- Living Mirrors: Infinity, Unity, and Life in Leibniz’s Philosophy by Ohad Nachtomy
The concept of life and the importance of the life sciences in Leibniz have recently become objects of much interest. The question concerning the status of life in Leibnizian metaphysics is one of the motivating factors. On many occasions, Leibniz affirms that matter is full of life and that compound substances are actually living beings with a soul and an organic body. Nachtomy’s book touches on these themes, but its originality lies in its contribution to understanding the relationship between life and the infinite.
The first chapters analyze the different meanings that the concept of infinity assumes in Leibniz. This step is crucial, since living beings have a structure extending into infinity. Nachtomy identifies three types of infinity: the absolute and actual infinity that expresses the divine nature, the potential and divisible infinity characteristic of mathematical quantities, and finally, a third infinity that concerns creatures and constitutes a maximum of its kind. The last type refers to machines of nature that contain an infinite but limited structure. A main feature of Nachtomy’s approach is the use of several analogies to highlight the similarities between the concepts at play here. For instance, if one compares the impossibility of infinite number with the necessary existence of the divine infinite, one might draw an analogy between the units that make up a number and the attributes that comprise the idea of God. Elsewhere, a comparison is drawn between arithmetic unity on the one hand, and substantial unity per se on the other, his justification being that both are the basis of a complex structure. Nachtomy is aware of the differences between these concepts, but the usefulness of these analogies, especially those with mathematical quantities, remains questionable. In the texts where Leibniz treats infinite number and the divine infinite jointly, it is not obvious that he means to compare the two rather than to oppose them. In fact, these concepts belong to distinct domains: God and creatures are actual realities, while numbers are only ideal. For Leibniz, depending on whether it is the former or the latter, the relationship between unity and totality is also conceived of differently.
The second part of the book links the infinity of substances with certain metaphysical aspects of life. At the heart of the Leibnizian doctrine lies the distinction between natural and artificial machines. Unlike Descartes, Leibniz wishes to differentiate nature from artifice qualitatively, rather than by degrees. Two characteristics seem particularly important in Nachtomy’s interpretation. On the one hand, the infinity of the machine of nature is not understood by the number of organs it comprises, but rather by its structure. In light of this, he draws a comparison between this structure and the law of series, which determines the individuality and activity of each substance. On the other hand, because God creates the machine of nature and determines its function, Nachtomy argues that we should understand it as an end, which also extends in its being infinitely. However, even if some of Leibniz’s texts could be interpreted in this way, it is not always clear that final causation is central to Leibniz’s concept of divine machines.
One of the most innovative features of Nachtomy’s analysis is his insistence on the role played by monads in living beings. Most commentators emphasize their bottom-up relationship, according to which monads are the building blocks of corporeal beings. In so doing, they forget that the dominant monad or soul must, to the extent that it gives structure to the organic body, be understood in terms of a top-down relationship. The animated monad is thus the foundation of the machine of nature, providing it with infinite unity, activity, and organization. Nachtomy draws a general conclusion from these considerations: Leibniz’s concept of the divine machine is an element in his metaphysics, not a theoretical framework for the empirical life sciences. It is true that Leibniz often claims that metaphysical explanations must be...