has an instance—and so here we do not escape the conceptual order. The Pegasus
argument from perfection, Descartes might say, falls to the Caterus objection. But if
Descartes cannot support his claim that God's nature includes existence without
independent a priori proof that God exists, Gassendi is right that it begs the question.
end p.103
Leibniz
Leibniz worked intensely on arguments from perfection in the 1670s. He held that
Descartes' argument was valid but incomplete, needing the addition of a proof that it is at
least possible that God exists. His own preferred argument was modal:
If a being from whose essence existence follows is possibleit existsGod is a being from
whose essence existence followsTherefore if God is possible, He exists. (Adams 1994,
137, n.9)
“A being from whose essence existence follows” is just a necessary being. So Leibniz's
argument is really that
If possibly a necessary being exists, it exists.
God is by nature a necessary being. So
If possibly God exists, God exists.
The first premise is just an instance of the characteristic axiom of the Brouwer system of
modal logic; the argument is sound in Brouwer. The conclusion leaves Leibniz's case for
God incomplete, needing, as Leibniz said of Descartes, a proof that possibly God exists.
Leibniz tries to provide one.
Leibniz's possibility-argument (Plantinga 1965, 54–56) treats God as the being whose
nature is a conjunction of all and only perfections, perfections being properties that are
“simple,” “positive,” and “absolute.” Simple properties do not consist of other properties.
They are primitive. Positive properties are those whose natures do not include the
negation of other properties. If the property F is a constituent of the property ¬F, every
simple property is positive. Positive properties needn't be simple, though. F • G is a
positive property if F and G are positive. A property is absolute if and only if its nature
involves no limitations of any sort. Leibniz's argument, then, is in essence this: it's
possible that God exist just in case all properties in the nature He'd have if actual are
compatible. But if properties are simple, they cannot be incompatible because properties
of which they consist are incompatible. If properties are positive, their natures do not
include the negations of other properties. That is, for all FG, if F and G are positive, F's
nature is not and does not include not having G, and G's is not and does not include not
having F. But properties F and G are incompatible, thinks Leibniz, only if F includes ¬G,
G includes ¬F, some property F includes includes ¬G, or some property G includes
includes ¬F. Thus, if any absolute properties are simple and positive, they are compatible.
Leibniz's argument raises a number of questions: Are there simple, absolute, positive
qualities? Do they include necessary existence? Do they include colors,
end p.104