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

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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 rigorous, lacked the symbolic machinery to describe instantaneous velocity or the area under a curve. The intellectual tools simply did not exist. This changed with the work of Newton and Leibniz, who independently developed calculus—a system of notation and rules that enabled thinkers to solve problems previously deemed inaccessible.

This was not merely a matter of calculating faster. It was a conceptual leap, a moment when symbolic invention unlocked new forms of reasoning. Derivatives and integrals were not just computational tricks but new ways of seeing the world. As historian Ivor Grattan-Guinness has noted, the invention of calculus was “the creation of a new language for new kinds of problems.”¹ The language came first; only then could the solutions follow.

Saussure’s Crisis of Expression

A similar drama unfolded in the life and work of Ferdinand de Saussure. Upon arriving in Paris, Saussure was met with acclaim. His appointment at the École des Hautes Études and his role as assistant secretary of the Société de Linguistique signaled a bright future in comparative philology. Yet this promising trajectory was soon disrupted. His enthusiasm waned, his publications diminished, and by the time he returned to Geneva, he had largely retreated into intellectual solitude.

What happened? According to Émile Benveniste, Saussure experienced a profound internal crisis—a “drama of the mind”—provoked by his growing disillusionment with the prevailing theories and especially the terminology of linguistics. He found the existing language of the field incoherent, ideologically muddled, and fundamentally incapable of expressing the structural insights he was developing. This frustration is laid bare in a letter to Antoine Meillet from January 4, 1894:

“The absolute ineptness of current terminology, the necessity to reform it, and, in order to do that, to show what sort of subject language in general is, come incessantly to spoil my pleasure in history, although I have no dearer wish than not to have to concern myself with language in general. In spite of myself, this will result in a book, in which I shall, without enthusiasm or passion, explain why there is not a single term used in linguistics to which I grant any meaning whatsoever.”²

Saussure could not advance linguistics until he redefined its foundational terms. The traditional pair—concept and sound pattern—seemed inadequate for his structural theory of signs. He proposed a new set of technical terms: sign, signifier (signifiant), and signified (signifié); langue/parole; synchronic/diachronic, all designed to clarify the internal relations of language in general, and the nature of the sign as a differential entity:

“We propose to keep the term sign to designate the whole, but to replace concept and sound pattern respectively by signifié and signifiant. The latter terms have the advantage of indicating the distinction which separates each from the other and both from the whole of which they are part.”³

This act of terminological innovation allowed Saussure to construct the discipline he called “general linguistics.” Without it, his ideas remained inchoate. With it, they redefined the study of language for generations to come.

Nietzsche and the Invention of a Philosophical Idiom

Friedrich Nietzsche underwent a comparable transformation. In 1886, he appended a retrospective preface to The Birth of Tragedy, written more than a decade earlier. There, in An Attempt at Self-Criticism, §6, he confesses a crucial failure:

“I now regret the fact that at the time I did not yet have the courage (or the presumptuousness?) to allow myself in every respect a personal language (eine eigne Sprache) for such an individual point of view and such daring exploits—that I sought laboriously to express strange and new evaluations with formulas from Schopenhauer and Kant, something which basically went quite against the spirit of Kant and Schopenhauer, as well as against their tastes!”⁴

This is not a minor stylistic regret. Nietzsche here identifies a systemic limitation: the conceptual languages of the past are not neutral tools, but worldviews. By using Kantian or Schopenhauerian vocabulary, he inadvertently framed his thought within their logic—a logic he was, in fact, trying to escape.

In response, Nietzsche began to forge his own philosophical idiom. Terms like will to power, eternal recurrence, and revaluation of all values do not simply name doctrines; they interlock, forming a grammar of thought unique to Nietzsche’s vision. Much like Saussure’s sign system, Nietzsche’s later vocabulary is not detachable from his insights—it is their condition of possibility. Without this self-made language, his ideas could not have taken shape.

Conclusion: When Language Precedes Insight

Whether in mathematics, linguistics, or philosophy, these three figures—Newton and Leibniz in their symbolic calculus, Saussure in his structural semiotics, Nietzsche in his conceptual revaluation—reveal a common structure. Intellectual advancement often hinges not on the solution of an old problem, but on the invention of a new language that makes the problem intelligible in the first place. In this sense, expression is not the final step of thought; it is its enabling condition. When existing vocabularies fail, the only path forward is to invent the very language in which understanding can begin.

Bibliography

1. Ivor Grattan-Guinness, The Norton History of the Mathematical Sciences: The Rainbow of Mathematics (New York: W. W. Norton, 1997), 453.
2. Émile Benveniste, Problems in General Linguistics, trans. Mary Elizabeth Meek (Coral Gables, FL: University of Miami Press, 1971), 23. The letter is cited from Cahiers Ferdinand de Saussure 21 (1964).
3. Ferdinand de Saussure, Course in General Linguistics, trans. and annotated by Roy Harris (London: Bloomsbury, 2013), 67.
4. Friedrich Nietzsche, The Birth of Tragedy and Other Writings, trans. and ed. Walter Kaufmann (New York: Vintage Books, 1967), 20.