Logik and Semiotik in der Philosophie von Leibniz (review)

BOOK REVIEWS 57 ~ than the "model of mathematics" is that what is being hypostatized is a "pure" set of relations with no content. Both abstract mathematical entities and concrete phenomenal entities provide different possible exemplifications or contents for these relations. Thus it is wrong to say that for Descartes and Malebranche intelligible extension just is the set of axioms and rules of solid Euclidean geometry. Instead, there is "in being" a set of pure and necessary relations that can be expressed in discursive terms, algebraic terms, geometric terms, and by material objects, all of which can be exemplifications of or the content of these relations. The being of the model of number, then, is a set of pure (empty) relations setting forth the possibility (but not necessitating the actuality) of exemplification. This is in contrast to the necessary actuality of being (God) on the model of substance. This empty set of relations fires the engines of modern science and leaves God in the dust. Hobart shows clearly, conclusively, and elegantly how Malebranche typifies the duality of the seventeenth-century mind, how the agonizing incomprehension of a substantial God is submerged by the ecstasy of mathematical enlightenment. "Small wonder," Hobart concludes, "Pascal loathed the geometer's god" (p. 147). Hobart's book is a model for work in the history of philosophy using contemporary analytic techniques controlled by the historical texts and contexts. It is a pleasure to welcome this well-written addition to the small corpus of standard and essential works on Malebranche and on the rise of modern science and philosophy. Richard A. Watson Washington University Hans Burkhardt. Logik and Semiotik in der Philosophie von Leibniz. Analytica series (investigations in logic, ontology, and the philosophy of language). Munich: Philosophia Verlag, 198o. Pp. 487 . Like the Roman deity Janus, Leibniz had two faces, one looking to the future and the other to the past. His future, his significance for present-day philosophy, is well known; in fact, advances in logic today have led to a greater appreciation of his achievements. But his past philosophical roots have not been emphasized. Specifically , Burkhardt points out, there are no thorough investigations of the debt Leibniz, the most important "Protestant Aristotelian," owed to scholasticism, "whose logic, ontology, and metaphysics [he] carefully studied and whose terminology he used all his life" (p. 2o). However, the recent publication of medieval and post-medieval scholastic texts and of competent interpretations has provided the basis for new insights into Leibniz's philosophy. Burkhardt's book is unique in that it takes both Leibniz's future and his past into account. It is basically an exhaustive catalogue of his teachings on logic and semiotics, densely summarized and related both to logic since Boole and Frege and to the philosophy Leibniz was heir to. It includes sketches of relevant doctrinal developments before Leibniz and comments on the state of the research and on controversies over interpretations. The following are some examples of Leibniz's relationship to his philosophical 572 JOURNAL OF THE HISTORY OF PHILOSOPHY 2I: 4 OCT 198 3 past. In inference theory his main focus was the syllogism and his non-syllogistic forms were all from the tradition (pp. 23, 65-6 ). Anselm was the first to discuss the relations between natural and ideal language in detail, and Leibniz was indebted in his language studies directly or indirectly to scholastic speculative grammar (pp. 86, 87). His semantics, important for his theories of definition, identity, and truth, was the traditional model of sign, concept, thing (pp. 18o-1). There was scholastic influence in his analytic definition of truth, and "the passage most often quoted for [his] truth theory turns out to be only the scholastic doctrine of the analogy of proportionality " (pp. 244, 258). When discussing contingent propositions in the context of the coherence aspect of his truth theory he "merely repeats scholastic analyses" (p. 249). Of the three themes comprising the core of his logica nova, Leibniz took the combinatory art from the Lullist current, the universal characteristic was a common object of speculation in the 17th century, and the logical calculus went back to Vieta--indeed J. Junge worked one out with formalization of relations before Leibniz...