Why Does the World Exist?: An Existential Detective Story by Jim Holt

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