Introduction: what is a “proof” anyway?

Almost everyone who thinks about faith runs, sooner or later, into one demand: “Prove to me that God exists.” And whoever fails to prove it concludes that faith is a matter of feeling, or a “leap” with no basis. It is worth stopping here, because this demand hides an error, and a fundamental one.

The demand “prove it” rests on two assumptions that are usually not said out loud. The first: whatever cannot be proved is a subjective matter, “to each his own truth,” and not a fact. The second: nothing can really be proved. The second assumption is true. Every proof, even in mathematics, starts from basic assumptions that were themselves never proved. And every general scientific law is a generalization: a few thousand cases were checked, and a conclusion was drawn about all the cases that were not checked. There is no way to prove that the generalization is correct. People usually fail to notice what follows from this. If you also accept the first assumption, then not only faith is “a subjective matter,” but science too, and so is the fact that the sun will rise tomorrow.

Whoever understands this stands before three paths, and we will discuss them shortly. But we can already say which path we will take: not to give up the demand to think, and not to demand a certainty that exists in no field. The right question about God is not “is it proved?”, since nothing is proved, but “is it reasonable, by the same common sense with which we know everything else?”

Faith is a claim about the world, not a feeling

Before we set out, one thing must be clarified, because many people get it confused. Faith is not a feeling. When a person says “God exists,” he is not reporting what he feels; he is claiming something about the world, like someone who says “there is water on Mars.” It is a claim that can be true or false. How do we know it is not just a feeling? Because people do not argue about feelings. If I like pizza and you do not, there is no dispute between us. But between a believer and an atheist (someone who says there is no God) there is a real argument. And a real argument is a sign that both are talking about the world, not about themselves.

This is not to say that religious feeling does not exist or is undesirable. The claim is only that it must be distinguished from faith. Fear of a tiger is not a tiger. The fear may be a sign that a tiger is nearby, and it may be the result of my having seen a tiger. But it is not the tiger itself. So too with religious feeling: it can lead to faith, and it can flow from it. But it is not faith.

Hence also the answer to a popular claim: “There are no atheists in foxholes.” That is, in times of danger everyone prays, so everyone secretly believes. Atheists answer with the opposite claim: this proves that faith is, at bottom, nothing but fear. The truth is that neither claim is worth much. The phenomenon fits both explanations, and therefore proves nothing. And in general, explaining why someone believes (“because of his upbringing,” “because of fear”) or why someone does not believe (“because of a crisis,” “because it is convenient”) is not an argument. It is psychology. The only question is whether the claim is true.

There are also believers who say: “My faith is an inner experience, and it does not have to answer questions of logic.” That is a comfortable position, but we need to check what it says. If faith is only an experience, and not a claim about the world, it is really atheism with a religious feeling. And if it does claim that God exists, there is no exemption from facing the objections. The same is true of someone who came to faith through a mystical experience. There is a difference between how I arrived at an idea and whether the idea is true. Even an idea that came in a dream must pass the test.

Intuition is a way of knowing

The second point: there is a way of knowing things even without proof. It is called intuition, and it can be described as “seeing with the eyes of the mind.” A gifted mathematician sometimes “sees” that the solution is 7, even before he has checked. Take an example from life. You are sure that everything has a cause. If a cup breaks, someone or something broke it. Now try to prove that. You will say: “That is how it always is.” But you have seen only a few thousand cases in your life, and you are sure it holds in the billions of cases you have not seen. Where does the confidence come from? Not from the eyes, since you have not seen everything. And not from a proof, since there is none. It comes from reason itself. David Hume, a Scottish philosopher who lived about 250 years ago, was even more precise. Even in the cases you did see, what did you actually see? You saw A, and then you saw B. You saw the ball hit the window, and then the window break. A thousand times. But the “causing” itself, the link between A and B, you never saw. There is no such thing as seeing a “cause.” We only see that one thing comes after another. And the link between them is added by reason. That is intuition. And you rely on it completely, and rightly so. What is the difference between intuition and feeling? About a feeling there is no argument. About an intuition there is an argument, and one side is right. One can check whether 7 really is the solution.

Now let us ask: what happens to someone who decides not to rely on anything that has not been proved? He is left with nothing. Take mathematics, the most “secure” field. Every proof in it starts from a few basic assumptions. In geometry, for instance, we assume that “through two points passes exactly one straight line.” No one has proved these assumptions. They simply seem true to us. If we do not rely on them, there is no mathematics. And we have already seen that science works the same way: the move from “a few thousand cases checked” to “always” is a leap that reason makes, without proof. Without that leap, there is no science.

In other words: both the mathematician and the scientist rely, without proof, on what their reason “sees.” And whoever relies on his reason in mathematics and in science has no reason to disqualify it precisely when we come to the question of God. Here something also becomes clear about the word “faith.” People say: “I don’t know, I only believe.” But by this test, “the sun will rise tomorrow” is also “only a belief.” Faith is not the opposite of knowledge. It is a kind of knowledge: reasonable knowledge, without absolute proof, like most of what we know.

What does each field rest on?

It is worth pausing on this point, because it seems strange at first sight, and without it everything that follows seems weak. Is it really true that nothing is proved? Here is a short tour of the fields of knowledge.

Let us start with logic itself. The most basic rule of thinking is that something cannot be both true and false at the same time. Try to prove this rule. Any proof you offer will use it, because without this rule the word “proof” has no meaning at all. In other words, the foundation of all thinking is something that cannot be proved, and yet all of us are completely sure of it.

Mathematics, as we have seen, starts from basic assumptions. Sometimes one assumption can be proved from others, but then the others remain unproved. In the end, something always remains that we simply accept. And here is a point worth remembering: already in antiquity, philosophers showed that every attempt to prove everything has only three possible outcomes. Either the proof goes back without end, and then it has no beginning. Or it goes around in a circle, and in the end assumes what it wanted to prove. Or it stops at an unproved assumption. There is no fourth option. All the knowledge we have stops, in the end, at something that was not proved.

Science rests on more assumptions of this kind than people usually think. It assumes that the senses can be trusted, and no one has proved that. It assumes that the laws of nature are constant, that what was true yesterday is true today, and that a law tested here holds in another galaxy too. And that cannot be proved without first assuming it. It assumes that every phenomenon has a cause, and that, as we have seen, no one has seen with his eyes. And it assumes that the simple explanation is preferable to the complicated one, without any proof that the world “prefers” simplicity. Without these assumptions there is no science, and none of them is proved.

History rests entirely on testimony: on what people told and wrote. None of us saw the destruction of the Second Temple, nor the First World War. We rely on those who told. That is an assumption, not a proof. And the law assumes that witnesses can be believed, and that what seems probable is probably also what happened.

Everyday life too. You are sure that there is a world outside your thoughts, and that the people around you are people and not a dream. Try to prove it. Philosophers tried for centuries, and failed. And yet no sane person doubts it.

The conclusion is not that “nothing can be known.” The opposite. The conclusion is that knowledge never depended on proof. In every field, we know things because they seem true to common sense, and we go on from there. And whoever demands of faith in God precisely what he demands of no other field is not exercising judgment. He is exercising prejudice.

Three paths

Let us now return to the two assumptions from the opening: “what is not proved is not a fact,” and “nothing can be proved.” Whoever understands them stands before three paths.

The first path is skepticism: accept both assumptions. If nothing is proved, and only what is proved is admissible, then no claim is admissible, and nothing can be known. The second path is fundamentalism: accept the first assumption, and flee from the second. That is, give up on reason and adopt certainties that come “from above,” in ways beyond reason. An idea that arrived this way is not exposed to criticism, and that is exactly what makes it attractive. It is important to see that these two opposites, the skeptic and the fundamentalist, have a common root: both identify truth with certainty. In the eyes of both, only what is proved with certainty can count as true.

The third path is to give up precisely the first assumption. True, there is no way to prove anything. But it is not true that an unproved claim is inadmissible. It is enough that a claim is reasonable, by common sense, in order to accept it. This is the only path that allows us both to think and to know, and it is the path we all take in every other field. On this path, faith in God is not certain either, exactly like every other claim about the world. It is a claim built by human reason, and therefore exposed to all its limitations. Hence also a rule of honesty: the same reason that built the faith can also criticize it, qualify it, and even reject it. Someone who says “let us examine,” but knows in advance that he will accept no other conclusion, is not examining. He is a fundamentalist in disguise.

There is also an educational lesson here. An education that identifies faith with certainty does harm: someone raised on it, who one day discovers that he has no certainty, concludes that he no longer believes. That is a mistake. Faith without certainty is the only faith there is.

And what about the question “how can one live like this, and even give one’s life, without certainty?” It has two answers. The first: even if this understanding creates a difficulty, the difficulty does not change the truth. If wisdom creates problems, we deal with the problems; we do not strive to be fools. The second: it is not true that only certainty can justify self-sacrifice. A soldier who gives his life in battle is not convinced with absolute certainty that he is right, and if he is convinced that way, he is naive. A person who understands his limits functions within uncertainty. Think of the law of the “pursuer”: you see a man chasing someone in order to kill him, and you are permitted to kill the pursuer in order to save the pursued. Do you know with certainty what is going on? Perhaps some detail is hidden from you. Suppose there is a 90% chance that he really is a pursuer, and a 10% chance that he is not. If you refrain from acting because of the 10%, you take a 90% risk that the pursued will die. And yet one must decide, and decide according to the more probable possibility. So it is with every moral decision. The more probable possibility is the right basis for a decision, even when there is no certainty. True, someone who knows that there is no certainty in anything will find it harder, in practice, to live out his values. But that is a practical problem, to be dealt with on its own terms, and not a reason to change what is true.

The argument “from the definition,” and why it is not enough

Before we get to the arguments that start from the world, it is worth knowing a famous argument that tries to prove that God exists without looking at the world at all, from his definition alone. It was formulated by Anselm, a monk and theologian who lived in England about a thousand years ago, and it goes like this: God is “that than which nothing greater can be thought.” If he existed only in the imagination, then a God who really exists would be greater than him. But we said that nothing is greater than him. Therefore he must really exist. In another formulation: “a God who does not exist” is a contradiction, like “a round triangle.”

The argument is much cleverer than people usually think, and most of the famous criticisms of it do not really bring it down. One of them, by a contemporary monk named Gaunilo, goes like this: let us define “the most perfect island that can be thought of.” An island that really exists is more perfect than an island that exists only in the imagination. Therefore, by the same logic, the perfect island must exist. And that is of course ridiculous. If the argument “proves” the existence of such an island, something in it must be broken. Another, by the German philosopher Immanuel Kant, says that existence is not a property: a hundred real shekels and a hundred imaginary shekels are exactly the same sum; existence adds nothing to them. Therefore, by this criticism, “a God who exists” is not greater than “God” either. Both are possible, but not decisive. They can be answered.1

And yet the argument has a hole. The feeling that “this thing really exists” we know only from things we have met in reality. When I think of “a God who really exists,” I am really only saying words. I do not actually experience him as existing. That is why the step “a God who really exists is greater” does not work: someone who has no perception of God as existing cannot even begin the argument. One might object: it is possible to stimulate the brain artificially and create in it the sensation that something exists. But an artificial sensation is precisely a state in which reason does not reflect reality, and from it nothing can be inferred about the world. So the argument does not stand on its own. In this sense Kant was right: existence cannot be proved from a definition alone. But he was right not because of the general rule he proclaimed, but because of this particular flaw. The argument is beautiful, and it may have value when joined to other arguments, but to reach God one must start from the world itself.