God Has Too Many Attributes to Exist

October 31, 2018

The following article originally appeared in the July/August 2011 edition of The American Rationalist.

At the beginning of any discussion of the (non) existence of God, one might do well to dismiss Stephen Jay Gould’s notion of “non-overlapping magisteria,” that is, the idea that those things with which science concerns itself and those things with which religion concerns itself are two wholly distinct realms into which reality, in some inexplicable fashion, has been carved. The argument for the nonintersection of these realms is tantamount to claiming that since such religious assertions as the existence of God are not approachable by the methods of scientific inquiry, they are, in effect, exempt from scrutiny and perhaps (in some people’s minds) are even demanding of one’s unquestioning belief.

That this is preposterous is practically self-evident. If the claims of religion reside wholly in supernatural realms not reachable by science, then they cannot impinge upon human experience. If they did, they would become part of the natural world and would then come under the microscope after all. If they cannot impinge upon our experience, there is no excuse for our acting as if our lives were informed by such matters. By definition, we cannot know (or care) about anything supernatural without granting admission to the supernatural into the world of sense data and defensible inference.

Richard Dawkins has argued at length and, one may say, with considerable success in The God Delusion that the hypothesis that God exists is not only a legitimate scientific hypothesis (i.e., a hypothesis that one may interrogate by way of the scientific method and the power of logic) but one that we may readily establish to be exceedingly improbable. His argument is essentially that any God capable of creating the universe in which we live, with all its observable complexity (ironically often cited as a reason to believe in God), would have to be even more complex than the universe itself, so that if one can posit the uncaused existence of such a God, one should encounter no difficulty in thinking that the universe itself, rather than God, has always existed without prior cause or beginning. (Indeed, the whole notion that the universe must have had a beginning is due only to the shabbiest and most unimaginative of analogies. The fact that a symphony or a baseball game or a novel has to have a beginning scarcely implies that the same is true for the universe.) Dawkins’s argument with regard to probability can be extended in the following way. When one is pondering the existence or nonexistence of entities belonging to some unexplored or little-explored realm of consideration, the sort of realm that God, were he to exist, must surely inhabit, a simple principle to keep in mind is that the more attributes such a hypothetical entity possesses, the less likely it is to exist. For example, suppose we hypothesize that there may be, somewhere in the universe, a real, living unicorn. In a cosmos as old and as thermo-chemically complex as our universe, it is quite conceivable that extensive space explorations might in time turn up, on the surface of some distant planet, a shambling creature bearing some semblance of a single horn on some semblance of a head, and we might take this as being respectably close to embodying the notion of a unicorn. If the unicorn’s only postulated attribute is that it should possess a horn on its head, then the probability that such a creature exists would be, if not numerically high, at least not vanishingly small.

But suppose while we are hypothesizing that a unicorn may be running about on some faraway world somewhere, we also specify that the creature is to be pink. Clearly, it requires more desperate speculation to suppose that we might encounter a pink horn-bearing animal someplace than would have been the case had we not added the attribute of pinkness. If we hypothesize that a pink unicorn that speaks French may exist somewhere, or a pink French-speaking unicorn having purple polka-dots, or a pink French-speaking purple polka- dotted unicorn with five legs, or a pink French-speaking purple- polka-dotted five-legged unicorn wearing a green-and-yellow striped bandana, then clearly we are hypothesizing a sequence of creatures whose probability of existence becomes progressively smaller and in fact tends toward zero the more attributes we add. For a much less fanciful example to illustrate the same point, we may turn to what mathematicians call “Goldbach’s conjecture”: the statement, currently never proven nor disproven, that every even number greater than 2, no matter how large, can be written as the sum of two prime numbers. (For example, 40 can be written as 11 + 29, or for that matter as 17 + 23.)

Many millions of even numbers have been tested to see whether they can be written this way, and to date no counter-example has been found, though this proves nothing, because we might not have looked far enough out. Let us speculate that there may be some counter-example, i.e., some even number that cannot be written as the sum of two prime numbers; we will call such a number (which may or may not exist) a “Goldbach exception.” Whatever one can say about this, at least in the absence of any rigorous proof to the contrary, the probability that a Goldbach exception exists is not zero. But suppose we start adding other attributes to the hypothesized number. Suppose we ask whether there exists a Goldbach exception that contains, somewhere in it, the string of digits 4503729.

Clearly, the likelihood that there is a Goldbach exception containing this precise digit string is less than the likelihood that just any old Goldbach exception exists. Suppose we add other attributes—let us ask whether there exists a Goldbach exception containing not only the digit string 4503729 but also, somewhere else, a string of eleven 4s in a row. This of course is more improbable still. And so it goes. The question of God partakes of this logic in much the same way. Dawkins has argued that it is extremely improbable that there exists what one might think of as a “minimal attributes” God—some primordial shudder that consciously got the universe going somehow and then faded into the background to let everything run itself, this being improbable because it would postulate the existence of an uncaused anterior entity more complex than the universe itself.

(Never mind the fact that since matter and energy can neither be created nor destroyed, an ex nihilo creation is essentially unthinkable in the first place.) But if we start adding attributes to this already unlikely “minimal” God, we get things with smaller probabilities still. Suppose, to start with, we hypothesize a God who not only in some fashion started the universe but stuck around to oversee everything. Since the quality of being inclined to function as such an overseer is an attribute, this somewhat more “attributed” God is a notch lower on the probability scale than where we began. Less probable than that is a God who not only started the universe and hung around to watch it develop, but dictated “holy” books to various Bronze Age scribes living on a little planet somewhere in an average galaxy.

Less probable still is a God who started the universe, stuck around, dictated books, and tortured Job on a dung heap as the biblical God is said to have done. Less probable still is a God who also came to Earth in human form (to try to redeem himself, as Jung theorized, for doing such atrocious things to Job). Less probable still is a God who also performed a miracle to alter the laws of biochemistry and cured your Aunt Tillie of her arthritis. Less probable still is God who has all those attributes and also exhorts you to send buckets of money to televangelists. This sequence of sky-dwellers becomes less and less likely as we go; remember, we started with a minimally attributed God who was extremely improbable in the first place. The problem inherent in all this, from the point of view of religionists, is that if one wants there to be a God, one does oneself no favors by loading him up with attributes. Paradoxically (again from the viewpoint of believers), on the one hand the more attributes hypothetical God is imagined to have, the less likely he is to exist; while on the other hand if a believer does not shower attributes upon God, then God is of little use in furthering the believer’s agendas.

Over the centuries, organized religions have, of course, indulged in precisely this sort of attributional proliferation, inventing gods who favor various countries over others, who espouse various specific political causes, who order acts of terrorism, who intercede in countless ways on behalf of those who pray to him, and so on. Yet the more the notion of God is thus embellished, the less probable it is—to the point of vanishingly tiny probability—that there is any validity in the concept whatever. On a practical level, given that there has never been the least shred of evidence for the existence of gods of any description, even those abstract beings with the least attributes, this paradox, for believers, has the potential to be lethal to the enterprise of perpetuating the myth of such purpose-serving gods as people have always insisted on inventing in order to manipulate their fellow humans. In particular, the gods dwelling in “sacred” texts, with their long and tedious narratives of attribution, are in a lot of trouble.