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

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