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§3. The Concept of a Perfection

§3. The Concept of a Perfection

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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

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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.

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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,

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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

be this:

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. .

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