Metaphysik und Mathemathik bei Giordano Bruno.

Since Atanasijevic's foundational monograph on Giordano Bruno's geometry, Bruno's mathematical works have been relatively unexplored, with the exception of Mulsow's commentary to the German translation of De monade and the papers by Aquilecchia, Otto and Heuser-Kessler (published in Die Frankfurter Schriften Giordano Bruno's und ibre Voraussetzungen, ed. K. Heipcke et al., Weinheim, 1991). Bonker-Vallon has now written a full-length monograph on the relation between metaphysics and mathematics in Bruno. The author leans heavily on Beierwaltes's views and regards Bruno's philosophy as "Einheitsdenken," standing in the tradition of ancient Neoplatonism and Cusanus (see, in particular 38-41, regarding Bruno's "Idealism"). In a critical review of early (Tocco and Lasswitz) and recent studies, she argues (1) that Bruno's "atomism in mathematics" has been misunderstood; (2) that no attention is paid to the crucial role of his doctrine of God in his epistemology; and (3) that the historical position of Bruno has not yet been accounted for. Her central thesis is that Bruno's philosophy is a closed system grounded in the metaphysical principle of the divine unity ("monas"). Reality and its first principle are accessible only by mathematical reflection, which in turn is grounded in the first principle of the divine unity (see chap. 1 regarding the link between mathematics and the metaphysical concept of nature).

Bonker's study is highly speculative and written in a burdensome style. Nevertheless it offers a clear interpretation of Bruno's philosophy and has the merit to propose a strictly "unitary" analysis of Bruno's metaphysics and mathematics, stressing the intimate bond between method and the structure of reality. A fortiori, the mathematical structure of the inner "explicatio" of God is essential to the understanding of nature's unfolding and corresponds to the innate conceptual tools of the reflecting subject. Although I accept the author's views on the crucial relation between God, the universe, and the human soul, I do not share her ahistorical and sometimes even fundamentally anachronistic interpretation of Bruno merely as an exponent of the "Einheitsmetaphysik."

Unfortunately, her strictly systematic approach has made her neglect some issues which a historical study of Bruno's mathematics should have accounted for. The author does not hold faith to her intention to assess the historical value of Bruno's mathematics, since she does not take into consideration sixteenth-century mathematical treatises as possible sources or as useful material for comparative analysis. Also the discussion of older mathematical sources is marginal. By contrast, Bonker frequently cites twentieth-century mathematical literature; however, most of these references are too short and enigmatic to be of any help. Bruno's alleged anticipations of modern science are either too arbitrary (regarding the unity of method on 68 and 249) or not argued for (e.g. the relation with Leibniz in chap. 8). Surprisingly the author seems unacquainted with P. Rossi's Clavis universalis and with S. Ricci's studies on the reception of Bruno in the seventeenth and eighteenth centuries. Finally, the initial claim regarding Bruno's contribution to the development of mathematics - that it consisted of an essential impulse towards the analysis of the scope of mathematical logic through the attempt to assess the premises of mathematical thought and to understand the divine unity with mathematical means - remains unwarranted.

LEEN SPRUIT University of Rome "La Sapienza"