Why Does the World Exist?: An Existential Detective Story

by Jim Holt

  But the notion that reality could embrace both being and nothingness struck me as wrong-headed, and I said so to Parfit. How could it make sense to talk of adjoining a “world of nothing” to an ensemble of something-worlds? It would not be like adding a barren planet, or a region of empty space. For a barren planet is something. And so, pretty much everyone agrees, is a region of empty space. Space has features. It can, for example, be either finite or infinite in extent. Nothingness is not like that.

  I wanted to put the point in the form of an equation:

  Something + Nothing = Something

  But even that seemed too weak. To add “nothing” to a cosmic possibility was an empty gesture. It was to do nothing at all.

  Parfit agreed. Nozick and the others were wrong, he believed. Nothingness is not a local possibility; it cannot be one world among many. The only reality consistent with Nothingness is the reality consisting of no worlds at all: the Null Possibility. You can have two different somethings, but you can’t have both something and nothing. It’s strictly an either/or deal.

  My second question for Parfit was a deeper one. Suppose he was right in thinking that what he called a Selector might yield the explanation for why reality took the particular form that it did. Would that be the end of the matter? Does cosmic explanation stop at the Selector level? Or could there be a further explanation as to why some particular Selector, among all the other plausible rival Selectors, prevailed?

  Think again of the analogy to the Miss Cosmos Pageant. The contestants are all the conceivable ways reality might have been—all the cosmic possibilities. One of these contestants has to be crowned the winner. Suppose the winner turns out to be the ethically best cosmic possibility: Miss Infinitely Good. Then we might suspect that the judges used goodness as the Selector: that, after all, would explain the choice of Miss Infinitely Good as the winner. But couldn’t we go on to ask why the judges used goodness as their Selector rather than, say, simplicity, elegance, or fullness?

  On the other hand, suppose the winner of the Miss Cosmos Pageant turned out to have no special features. Suppose it was Miss Mediocre. Then we might conclude that the judges didn’t use any Selector at all. They didn’t care about what the contestants were like, what their special virtues might be. They simply drew straws. But couldn’t we go on to ask why the pageant’s judges didn’t bother to use a Selector to choose the winner?

  Parfit acknowledged the need for further cosmic explanation. “Reality may happen to be as it is, or there may be some Selector,” he had written. “Whichever of these is true, it may happen to be true, or there may be some higher Selector. These are the different possibilities at the next explanatory level, so we are back with our two questions: which obtains, and why?”

  So first you need a Selector to explain why reality is the way it is. Then you need a meta-Selector at the next explanatory level to account for why that Selector was the operative one in choosing how the world turned out. And then you need a meta-meta-Selector at a still higher explanatory level to account for why that meta-Selector was tapped. And so on. Could this explanatory regress ever come to an end? And, if so, how could it end? With some highest Selector? Then wouldn’t that be the ultimate brute fact?

  When I put this question to Parfit, he conceded that the quest to explain reality would likely end with such a brute fact. How could this be avoided? You might try to avoid it by saying that a Selector could select itself. For instance, if goodness proved to be the highest Selector, one might try to say that this is true because it’s for the best. That is, goodness chose itself as the ruler of reality. But Parfit didn’t buy that. “Just as God could not make himself exist, no Selector could make itself the one that, at the highest level, rules,” he maintained. “No Selector could settle whether it rules, since it cannot settle anything unless it does rule.”

  Nonetheless, Parfit insisted, an explanation that ends with a brute fact is better than no explanation at all. Indeed, he observed, scientific explanations invariably take this form. Such an explanation can still help us to discover what reality, on its grandest scale, might actually be like—say, by giving us a reason to believe that reality comprises worlds beyond our own.

  As Parfit sipped his coffee, I brought out a little diagram that I had made over the weekend. It showed how the various Selectors might be related to one another, and to reality. At the bottom of the paper, I had sketched the reality level. There I had set out some of the cosmic possibilities that Parfit had talked about. At the level above that—the first explanatory level—I had jotted down some of the plausible Selectors. And at the level above that—the second explanatory level—I had indicated some of the meta-Selectors. Then I had drawn arrows between the different levels to indicate the various explanatory relationships that might obtain. The diagram looked like the one on the facing page.

  “I see you’ve worked out all the logical implications,” Parfit said as he leaned forward and squinted at my diagram.

  Most of these implications had already been drawn by Parfit himself, and they were pretty straightforward. The Simplicity Selector, for example, picks out Null possibility from among the cosmic possibilities. Thus, if there had been nothing at all, that would have been explained by the fact that nothingness was the simplest way reality might have been.

  Similarly, the Goodness Selector picked out the Axiarchic possibility—a universe consisting only of good worlds. Thus, if reality turns out to take that form, it would be explained by the fact that this was the best way reality could have been. But, if reality did take that form, what could explain the fact that the Goodness Selector ruled? Only that the Goodness Selector, being so good, was itself selected by Goodness at the meta-level. And here, as Parfit had observed, we run into a problem: A Selector cannot select itself. It cannot settle whether it rules unless it does rule. Otherwise put, no explanation of reality is capable of explaining itself.

  To indicate that Goodness could not, on pain of circularity, explain itself, I had drawn an “X” across the arrow leading from Goodness at the meta-Selector level to Goodness at the Selector level.

  But not all Selectors are prone to this sort of circularity. That is, not all Selectors select themselves. And that fact was reflected in what I felt was the most interesting arrow in my diagram: the one that went from Simplicity at the meta-explanatory level to Null at the explanatory level.

  This arrow, too, was inspired by what Parfit had written. At the very end of his “Why Anything?” essay, he had made an alluring observation: “just as the simplest cosmic possibility is that nothing ever exists, the simplest explanatory possibility is that there is no Selector.” I had taken this to mean that the No Selector possibility at the explanatory level is like the Null possibility at the reality level: each would be explained by Simplicity. Then if Simplicity rules at the meta-explanatory level, it would not pick itself as the Selector at the explanatory level. Rather, it would decree that there would be no Selector at all.

  Was this indeed what Parfit meant?

  “That’s right,” he said with a smile.

  And what would reality look like if there were no Selector? Well, it almost certainly wouldn’t take the very special form of nothingness, the emptiest of all cosmic possibilities. “If there is no Selector,” Parfit had written, “we should not expect that there would also be no Universe. That would be an extreme coincidence.” By the same token, it seemed to me, we should not expect it to take any other special form. If there were no Selector, we should not expect reality to be as full as it could possibly be, as good as it could possibly be, as bad as it could possibly be, as mathematically neat as it could possibly be, and so on. Rather, we should expect such a blindly chosen reality to be one of the countless cosmic possibilities that have no special feature at all. In other words, we should expect reality to be thoroughly mediocre. Did Parfit agree with this reasoning?

  He nodded that he did.

  So if Simplicity is the ultimate Selector, this would explai
n why there is something rather than nothing! Heidegger, in his fuddled way, may have had a point after all. Das Nichts selbst nichtet: “Nothing noths itself.” If nothingness prevails at the explanatory level, then there is no Selector explaining the way reality turned out. But if there is no Selector, then the way reality turned out would be a random matter. In that case, it would be exceedingly odd if reality turned out to be nothingness. For the Null Possibility is a very special outcome, being the simplest of all cosmic possibilities. So nothing (at the explanatory level) noths itself (at the cosmic level)—with the upshot that reality comprises something rather than nothing. All by dint of Simplicity ruling at the highest level.

  If Simplicity is the ultimate explanation of things, this would also account for why the actual cosmos seems to be so disappointingly average: an indifferent mixture of good and evil, of beauty and ugliness, of causal order and random chaos; inconceivably vast, yet falling well short of the full cornucopia of possible being. Reality is neither a pristine Nothing nor an all-fecund Everything. It’s a cosmic junk shot.

  Such was the conclusion that I had teased out of Parfit’s scheme. But, frustratingly, it still fell short of being a complete explanation. If Simplicity did indeed rule at the highest level, did this merely happen to be true? What about rival meta-Selectors, like Fullness? (I had put a question mark under it on my diagram.) And what if there were no meta-Selector at all? (Another question mark on my diagram.) Was the most general explanation of reality doomed to end with an inexplicable brute fact?

  Parfit had done his bit. He had dispelled much of the fog surrounding the mystery of existence. And he had given me a very nice lunch in the bargain. It was time for him to return to his study, where he would reimmerse himself in questions of moral philosophy, of values and desires and reasons. And it was time for me to leave the rarefied cloister of All Souls and return to the rude world of Vile Bodies.

  I thanked Parfit effusively, saw myself to the college gate, and turned onto the High Street, whose shadows were lengthened by the late-afternoon sun.

  A WEEK LATER I was back in New York, still vexing over the now-crumpled diagram I had shown to Parfit. Then, walking one evening in the tonic squalor of the East Village, a million miles from All Souls, I had an epiphany. The last piece of logic snapped into place. I had the proof.

  Epistolary Interlude

  The Proof

  Wednesday morning

  2 Fifth Avenue, New York

  Dear Professor Parfit,

  It was so nice spending the afternoon with you at All Souls. In reflecting on our conversation, I think I may have hit upon a complete and unique explanation for the most general form reality takes—an explanation that finally resolves the question, Why is there something rather than nothing?

  I begin by assuming two principles:

  (I) For every truth, there is an explanation of why it is true.

  (II) No truth explains itself.

  The first of these, of course, is what Leibniz called the Principle of Sufficient Reason. It says that there are no brute facts. I take Sufficient Reason to be not so much a truth in itself, but rather a provisional guide to inquiry, one that says, “Always look for an explanation unless you find yourself in a situation where further explanation is impossible.”

  The second principle is a more general version of your point that no Selector can select itself. It is meant to rule out circularity. A cause cannot cause itself. A rationale cannot justify itself. God cannot create himself. A set cannot be a member of itself. In set theory, this is called the Axiom of Foundation. So I’ll call principle (II) “Foundation.”

  Now here’s the argument that there is one, and only one, complete explanation for the form that reality takes.

  At level 0, the level of reality, you have all the “cosmic possibilities” for how reality might have turned out. These range from the Null possibility to the All Worlds possibility, and they include every one of the countless intermediate possibilities, where some conceivable worlds of some types exist, but not others. One of these cosmic possibilities has to obtain, as a matter of logical necessity. Call the cosmic possibility that actually does obtain A, for “actual.”

  At level 1, the lowest explanatory level, you have all the plausible Selectors—all of the possible explanations that might account for the way reality at level 0 turns out. These include Simplicity, Goodness, Causal Orderliness, and Fullness, as well as the No Selector possibility—the possibility that there is no explanation at all.

  At level 2, the meta-explanatory level, you have all the plausible meta-Selectors—all of the possible explanations that might account for which Selector prevails at level 1. These include—again—Simplicity, Goodness, Causal Orderliness, and Fullness, as well as the No Meta-Selector possibility.

  Now let’s consider some cases.

  First, suppose that no Selector explains why reality takes the form it does, and that there is no further explanation for why there is no Selector. Then it is a brute fact that reality takes the form A. But this violates Sufficient Reason. Dead end.

  Next, suppose that one of the Selectors at level 1 does explain why reality takes form A. Call this Selector S. Then either there is an explanation for why S prevailed in determining reality, or there isn’t. If there isn’t, then it is a brute fact that S is the Selector. But this violates Sufficient Reason. Dead end.

  So suppose there is an explanation for S being the Selector. In other words, suppose there is a meta-Selector (at level 2) that selected S (at level 1). Call this meta-Selector M.

  Now ask, What could M be?

  We know that M could not be the same as S. That would violate the Principle of Foundation. For instance, if S were Goodness (in which case reality would have taken the ethically best possible form), the explanation for that could not be that it is ethically best that Goodness should be the Selector. The same goes for the other Selectors that pick out cosmic possibilities intermediate between the Null possibility and the All Worlds possibility—like the Causal Orderliness Selector, or the Mathematical Elegance Selector, or the Evil Selector. These Selectors all select themselves at the meta-level, and that is circular.

  In fact, only two meta-Selectors at level 2 could serve as M. These are Simplicity and Fullness. Neither of these selects itself, and hence neither violates the Principle of Foundation. If Simplicity were the meta-Selector that prevailed at level 2, it would not select itself at level 1. Rather, it would select the No Selector possibility, since that is the simplest of the explanatory possibilities—that there is no explanation. And if Fullness were the meta-Selector that prevailed at level 2, it would not select itself at level 1. Rather, it would select all the Selectors at level 1.

  Thus, assuming the Principle of Foundation, it is a logical truth that there are only two possible meta-Selectors at level 2: Simplicity and Fullness. One or the other of them has to constitute the ultimate explanation.

  So there are two cases left to consider.

  Case 1: Simplicity is the meta-Selector. Then it would pick out the No Selector possibility at level 1 (just as Simplicity at level 1 would pick out the Null possibility at level 0). But if there is no Selector at level 1, then A, the cosmic possibility that reality takes, would be randomly picked, a matter of pure chance. Yet this would not be a brute fact; rather, it would be explained by Simplicity at the meta-explanatory level.

  Case 2: Fullness is the meta-Selector. Then it would pick out all the Selectors at level 1 (just as Fullness at level 1 would pick out the All Worlds possibility at level 0). But it is logically impossible for all Selectors at level 1 to dictate the form reality takes. That is because they contradict one another. Reality cannot be perfectly full and perfectly empty at the same time. Nor can it be ethically the best and causally the most orderly at the same time (since the occasional miracle could make reality better). And it certainly can’t be the ethically best and the most evil at the same time. At most, the Selectors at level 1 could all operate together only
as partial Selectors. Then A, the cosmic possibility selected at level 0 to be reality, would be thoroughly mediocre. It would be as full and as empty as possible, as good and as evil as possible, as orderly and as chaotic as possible, as elegant and as ugly as possible, and so on.

  In case 1, A would be chosen at random from among the cosmic possibilities. In case 2, A would be the most mediocre of the cosmic possibilities. These are the only level 0 reality outcomes that are consistent with the principles of Sufficient Reason and Foundation. And they are overwhelmingly likely to amount to the same thing! A cosmic possibility chosen at random is overwhelmingly likely to be thoroughly mediocre.

  This is a matter of sheer numbers. Of all the possible forms reality might take, only a vanishingly small proportion of them possess special features—like being perfectly simple, or perfectly good, or perfectly full. The vast majority have no special feature at all. They are generic realities.

  And what would such a generic reality look like? First of all, it would be infinite. Realities consisting of infinitely many worlds are vastly more numerous than those consisting of finitely many worlds. (This, of course, follows from an elementary result in set theory. The number of finite subsets of the natural numbers, though infinite itself, is of a smaller order of infinity than the number of infinite subsets of the natural numbers.)

  But even in its infinity, a generic reality would fall far short of encompassing everything possible—infinitely short, in fact. (In set-theoretic terms, the complement of an infinite generic reality is also infinite.) A generic reality is thus infinitely removed from the All Worlds Possibility as well as from the Null Possibility.