MATHEMATICAL REASONING, ARCHITECTONICS, AND THE PRE-ESTABLISHED HARMONY IN LEIBNIZ

Throughout his life, Leibniz remained adamant in his defense--against the attacks of Spinoza and the Cartesians--of teleological reasoning. Perhaps the clearest and most complete statement of his argument in favor of teleology occurs in a passage from his "Principles of Nature and of Grace, Based on Reason" (1714); and it is with a critical examination of the argument which is presented there that the present work is primarily concerned.;Considerable space is also given over to a consideration of Leibniz's particular version of the cosmological proof of the existence of God; and especial attention is paid to that argument by which Leibniz attempted to establish the nature of the "first cause." With this we come to Leibniz's defense of teleological reasoning, which was based upon an appeal to the existence of an intelligent and purposive creator of the universe.;The passage from the "Principles" culminates in a discussion of the doctrine of pre-established harmony, which Leibniz took to be the basis of one of the strongest proofs of the existence of God and which constituted the very substance of his novel interpretation of the teleological activity of God. But the discussion of the doctrine of pre-established harmony is postponed in order to consider a number of issues upon which a proper understanding or that doctrine depends. In particular, a detailed, critical examination of Leibniz's logic of composition and containment, of his theories of definition, and of his doctrine of truth (praedicatum inest subjecto) is undertaken in order to establish that Leibniz was committed to a denial of the reality of relations. This discussion culminates in a consideration of Leibniz's doctrine of possible worlds, of the problem of disharmonious worlds, and, finally, of the doctrine of pre-established harmony. The conclusion to which we are driven is that Leibniz's theory of truth must land him in an inescapable solipsism and that any pretended proof of the existence of God that makes appeal to a harmony amongst perceivers must involve a vicious and blatant petitio--Leibniz must first establish the existence of a wise creator in order to know that there are minds other than himself and to know that these minds perceive in harmony.;In the course of the dissertation, there are distinguished three quite different principles, to which Leibniz nonetheless gave a common name--viz., "the principle of sufficient reason." These three principles jointly formed the basis of what Leibniz called "architectonics." To architectonics, Leibniz opposed "mathematical reasoning," which he viewed as being based upon the principle of contradiction. A discussion is undertaken to show how the "principle of the best," which is the proximate principle of teleological reasoning, is derived from Leibniz's principles of sufficient reason, which are the remote principles of Leibniz's teleology.;The analysis of the argument of the "Principles" occasions the discussion of a number of different, albeit related issues in Leibniz's philosophy. Inter alia, it occasions a detailed discussion of Leibniz's dynamic conception of matter, which he proposed in opposition to the Cartesian "geometrical" conception of matter; for Leibniz viewed his dynamics as requiring a return to "the way of final causes," which both Descartes and Spinoza had sought to banish from physical science. The arguments by which Leibniz attempted to establish the need for teleological reasoning in natural philosophy are here subjected to critical review.