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§3. The Concept of a Perfection
Leibniz tries to characterize a perfection in the Discourse §. He says:
“One thing which can surely be said about [perfection] is that those forms
or natures which are not susceptible of it to the highest degree, say the
nature of numbers or of ﬁgures, do not admit of perfection.”
Leibniz says that number, with respect to its size (relative to others),
does not admit of perfection: there is no greatest number. The same is
true for area. However, the power and knowledge of God does admit of
perfection, since omnipotence and omniscience are the suitably deﬁned upper limits. Omnipotence is being able to create any possible world, say, and
omniscience is knowing all these worlds (their content and possible history)
down to the last detail, and knowing which world is best and why. Thus
omniscience and omnipotence are perfections of God.
The intuitive idea seems to be that the properties of a thing that render
it more or less perfect must at least be properties that have a natural upper
bound derived from the nature of the property and /or from the nature of
the thing. A property of a thing that may increase beyond any limit (as
given by the nature of that thing) cannot be a perfection. This gives a necessary condition for a perfection.
. Let’s try to get the feel of the intuitive idea by looking at some commonsense examples. First consider artifacts: a perfect watch or a perfect
ruler. A perfect watch keeps accurate (exact) time, down to the least unit
of time that counts for anything. As physics develops, it needs more accurate
watches (such as atomic clocks). A perfect ruler has, say, a perfectly straight
edge marked with perfectly accurate units of length (again modulo what we
can distinguish in practice). There is a concept of a perfectly straight edge
(line) as a limit, but there is not a concept of a perfectly long line, since
length, like area, has no intrinsic upper bound.
Consider next the roles that we assume in certain activities and these
activities themselves. A perfect shortstop makes no errors over a season,
completes all the double plays, and much else, and all this with a certain
grace and style, yet still within the limits of normal human capacity and
skill. A perfect shortstop does not have superhuman quickness, speed, or
throwing arm. Certain constraints and limits are given by the normal range
of human abilities.
We can also form some notion of a perfect baseball game; and this is
different from that of a perfect game of any kind, which is a much more
difﬁcult notion and perhaps so vague as not to be usable. (In baseball, the
term “perfect game” refers to a no-hitter of a certain kind. But this is not
a perfect game! It is too unbalanced in desirable qualities.) Try other notions
of perfection: a perfect piece of music, a perfect sonata, a perfect classical
sonata, a perfect Mozart piano sonata. Or specialize to a perfect opera, a
perfect Italian opera (style), a perfect Verdi opera (individual style), and so
on. Each notion is sharper than the preceding.
. Reviewing these examples shows that the intuitive idea of perfection
seems to be either of the following:
(a) An appropriate balance in how a plurality of criteria are satisﬁed or
exempliﬁed, which balance has a kind of internal limit that arises from the
concept of the object in question together with certain natural constraints.
In this case, should any of the criteria be satisﬁed to a greater or lesser
degree, the balance would be worse. Or:
(b) In some cases, e.g., that of a straight line, one feature may have an
internal limit and may sufﬁce for the object in question to be perfect.
This explanation of the intuitive idea of perfection is vague. I think
that it can be made sharper only by examples and contrasts, and by ﬁxing
on the particular use we want to make of it. Thus contrast perfectionist
pluralism as a moral doctrine with the idea of maximizing happiness (as
the sole ﬁrst principle) as it appears in classical utilitarianism. The latter has
no internal limit. Any limits are imposed from the outside as constraints:
one maximizes happiness subject to the given constraints, whatever they
are. And the constraints may vary from case to case.4 This is a signiﬁcant
feature of it.
Hence what seems essential to perfectionism is that the concept of perfection in a given case should specify its limit or balance, at least in signiﬁcant part, from within: from the nature of the perfectionist properties
and/or the nature of that which is perfect or has the balance of perfections.
So perfection involves the concept of completeness as internally speciﬁed:
while anything less is worse, nothing more is needed. A limit or balance
is reached that is not determined from the outside by constraints that may
vary arbitrarily from case to case, as in the way in which maximizing happi4. F. H. Bradley in Ethical Studies (Indianapolis: Bobbs-Merrill, ), chap. , makes much of
this point in his attack on J. S. Mill’s utilitarianism.
ness is constrained by limited resources, or limited time and energy, and
changing from time to time. No doubt this leaves much obscure!
. What is metaphysical perfection? In this case, the perfections are perfections of a perfect being. God is an absolutely perfect being. So Leibniz
thinks that we have the concept of such a being with the properties of
omniscience and omnipotence, as well as the moral perfections: wisdom,
goodness, and justice. Further, such a being not only exists, since existence
is a perfection; but also it exists necessarily. God is necessarily existent. God
is also simple and not consisting of parts. God, as the absolutely perfect
being, is also independent of all created beings in the sense that God’s existence does not depend on their existing. God is also self-sufﬁcient.
I shall not discuss these ideas; I merely mention them here to give some
sense to the concept of metaphysical perfection: the concept of God as the
absolutely perfect being who creates the world as the best of all possible
Recall that, aside from his argument for God’s necessary existence in
Theodicy, paragraphs –, Leibniz is not in that work trying to prove to us
that the world is the best, or the most perfect, possible. The reasons sufﬁcient to do that are far beyond our comprehension; they can be known
only to God. Rather, Leibniz’s aim is to provide a defense of faith: we are
given a way of taking the world that presents us with grounds for believing
that the world is the best possible. In discussing the question whether God
caused Judas to sin, answering that God did not, Leibniz says: “It is enough
to know [that God made the best choice of worlds] without understanding
it” (Discourse:§). Enough for what? For faith and piety.
§. Leibniz’s Predicate-in-Subject Theory of Truth
. I now give a very brief sketch of what I shall call Leibniz’s predicate-insubject theory of truth. I do this as preparation for considering next time
his account of freedom, which is intended to explain why it is, for example,
that God in creating Judas does not cause Judas to sin, and how it is that
although God foresees and permits Judas’s sin, Judas sins freely. This account of truth must allow Leibniz to hold that:
(a) The world is freely created by God, who has attributes of reason,
moral perfection, and will, and who creates the world for the best of reasons, not arbitrarily or by logical necessity.
(b) This requires that the actual world must be the best of all possible
worlds; and the created things that make up the world—the complete substances—must be genuinely created things, having their own active forces
and tendencies that move them to act in accordance with their own principles.
As we will discuss next time, Leibniz views created things as moved by
their own active powers, while he thinks that Descartes does not; and he
sees created things not as Spinoza does, as mere attributes and modes of
the one complete substance, but as genuine substances.
. One way to present Leibniz’s view is to think of him as starting from
an idea of what a true proposition is. His basic thought might be said to
A proposition is true if and only if the concept expressed by its predicate
is contained in the concept expressed by its subject.
Thus Leibniz says: “[T]he predicate is present in the subject; or else I do
not know what truth is.”5
“Necessary and Contingent Truths” (ca. ) has a quite full statement
of Leibniz’s predicate-in-subject theory of truth. In the quotations from this
essay below, the ﬁrst asserts that all knowledge has an a priori reason for
its truth; the second deﬁnes necessary truths as about the essences of things
lying in the divine reason, and the third characterizes contingent truths as
about the existence of things in space and time.
. An afﬁrmative truth is one whose predicate is in the subject;
and so in every true afﬁrmative proposition, necessary or contingent, universal or particular, the notion of the predicate is
in some way contained in the notion of the subject. Moreover,
it is contained in the notion of the subject in such a way that
if anyone were to understand perfectly each of the two notions
just as God understands it, he would by that very fact per5. The Leibniz-Arnauld Correspondence, ed. and trans. H. T. Mason (Manchester: Manchester
University Press, ), letter of July , p. .