Perhaps the most persistently misunderstood aspect of Leibniz’s thought is his principle of contingence. The theory is deeply rooted in Leibniz subject-predicate logic, and it is therefore not surprising, given the complexity of this philosophy, that he would be vulgarly misunderstood—most famously as Dr. Pangloss from Voltaire’s Candide. What I have tried to do in this paper is to clarify Leibniz’ theory of contingent existence, to defend it against a criticism about moral perfection, and ultimately to show there is a legitimate place for this theory in Leibniz’ philosophy.

Leibniz theory of truth rests on a procedure that he terms “analysis.” This is the elimination of defined, complex ideas by making analytic use of their definitions. What Leibniz calls the “Principle of Sufficient Reason” is a principle asserting that, if a proposition is true, then it is possible to show that its predicate is contained in its subject by means of an analysis or demonstration which may or may not proceed infinitely, (and in the case that it requires infinite analysis, God alone can carry out the analysis fully.) Another important principle Leibniz calls the “Principle of Contradiction” is to the effect that if the analysis of a proposition shows its predicate to be contained in its subject after a finite number of steps, then the proposition is true. Such finitely analytic true propositions Leibniz says are “necessary truths” or “truths of reason.” On the other hand true but infinitely analytic propositions are “contingent truths” or “truths of fact” (M. § 31-33). It is clear that the Principle of Contradiction is the principle of necessary truths.

So, according to the Principle of Sufficient Reason every true proposition is finitely or infinitely analytic in the mind of God. However, according to the Principle of Contradiction every finitely analytic proposition is true. The converse of the Principle of Contradiction is every true proposition is finitely analytic, which is not the same as the Principle of Sufficient Reason. Neither of these principles guarantees the truth of infinitely analytic propositions, which is to say that contingent truths are by virtue of this not necessarily true, although accepting contingent truths as truths is not on this account irrational. And since the Principle of Sufficient Reason concerns truths, there must be a further principle where a supply of infinitely analytic truths can be of some use.
First, it is essential to remark that, with the exception of contingent propositions whose subject is God, contingent truths concern contingently existing things. For, on Leibniz’ account, a contingently true proposition must have a subject. Now, this subject cannot be an “abstract object,” since truths concerning these are necessary. And, propositions about God aside, the only remaining entities on the Leibnizian account are the contingently existing things. God’s mind, on this account, is where the possible-worlds semantics can be examined more closely. Of the infinitely-many possible worlds (contained with infinitely-many possible substances) God selects one, the best, and “actualizes” it, to use Alvin Plantinga’s Neo-Leibnizian phraseology.

Every possible substance is a member of some possible world, and its complete notion involves its entire history in the development of that possible universe (D.M. § 9). Now thanks to the “pre-established harmony,” there corresponds to every state in the development of a possible substance a state of every other possible substance of its possible world: a correspondence capable of varying degrees of closeness of agreement between its members (M. § 80-82). Thus within a possible world every substance “represents” every other substance more or less “distinctly.” In other words, it perceives the other substance with a greater or lesser degree of “clarity” or “confusion” in the plenum of interconnected monads. In this way, at each stage of its development every possible substance “perceives” or “mirrors” its entire universe, and moreover it does so more or less clearly according as the mean value of the degree of clarity of its perception of individual substances varies. Leibniz calls the degree of clarity with which at a given state a possible substance mirrors its universe its amount of perfection for that state (M. § 54). Now what Leibniz terms the “amount of perfection” of a possible substance is a measure of its amount of perfections of a possible substance is a measure of its amount of perfection for all states. So, every possible universe also has an amount of perfection: the sum of the total amounts of perfections possible in the substances belonging to it.
The principle by which God selects among the possible worlds the best of them—one with the greatest maximization of “order” and “variety”—call this the Best-Possible-Worlds Principle (Theodicy § 120, 124; M. § 58). This principle is a formulation of the thesis that in His decision of creation God acted in the best possible way: according to it the actual world is that one among the possible worlds which an infinite process of comparison showed it to be the best.

The Best-of-Possible-Worlds Principle specifies that in nature some quantity is at a maximum or a minimum. It requires mathematical techniques similar to those found in calculus. This principle enables us to understand what Leibniz means concerning contingent truths as analytic, but requiring an infinite process for their analysis. A given proposition concerning a contingent existence is true, and its predicate is indeed contained in its subject, if the state of affairs characterized by this inclusion is such that it involves a greater amount of perfection for the world than any other possible. So it is the infinite comparison required by the Best-Possible-Worlds Principle that in infinite process is imported into the analysis of truth dealing with contingent existence.

It will be made clear that Leibniz’ Principle of Contingence is his Best-Possible-Worlds Principle. And it is in virtue of this principle that infinitely analytic propositions can be truths. Leibniz writes to Arnauld that “a contingent existent owes its existence to [the Best-Possible-Worlds Principle], which is sufficient reason for existents.” Leibniz calls the “necessity” of contingent truths moral necessity as opposed to the metaphysical necessity of necessary truths, and he states that “moral necessity stems from the choice of the best.” In Section 46 of the Monadology Leibniz speaks of “the contingent truths whose principle is that of suitability or of the choice of the best.” And he maintains that “contingent propositions have demonstrations… based on the principle of contingence or existence… on what seems best among the several equally possible alternatives.”

Now, the Principle of Sufficient Reason demands exactitude. It states that a contingent truth is susceptible of an analysis which, though infinite, converges on something. But such exactitude could equally well have been gained had God chosen the worst of all possible worlds. The Principle of Sufficient Reason requires merely that contingent truths are analytic. The Best-Possible-Worlds Principle shows how this is the case. As Leibniz repeatedly said, the Principle of Sufficient Reason leaves open to God’s choice an array of alternatives for possible actualization—of which the best possible world is the only one. Therefore, though it is true that the Principle of Sufficient Reason requires some complementary principle of exactitude, Leibniz would have been the first to deny that this must be the Best-Possible-Worlds Principle.

So far we have been occupied with the theory of contingent existences. That is, the principle that all true propositions are analytic, finitely or infinitely (Principle of Sufficient Reason); that all finitely analytic propositions are true (Principle of Contradiction); and that all infinitely analytic propositions—and thus all propositions whose infinite analysis converges on some characteristic of the best of all possible worlds—are true (Best-Possible Worlds Principle). At this point we are faced with an objection which would rule contingence out from the system of Leibniz once and for all. The objection is that the contingence of God’s goodness and the necessity of His existence is a contradiction within Leibniz’ system, and in which the Problem of Evil seems to be at hand. On the Leibnizian account, either God’s goodness is contingent or it is necessary. Should Leibniz have held that both God’s existence and goodness are necessary, and succumb to a kind of Spinozistic determinism? (And what might “necessary goodness” refer to on the Natura Naturans thesis?) This thesis is quite attractive, although accepting it would collapse nearly all of Leibniz into Spinoza. In formulating a “religiously adequate” account of God as the necessary being, Leibniz was not prepared to affirm both and say that “God’s goodness is a necessary predicate of His existence as a necessary being.” Nor was he prepared to say that “God’s existence is contingent and therefore His goodness is too.”

Leibniz maintains the existence of God as the ens necessarium (“necessary being”) and invokes a modal argument to show that the ens necessarium exists provided only that its existence is possible. If the proposition “God exists” is possible on this account, then ipso facto it is rational to believe it is true, says Plantinga (Necessary Being, Free Will Defense). It remains for Leibniz to demonstrate that “God exists” is possible.

Leibniz’ own argument is one from causality, found in the Leibniz-Arnauld correspondence: if the ens necessarium is not possible, then no existence is possible. If the ens necessarium is possible, then He exists. If we say that ens necessarium does not exist, then it would follow that nothing exists. But something does exist. Hence the ens necessarium exists. In other words, God is a causally necessary condition of the existence of anything else, but whereas His own existence has no necessary conditions. Now the absence of a necessary condition of the existence of anything else is a sufficient condition of the nonexistence of that thing. And if a being has no causally necessary conditions, then its nonexistence has no causally sufficient conditions. And hence if God does exist, His going out of existence could have no causally sufficient conditions and is therefore causally impossible. If God has no necessary conditions, then it is analytic that His “going out of existence,” if it occurred, would be an uncaused event, since there are no causally sufficient conditions for that occurrence. Likewise, His “coming into existence” is causally impossible, since it is analytically true that God is not dependent upon anything else. He has no cause, and therefore His coming into existence would be an event which would have no causally sufficient conditions. So, if God does exist, He cannot cease to exist; nor could He have begun to exist.

But God’s goodness is not included in the above argument. Let me now put it in. Since God exists necessarily—His existence being contained in His essence—it follows that God has the highest possible degree of perfection. Perfection in this sense is His metaphysical perfection, containing “as much reality as is possible,” which Leibniz made clear in the Monadology and to Arnauld. But God is purported to be perfect not only in the metaphysical sense, but perfect in the moral sense as well. While Leibniz is certain of God’s moral perfection, he does not maintain it is necessarily true. He maintains that while His existence is necessary, His goodness as a creator, i.e. moral perfection, is contingent and the result of His free choice. And hence, being the good creator as He is, He freely chooses to be morally perfect.

We must cope now with the question of the relation between God’s necessary metaphysical perfection and His contingent moral perfection. In order to do this we must once more call to mind Leibniz Principle of Sufficient Reason. As we have already seen, this asserts that every true proposition can be show to be analytic by a (possibly infinite) process of analysis. Using this principle we can clarify the logical relation between the two types of divine perfection. Divine moral perfection has a sufficient reason, and this in turn another sufficient reason ad infinitum. But this sequence of sufficient reason converges on God’s metaphysical perfection, on His existence. Or putting it another way, we can say that God’s moral perfection is indeed a logical consequence of His metaphysical perfection, but a consequence which cannot be proven logically within a finite number of steps. In this way, as Leibniz insists, the proposition asserting God’s moral perfection is contingent. God is only morally perfect by free choice, not necessitation.

Thus it is precisely the infinite regress which naturally invokes a reductio ad absurdum response to God’s goodness being contingent. But Leibniz implicitly maintains that infinite processes are not ipso facto erroneous, since a kind of mathematical convergence is possible. To assert convergence is to say there is a limit to the infinite series, and may be itself unknown. Leibniz, after all, invented calculus independently of Newton. And it is his notation which is has been in general use since.

The philosophy of Leibniz rests on the three fundamental principles discussed in this paper. It is the Best-Possible-Worlds Principle, not the Principle of Sufficient Reason, which constitutes Leibniz’ contingency theory and his moral perfection theodicy. It is the Principle of Sufficient Reason which allows for the distinction between God’s metaphysical perfection and moral perfection, and enables Leibniz to maintain both the contingency of God’s goodness and the necessity of His existence.