How Arguments About God Work

Aquinas presented his arguments for God's existence as demonstrations. Not as considerations, not as evidence, but as proofs of the kind a geometer offers.

A philosopher of religion today will present some of the same arguments and claim something weaker: that they raise the probability of the conclusion. The arguments have not changed much. What has changed is what anyone thinks an argument of this kind can accomplish, and understanding that shift is what makes the intermediate tier legible rather than baffling.

Proof in the strict sense

This is what proof meant in the tradition that produced most of the classical arguments. The model is mathematical: start from what cannot be doubted, proceed by steps that cannot fail, and arrive at a result with the same standing as the starting point.

Only two things can go wrong with an argument of this kind, and both are checkable. Either the inference does not hold, so that the premises could be true with the conclusion false, or a premise is not in fact certain. Almost all the historical work on these arguments consists of the second sort of attack.

There is a feature of demonstration that explains the whole retreat, and it is easy to state. A valid argument transmits certainty from premises to conclusion, and it can transmit nothing that the premises do not have. So a demonstration of God's existence needs premises more secure than its conclusion, for the audience that doubts the conclusion.

That is the difficulty. The premises that generate God in these arguments are metaphysical: that everything contingent has a cause of its existing, that a causal series of a certain kind cannot go on without limit, that whatever begins to exist has a cause, that greatness admits of a maximum. Each of these can be defended, and each of them is less obvious to someone who doubts the conclusion than the conclusion is to someone who accepts it. Hume in the Dialogues Concerning Natural Religion, published in 1779 after his death, and Kant in the Critique of Pure Reason of 1781 both pressed the point at length, and the effect on the field was permanent. A premise that only convinces those already convinced does not demonstrate anything.

None of this shows the arguments are worthless, and drawing that conclusion is the standard overreaction. It shows that they are not demonstrations, which leaves open the question of what they are.

A note on the word is worth having, since it does more damage in public argument than any other. Demanding proof of a claim about what exists is demanding something almost no such claim meets. There is no proof in this sense that other people have minds, that the past occurred, or that any particular scientific theory is true, and the reasonable standard for those is not proof but support. Applying to one question a standard applied to nothing else is not rigour.

Support without proof

The structure is the same one used for any hypothesis that cannot be checked directly. A piece of evidence supports a hypothesis when the evidence is more to be expected if the hypothesis is true than if it is false, and counts against the hypothesis when the reverse holds.

Two features of this follow immediately and both are constantly ignored.

The assessment is comparative. Asking whether some feature of the world is what a theist would expect settles nothing on its own, because the question is whether it is more expected on theism than on the alternatives. A fact that both hypotheses predict equally well is evidence for neither, however striking it is. This is why arguments in the intermediate tier spend so much time on what naturalism would lead one to expect: without that half, the calculation has one term.

And the outcome depends on two things rather than one. How well each hypothesis leads you to expect the evidence is the first. How likely each hypothesis was before the evidence came in is the second, and evidence that strongly favours a hypothesis can leave it improbable if it started improbable enough. That second factor is where the question of who has to argue comes back, this time with content.

A consequence of the shift that catches people out: on this framework an argument can be a good argument and leave its conclusion false or unlikely. Nothing has gone wrong when a theist grants that suffering is evidence against theism, or when an atheist grants that the universe's order is evidence for it. Both are granting that a consideration pushes in one direction while holding that the total balance goes the other way, which is an ordinary thing to say about evidence and an impossible thing to say about proof. This is also why the problem of evil is now almost always presented as evidential rather than as a demonstration of inconsistency.

Putting the pieces together

Basil Mitchell set this out in The Justification of Religious Belief in 1973, holding that the question does not admit of formal proof and that the reasonable procedure is to weigh a range of considerations together. Richard Swinburne, who succeeded him in the same Oxford chair, built a cumulative case with the apparatus of probability theory in The Existence of God in 1979, revised in 2004, and concluded that on the total evidence theism is more probable than not.

The standard objection is that a collection of failures is still a failure. Ten leaky buckets hold no water. Ten arguments each of which has been refuted do not become a proof by being stacked.

The reply distinguishes two structures that the objection runs together.

In a chain of reasoning, weakness compounds. If each step is doubtful, the conclusion is more doubtful than any step, and adding steps makes matters worse.

In a body of independent evidence, weakness accumulates in the other direction. No single fact establishes who committed a crime, and a set of independent facts each of which is somewhat more likely on one suspect's guilt than on anyone else's can establish it jointly. Nothing fallacious is happening, and this is how nearly all reasoning about the past and about unobserved causes proceeds.

So the question is which structure a given case has, and three conditions have to be met for accumulation to work.

The pieces must be genuinely independent. Three arguments that all rest on the same disputed principle are one argument written three ways, and the appearance of convergence is an artefact.

Each piece must actually favour the hypothesis over its rivals. A consideration that is merely consistent with theism contributes nothing, and a case assembled from such considerations can be arbitrarily long without accumulating anything.

And the case has to be assessed whole. Refuting the strongest member does not dispose of it, and defending the strongest member does not establish it.

Mitchell and Swinburne differ over how the weighing should be done, and the difference marks a genuine fork. Swinburne quantifies, which makes the reasoning inspectable and exposes it to the charge that the numbers were chosen to produce the result. Mitchell leaves the weighing to informed judgement, which is more honest about what is actually happening and harder to check.

One symmetry is worth stating plainly, because cumulative reasoning is usually presented as a theistic device. The structure is available to the other side and is used there. Suffering, the hiddenness of God to sincere seekers, the sheer success of explanations that mention no agent, and the natural history of religious belief are assembled into cumulative cases against theism in exactly the same form. Whoever accepts the method accepts it for both.

Where to begin

Antony Flew argued for this in "The Presumption of Atheism" in the Canadian Journal of Philosophy in 1972, and the phrase has been in circulation ever since, usually with less care than he gave it.

Flew's claim was procedural rather than substantive. He was not arguing that atheism is true or even that it is likely. He was arguing about where a debate should begin, on the model of a criminal trial: the defendant is presumed innocent, the prosecution carries the case, and if the case fails the presumption stands without anything having been established about the defendant. Transposed, the theist argues, and if the arguments fail, the debate ends with the negative position intact.

Three things should be said about it, and taken together they turn a dispute about procedure into a dispute with content.

The courtroom model was addressed in the second article of this tier and the point bears repeating in this setting. A trial must produce a verdict, so it needs a rule for what to do when the evidence is inconclusive. Inquiry has no such requirement, and suspending judgement remains available at the end of an inconclusive investigation.

The presumption depends on the definitions. Flew's own preference for defining atheism as the absence of belief and his defence of the presumption are connected, and the connection is not accidental. Define atheism as a proposition and the presumption has to be argued for. Define it as a psychological state and it comes close to following from the definition, which is a reason for suspicion rather than a reason for acceptance.

And restated in probabilistic terms it becomes a claim that can be assessed. What a presumption amounts to on that framework is a claim about prior probability: that theism starts out unlikely enough that inconclusive evidence leaves it unlikely. Stated that way it is a substantive thesis with arguments on both sides. Swinburne holds that theism has a high prior because it posits one being with unlimited properties, which he takes to be a simpler hypothesis than the alternatives. Critics respond that a being with a mind, purposes, and unlimited powers is not simple in any sense that makes a hypothesis likely in advance, and that simplicity of statement is not evidence about the world.

That argument can be conducted. Which is the gain from the reframing, since arguing about who is required to speak first is a way of having no argument at all.

What this tier has done

The five articles have fixed the terms of the subject without settling any of it.

The first set out what is being claimed, since the arguments in later tiers are arguments for a specific being with specific attributes and not for anything vaguely divine. The second separated the positions and raised the question of who is obliged to argue. The third gave the relation between God and everything else, which is what most of the classical arguments are really about. The fourth asked what faith contributes and found that the interesting dispute is not faith against reason but a dispute about which beliefs need support from others. This one has established what kind of case is on offer.

The intermediate tier assesses the cases themselves: the arguments from the existence and order of the universe, the argument from the concept of God alone, the arguments from morality and from religious experience, and the case against theism from suffering. Every one of them will be a probabilistic argument or a component of a cumulative case, and none will be a proof. That is not a weakness in them. It is the standard that applies to every interesting claim about what the world contains.