Continuity, containment, and coincidence: Leibniz in the history of the exact sciences
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Continuity, containment, and coincidence: Leibniz in the history of the exact sciences Vincenzo De Risi (ed.): Leibniz and the structure of sciences: modern perspectives on the history of logic, mathematics, and epistemology. Dordrecht: Springer, 2019, 298pp, 103.99€ HB Christopher P. Noble1
© Springer Nature B.V. 2020
Leibniz and the Structure of Sciences is an excellent collection of papers treating Gottfried Wilhelm Leibniz’s projects across a range of sciences including logic, mereology, calculus, geometry, and the mathematics of the infinite. Each paper represents a useful contribution to the extant scholarly literature and helpfully points the way for continued inquiry. The volume should be of value to scholars of Leibniz with interests in the ‘exact sciences’ and the formal dimensions of his thinking, as well as to historians and philosophers concerned with understanding how Leibniz’s thinking anticipates later approaches. The volume is noteworthy in the latter respect because of the way that it situates Leibniz within the larger histories of science and mathematics. While the scholars represented in the volume are sensitive to the need to understand Leibniz’s views within their seventeenth-century intellectual contexts, several also adopt a self-consciously anachronistic approach to their subjects. Thus, the volume includes reconstructions of Leibniz’s projects that put them into dialogue with the views of later figures including Georg Cantor, Richard Dedekind, George Boole, and C. S. Peirce. This is literally the case with respect to Cantor, as Richard T. W. Arthur’s contribution takes the form of an imagined conversation between Leibniz and the later mathematician. These reconstructions show that even when Leibniz’s efforts may have failed outright, were hindered by commitments he maintained to traditional views, or otherwise did not themselves bear fruit, they often came tantalizingly close to realizing crucial later theoretical discoveries. Hence, his approaches may be contrasted productively with those of later theoreticians, revealing both historical continuities as well as theoretical and methodological roads not taken. The portrait of Leibniz that thus emerges from the volume is that of an intellectual who not only * Christopher P. Noble [email protected] 1
Division of Humanities, New College of Florida, Sarasota, FL, USA
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was responsible for some of the most important intellectual innovations of the seventeenth century, but who was also quite often ahead of his time. The first paper, “Leibniz on the Logic of Conceptual Containment and Coincidence,” by Marko Malink and Anubav Vasudevan, contrasts two different formal logical calculi developed by Leibniz. While one formulation relies on Leibniz’s well-known commitment to truth as the containment of the predicate in the subject concept, the second is founded on an alternative notion of conceptual coincidence and “prefigures in many important respects the algebraic approach to logic which rose to prominence in th
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