G) There is a possible world in which gratuitous evil exists.
In other words, if God is the necessary being in question, then it is not even possible for there to be gratuitous evil. But this is a wildly implausible result. First of all, the concept of gratuitous evil seems perfectly coherent, and this suggests that it is at least possible. Moreover, we can easily conceive of gratuitous evil—it is not the least bit difficult to think of a horrific evil and then imagine that there is no morally sufficient reason for God to permit or create it. In fact, even theists who deny the existence of gratuitous evil typically agree that there at least appears to be gratuitous evil, which suggests that the actual world could very well be the possible world of G. So even if God is properly conceptualized as a necessary being, he is a poor candidate for the necessary being needed to explain contingency because "electing" him to that "office" would have the absurd consequence that gratuitous evil is impossible. Therefore, the MCA is still not rationally acceptable.
C. The Demonstration of or Reasonable Belief in a Necessary Being
Despite the arguments of the previous section, some theists may insist that God is both a necessary being and a good candidate for the one needed to explain existence. Suppose we grant this for the sake of argument. Even so, the MCA is rationally acceptable only if it demonstrates or at least makes it reasonable to believe that there is a necessary being that explains existence. Has this been accomplished? A necessary but controversial part of the MCA is the PSR that constitutes its second premise, so the MCA can rationally justify theism only if the PSR is true or at least rationally acceptable.
First of all, it is doubtful that the PSR is true or even probably true. It is certainly not a necessary truth: it is neither conceptually true nor true by definition, its negation does not imply a contradiction, and there is no problem imagining a world where it is false (where beings exist brutely or without explanation). Nor is it an empirical fact; we simply have not empirically discovered the explanations or sufficient reasons for contingent beings. This is not at all surprising, for empirical investigation might be incapable of satisfying the PSR's requirements even in principle if, for example, every empirical discovery leads only to further questions. At best, the PSR is simply an assumption underlying and motivating these very same empirical investigations.
On the other hand, one might argue inductively that the PSR is probably true given our numerous and growing successes in explaining contingent beings, but there are at least a few reasons to doubt this. First, all of our successes in explaining contingent beings have been found in more contingent beings, not in anything necessary. Since the PSR requires at least one necessary being that explains contingent beings, which is not at all suggested by our numerous and growing successes in explaining contingent beings with more contingent beings, our explanatory success does not support the PSR.
Moreover, our numerous and growing successes in explaining contingent beings are at least as likely to occur on the assumption that these contingent beings belong to either
- some finitely regressing collection of contingent beings with an inexplicably existing, contingent starting point that explains the other contingent beings in the collection
- an infinitely regressing collection of contingent beings in which the existence of each individual contingent being is explained by one or many previous such beings even though the collection itself exists inexplicably
as compared to
- some finite or infinite collection of contingent beings that is explained by at least one necessary being.
Put another way, our numerous and growing successes in explaining contingent beings are at least as compatible with the first two scenarios, where the PSR is false, as with the final scenario, where the PSR is true. So, once again, the PSR is not supported by our numerous and growing successes in explaining contingent beings.
Given the considerations above, at best one might conclude that the PSR is more reasonable than its negation—i.e., that it is rational to accept. I think that most of us can agree that the PSR is both enticing and prima facie reasonable. After all, we expect things to have an explanation. Isn't it counterintuitive to think that something could just exist without any explanation? Doesn't it make sense to ask why things are this way instead of some other way? Philosophers and laypersons ask questions of this sort every day, and make this explanatory demand of anything they might be curious about. Because this does not initially strike us as absurd, the PSR seems reasonable. But it is only prima facie reasonable; it is subject to rational defeat. In the next three paragraphs I will provide reasons not to accept the PSR.
First, consider our psychological nature. We are by nature curious, inquisitive creatures that want a comprehensive understanding of the world—we want to completely "make sense" of it. We not only want to know why things are the way that they are, but we assume that there must always be an answer to these questions—that the world is rational through and through. But why should we assume this? Why should we think that the world conforms to our expectations? There are innumerable examples where the world does not conform to our desires or to our expectations of what "makes sense." So why should we think that it must be completely explainable? Merely having that epistemic demand does not make it reasonable, and the fact that the world disappoints us in so many other ways gives us reason to think it is actually unreasonable. Perhaps it is more reasonable to see the PSR as an unjustified assumption imposed on the world by creatures that desire or expect to make perfect sense of the world by explaining it completely. Perhaps it is not contingent beings that cry out for complete explanation, but human beings that "cry out" for one.
Second, according to the PSR there must be an explanation for why contingent beings exist, even if they are finitely regressing with an eternally existing starting point, or if they form an infinite regress. But then there can be no logically contingent yet ontologically noncontingent beings; instead, all contingent beings must be ontologically contingent because they depend upon a necessary being for their existence. However, contingent beings that are logically contingent yet ontologically noncontingent are possible—in fact, God himself seems to be one! There could easily be some ontologically noncontingent beings among our world's logically contingent beings. This is another strike against the rational acceptability of the PSR.
Third, there is empirical evidence of virtual particles that begin to exist in a quantum mechanical vacuum without a sufficient reason for their existence. These particles have a probabilistic cause instead of a determining one. This suggests that the PSR is actually false.
Moreover, there are independent reasons to doubt the existence of a concrete necessary being, and these provide additional reasons to reject the MCA. Earlier I mentioned abstract necessary beings like propositions and numbers, but these things are not capable of explaining the existence of contingent beings (or anything concrete for that matter). Instead, we need a concrete necessary being to do the explaining. But the existence of such a being conflicts with the following propositions:
(N) There is a possible world in which no concrete beings exist.
(O) There is a possible world in which the only concrete beings that exist are contingent.
These premises are certainly prima facie plausible given on our modal intuitions: we can easily conceive of a possible world composed entirely of empty space and abstract necessary beings, and we have no difficulty imagining a world like that where some concrete contingent beings are thrown into the mix. Furthermore, unlike abstract beings whose nonexistence is impossible because it entails a contradiction, the nonexistence of any concrete being survives critical reflection and seems to remain a genuine possibility. This suggests that there are probably no concrete necessary beings. Of course, ontological arguments for God's existence could defeat this, but they have been refuted elsewhere and so do not defeat our reasonable doubt about the existence of a concrete necessary being. Consequently, the PSR and the existence of a concrete necessary being should not be accepted, and thus the MCA is not rationally acceptable.
IV. Atheism, Theism, and the Questions of Existence
Now I would like to return to the "questions of existence" that motivate the MCA and discuss them in light of the arguments that I have given. Recall that these questions are:
(E1) Why does something exist instead of nothing?
(E2) Why does this something exist instead of some other something?
Because it feels quite natural to ask these questions, and does not initially strike us as absurd to do so, we consider it reasonable to assume that they have an answer (which is presupposed by asking the questions). However, to assume that these questions have an answer is tantamount to assuming the truth or rational acceptability of the PSR along with the need for a necessary being to fulfill the PSR's explanatory demand. But I have provided multiple reasons not to accept both the PSR and the existence of a concrete necessary being. Thus, it does not seem reasonable to think that these questions have an answer. Instead, it is more reasonable to think that either: (a) we can explain the majority of contingent beings via some eternally existing, logically contingent yet ontologically noncontingent
But how can the beings of either option be inexplicable in principle if they are logically contingent? For the first option, one reason is ontological noncontingency: if a
Moreover, it would not be a logical role such that the necessary being entails the existence of the ontologically noncontingent, or of the infinite collection of ontological contingents, for this would negate the logical contingency of the beings in both options: if the explanatory being exists necessarily, and the existence of the other necessarily follows from this, then what follows would also be necessary. But then we would no longer be talking about contingent beings, but about (extrinsically) necessary beings that are nonetheless dependent on and explained by the existence of the original (intrinsically) necessary being. What's more, this dependence on the original necessary being would negate the ontological independence of the ontologically noncontingent
Finally, I want to briefly return to the respective abilities of theism and atheism to answer the questions of existence. As already noted, it is not unusual for believers to assert that God is necessary to answer these questions. However, if God is a logically contingent being (as I have argued), then this assertion is false because God cannot answer these questions. For even if we assume that God exists and created all other contingency, he is something that is capable of either existing or not existing, and thus we can ask: "Why does God exist instead of nothing or something else?" But this cannot be unanswered. First, God is a logically contingent being, not a necessary being that explains his own existence. Second, his existence cannot be explained by some other
I have examined a version of the modal cosmological argument motivated by the questions of existence. After formulating and discussing the argument, I have shown that it is invalid and thus does not demonstrate God's existence. I have also argued that the argument is not rationally acceptable because (1) it relies on the PSR, which is highly dubious and probably false, (2) it relies on the unlikely existence of at least one concrete necessary being to explain contingent existence, and (3) it requires the unwarranted assumption that God would be a good candidate for the necessary being posited for this explanatory role. Finally, I have argued that the questions of existence motivating the modal cosmological argument do not have an answer, and that theism cannot answer them any more than atheism can. So theism provides no greater explanatory power than atheism here. If believers want to find rational justification for theism, they must find it elsewhere.
 Here we can distinguish intrinsically necessary beings from extrinsically necessary ones. The former must exist all by themselves (and so are self-explanatory), while the latter must exist because they are entailed by (and so explained by) at least one intrinsically necessary being. Since some philosophers conceive of God as an intrinsically necessary being, this is the kind of necessary being that will take center stage in this paper. Moreover, I am unaware of any promising candidates for an extrinsically necessary being; I refer to them generically and only as conceivable things.
 See Paul Herrick's "Job Opening: Creator of the Universe—A Reply to Keith Parsons" (2009) on the Secular Web. It seems absurd to me to think that this terrible world could be a creation of love, but that is a separate discussion.
 "Why does this something exist instead of some other something?" might be answered by "Because God freely created this collection out of love." So God's free creation does have the potential to answer the questions of existence despite the unanswered question about why God chose one thing over another.
 Even weaker versions of the PSR can be used in a modal cosmological argument. For example, the premise that there is an explanation for the existence of contingent beings (P3 of this paper's argument) could be the PSR used for a modal cosmological argument. In fact, P3 could essentially replace P2 of the argument in this paper. However, P2 is preferable to P3 because P2 promises answers to the questions of existence, while P3 allows there to be brute or unexplained existence through noncontingent things. Because P3 does not claim that every existing thing has an explanation for its existence, it is slightly weaker than P2. But nothing is gained by adopting this version of the argument; my later criticisms of P2 could just as well apply to P3. An even weaker version of the PSR says that everything that can have an explanation for its existence does in fact have an explanation for its existence. Much like P3, this version of the PSR does not promise answers to the questions of existence—it allows for there to be brute or unexplained existence via things that cannot have an explanation for their existence. Thus, P2 is also preferable to this version because it promises answers to these questions. Also, adopting this version of the PSR does not seem to provide any benefit. Though weaker than other versions of the PSR, to be used in a modal cosmological argument that invokes God as the one necessary being that explains contingency, it would need to be conjoined with something like "all contingent beings can have an explanation for their existence" in order to derive P3. And P3 is needed in turn to derive the existence of a necessary being that explains contingency. Thus, if my criticisms of P2 can be applied to P3, then they can also be applied to a modal cosmological argument using this third version of the PSR.
 This entailment assumes the truth of the intuitive, age-old metaphysical principle "Out of nothing, nothing comes." I suppose that this assumption could be challenged on scientific grounds, but I am not sure that scientific accounts actually posit an absolute or true nothingness from which everything came. Since I am no expert in physical cosmology, for the sake of argument I will take it to be true and the inference from P3 to P4 to be valid. (An MCA proponent might also deflate the problem by treating nothingness itself as a being—e.g., by arguing that P4 does not follow from P3 because nothingness might be "another being" that explains the existence of contingent beings.)
 These two attempts to explain the existence of contingent beings with other contingent beings can be invoked as responses to other cosmological arguments—in particular, those that posit God as the cause or explanation of the universe beginning to exist, or as the first cause of the chain of effects that we observe. Specifically, we can either (a) explain the universe or the first cause of the chain of observed effects in terms of some naturalistic, eternally existing contingent being or beings, or (b) we can reject the need for a single cause or explanation by positing an infinite regression of naturalistic, contingent beings, where each being is caused or explained by one or more previous ones. A very important aspect of the MCA is that by explicitly denying that these tactics will work for the MCA, the MCA comes across as a stronger cosmological argument with a better chance of succeeding.
 Richard Gale, "The Failure of Classical Theistic Arguments" in The Cambridge Companion to Atheism ed. Michael Martin (New York, NY: Cambridge University Press, 2007), p. 95.
 For example, Spinoza believed that nature itself necessarily exists, and that everything that happens does so necessarily. This guarantees an explanation for everything that exists without postulating a supernatural being. Of course, Spinoza identified nature with God, but his use of "God" was simply to denote nature itself, not the supernatural being of traditional theism.
 Rene Descartes, Meditations on First Philosophy, 3rd edition trans. Donald Cress (Indianapolis, IA: Hackett Publishing Company, 1993), p. 45.
 It is important to note that this is a logical incompatibility between God and a certain kind of evil, not an incompatibility between God and evil per se.
 As noted in endnote 5, the MCA could employ even weaker versions of the PSR than that constituted by P2, which is "the PSR" that I am referring to here. Because of this, one may worry that my criticism of "the PSR" only applies to P2, not to the weaker versions. However, this is at least not the case with P3—a slightly weaker version of the PSR that is nonetheless subject to all of my criticisms of P2. On the other hand, things are a bit more complicated with the weakest version of the PSR (everything that can have an explanation for its existence does have such an explanation), so perhaps not all of my criticisms of "the PSR" could be leveled against it. But this should not worry us here because, as noted in endnote 5, a modal cosmological argument premised on the weakest version of the PSR would need to be conjoined with an additional premise in order to derive P3, which in turn is needed to reach God as the necessary being that explains contingency. Thus, even if some of my criticisms of "the PSR" do not apply to the weakest PSR, they will still apply to any modal cosmological argument that uses it.
 Richard Gale, "The Failure of Classical Theistic Arguments," p. 96.
 Quentin Smith, "A Defense of a Principle of Sufficient Reason."
 Michael Martin, Atheism: A Philosophical Justification (Philadelphia, PA: Temple University Press, 1990), Chapter 3; Nicholas Everitt, The Non-Existence of God (New York, NY: Routledge, 2004), Chapter 3; Richard Gale, "The Failure of Classical Theistic Arguments," pp. 86-89.
 The first contingent being (or beings) need not exist eternally; perhaps it (or they) came into existence from nothing at all. Again, this view might be scientifically justifiable, but I am in no position to judge it, so I will presume that a starting point of true nothingness is not plausible.
 This option does not allow God to freely choose what he creates and so would not work for traditional theists. If God is this necessary being and his existence logically entails that of the other beings, then the existence of the other beings necessarily follows from God's existence, not from his free choice to actualize them. In other words, God cannot freely choose to create things that, like him, necessarily exist.
 I would like to thank an anonymous reviewer for helpful comments on this paper.
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