Inventing the Language of Thought: Saussure, Nietzsche, and the Conceptual Innovation of Calculus

AI art Introduction In science and philosophy, some problems remain intractable not for lack of intellect, but due to the absence of an adequate language in which to formulate them. Concepts may be dimly intuited—even felt with urgency—yet resist articulation until a fitting symbolic system is constructed. This principle is well illustrated by the development of calculus, where a new mathematical idiom allowed thinkers to address the problem of change. The same logic applies beyond mathematics. In the intellectual evolution of Ferdinand de Saussure and Friedrich Nietzsche, we observe moments when inherited terminology failed, prompting the creation of novel conceptual vocabularies that opened entirely new terrains of thought. The Expressive Breakthrough of Calculus Before the seventeenth century, problems involving motion, limits, and infinitesimal change lay beyond the expressive capacity of classical mathematics. The frameworks inherited from Euclid and Archimedes, while rigo...