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The Infinitesimal Calculus of the Soul: Moses Mendelssohn's Phädon

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The Infinitesimal Calculus of the Soul: Moses Mendelssohn's Phädon chapter 4 The Infinitesimal Calculus of the Soul: Moses Mendelssohn’s Phädon Bruce Rosenstock 1 Introduction In the revised third dialogue of Mendelssohn’s early work Philosophische Gespräche,1 the interlocutor Kallisthen makes the following declaration: “Leibniz and Newton! I cannot pronounce these names without, as that stu- dent of Plato in his time did, thanking providence that it let me be born after them”.2 Both by bringing together the names of Leibniz and Newton, and from the context, Mendelssohn intends for us to understand that it is the invention of the infinitesimal calculus that especially inspires Kallisthen’s declaration of gratitude to providence.3 The particular problem that the third dialogue 1 Philosophical Dialogues, 1755; revised, 1761. 2 Mendelssohn (1761), 120. In 1761, Mendelssohn republished his Philosophische Gespräche in a collection he entitled Philosophische Schriften. The text is largely unchanged except for a significantly expanded third dialogue and the title of the whole text, which Mendelssohn shortened to Gespräche (Dialogues). Translations from and references to Mendelssohn’s philosophical essays that I will discuss in this chapter (apart from the Phädon) will be to Dahlstrom’s English edition, hereafter PW. After the reference to the page in PW, I will pro- vide a reference to volume and page in the standard German edition of Mendelssohn’s works, Gesammelte Schriften Jubiläumsausgabe, hereafter JubA (see Bibliography for details). The quotation from the Gespräche is found at JubA 1: 365. 3 The infinitesimal calculus (calculus infinitesimalis) had been invented independently by Isaac Newton and Gottfried Leibniz. For a full discussion of the development of the calculus from Newton and Leibniz to the middle of the eighteenth century, see González- Velasco (2011), 230–367. While there was considerable debate about how to interpret the nature of the “infinitesimal” in Mendelssohn’s day, the theoretical foundations of the infini- tesimal calculus were not in doubt. Mendelssohn would certainly have been familiar with Christian Wolff’s introduction to infinitesimal calculus, Dissertatio Algebraica de Algorithmo Infinitesimali Differentiali (Leipzig, 1704). In his December 1760 Literaturbrief for the journal Briefe, die neueste Literatur betreffend, Mendelssohn discusses the more recent work of the mathematician Leonhard Euler, Institutiones calculi differentialis (Euler [1755]). In his review, Mendelssohn translates Euler’s discussion of Newton and Leibniz as the two discoverers of the infinitesimal calculus. Then Mendelssohn adds his own praise for the achievement of Newton and Leibniz, “each of whom has in his own sphere infinitely extended the realm of human insight” (JubA 5.1: 308). Hans Lausch points out that as early as 1757 Mendelssohn © koninklijke brill nv, leiden, 2019 | doi:10.1163/9789004285163_005 The Infinitesimal Calculus of the Soul 77 addresses is whether, if the universe is infinite, it can also be spoken of as one single entity. If it cannot be described as a single entity, then God could not have chosen it from among all possible worlds as the best, the Leibnizian doc- trine that Kallisthen is trying to defend in the third dialogue. Kallisthen says: I well know that in the opinion of some philosophers it is utterly impos- sible for the progression into infinity to be completely comprehended, precisely because the essence of such a series consists in endlessly pro- gressing. Hence, they say, the mathematically infinite is a magnitude whose boundary one does not determine. PW 117; JubA 1: 362 Kallisthen goes on to explain that Leibniz had argued against this mathemati- cal interpretation of infinity. Leibniz had shown that an infinite series could be “completely comprehended” and that its “boundary” could be mathematically determined. Kallisthen states that for Leibniz “we find the infinite everywhere in nature” (PW 117; JubA 1: 363). According to Leibniz, this infinite universe, despite its infinite duration in time, can be measured by God’s intellect in the same way that mathematicians can measure (using the infinitesimal cal- culus) the infinite progression of a series toward its boundary or limit. God, specifically, can measure the grade of perfection of this infinite universe and thereby compare it to every other possible universe. Kallisthen concludes, in agreement with Leibniz, that this universe must possess the highest grade of perfection, otherwise God in his perfect benevolence would not have chosen to bring it into being. Thus, Mendelssohn’s early work, the Dialogues, defends Leibniz’s thesis that “this world is the best of all possible worlds” precisely on the grounds that an infinite universe is measurable as one single entity with a determinate grade of perfection. Mendelssohn thus shows that the infini- tesimal calculus undergirds one of the central pillars of Leibniz’s philosophy. But this is not for Mendelssohn the end of the usefulness of the infinitesimal calculus in philosophy. In this essay I will address Mendelssohn’s use of the infinitesimal calcu- lus in his discussion of the nature of the human soul (Seele). I will argue that Mendelssohn’s appropriation of Plato and Platonism can best be understood through the lens of his application of the infinitesimal calculus to the question showed his knowledge of differential calculus in a brief note entitled Mathematisches (JubA 2: 9ff); cf. Lausch (2000), 119–135, esp. 129–32 for a discussion of Mendelssohn’s knowl- edge of the infinitesimal calculus. For a discussion of Mendelssohn’s mathematical interests more generally, Visser (2011), 83–104..
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