Segni e algoritmo nell'analisi leibniziana

Descartes' Regulae are the first text in which the idea of ​​a universal mathematics is put in connection with algebra. Young Descartes thinks of geometrical figures as a representation of algebraic procedures so as to guarantee its feasibility: i.e., an epistemological foundation of analysis. The young Leibniz starts from a similar problem. He distinguishes, with Hobbes, between notes and signs (memory and communication), but, against Hobbes, he argues that operations based on arbitrary signs provide truths that are not necessarily arbitrary. Against Descartes, he decisively focused on the tools of knowledge, rather than on the faculties of the mind—the principal tool being systems of signs, or characters, governed by combinatorial and operational rules. Yet the only analysis that Leibniz brought to some completion is differential and integral calculus. It is indeed similar to the art of characters, because it is an ‘art of invention’, it is based on well-used signs, and it is comparable to a ‘filum meditandi’. In controversies against critics of his calculus, as well as in his further research on the foundation of infinitesimal techniques, Leibniz gives an increasingly prominent role to sets of rules for the elimination of evanescent quantities rather than to the existential interpretation of signs