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Irreligion

A Mathematician Explains Why the Arguments for God Just Don't Add Up

Hill and Wang

The Argument from First Cause (and Unnecessary Intermediaries)

The very first phrase of the Book of Genesis, "In the beginning," suggests the first-cause argument for the existence of God. In clarifying the argument's structure, Bertrand Russell cites a seemingly different account of the beginning — the Hindu myth that the world rests on an elephant and the elephant rests on a tortoise. When asked about the tortoise, the Hindu replies, "Suppose we change the subject."

But let's not change the subject. As I will throughout the book, I begin with a rough schema of the argument in question:

1. Everything has a cause, or perhaps many causes.

2. Nothing is its own cause.

3. Causal chains can't go on forever.

4. So there has to be a first cause.

5. That first cause is God, who therefore exists.

If we assume the everyday understanding of the word "cause" and accept the above argument, then it's natural to identify God with the first cause. God's the one, according to a religious acquaintance of mine, who "got the ball rolling." A slight variation of this is the so-called cosmological argument, which dates back to Aristotle and depends on the Big Bang theory of the origins of the universe (or some primitive precursor to it). It states that whatever has a beginning must have a cause and since the universe is thought to have a beginning, it must have a cause.

So have we found God? Is He simply the Prime Bowler or the Big Banger? Does this clinch it? Of course not. The argument doesn't even come close. One gaping hole in it is Assumption 1, which might be better formulated as: Either everything has a cause or there's something that doesn't. The first-cause argument collapses into this hole whichever tack we take. If everything has a cause, then God does, too, and there is no first cause. And if something doesn't have a cause, it may as well be the physical world as God or a tortoise.

Of someone who asserts that God is the uncaused first cause (and then preens as if he's really explained something), we should thus inquire, "Why cannot the physical world itself be taken to be the uncaused first cause?" After all, the venerable principle of Occam's razor advises us to "shave off" unnecessary assumptions, and taking the world itself as the uncaused first cause has the great virtue of not introducing the unnecessary hypothesis of God.

Moreover, all the questions stimulated by accepting the uncaused existence of the physical world — Why is it here? How did it come about? and, of course, What caused it? — can as easily and appropriately be asked of God. Why is God here? How did He come about? What caused Him? (This reflexive tack is not unrelated to the childhood taunt of "What about your mama?" Rather, it's "What about your papa?") The cogency of this sort of response to the first-cause argument is indicated by Saint Augustine's exasperated reaction to a version of it. When he was asked what God was doing before He made the world, Augustine supposedly answered, "He was creating a hell for people who ask questions like that."

A related objection to the argument is that the uncaused first cause needn't have any traditional God-like qualities. It's simply first, and as we know from other realms, being first doesn't mean being best. No one brags about still using the first personal computers to come on the market. Even if the first cause existed, it might simply be a brute fact — or even worse, an actual brute.

Furthermore, efforts by some to put God, the putative first cause, completely outside of time and space give up entirely on the notion of cause, which is defined in terms of time. After all, A causes B only if A comes before B, and the first cause comes — surprise — first, before its consequences. (Placing God outside of space and time would also preclude any sort of later divine intervention in worldly affairs.) In fact, ordinary language breaks down when we contemplate these matters. The phrase "beginning of time," for example, can't rely on the same presuppositions that "beginning of the movie" can. Before a movie there's popcorn-buying and coming attractions; there isn't any popcorn-buying, coming attractions, or anything else before the universe.

The notion of cause has still other problems. It is nowhere near as clear and robust as it was before the eighteenth-century Scottish philosopher David Hume and twentieth-century quantum mechanics finished qualifying it. Hume argued that the phrase "A causes B" means nothing more than "A has been followed by B in every instance we've examined." Every time we've dropped the rock, it's fallen. Since it's quite easy to imagine our dropping of the rock not being followed by its falling, however, the connection between cause and effect cannot be a logically necessary connection. The link between an event and its causes is contingent and rather squishy. We can't move as confidently from an event to its cause(s) as we might have believed. Causes are discoverable by experience, but not by armchair a priori reasoning, making "cause" much less sturdy a notion than the first-cause argument presupposes. Constructing a structure out of steel is much easier than building one out of noodles, and arguments are metaphorically somewhat similar.

And if to Hume's and other modern accounts of causality and scientific induction we add the implication of quantum mechanics that "cause" at the micro level is at best probabilistic (not to mention all the quantum weirdnesses that have been cataloged by physicists), the first cause argument loses much of its limited force. In fact, some versions of quantum cosmology explicitly rule out a first cause. Other accounts imply that the Big Bang and the birth of universes are recurring phenomena.

Interestingly, the so-called natural-law argument for the existence of God has a structure similar to the first-cause argument and is thus vulnerable to a similar bit of jujitsu. It can even be explained to the chattering little offspring in the backseat. He is the one who asks, "Why is that, Daddy?" and responds to your explanation with another "Why?" He then responds to your more general explanation with "Why?" once again, and on and on. Eventually you answer, "Because that's the way it is." If this satisfies the kid, the game is over, but if it goes on for another round and you're a religious sort, you might respond with "Because God made it that way." If this satisfies, the game is over, but what if the kid still persists?

Phrased a bit more formally, the natural-law argument points to the physical regularities that have been laboriously discovered by physicists and other natural scientists and posits God as the lawgiver, the author of these laws. Whatever power the argument has, however, is greatly diminished by asking, as the endearingly curious kid might, why God "made it that way." That is, why did He create the particular natural laws that He did? If He did it arbitrarily for no reason at all, there is then something that is not subject to natural law. The chain of natural law is broken, and so we might as well take the most general natural laws themselves, rather than God, as the arbitrary final "Because." On the other hand, if He had a reason for issuing the particular laws that He did (say, to bring about the best possible universe), then God Himself is subject to preexisting constraints, standards, and laws. In this case, too, there's not much point to introducing Him as an intermediary in the first place.

Still, philosophers ranging from Aristotle to Aquinas to Gottfried Leibniz have insisted that something must explain the universe — its laws and even its very existence. Leibniz famously and succinctly asked, "Why is there something rather than nothing?" Indeed, why is there stuff? Invoking his principle of sufficient reason, which states that there must be sufficient reason (or cause) for every fact, he answered his own question. The sufficient reason for the universe, he stated, "is a necessary Being bearing the reason for its existence within itself." The necessary being is God, the first cause, who caused or brought about not only the physical world but also somehow Himself.

This suggests that one reasonable reaction to these refutations of the first-cause and natural-law arguments is to question Assumption 2 that nothing is its own cause. Some have tried to make logical sense of the first cause causing not only the second cause(s) but also itself or, analogously, the most general law explaining not only the next most general law(s) but also itself. The late philosopher Robert Nozick considers such self-subsumptive principles in his book Philosophical Explanations. There he entertains the idea of an abstract self-subsumptive principle, P, of the following type: P says that any law-like statement having characteristic C is true. Principle P is used to explain why other, less general laws hold true. They hold true because they have characteristic C. And what would explain why P holds true? A possible answer might be that P itself also has characteristic C. In short, P, if true, would explain itself.

Even Nozick acknowledged that this "appears quite weird — a feat of legerdemain." Still, there are not many alternatives. The chain of causes (laws) is either finite or infinite. If it's finite, the most basic cause (most general law) is either a brute, arbitrary fact or self-subsuming. Nozick also wrote of certain yogic mystical exercises that help to bring about the experiential analogue of self-subsumption. He theorized that "one of the acts the (male) yogis perform, during their experiences of being identical with infinitude, is auto-fellatio, wherein they have an intense and ecstatic experience of self-generation, of the universe and themselves turned back upon itself in a self-creation." This isn't the traditional image of the Creator, and, if so moved, the reader may supply his own joke here.

The Argument from Design (and Some Creationist Calculations)

The trees swaying in the breeze, the gentle hills and valleys, the lakes teeming with fish, are all beautifully exquisite. How could there not be a God? One of the most familiar sentiments behind arguments for the existence of God, this one points to the complexity and/or purpose inherent in nature. So-called teleological arguments (or arguments from design) vary slightly in form, but all attribute this perceived purpose or complexity to a divine creator. This is their basic structure:

1. Something — the diversity of life-forms, the beauty of the outdoors, the stars, the fine structure constants — is much too complex (or too perfect) to have come about randomly or by sheer accident.

2. This something must have been the handiwork of some creator.

3. Therefore God, the Creator, exists.

An alternative version points to the purpose that some see permeating nature:

1. The world in general or life-forms in it seem to be evidence of clear intention or direction.

2. There must be an intender or director behind this purpose.

3. This entity must be God, and therefore God exists.

I should first mention that there are unobjectionable uses of teleological explanations, ones that make reference to purpose and intention, especially when such explanations can be easily reformulated in nonpurposive terms. For example, "The thermostat is trying to keep the house at a steady temperature" can be rephrased in terms of metals' differential rates of expansion. When it gets hot, this metal expands faster than the other one and tips a switch turning the furnace off, and when it gets cool, the metal contracts faster, turning the furnace back on. No one is really attributing intentionality to the metals.

The teleological argument dates back to the Greeks, but probably its best-known proponent is the English theologian William Paley, whose watchmaker analogy is often cited by creation scientists and others. Paley asks us to imagine wandering around an uncultivated field and coming upon a watch lying on the ground. He compares evidence of design in the watch, which all would certainly acknowledge, to the evidence of design in nature — plants, animals, and the like. Just as the watch clearly had a human creator, Paley argues, the designs in nature must have had a divine creator. (Exclaiming "Oh my God!" upon discovering a gold Rolex next to some beautiful flowers does not count in the argument's favor.)

Interestingly, this watch analogy goes back even further, to Cicero, whose clocks, however, were sundials and water clocks. Watches with simple quartz and silicon components and their future refinements might also be cited. Although all these timekeeping devices could be taken to be something else (the latter might be confused, for example, with sand on a beach), people are familiar with their own cultural artifacts and would still recognize their human provenance. We know what humans make, but no such familiarity can be assumed with the alleged divine artifacts.

The most glaring weakness in teleological arguments is, however, Assumption 1. What is the probability of such complexity? How do we know that something is too complex to have arisen by itself? What is the origin of this complexity? Creationists explain what they regard as the absurdly unlikely complexity of life-forms by postulating a creator. That this creator would have to be of vastly greater complexity and vastly more unlikely than the lifeforms it created does not seem to bother them. Nonetheless, it's only natural to ask the same question of the creator as one does of the alleged creations. Laying down a recursive card similar to that played with the first-cause argument, we ask about the origin of the creator's complexity. How did it come about? Is there a whole hierarchy of creators, each created by higher-order creators and all except for the lowliest, ours, creating lower-order ones?

Let me underline this last irreligious bit in a slightly different manner. If a certain entity is very complex and it's deemed extraordinarily unlikely that such complexity would have arisen by itself, then what is explained by attributing the entity's unlikely complexity to an even more complex and even more unlikely source? This creationist Ponzi scheme quickly leads to metaphysical bankruptcy.

I remember the girlfriend of a college roommate who had apparently misunderstood something she'd read on mnemonic devices. To memorize a telephone number, for example, she might have recalled that her best friend had two children, her dentist had five, her camp roommate three, her neighbor on one side had three dogs, the one on the other side seven cats, her older brother had eight children if you counted those of his wives, and she herself was one of four children. The telephone number must be 253-3784. Her mnemonics were convoluted, inventive, amusing, unrelated to any other structure, and always very much longer than what they were designed to help her remember. They also seem to make the same mistake creationists make when they "explain" complexity by invoking a greater complexity.

The beguiling metaphor that the argument from design appeals to can also be phrased in terms of a large Lego model of, say, Notre Dame Cathedral. If one came upon it, one would be compelled to say that the blocks were put together by intelligent humans. Furthermore, if the model was taken apart and placed in a large bag and the bag was shaken for a long time, one would be quite resistant to the idea that the Lego pieces would fashion themselves into a cathedral again.

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Excerpted from Irreligion by John Allen Paulos. Copyright © 2008 John Allen Paulos. Excerpted by permission of Hill and Wang.
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