originally published at https://lapageblanche.com/le-depot/auteur-e-s-index-i/38-andrew-nightingale/2-le-role-de-la-rethorique

The Role of Rhetoric (Aphoristic Revision)

The parallel postulate was never necessary, only asserted.
Euclid held it back as long as he could, building a Neutral Geometry true everywhere. But in the end he chose—persuaded by coherence, by tradition—that only one line runs parallel through a given point. This was less proof than persuasion.

That choice shows how we think.
The crystallization of intuition into formal mathematics is a rhetorical process. The vague becomes exact, the fluid hardens into proof. We pretend logic alone dictates the result, but behind every axiom stands persuasion.

Non-Euclidean geometry proved the point. More than one parallel line can exist. Triangles on a sphere can have three right angles. The Earth itself gave evidence, but we preferred the frame that made space measurable, quantifiable, ours. Even science, in claiming territory, leans on rhetoric.

Rhetoric is not an ornament of thought but its orientation. It decides which truths are admitted, which distances are counted, which realities are named. To prove is also to persuade. To formalize is to crystallize choice into necessity.

Aristotle called rhetoric an art of persuasion; I call it the art of orientation.
It stands at the border where mathematics becomes possible, where science borrows from poetry. Rhetoric guards poetry, translating its openness into form. It shows us that truth, even when written in symbols, is always chosen—always persuaded into being.