this thesis are located in theses connected with his program for a universal science (scientia universalis). This program had two parts: a universal notation (characteristica universalis), whose purpose was to provide a method for recording scientific facts as perspicuous as algebraic notation, and a formal system of reasoning (calculus ratiocinator) for reasoning about the facts recorded. Supporting Leibniz’s belief in the possibility and utility of the characteristica universalis and the calculus ratiocinator is his thesis that all concepts arise from simple primitive concepts via concept conjunction and concept complementation. In virtue of this thesis, he held that all concepts may be analyzed into their simple, primitive components, with this proviso: in some cases there is no finite analysis of a concept into its primitive components; but there is an analysis that converges on the primitive components without ever reaching them. This is the doctrine of infinite analysis, which Leibniz applied to ward off the threat to contingency apparently posed by his account of truth. He held that an elementary proposition is necessarily true if and only if there is a finite analysis that reveals that its predicate concept is included in its subject concept. By contrast, an elementary proposition is contingently true if and only if there is no such finite analysis, but there is an analysis of its predicate concept that converges on a component of its subject concept.
The theological argument may be put this way. There would be no world were God not to choose to create a world. As with every choice, as, indeed, with every state of affairs that obtains, there must be a sufficient reason for that choice, for the obtaining of that state of affairs – this is what the principle of sufficient reason amounts to, according to Leibniz. The reason for God’s choice of a world to create must be located in God’s power and his moral character. But God is allpowerful and morally perfect, both of which attributes he has of necessity. Hence, of necessity, God chose to create the best possible world. Whatever possible world is the best possible world, is so of necessity. Hence, whatever possible world is actual, is so of necessity. A possible world is defined with respect to the states of affairs that obtain in it. Hence, whatever states of affairs obtain, do so of necessity. Therefore, there are no contingent propositions. Leibniz’s options here were limited. He was committed to the thesis that the principle of sufficient reason, when applied to God’s choice of a world to create, given God’s attributes, yields the conclusion that this is the best possible world – a fundamental component of his solution to the problem of evil. He considered two ways of avoiding the conclusion of the argument noted above. The first consists in claiming that although God is metaphysically perfect of necessity, i.e., has every simple, positive perfection of necessity, and although God is morally perfect, nonetheless he is not morally perfect of necessity, but rather by choice. The second consists in denying that whatever possible world is the best, is so of necessity, relying on the idea that the claim that a given possible world is the best involves a comparison with infinitely many other possible worlds, and hence, if true, is only contingently true. Once again the doctrine of infinite analysis served as the centerpiece of Leibniz’s efforts to establish that, contrary to appearances, his views do not lead to necessitarianism, i.e., to the thesis that there is no genuine contingency. Much of Leibniz’s work in philosophical theology had as a central motivation an effort to formulate a sound philosophical and theological basis for various church reunion projects – especially reunion between Lutherans and Calvinists on the Protestant side, and ultimately, reunion between Protestants and Catholics. He thought that most of the classical arguments for the existence of God, if formulated with care, i.e., in the way in which Leibniz formulated them, succeeded in proving what they set out to prove. For example, Leibniz thought that Descartes’s version of the ontological argument established the existence of a perfect being, with one crucial proviso: that an absolutely perfect being is possible. Leibniz believed that none of his predecessors had established this premise, so he set out to do so. The basic idea of his purported proof is this. A perfection is a simple, positive property. Hence, there can be no demonstration that there is a formal inconsistency in asserting that various collections of them are instantiated by the same being. But if there is no such demonstration, then it is possible that something has them all. Hence, a perfect being is possible.
Leibniz did not consider in detail many of the fundamental epistemological issues that so moved Descartes and the British empiricists. Nonetheless, Leibniz made significant contributions to the theory of knowledge. His account of our knowledge of contingent truths is much like what we would expect of an empiricist’s epistemology. He claimed that our knowledge of particular contingent truths has its basis in sense perception. He argued that simple enumerative induction cannot account for all our knowledge of universal contingent truths; it must be supplemented by what he called the a priori conjectural method, a precursor of the hypothetico-deductive method. He made contributions to developing a formal theory of probability, which he regarded as essential for an adequate account of our knowledge of contingent truths.
Leibniz’s rationalism is evident in his account of our a priori knowledge, which for him amounted to our knowledge of necessary truths. Leibniz thought that Locke’s empiricism did not provide an acceptable account of a priori knowledge, because it attempted to locate all the materials of justification as deriving from sensory experience, thus overlooking what Leibniz took to be the primary source of our a priori knowledge, i.e., what is innate in the mind. He summarized his debate with Locke on these matters thus:
Our differences are on matters of some importance. It is a matter of knowing if the soul in itself is entirely empty like a writing tablet on which nothing has as yet been written (tabula rasa), . . . and if everything inscribed there comes solely from the senses and experience, or if the soul contains originally the sources of various concepts and doctrines that external objects merely reveal on occasion. The idea that some concepts and doctrines are innate in the mind is central not only to Leibniz’s theory of knowledge, but also to his metaphysics, because he held that the most basic metaphysical concepts, e.g., the concepts of the self, substance, and causation, are innate. Leibniz utilized the ideas behind the characteristica universalis in order to formulate a system of formal logic that is a genuine alternative to Aristotelian syllogistic logic and to contemporary quantification theory. Assuming that propositions are, in some fashion, composed of concepts and that all composite concepts are, in some fashion, composed of primitive simple concepts, Leibniz formulated a logic based on the idea of assigning numbers to concepts according to certain rules. The entire program turns on his concept containment account of truth previously mentioned. In connection with the metatheory of this logic Leibniz formulated the principle: ‘eadem sunt quorum unum alteri substitui potest salva veritate’ (‘Those things are the same of which one may be substituted for the other preserving truth-value’). The proper interpretation of this principle turns in part on exactly what ‘things’ he had in mind. It is likely that he intended to formulate a criterion of concept identity. Hence, it is likely that this principle is distinct from the identity of indiscernibles, previously mentioned, and also from what has come to be called Leibniz’s law, i.e., the thesis that if x and y are the same individual then whatever is true of x is true of y and vice versa. The account outlined above concentrates on Leibniz’s mature views in metaphysics, epistemology, and logic. The evolution of his thought in these areas is worthy of close study, which cannot be brought to a definitive state until all of his philosophical work has been published in the edition of the Akademie der Wissenschaften in Berlin. See also DESCARTES, IDENTITY OF INDIS- CERNIBLES , LOCKE , POSSIBLE WORLDS , RATIO – NALISM , SPINOZ. R.C.Sl.