Monday, May 01, 2006

Truth in Leibnizian Philosophy

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 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.

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