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How to Prove a Negative

I’ve heard numerous folks, atheists as well as theists, declare that we can never prove there’s no God because it’s impossible to prove a negative.

We can indeed prove negatives, and we do so all the time. In fact, if we couldn’t prove a negative, we couldn’t prove a positive either, since every positive statement implies negative statements (an infinite number of them, actually). If I prove that ‘all the marbles in this box are white’, I automatically also prove that ‘none of the marbles in this box are blue’, ‘none of the marbles in this box are transparent’, and so on.

What I think people are getting at when they come out with the claim that we can’t prove a negative is that given a limited number of observations, we often can’t demonstrate that something doesn’t exist, because an exhaustive search is impracticable. We can’t prove that there are no fairies, because although reports of fairies have been convincingly explained on the supposition that there are no fairies, and no credible observation of a fairy has been documented, still, we can’t rule out the possibility that fairies might be very shy and very good at hiding, perhaps confined to a few remote locales and also able to turn invisible at will, and therefore, the possibility remains that some fairies have eluded all observation.

Yet does anyone really doubt that mammoths became extinct a long time ago? If they had survived, they would have been seen, and since they have not been seen, they have not survived. If you want a logical proof, here it is:

1. If mammoths were alive today, they would have been seen (m → s).

2. No mammoths have been seen alive in the past ten thousand years (~ s).

3. Therefore, there are no mammoths alive today (~ m).

It’s true that you can raise a doubt about statement 1. or statement 2. But you can always question the premisses of any proof—that has nothing to do with any special difficulty in proving a negative.

Observation is not the only way to prove the non-existence of some entity. We can prove that a square circle does not exist because it is logically impossible: it is self-contradictory. We can prove that a perpetual motion machine does not and cannot exist, because its existence would contravene the laws of physics. In cases like these, proving a negative may be a lot easier than proving a positive: if there is no self-contradiction or contradiction of natural laws, this doesn’t show that the entity exists, whereas if there is a contradiction, the entity does not exist.

We all know what a Pegasus looks like, we have seen pictures, and we have a definition of a Pegasus: it is a horse with wings, and its wings enable it to fly. Can a Pegasus exist? No, we can prove that this is impossible. Wings of that length could never provide enough uplift to enable something as heavy as a horse’s body to be carried through the air.

In H.G. Wells’s story, The Food of the Gods, a substance is discovered which, when fed to any animal, enables that animal to grow to a gigantic size. The story features, among other things, a giant wasp, able to fly and buzz and sting just like a normal-sized wasp, only much more terrifying because so much bigger. Such an organism could not exist, for a number of reasons. I will just mention two of them.

With any animal that relies on the motion of its wings for flight, an increase in scale will eventually cause it to be unable to fly. This is because the wings increase by area, while the mass of the body increases by volume. A very large-scale flying insect could not fly. Second, the way insects breathe cannot be simply scaled up. Insects breathe through a special kind of tube which just won’t work on a larger scale (unless the proportion of oxygen in the air were to be increased). This is one reason why, despite the fact that there are far more species of insect than of any other type of animal, there are no giant insects. Wells’s giant wasp would immediately suffocate. Therefore, a living giant flying wasp (assuming it’s simply a scaled-up version of an ordinary wasp, with no other anatomical changes) cannot exist.

So we can prove that some things don’t exist. However, there are ways to protect something from being proved not to exist. One way is to be so vague about the non-existent entity that it eludes any attempt to make deductions from its defined qualities. Another way is to make ad hoc adjustments to the qualities of the nonexistent thing. For instance, we might say that a Pegasus can fly because its body merely looks like a horse: it is really a fiberglass model of a horse, or because the Pegasus’s wings are just for show: it actually flies because it contains an antigravity motor. Or perhaps the Pegasus exists and is able to fly, on a world with a denser atmosphere or lower gravity than ours.

Or we can deny the premisses of the proof. We can, for example, deny the accepted laws of nature, saying that aeronautical engineers are mistaken about the mechanics of flight or biologists about the breathing equipment of insects.

The conclusions of any proof can always be avoided. This has nothing to do with proving a negative: we can do just the same with proving a positive. Does this mean that the whole exercise of proving something is pointless?

Not necessarily. Every proof is an argument and every argument can be presented as a proof. By framing an argument we put the defender of the nonexistent object in a position he may not have expected. He now has to defend claims he may not have realized earlier that he had to defend. Upon reflection, he may decide he doesn’t wish to defend them. Alternatively other people, listening to his arguments, may find them less persuasive now they see what other assertions have to be made to rescue those arguments. The advocate of a perpetual motion machine commits himself to denying the first and second laws of thermodynamics. The process of debate exposes what is really entailed in defending a particular position, and this may be very different from what was seen at first glance.

When a defender of the Pegasus tells us that the Pegasus’s body is made of hollow fiberglass, we may raise our eyebrows. When a defender of the all-loving, all-powerful God tells us that earthquakes and epidemic diseases are engineered by fallen angels, whom God could not keep in line because he ‘just had to’ guarantee their free will, we may raise our eyebrows even higher.

It’s always possible to rescue God’s existence from refutation by redefining ‘God’. Proving the nonexistence of God is always proving the nonexistence of God defined in a specific way, and it is therefore surprisingly similar to theological debates on ‘God’s nature’. If it ever turns out that there is, after all, a God, then atheists will have contributed to the accurate description of God’s nature. If, as I think, there is no God, then capable theistic philosophers like Augustine, Aquinas, Ockham, Descartes, and Swinburne have inadvertently contributed to demonstrating God’s nonexistence.

Why Does God Pretend Not to Exist?

How long, God? Will you hide your face forever?

—Psalm 89:46

 

One of the most basic and obvious facts about God is that he is never observed by ordinary people in their everyday lives, nor by scientists seeking to get at the truth about reality by empirical observation. Although the Torah has numerous reports of humans seeing various parts of God’s anatomy (Genesis 32:30; Exodus 33:23), these are now always taken metaphorically. Theists now agree with ‘John’ that “No man has seen God at any time” (John 1:18).

God cannot be discerned by sight, smell, sound, or touch. Nor can any activities demonstrably God’s be detected by the most sensitive of scientific instruments. We have already (in Chapter 9) looked at the suggestion that people have other ways of perceiving God, ways not dependent on the evidence of their five bodily senses, and we have seen that this is a mistake.

Among devout believers in God, bouts of ‘loss of faith’ are as commonplace as influenza. Believers are always liable to be haunted by the terrifying specter of Doubt. They often report that there have been times when they have felt they should believe, but can’t.⁶⁷ The fringes of Christian communities are inhabited by individuals who want desperately to believe but can never manage to summon up the ‘faith’. There’s no counterpart of this phenomenon in any other area of human knowledge. The closest thing I know is Winston Smith’s frantic attempt under torture, in Nineteen Eighty-Four, to convince himself that two plus two equals five.

We can imagine a world in which no one, or hardly anyone, would seriously doubt that there was a God, because his existence would frequently be corroborated by experience.

Suppose . . . that an articulate voice were heard in the clouds, much louder and more melodious than any which human art could ever reach: Suppose, that this voice were extended in the same instant over all nations, and spoke to each nation in its own language and dialect: Suppose, that the words delivered not only contain a just sense and meaning, but convey some instruction altogether worthy of a benevolent being, superior to mankind: could you possibly hesitate a moment concerning the cause of this voice? and must you not instantly ascribe to it some design or purpose? (Hume, Dialogues, p. 213)⁶⁸

There are many other ways in which the existence of God could be made plainly manifest to everyone.

If someone thought God regularly spoke to her, say, in a voice heard inside her head, we’d be inclined to suppose this a kind of hallucination. But if the purported utterances by God were genuinely informative, imparting much detailed information that the recipient of these messages had not been able to find out independently, we would become convinced that some rather remarkable entity was indeed communicating with her by this method. And if everyone, or just some people, received such messages from this apparent entity as a matter of course, and the different messages all fit together nicely, and all imparted genuine information, then we would all be convinced there really was some such entity. Other information might convince us this entity had more of the attributes of a god.

Alternatively, God might simply appear to people. God could manifest himself in human form, just as he is often described in Genesis. It would be quite easy for the human form to say and do things which made it clear that it was the embodiment of God. Or God could take a non-human form, such as a gleaming cylinder topped by a halo, available for conversation with humans and full of fascinating and sometimes helpful information. Or God could dictate a book to someone, not filled with the human ignorance of the Bible or the Quran but containing ample information which only an entity vastly more knowledgeable than any human could have set down.

The fact that God is not observable does not in itself indicate that there’s no God. We all accept the existence of entities which we have not perceived. I accept the existence of quarks and magnetic fields. Currently most physicists accept the existence of ‘dark matter’, and actually believe that dark matter makes up most of the matter in the universe. Yet no one has yet observed any dark matter, either visually or with the aid of special instruments. Physicists accept that there’s a whole lot of dark matter out there, because this supposition makes sense of many of their other observations.

God, however, sheds no light on our factual knowledge. We don’t understand algebra, economics, gardening, or electronics any better by supposing there’s a God, whereas we would, for instance, understand gardening better if we had a knowledge of biochemistry or plant biology. We can make just as good sense of the world on the supposition that there’s no God as on the contrary hypothesis.

It can be tricky to determine whether some entity not directly observable exists, as people found out when Louis Pasteur began to argue that bacteria exist. But God is an intelligent mind who, we are often informed, wants humans to believe he exists. He is also all-powerful, and therefore could easily make his existence clear to humans. So here we have a contradiction.

This thought gives rise to an argument, or family of related arguments, known historically as the Argument from Silence, the Argument from Divine Hiddenness, or the Argument from Nonbelief.

1. God could easily have shown strong evidence of his existence to humans—strong in just the same way that the evidence of the existence of trees, stars, and other people is strong.

2. God wants humans to believe that he exists.

3. Therefore God must have given strong evidence of his existence to humans.

4. Humans have no strong evidence that God exists.

5. Therefore God has not shown humans strong evidence of his existence.

6. Therefore, God does not exist.

In a slightly different form, the Argument goes like this:

1. God could easily have arranged things so that everyone would believe that he exists.

2. God wants humans to believe that he exists.

3. Therefore God must have arranged things so that everyone would believe that he exists.

4. Many humans do not believe that God exists.

5. Therefore God has not arranged things so that everyone believes that he exists.

6. Therefore, God does not exist.

One common theist response is ‘How dare you make demands of the Almighty?’ This misses the point. The atheist is not asking God to do anything. The atheist is merely scrutinizing the claims of the theists, to see what they’re worth. If I ask a believer in the Loch Ness Monster about Nessie’s food supply, I don’t expect to be asked ‘How dare you make demands of Nessie?’ In either case, we’re just concerned with the possible truth of some claim, so naturally we have to test that claim by looking at what the claim would imply if it were true.

Furthermore, if God is omnipotent, then every logically possible state of affairs is just as easy for God to bring about as every other. Omnipotence implies, not just that God can do anything, but that he can do any one thing just as easily as anything else. So another, more jocular comment on this theist response would be: ‘Precisely because he is Almighty, what we are demanding of him amounts to nothing’.

Since God could easily have ensured that his existence was as obvious to humans as the existence of trees or stars, the fact that this is far from being the case demonstrates that God, if he exists, has made a conscious decision to pretend not to exist, yet theists nearly always claim that God wants humans to believe in his existence:

Craig may appear to dispute this. He says:

Although I’ve found that atheists have a hard time grasping this, it is a fact that in the Christian view it is a matter of relative indifference to God whether people (merely) believe that he exists or not. For what God is interested in is building a love relationship with you, not just getting you to believe that he exists. (Craig and Sinnott-Armstrong, p. 109)

What Craig says here is not in the least hard to grasp, but it is highly idiosyncratic to Craig. If they think God doesn’t care much about humans believing in his existence, why did the Christians spend thirteen hundred years torturing to death anyone who disputed it?

All flippancy aside, Craig’s view here is shared by at best a tiny minority of Christians, most of them late-twentieth-century Americans. If we look at what the New Testament says about conversion to Christianity, we find that belief is often mentioned, while a love relationship is rarely so much as hinted at. “He who has believed and has been baptized shall be saved, but he who has disbelieved shall be condemned” (Mark 16:16).

At any rate, you can’t enjoy a love relationship with an individual of whose existence you’re unaware, so belief in God’s existence is a prerequisite of any such love relationship. Craig himself has spent much of his life trying to convince people that God exists, so he presumably really does suppose this is a belief God prefers to have disseminated.

The Moral Freedom Defense

A popular theist reply to the atheist Argument from Hiddenness is to say that if God’s existence were palpable, this would unduly coerce people, taking away their moral freedom. I’ll call this the Moral Freedom Defense. Variants of this argument are advanced by Swinburne, Van Inwagen, and Michael J. Murray.⁶⁹ The common element is that a person who was absolutely convinced of God’s existence would fear God’s retribution for wrongdoing, and would therefore choose to behave well out of simple fear of this retribution. In this connection, Van Inwagen makes much of Hell, and Murray too mentions eternal punishment.

To me, this argument is quite startling, for a number of reasons:

• 1. The Moral Freedom Defense presupposes that we have no good evidence that God exists. If we did have such evidence, then it would be pointless to come up with an explanation of why we don’t have it. I suppose it might be claimed that we have some good evidence, but not enough to be conclusive, but that balancing act would be ungainly.

• 2. If belief in God’s existence makes you believe in eternal punishment for wrongdoing and thus gives you an incentive to behave better, and that means you can’t be properly tested for your moral rectitude, then those who do now believe in God’s existence can’t be properly tested for their moral rectitude. The good behavior of those who believe in God must be devalued compared with the good behavior of those who disbelieve in God (with presumably those who merely suspect there might be a God given an intermediate rating). This means that the good behavior of atheists is worth more than the good behavior of theists, which would be gratifying.

• 3. Proponents of the Moral Freedom Defense in fact spend part of their time arguing that God’s existence is a reasonable conclusion on the facts, and then, when asked about the Argument from Hiddenness, they tacitly concede that God’s existence is not a reasonable conclusion on the facts. It follows that these proponents, when they try to persuade others that God exists, are undermining God’s purpose in pretending not to exist.

• 4. To pretend not to exist, God must arrange things so that all the arguments available to us for his existence are unsound. Therefore, the arguments for God’s existence proposed by the theists are all unsound, which is just what we suspected. But if these arguments are all unsound, then the best theory is, not that God is pretending not to exist, but that God (with total sincerity) just doesn’t exist.

• 5. The argument presupposes that if you believe in God, you will automatically conclude that God has arranged punishment for sin in an afterlife. But many people, like the authors of the Torah, have believed in God without believing in an afterlife. If someone were to be convinced of the existence of God and an afterlife, but never heard Christianity or Islam preached, that person would not suspect that there was punishment for wrongdoing in the afterlife. The notion of eternal punishment for wrongs committed in this life would strike anyone who was not already familiar with it, but had somehow come to believe in the God of classical theism, as simply preposterous. (I’m not concerned here to comment on the merits of eternal punishment; I’m just pointing out that belief in God or an afterlife does not automatically lead to belief in retribution in the afterlife.)

• 6. The three authors mentioned are all in the Protestant tradition. If original Protestantism meant one thing above all others, it meant that you cannot, by your good works or your belief in the existence of God, escape the fires of Hell. You can only do that by having faith in Christ. Evidently, these three authors are liberal rather than evangelical Protestants, and believe (as Muslims do) that people’s fate in the afterlife will be largely governed by their good or bad behavior in this life. But the mere fact that the founders of their tradition thought otherwise helps to bring out the arbitrary quality of the present authors’ reasoning, their assumption that if you come to believe in God you will automatically be intimidated into behaving more morally.

• 7. For two thousand years Christians have been preaching that all who do not accept their preaching will roast for ever in Hell, and precisely for this prudential reason had darn well better accept it. The Jesus of the gospels preached that we should fear God because he can send us to Hell (Matthew 10:28; Luke 12:5). Until well into the twentieth century, ‘brands plucked from the burning’ was the cliché, in Protestant countries, to characterize baptisms by foreign missionaries. For a vivid account of a typical instance of fear of Hell in a Catholic culture, take a look at Joyce’s Portrait of the Artist as a Young Man, Chapter 3. Until about eighty years ago, one of the nicest things you could say about someone was that he was ‘God-fearing’.

But now we’re told that God would rather have people disbelieve in him than believe in him for fear of Hellfire. I don’t want to nail the theists to the cross of their historical errors, but if they’re now going to abandon a key element of what they have been preaching for two thousand years, they ought to explain how theism got it so seriously wrong for so long.

• 8. Theists often maintain that belief in God is desirable because it is conducive to morally good behavior. But a proponent of the Moral Freedom Defense cannot consistently offer any such argument.

• 9. Morally good behavior is held to be unworthy, or at least suspect, if influenced by belief in God. The Defense therefore seems to hint at some correct motive for moral behavior, untainted by belief in God. Rigorously followed through, it would lead to the view that many motivations for moral behavior are undesirable. For instance, a Hindu who disbelieves in the God of classical theism but believes that if he behaves badly he may be reincarnated as a praying mantis would also be compromised, in having an extraneous incentive to behave correctly. It would certainly be interesting to hear the correct motive for moral behavior, the one God would prefer us all to have. Evidently it would have to be intrinsically atheistic.

Aside from these difficulties, how plausible is it that the optimal choice of an almighty and all-knowing God’s would be to select souls for eternal segregation according to their behavior in this Vale of Tears, for which purpose it is necessary to deceive them into supposing that there is no God? How could omniscience feel the need to run quality checks on human souls, quality checks which will only work if the owners of these souls are deluded?

The notion that such a God would grade human souls according to their moral choices is itself barely coherent. Either the crucial moral choices stem from some fundamental aspect of the individual soul, in which case God could foresee the choices without having them actually played out, and could therefore preempt that train of events by creating only those souls pre-designed to make the right choices, or the crucial moral choices share in the indeterminacy associated with free will, in which case they are the type of choices which you might make differently if you could live your life several times over. But in that case, it would be unjust for an omniscient authority to punish people eternally for making the choices they just happened to make in the one earthly life allotted to them.

The Appeal to Unintelligibility

Theists sometimes respond to criticisms of their claims by saying that God is far beyond our understanding. The claim that God is unintelligible may take the form of claiming that God has an unknown purpose in pretending not to exist. The claim is, not merely that God has a purpose that we don’t know about, but additionally that God cannot divulge that purpose to us. If we knew what God’s purpose was in pretending not to exist, then this might easily incline us to believe that he exists.

This is a kind of ultimate deterrent: it annihilates any argument. Yet like other ultimate deterrents, it annihilates assets on both sides equally. Everything the theist tells us about God, and every possible case he can make for the existence of God, appeals to our understanding of God and of his motives, character, and qualities. The theist tells us that there is a God, and that God is this way and that way. If we cannot begin to understand God’s purposes, then all the theist’s assertions about God are in vain. Theism requires that God be comprehensible in broad outline, if not in perfect detail.