One might be tempted to say that atheism is the belief—or at least includes the belief—that there exist no gods. This is not a good characterization of atheism. The initial problems is that there is no firm set of essential properties for gods (lower case ‘g’). A god might lack all of the interesting properties of Gods: a god might be very powerful, but not omnipotent, very knowledgeable, but not omniscient, and so on. Or, a god might not be very knowledgeable at all, but exemplify other skills and powers we simply haven’t imagined. It is another possibility that gods might exist as Parson’s ‘non-existent’ objects exist.  And yet another possibility is that gods might exist non-concretely—as neither a concrete nor an abstract object—in the way that Williamson, Linsky, and Zalta describe.  Or, of course, there might be pantheistic or panentheistic gods. Atheists need not be committed to denying the existence of such gods, and arguments for atheism generally have no implications for the existence of such gods.
So, we might think that atheism is better characterized as the belief that God does not exist where ‘God’ is understood to include (at least) the best possible being. We know that the best possible being exists in some possible world or other. Even if he is tied for best, something, somewhere is best. But the atheist might remind us that existing in a possible world does not entail existing simpliciter. A highjumper who has cleared 9’2” exists in some possible world, but that highjumper does not exist simpliciter. So existing in a possible world does not entail existing.
Or does it? Perhaps the most important 20th century metaphysician was both an atheist and a polytheist.
So it looks like atheists may not be committed to believing that the best possible being does not exist simpliciter. Atheists might believe that the best possible being exists, but happens not to exist in our particular region of metaphysical space. On the ontology supporting such a view all possible worlds exist (not just ours), and all worlds include concrete beings, but not all worlds include the best possible being. The atheist believes that our particular world does not.
Arguments for Atheism
So then what are the best arguments for atheism? What sorts of arguments would lead one find atheism plausible? Maybe we should talk first about the evidence against miracles. The most famous argument against the rationality of belief in miracles is Hume’s argument in Of Miracles, Section X, An Enquiry Concerning Human Understanding. Despite the impressive provenance of the argument, Hume’s argument is plainly question-begging. Hume’s successors—Mill, Mackie, Flew, and Sobel—revive the argument against miracles and all of their arguments are also question-begging. Hume’s argument that “no human testimony can have such a force as to prove a miracle and make it the foundation of a system of religion” assumes the very conclusion that it aims to establish. The argument in Of Miracles is what John Earman called Hume’s abject failure. 
Perhaps we should look elsewhere. Is there anything about natural laws or scientific explanation that is inconsistent with the occurrence of miracles? In fact, there’s not a single scientific fact that is inconsistent with the occurrence of miracles since miracles do not contravene natural laws. Miracles do not contravene natural laws since we know apriori that nothing could contravene a natural law. A natural law is at least an exceptionless regularity. Miracles are not exceptions to exceptionless regularities, but no one who is thinking believes they are. The view that miracles require the ‘suspension’ of natural law is just confused about what constitutes a miracle.
We are in search of the best arguments for atheism. Is there an argument for atheism from religious disagreement or the problem of hell or the problem of religious ethics or evolution? Can’t we find some reasons for atheism in one or more of these areas? The simple answer is no, you can’t, since there isn’t any evidence against theism in any of these areas. Theism is the view that there exists a God of a certain personal sort—or better that there exists a God of a certain sort in our region of metaphysical space. We can lay it down flatly that objections to doctrinal views do not constitute evidence against theism. It’s just a mistake to conclude that you have reason to abandon theistic belief since you do not believe one or more religious doctrines. If you have a problem with a religious doctrine, that is one matter. Take it up with the theologians. If you have a problem with the existence of a theistic God, that is another matter entirely. Take it up with the philosophers.
But what about the Christian God and Christian theism? Does dispute over doctrine have implications for the existence of the Christian God or the viability of Christian theism? The answer is again, no. The Christian God is a theistic God. You can believe that the Christian God exists and deny that most or all of the extant doctrines accurately characterize Christian theism. And there is absolutely nothing new in doing so. Every form of Christian theism rejects reems of doctrine that other Christian theists endorse. But isn’t there some epistemological problem with all of this disagreement among Christian theists? Again, the obvious answer is no. Disagreement over theological and metaphysical issues is exactly what we should expect given the nature of the area. Lot’s of metaphysicians hold views on issues over which there is vast disagreement—the nature of time, space, properties, objects, composition, persistence, persons, etc.—but that does not make them anything less than rational.
Still in search of the best arguments for atheism. Is there an argument for atheism from naturalistic explanation? Suppose it is argued that for every supernatural explanation SE of an event e there is a competing and better naturalistic explanation NE. Assertions like this are pretty common and seem to provide some support for atheism. The problem is that the supposition is false. It is false that for every supernatural explanation for an event e there is a better naturalistic explanation for e. The fact is that no naturalistic explanation of any event is an ultimate explanation. So there are no naturalistic explanations that are complete explanations. Ultimate explanations terminate in an intrinsically necessary explanans—an explanans that exists as a matter of conceptual necessity. No natural objects, events, states of affairs—pace Spinoza—exist as a matter of conceptual necessity, so there are no ultimate NE’s. But then there is no event e that has a complete naturalistic explanation. But what about theistic explanation? Theism can provide an ultimate explanation for every event and can do so in a way that preserves contingency. Theists need only take as the object of God’s creation the totality of metaphysical space—all possible worlds and all possibilia—and the right sort of ultimate explanation is directly forthcoming.  Naturalistic explanation is always incomplete. So it is just false that naturalistic explanation is in general better than theistic explanation.
Problems of Evil
At last we arrive at the many problems of evil. Surely the problems of evil present a serious argument for atheism. The problems of evil all maintain that there is some metaphysical or conceptual relationship between moral perfection and the prevention of gratuitous evil. But what exactly do they mean by ‘gratuitous evil’? Gratuitous evil is sometimes called pointless evil and it is generally understood to be an intrinsically evil state of affairs that is not necessary to any greater good. And there’s a immediate problem. It is very easy to show that, for every intrinsically evil state of affairs S, there is some greater good or other S’ such that S’ entails S. So, on this standard account of gratuitous evil, every intrinsically evil state of affairs, in every world, is non-gratuitous.  The problem of evil vanishes.
But suppose we gin up some account of gratuitous evil according to which gratuitous evil is at least possible. The relationship between moral perfection and gratuitous evil is typically formulated in the following way.
Necessarily, a morally perfect being prevents every gratuitously evil state of affairs that it can prevent.
This is more or less the standard view. We find versions of the standard view defended in philosophers as diverse as John Mackie, William Rowe, Keith Yandell, Stephen Wykstra and Alvin Plantinga. The standard view is that there’s something about gratuitous evil which makes it such that a perfect being must prevent as much of it as he can. But of course, as Mackie has observed, there are no non-logical limits to what an omnipotent being can do. It follows directly that God—the morally perfect God of St. Anselm—prevents every gratuitously evil state of affairs in every world in which God exists. Once we observe that God is a necessarily existing being—God exists in every possible world—we quickly derive from the standard position that God prevents all possible gratuitous evil.
God prevents every gratuitously evil state of affairs in every possible world.
But it is evident that not even an omnipotent being could eliminate every gratuitously evil state of affairs in every possible world. It cannot be done.  Since it is impossible that God prevent every gratuitously evil state of affairs in every possible world, the standard position is false. There is no metaphysical or conceptual relationship between moral perfection and gratuitous evil. Since the standard position is false, the existence of God is perfectly compatible with gratuitously evil states of affairs. The problem of evil presents no serious worries for theism.
Let’s consider, finally, the argument from divine hiddenness. Is this a convincing argument for atheism? There are numerous versions of the problem—or better, there are various problems going under the same name—but consider the objection that God’s existence simply isn’t obvious enough to finite creatures. This version of the hiddenness objection is of course flatly denied among no less a believer than St. Paul. We have St. Paul’s testimony in Romans 1:20.
In creation itself God’s existence and nature is obvious to us all, according to St. Paul, and so we have no excuse for failing to believe that God—the God of invisible power and deity—exists. There might be an epistemological failure in your lack evidence for God’s existence, according to St. Paul, but the failure is yours, not God’s. The argument from hiddenness makes the epistemological assumption that if the evidence for God’s existence really were obvious to all, then we would all be in possession of that evidence. But that’s false, according to St. Paul, since the evidence for God’s existence and nature is indeed obvious to all, but not everyone takes possession of it.
But even if you are not in possession of the evidence in nature for God’s existence and nature, you are in possession of—among countless other sources of evidence for God’s existence and nature—St. Paul’s testimonial evidence about God’s existence and nature. Is there nonetheless another problem of divine hiddenness? How about the following formulation: since God never acts to preclude the possibility of being in relationship with finite creatures, there cannot exist finite creatures who are seeking a relationship with God but never finding it. Setting aside whether this principle is in general true, is there really anyone who has sought a relationship with God and never found it? If ‘seeking a relationship’ means seeking a constant sense of consolation and reassurance, then I suspect the answer is yes. But it does evince a serious ignorance of the history of religious experience to expect that God would be the source of constant consolation and reassurance. St. John of the Cross, Teresa of Avila, and Mother Teresa—all experts in religious experience—have all warned us not to confuse God’s withholding consolation from the lives of finite creatures with God’s withholding himself from the lives finite creatures. God is always present, but divine consolation is not. The absence of God’s reassurance and consolation is not evidence that God does not exist, but it is evidence that we finite creatures probably do not have a firm grasp on the implications of God’s love and moral perfection. Divine love and moral perfection is consistent with the total absence of consolation in the religious experience of many of the great mystics. This is what these experts report. Concerns about the consistency of divine love and the absence of consolation or reassurance is likely a reflection on our limited grasp on the nature of divine love.
Atheological arguments do present occasions for working out some implications of theistic belief. We should be thankful we have them. But unsurprisingly there just isn’t a powerful argument for atheism, and the cumulative case for atheism isn’t much better. As far as I can see, these athelogical arguments would not move even a leaning theist—say, someone whose credence for theism is ballpark .6—to leaning atheist—someone whose credence for atheism is ballpark .6. Nevertheless theists should in fact take the occasions these arguments offer for clarifying the more interesting philosophical implications of their beliefs.
 Terence Parsons, ‘Are There Nonexistent Objects?’ American Philosophical Quarterly 19 (4): (1982) 365 – 371.
 See Bernard Linsky and Edward Zalta, ‘In Defense of the Simplest Quantified Modal Logic’, James Tomberlin (ed.), Philosophical Perspectives 8: Logic and Language, (Atascadero: Ridgeview Press, 1994) 431–458. See also Tim Williamson, ‘Necessary Existents’, In A. O’Hear (ed.), Royal Institute of Philosophy Supplement. (Cambridge University Press, 2002) 269-87.
 See David Lewis, Philosophical Papers I (Oxford: Oxford University Press, 1983) p. xi. It might be worth mentioning a discussion with Peter Forrest on the probability that a god actually exists given Lewis’s pluriverse. ℶ2 = P(P(ℕ)) = the cardinality of possible worlds. We found that, for Lewis, there is about a 1/e chance that there is no actual god. That is, given just the number of gods and the number of worlds, the chances are about 65% that one of those gods is actual. There is of course other evidence both for and against the existence of the Lewisian gods.
 See David Johnson, Hume, Holism, and Miracles (Ithaca: Cornel University Press, 1999) and John Earman, Hume’s Abject Failure: The Argument Against Miracles (Oxford: Oxford University Press, 2000).
 See ‘Theistic Modal Realism I: The Challenge of Theistic Actualism’, Philosophy Compass Vol. 12, (2017) 1 – 14 and ‘Theistic Modal Realism II: Theoretical Benefits’, Philosophy Compass Vol. 12 (2017) 1 – 17.
 Sometimes we find that gratuitous evil is understood as an intrinsically evil state of affairs that God could not have prevented without moral loss. And it’s urged—and sometimes argued—that this account differs from the standard account. It doesn’t. The argument from libertarian freedom offered to show the inequivalence is unsound. For arguments along similar lines see Klaas Kraay, ‘God and Gratuitous Evil (Part I)’ Philosophy Compass Volume 11, Issue 12 (2016) 773. See also Hasker, ‘The Necessity of Gratuitous Evil’, Faith and Philosophy, 9 (1992), 23–44
 For details on this argument see Michael J. Almeida, ‘Theistic Modal Realism?’ Oxford Studies in Philosophy of Religion, Volume III Jon Kvanvig (ed.) (Oxford: Oxford University Press, 2011) 1-15 and ‘Necessary Gratuitous Evil’ (manuscript).