Pareti, Germana (Author)
Not least among the problems that early 18th-century mathematics left for the analysts at the end of that same century, was that of the “metaphysics of the infinite,” or more precisely, the “metaphysics of infinitesimal calculus,” which consisted in rigorously establishing the rules of such calculus. Leibniz originated the “metaphysics of the infinite,” which was then fuelled by the echoes of the dispute between Leibnizians and Newtonians and was apparently silenced by Berkeley’s criticism in The Analyst (1734). It was revived by the theories of mid-century minor mathematicians, including major figures like d’Alembert and, later, Lagrange. The “metaphysics of the infinite” was also the theme proposed in 1784 in a competition organised by the Academy of Sciences of Berlin, in which Lazare Carnot participated (anonymously). Despite being inconclusive, his doctrine of the compensation des erreurs, which he returned to in his Réflexions (1797), described state-of-the-art concepts regarding the “infinitely small” and prepared the ground for the more mature rigorousness of the mathematicians of the following century. This chapter came to an end with Russell’s irreverent judgment on the useless and erroneous nature of infinitesimals.
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