The topic
is the concept of existence, not its fact—not why there's something rather than nothing—but the bare concept brings its own austere
delights. Philosophical problems arise from our conflicting intuitions, but
“existence” is a primitive element of thought because our intuitions of it are
so robust and reliable. Of course, we disagree about whether certain
particulars (such as Moses) have existed and even about whether some general
kinds (such as the real numbers) exist, but disputes don’t concern the concept
of existence itself. If Moses’s existence poses any conceptual problem, it concerns
what counts as being him, not what counts as existence. Adult readers never
seriously maintain that fictitious characters exist; they disagree about
whether a given character is fictitious. Even the question of the existential
status of numbers is a question about numbers rather than about existence. As
will be seen, sometimes philosophers wrongly construe these disputes as being
about existence.
When essay
19.0 asked “Can infinite quantities exist?” existence’s meaning wasn't in play—infinity’s
was. Existence is well-suited for the role as a primitive concept in philosophy
because it is so unproblematic, but it’s unproblematic nature can be thought of
as a kind of problem, in that we want to know why this concept is uniquely
unproblematic. We would at least like to be able to say something more about it
than merely that it’s primitive, but in philosophy, we acquire knowledge by
solving problems, and existence fails to provide any but the unhelpful problem
of its being unproblematic. The problem of infinity provides, in the end, some
purchase on the concept of existence, which concept I assumed in dealing with
infinity.
In one
argument against actual infinity, I proposed as conceptually possible that separate
things might be distinguishable only concerning their being separate things. If we assume that infinite sets can exist, the implication is the
contradiction that an infinite set and its successor—when still another point
pops into existence—are the same set because you can’t distinguish them. (In
technical terms, the only information that could distinguish the set and its
successor, given that their members are brutely
distinguishable, is their cardinality, which is the same—countably infinite—for
each set.)
What’s
interesting is the role of existence,
which imposes an additional constraint on concepts besides the internal
consistency imposed by the mathematics of sets. Whereas we are unable to
distinguish existing points, we are able—in a manner of speaking—to distinguish
points that exist from those that don’t exist. While no proper subsets are
possible for existing brutely distinguishable points, the distinction within the abstract set of points between “those”
that exist and “those” that don’t exist allows us to extend the successor set
by moving the boundary, resulting in contradiction.
If finitude
is a condition for existence, we’ve learned something new about the concept of
existence. Its meaning is imbued with finitude, with definite quantity.
Everything that exists does so in some definite quantity. Existence is that property of conceptual referents such that
they necessarily have some definite quantity.
Existence
is primitive because almost everyone knows the term and can apply it to the
extent they understand what they’re applying it to. The alternative to
primitive existence is primitive sensation, as when Descartes derived his
existence from his “thinking.” But sensationalism
is incoherent; “experiences” inherently lacking in properties (“ineffable”)
are conceived as having properties (“qualia”). The heirs of extreme logical empiricism, from Rudolf Carnap to David Lewis,
have challenged existence’s primitiveness. Carnap defined existence by the
place of concepts in a fruitful theory. Lewis applies this positivist maxim to
conclude that all possible worlds exist. Lewis isn’t impelled by an independent
theory of logical existence, such as a Platonic theory that posits actually
realized idealizations. Rather, the usefulness of possible worlds in logic
requires their acceptance, according to Lewis, because that’s all that we mean
by “exists.” Lewis is driven by this theory of existence to require infinitely
many existing possible worlds, which disqualifies it on
other grounds. But the grounds aren’t separate. When you don’t apply the
constraints of existence because you deny their intuitive force, you lose just
that constraint imposing finitude. The incoherence of
sensationalism and actual infinitism argues for a metaphysics upholding the primacy
of common-sense existence.
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