Starting points that are not proved from something narrower on the same page.
Status: Working notes Faith & Logic Published October 21, 2025 Updated October 5, 2026
A first principle is a beginning. The Greek is archē (ἀρχή) — starting point, origin, rule. In a demonstration, it is a premise you do not derive from a still earlier premise in that inquiry. If every line had to be proved by a prior line, the argument would never start. That is the regress problem. First principles are how an argument refuses infinite postponement.
This page names the job of a starting point, the kinds of starting point, and what later slogans have done to the phrase. Identity, non-contradiction, and excluded middle are first principles of a special kind. They are treated at length on Laws of Thought.
Aristotle’s account in the Posterior Analytics is still the clean definition. A demonstration (apodeixis) is a syllogism that produces knowledge. Its premises must be true, primary, immediate, better known than the conclusion, prior to it, and causes of it. “Primary” and “immediate” mean: there is no middle term between this premise and a narrower one that would prove it inside this inquiry.
Three distinctions keep the word from going soft.
Principle vs conclusion. A conclusion is what you reach. A principle is what you start with. Treating a favorite conclusion as if it were a principle is the most common leak in popular “first principles” talk.
Principle vs axiom. In later use, an axiom is a stipulated starting rule inside a formal system. Euclid’s postulates are axioms of geometry. They are first for that science. They are not first for every science. Axiom, as defined on this site, is not a synonym for the three laws, and it is not a synonym for “whatever I refuse to argue.”
Principle vs hypothesis. A hypothesis is granted for the sake of a stretch of argument. A first principle is not granted that way. Aristotle treats non-contradiction as the firmest principle precisely because you cannot even deny it without using it. That is a different status from “assume P and see.”
Without a starting point you get one of three failures.
The work of this page is to make the stop honest. Name what you are not proving here. Name why that line can bear weight. Then build.