Can We Prove the Existence of God?

Can we prove the existence of God? What exactly does it mean to prove something? What would count as a proof of God’s existence? To explore these questions, let’s consider one popular argument for God’s existence and test it against some different criteria for proofs. Here’s the argument:

1. If God does not exist, there are no objective, culture-transcending moral duties.

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2. There are objective, culture-transcending moral duties.

3. Therefore, God exists.

Is this a proof of God’s existence? One suggestion is that any sound argument constitutes a proof. An argument is sound if and only if (a) all its premises are true and (b) it is deductively valid, in the sense that its conclusion follows necessarily from its premises (i.e., it’s logically impossible for the premises to be true but the conclusion to be false).

Is our argument sound? It’s certainly deductively valid: it has the valid argument form of modus tollens (if P then Q; not Q; therefore, not P). Moreover, both of its premises are true. There are indeed objective, culture-transcending moral duties, such as the duty to care for one’s children, and it’s very hard to see what would ground such moral obligations if there were no God. At any rate, I believe that both premises are true, and so do many other people. But does everyone believe both premises? Well, no—and therein lies the rub.

Limitations of Sound Arguments

There’s another obvious problem with the idea that any sound argument amounts to a proof. Consider the following argument for the existence of God:

1. Either the moon is made of green cheese or God exists.
2. The moon is not made of green cheese.
3. Therefore, God exists.

Or this one:

1. Everything the Bible says is true.
2. The Bible says that God exists.
3. Therefore, God exists.

Both of these arguments are deductively valid and have true premises. Yet we can see that there’s something very fishy about the arguments. If someone were to ask you to prove the existence of God, you’d be unlikely to offer either of these arguments with any seriousness. Why? Simply because only someone who already believes in the existence of God would concede the first premise of each argument. The arguments are fallaciously circular in the sense that one would have to accept the conclusion before one could reasonably accept the premises. Even though the arguments are valid and (Christians would say) sound, they’re worthless as proofs. They have little, if any, persuasive force.

Is our original argument circular in the same sort of way? Is it clear that one or other of the premises wouldn’t be granted by someone who doesn’t already believe in God? The argument doesn’t appear to be circular in that question-begging way. After all, there are many atheists who accept that there are objective moral duties (and plenty more who argue as though there are). Furthermore, a number of atheist philosophers have agreed with the first premise of the argument.

This raises a further question and invites a further refinement of our criteria for proofs. If atheists have granted both premises of the argument, and they recognize that the argument is logically valid, why don’t they accept the conclusion that God exists? The short answer is that few atheists would affirm both premises. Those who affirm premise one will typically deny premise two, and vice versa. The explanation for this, of course, is that anyone who accepts both premises is logically committed to the conclusion—and most atheists simply don’t want to accept the conclusion.

Once you see that an argument is logically valid, you can’t consistently affirm its premises and deny its conclusion. So you have two options in order to maintain consistency. You can either (a) affirm the premises and the conclusion or (b) deny the conclusion and at least one of the premises. When presented with an argument like the one above, atheists will typically follow the second option rather than the first. Why? The reasons are complex but the short answer, from a biblical perspective, is simply—human sin. One of the defining characteristics of unbelievers is that they “suppress the truth in unrighteousness” (Romans 1:18).

Proof and Persuasion

If the conclusion of a sound argument is rejected because of sinful suppression, clearly that’s no fault of the argument. But it does raise the question of the relationship between proof and persuasion. Should we define a proof as an argument that is not only sound but also persuasive? The difficulty here is that we’ve now introduced a significant element of human subjectivity. What’s persuasive to me might not be persuasive to someone else.

Tying the notion of proof to persuasion isn’t a very promising route. There are simply too many subjective and circumstantial factors to take into account on that front. So let’s try to get back to some more objective criteria for judging arguments.

Often mathematical proofs are held up as the gold standard of objective proofs. For example, we can prove (using a strategy known as induction) that for every natural number N, either N or N+1 is divisible by two. What people often don’t realize is that mathematical proofs are always constructed within the context of a pre-accepted system: a formal scheme that specifies both axioms (foundational propositions) and rules of inference (by which various other propositions can be deduced from the axioms). Mathematical proofs are always system-dependent: the proof is only as good as the underlying system.

So if we’re to take mathematical proofs as our model, what “system” should we use to prove the existence of God? Presumably the rules of inference will be the laws of logic. What about the axioms? Some would insist that the axioms of a proof must be beyond rational question: they must be self-evidently true, or indubitable, or logically undeniable, or directly observable by the senses. These are the sort of axioms that everyone should accept.

This sounds promising, but even these criteria face objections. Intelligent and well-informed people have disagreed over which truths (if any) are self-evident, indubitable, and logically undeniable. And different people have different sense observations. The quest for universally acceptable premises comes unstuck again.

Certainty, Circularity, and Social Security Cards

Also inspired by mathematical proofs is the idea that a proof must have an absolutely certain conclusion: its conclusion simply cannot be rationally denied. However, the conclusion of a proof cannot be more certain than its premises; thus an argument with an absolutely certain conclusion must have absolutely certain premises. Does our test-case argument fit that bill?

I would say that anyone who denies there are objective, culture-transcending moral duties is irrational. (I’d argue this is presupposed by Paul’s argument in Romans 1-2.) Anyone who denies those moral duties is either lying, self-deceived, or suffering from cognitive dysfunction. But that’s a distinctively Christian perspective, so now we’re back to the problem of circularity.

Soon after I relocated from Britain to the United States, I had to visit the local Social Security Administration office to apply for a Social Security Number. The nice lady behind the counter required me to prove several things, so I showed her some documentation, including my British passport, my work visa, my immigration card, and a letter from my employer. But had I really proven anything to her?

It’s logically possible that the documents were elaborate forgeries. But how reasonable would it have been for her to demand more rigorous proof? Should I have eliminated every logical possibility that would undermine or contradict my claim, including the possibility that I was using a Jedi mind-trick or that she was actually in a dream?

However tempting it may be to set a high bar for a proof, the higher we set the bar the less reasonable it becomes to demand such a proof. So where does that leave our original question? Can we give any useful answer to it?

Person-Dependent Proofs

Here is my modest proposal: We should think of proofs in terms of proofs for a particular person. In much the same way that mathematical proofs are system-dependent, so proofs of the existence of God need to be seen as person-dependent. The question “Can we prove the existence of God?” then becomes “Can we prove the existence of God to so-and-so?” My suggestion is that if we can show, without begging the question, that the existence of God logically follows from propositions that a person already accepts, or is willing on reflection to accept, then we have indeed proven the existence of God to that person. If they fail to see that the existence of God follows from what they already believe or take for granted, or if they prefer to abandon other beliefs rather than to affirm the existence of God, the problem doesn’t lie in the proof.

What does this mean for our test-case argument? If we understand proof along the lines I’ve suggested, the argument is indeed a proof for particular people, not necessarily for everyone. What’s more, on this understanding there are numerous proofs of God’s existence. There are many arguments that demonstrate the existence of God from beliefs or assumptions that people already hold. (Consult the resources listed below for examples.) Some of these proofs might be deemed more effective or more persuasive than others, depending on the target audience, but as we’ve seen, proof and persuasion are two distinct things.

Yes, We Can Prove God Exists

So yes, we can prove the existence of God; but how exactly we prove the existence of God will depend on the particular person we’re dealing with and what they’re willing to grant.

There is, however, another question I think we should also ask: “Do we need to prove the existence of God?” My short answer: “No, but it’s still important to be able to do so.” I take the view, following John Calvin and other Reformed scholars, that Romans 1:18-32 teaches a universal knowledge of God: a sensus divinitatis that is part of our human nature. On this view, every human being possesses a natural knowledge of the living and true God, even though they sinfully distort and suppress that knowledge. It’s precisely this fact that serves as the basis for God’s universal judgment. People don’t need to have the existence of God proven to them by us. Natural revelation, we might say, is proof itself and proof enough. It’s as though God is continually showing his self-certified “documentation.” Furthermore, I agree with the so-called Reformed epistemologists (Alvin Plantinga being the most well-known) that we hold many beliefs, including many beliefs about God, in a “basic” way; that is, not on the basis of proofs or arguments or inferences from observational evidence. So no one needs to be able to prove the existence of God in order to have a rational belief in God.

Nevertheless, proofs of God’s existence, when formulated consistently with biblical revelation, can still serve many useful purposes. They can clarify our understanding of God, his attributes, and his relationship to the creation; they can increase our appreciation of God’s majesty and our utter dependence on him; they can help to neutralize the objections of unbelievers and the doubts of believers; and they can expose the irrationality and self-deceit of unbelief—all to the glory of God.

For further reading:

• John M. Frame, Apologetics to the Glory of God (P&R Publishing, 1996), chapters 3 and 4.
• Stephen T. Davis, God, Reason, and Theistic Proofs (Edinburgh University Press, 1997).
• William Lane Craig and J.P. Moreland, eds, The Blackwell Companion to Natural Theology (Blackwell Publishing, 2009).
• Alvin Plantinga, Warranted Christian Belief (Oxford University Press, 2000), chapters 6 & 7.
• Alvin Plantinga, “Appendix: Two Dozen (or so) Theistic Arguments,” in Deane-Peter Baker, ed., Alvin Plantinga (Cambridge University Press, 2007). (An unedited version is available here.)