Leibniz’s Core Principles and Doctrines

(Not fully exhaustive, but close enough for us)

• The subject-predicate form of propositions is basic. And for a proposition to be true, its predicate must be contained in the subject.
• Finite analysis: The containment of the predicate in the subject is shown by a simple analysis of the terms. A finitely analyzable statement’s opposite cannot be asserted without a contradiction.
• Infinite analysis: The procedure necessary in order to understand contingent propositions. E.g., to fully understand the concept of Socrates, we would have to know all of Socrates’ predicates. The denial of such propositions does not yield a contradiction. Only God can do infinite analysis.
• The Principle of Contradiction: Two contradictory propositions cannot both be true. A proposition is either true or false. A proposition cannot be both true and false at once, and it is impossible for a proposition to be neither true nor false. This principle yields truths of reason.
• The Principle of Sufficient Reason: Nothing can be true or real or existing unless there is a sufficient reason that makes it so and not otherwise. This principle yields truths of fact.
• The Principle of Perfection (or the Principle of the Best): God acts for the objectively best and humanity acts with a view to what seems to be the best. This is, after all, the best of all possible worlds.
• The Principle of the Identity of Indiscernibles: There cannot be two identical substances. Or, numerically different individuals must be qualitatively dissimilar.
• The Principle of Continuity: Nothing is accomplished all at once. Nature makes no leaps.
• A Principle of Differentiation: Monads differ from one another in respect to their degree of consciousness.
• The Internal Principle of Change: Appetition or desire. Inherent in monads.
• The Doctrine of Preestablished Harmony: God created each monad with its particular dispositions such that it is coordinated and corresponds with all other monads at all times.