 Leibniz conceived of metaphysics as an a priori demonstrative science. In its ideal form metaphysics would be presented in a manner analogous to Euclid’s Elements, where propositions are rigorously demonstrated on the basis of definitions and axioms. The point of departure for this conception of metaphysics is Leibniz’s theory of truth. Leibniz thought that truth consisted in conceptual containment: a proposition is true just in case the concept of the predicate is contained in the concept of the subject. This implies that all metaphysical truths are conceptual truths. Leibniz thought that a concept could be defined by analyzing it into simpler component concepts. A rigorous demonstration, for Leibniz, consists in a “chain of definitions” (catena definitionum) where one moves from premises to a conclusion via the substitution of definitionally equivalent terms (A II.i.398; L 198). In order for such demonstrations to attain the degree of certainty found in geometry they would need to be set forth in a purely formal system, which Leibniz termed his “universal characteristic” (characteristica universalis). The universal characteristic would allow one to express in a purely formal manner the composition of any concept on the basis of a set of primitive concepts. This system of representation, in conjunction with a logical calculus for expressing identity and inclusion relations among concepts, would enable one to set forth a strictly demonstrative metaphysics (see Rutherford 1996 for a detailed discussion of Leibniz’s conception of a demonstrative metaphysics).