Why Does the World Exist?: An Existential Detective Story Read Online Free Page B

(John Updike was so struck by this scenario that he used it in the conclusion of his novel Roger’s Version as an alternative to theism as an explanation for existence.)
    All that from 0 = 1–1. The equation is more ontologically fraught than one might have guessed.
    Simple arithmetic is not the only way that mathematics can build a bridge between Nothingness and Being. Set theory also furnishes the materials. Quite early in their mathematical education, indeed often in grade school, children are introduced to a curious thing called the “empty set.” This is a set that has no members at all—like the set of female U.S. presidents preceding Barack Obama. It is conventionally denoted by {}, the set brackets with nothing inside of them, or by the symbol Ø.
    Children sometimes bridle at the idea of the empty set. How, they ask, can a collection that contains nothing really be a collection? They are not alone in their skepticism. One of the greatest mathematicians of the nineteenth century, Richard Dedekind, refused to regard the empty set as anything more than a convenient fiction. Ernst Zermelo, a creator of set theory, called it “improper.” More recently, the great American philosopher David K. Lewis mocked the empty set as “ a little speck of sheer nothingness, a sort of black hole in the fabric of Reality itself … a special individual with a whiff of nothingness about it.”
    Does the empty set exist? Can there be a Something whose essence—indeed, whose only feature—is that it encompasses Nothing? Neither believers nor skeptics have produced any strong arguments for or against the empty set. In mathematics it is simply taken for granted. (Its existence can be proved from the axioms of set theory, on the assumption that there is at least one other set in the universe.)
    Let’s be metaphysically liberal and say that the empty set does exist. Even if there’s nothing, there must be a set that contains it.
    Admit that, and a regular ontological orgy gets under way. For, if the empty set Ø exists, so does a set that contains it: {Ø}. And so does a set that contains both Ø and {Ø}: {Ø, {Ø}}. And so does a set that contains that new set, plus Ø and {Ø}: {Ø, {Ø}, {Ø, {Ø}}}. And on and on.
    Out of sheer nothingness, a remarkable profusion of entities has come into being. These entities are not made out of any “stuff.” They are pure, abstract structure. They can mimic the structure of the numbers. (In the preceding paragraph, we “constructed” the numbers 1, 2, and 3 out of the empty set.) And numbers, with their rich web of interrelations, can mimic complicated worlds. Indeed, they can mimic the entire universe. At least they can if, as thinkers like the physicist John Archibald Wheeler have speculated, the universe consists of mathematically structured information. (This view is captured by the slogan “it from bit.”) The whole show of reality can be generated out of the empty set—out of Nothing.
    But that, of course, presumes there is Nothing to start with.

3
    A BRIEF HISTORY OF NOTHING
    Hartley told his Mother, that he was thinking all day—all the morning, all the day, all the evening—“what it would be, if there were Nothing! if all the men, & women, & Trees, & grass, and birds & beasts, & the Sky, & the Ground, were all gone: Darkness & Coldness —& nothing to be dark & cold.”
    —SAMUEL TAYL OR COLERIDGE , letter to Sara (“Asra”) Hutchinson, June 1802 (Hartley was Coleridge’s son.)
    NOTHING! thou elder brother even to shade
That hadst a being ere the world was made,
And (well fixed) are alone of ending not afraid.
    —JOHN WILMO T, EARL OF ROCHESTER, “Upon Nothing”
    Nothing, said Heidegger,
the modernist
eminence,
noths.
    —ARCHILOCHUS JONES, “Metaphysics Explained for You”
    W hat is nothing? Macbeth answered this question with admirable concinnity: “Nothing is, but what is not.” My dictionary puts it somewhat more paradoxically—“ nothing (n.) : a thing