There is an embarrassing paucity of a succinct presentation of good, serious arguments against the existence of God, or gods, online, as well as an equally embarrassing overabundance of theist rhetoric. This is an unfortunate state of affairs, so I have resolved to compile here a number of arguments that I deem convincing to some extent. Regarding the arguments that a reader will not find compiled here: some of them I must have found unconvincing; others must have, without a doubt, eluded my attention. The goal of these arguments is to present a cogent case against theism — they are not positive arguments for atheism. They are meant to be publicly and conveniently and freely accessible online. They are also meant to be intellectually accessible, and thus free of excessive philosophical or theological jargon, applicable to any theist religion or viewpoint, and also quick, which means that some subtleties may have to be sacrificed on the altar of rough-and-readiness.
It is important to establish concordance on the terms and conditions involved. By “theism”, I refer to the claim that there is a God (monotheism) or that there are gods (polytheism). I will take these entities to be supernatural in some way and to some extent: that is, these entities transcend the natural order of things, the natural phenomena which, in principle, we can observe and explain through established scientific methods. Most of the arguments that follow will concern more narrowly monotheism, and in particular the claim (common among Abrahamic religions) that there exists a being who possesses all perfection, such as: omnipresence, omnipotence, omniscience, omnibenevolence, absolute freedom, infinite intellect etc. By “atheism”, I refer simply to the rejection of theism. It is common to associate with these two terms the different term “agnosticism”. Agnosticism does not consist in a claim; it consists in the lack of a claim about God or gods: an agnostic refuses to make a claim about the existence of a God or gods, suspending belief. I will not be concerned with agnosticism, even though most of the arguments presented here constitute refutations of agnosticism as well, since they preclude the existence of a God or gods (while agnosticism leaves it open).
1. The Stone Paradox
This is perhaps the most well-known, since at least the medieval times. It targets a specific feature of God, namely his alleged omnipotence. In a sentence, the conclusion is that there cannot possibly be an omnipotent being.
a. Either God can make a stone so heavy that he cannot lift, or he cannot.
b. If God can make such a stone, then there is something that God cannot do: namely, lift the stone.
c. If God cannot make such a stone, then there is something that God cannot do: namely, make such a stone.
d. Therefore, either way, there is something that God cannot do.
e. If God exists, then God must be omnipotent.
f. If God is omnipotent, there is nothing that God cannot do.
g. From d., f., and e., it follows that God doesn’t exist.
2. The Impassibility Paradox
The impassibility paradox, discussed most frequently among Catholic circles, is similar to the stone paradox, in pointing out that there cannot be a being that has the attributes we would like to attach to God. Yet, rather than focusing on a single attribute, such as omnipotence, and showing that it is incoherent, this paradox shows that two attributes, which are coherent when considered in isolation, are inconsistent or incompatible with each other. Those attributes are the impassibility of God (specifically, his invulnerability to suffering) and his compassionateness.
a. God is impassible and compassionate.
b. Being compassionate is defined as being able to sympathize and exercising sympathy with fellow sentient beings. Sympathy is defined as experiencing the same, or similar, feelings as those experienced by sentient beings.
c. Being impassible is defined as being emotionally unaffected by the states or actions of other sentient beings. (That includes both feeling pain and feeling joy, though the former is more pertinent in this case.)
d. Human beings experience emotional suffering.
e. It follow from b. and d., that God must experience suffering too.
f. But — e. and c. are logically inconsistent, or incompatible.
g. Therefore, there is no being that is both impassible and compassionate.
3. The Problem of Evil
This argument shares with the aforementioned paradox a common premise, namely d. (see above). This premise is a matter of empirical fact that is hard to deny — it is plainly true that some people experience some suffering. Depending on how we are willing to quantify such suffering we can obtain more or less extreme versions of the problem of evil. I will present a moderate version below. The upshot of this argument is that the empirical fact cannot be squared with God’s alleged omnibenevolence.
a. Some human beings experience some suffering.
b. God is omnibenevolent.
c. Being omnibenevolent is defined as (at least) wanting to eliminate all suffering.
d. If God were also omnipotent and omniscience, then the omnibenevolent God would eliminate all suffering.
e. Premises a., c. and d. entail that God does not want to eliminate all suffering.
f. Therefore, God is not omnibenevolent.
To be sure, premise a. seems like a serious understatement. It appears that there is a lot of suffering and cruelty in the world. The theist cannot claim that the cruelty is unavoidable, because that would imply that God cannot avoid it, and so that God is not omnipotent. The theist can get out of this problem only by arguing that all the observed suffering is somehow morally necessary and justified — an extremely tall order, by any measure.
In a similar vein to the problem of evil, as Oppy (2018) notes we get arguments that are logically incompatible with empirical facts: e.g.: “if God existed, then God would have made a world in which everyone always freely chooses the good (Mackie 1955); or, God would have made God’s existence (more) obvious to all (Schellenberg 1993); or, God would have ensured that all human beings came to believe in God before they died (Drange 1998).”
4. The Omniscience Paradox
A lesser known, but no less damning, argument tackles the last of the big three attributes of God, his omniscience. The argument, as far as I know, first appears in Patrick Grim (1991). It entails that, logically speaking, we can show that there is a sentence that, no matter what, God doesn’t know it.
Consider the sentence “A” below:
A: God does not believe that “A” is true. (Yes, “A” is a self-referential sentence that says of itself that God doesn’t believe it’s true. Self-referential sentences might seem strange at first, but they actually do occur and can even be perfectly true, or false. Consider for example: “This sentence is written in English”, “This sentence has 1242415 characters”, “This sentence is the third example I am giving”, etc.)
Here is the argument:
a. Either A is true, or it isn’t.
b. If A is true, then God doesn’t believe it, and so of course doesn’t know it.
c. But since A is true by assumption, there is a sentence, A, such that God doesn’t know it.
d. If A is false, then it is false that God doesn’t believe that “A” is true. So, God believes that “A” is true.
e. But since A is false by assumption, there is a sentence, A, which is false, but God doesn’t know that is is false (since God believes it to be true).
(Equivalently: there is a sentence, B, that says of A that it’s false: B: “A is false”. By assumption, B is true and God doesn’t know B.)
f. Either way, there is a sentence that God doesn’t know, and so he’s not omniscient.
5. Reverse Ontological Argument, I
Both this and the next argument attempt to reverse a type of argument that is commonly given in favor of theism with a venerable history, known as ontological arguments. Unlike those arguments themselves, their reversed, atheistic counterparts are not well-known, but they are actually equally if not more powerful. I will start with a more accessible version. This, as well as the next, argument depend on the assumption — granted by the atheist for the sake of argument — that God is the greatest conceivable being. This means that, for any property or attribute, if it is better to have it than not have it, then God has that property or attribute. For example, being omnipotent seems better than not being omnipotent — obviously! — so God must be omnipotent. But now consider the following:
a. God is a greatest conceivable being.
b. For any property P, if having P is better than not having P, then God has P.
c. Non-existence is better than existence.
d. Therefore, God has non-existence.
To be clear, by “better” we mean “better for the entity in question”. Surely, the existence of my pen may be good for me, but the question is rather: is the existence of the pen better than the non-existence of that pen for the pen itself? Premise c. assume a negative answer.
The theist cannot reply by saying that existence (and non-existence) is not a property, since the original ontological arguments explicitly require that we assume that existence (and non-existence) is a property.
There is a solid and oft-cited case that non-existence is indeed better, at least in the case of human beings. Similar reasons, such as wear and teat, eventual destruction, can be mentioned in the case of inanimate objects. Why should it not be the case for God then?
Perhaps, God would be immune to all the reasons that render non-existence better for material entities, possessing as he does all the other omni-attributes. This may be the case, but this maneuver renders the question of the relative merits of existence too unlike cases familiar to humans from which we can evaluate such merits. The main upshot of this argument thus is not to directly refute atheism, but rather to neutralize a major argument in its favor (the ontological argument) by showing that the possibility of its reverse counterpart shows the original to be at best moot and inconclusive.
6. Reverse Ontological Argument, II
This one is a better, but also slightly more involved argument, sharing a lot of common ground with the previous one. It is a modal argument, since it relies on possible worlds, which represent what is possible and not merely actual.
a. God is a greatest conceivable being.
b. For any property P, if having P is better than not having P, then God has P.
c. Let P = necessary existence. That is, P is the property of existing necessarily, that is, existing in all possible worlds, that is, existing no matter how the actual world is or might have been.
d. Having P is better than not having P: it is better to exist necessarily than to exist contingently, i.e. to exist in only some possible worlds.
e. By a., b., and d., God exists in all possible worlds.
e. Conceivability implies possibility: if a sentence is conceivable, then it is possible, i.e. there is a possible world in which it is true.
f. It is conceivable that God does not exist.
g. By e. and f., there is a possible world where God doesn’t exist.
h. By e. and g. we get a contradiction. Therefore, there is no greatest conceivable being.
Premise e. is the only extraneous premise, but it is one that is considered canonical in philosophical and theological literature, and one appealed to by many theists too, in several contexts.
7. Probabilistic Arguments
The arguments presented above share, more or less, a commonality — they have the form of (quasi-)deductive arguments, that is, arguments that follow a rigid logical structure and, crucially, whose conclusion necessarily follows from the premises (whether the premises are actually true or false) by virtue of logic. However, there is an industry of non-deductive arguments, and in particular abductive arguments against theism.
An argument is abductive when it purports to explain an observed fact or phenomenon by reference to the best explanation. Imagine that you wake up one morning and cannot find your favorite notebook. You conclude that you left it in your office, and you don’t conclude that an intergalactic alien group conspired to steal it from you. This is because the former is far more probable than the latter. This is also known as inference to the best explanation. This type of reasoning is extremely pervasive in science, and in fact it is by and large the only way of establishing scientific fact.
The general shape of atheistic abductive arguments is:
a. There is a phenomenon or fact X.
b. If God existed, then X would (most likely) not have been the case.
c. Therefore, it is most unlikely that God exists.
Two quick examples include:
Everitt (2004): The universe is vast, chaotic, and extremely indifferent to human affairs and independent of human influence; if God existed, then the human domain would most likely not be so unimportant; therefore it is most unlikely that God exists.
Dawkins (1986): Biological creatures, including humans, are in many ways “suboptimal” — there are many mechanical, and even mental, tasks we cannot perform, we are prone to disease, and we have naturally short lifespans; if God existed, then biological systems would be at least more, if not fully, optimal; therefore, it is most unlikely that God exists.
8. The Omnipresence Problem
This is not a logical paradox, but an inconsistency between the theistic belief that God is omnipresent and contemporary physical theories of space.
a. If God is omnipresent, then God is everywhere in space.
b. God is not identical to (constituents of) space.
c. Contemporary physics: space is entirely composed of constituent atoms. (That is, there is no space “between” space-atoms.)
d. If God occupies any space, then God must be identical to some (constituents of) space.
e. Since b. and d. are inconsistent, it follows that God is not omnipresent.
A theist might, of course, doubt what contemporary physics proclaims about space. It is hard to see what the alternative would be however. An alternative theory of space, known as relationism, maintains that space does not really exist absolutely, but only arises as a relation between objects. It would be a gross category mistake to think of God as occupying space on this view.
9. Empiricist Argument, I
Like the omnipresence problem, or even the problem of evil, this argument relies on a premise which requires independent motivation, rather than on pointing out an internal inconsistency of theism as, say, the stone paradox. The relevant premise is a bifurcation of our knowledge into knowledge which we have by analysis of concepts and knowledge which we have through experience. If we accept this bifurcation as exhaustive, then there is no room for knowing the existence of God.
a. Every meaningful sentence is either synthetic or analytic.
b. A sentence is analytic just in case it is verifiable simply through knowledge of the meanings of the terms in it. (For example, all one needs to know in order to figure out whether the sentence “All bachelors are unmarried men” is true is simply the meaning of the words “bachelor” and “unmarried” and “men”.)
c. A sentence is synthetic just in case it is verifiable (in principle) through sensory experience of the world. (This category will include most ordinary sentences, such as “It is raining on July 1st 2020 in Moscow.”)
d. The sentence “God exists” is not analytic: it is not part of the definition of “God” that he exists, for that would be question-begging.
e. The sentence “God exists” is not synthetic: we cannot, even in principle, verify it through sensory experience of the world, for God is immaterial.
f. Therefore, the sentence “God exists” is not a meaningful sentence.
10. Empiricist Argument, II
This is an epistemological argument, which is to say it has to do with our knowledge of the world and other epistemological notions, and mainly explanation. The general shape of it is this: we can explain any and all phenomena we want to explain within a scientific framework, without appealing to God. Therefore, theoretical economy mandates that we don’t appeal to God. The argument is due to Oppy (2018).
To understand the argument we need to define naturalism. Alas, there is no precise definition of naturalism, but something like the following is more than sufficient for our purposes: “naturalism [says] that all spatiotemporal entities must be identical to or metaphysically constituted by physical entities” It is more intuitive to think of naturalism as a nothing-but statement, according to which there exists nothing but “causes, beings and forces” which are natural, which is to say they are observable or scrutable through the natural sciences (physics, chemistry, biology, etc.). So, a ghost, paradigmatically conceived as an immaterial, self-illuminating entity, is a supernatural being; a dog isn’t. Another way to understand supernatural things is to think of them as capable of violating one or more laws of science.
God is supernatural because God is not subject to the laws of nature. But also because immaterial, omnipresent and timeless — and so on. Here is the argument then:
a. God is supernatural.
b. Theism is the position that God exists, and so theism is a supernaturalist position (it accepts the existence of natural phenomena and objects).
c. Naturalism is theoretically simpler than theism.
d. “There [are] no data that naturalism does not explain at least as well as theism.”
e. By Ockham’s Razor, we’d better believe naturalism than theism.
f. Therefore, we should not believe that there exists a God.
Clearly, the heavy lifting in this argument is done by premise d., which Oppy defends with an impressive array of arguments. For example, theists often “argue as follows: Naturalists can give no explanation of the existence of the universe; but theists can explain the existence of the universe in terms of the creative activities of God. So, on this point, theism is ahead.” But, as he notes, “Whatever range of options is open to the theist to explain the existence of God, exactly the same range of options is open to the naturalist to explain the existence of the universe. If it is open to the theist to say that God exists of necessity, then it is open to the naturalist to say that the universe exists of necessity. If it is open to the theist to say that God’s existence involves an infinite regress, then it is open to the naturalist to say that the existence of the universe involves an infinite regress. If it is open to the theist to say that the existence of God has no explanation, then it is open to the naturalist to say that the existence of the universe has no explanation[…]”
The interested reader should the article itself.
