Why Does the World Exist?: An Existential Detective Story (8 page)

If a cinematic example is too fanciful for you, consider a more austere, scientific one. Suppose the world consisted of just two objects, an electron and a positron in mutual orbit. Relative to this “pair world,” is there a possible “singleton world” in which only the positron exists? One might think so. But the move from the pair world to the singleton world would violate one of the bedrock principles of physics: the law of charge conservation. The net charge of the pair world sums up to zero, since the positron has charge +1 and the electron has charge –1. The net charge of the singleton world is +1. So moving from the pair world to the singleton world is tantamount to the creation of a net charge—a physical impossibility. Although the electron and positron are individually contingent, each is existentially linked to the other by the law of charge conservation.

Then how about moving from the pair world directly to nothingness? Alas, that’s not physically possible either, for eliminating the electron-positron pair would violate another bedrock principle of physics: the law of mass-energy conservation. Some new entity—a photon, say, or another particle-antiparticle pair—would have to appear in their wake, as a matter of physical necessity.

The hitch here seems to be the same one that both Bergson and Rundle encountered, but in a different guise. In all three cases, absolute nothingness is thought of as a
limit
, one to be approached from the world of being. Bergson tried to approach it by imaginatively annihilating the contents of the world, only to be left with his own consciousness. Rundle tried a similar imaginative route and also fell short of the goal, ending up with an empty spatial container. Both concluded that absolute nothingness was inconceivable. The subtraction argument tries a different tack, seeking to reach nothingness via a series of logical moves. But the reasonable-sounding intuition behind the subtraction argument—
if there are some objects, there could have been fewer of them
—runs afoul of a set of fundamental physical principles: the laws of conservation. And even if those laws were somehow suspended, it is by no means clear that the world’s ontological census could be steadily reduced by decrements of one, all the way down to zero. Perhaps the absence of one thing, in either imagination or reality, always entails the presence of another. Delete George Bailey from the scheme of things and up pops Pottersville.

The apparent moral is this: it’s no simple matter to get from Something to Nothing. The approach is asymptotic at best, always falling short of the limit, always leaving some remainder of being, however infinitesimal. But is that surprising? To succeed in reaching Nothing from Something, after all, would be to solve the riddle of being in reverse. Any logical bridge from one to the other would presumably permit two-way traffic.

If it seems easier in the imagination to get from Something to Nothing than the reverse, that’s because both the starting point and the terminus are known in advance. Suppose you sit down at a computer terminal in the reading room of the New York Public Library on Forty-second Street. There’s a single character on the screen—say, “$.” You press the
delete
button, and the screen becomes blank. You have effected a transition from Something to Nothing. Now suppose you happen to sit down at a terminal with a blank screen. How do you go from Nothing to Something? By pressing the
undelete
button. When you do so, however, you have no idea what will appear on the screen. Depending on what the previous user was up to, it could be a lapidary message or a mere jumble of characters. The transition from Nothing to Something seems mysterious, because you never know what you’re going to get. And the same is true at the cosmic level. The Big Bang—the physical transition from nothing to something—was not only inconceivably violent, but also inherently lawless. Physics tells us that there is in principle no way of predicting what might pop out of a naked singularity. Not even God could know.

Instead of struggling to cross an impassable conceptual divide between Something and Nothing, it might be more profitable to forget about the world of being and concentrate on nothingness instead. Can absolute nothingness be coherently described, without falling into some kind of contradiction? If it can be, this might raise our confidence that it’s a genuine metaphysical possibility.

But defining absolute nothingness can be a tricky business. As a first shot, one might start with this proposition:

Nothing exists.

Translated into formal logic, this becomes:

For every
x
, it is not the case that
x
exists.

Already we have a problem: “exists” does not name a property, one that things might either have or fail to have. It makes sense to say, “Some tame tigers growl and some do not.” But it makes no sense to say, “Some tame tigers exist and some do not.”

If we limit ourselves to proper predicates—“is blue,” “is bigger than a breadbox,” “is smelly,” “is negatively charged,” “is all-powerful,” and so forth—then the task of defining absolute nothingness appears to become much messier. Now we need an unbounded, perhaps infinite list of propositions to pin down the null possibility: “There is nothing that is blue,” “There is nothing that is smelly,” “There is nothing that is negatively charged,” and so forth. Each of these propositions has the form:

For every
x
, it is not the case that
x
is
A.

Or, more concisely:

There are no
A
s.

Each proposition in the list will rule out the existence of all objects with a certain property: all blue things, all smelly things, all negatively charged things, and so on.

If our list of nonexistents contains a proposition for every metaphysically possible property, then we will have succeeded in defining absolute nothingness by this
via negativa
. But how can we be sure that the list is exhaustive? A single omission will defeat the nullity project, by allowing the existence of some category of objects that either we forgot about or that is currently beyond our imagination. If we were drawing up the list a century ago, for example, we would have left off the proposition “For every
x
, it is not the case that
x
is a black hole.”

One might try to get around this problem of exhaustiveness by dividing all possible types of things into a few fundamental categories. Descartes, for example, divided the world of being into just two kinds of substance: minds, whose essence is thought, and physical bodies, whose essence is extension. So we might try to define absolute nothingness by the pair of propositions “There are no mental things” and “There are no physical things.” This neat pair would rule out the existence of consciousness, souls, angels, and deities, along with electrons, rocks, trees, and galaxies. But would it rule out the existence of mathematical entities, like numbers? Or abstract universals, like justice? Such things seem to be neither mental nor physical, yet their existence would certainly seem to spoil the state of absolute nothingness. And there may be a whole range of other possible substances, other species of being, undreamt of either by Descartes or by us.

There is one property, however, that every conceivable object, whether animal, vegetable, mineral, mental, spiritual, mathematical, or anything else, is guaranteed to possess. And that is self-identity. I have the property of being me. You have the property of being you. And so on. Indeed, “identity” is defined in logic as the relation that each and every thing bears to itself and to no other thing. In other words, it is a logical truth that:

For every
x
,
x
=
x
.

To exist, therefore, is to be self-identical.

With the identity relation, the statement “Something exists” becomes:

There is an
x
such that
x
=
x.

So, to capture absolute nothingness in the trap of logic, all we have to do is negate this assertion. The result is:

It is not the case that there is an
x
such that
x = x
.

Or, equivalently:

For every
x
, it is not the case that
x = x.

In English, this says, “Everything fails to be self-identical.” The proposition is even more lapidary when expressed in the symbols of formal logic:

(
x
) ~ (
x = x
).

(The symbol “(
x
)” is the universal quantifier, to be read as “for every
x
,” and “~” is the negation operator, to be read as “it is not the case that.”)

So there it is, a neat little logical glyph that says, Absolutely nothing exists. But is there a possible reality that makes it true? One prominent American philosopher, the late Milton Munitz, insisted that there is not. In his book
The Mystery of Existence
, Munitz argued that the proposition asserting that something exists—“There is an
x
such that
x
is identical to itself”—is a truth of logic. Therefore, he claimed, its negation—my neat little glyph above—is “
strictly meaningless
.”

Munitz is correct, but in a rather trivial sense. Logicians, in order to streamline their formal systems, routinely rule out nothingness. They assume that there is always at least one individual in the universe of discourse. (This makes it easier to define truth, among its other advantages.) With this expedient, the proposition “There is an
x
such that
x
is self-identical” becomes a logical truth. But it is an artificial one. As Willard Van Orman Quine, the dean of twentieth-century American philosophy, pointed out, the stipulation of a nonempty domain is “
strictly a technical convenience
.” It carries with it “no philosophical dogma about necessary existence.” Bertrand Russell went further, regarding the conventional assumption of existence as something of a blot on logic.

To get rid of this blot, logicians who agree with Russell have invented an alternative system of logic, one that does allow for the possibility of nothingness. Such a system is called “universally free logic,” because it is
free
of existence assumptions about the
universe
. In a universally free logic, the empty universe is permitted, and statements asserting the existence of something or other—statements like “There is an object which is self-identical”—cease to be logical truths.

As Quine discovered, there is a remarkably easy test for truth and falsity in the empty universe. All
existential
propositions—that is, propositions beginning “There is an
x
such that …”—are automatically false. On the other hand, all
universal
propositions—those beginning “For every
x
…”—are automatically true. Why should all universal propositions be true in an empty universe? Well, take the proposition “For every
x, x
is red.” In a world of no objects, there are certainly no objects that fail to be red. Hence, there are no counterexamples to the claim that everything
is
red. Such universal propositions are thus said to be
vacuously
true. Quine’s truth test for the empty universe is a wonderful thing—or, as he preferred to put it, “
a triumph of triviality
.” It can decide the truth of any proposition, even very complex ones. (If the proposition has both existential and universal components connected by “and” or “or,” you simply apply the method of truth tables, originally invented by Wittgenstein and now familiar to every student of elementary logic.) It settles, in a consistent way, what would be true and false in an empty universe—that is, in a state of absolute nothingness. It shows that no contradiction can be derived from the assumption that nothing exists. And this is very interesting to the metaphysical nihilist. It means that absolute nothingness is self-consistent! Contrary to what so many skeptical philosophers have believed, it is a genuine logical possibility. We may not be able fully to conceive it in our imagination, but that does not mean there is anything paradoxical about it. It may sound preposterous, but it is not absurd. Logically speaking,
there might have been nothing at all
.

Let’s call this possible reality the Null World, making sure to remember that it’s a “world” only by ontological courtesy, as it were. Unlike other possible worlds, it involves no spacetime, no container or stage or arena of any sort. When we talk about “it,” we’re not taking about any kind of object; we’re merely talking about one of the various ways reality might have turned out—a way neatly captured by the formula

(
x
) ~ (
x = x
).

And this formula is not itself part of the Null World—absolutely nothingness would forbid that! It is merely our way of referring to the Null World, of logically encoding what it means for nothing whatever to exist.

Logical consistency is a great virtue. But it’s not the only virtue possessed by the Null World. Nothingness is also, as Leibniz was the first to point out, the
simplest
of all possible realities. Simplicity is greatly prized in science. When rival scientific theories are equally supported by the evidence, it is the simplest of them—the one that postulates the fewest causally independent entities and properties, the one least susceptible to a trimming by Occam’s razor—that scientists favor. And this is not just because simpler theories are prettier, or easier to use. Simplicity is held to be a marker of intrinsic probability, of truth. It is complex realities that are thought to stand in need of explanation, not simple ones. And no possible reality is simpler than the Null World.

The Null World is also the
least arbitrary
one. Having no objects at all, its census is a nice round zero. Any alternative world will have a nonzero census. It may contain a finite number of individuals, or it may contain an infinite number. Now, unless you are a numerologist, any finite number is bound to look arbitrary. Our own universe, for instance, seems to consist of a finite population of elementary particles (the number of which is estimated to be around 10 followed by eighty zeros). In addition, there may be nonphysical individuals hanging around, like angels. If you added all these objects up, the total census of the actual world would look like a very long odometer reading on your dashboard—lots and lots of arbitrary digits. It would seem just as arbitrary if the world contained a smaller number of objects, like seventeen. Even an infinite world would be arbitrary. For there is not just one size of infinity, but many sizes—infinitely many, in fact. Mathematicians denote the different sizes of infinity by using the Hebrew letter aleph: aleph-0, aleph-1, aleph-2, and so on. If our own world turns out to have an infinite census of objects, why should it be, say, aleph-2 rather than aleph-29? Only the Null World escapes this kind of arbitrariness.